stanford universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · y 7mÌ?8...

43

Upload: others

Post on 31-Jul-2020

0 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

������������ �������������������� ��������� �! "��#�%$'&��(�)���� "������+*� -,����

.0/214365�728:9<;=/2.0/?>2@BA:CEDF3=92GH/?I�@KJLJLDFM"5�7N92O=/2PQ/<R4SUTV5�M)92R-/<;=/2W=5XJL5X8�Y�ZBDV5�7N9?5�72A\[]/?^:/<_`SUa2@KJb47?Ddc�@KJLSUDdegf�Y�hjik5�TFDFhlY�JL7?DF5m9EnoY�S�RH7:8�@BTd@BSK9<ipRrqXs�s�q�t#uLvBt�q�w

xQy<z#z|{E}B~jy<���!���������o�#��y?z��

.�JUY�h�@BSUS�Y�J�RQ/?;=/<W=5XJL5X8�Y�ZBDF5�7PH@K�?5XJLeUM(@B7�e4Y�h0I\@B�La?5�72DF�K5�To5�7?A�R�@KJLY�S��?5���@-��7:8�DF7:@K@KJLDV7:8���#uLv���w|P���728�DF7:@K@KJLDF728Q���Q9<b`ikn�RnoY�S�RH7:8�@BTd@BSK9<ipR�qXs�s�q�t#uLvBt�q�w.�a:Y�7:@��4���mvKs��� �¡�t#ugt���t��E¢N>ER4£¤�����mvKs���¡Xs��#u¥�� ��Xs�ju¦M"5�DFT��j5XJLC:§`SU@B5�SK/©¨2�KTF5m/ª@BA2¨

;�@KcEDFSLDdY�7)SU¨:«?M�Dde�e�@BA�e�YxQy­¬®0��}K�#��y<�°¯¤�o{Ey?z#±%²?���°³�yN�0{E´µ�µ�o�

^�¨27:@�9?¡Xs�s�s

v

Page 2: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

������������ �������������������� ��������� �! "��#�%$'&��(�)���� "������+*� -,����

.0/?14365�7:8�¶9�;=/?.0/?>2@BA:CEDF3¸·9?GH/?I�@KJLJLDFM"5�7�¹9?O=/2PQ/<R4SUTV5�M�º92R-/<;=/2W=5XJL5X8�Y�ZBDV5�7¼»925�72A¼[­/?^:/<_`SLa:@KJ-½

b47?Ddc�@KJLSUDdegf�Y�hjik5�TFDFhlY�JL7?DF5m9EnoY�S�RH7:8�@BTd@BSK9<ipRrqXs�s�q�t#uLvBt�q�w

¾ ¿ÁÀ�Â2Ã]ÄNÅpÆ0Ã

OÇa2@H�K5�7:Y�7?DF�K5�T­�2JUY�«?Td@BM�Y�hÈeUa2@HY�72@�u¦A2DFM(@B72SLDdY�725�T�9��?¨2TFSU5XeUDV7:8:9�Y#c�@KJLA:JLDdc�@B7)A2@Ke�Y�725XeUDdY�7�3k5Bc�@=a25�Sk«]@K@B7S�eU¨2A?Dd@BA"h�Y�J�Y#c�@KJpeUa2DdJUegf(f�@B5XJLSK9:7:Y�e6Y�72Tdf�h�Y�JkDFeUSj�?a:@B72Y�M(@B7:Y�TdY�8�DF�K5�T<JU@BTF5XeUDFY�7�e�Y¤eUa:@H@Kc�Y�TF¨:eUDdY�7�Y�hÈMQ¨?TdeUDFA2DÉuM(@B72SLDdY�725�T:A:@Ke�Y�725XeUDFY�7"DF72S�eU5X«<DFTFDdeUDd@BSB9|«<¨:e!hlY�J6DdeUS!�2JUY#cEDFA?DF7:8 5 JUY�«?¨?S�eK9�JU@B5���eUDdc�@�9ma2Dd8�a"SU�­@K@BA¤Ê<YË3pÌ?@BTVA�3�DdeUa3�a2DV�La�e�Y-e�@BSUe�7�¨?M(@KJLDF�K5�T:SU�Ía:@BM(@BSK/jO�a:@p�2JU@BS�@B7�e�S�eU¨?A:f-@�Î:5�M"DF7:@BSjeUa2DFS!Ê?Y#3pÌ?@BTFA(¨?SUDF7:8 a2Dd8�a�Y�JÍA:@KJB9�@BSLS�@B7mueUDF5�TFTFf�7:Y�7mu¥Y�SU�KDVTFTF5Xe�Y�JUf��µ��Ï _=�6SU�Ía:@BM(@BSK9?SUfES�e�@BM�5XeUDF�K5�TFTdf�c|5XJUfmDF7:8(eUa2@=Td@Kc�@BT]Y�h!JU@BS�Y�TF¨:eUDFY�7�Y�h0eUa:@=JL@B5���eUDdY�7ZKY�7:@�9EeUa:@�SUDFZK@�5�72A(JU@Ke�@B7�eUDdY�7�Y�hNDF7:h�Y�JLM"5XeUDdY�7(DF7"eUa:@���Y�M(�?¨2eU5XeUDdY�725�T2A:Y�M�5�DF7N9�eUa:@HDF72DdeUDV5�TE��Y�7?A2DdeUDdY�72SB9�5�72AeUa:@ÇY�JÍA:@KJ�Y�h]eUa:@�SL�La:@BM(@�/Ð��e�DFS�hlY�¨?72A�eUa25Xe�eUa2@KJU@��K5�7"«]@Ç�?JUY�hlY�¨?72A(A2DÉÑ]@KJU@B72��@BS�DF7��]@B5XC¤�?JU@BSUSU¨:JL@BSj5�Sj36@BTFT5�S�DV7�eUa:@=�]@KJLDdYmA�Y�h�Y�SU�KDVTFTF5XeUDdY�7N9:7:Y�e�Y�72Tdf�hlY�J��K5�SU@BS�DF7�3�a?DF�La)eUa2@ JU@B5���eUDdY�7�h�JUY�7�e�DFSp¨27?A:@KJ�u¥JU@BS�Y�TFc�@BAN9:«?¨:eh�Y�J4�K5�S�@BS`DF7)34a2DF�La�eUa:@Q��Y�M(�<¨:eU5XeUDdY�7�DVS���Y�JUJL¨2�2e�@BA�A2¨2@=e�Y�5�e�Y�YXu¦SUM�5�TFTo��Y�M(�<¨:eU5XeUDdY�725�T�A:Y�M"5�DF7N/kI\@KeUamuYmA2S=h�Y�JQ@BSUeUDFM"5XeUDF7:8�eUa:@�JU@BÒE¨2DdJL@BA�SUDdZK@�Y�hpeUa:@���Y�M(�<¨:eU5XeUDdY�725�T6A:Y�M"5�DF7�e�Y\JU@BA?¨2��@���Y�S�eUSQ3�a2DVTd@"5Bc�Y�DFA?DF7:8@KJUJUY�72@KY�¨2SÇS�Y�TF¨2eUDdY�72Sp5XJU@=�?JUY��]Y�S�@BA)5�72A)e�@BS�e�@BAÈ/

ÓUÔ�Õ¦ÖÍ×#Ø|ÖLÙ¥Ú�ÛBÙ¥Ø|×#ÚÝÜKÙ�ÞËß!ÚÝà|ÖLÕ�Ù¥ápÚÝÜKÙNâLã?äHÚÝå¦æXÖLÜ|ç©å�ÖÍèEÖÍÜ|×Hé�ÚgÕ¥âëê�àXÖLåÝÚ�ì?Ü#íëç©Ü|Ú�Ú�Õ¥ç©Ü|í#î|ÚÝáÇÖÍç©èdï2à�Ú�Ù¥Ú�Õ¥æXð0ê�Ú�ÖÍêÝñ Ø#åÝèòÖËñ Ú�×#Øó éoê�ê�âKåÝçòÖLÙ¥Ú`ôoÚÝê�Ú�ÖUÕ¥ågæ#Ú�Õ�Þ]ß0ÚÝàXÖUÕ�Ù¥ápÚÝÜKÙ6âLãÐä`ÖUÙ¥æ|ÚÝáÇÖUÙ¥çòå�êÝîÈåÝØ#Õ�Õ¥ÚÝÜKÙ¥èªõ(éoê�ê�ç©êµÙ¦ÖÍÜKÙÇö:Õ¥âÍãÉÚ�ê�ê�âÍÕ�Þ�ÛBÙ¦ÖLÜ#ã÷âÍÕ¦×(ø0Ü#çòùëÚ�Õ¥ê�çªÙ�õ�î]ÚÝáÇÖLç©èFï

ãÉÚÝ×#úBçªû�ð0åÝêÝñ êµÙ¦ÖÍÜ#ã÷âÍÕ¦×�ñ ÚÝ×#Øü ôoÚÝê�Ú�ÖUÕ¥ågæ#Ú�Õ�ÞXß0ÚÝàXÖUÕ�Ù¥ápÚÝÜKÙNâÍã?ä`ÖUÙ¥æ|ÚÝáÇÖUÙ¥ç©åÝêÝî|Ú�áÇÖÍç©èdï<ý|ÖLÕ�Õ�õ|ð0áÇÖLÙ¥æ�ñ Ø|åÝèòÖËñ Ú�×ËØþ äHÚ�á6ý�Ú�ÕÈâLã:Ù¥æ|Ú!ôoÚÝê�Ú�ÖUÕ¥ågæ=ÛKÙ¦ÖLÿ:Þ|Ô�Õ¥âëØ#à`ß������ëÞ���âÍêoé�èòÖÍápâÍê��0ÖLÙ¥ç©âëÜ|ÖÍè�EÖÍý�âLÕ¦ÖLÙ¥âLÕ�õ�î#ÚÝáÇÖLçòèdï<ÖÍê�èòÖLá�ð0è ÖLÜ|èdñ íëâUù ö:Õ¥âÍã÷ÚÝê�ê�âÍÕ�Þ]ß!ÚÝàXÖUÕ�Ù¥ápÚÝÜKÙ6âLãÐäHÚ�ågæ|ÖÍÜ|ç©å�ÖLèoÖÍÜX×"éoÚ�Õ¥âëê�à|ÖÍåÝÚHì?Ü#íëç©Ü|ÚÝÚgÕ¥çòÜ#í#îÈÚÝáÇÖLç©èFï4ÖUÕ¥ú|ð0ê�ÚÝÖÍêÝñ Ø|åÝèòÖBñ ÚÝ×#Ø��FÖLØ#Ù¥æ#âÍÕ6Ù¥â ûÈæ#âëá

åÝâLÕ�Õ¥ÚÝê�à�âëÜ|×#ÚÝÜ#åÝÚÐê�æ|âÍØ|èò×Hý�Ú!ê�ÚÝÜKÙ� � ö:Õ¥âÍã÷ÚÝê�ê�âÍÕ�ÞXß!ÚÝàXÖUÕ�Ù¥ápÚÝÜKÙNâÍã<ä`ÖUÙ¥æ|ÚÝáÇÖUÙ¥ç©åÝêÝî|Ú�áÇÖÍç©èdï<ê���âKð0áÇÖUÙ¥æ�ñ Ø|åÝèòÖBñ ÚÝ×#Ø¡

Page 3: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

� ���`íÄ�������Æ0Ã������PH@Ke�Y�725XeUDdY�7��?a:@B7:Y�M(@B7?5�a25Ëc�@(«­@K@B7\@�Î:5�M"DF7:@BA¼eUa:@KY�JU@KeUDV�K5�TFTdf�5�72A¼��Y�M(�?¨2eU5XeUDdY�725�TFTdf\7:YË3rh�Y�JHY#c�@KJ-5

��@B7�eU¨:JUf�9:«]@K8�DF7272DV7:8-3�DFeUa�eUa2@HJL@K�2JU@BS�@B7�eU5XeUDdY�7)Y�h�eUa:@ Y�7:@�u¦A2DFM"@B72SUDdY�725�T<�2JUY��<5X8�5XeUDF7:8(A:@Ke�Y�725XeUDdY�7�h�JUY�7�eÇ5�S5"A2DVSU��Y�7�eUDV7�¨2DFe¦f�5��K��Y�JÍA2DF7:8(e�Y)ika25X�?M"5�7:ug^�Y�¨:8�@Ke-�¥ip^E�6eUa:@KY�JUf �Év"!E��#¥/kOÇa:@ eUa:@KY�JUf�Y�h%$­@BT'&©A2YËcmDF�La(� �)#¥9<c�Y�7Ï4@B¨2M"5�727*�ªt�#¥9j5�72A PHYE@KJLDF7:8+�ª��#¥9Ð3�a2DF�Ía�a25�S¤��Y�M(@�e�Y�«]@�Cm7:YË347���Y�TFTd@B��eUDFc�@BTdf�5�S-eUa2@,$]ÏHP A:@Ke�Y�7?5XeUDdY�7M(YmA:@BT�9�JL@K�2JU@BS�@B7�eUS�eUa2@4A:@Ke�Y�725XeUDFY�7�5�S�eUa:@���Y�7mÊ­¨:@B72��@�Y�hÈ5QSUa:Ym�UC(3k5Bc�@`M(YËcmDF7:8¤5Xe�eUa:@HA:@Ke�Y�725XeUDdY�7�S��]@K@BA-\9�hlY�TVTdYË36@BA(«Ef¤5 �Ía:@BM"DF�K5�T:JL@B5���eUDdY�7"ZKY�7:@�Y�h?Ì<7?Dde�@pTd@B7:8�eUaN/!OÇa:@pJU@BTF@B5�S�@pY�hN�La:@BM"DV�K5�T:@B7:@KJU8�f�SU¨2S�eU5�DV72S!eUa:@�2JUY��<5X8�5XeUDdY�7Y�h�eUa:@"A2@Ke�Y�725XeUDdY�7h�JUY�7�eK/¤OÇa2DFS4JU@BTF5XeUDFc�@BTdf\SUDVM(�?Td@¤M(YEA2@BT�9]3�a2DF�Ía\JL@K�2JU@BS�@B7�eUS`eUa:@(�La:@BM�DF�K5�TJU@B5���eUDdY�7«Ef\5)SLDF7:8�Td@QhlY�JU3k5XJLAJL5Xe�@��2JLYE��@BSUSB9ÈDFSHCE7:Y#3�7e�Y)�K5X�2eU¨:JU@"M�5�7�f�9ÈDdh�7:Y�e M(Y�S�eK9ÈY�h�eUa:@�@BSUS�@B7�eUDF5�T�?a�fESLDF�K5�Tk�?a:@B7:Y�M"@B725�5�SUS�Ym�KDF5Xe�@BA%34DdeUa%A:@Ke�Y�725XeUDFY�72SK9k5�72A%5�S�SL¨2�La eUa:@�M(YmA:@BTpa25�S(«]@K@B7 @�Îme�@B72A:@BA «�f57�¨?M-«]@KJ¤Y�h�JU@BS�@B5XJÍ�La:@KJLS�e�Y�M(Y�JL@���Y�M"�?Td@�Î A:@Ke�Y�7?5XeUDdY�7 ��Y�7mÌ?8�¨:JÍ5XeUDdY�72S¤YËc�@KJ"eUa2@�f�@B5XJÍS.�©w�9Í �#¥/0/ a2DFTd@JU@B��@B7�e�5�A:cX5�72��@BSpDF7)��Y�M(�<¨:eU5XeUDdY�725�T]�]YË36@KJÇa25Ëc�@=8�JU@B5XeUTdf�@B72a25�72��@BA�eUa2@`5X«<DFTFDdegf"e�Y"7�¨?M(@KJLDF�K5�TFTFf�SUDFM¤¨2TF5Xe�@M¤¨2TdeUDFA2DVM(@B72SUDdY�7?5�T:A:@Ke�Y�725XeUDdY�7��?a:@B72Y�M(@B725Q3�DdeUa���Y�M"�?Td@�Î�JU@B5���eUDFY�7�CEDF72@KeUDF�KSK9�DFe6DFS�eUa:@�$]ÏHP A:@Ke�Y�7?5XeUDdY�7N95�72A�DF72S�eU5X«?DVTFDdeUDd@BS05�SUS�Ym�KDF5Xe�@BA�3�DdeUa(eUa2DVSÐY�7:@�u¦A2DFM"@B72SUDdY�725�TmJL@K�2JU@BS�@B7�eU5XeUDdY�7N9�eUa25Xe�DFS�M(Y�S�ejY�h�e�@B7�¨2S�@BA"5�S�eUa:@�K5�7:Y�72DV�K5�TN�2JUY�«?TF@BM�5X8�5�DF72S�ep3�a?DF�La�7E¨2M(@KJÍDF�K5�T]SU�La:@BM"@BS�5XJU@=cX5�TFDFA?5Xe�@BAN/

�Ý72S�eU5X«?DVTFDdeUDd@BS 5�SUSUYE�KDF5Xe�@BA�3�DFeUa�A:@Ke�Y�725XeUDFY�7�3k5Bc�@BSK9�3�a2DFTd@�Ì<JLS�e=JU@B��Y�8�7?DdZK@BA�@�Îm�]@KJLDFM(@B7�eU5�TFTdf1�ªq�#¥9!36@KJU@S�@K@B7�e�Y�YE�K�K¨2J=hlY�JQeUa:@�vKP2$]ÏHP M(YmA:@BTЫEf¼��JU�]@B7�«]@B�UC¼cmDF5)TFDF7:@B5XJ=SUeU5X«?DFTFDdegf\5�725�TFfESUDVS��ÉvKsm9#v�v3#�5�72A�7:Y�7muTFDF72@B5XJkSUeU5X«?DFTFDdegf�5�725�TdfmSUDFS��ÉvB¡�#05�72A�«�f�>!DF�UC�@Ke�eH5�72A4/�Y�YmA(�ÉvB��#�¨?SUDF7:8�5(7�¨?M(@KJLDF�K5�TNM(@KeUa2YEA�«?5�SU@BA�Y�7)eUa:@�La?5XJL5���e�@KJLDFS�eUDV�"7:@KeK/�[m¨2�Ía�?¨2TFSU5XeUDV7:8�DV72S�eU5X«?DFTVDdeUDd@BS�a?5Bc�@�SUDV72��@(«]@K@B7@�ÎE�?TFY�JU@BAeUa:@KY�JU@KeUDF�K5�TVTdf+�Év��5!<vB��#p5�72A��Y�M(�?¨2eU5XeUDdY�725�TFTdf6�Év��:9#vËw�9ËvB �#�hlY�JÇY#c�@KJLA:JLDFc�@B7�A:@Ke�Y�725XeUDdY�7�365Ëc�@BSK/6O�a:@`YËc�@KJLA:JÍDdc�@=hµ5���e�Y�JB987092DFSp5(�<5XJL5�M(@�ue�@KJHeUa25Xe4JL@BTF5Xe�@BS�eUa2@¤S��]@K@BA��9-��pY�h�5"8�Ddc�@B7¼A:@Ke�Y�725XeUDFY�7�e�Y�eUa:@�ipa25X�?M"5�7mug^�Y�¨:8�@Ke�Y�J-ip^�c�@BTdYm�KDde¦f�9�-�:<;?93�a2DV�La��Y�JUJU@BS��]Y�72A?S4e�Y�eUa:@"A2@Ke�Y�725XeUDdY�7�S��]@K@BA¼�2JUYmA2¨2�KDF728�S�Y�72DV�=Ê?Y#3 «]@Ba2DF72A�eUa:@�365Ëc�@�/(OÇa:@"ip^)S��]@K@BA��Y�JUJU@BSU�­Y�7?A2S`e�Y�eUa:@�M"DF72DFM¤¨2M �2JUY��<5X8�5XeUDdY�7�S��]@K@BA�72@B��@BSUSU5XJUfe�Y\SL¨2S�eU5�DF7�5�A:@Ke�Y�725XeUDdY�7�JU@B5���eUDdY�7N/�OÇa:@YËc�@KJÍA:JLDdc�@=hµ5���e�Y�J4DVSpeUa:@B7�A:@�Ì­7:@BA)5�S

7,=?> --�:<;�@%A �ÝvË�

_Hc�@KJÍA:JLDdc�@B7 A:@Ke�Y�725XeUDFY�72S)��Y�JUJU@BS��]Y�72A°e�Y Y#c�@KJLA:JLDdc�@�hµ5���e�Y�JLSB7 @�Î:��@K@BA2DF7:8 ¨27?Dde¦f�/�noDF7:@B5XJ)S�eU5X«<DFTFDdegf�

Page 4: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

5�725�TdfmS�@BS��ÉvKsm9Ëv�vX9|v��)#�DFA:@B7�eUDdh�f�eUa:@(S�eU5X«?DFTVDde¦f�«]Y�¨27?A25XJLDd@BS4hlY�J eUa2@¤Y#c�@KJLA:JLDFc�@B7�A:@Ke�Y�725XeUDdY�7�34DdeUa2DF7�eUa:@(�?5|uJL5�M(@Ke�@KJQS��?5���@�A:@�Ì­7:@BA«�f¼eUa:@C$]ÏHP M(YmA:@BT�¢ÈeUa:@"7E¨2MQ«]@KJ Y�h6DF7?S�eU5X«?DFTFDFe¦f�M(YmA:@BS DFS SU@K@B7�e�Y�DF72��JL@B5�S�@"5�S75X�2�2JLY�5��La:@BSH¨272Ddegf�9?D�/ª@�/d92eUa2@¤ip^"��Y�7?A2DdeUDdY�7N/6PH@BS��?Dde�@=JÍ5XeUa:@KJ�@�Îme�@B72SUDdc�@Q7�¨2M"@KJLDF�K5�TN@�Î:5�M"DF725XeUDFY�7)Y�h!eUa2DFS�K5�7:Y�72DV�K5�TjvKP ¨272SUe�@B5�A:f)A:@Ke�Y�725XeUDdY�7��2JUY�«?Td@BM ��@�/ª8:/d9D�Év��:9ËvËw�9|vB �#��Í9?eUa:@KJU@QDFSÇ7:Y"34DFA:@BS��2JL@B5�A)��Y�72S�@B72SU¨?SpY�7a:Y#3�«]@BS�e4e�Y�JL@BS�Y�Tdc�@¤eUa2DFS��µ5�72A\a2@B72��@�9]«�f)@�Îme�@B72SUDdY�7È9­5�M(Y�JU@���Y�M(�?Td@�Î?�ÇJU@B5���eUDdc�@¤Ê?YË3ÇÌ?@BTFAN9­DF7�e�@KJLM�S4Y�heUa:@�JU@BÒ�¨?DdJU@BA�A:@K8�JL@K@�Y�hpJU@BS�Y�TV¨:eUDdY�7�Y�hkeUa:@�JU@B5���eUDdY�7 ZKY�7:@�9!eUa:@�5�M(Y�¨?7�eQY�hÇDF7:h�Y�JLM"5XeUDdY�7�JL@BÒ�¨2DFJU@BAe�Y\«]@�K5X�2eU¨:JL@BA�DF7�eUa:@Q��Y�M(�<¨:eU5XeUDdY�725�T�A:Y�M"5�DF7N9?eUa:@-@�Ñ]@B��e`Y�hjDF72DdeUDF5�TN��Y�7?A2DdeUDdY�72SB925�72A�eUa:@¤A:@K8�JU@K@¤Y�hj5��K�K¨:JL5���fY�h­eUa:@Ç7�¨?M(@KJLDF�K5�T:SU�Ía:@BM(@ÇeUa?5Xe�DFS!JU@BÒE¨2DdJU@BAÈ/![mDF7?��@6eUa?DFS!JU@B5���eUDdY�7"M"YEA:@BTmh�Y�JLM"SjeUa:@p«?5�SUDFS!Y�7"3�a2DF�Ía¤5-TF5XJU8�@7E¨2M-«]@KJ`Y�hkMQ¨2TFeUDFA2DFM(@B7?SUDdY�725�T6�µS�e�@B5�A:f�5�72Ae�JL5�72SLDd@B7�eÍ�HSLDFMQ¨?TF5XeUDdY�72SH5XJU@(h�Y�¨272A:@BAN9È5�7?A«­@B�K5�¨?S�@(eUa:@�vKP�?¨2TVSU5XeUDF7:8"A:@Ke�Y�7?5XeUDdY�7DFS�¨2SU@BA�S�Y�3�DFA:@BTFf�5�SH5FEÝe�@BSUe�G��?JUY�«?Td@BM hlY�J`a2Dd8�a�JU@BS�Y�TF¨:eUDFY�7�7�¨?M(@KJLDF�K5�T�SU�La:@BM"@BSK9Dde=DFS ��JÍDdeUDF�K5�T!e�Y�¨27?A:@KJLS�eU5�72A¼�2JL@B�KDFS�@BTdf\3�a25Xe=A:YE@BS=5�72A�A:YE@BS=7:Y�eQ��Y�72S�eUDdeU¨:e�@"5�7�5��K�K¨:JL5Xe�@�JL@BS�Y�TF¨:eUDdY�7Y�heUa2DFS�Ê?Y#3pÌ?@BTFAN/ OÇa2@-�2JU@BSU@B7�e S�eU¨2A2f�A:@BSU��JLDd«]@BSH5�S�fESUe�@BM"5XeUDF��S�eU¨2A:f)Y�h�JU@BS�Y�TF¨2eUDdY�7�Y�h�eUa2DFS�Ê?YË3pÌ<@BTFA\¨?SUDF7:8a2Dd8�a�Y�JÍA:@KJ�SU�Ía:@BM(@BS�DV7�Y�JLA:@KJÇe�Y��KTV5XJLDdh�f�eUa:@BS�@Q5�72A)Y�eUa:@KJ�DVSUSU¨:@BSk�]@KJUeU5�DF7?DF7:8¤e�Y�A:@Ke�Y�725XeUDdY�7\SUDFM¤¨2TF5XeUDdY�7È/

H I Ä��4ÀKJML%N OP��Ä<NQ�KJUÅ6Ã����R� ÅS�P�UTV�KNWLjÄ<�LÆÐÅSJBX L!Ã�YP���K��JM�[ZS\]_^a` $ bdc�edfhg%i�gkj°�Pl_m%n8opiab�g%qOÇa2@¤8�Y#c�@KJL72DF728�@BÒ�¨?5XeUDdY�72S ¨2S�@BAe�Y\SUDFM¤¨2TF5Xe�@�eUa:@"DF7�cEDVSU�KDFAN9­Y�7:@�u¦A2DFM"@B72SUDdY�725�T0�2JLY��?5X8�5XeUDdY�7Y�hk5)A:@KeÝu

Y�725XeUDdY�7\3k5Bc�@¤3�DdeUa�5�SUDF7:8�TF@-S�e�@K�È9­DdJUJU@Kc�@KJLSLDd«?Td@ �La2@BM"DF�K5�T�JU@B5���eUDdY�7¼5XJU@QSUa2YË3�7\«]@BTdYË3=9?JU@K�2JU@BS�@B7�eUDF7:8���Y�7muS�@KJUcX5XeUDdY�7)Y�hÐM"5�SLSK92M(Y�M(@B7�eU¨2M)92@B72@KJU8�f�9?5�72A�SU�­@B�KDF@BSK/

rsut8v rw�� rs-��xzy r{ � rs � ��¡��

3�a:@KJL@QeUa:@¤c�@B��e�Y�J-��Y�7�eU5�DF72DF728���Y�72SU@KJUc�@BA¼c|5XJLDV5X«?Td@BSK9 rsQ9]eUa:@¤Ê<¨mÎ�c�@B��e�Y�JË9 rw"9N5�72A\eUa:@�c�@B��e�Y�J=��Y�7�eU5�DF7?DF7:8S�Y�¨:JÍ��@=e�@KJLM"SK9 r{ 9?5XJU@�92JU@BSU�­@B��eUDFc�@BTdf�9

Page 5: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

rs|y}~~~~~~~~���h������M���������

rw�� rs-�Dy}~~~~~~~~�

�h���� A vB��9�*v��N� ��h�8��M��������� { � rs=�ky

}~~~~~~~~�sss�[� �����)�%��������

�M��������� �����

3�a:@KJL@��ÁM"5Ëf�«­@`3ÇJÍDde�e�@B7��y �� � v v �h� A¡ v ���)� �����

�Ý7 eUa:@�5X«]YËc�@�JL@BTF5XeUDdY�72S(eUa2@)c|5XJLDV5X«?Td@BS(a25Ëc�@�«]@K@B7 M"5�A:@�A2DVM(@B72SUDdY�7?Td@BSUSQ3�DdeUa�JU@BS��]@B��e"e�Y�eUa:@�¨272Ddh�Y�JLMS�eU5Xe�@-5�a2@B5�A)Y�h�eUa2@=A:@Ke�Y�725XeUDdY�7)h�JUY�7�e-��eUa:@-¨27�«?¨:JÍ7:@BA�SUeU5Xe�@#�Í/�14@KJU@ � JU@K�?JU@BS�@B7�eUSÇA:@B72SUDFe¦f�9)��DFSkeUa:@=SUeU5XeUDF��2JU@BSLSU¨:JU@�9 � DFS4eUa:@Qc�@BTdYE�KDFe¦f�9]5�72A � DFS�eUa:@-JÍ5XeUDdY�Y�h�SU�­@B�KDdÌ<� a:@B5XeUSK/ � DFS45�7:Y�7mu¦A2DVM(@B72SUDdY�7?5�TNa:@B5Xe4JL@BTd@B5�S�@�?5XJL5�M"@Ke�@KJ�3�a2DV�La(�La?5XJL5���e�@KJLDdZK@BS�eUa:@Ç5�M(Y�¨27�ejY�h­@B7:@KJU8�f�JU@BTd@B5�SU@BA"A2¨:JLDV7:84eUa2@ÇJU@B5���eUDdY�7N9E5�72A����­JL@K�2JU@BS�@B7�eUSeUa:@�5���eUDdcX5XeUDdY�7�@B7:@KJU8�f�/ � DFSQeUa:@�JL@B5���eU5�7�e(M"5�SUS¤h�JL5���eUDdY�7 3�a2DF�Ía�cX5XJLDd@BSQh�JUY�M s\e�Y vX9Ð3�a2DFTF@ � DFSQeUa:@JU@B5���eUDdY�7:u¥JL5Xe�@(MQ¨2TFeUDd�?TFDd@KJË923�a2DF�Ía�S�@KeUSHeUa:@�S��?5XeUDV5�T�5�72A¼e�@BM(�]Y�JL5�T0SU�K5�Td@BS`DF7�eUa:@¤�2JUY�«?Td@BM�/4OÇa:@Q@BÒ�¨?5XeUDdY�7Y�hNS�eU5Xe�@�h�Y�J�5�7�DFA:@B5�Tm8�5�S�DVSj¨2S�@BA"a2@KJU@�9�5�72A(eUa2@Ç8�5�S�DVSÐ5�SUSU¨2M(@BA"e�Y=«]@Ç�K5�TdY�JLDF�K5�TFTFfQ�]@KJUh�@B��e�� � y ��Y�72S�eU5�7�eÍ�Í/

OÇa2@��2JL@BS�@B7�e�S�eU¨2A2f�hlYm�K¨2S�@BS¤Y�7�S�Y�TF¨:eUDFY�7�Y�h�eUa2@�8�Y#c�@KJL72DF7:8@BÒE¨25XeUDdY�72SQh�Y�J¤eUa2@�S��]@B�KDÉÌ­�"�2JUY�«<Td@BM Y�heUa:@=Y#c�@KJLA:JLDFc�@B7�A:@Ke�Y�725XeUDdY�7�365Ëc�@Q34DdeUa�YËc�@KJLA2JLDdc�@=hµ5���e�Y�J�7.y v)�ò�E9?h�Y�J�eUa:@ �?5XJÍ5�M(@Ke�@KJLS � y tXsm9 � y vX/ò¡E95�72A4� � y tXsm9­��Y�72A2DdeUDdY�7?Sk3�a2DF�Ía�5XJU@=Cm7:YË347�e�Y"8�@B7:@KJÍ5Xe�@¤5"SLDF7:8�Td@ DF72SUeU5X«?DFTFDdegf�M(YmA:@=5��K��Y�JLA?DF7:8"e�Y�TFDF7:@B5XJS�eU5X«?DVTFDde¦f"5�7?5�TdfESU@BS��ÉvKsm9Ëv�vX9Ëv��)#o5�72A�5��K��Y�JLA2DV7:8�e�Y¤cX5XJLDdY�¨?S67E¨2M(@KJÍDF�K5�T<SUeU¨2A2Dd@BS��Év��:9#vËw�9ËvB �#¥/�R47)5�Tde�@KJÍ725XeUDdc�@YËc�@KJÍA:JLDdc�@���Y�72A2DdeUDFY�7N987�yÁv)�òtE9]DFS�5�TVS�Y�@�Îm�?TdY�JU@BA\DF7�5�hl@K3rTFDFM�Dde�@BA��K5�S�@BSHa:@KJU@�/�n�DF7:@B5XJHS�eU5X«?DFTFDFe¦f�5�725�TdfmSUDFSSU¨:8�8�@BSUeUSÇeUa25XepeUa:@KJL@-5XJU@ e¦36Y�¨?72S�eU5X«?Td@`M(YmA:@BSp8�@B7:@KJÍ5Xe�@BA�h�Y�JÇeUa2DFSpTdY#3�@KJ�YËc�@KJLA:JÍDdc�@�9?5�TdeUa:Y�¨28�a)7�¨2M"@KJLDF�K5�TSUDFM¤¨2TF5XeUDFY�72SNDF72A2DV�K5Xe�@jeUa:@�A:Y�M�DF725�72��@ÐY�h2547:Y�72TFDF72@B5XJB9ËSUDF728�Td@jM(YmA:@�9|TV5XJU8�@�5�M(�?TVDdeU¨2A:@!�?¨2TVSU5XeUDF7:8ÇDF7?S�eU5X«?DFTFDFe¦fh�Y�J�7.yrv)�òt.�Év��)#¥/

OÇa2@j��Y�M(�?¨:eU5XeUDdY�7?5�T��2JUY�«?TF@BM DFSNDF72DdeUDV5Xe�@BA a:@KJU@ÐcmDF5ke¦36Y45�Tde�@KJÍ725XeUDdc�@�M(@KeUa2YEA2SB�jvË�]5k�2JUY��?5X8�5XeUDV7:8�SUa:Ym�UCh�JUY�7�eK9�5�72A�¡��H5��2JUY��?5X8�5XeUDF728.$NÏ4P A:@Ke�Y�725XeUDFY�7365Ëc�@�/";Ç@BSU¨2TFeUSHSLa:YË3�DV7:8�eUa2@(@�Ñ­@B��eUS-Y�h�eUa:@"5�Tde�@KJÍ725XeUDdc�@DF72DFeUDF5�T���Y�72A?DdeUDdY�72S�5XJU@��2JU@BSU@B7�e�@BA DF7%[E@B��eUDFY�7 �:/ò�E/�>:Y�J"eUa2@�Ì<JLS�e�5�Tde�@KJL725XeUDdc�@)S�@Ke(Y�hHDF72DdeUDV5�T���Y�72A2DFeUDdY�72SK9eUa:@¼�2JU@BSUSL¨:JU@�9ÇA:@B72SLDde¦f�9Ç5�72A c�@BTdYm�KDde¦f Y�7 @BDFeUa:@KJ�SLDFA:@�Y�h-eUa:@\�?JUY��?5X8�5XeUDF7:8�SUa:Ym�UC%h�JUY�7�e�5XJL@¼�Ía:Y�S�@B7°e�Y��Y�JUJU@BSU�­Y�7?A-e�Y`eUa:@`vKP Y#c�@KJLA:JLDFc�@B7¤A2@Ke�Y�725XeUDdY�7N/!>:Y�JÐeUa:@6�?5XJL5�M(@Ke�@KJÍS0TVDFS�e�@BA¤5X«­Y#c�@�9�SUDFM¤¨2TdeU5�72@KY�¨2SoS�Y�TV¨:eUDdY�7

t

Page 6: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

Y�hoeUa2@H;45�7:CEDV7:@�u¦14¨28�Y�72DdY�ek5�72A�;�5BfmTd@BDd8�a�TFDV7:@�@BÒE¨25XeUDdY�72S6�2JLYEA2¨?��@BS�5"ip^¤S��]@K@BA�Y�h�-�:<;Ky ��ò Xs�q�tE/6>:Y�J�5S��]@B�KDÉÌ?@BA"YËc�@KJLA:JÍDdc�@4Y�h�7.y�v)�ò�E9:h�Y�J�@�Î:5�M(�?TF@�9�eUa:@HDF72DdeUDV5�T:SUa:Ym�UC"S��]@K@BA�DFS%-�y  �ò�mvB�|�:/�RHS65�7�5�Tde�@KJÍ725XeUDdc�@DF72DFeUDF5�T]��Y�72A2DdeUDdY�7È9EeUa2@-M(Y�JU@=¨2SL¨25�TNS��?5XeUDF5�TÈ�2JUYXÌ<Td@BSp5�SLS�YE�KDV5Xe�@BA�3�DdeUa�eUa2@�$]ÏHP�A2@Ke�Y�725XeUDdY�7N9234DdeUa�h�5XJUÌ?@BTFA��Y�72A2DFeUDdY�72S���Y�JLJU@BS��]Y�72A2DF728(e�Y�eUa2@QS��]@B�KDÉÌ?@BA�YËc�@KJLA2JLDdc�@�9N5XJU@��La:Y�S�@B7È/4OÇa:@¤DF72DdeUDV5�TN�2JU@BSUSL¨:JU@=�2JLYXÌ<Td@-5���JUY�SLSeUa:@(DF72DFeUDF5�Tu$]ÏHP�A:@Ke�Y�725XeUDdY�7�DFS`SUa2YË3�7N9]h�Y�J`@�Îm5�M(�<Td@�9ÈDF7¼>0DF8�¨:JU@�vX9È3�a:@KJU@¤eUa:@�3k5Bc�@"�2JLY��?5X8�5Xe�@BS`e�Y)eUa:@JLDd8�a�eK/�R4S 34DFTFT�«­@(SUa2YË3�7�DF7�[m@B��eUDdY�7�:/ò�E9oeUa:@"DV72DdeUDF5�T0��Y�72A2DdeUDFY�72S DF7¼eUa:@(�2JUY�«<Td@BM a25Bc�@"JL@BTF5XeUDdc�@BTdf¼TFDde�eUTd@DF7mÊ­¨:@B72��@�Y�7%eUa:@�@Kc�@B7�eU¨25�THTFDFM�Dde(��fE�KTd@�«­@Ba?5BcmDdY�J"Y�h`eUa:@�DF7?S�eU5X«?DFTFDFe¦f­¢kDV72DdeUDF5�T6e�JL5�72SLDd@B7�eUS�A2Dd@)Y�¨:e�h�5�DdJÍTdfÒE¨2DF�UCmTdf�/

RrSU¨2DFeU5X«?Td@ S��?5XeUDF5�ToSU�K5�Td@-DF7�eUa:@=�2JUY�«<Td@BM�DFSpY�7:@-«?5�S�@BA�Y�7�eUa:@BE�a25�Tdh!JU@B5���eUDFY�7�Td@B7:8�eUadGm9d�K�  9?D�/ª@�/d9<eUa:@A2DFSUeU5�72��@(«]@Ba2DF72A\eUa:@"SUa:Ym�UCDF7¼3�a2DV�La�a25�Tdh�eUa:@(JU@B5���eU5�7�eUSQ5XJL@"��Y�72SU¨2M(@BAÈ/�¡ Ddc�@B7(709È5)SU¨2DFeU5X«?Td@ � 9ÈeUa:@JU@B5���eUDdY�7:u¥JL5Xe�@-M¤¨2TdeUDd�?TVDd@KJ�SUa2YË3�7)DF7�@BÒE¨25XeUDdY�7������Í9?�K5�7�«­@ S��]@B�KDÉÌ<@BA�e�Y"8�DFc�@=5¤SU�?5XeUDF5�TN¨272DFe�«?5�SU@BA�Y�7,� �  /RHSjA:Y�7:@ÇDF7,�ÉvËw�9|vB �#¥9�5 � Y�hÈ¡��Xsm/ wXt=DFSШ2SU@BA�e�Y-S��]@B�KDdh�f-eUa:@S� �  5�S�5=S��?5XeUDF5�T:¨?72Dde0hlY�J¢7.y v)�ò�E/ � y �Xs���ò�mvDFSp¨2SU@BA)hlY�J�eUa:@£7,yrv)�òt"�K5�SU@�/]_^¥¤ �+m%¦*e�fhi�§¨n�©4��eªop«kbD¬%b�©�b<j<­OÇa2@Ç�2JU@BS�@B7�e�SUeU¨2A:f�¨2S�@BSjeUa2@4��SLS�@B7�eUDV5�TFTdf�Ï�Y�7mu�_ SU�KDFTFTF5Xe�Y�JLf��µ��Ï`_=�jM(@KeUa:YmA��ÉvBq®!E¡�¡�#Nh�Y�J6S��<5XeUDF5�T2DF7�e�@KJ�u

�]Y�TF5XeUDdY�7\Y�hjeUa:@�S�fmS�e�@BM Y�hj8�YËc�@KJÍ72DF7:8�@BÒ�¨?5XeUDdY�72SK/ ��Ï _ÁM(@KeUa:YmA2SH��Y�72S�eUDdeU¨:e�@(5��KTF5�SUSHY�h�a2DF8�a\5��K�K¨:JÍ5���f�9SUa:Ym�UC\�K5X�2eU¨:JLDF728�7E¨2M(@KJLDF�K5�T0SU�Ía:@BM(@BS`h�Y�JHa�f��]@KJU«]Y�TFDV�=S�fmS�e�@BM"SHY�h���Y�72S�@KJLc|5XeUDdY�7TF5Ë3�SK9]«?5�S�@BA¼Y�7¨:�E3�DF72A«?DF5�SU@BA�A?DÉÑ­@KJL@B72�KDF7:8DF7�TdYm�K5�Tp�La25XJL5���e�@KJÍDFS�eUDF��Ì?@BTVA2SK/���e(a25�S"a2DF8�a�5��K�K¨2JL5���f ��eUa?DdJLA�Y�JLA:@KJ(Y�J�a?Dd8�a:@KJë�-DF7SUM(YEY�eUaJU@K8�DdY�7?S4Y�h6eUa:@¤Ê?Y#3=9È5�72A�K5X�2eU¨:JU@BS=eUa:@(M(Y�eUDdY�7Y�h�¨?7:JU@BS�Y�Tdc�@BAS�e�@K@K��8�JÍ5�A2Dd@B7�eUS`3�DdeUa:Y�¨:e`DF7�e�JUYXuA2¨2�KDV7:8)S��?¨:JLDFY�¨2SHY�SU�KDFTFTF5XeUDFY�72SK/"14@B72��@���Ï _ DFS=�?5XJUeUDF�K¨2TV5XJLTdf�36@BTFTjSU¨?Dde�@BAhlY�J-JU@BS�Y�TF¨:eUDFY�7Y�h�Ê<YË3pÌ?@BTVA2S DF73�a2DV�La�eUa:@KJU@Ç5XJL@ÇSUa:Ym�UCmSÐY�JÐÊ<5�M(@ph�JUY�7�eUSK/!��Ï _ ¨2S�@BSÐ5�7"5�A?5X�2eUDdc�@p�]Y�Tdfm7:Y�M"DF5�TEDF7�e�@KJU�]Y�TF5XeUDdY�7(��Y�72S�e�Jͨ2��e�@BAY�7)eUa:@ «<5�SUDFSkY�h!A:@B�KDFSUDdY�7?S�e�Y"5Ëc�Y�DFA�SUe�@K@K��8�JL5�A2Dd@B7�eUSÇDF7�eUa:@=A?5XeU5m/�OÇa:@`�]Y�Tdfm7:Y�M"DF5�T­DFSp5�TFSUY(«?DF5�S�@BA�e�Y(@�ÎEue�JL5X�]Y�TF5Xe�@�A?5XeU5=h�JUY�M eUa:@4A2DdJU@B��eUDdY�7"Y�h]DV7:hlY�JÍM"5XeUDdY�7(�2JLY��?5X8�5XeUDdY�7\�µD¥/ª@�/d9E¨:�E3�DF7?A<�Nh�Y�J��<a�fmSUDF�K5�T2��Y�7?SUDFS�e�@B72��f5�72A�SUeU5X«?DFTFDdegf�/(OoY�@B7?SU¨:JU@(eUa25XeQSUa:Ym�UCmS=5�72A�Y�eUa:@KJQS�e�@K@K��8�JL5�A?Dd@B7�eUS-DF7eUa:@(Ê?Y#3�5XJU@"�?JUY��]@KJLTdf��K5X�2eU¨2JU@BA�µD�/ª@�/d96M(YËc�@�5Xe�eUa:@)��Y�JUJU@B��e"SU�­@K@BA­�Í9�5A2DFSU��JU@Ke�@���Y�72S�@KJLc|5XeUDdc�@)h�Y�JLM Y�h�eUa2@�@BÒE¨25XeUDdY�7?S(DFSQ¨?S�@BA�3�DdeUa�eUa:@DF7�e�@KJU�]Y�TF5XeUDdY�7)M(@KeUa2YEAN/

O�YQ5Ëc�Y�DFA�@B7�e�JUY��Ef�u¥cmDdY�TF5XeUDV7:8=@�Îm�?5�72SUDdY�7�SUa:Ym�UCmS�7:@B5XJ6S�Y�72DF�p�]Y�DF7�eUSK9�34a2DF�La�DFSÐ3�a:@KJL@��La25XJÍ5���e�@KJLDFS�eUDF��c�@�u

Page 7: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

TdYm�KDdeUDd@BS��La25�7:8�@pSUDF8�7N9|a?Dd8�a=Y�JLA2@KJ0A2DVSUSUDd�?5XeUDFY�7=DFS05�A2A:@BA-DV7-eUa:@��2JU@BS�@B7�e!S�eU¨2A:f`cmDF5�eUa2@�nÈYm�K5�Tmno5|Î->:JÍDd@BA:JLDF�Ía2S�µnon�>j�ÐSU�Ía:@BM(@�9m3�a2DF�Ía"5�A2A2S�@�ÎEe�JÍ5Q7E¨2M(@KJLDV�K5�T:cEDVSU��Y�SUDdegf¤eUa2JUY�¨:8�a:Y�¨:e�eUa:@���Y�M(�<¨:eU5XeUDdY�725�T­A:Y�M"5�DF7�5Xe�@B5��ÍaeUDFM(@�S�e�@K�È/R c|5XJÍDF5�7�e¤Y�7 eUa:@�n�no> SU�La:@BM"@�9ÐeUa:@�;�Y�@�>!DÉÎ �µ;�>j�-SU�La2@BM(@�9jY�72Tdf�5�A2A?S-@�Îme�JL5¼7�¨2M"@KJLDF�K5�TcmDFSU��Y�SUDdegfQ34a:@B7�eUa:@KJU@�DVSÐ5=S�Y�72DF�k�]Y�DF7�eÐTdYm�K5�TFTdf�9�D�/ª@�/d9�3�a:@KJU@peUa:@�@BDd8�@B7�cX5�TF¨:@BS��La25�7:8�@4SUDd8�72SK/!OÇa2DVSÐSU�La:@BM"@�DFS5�TFS�Y @�Îm�?TdY�JL@BA(DF7�eUa:@p�2JU@BSU@B7�e�SUeU¨2A:f�/!R4TdeUa2Y�¨:8�a�eUa:@�n�no>SU�La2@BM(@�DFS!eg3�DF��@Ç5�S���Y�M"�?¨:eU5XeUDdY�725�TVTdf-@�Îm�]@B72SUDdc�@5�SpeUa:@=;4> SL�La:@BM(@�9<DF7�8�@B7:@KJL5�TÈn�no>�SUa:Y�¨2TVA�«]@ ¨2S�@BA�3�DFeUa���Ï`_r«­@B�K5�¨?S�@ DdepDFSpM(Y�JU@ JUY�«<¨2S�ekhlY�JÇA?D�¯��K¨2Tde�2JUY�«<Td@BM"SK/

_`7?��@�eUa:@�7E¨2M(@KJLDV�K5�Tp5X�2�2JUYËÎmDFM�5XeUDdY�7�Y�h`eUa:@�S��?5XeUDV5�Tpe�@KJLM"S"a?5�S"«]@K@B7%��Y�M(�?TF@Ke�@BA%¨2SUDF728¼eUa2@���Ï _M(@KeUa:YmAN9:eUa:@Q��Y�72S�@KJUcX5XeUDdY�7)@BÒE¨25XeUDdY�72SQ��¡��p�K5�7)«]@ 3ÇJLDFe�e�@B7)DF7)eUa:@ h�Y�JLM

rs t y r70� rs-� ��t��

RreUa2DdJÍA)Y�JLA:@KJ`Op�`P �µOoY�eU5�T0�j5XJLDV5XeUDdY�7�P`DFM"DV72DFSUa2DV7:8���;�¨27:8�@�u¦W-¨:e�eU5�M(@KeUa2YEA¼DFSÇeUa2@B7�¨2S�@BA�hlY�JHeUa:@QeUDFM(@A2DFSL��JU@KeUDdZB5XeUDdY�7N9XSUDF7?��@�eUa:@6M(@KeUa:YmAQa25�S0a2Dd8�aQ5��K�K¨:JL5���f-5�7?AN9�M(Y�JU@�DVM(�]Y�JUeU5�7�eUTFf�9|5HTF5XJU8�@�eUDFM(@�SUe�@K�¤S�eU5X«<DFTFDdegfJU@K8�DdY�7�3�a2DV�La�DF72�KTF¨2A2@BSj5QSU@K8�M(@B7�ekY�hN�?¨2JU@BTdf(DFM"5X8�DF7?5XJUf(TFDF7:@B5XJ�8�JUYË3ÇeUa�JL5Xe�@BSB/�OÇa2DFS�hl@B5XeU¨2JU@4@B7?SU¨:JU@BS�eUa25Xeh�Y�J�5�SU¨ª¯��KDd@B7�eUTdf�SLM"5�TFTpeUDFM"@�S�e�@K���µ5��K��Y�JÍA2DF7:8�e�Y eUa:@¼i6Y�¨2JL5�7�eÝu¦>2JLDd@BA:JLDV�La2SÝu¦no@Kc�f�Y�J)ik>!n ��Y�72A?DdeUDdY�7<�Í9eUa:@\eUDFM(@\A?DFSU��JU@KeUDdZB5XeUDFY�7%3�DFTVTÇ7:Y�e�DV7�e�JUYmA2¨2��@\DF72S�eU5X«?DVTFDde¦f e�Y eUa2@�JU@BSU¨?TdeK/°/°a?DFTd@�eUa:@KJL@\5XJU@¼Y�eUa:@KJ�eUDFM(@DF7�e�@K8�JL5XeUDdY�7 M(@KeUa:YmA2S=eUa25Xe¤5XJU@�A:@BSLDd8�7:@BA�S��]@B�KDÉÌ­�K5�TFTdf�e�Y¼S�Y�Tdc�@�S�fESUe�@BM"S=Y�hk@BÒE¨25XeUDdY�72S-3�DdeUa�S�eUDdÑ SUY�¨:JL��@e�@KJLM"S(��@�/ª8:/d9È�4_ PH�±�ª¡���#��HM(Y�JU@�@�¯��KDd@B7�eUTdf�9]eUa:@Kf\5XJL@�72Y�e4�?5XJLeUDF�K¨2TF5XJLTFf�36@BTFT0SU¨2Dde�@BA¼e�Y)S�Y�TdcmDF7:8�eUa:@�7:Y�7muJU@B5���eUDdc�@(��Y�72SU@KJUc|5XeUDFY�7\@BÒE¨25XeUDdY�7?SK/-[mDF72��@QeUa:@¤�K¨2JUJU@B7�eHSUDVMQ¨2TV5XeUDdY�7�Y�72TFf�DF7�c�Y�TFc�@BSH5�SUDV7:8�Td@-S�e�@K�JU@B5���eUDFY�7N9¨2S�@�Y�hHeUa:@)Op�`P ;4¨27:8�@�u¦W=¨2e�eU5�M(@KeUa:YmA DFS¤�2JU@Kh�@KJUJU@BAN¢6eUa:@\ik>!n ��Y�72A?DdeUDdY�7�DF7�eUa2DFS��K5�S�@�DV72��Y�JU�]Y�JL5Xe�@BSeUa:@�SUY�¨:JL��@�e�@KJÍM e�Y DV72SU¨:JU@)S�eU5X«<DFTFDdegf�/ �Ý7%SUDFM¤¨2TF5XeUDFY�72S(JU@BS�Y�TFcEDF728�5�M(Y�JU@¼��Y�M(�?Td@�Î �La:@BM�DF�K5�T�JL@B5���eUDdY�7M(@B�Ía25�72DFSUM�9EY�h0��Y�¨:JLS�@�9:Y��]@KJL5Xe�Y�J4S��?TFDde�eUDV7:8-3�DFeUa�DFM"�?Td@BM(@B7�eU5XeUDdY�7�Y�h05�S�eUDdÑ�_`P`�%S�Y�TFc�@KJÇSU¨2�La)5�Sk�4_ PH�DFSp¨2SL¨25�TFTdf��2JU@Kh�@KJUJU@BAN/Ð>2¨:JLeUa:@KJ�A:@KeU5�DFTVSkY�7�eUa:@=7E¨2M(@KJLDV�K5�TNM(@KeUa:YmA2SǨ2S�@BA)a2@KJU@-M"5Ëf�«]@`h�Y�¨272A)DF70�ª¡|�)#¥/

�j5�TFDVA25XeUDdY�7\Y�hjeUa:@�7�¨2M"@KJLDF�K5�ToM"@KeUa:YEA?S4¨2SU@BA\a:@KJL@¤a25�S4«]@K@B7¼�­@KJLhlY�JLM"@BA�DF7�e¦36Y�3k5BfmSK�¤vË�pcmDF5�5X�2�?TFDÉu�K5XeUDdY�7)e�YFEÝe�@BS�e�G"�2JLY�«?Td@BM"S63�DdeUa�@�Î:5���eÇY�JÇCm7:Y#3�7�S�Y�TF¨2eUDdY�72SK9m5�72A�¡���cmDF5�8�JLDFA�JL@BS�Y�TF¨:eUDdY�7�S�eU¨?A2Dd@BSkh�Y�JÇeUa:@�?¨2TVSU5XeUDF7:8�A:@Ke�Y�725XeUDdY�7�5�SÇA:@BSU��JLDF«­@BA�DF7�[m@B��eUDdY�72Sp�:/Fv=5�7?A��:/ò¡E/�OÇa:@`eUa:JL@K@BEÝe�@BS�e�G(�2JLY�«?Td@BM"SpDF7vË�kDV72�KTF¨2A:@5�72Y�7mu¥JU@B5���eUDdc�@�SUa:Ym�UCeU¨:«]@"3�DFeUa�5�7�@�Î:5���e�S�Y�TF¨:eUDdY�7È9oeUa:@��2JUY�«?Td@BM Y�hpe¦36Y¼DF7�e�@KJL5���eUDF728�SUa:Ym�UCmSQ��JL@B5Xe�@BA«Ef�5"A2Y�¨:«?Td@`SUa:Ym�UC�eU¨:«]@�9:5�72A�5(SUa2YE�LC�3k5Bc�@¤DF7�e�@KJL5���eUDF7:8(3�DFeUa�5(Ê?YË3pÌ<@BTFA)DF7�3�a2DV�La�eUa:@KJU@=DVSp5"S��?5XeUDF5�TVTdf

w

Page 8: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

Y�SU�KDFTVTF5Xe�Y�JUf�A2@B72SUDdegf�Ì?@BTVAN/ÐP4@KeU5�DVTFSpY�7)eUa:@ JL@BSU¨2TdeUSkY�h0eUa:@ e�@BS�eÇ�?JUY�«?Td@BM"Sk5XJU@QA:@BSU��JLDd«]@BA�DF70�ª¡|�)#¥/6PHDdÑ­@KJU@B7�eY�JLA:@KJ¤��Ï _ SL�La:@BM(@BS¤36@KJU@�@�Î:5�M"DF72@BAN905�7?A Dde-365�SQhlY�¨?72A�eUa25Xe¤eUa:@�eUa2DdJLA�Y�JÍA:@KJQ��Ï`_ SU�La2@BM(@�SLa:YË36@BASUDd8�7?DÉÌ<�K5�7�eHDFM"�2JUYËc�@BM"@B7�eUS DF7\JU@BS�Y�TV¨:eUDdY�7¼Y�hjÌ<72@¤SU�K5�TF@�A2@B72SUDdegf�S�e�JL¨2��eU¨2JU@BSHYËc�@KJ=eUa:@(S�@B��Y�7?AY�JLA:@KJ ��Ï _SU�Ía:@BM(@�/414@B72��@¤hlY�JHeUa:@Q�2JU@BS�@B7�e4�?JUY�«?Td@BM)9<M(Y�S�e�JL@BSU¨2TdeUS�3�DFTFTN«]@¤SUa:YË347�h�Y�J4eUa2DFJLA)Y�JLA:@KJ`��Ï _�SU�La:@BM"@BSK9@�Î:��@K�2e�5�S�72Y�e�@BAN/

² ³ L�´�KJ�íÂ>:Y�TVTdYË3�DV7:8��2JL@KcEDdY�¨?SoS�eU¨2A?Dd@BS�5�7?A=eUa:@kM(@KeUa:YmA:Y�TdY�8�f=Y�¨2eUTFDF7:@BAQDF7¤[E@B��eUDFY�7¤�E9�eUa:@kSUa:Ym�UC-�2JU@BSUSU¨2JU@j«]@Ba2DF72A

eUa:@�@Kc�Y�TdcEDV7:8�A:@Ke�Y�725XeUDFY�7-3k5Bc�@ ��hlY�JÍMQ¨2TV5Xe�@BA-DF7�[E@B��eUDdY�7Q�E/FvË�oDFSN@KcX5�TF¨25Xe�@BAQh�Y�Jo8�5�TFTdY��<DF7:8Ç�?a2@B7:Y�M(@B725m/0OÇa2DFSDFS�A:Y�7:@�«Ef"M(Y�72DFe�Y�JLDF7:8 eUa:@£µ�¶®·M¸)µEM"5|ÎmDVMQ¨2M��2JU@BSUSL¨:JU@�DF7"eUa:@�cmDF�KDF72DFe¦f�Y�hNeUa:@4SLa:YE�LC(3�a2DF�Ía�DFS�DF72DdeUDV5Xe�@BAN/���eDFSkDFM(�]Y�JUeU5�7�e6eUa25XepY�7:@ A:YE@BSp7:Y�epTdY�Y�C4¹ºµ»¶h¼�¸ºµ¥µ¾½ DF7�eUa:@ ��Y�M(�?¨:eU5XeUDdY�7?5�TNA:Y�M"5�DF7�h�Y�JÇ5¤M�5|ÎmDFM¤¨2M��2JU@BSLSU¨:JU@5�SjA:Y�72@�9�hlY�JÐ@�Î:5�M(�?TF@�9�DF7,�ª¡�t�#¥9ESLDF72��@p5`8�TdY�«?5�T:S�@B5XJÍ�La"�K5�7"�K5�¨?S�@�5�7�@KJUJUY�72@KY�¨2SUTdf�E��KTFDd�2�]@BA�G4�]@B5XC-�2JU@BSLSU¨:JU@�2JUYXÌ­Td@(e�Y�«]@"8�@B7:@KJÍ5Xe�@BAN/�P`¨:JLDF7:8�eUa:@���Y�M(�?¨2eU5XeUDdY�7�Y�hp5�8�5�TFTdY��?DF728�A:@Ke�Y�725XeUDdY�7N9ÐDdeQDFS �]Y�SUSUDd«<Td@�hlY�J¤eUa:@SUa:Ym�UC �?JU@BSUSU¨:JL@)e�Y A:JUY��°TdYË36@KJ�eUa25�7%�2JL@BSUSU¨:JU@BS"3�@BTFT�«]@Ba2DF72A�eUa:@¼SUa:Ym�UC%5�S�5�JU@BSU¨2TFe"Y�h eUa:@�8�5�TFTFY��?DF7:8�?a:@B72Y�M(@B725m/���hÇY�7:@)S�@B5XJL�Ía:@BS(h�Y�J(eUa:@)M"5|Î:DFMQ¨?M �?JU@BSUSU¨:JL@�8�TdY�«?5�TVTdf�9�Dde�DFS¤�]Y�SUSUDd«?TF@�eUa25Xe�eUa:@��2JU@BSLSU¨:JU@Y�h6Y�7:@"Y�h6eUa:@(�]@B5XCES 36@BTFT!«]@Ba2DF7?A�eUa:@"SLa:YE�LC¼DVS JU@B��Y�JLA:@BA�5�7?A�M"DFS�eU5XC�@B7�hlY�J=eUa2@"SUa:Ym�UC¼�2JU@BSUSU¨2JU@�/(OÇa2DFS�?a:@B72Y�M(@B7:Y�7(DFSÐSUa2YË3�7(DF7�>!Dd8�¨:JL@BS�¡X5X«È9�3�a?DF�La(��Y�M(�<5XJU@BSj��Y�M(�?¨2eU5XeUDdY�72SÐY�h­�?¨2TFSL5XeUDF7:8`A:@Ke�Y�725XeUDdY�72SШ?72A:@KJeUa:@`SU5�M(@`��Y�72A2DdeUDFY�72SK9�34DdeUa�eUa2@HSU5�M"@4JU@BSUY�TF¨:eUDdY�7�Y�hÈeUa:@HJU@B5���eUDdY�7�ZKY�7:@`5�72A���Y�M(�?¨:eU5XeUDFY�725�T<A2Y�M"5�DF7N9E«?¨:e3�DdeUa�8�TFY�«?5�TÈ5�72A�TFYE�K5�T]�2JL@BSUSU¨:JU@ M"5|Î:DFM"5��<TdY�e�e�@BAN92JU@BSU�­@B��eUDFc�@BTdf�/

OÇa2@4h�Y�TFTdY#3�DF7:8-SU@B��eUDdY�72SpA:@BSU��JÍDd«]@���Y�M(�?¨:eU5XeUDFY�725�T­JU@BSU¨2TdeUS�h�Y�J6eUa2@4@�Ñ]@B��eUSpY�hÈeUa:@ SUDFZK@4Y�hÈeUa2@H��Y�M(�<¨:eU5|ueUDdY�725�T­A:Y�M"5�DV7N9�eUa:@4JU@BS�Y�TF¨2eUDdY�7"Y�hNeUa:@HJU@B5���eUDdY�7�ZKY�7:@�9EeUa:@`DF72DdeUDV5�T:��Y�72A2DdeUDdY�7?SK9�5�72A�eUa:@4@�Ñ­@B��eUSkY�hÈA2DdÑ­@KJU@B7�e7E¨2M(@KJLDF�K5�T�SU�La:@BM"@BS"Y�7 SLDFMQ¨?TF5XeUDdY�7 Y�h`eUa:@��<¨2TFSU5XeUDF728�vKP A:@Ke�Y�725XeUDdY�7 365Ëc�@�/ >:YE�K¨?S�DFS"�?TF5���@BA%Y�7 eUa:@YËc�@KJÍA:JLDdc�@B7°y v)�ò�E965�TdeUa:Y�¨:8�a A:Y�M�5�DF7�SUDdZK@)S�eU¨2A2DF@BS¤5�TVS�Y@�ÎE�?TFY�JU@�@�Ñ­@B��eUS(Y�hH5�7%5�Tde�@KJL7?5XeUDdc�@�YËc�@KJLA:JÍDdc�@�97(y v)�òtE9ÈY�7eUa:@"A:@Ke�Y�725XeUDFY�7@Kc�Y�TF¨:eUDdY�7N/QOÇa:@�JU@BSU¨2TFeUSHSLa:YË3�7DF7�[E@B��eUDFY�72S`�:/FvX9È�:/ò¡E9o5�72A�:/ò����Y�JLJU@BS��]Y�72Ae�Y"eUa:@¤�|JLA)Y�JLA:@KJÇ��Ï`_ M(@KeUa:YmA)3�DdeUa�eUa:@QnÈYm�K5�TÈno5|Î�>:JLDF@BA:JLDF�Ía2S=�µnon�>Ð�pSU�La:@BM"@�/

 

Page 9: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

¿k^a` �Cb�¦*À�mDoºn´oºiab�gkn�©H& b�¦*n�iag��_iaÁªe_`72@-Y�hÐeUa:@¤«?Dd8�8�@BS�e`�La?5�TFTd@B7:8�@BS4Y�hjSUDFM¤¨2TF5XeUDF728�¨272S�eU5X«<Td@=YËc�@KJÍA:JLDdc�@B7¼A:@Ke�Y�725XeUDdY�7?S4DFS4eUa:@¤a2Dd8�a�A2@K8�JU@K@

Y�hkJU@BS�Y�TF¨2eUDdY�7�JU@BÒE¨2DdJU@BAe�Y\JU@BS�Y�Tdc�@�eUa:@�DF72SUeU5X«?DFTFDdegf�/"�Ý7�Y�JLA:@KJ=e�Y\JU@BS�Y�Tdc�@�eUa:@�JU@B5���eUDFY�7�ZKY�7:@�«­@Ba?DF72A¼eUa:@�2JUY��<5X8�5XeUDF7:8)SUa:Ym�UC¼365Ëc�@�9�5)TF5XJL8�@���Y�M"�?¨:eU5XeUDdY�725�TÐA2Y�M"5�DF7�DFSHY�h�e�@B7�7:@K@BA:@BAN/¤OÇa2DFS`DFSH�?5XJLeUDF�K¨2TF5XJLTFf)e�JL¨:@Ddh!5"TdY�7:8Xu¥eUDVM(@-S�Y�TF¨2eUDdY�7�DFSp«]@BDF728�SUY�¨:8�a�eK/p>:Y�JH5"�?5XJLeUDF�K¨2TF5XJÇ��Y�M(�<¨:eU5XeUDdY�7N9<Y�7:@-DFSpe�@BM"�2e�@BA�e�Y�C�@K@K�\Y�72TFf5"TFDVM"Dde�@BA)7E¨2M-«]@KJpY�hÐ8�JLDVA��­Y�DV7�eUSp«]@Ba2DV72A�eUa:@-SUa:Ym�UC�Y�JHA:@Ke�Y�725XeUDdY�7�365Ëc�@�9<3�DFeUa)eUa:@=JU@B5�SUY�72DF7:8(eUa25Xe4eUa:@DF7:h�Y�JLM"5XeUDFY�7�36@BTFT­«]@Ba2DF72A�eUa:@ 365Ëc�@ @BDdeUa:@KJÇ7:@Kc�@KJÇ�K5XeU�Ía:@BS�¨2��34DdeUaN9EY�JÇA:Y�@BSp72Y�ek5|Ñ]@B��eK92eUa:@`3k5Bc�@-A?¨:JLDF7:8eUa:@=��Y�M(�<¨:eU5XeUDdY�7N/�O�a2DFSkDFSk�?5XJUeUDV�K¨2TF5XJLTdf�e�@BM(�2eUDF7:8�e�Y�A2Y"DF7)TdY�7:8�eUDFM(@=SUeU¨2A2Dd@BSpSUDV72��@`eUa:@=��Y�M(�?¨:eU5XeUDFY�725�T��Y�S�e6DF7�c�Y�TFc�@BA�DF7(C�@K@K�<DF7:8-5=TV5XJU8�@�A:Y�M"5�DV7(«]@Ba2DF72A�eUa:@4SUa:Ym�UC(DFSja2DF8�aN/��Ý7"eUa2@Ç�2JU@BS�@B7�e�S�eU¨?A:f�9�a:Y#3�@Kc�@KJË9�36@A:@BM(Y�7?S�e�JL5Xe�@(eUa25Xe=Y�72@"MQ¨2SUe «­@(�K5XJU@Khµ¨2TÐDF7�M�5XCEDF728�SL¨2�La�5)��Y�SUeÝu¦��Y�72SU�KDdY�¨2SQSUDFM(�<TFDÉÌ<�K5XeUDdY�7È9­5�S eUa?DFS �K5�7Td@B5�A�e�YQeUa:@48�@B7:@KJL5XeUDdY�7�Y�hN@KJUJUY�72@KY�¨2SjÊ<YË3°�2JUY��]@KJUeUDd@BSK/!14@KJU@�9�36@4A2@�Ì<7:@45Q��Y�7�c�@B7?Dd@B7�e63k5Bf"Y�hÈ�K5�TF�K¨?TF5XeUDF7:8eUa:@(M"DF7?DFMQ¨?M 7�¨?M-«]@KJHY�h��]Y�DF7�eUS47:@K@BA2@BA\e�Y�«]@¤C�@K�2e`«­@Ba?DF72A)eUa:@(A:@Ke�Y�7?5XeUDdY�7�A2¨:JLDV7:8�5��K5�TF�K¨2TF5XeUDFY�7�h�Y�JeUa:@ Ê<YË3 �2JLY��­@KJLeUDd@BSp7:Y�epe�Y"«]@=5|Ñ]@B��e�@BA�«Ef�e�Jͨ272�K5XeUDdY�7)Y�hÐ��Y�M(�<¨:eU5XeUDdY�725�TÈA2Y�M"5�DF7N/

OÇa2@4�2JLY�«?Td@BM"Sk��JU@B5Xe�@BA�«Ef�Y#c�@KJUZK@B5�TdY�¨2S�e�JL¨272�K5XeUDdY�7�Y�h�eUa:@ ��Y�M(�?¨:eU5XeUDdY�7?5�T­A2Y�M"5�DF7�DF7�eUa:@ 7�¨2M"@KJLDF�K5�TSUDFM¤¨2TF5XeUDFY�7 Y�h=5�7 Y#c�@KJLA:JLDFc�@B7 vKPÂ$NÏ4P A2@Ke�Y�725XeUDdY�7°5XJU@\SUa2YË3�7°DF7%>!Dd8�¨:JL@BS�� 5�72A%�:/ OÇa2@BS�@�JU@BSL¨2TdeUSK9��Y�M(�?¨2e�@BA h�Y�J(5�vKP�A:@Ke�Y�7?5XeUDdY�7��2JUY��?5X8�5XeUDF728\e�YeUa:@�JLDd8�a�e-34DdeUa 5�7�Y#c�@KJLA:JLDdc�@�Y�h�7Ãy v)�ò�E9�SUa2YË3 eUa:@SUa:Ym�UC��2JU@BSUSU¨2JU@QTdY�728�eUDFM"@¤a2DVS�e�Y�JUf�/ OÇa:@�A:Y�M"5�DF7¼S��?5���@�JU@KeU5�DV7:@BA¼«­@Ba?DF72A�eUa2@Q�2JLY��?5X8�5XeUDF7:8�SUa:Ym�UC\hlJUY�7�e��Y�72SUDVS�eUS6Y�h�vKsº�K�  &©Sk5�72A)tXsº�K�  &©SB9Eh�Y�Jk>0DF8�¨:JU@BSp�-5�7?A��:9mJU@BSU�­@B��eUDFc�@BTdf�/jG6Y�eUa���Y�M"�?¨:eU5XeUDdY�72Ska25Ëc�@`eUa:@ SU5�M(@S��?5XeUDV5�T<8�JÍDFA�JL@BS�Y�TF¨:eUDdY�7�Y�h�¡Xs��]Y�DF7�eUS��]@KJÄ� �  5�72A�eUa:@ SU5�M(@ DF72DFeUDF5�T2��Y�72A2DFeUDdY�72S`��eUa25XepY�hÈeUa:@`�2JUY��<5X8�5XeUDF7:8SUa:Ym�UC2�Í¢�eUa:@6Y�72Tdf=A?DÉÑ­@KJL@B72��@6DVSoDF7QeUa:@kSUDdZK@6Y�h2eUa:@kA:Y�M"5�DF7QeUa25Xe!DFSo«]@BDF728���Y�M(�?¨:eU5XeUDFY�725�TFTdf=¨:�NA25Xe�@BAQ«]@Ba2DF72AeUa:@�A:@Ke�Y�725XeUDdY�7¼h�JUY�7�eK/4��eHDVS4S�@K@B7¼eUa25Xe`eUa:@¤@Kc�Y�TF¨:eUDFY�7�Y�hjeUa2@¤�]@B5XC)�2JL@BSUSU¨:JU@Q«]@Ba2DF72A)eUa2@¤SUa2YE�LC�@�Îma?Dd«?DdeUSc�@KJUf�A2DÉÑ]@KJU@B7�e¤«]@Ba25BcmDdY�JLSB9�A:@K�]@B72A2DF728�Y�7�eUa:@)SUDdZK@�Y�h�eUa2DVS¤��Y�M"�?¨:eU5XeUDdY�725�TkA:Y�M�5�DF7�S��?5���@�/��Ý7�>0DF8:/ �E9eUa:@ Y�SU�KDVTFTF5Xe�Y�JUf��]@B5XC��2JU@BSLSU¨:JU@`�2JUYXÌ­Td@,EÝh�5�72SMG�Y�¨:eÇ3�DdeUa)DV72��JU@B5�SUDF728QeUDFM"@�92SU¨:8�8�@BS�eUDF728(eUa25XeÇeUa:@ 8�5�TFTFY��?DF7:85�M(�?TVDdeU¨2A:@"Y�h�eUa:@��]@B5XC�A:@Ke�Y�7?5XeUDdY�7��2JU@BSUSL¨:JU@�DFS¤DF72��JL@B5�SUDF7:8�5�S�eUa2@�3k5Bc�@��2JUY��<5X8�5Xe�@BSK/�Åj@Ke"DF7�>!Dd8:/¼�:9Dde DFS S�@K@B7�eUa25Xe eUa:@(Y�SU�KDVTFTF5Xe�Y�JUf\�2JU@BSUSU¨2JU@��2JUYXÌ<Td@ E�SUa2JLDF7:CmS�G�3�DdeUa�DF72��JL@B5�SUDF7:8�eUDFM(@�9oSL¨:8�8�@BS�eUDF7:8)eUa?5Xe=eUa:@8�5�TFTdY��<DF7:8(5�M(�?TFDFeU¨2A:@`Y�h!eUa:@=SUa:Ym�UC��2JU@BSLSU¨:JU@=DFSpA2@B��JU@B5�SUDF7:8�5�SÇeUa:@=SUa2YE�LC��?JUY��?5X8�5Xe�@BSK/k.�a:@B72Y�M(@B725(SU¨2�Ía5�SpeUa2DVSK9m3�a:@KJU@`eUa:@=��Y�M(�<¨:eU5XeUDdY�725�T]JU@BSL¨2TdeUSk5XJU@=S�@B72SLDdeUDdc�@`e�Y"eUa:@ SUDdZK@ Y�h0eUa:@ ��Y�M(�?¨2eU5XeUDdY�725�TÈA:Y�M�5�DF7N9:5XJU@a2Dd8�a?Tdf�¨272A2@BSUDdJL5X«?TF@�/

q

Page 10: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

P`DÉÑ]@KJU@B72��@BS�DF7 eUa:@�TdY�7:8¼eUDFM(@�a?DFS�e�Y�JLDd@BS¤SUa:Y#3�7�DF7 >!Dd8�¨2JU@BS¤�\5�72A �JU@BSU¨2TdeQhlJLY�M eUa:@�hµ5���e¤eUa?5XeK9�5�SeUa:@-SLa:YE�LC��2JUY��?5X8�5Xe�@BSK9?Ê?YË3 �2JUY��]@KJUeUDd@BSk«]@Ba2DV72A�eUa:@-SUa:Ym�UC�@Kc�@B7�eU¨25�TFTdf)�K5XeU�Ía\¨:��e�Y�eUa:@-SLa:YE�LC�cmDF5 � vÇÆ3k5Bc�@BS¤3�a2DF�Ía�e�JL5Ëc�@BT�5Xe�5�SU�­@K@BA�8�JU@B5Xe�@KJ�eUa25�7(-\/)��h6e�YEY\SLM"5�TFTj5¼A:Y�M"5�DF7�S��?5���@�«]@Ba2DV72AeUa:@�SLa:YE�LC�DFSJU@KeU5�DF72@BA�DF7(eUa2@���Y�M(�?¨:eU5XeUDFY�7\��@�/ª8:/d9NvKs£���  &©S�DF7">!Dd8�¨2JU@4���Í9EeUa:@��]Y�DF7�eUSj5Xe�eUa2@Ç@BA:8�@�Y�hNeUa2@���Y�M(�?¨:eU5XeUDFY�725�TA:Y�M"5�DV7%��@B5�S�@¼e�Y�«]@�¨:�NA25Xe�@BA%5Xh�e�@KJ�5 ��@KJUeU5�DF7 5�M"Y�¨27�e�Y�h eUDFM(@�DF7�e�Y�eUa:@¼��Y�M(�?¨:eU5XeUDdY�7È9634a2DF�La Td@B5�A2Se�Y\5���Y�JUJL¨:�2eUDFY�7Y�h6eUa2@�A25XeU5�DF7�eUa25Xe=JU@K8�DdY�7È/�OÇa:@ � vÈÆ"365Ëc�@BS-@BM"5�7?5XeUDF7:8�h�JUY�M eUa:@���Y�JUJL¨:�2e�@BA�A25XeU5@Kc�@B7�eU¨25�TFTdf��K5XeU�La¼¨:��3�DFeUa�eUa:@=SUa:Ym�UC)DdeUS�@BTFhg9meUaE¨2Sp@KJUJUY�72@KY�¨2SUTdf�5�Tde�@KJLDF7:8"SLa:YE�LC��2JUY��]@KJUeUDd@BSK/

R SUDFM"�?Td@�365Ëf�e�Y��2JL@Kc�@B7�eQeUa:@BS�@"�?a2@B7:Y�M(@B725)h�JUY�M YE�K�K¨:JLJLDF7:8:9ÈY�hp��Y�¨:JÍS�@�90DVS e�Y\DF7?�KTF¨2A:@(5�TFTjSU�?5XeUDF5�T7:YmA:@BS=«]@Ba2DV72AeUa:@"�2JLY��?5X8�5XeUDF7:8¼A:@Ke�Y�725XeUDdY�7 365Ëc�@�5Xe�5�TFTÐeUDVM(@BS-DF7�eUa:@���Y�M(�<¨:eU5XeUDdY�7N/)�Ý7�eUa2DVS 365Ëf�9j5�TFT7:YmA:@BS=5XJU@�«­@BDV7:8�¨:�NA25Xe�@BA�5Xe-@B5��Ía�eUDVM(@"S�e�@K�È9!5�72A�eUa:@���Y�JUJU@B��eQDV7:hlY�JÍM"5XeUDdY�7�DFS=5�TF365ËfESQ�2JUY��?5X8�5Xe�@BA�e�YeUa:@�SUa:Ym�UC�h�JUY�7�eK/.Åj@KeQh�Y�J¤SUeU¨2A2Dd@BS=DV7�3�a2DV�La�eUa2@�TdY�7:8�e�@KJLM «]@Ba25ËcEDFY�J-Y�hpeUa:@�SUa:Ym�UC�DFS-Y�hÇDF7�e�@KJU@BS�eK9!eUa:@��Y�M(�?¨2eU5XeUDdY�725�T2��Y�S�e�Y�h­JL@KeU5�DF72DF7:8 5=A2Y�M"5�DF7�eUa25Xe�DV72�KTF¨2A:@BS!5�TFTm�]Y�DF7�eUSЫ]@Ba2DF7?A-eUa:@��2JUY��?5X8�5XeUDF728=SUa:Ym�UC(�K5�7«]@B��Y�M(@¤�2JUY�a2Dd«<DdeUDdc�@BTdf�TF5XJU8�@�/H�geHDFS4eUa�¨2SH�2JLY��­Y�SU@BA�eUa25XeHeUa:@�SUDdZK@¤Y�hjeUa:@���Y�M(�?¨:eU5XeUDdY�7?5�T�A:Y�M�5�DF7\SLa:Y�¨2TFA«]@Ç�La:Y�SU@B7"S�Y-5�S�e�Y-��Y�7�eU5�DV7(eUa:@�ÉPÊÌË�Ê¥ÉPꬃ 7E¨2M-«]@KJ!Y�h]�]Y�DF7�eUS!eUa?5Xe�DF72SU¨2JU@�eUa?5Xe�7:Y=��Y�JUJL¨2�2e�@BA � v,Æ�3k5Bc�@BS3�DFTVT<«]@ 5X«?Td@ e�Y��K5XeU�La¼¨:��3�DdeUa�eUa2@=SUa:Ym�UC�3�DdeUa2DV7�eUa2@=��Y�M(�?¨:eU5XeUDdY�7?5�TNeUDFM(@ Y�hÐDF7�e�@KJU@BS�eK/

>!Dd8�¨:JL@pt=SUa:YË34S!Y�7"5 7:Y�72A2DVM(@B72SUDdY�7?5�TFDdZK@BA ÎEu¥ejA2DF5X8�JÍ5�M a:YË3=9�DF7(5`c�@KJUf�5X�2�2JUYËÎmDFM�5Xe�@p365Ëf�9E��Y�JUJͨ:�2e�@BADF7:h�Y�JLM"5XeUDFY�7��K5�7��K5XeU�La)¨:��e�Y�eUa:@4�?JUY��?5X8�5XeUDF7:8¤SUa:Ym�UC"h�JUY�7�eK/jRke�eUa2@4Y�72SU@Ke�Y�hÈeUa2@HSUDVMQ¨2TV5XeUDdY�7N9�eUa:@`SUa:Ym�UC��Y�J�$]Ï4P A:@Ke�Y�725XeUDdY�7<�=S�eU5XJUeUSQhlJLY�MWÎ1y s�5�72A��2JUY��?5X8�5Xe�@BS¤e�Y\eUa:@�JLDF8�a�e-5Xe�5�7�5X�?�2JUYBÎ:DFM"5Xe�@�S��]@K@BA�PDF7�e�Y�5���Y�M(�<¨:eU5XeUDdY�725�TjA2Y�M"5�DF7�Y�hpTd@B7:8�eUa(�Ç9o34a2DF�La�DVS 8�Ddc�@B7�DV7�¨272DdeUS`Y�hkeUa:@"JL@B5���eUDdY�7�a25�TFhVu¦Td@B728�eUa � �  />:Y�Jp5�7�YËc�@KJLA:JÍDdc�@B7�A2@Ke�Y�725XeUDdY�7�3�DdeUaÏ74y v)�ò�Q5�7?A�A:@Ke�Y�725XeUDFY�7�SU�­@K@BAC-ÑÐ  �ò�E9Eh�Y�J6@�Îm5�M(�<Td@�9ESLDFMQ¨?TF5XeUDdY�72SSUa:Y#3 eUa25Xe�eUa:@�SU�­@K@BA Y�h � vÃÆ�3k5Bc�@BS�8�@B72@KJL5�TFTdf�Ê­¨2��eU¨25Xe�@�DF72DdeUDF5�TVTdf\«]@Keg3�@K@B7 vKs5�72A v�vX/�O�5XCmDF7:8¼eUa:@M(Y�JU@�5X8�8�JU@BSUSLDdc�@�cX5�TF¨:@�Y�hÇeUa:@�DF72DdeUDV5�T � vÃÆ�365Ëc�@�5�S � vÃÆCyÓÒÓy v�vX9jeUa?DFS-M(@B5�7?SQeUa2@�A2DÉÑ]@KJU@B72��@�DF7S��]@K@BA2S`«]@Ke¦36@K@B7�eUa:@ � vÈƤ3k5Bc�@�5�7?A�eUa:@"SUa:Ym�UC¼h�JUY�7�e=DVSÔÒ � -Ây�¡�ª�:/"Rke-eUDFM(@ÈÕÖ 9ÈeUa:@B7È9ÈeUa:@"SUa:Ym�UCa25�S e�JÍ5Bc�@BTd@BA eUa:@�A2DVS�eU5�72��@(Y�hkeUa:@"��Y�M(�?¨2eU5XeUDdY�725�T�A2Y�M"5�DF7N9���9�S�Y)eUa?5Xe-�]Y�DF7�eUSK9oS�eU5XJUeUDV7:8�5Xe�Î+y�sm9!5XJU@@BTFDFM�DF725Xe�@BA�Y�J�EÝeUa:JUYË347�Y�¨2e�G�Y�hoeUa:@ ��Y�M(�?¨2eU5XeUDdY�7�5Xhle�@KJÇeUa?DFS�eUDVM(@�/�[m¨2�K��@BSUSLDdc�@`�­Y�DV7�eUSk5XekeUa:@ Td@Kh�e6@B7?A�Y�heUa:@"A:Y�M�5�DF7��Y�7�eUDF7E¨:@�e�Y)«]@�@BTFDFM"DF7?5Xe�@BA¼DV7\eUDVM(@(5�S`eUa:@"A:@Ke�Y�725XeUDdY�7h�JUY�7�e �2JUY��?5X8�5Xe�@BS=e�Y)eUa:@(JLDd8�a�eK9ÈS�YeUa25Xe eUa:@"A?DFS�eU5�72��@�«]@Ke¦36@K@B7�eUa:@"A:@Ke�Y�7?5XeUDdY�7�5�72AeUa:@"Td@Kh�e`@B72AY�h6eUa:@(A:Y�M"5�DF7�DFS`5�Td3k5BfmS���/¤OÇa2@ � v×Æ3k5Bc�@(5�SUS�Ym�KDF5Xe�@BA\3�DdeUa�eUa2@=Ì?JLSUeÇ�]Y�DF7�e�e�Y�«]@-@BTFDVM"DF725Xe�@BA��µ5XeÔØ�y¸s��Í9­�?JU@BSU¨2M"5X«<Tdf���Y�7�eU5�DF72DF728�A25XeU5�eUa25Xe

vKs

Page 11: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

a25Ëc�@�7:Y�e=«]@K@B7�¨2�]A?5Xe�@BA�5�72A�eUaE¨2S=5XJU@���Y�JUJL¨:�2e�@BAÈ9o@Kc�@B7�eU¨25�TFTdfDF7�e�@KJL��@K�2eUS=eUa2@�SUa:Ym�UC�5�S-SLa:YË3�7�DF7�>!Dd8:/tE/\>2Y�JÙ7Èy v)�ò�E9ÐeUa?DFSQDV7�e�@KJL��@K�?eUDdY�7�Ym�K�K¨:JLS¤5Xe¤eUDFM(@��Óy ÕÚ � Ö v ÕÖ y ÕA3Û Ü v ÕÝ Û Þ 5�72A�5Xe�eUa:@�TdYm�K5XeUDdY�7Î�y Ú ÕÚ � Ö y?ßàß ÕA3Û Ü /Ç14@B72��@QDF7�Y�JLA:@KJ4e�Y�DF7?SU¨:JU@`eUa25XeHeUa:@Q��Y�M"�?¨:eU5XeUDdY�7¼DFSÇ��Y�JUJL@B��eK9­eUa2@�EÝeUDFM(@Qe�Y�DF7?DdeUDF5XeUDdY�7Y�hNA25XeU5-��Y�JLJL¨:�2eUDdY�7dGR�°M¤¨2S�eЫ]@�TF5XJU8�@KJ�eUa25�7"eUa:@�áhâ3ã3Ê¥ä�â�á4eUDFM(@�e�Y=3�a2DF�Ía"5=S�Y�TV¨:eUDdY�7"DFSjJU@BÒ�¨?DdJU@BAN/���7�Y�eUa:@KJ36Y�JLA2SK9meUa:@=��Y�M(�<¨:eU5XeUDdY�7)M¤¨2S�ek«]@`��Y�M"�?Td@Ke�@ h�Y�JpeUa:@`�?¨:JU�]Y�S�@HY�hoeUa:@=SUeU¨2A:f�¼"â9åæ¶)äàâpeUa:@=SUa:Ym�UC�DFSk5|Ñ­@B��e�@BA«Ef�eUa:@"Ì<JLS�eQ��Y�JLJL¨:�2e�@BA � vÃÆ�365Ëc�@�Y�«2eU5�DF7:@BA�h�JUY�M A?5XeU5��]Y�DF7�eUS-@BTVDFM"DF725Xe�@BA�hlJUY�M eUa:@���Y�M(�?¨:eU5XeUDFY�725�TA:Y�M"5�DV7N/°O�a�¨2S�Ddh`5�S�Y�TF¨2eUDdY�7 h�Y�J�eUa:@\YËc�@KJLA:JÍDdc�@B7 vKP A:@Ke�Y�725XeUDdY�7°DFS"S�Y�¨28�a�e�3�a2DF�Ía DFS(cX5�TFDFA ¨:� ¨27�eUDFT7:Y�72A?DFM(@B72SUDFY�725�T]eUDFM(@z�-9?eUa:@���Y�M(�?¨2eU5XeUDdY�725�T0A:Y�M"5�DF7\SUDdZK@£� SUa2Y�¨2TFA)«]@QSU�­@B�KDdÌ?@BA)h�Y�J4eUa:@¤�2JU@BSU@B7�eH�K5�S�@SU¨2�Ía)eUa25Xe

�èç �Ò � - v �- y<éê�1ëÃìR� �����

3�a:@KJL@QeUa:@(��Y�72SUeU5�7�e£ì±= Ö¢í Ú � ÖDîÚ /Q;ÇY�¨:8�a5X�2�2JLYBÎ:DFM"5XeUDdY�72SHh�Y�J`eUa:@��?5XJL5�M(@Ke�@KJLSÔÒQ9<-\9]5�7?A(ìÁhlY�J(vKPA:@Ke�Y�725XeUDFY�72Sp3�DdeUa�Y#c�@KJLA:JLDFc�@BSÇY�hk7,yrv)�òt"5�72A�vX/ò�E92hlY�J�@�Îm5�M(�<Td@�9?5XJU@ 8�Ddc�@B7\DF7)O05X«?Td@"v «]@BTdY#3=/

_Hc�@KJÍA:JLDdc�@z7 - Ò ìvX/ò�  E/ò� v�v vX/ò � vX/òt  E/ò�|� vB¡ ¡E/òt|�ïuðºñ�òôó,õö<÷køpøhù�ú�ûºü¾ý�þ ÿ ��� þ���� �� ú�8ü��pü ÿ�ü�þ��� � ÿ�ú��hþæÿ ü ú��

� ø �� ����pü��pü ÿ�ü�þ����������uþ ����� ø �� �����þ��� � �ú�� � ÿ þ��5ÿ"! ú®ù_ÿ$# � ÿ%�uúRú ��� ù& ºù ü ���� Mú�� � ü' � ù � £ü(��ÿ$# � øpù ��)� �5ÿ � ÿ$�� +*®öRHS 5�7¼@�Îm5�M(�<Td@�9ÈDdhÐY�7:@(DFS`DF7�e�@KJU@BS�e�@BADF7¼eUa:@�S�Y�TF¨:eUDFY�7\h�Y�J`eUa:@�YËc�@KJLA2JLDdc�@B7A:@Ke�Y�725XeUDdY�734DdeUa 76y v)�ò�

¨:��¨27�eUDFT0eUa:@�72Y�72A2DFM(@B7?SUDdY�725�ToeUDFM(@P�±y���sm9oeUa:@B7�h�JUY�M @BÒE¨25XeUDdY�7%�����Í9_��ë�wXtE9�D�/ª@�/d905)��Y�M(�?¨:eU5XeUDFY�725�TA:Y�M"5�DV7 Y�h¤5Xe)Td@B5�S�e,�Wy wXt JU@B5���eUDFY�7 a25�Tdhlu¦Td@B7:8�eUa2S�SUa:Y�¨?TFA%«]@JU@KeU5�DF7:@BA°«]@Ba2DF7?A%eUa:@�SUa:Ym�UC hlJUY�7�e)DF7Y�JLA:@KJHe�Y)DF72SU¨2JU@=eUa:@�5��K�K¨:JL5���f\Y�hÐeUa:@¤��Y�M"�?¨:eU5XeUDdY�7N/`Rke`eUa:@QÌ<725�ToSUY�TF¨:eUDdY�7\eUDFM(@z� y ��sm9È5Xe43�a?DF�La\eUa:@E���Y�JUJL¨2�2e�@BA�G � vÃÆ"�Ía25XJL5���e�@KJLDFSUeUDF��a?5�SQ�K5�¨:8�a�e(¨:��34DdeUa�eUa:@��2JUY��?5X8�5XeUDV7:8¼A2@Ke�Y�725XeUDdY�7 hlJUY�7�eK9!eUa:@�hlJUY�7�ea25�S�e�JL5Bc�@BTd@BA¼5(e�Y�eU5�T0A2DFS�eU5�7?��@ Y�hj5X�2�2JUYËÎmDFM�5Xe�@BTdfCÎ.y v�væ��,X¡�ª�Ùy �|����JL@B5���eUDdY�7�a25�TFhVu¦Td@B728�eUa2SÇA2¨:JÍDF7:8�eUa:@@B7�eUDdJU@-��Y�M(�<¨:eU5XeUDdY�7N/�Rke4eUa2DFSkeUDFM"@�9?a:YË36@Kc�@KJB9<eUa:@-5���eU¨25�T�A:Y�M"5�DF7�JU@KeU5�DV7:@BA�DF7)eUa2@-��Y�M(�?¨:eU5XeUDFY�7�DFSpY�72TFf�+y¸wXt-DF7�Td@B7:8�eUaN9EDF72A2DF�K5XeUDV7:8`eUa25Xe672@B5XJLTdf( Xs�- Y�h]eUa:@4e�Y�eU5�T­�­Y�SLSUDd«?Td@pA:Y�M�5�DF7"a25�S�«]@K@B7"@BTFDFM�DF725Xe�@BA�h�JUY�M

v�v

Page 12: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

eUa:@"�µS�eUDFTVT­5��K�K¨2JL5Xe�@#�k��Y�M(�?¨2eU5XeUDdY�7N/jOÇa2DVS���Y�72SUeUDdeU¨:e�@BSÇ5�SU¨:«<S�eU5�7�eUDV5�T­SL5BcmDF7:8�SpDF7���Y�M(�?¨2eU5XeUDdY�725�T]��Y�S�eÇY#c�@KJeUa:@�SUDFM(�<Td@"�2JUYm��@BA2¨:JL@�DF7 3�a2DF�Ía 5�TVT�7:YmA:@BSQ«]@Ba2DF72A�eUa2@�SUa2YE�LC �µD�/ª@�/d9jh�Y�J(5\A:Y�M�5�DF7 TF@B7:8�eUa�Y�h4�|�����¤5XJU@JU@KeU5�DF72@BA�DF7�eUa:@=��Y�M(�<¨:eU5XeUDdY�7N/

OÇa2@�5�7?5�TdfESLDFS45�SLS�YE�KDV5Xe�@BA3�DdeUa¼@BÒ�¨?5XeUDdY�7%�����HS�e�JLDF��eUTFf�a:Y�TFA2S4h�Y�J=5�SUe�@B5�A2DFTdf��?JUY��?5X8�5XeUDF7:8)A:@Ke�Y�7?5XeUDdY�73k5Bc�@�90Y�h���Y�¨:JLSU@�9of�@Ke Y�7:@"�K5�7�A2@BM(Y�72S�e�JL5Xe�@(eUa?5Xe eUa:@(JU@B5�T!eUDFM(@�u¦A2@K�­@B7?A:@B7�e S�Y�TV¨:eUDdY�7a25�S cmDdJUeU¨25�TVTdf)eUa:@SU5�M(@��2JUY��]@KJUeUDF@BSK/�;Ç@BSL¨2TdeUSQhlY�J�5\SLDFMQ¨?TF5XeUDdY�7�Y�h�eUa:@47×y v)�ò�\YËc�@KJÍA:JLDdc�@B7�A:@Ke�Y�725XeUDFY�7N9jS�eU5XJUeUDF728�3�DdeUa�5EÝ�2JUY��<5X8�5XeUDF7:8QSLa:YE�LC�hlJUY�7�e�G-5Xe�eUa:@�TdYm�K5XeUDdY�7ÙÎ4y wXtE9m5XJU@�SUa2YË3�7�DF7">!Dd8�¨:JU@H�E/!R t|eUa�Y�JLA:@KJ6��Ï _ M(@KeUa:YmADFS�¨2S�@BA�a2@KJU@�e�Y��K5�TF�K¨2TF5Xe�@HeUa:@HSUa:Ym�UC�.|A:@Ke�Y�725XeUDdY�7�TdYm�K5XeUDdY�7�5�S�5-h�¨27?��eUDdY�7"Y�hNeUDFM"@�¢�eUa:@`M(Y�eUDdY�7�Y�hÈ5-SLDF7:8�Td@� v,Æp�La25XJL5���e�@KJÍDFS�eUDF�X9�@BM"5�725XeUDF7:8 h�JUY�M Î,y s=5XejeUDVM(@0/Dy sm9�DFSÐ5�TFSUY-��Y�M(�?¨:e�@BA�5�72A(DFSjSUa2YË3�7(DF7(>!Dd8�¨2JU@��E/RHTFT]DF7:h�Y�JLM"5XeUDdY�7�«]@Ba2DF72A�eUa:@ SUa:Ym�UC�h�JUY�7�eÇDVS�C�@K�?eÇDF7�eUa:@ ��Y�M(�?¨:eU5XeUDFY�725�TÈA:Y�M"5�DV7N/ÐRkeÇ5(7:Y�72A2DFM"@B72SUDdY�725�TeUDFM(@4Y�hÈ5X«]Y�¨:ej��sm9meUa:@�eg3�Y¤3k5Bc�@`hlJLY�7�eUS65XJU@�Y�«<S�@KJUc�@BA�e�YQDF7�e�@KJLS�@B��eK/�[:DF72��@ÇeUa:@4365Ëc�@`hlJUY�7�eUS�3�@KJU@HDF72DdeUDV5�TFTdfwXt)JL@B5���eUDdY�7�a25�TFhVu¦Td@B728�eUa2S=5X�?5XJUeK90eUa2DFS=eUDFM(@"Y�hpDF7�e�@KJLS�@B��eUDdY�7�Y�hkeUa:@"3k5Bc�@BS�DFS eUa:@�SU5�M(@�5�SQeUa:@(EÝeUDFM"@"e�Y��Y�JUJL¨2�2eUDdY�7Y�hpA25XeU5ºGm9u�-9o�?JU@BA2DF��e�@BA�«EfeUa:@�5X�2�?JUYBÎ:DFM"5Xe�@"eUa2@KY�JUf�9�@BÒE¨25XeUDdY�7 �����Í/�O�a:@"�KTdY�S�@B7:@BSLS=Y�hkeUa:@��Y�M(�?¨2e�@BA¤DV7�e�@KJLSU@B��eUDdY�7�eUDFM(@ �¥�Ãа��s���e�Y`eUa25Xe!�2JU@BA?DF��@BA-«Ef-@BÒE¨25XeUDdY�7)�����0DFS�JU@BM"5XJLC|5X«?TF@�/���eÐDFS�5�TVS�Y 7:Y�e�@BAeUa25Xe4eUa:@QSUa2YE�LC1.|A:@Ke�Y�7?5XeUDdY�7¼hlJUY�7�e4a?5�S45���eU¨25�TVTdf�e�JL5Bc�@BTd@BA5�A2DFS�eU5�72��@QDF7�eUa:@¤��Y�M(�?¨:eU5XeUDFY�7��µ>!Dd8�¨:JL@Q���pY�h5X«]Y�¨:e¤�|��¡�JU@B5���eUDdY�7�a25�Tdhlu¦Td@B7:8�eUa?SK9oc�@KJUf �KTdY�S�@�e�Y\eUa:@��2JU@BA2DF��e�@BA�A2DFS�eU5�72��@�Y�h��|���\JL@B5���eUDdY�7 a?5�TdhVu¦TF@B7:8�eUa2S7:Y�e�@BA��2JU@KcmDdY�¨2SUTdf�hlY�JÇeUa2@=5X�2�2JUYËÎmDFM�5Xe�@-5�725�TdfmSUDFSK/

>!Dd8�¨:JL@BS�wQe�Y�v�v 5�72A�vB¡¤e�Y�v��(@�Î:a2Dd«?Ddek5(S�fmS�e�@BM"5XeUDF� SUeU¨2A:f"Y�h0eUa:@`@�Ñ­@B��eUS�Y�h0��Y�M"�?¨:eU5XeUDdY�725�TNA2Y�M"5�DF7SUDdZK@�9ph�Y�J�eg3�Y�A2DÉÑ]@KJU@B7�e"YËc�@KJÍA:JLDdc�@BSK9[7 y v)�ò� 5�72A¸vX/òtE9ÇJL@BS��]@B��eUDdc�@BTdf�/ ��7 «]Y�eUa S�@KeUS�Y�h=��Y�M(�?¨:eU5XeUDFY�72SK9� y  �t�DVS=S�@BTd@B��e�@BAN9!5�72A�¡Xs�8�JLDFA@BTd@BM"@B7�eUS-�­@KJ-JU@B5���eUDdY�7�a?5�Tdh6TF@B7:8�eUa0� �  5XJU@�¨2S�@BA�DF7eUa2DFS=SU@B��eUDdY�7�h�Y�JA:@Ke�Y�725XeUDFY�7�JU@BS�Y�TF¨2eUDdY�7N/(OÇa:@BS�@"��Y�M"�?¨:eU5XeUDdY�72S 5�TVTdYË3�5�c�@KJLDÉÌ<�K5XeUDdY�7Y�h6eUa:@"JLY�¨:8�a@BS�eUDFM"5Xe�@�hlY�J-A2Y�M"5�DF7SUDdZK@�h�JUY�M @BÒE¨25XeUDdY�7 �����Qe�Y�«]@)M"5�A:@�/ >2Y�J"@�Îm5�M"�?Td@�9jh�Y�J"5�7�YËc�@KJLA2JLDdc�@)Y�hR7°y v)�ò�E9k5��Y�M(�?¨:eU5XeUDFY�725�TA:Y�M"5�DV7�Y�h � y vB�Xs�JU@B5���eUDFY�7 a25�TFhVu¦Td@B728�eUa2S DFS @BS�eUDVM"5Xe�@BA�h�JUY�M ����� e�Y�8�¨25XJL5�7�e�@K@�eUa?5XeQ7:Y � vÈÆ�3k5Bc�@BS@BM"5�725XeUDV7:8`hlJUY�M�@BTFDVM"DF725Xe�@BAQ�]Y�DF7�eUS03�DVTFT�«]@k5X«?Td@ke�Y �K5XeU�La�¨2�Q3�DFeUaQeUa2@kA2@Ke�Y�725XeUDdY�7N/ÐRH7�EÝ@�Î:5���e�G=S�Y�TV¨:eUDdY�7DFSjÌ?JLS�e�Y�«2eU5�DF7:@BA�3�DdeUa�5Q��Y�M(�?¨:eU5XeUDFY�7�3�a?DF�La�JU@KeU5�DF72S�@Kc�@KJUf�SUDV7:8�Td@Ç7:YmA:@�«]@Ba2DV72A�eUa:@��?JUY��?5X8�5XeUDF7:8�SUa:Ym�UC­/RHTde�@KJL725XeUDdc�@Ç��Y�M"�?¨:eU5XeUDdY�72S�5XJU@ÇeUa:@B7��]@KJUh�Y�JLM(@BA�h�Y�J�SU¨2�K��@BSLSUDdc�@BTdf¤DF72��JU@B5�SUDV7:8 A:Y�M"5�DF7(SUDFZK@BSK/Ð>0DF8�¨:JU@�w�9�h�Y�J@�Î:5�M(�?Td@�9­A2DFS��?TV5BfmSÇJU@BSU¨?TdeUSph�Y�JH5���Y�M(�?¨:eU5XeUDFY�7�3�DFeUa�5�A2Y�M"5�DF7�TF@B7:8�eUa ��«]@Ba2DF7?A)eUa:@QSLa:YE�LC:�pY�h%�1y��)� � 5�S���Y�M"�?5XJU@BA)3�DFeUa)eUa:@BEÝ@�Î:5���e�G�SUY�TF¨:eUDdY�7N/jO�a:@=SUa:Y�JUe�@B72@BA�A:Y�M"5�DF7)�K5�¨?S�@BS�5�7�@KJUJUY�7:@KY�¨2SLTdf�S�eU5X«<Td@-SUa:Ym�UC

vB¡

Page 13: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

�2JU@BSLSU¨:JU@¤�2JUYXÌ<TF@Qe�Y)«]@��2JU@BA2DV��e�@BAN9N5�72AeUa:@�Ì?JLSUeHSUa2YE�LC\�2JL@BSUSU¨:JU@¤�]@B5XC\DFS`7:Y�e @Kc�@B7��K5X�2eU¨:JU@BA���Y�JUJL@B��eUTdf�/>!Dd8�¨:JU@p HSUa:Y#3�S!eUa25XeK9�3�DFeUaQ5`A:Y�M"5�DV7QY�h­t)� �  9�eUa:@6Ì?JLSUe0SUa2YE�LC-�2JU@BSLSU¨:JU@6�]@B5XC-DFS!�K5X�2eU¨:JU@BAÈ9�eUa�¨2S0�2JLYËcmDFA2DF7:85�7 ¨?72S�eU5X«?Td@)SUa2YE�LC��?JU@BSUSU¨:JL@)�2JUYXÌ<Td@�/ ikY�JUJU@B��eUTdf �K5X�2eU¨:JÍDF7:8eUa:@)Ì?JÍS�e"�]@B5XC�DVS"�KTd@B5XJLTdf�7:@B��@BSUSL5XJUf�@Kc�@B7e�Y�«]@K8�DF7�e�Y�h�Y�JLM eUa:@)8�5�TFTdY��<DF7:8¼�?a:@B7:Y�M(@B72Y�7�hlY�J(eUa:@�A2@Ke�Y�725XeUDdY�7N/+Åj@Ke"eUa:@���Y�M"�?¨:eU5XeUDdY�725�TpA2Y�M"5�DF7Td@B7:8�eUa ��«­@Ba?DF72AeUa:@�SLa:YE�LC:� Y�hÇt)� �  S�YEY�7��K5�¨2SU@BS-eUa:@�JU@BSU¨2TdeUS=e�Y�A:@KcmDF5Xe�@�h�JUY�M eUa:@�@�Îm5���e�S�Y�TF¨:eUDFY�7�A2¨:@e�Y���Y�JUJL¨:�2eUDFY�7�«Ef)@KJUJUY�7:@KY�¨2S � vÇÆ-365Ëc�@BSK/ ;Ç@BSU¨2TFeUSÇ3�DdeUa\5���Y�M"�?¨:eU5XeUDdY�725�T0A:Y�M"5�DV7�Y�h�vKsº� �  9­SUa2YË3�7¼DF7>!Dd8�¨:JU@`qE9ESLa:YË3 5X8�JU@K@BM(@B7�ek3�DdeUa(eUa:@H@�Î:5���e6S�Y�TV¨:eUDdY�7�¨2��e�Y�5X«­Y�¨2ejeUa:@HeUa2DdJLA(�]@B5XC­/ÐOÇa:@�Y#c�@KJL5�TFT<�2JUYXÌ<TF@�DFS5 SUDd8�7?DÉÌ<�K5�7�e0DFM"�2JUYËc�@BM"@B7�eÐY#c�@KJ�eUa:@k�2JLDFY�J0eg3�YQ�K5�S�@BSK9�a2YË36@Kc�@KJB/jOÇa:@p5X8�JU@K@BM(@B7�ej3�DFeUaQeUa2@6@�Î:5���e�S�Y�TV¨:eUDdY�7DFM(�?JUYËc�@BSQSU¨:«?S�eU5�7�eUDF5�TFTFf\5�S=eUa2@���Y�M(�?¨:eU5XeUDFY�725�T�A:Y�M�5�DF7�SUDdZK@�DFS=DF72��JL@B5�S�@BA�e�Y\tXsº���  5�72A�eUa:@B7�e�Y�wXt)�K� �µ>!Dd8�¨:JU@BS-vKs(5�72A�v�vX92JU@BSU�­@B��eUDFc�@BTdf:�Í925�TFeUa:Y�¨:8�a�eUa:@�2ªâæä"Ê'¶ á-Y�h�eUa2@=�?¨2TFSL5XeUDdY�7�DF7�SUa:Ym�UC��2JU@BSUSU¨2JU@ ��Y�7�c�@KJU8�@BSTd@BSUS4JL5X�?DVA2Tdf�eUa25�7A:Y�@BS4eUa:@¤�]@B5XC��2JU@BSUSL¨:JU@-5�M(�<TFDdeU¨2A:@�/4Rke`��Y�M"�?¨:eU5XeUDdY�725�T!A:Y�M�5�DF7�SUDFZK@BS4Y�h4vBtXsº� �  9N7:YA2DÉÑ]@KJU@B72��@"DVS`Y�«?S�@KJUc�@BA�«]@Keg3�@K@B7�eUa:@"JU@BSU¨?TdeUS`Y�«2eU5�DF7:@BA�5�72AeUa:@"@�Î:5���eQS�Y�TV¨:eUDdY�7N9ÈSUDV72��@�eUa:@�A:Y�M"5�DV7�SUDdZK@a:@KJU@=TVDd@BS43�¨?S�ep«]@BTdYË3 eUa2@=��Y�M(�?Td@Ke�@BTdf�5��K�K¨:JL5Xe�@¤SUDFM¤¨2TF5XeUDdY�7)5��K��Y�JÍA2DF7:8(e�Y"eUa2@=eUa:@KY�JUf�DF7�@BÒE¨25XeUDdY�7 �����Í/

[mDVM"DFTF5XJÐY�«?SU@KJUc|5XeUDFY�72S�5XJL@4M"5�A:@43�a:@B7�eUa:@4Y#c�@KJLA:JLDFc�@4DFS�JU@BA2¨2��@BA�e�YP7,yrv)�òtE9:5�S6SUa:Y#3�7�DV7�>!Dd8�¨:JU@BS4vB¡e�Y\v��:/ÇRHSÇY�«<S�@KJUc�@BA�«Ef)G6Y�¨:JLTFDdY�¨:έ9uâ�5�¸ºµ'6£�Év��)#¥9<3�a?DFTd@ TFDF7:@B5XJ4S�eU5X«?DFTFDFe¦f�5�725�TdfmSUDFSÇSU¨28�8�@BS�eUS�eUa?5Xe�eUa:@KJU@¤5XJU@e¦36Y ¨272S�eU5X«<Td@�M(YmA:@BS�8�@B7:@KJL5Xe�@BA�5Xe�eUa?DFS�TFYË36@KJ�Y#c�@KJLA:JLDdc�@�9�7E¨2M(@KJÍDF�K5�T�SUDVMQ¨2TV5XeUDdY�72SoDV72A2DF�K5Xe�@jeUa2@6A:Y�M�DF725�72��@Y�h�5�SUDV7:8�Td@�M(YEA2@�9]TV5XJU8�@(5�M(�?TFDdeU¨?A:@-�?¨?TFSU5XeUDF7:8�DF72S�eU5X«?DVTFDde¦f�/ RHS`hlY�J`eUa:@�7(y�v)�ò���K5�S�@�9ÈeUa:@(��Y�M(�?¨2eU5XeUDdY�7DFS`�KTdY�S�@KJ`e�Y)eUa:@ EÝ@�Î:5���e�G�S�Y�TF¨2eUDdY�7¼3�a:@B7\eUa:@(A:Y�M"5�DF7SUDdZK@(DFSH�KTdY�S�@KJ e�Y)eUa?5XeH�?JU@BA2DF��e�@BA¼«Ef�@BÒ�¨?5XeUDdY�7%������µA:Y�M"5�DV7�SUDdZK@�� y ¡mvB�(h�Y�J �Ãy  �tE¢<S�@K@-O05X«?Td@"vË�Í/O05X«?Td@`¡=�2JLYËcmDFA:@BS�5¤SU¨2M�M"5XJUf�Y�hÈa:YË3 eUa:@H��Y�M(�?¨:e�@BA�JU@BSU¨?TdeUS4��@�/ª8:/d925�S6SUa:Y#3�7�DV7�>!Dd8�¨:JU@BSpw`e�Y�v�v`5�72A

vB¡�e�Y�v����p��Y�M(�?5XJU@=34DdeUa�eUa:Y�S�@=@BSUeUDFM"5Xe�@BA)h�JUY�M�eUa:@=5X�?�2JUYBÎ:DFM"5XeUDFY�7)DF7�@BÒ�¨?5XeUDdY�7������Í/�>2Y�J�@�Î:5�M(�?Td@�9:h�Y�J7Fy v)�ò�E9o@BÒE¨25XeUDdY�7%�����`�2JU@BA2DF��eUSHeUa25Xe=5)��Y�M"�?¨:eU5XeUDdY�725�TÐA2Y�M"5�DF7Y�hÄ�°yÁ���µDF7¨272DFeUS4Y�hÄ� �  ��3�DVTFT��K5�¨?S�@eUa:@�DV72DdeUDF5XeUDdY�7Y�hp5�A2@KcEDF5XeUDFY�7�hlJLY�M eUa:@(EÝ@�Î:5���e�GS�Y�TF¨:eUDdY�7e�Y\YE�K�K¨2JQ5Xe-5)eUDVM(@K� y �7,Ev)�ò � �y v)�ò�E/�RHS5���Y�M(�?5XJÍDFS�Y�7N9jeUa2@)eUDFM(@)5Xe(3�a2DF�Ía�eUa:@���Y�M(�?¨:e�@BA SUY�TF¨:eUDdY�7�3�DdeUa �Ñy �5���eU¨25�TFTdf�A:@KcmDF5Xe�@BS(h�JUY�M eUa:@EÝ@�Î:5���e�G\S�Y�TV¨:eUDdY�7�DFS�� y ¡�òtE9!M(@B5�72DV7:8)eUa25Xe-eUa2@���Y�M(�?¨:eU5XeUDFY�7�DFS=��Y�JUJͨ:�2e�@BAǵ»¸+5aâ�ä eUa?5�7�@BS�eUDFM"5Xe�@BA�«�f�����Í/�OÇa?DFS�E�A:@KcmDF5XeUDdY�7�G-hlJLY�M eUa:@ÏEÝ@�Îm5���e�G�JU@BSL¨2Tde�DFS�A:@Ke�@KJLM"DV7:@BA(«Ef(@Kc|5�TF¨?5XeUDF7:8-eUa2@47:Y�72A?DFM(@B72SUDFY�725�TEeUDFM(@5XeÇ3�a?DF�La�eUa:@ �]@B5XC��2JU@BSUSU¨2JU@HDV7�eUa:@=��Y�M(�?¨:eU5XeUDFY�7�3�DdeUa�eUa:@=SUa2Y�JUe�@B7:@BA)A:Y�M"5�DV7�«­@K8�DV72S6e�Y"A:@KcEDV5Xe�@���«�f�5�2JU@BSL��JLDd«]@BA��]@KJL��@B7�eU5X8�@#�Hh�JUY�M eUa:@��]@B5XC��2JL@BSUSU¨:JU@(��Y�M(�<¨:e�@BA�¨2SUDF728�eUa:@ EÝ@�Î:5���e�G�S�Y�TV¨:eUDdY�7N9NDF7¼3�a2DV�La5�TFT

vB�

Page 14: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

7:YmA:@BSp«]@Ba2DF7?A�eUa:@QSUa:Ym�UC�5XJU@=JU@KeU5�DF72@BAN/

P4Y�M�5�DF7\[mDdZK@ OÇDVM(@��¸e�Y�PH@KcmDF5XeUDdY�7)h�JUY�M E��jÎm5���e�G)[EY�TF¨:eUDFY�78 � � :9 7.y v)�ò� 7.yrv)�ò� 7.yrv)�òt 7.yrv)�òt��@BS�eK/d9<@BÒ�7È/�������� ��Y�«?S�@KJUc�@BA­� ��@BS�eK/d9?@BÒE7N/�������� ��Y�«<S�@KJUc�@BA<�

� vX/ò� ¡E/òt vX/ò¡ ¡t ¡E/ w   ¡E/©s  vKs tE/ò� vBq �E/òq vB tXs ¡��E/ò� t�t vBqE/ w t|�wXt ��qE/òq wX  ¡�qE/òt wX�ïuðºñ�òôó<;�ö>= � ÿ�ü¾ý�þ ÿ � �þ��� £ú�? �)� ù ��� A@B ù ú®ýC �ú�ýRø��ºÿ þ ÿ�ü¾ú�� �&D ÿ�ü¾ý � ú�E hþæÿ þF Mú®ù ù)�pøpÿ�ü¾ú��

ú�ù_ÿ)# � ÿ%�uú�ú ��� ù& ºù ü ���� �ú�� � ü' � ù � 1�: ú®ù � þ ù ü ú�� � �ú�ý�ø7�ºÿ þ ÿ�ü¾ú��hþ��1 ºú®ýÔþ ü�� � ü�G �H� öO05X«?Td@(¡�SU¨:8�8�@BS�eUS`eUa25Xe`eUa:@¤JUY�¨:8�a¼@BS�eUDVM"5Xe�@(DF7�@BÒE¨25XeUDdY�7%�����4DFSH5���eU¨25�TFTFf�YËc�@KJLTFf\��Y�72S�@KJLc|5XeUDdc�@�9�SUDF72��@

eUa:@`JU@BSU¨?TdeUS�Y�«?eU5�DF7:@BA�¨2SUDF728-5¤8�Ddc�@B7)��Y�M(�?¨:eU5XeUDFY�725�T]A:Y�M"5�DF7�5X�2�]@B5XJke�Y¤«?JU@B5XC�A:Y#3�7�3�@BTFTD¸ åI5aâ�ä�eUa:@HeUDFM(@�2JU@BA?DF��e�@BA�«Ef"eUa:@`@BÒE¨25XeUDdY�7N/ÐOÇa?DFS�DVS�TFDFC�@BTdf"A2¨:@He�Y�eUa:@4hµ5���ekeUa25XekeUa:@`��Y�JUJL¨:�2eUDFY�7�Y�h�eUa:@HSLa:YE�LC�A25XeU5�A:YE@BS7:Y�e¤DF72S�eU5�7�eU5�7:@KY�¨2SUTFfM�5�72Ddh�@BS�e=DdeUS�@BTdhk«?¨2e=JL5XeUa:@KJQeU5XC�@BS¤5\��@KJUeU5�DF7�5�M(Y�¨27�e-Y�hpeUDFM"@"e�Y�«?¨?DFTFA�¨:��«]@Kh�Y�JU@M"5�72DFhl@BS�eU5XeUDFY�7N/���ÒE¨25XeUDdY�7������4M(@KJU@BTdf)@BSUeUDFM"5Xe�@BSHeUa:@-eUDVM(@Q34a:@B7�eUa:@QÌ?JLSUe � vÇÆ=3k5Bc�@"�K5XeU�Ía:@BS ¨:�\3�DdeUaeUa:@-SLa:YE�LC<¢<eUa2DFSp@BSUeUDFM"5Xe�@QDVSÇ5���eU¨25�TFTdf�ÒE¨2Dde�@-5��K�K¨:JÍ5Xe�@�9­5�S4A:@BM(Y�72S�e�JÍ5Xe�@BA�DF7�>!Dd8�¨2JU@Q�E/kG6¨2eÇeUa:@=@BS�eUDVM"5Xe�@A:YE@BS(7:Y�e(eU5XC�@�DF7�e�Y�5��K��Y�¨27�e"eUa:@(âKJ�5aâ�Ë�5kY�h`��Y�JUJL¨2�2eUDdY�7�Y�h4eUa2@�SLa:YE�LC�A?5XeU5%��«�f�MQ¨?TdeUDd�?Td@+EÝ@KJUJUY�7:@KY�¨?S�G� v°Æ�3k5Bc�@BSÍ�(eUa25Xe"DFS�JU@BÒE¨2DdJU@BA�e�Y��K5�¨?S�@�@B7:Y�¨:8�a A?5�M"5X8�@�h�Y�J"eUa:@�SUa:Ym�UC�A25XeU5e�Y�«]@�cmDFSUDd«?TF@�/ 14@B72��@@BÒE¨25XeUDdY�7 �����=�K5�7�«]@"¨2S�@BA�34DdeUa���Y�7mÌ<A:@B7?��@(e�Y�«]@"5X«?Td@(e�YF·"¶)˪ã â�äHL5¸+59ÊML)âæµ ½0â3ãI59Ê¥É�¸+5aâK905)�?JLDdY�JLD�9]eUa:@�SUDdZK@Y�h!eUa:@-��Y�M(�<¨:eU5XeUDdY�725�T�A:Y�M"5�DF7)eUa?5Xe�DFSpJU@BÒE¨2DdJL@BA�e�Y�8�@B7:@KJL5Xe�@¤5�7�5��K�K¨:JÍ5Xe�@��µ5�72A\��Y�M(�?¨:eU5XeUDdY�7?5�TFTdf�MQ¨2�ÍaTd@BSUSÇ@�ÎE�]@B72SUDFc�@#�6S�Y�TF¨:eUDdY�7)5Xe�eUa:@=A:@BSUDdJL@BA�eUDFM(@�/

¿k^¥¤ �6e�n�§opi�b�gON b�gke��6edq5b�©amkopi�b�gOÇa2@KJU@�a25�S-«­@K@B7�S�Y�M(@�A2@K«?5Xe�@�DF7JL@B��@B7�e�7�¨?M(@KJLDF�K5�TÐS�eU¨?A2Dd@BS Y�hÇA:@Ke�Y�7?5XeUDdY�7��?a2@B7:Y�M(@B725�5�S-e�Y\a:Y#3

M"5�7�f-8�JLDVA-�]Y�DF7�eUS0�­@KJ0JU@B5���eUDdY�7(a?5�TdhVu¦TF@B7:8�eUaN9º� �  9�5XJU@kJU@BÒE¨2DdJL@BA-e�Y`hµ¨2TFTdf`JU@BS�Y�TFc�@6eUa2@kA2@Ke�Y�725XeUDdY�7(S�e�JL¨?��eU¨:JU@�/OÇa:@KJL@"a25Bc�@�«­@K@B7�SU¨:8�8�@BS�eUDdY�7?S=eUa25Xe-5�SQM"5�7�f5�S¤¡Xs��]Y�DF7�eUS`�]@KJz� �  5XJU@�JU@BÒ�¨?DdJU@BA1�Év��:9#vËw®#¥903�a2DVTd@�Y�eUa:@KJ

v��

Page 15: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

S�eU¨2A?Dd@BSka25Bc�@=SU¨28�8�@BS�e�@BA�vKsm92Y�Jp@Kc�@B7�t¤�]Y�DF7�eUS6�]@KJÄ� �  5XJU@ SU¨¨¯��KDd@B7�ekhlY�JÇ5��K�K¨2JL5Xe�@=JU@BS�Y�TV¨:eUDdY�76�ª¡�t�#¥/�14@KJU@�95(S�fmS�e�@BM"5XeUDF�-S�eU¨2A:f�¨2SUDF7:8�eUa:@-�|JÍA�Y�JLA:@KJ���Ï`_�M(@KeUa2YEA)34DdeUa)non�> 5�72A�3�DdeUa)A2DÉÑ]@KJU@B7�epS��?5XeUDF5�T]8�JLDVA�JU@BSÝuY�TF¨:eUDFY�7¼�µ7E¨2MQ«­@KJÍS�Y�hÈ8�JÍDFA"�]Y�DF7�eUS��]@KJÄ� �  ��DFS��2JU@BS�@B7�e�@BAN/�i6Y�M(�<¨:eU5XeUDdY�72S65XJU@`A:Y�7:@`a:@KJU@HhlY�Jp5�7�YËc�@KJLA:JÍDdc�@Y�hD74y v)�ò�E9?¨:��e�Y�7:Y�72A?DFM(@B72SUDFY�725�T2eUDFM"@�/ky°��sm92SU¨ª¯��KDd@B7�e6e�Y(Y�«<S�@KJUc�@-a:Y#3 eUa:@=S��?5XeUDV5�T<8�JÍDFA�SUDdZK@ 5|Ñ­@B��eUSeUa:@(SUa:Ym�UC��2JU@BSUSU¨2JU@QJL@BSU¨2TdeUSK/ OÇa2@¤��Y�M(�<¨:eU5XeUDdY�725�T!A:Y�M"5�DV7¼TF@B7:8�eUa¼«­@Ba?DF72A)eUa:@��2JLY��?5X8�5XeUDF7:8)SUa:Ym�UC�eUa25XeDFS¤¨2S�@BA�a:@KJU@�DFS¤�K5�TF�K¨2TF5Xe�@BA�h�JUY�M eUa:@)��Y�72S�@KJUcX5XeUDdc�@�@BS�eUDFM"5Xe�@)DF7 @BÒE¨25XeUDdY�7 �����Í9�a:@B72��@)A25XeU5¼��Y�JUJL¨2�2eUDdY�7A:YE@BS472Y�e4Ym�K�K¨:J A2¨:@Qe�Y�5�SUa:Y�JUe�@B72@BA\��Y�M(�<¨:eU5XeUDdY�725�T!A:Y�M"5�DV7N/�;Ç@BSL¨2TdeUSH5XJU@Q�?JU@BS�@B7�e�@BA¼5�S`>!Dd8�¨:JL@BSQvBt�e�YvB E/=>:Y�J=5�TFT0�K5�S�@BSK9È5�«?5�S�@BTVDF7:@QSU�?5XeUDF5�T�8�JLDFA¼SUDdZK@¤Y�h6 Xs��]Y�DF7�eUS4�]@KJR� �  DFSH¨2S�@BA¼e�Y��2JUY#cEDVA:@Q5�7¼@BSUS�@B7�eUDF5�TFTFfEÝ@�Î:5���e�G�S�Y�TV¨:eUDdY�7�h�Y�J���Y�M(�?5XJLDVS�Y�7N/>!Dd8�¨:JL@¼vBt��2JUY#cEDFA2@BS-eUa:@�JU@BSL¨2TdeUS=Y�h�eUa:@)��Y�M(�?¨:eU5XeUDdY�7 3�DdeUa�t��­Y�DV7�eUSQ�]@KJ�� �  /¼OÇa2@��2JU@BSLSU¨:JU@��­@B5XC

5�M(�?TVDdeU¨2A:@BS�5XJU@8�@B7:@KJL5�TFTdf S�@K@B7°e�Y�«]@M(Y�JU@¼eUa25�7rvKs�- TdYË36@KJ)eUa25�7°eUa:Y�S�@8�Ddc�@B7°«Ef eUa:@ÃEÝ@�Î:5���e�G Y�J«?5�S�@BTVDF7:@�S�Y�TV¨:eUDdY�7N903�DdeUa 5�7�Y#c�@KJU�2JU@BA2DV��eUDdY�7�Y�hÇSLa:YE�LC��2JU@BSLSU¨:JU@�M�DF72DFM¤¨2M 5�S¤3�@BTVT�/�OÇa:@��­@KJÍDdYEA�Y�hÇeUa:@Y�SU�KDFTVTF5XeUDdY�7 DFS(5�TFSUY�S�@K@B7 e�Y�«]@)Ò�¨?Dde�@�A2DÉÑ]@KJU@B7�e(hlJUY�M eUa?5Xe"Y�h4eUa2@�«?5�S�@BTFDV7:@�M"@BSUaN/%OÇa:@)JL@BSU¨2TdeUS¤Y�h`eUa:@��Y�M(�?¨2eU5XeUDdY�7"3�DFeUa)vKs �]Y�DF7�eUSj�­@KJk� �  5XJU@�SUa2YË3�7"DV7(>0DF8:/kvB�E9m5�72A"DFejDFSjS�@K@B7(eUa?5Xe�5=TF5XJL8�@ÇDFM(�2JUY#c�@BM(@B7�e�DF7�2JU@BSLSU¨:JU@=5�M(�<TFDdeU¨2A:@ DFS�Y�«2eU5�DF7:@BA�3�DdeUa)eUa?DFSkÌ<7:@KJHS��?5XeUDF5�TÈ8�JLDFA�SUDFZK@�9<5�TdeUa:Y�¨28�a�eUa:@KJU@QJU@BM"5�DF7�TF5XJU8�@=@KJUJLY�JLSDF7\�2JU@BSUSL¨:JU@¤�­@B5XC\5�M(�?TFDdeU¨?A:@=h�Y�J eUa:@�@B5XJLTFDd@KJH�]@B5XCESK/=O�a:@Q@KJLJUY�7:@KY�¨2SH�]@KJLDdYmA�Y�h�eUa:@�Y�SU�KDFTFTF5XeUDFY�7�JU@BM�5�DF72SeUa:@HY�«�cmDdY�¨2S�SUDd8�7�eUa25Xek��Y�7�c�@KJU8�@B7?��@`a?5�S�7:Y�e6Ym�K�K¨:JUJU@BA�3�DdeUa�eUa2DFS�TF@Kc�@BT?Y�hNJU@B5���eUDFY�7�ZKY�72@4JU@BSUY�TF¨:eUDdY�7�3�a:@B7��Y�M(�?5XJL@BA�e�Y\eUa:@�«?5�SU@BTFDF7:@"M(@BSLaN/)OÇa:@���Y�M(�<¨:eU5XeUDdY�7�A:Y�7:@�34DdeUa�¡Xs��]Y�DF7�eUS=�]@KJ�� �  SUa2YË3�SQSUDd8�72DÉÌ­�K5�7�eDFM(�?JUYËc�@BM(@B7�eUS=Y#c�@KJQeUa2@"�2JU@KcmDdY�¨2S`eg3�Y¼�K5�S�@BSK9Ð5�S @KcmDFA:@B7�e-DF7�>!Dd8:/\vËw�/�OÇa:@(�?JU@BSUSU¨:JL@(�­@B5XC5�M(�?TVDdeU¨2A:@BSa25Ëc�@=5�TFM(Y�S�ep��Y�7�c�@KJU8�@BAN925�72A�eUa:@H8�5�TFTdY��<DF7:8¤�­@KJÍDdYEA�A:@KcmDF5Xe�@BSkhlJLY�MÁeUa?5Xe6Y�h�eUa:@`«?5�S�@BTFDV7:@4M(@BSLa�«Ef�Y�7?Tdf�5h�@K3%�]@KJL��@B7�eK/_/ a:@B7(eUa:@pJL@B5���eUDdY�7"ZKY�7:@4DFS!JU@BS�Y�Tdc�@BA"«�f¤��s �]Y�DF7�eUS!�­@KJk���  9�«]Y�eUa��2JU@BSUSL¨:JU@k�]@B5XC¤5�M(�<TFDdeU¨2A:@5�72A)8�5�TVTdY��?DF7:8��]@KJLDdYmA�5XJU@-M¤¨2�La��KTdY�S�@KJÇe�Y"eUa2@=«?5�S�@BTFDV7:@`JU@BSU¨2TdeK/

RHTdeUa:Y�¨:8�a Y�«EcmDdY�¨2S)DFM(�?JUYËc�@BM(@B7�eUS�36@KJU@�S�@K@B7 3�a2@B7 eUa:@�S��?5XeUDF5�T`8�JLDVA JL@BS�Y�TF¨:eUDdY�7 DF7?��JU@B5�S�@BAN9`Dde)DFSA2D�¯��K¨2Tde!e�Y-A:@Ke�@KJLM�DF7:@z¸P28ä3Ê9¶ºä"Ê25�7(Y��?eUDFM"5�T2S��<5XeUDF5�T:8�JLDFA�JL@BS�Y�TF¨:eUDdY�7È/0>:JLY�M�>!Dd8�¨:JU@BS�vBt=5�72A�vB�E9mDdejDFS��KTd@B5XJeUa25Xe�t`5�72A)vKs=�­Y�DV7�eUS0�]@KJk� �  5XJU@Ç7:Y�ej5�A:@BÒE¨25Xe�@Çe�Y=�K5X�?eU¨:JU@peUa:@ÇA:@Ke�Y�7?5XeUDdY�7(��Y�JUJU@B��eUTdf¤h�Y�JjeUa:@BS�@ÇS�eU5�7?A25XJLAYËc�@KJÍA:JLDdc�@B7�A:@Ke�Y�7?5XeUDdY�7���Y�72A2DdeUDFY�72SK/=�jc�@B734DdeUa�vKs��]Y�DF7�eUSH�]@KJ�� �  9NeUa:@�@KJUJUY�JLS DF7¼SUa:Ym�UC¼�2JU@BSLSU¨:JU@Q�­@B5XC5�M(�?TVDdeU¨2A:@-��h�Y�JkeUa:@�Ì<JLS�ejeg3�Y��]@B5XCESë�j5�72A�8�5�TFTdY��?DV7:8=�]@KJLDdYmA�5XJU@HTF5XJU8�@H@B7:Y�¨:8�a�eUa25XekDde�M"5Ëf"«]@4��Y�72�KTV¨2A:@BA3�DdeUa���Y�7mÌ<A2@B72��@�eUa?5XeQeUa:@)S�Y�TV¨:eUDdY�72SQa25Bc�@)7:Y�e���Y�7�c�@KJL8�@BAN/�OÇa:@��La:Y�DV��@�«]@Keg3�@K@B7 ¨2SLDF7:8\¡Xs¼�]Y�DF7�eUS-�]@KJ

vBt

Page 16: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

� �  5�72A���s\�]Y�DF7�eUS=�]@KJ£� �  DFS-5\M(Y�JU@�A2D�¯��K¨?Tde Y�7:@�e�YM"5XC�@�/�ikTd@B5XJLTdf¼eUa:@�JU@BSU¨2TdeUS-Y�«2eU5�DF7:@BA�¨2SUDV7:8)��s�]Y�DF7�eUS��]@KJ�� �  5XJL@¤SU¨2�­@KJÍDdY�J�e�Y�eUa:Y�S�@�Y�«2eU5�DF72@BA\¨2SLDF7:8�¡Xs��]Y�DF7�eUS��]@KJ�� �  9]f�@KeH34a2DFTd@=eUa2@Q�2JL@BSUSU¨:JU@-�­@B5XC5�M(�?TVDdeU¨2A:@BS=a?5Bc�@�5�TFM(Y�S�e¤��Y�7�c�@KJU8�@BA�3�DFeUa ¡Xs��]Y�DF7�eUS=�]@KJ�� �  9ÐDde-DFS-eUa:@��]@KJLDdYmA�eUa25Xe¤SUa:Y#3�S-eUa2@�M"5�3�Y�J«]@B7:@�Ì?ejY�h�¨2SUDF7:8 ��sQ�]Y�DF7�eUS��]@KJ¢���  /Ð��7�h�5���e6eUa:@KJU@`DFS�SUeUDFTFT25QcEDVSUDd«?Td@k�?a?5�S�@4A2DdÑ­@KJU@B7?��@�«]@Ke¦36@K@B7�eUa:@�JU@BSL¨2TdeUS5Xe-��s\5�72A�5Xe� Xs��]Y�DF7�eUS �]@KJz� �  /�OÇa:@��Ía:Y�DF��@�Y�hk3�a?DF�La�JL@BS�Y�TF¨:eUDdY�7�e�Y\¨2S�@�3�DFTFT!¨2TdeUDVM"5Xe�@BTdfA:@K�]@B72AY�7eUa:@¤Y�«Q3�@B��eUDdc�@�Y�hjeUa:@�S�eU¨2A:f)«]@BDF7:8��K5XJUJLDd@BA\Y�¨:eK9N5�72A¼a:YË3 DFM"�­Y�JLeU5�7�eH��Y�M(�?¨:eU5XeUDdY�7?5�T0��Y�SUe`DVSK/4OÇa2@QY�72TFfJU@B5�T<��Y�72�KTF¨2SUDFY�7(eUa25XekM"5Bf(«]@�A:JÍ5B3�7�a:@KJU@�DFS�eUa25Xe6¡XsQ�]Y�DF7�eUSÐ�]@KJ¢� �  SUa:Y�¨2TFA�«]@ÇeUa2@zÉPÊ¥ËdÊ¥ÉPꬃ JU@BS�Y�TV¨:eUDdY�7¨2S�@BA�e�Y�S�eU¨2A:f�eUa:@=Y#c�@KJLA:JLDdc�@B7�A:@Ke�Y�725XeUDdY�7�3�DdeUa)SUDF728�Td@ S�e�@K��CmDF7:@KeUDF�KSK/

¿k^¥] �SRSed§opq,bUTQ�g%i�opi�n�©`�Cb�g%¬%i�opi�b�g¢qRHS6�2JU@KcmDdY�¨2SUTdf(7:Y�e�@BAÈ9mDV72DdeUDF5�T2��Y�7?A2DdeUDdY�72S�h�Y�J�«]Y�eUa�5-�?JUY��?5X8�5XeUDF7:8�SUa:Ym�UC¼��3�DdeUa�¨:�?S�e�JU@B5�M 5�72A�A:Y#3�7mu

S�e�JU@B5�M ��Y�72A2DdeUDFY�72S`��Y�JUJU@BS��]Y�72A2DV7:8�e�Y�eUa:@"YËc�@KJÍA:JLDdc�@B7�A2@Ke�Y�725XeUDdY�7<�`5�7?A�5�$]ÏHP�A2@Ke�Y�725XeUDdY�7�a25Ëc�@�«]@K@B7@�Îm�?TdY�JU@BA DF7�eUa:@)�?JU@BS�@B7�e"S�eU¨2A:f�/%[m5�M(�?TF@�JL@BSU¨2TdeUS�SUa:Y#3�DF7:8eUa:@)e�@BM"�­Y�JÍ5�Tk@Kc�Y�TF¨:eUDdY�7�Y�hH�]@B5XC��2JU@BSLSU¨:JU@«]@Ba2DF72A�eUa:@Q�2JUY��?5X8�5XeUDV7:8�A:@Ke�Y�725XeUDFY�7�3k5Bc�@¤hlY�J4eUa:@�$]ÏHP A:@Ke�Y�725XeUDdY�7¼5�S�DV72DdeUDF5�T]��Y�72A2DFeUDdY�7�5XJU@¤SUa:YË347�DF7>!Dd8�¨:JU@BS vBq�5�7?A�¡Xsm9?hlY�JpJU@BSUY�TF¨:eUDdY�72S�Y�hkvKs(5�72A���s�8�JLDFA��]Y�DF7�eUS6�]@KJ � �  9mJU@BS��]@B��eUDdc�@BTFf�/jOÇa:@BS�@`JU@BSU¨?TdeUSkM"5Bf«]@p��Y�M(�?5XJU@BA(34DdeUa(>!Dd8�¨:JU@BSpvB� 5�7?A)vB E9�JU@BS��]@B��eUDdc�@BTFf�9�hlY�J�eUa:@ÇSUa:Ym�UC¤eU¨:«]@p5�SjDF72DdeUDV5�TE��Y�7?A2DdeUDdY�7N/�/°a?DFTd@keUa:@DF72DFeUDF5�Tm@Kc�Y�TF¨:eUDdY�7�Y�hN�2JU@BSUSL¨:JU@pY�«EcEDdY�¨?SUTdf�A2DÉÑ]@KJLSЫ]@Ke¦36@K@B7�eUa2@�e¦36Y�S�@KeUS�Y�h]JU@BSL¨2TdeUSK9ESUDF72��@�DV72DdeUDF5�Tm��Y�72A2DFeUDdY�72S5XJU@¤eUa:@�Y�72Tdf)�?5XJÍ5�M(@Ke�@KJLSH3�a2DF�Ía\5XJL@¤A2DdÑ­@KJU@B7�eK9]eUa:@¤�?TdY�eUSH5XJU@�c�@KJUf��KTdY�S�@BTFf�M"5XeU�La2@BA¼DV7�JU@BTV5XeUDdc�@�EÝeUDVM(@ G5Xh�e�@KJ�eUa:@\eUa2DdJLA%�­@B5XC�Y�h eUa:@\Y�SU�KDFTFTV5XeUDdY�7N/°�ge�DFS"S�@K@B7 eUa25XeK9p@Kc�@B7°hlY�J�5�7 ¨?72A:@KJ�u¥JU@BSUY�Tdc�@BA �2JUY��<5X8�5XeUDF7:8A:@Ke�Y�725XeUDFY�7%�ÝvKs�8�JÍDFA��]Y�DF7�eUSH�]@KJR���  9]>!Dd8�¨2JU@BS�vB��5�7?A�vBq��Í9NeUa2@�DV72DdeUDF5�T���Y�72A2DdeUDdY�7?S4a25Ëc�@�JU@BTF5XeUDdc�@BTdf\TFDde�eUTd@@�Ñ]@B��e4Y�7\eUa:@-��Y�M(�<¨:e�@BA��?JU@BSUSU¨:JL@ �­@B5XC)5�72A�eUa:@-�]@KJLDFYEA�Y�hÐY�SU�KDVTFTF5XeUDdY�7)Y�7?��@¤¡#ug��Y�SU�KDFTFTF5XeUDFY�72SÇa25Ëc�@Q«]@K@B78�@B7:@KJL5Xe�@BAÈ/�OÇa:@BSU@ JU@BSU¨2TdeUSp5XJL@=h�¨2JUeUa:@KJÇÒE¨25�7�eUDdÌ?@BA)5�72A���Y�M(�<5XJU@BA�DF7�eUa:@-hlY�TFTFYË3�DF728�SU@B��eUDdY�7N/

¿k^ ¿ �Cb�¦*À¢n´f�iaq5b�gr ¦*b�gkj �Fm¢¦*e�fhia§¨n�© �_§h«%ed¦*edqO�Y�eUa2DFS��­Y�DV7�eK9m5�TFT<JU@BSU¨2TdeUS6SUa:Y#3�7���@�Îm��@K�?eÇDF7�>!Dd8�¨2JU@H����a25Ëc�@ «­@K@B7�Y�«2eU5�DV7:@BA�¨?SUDF7:8QeUa2DdJLA�Y�JLA:@KJp��Ï _

SU�Ía:@BM(@BSK963�a2DF�Ía�5XJU@�S�@K@B7�e�Y�«]@)5X«?Td@�e�Y��K5X�2eU¨:JL@�eUa2@)8�5�TFTdY��?DF728\�?a2@B7:Y�M(@B725¼Y�h�eUa2@)Y�7:@�u¦A2DFM(@B7?SUDdY�725�TA:@Ke�Y�725XeUDFY�72S`��Y�72SUDFA:@KJL@BA\a:@KJL@¤ÒE¨2Dde�@Q3�@BTFT¥/HOÇa2@KJU@¤5XJL@¤M"5�7�f�Y�eUa2@KJ`SL�La:@BM(@BS ¨?S�@BA�«Ef�Y�eUa:@KJ`JU@BSU@B5XJL�La:@KJÍSK9a:Y#3�@Kc�@KJB9NeUa?5Xe`a?5Bc�@�«]@K@B7\A:Ym�K¨2M(@B7�e�@BA¼DF7�eUa2@¤TFDFe�@KJL5XeU¨:JU@QhlY�J`eUa:@¤YËc�@KJLA2JLDdc�@B7¼A:@Ke�Y�725XeUDdY�73�DFeUa�7 y�v)�ò�

vB�

Page 17: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

5�72A 34DdeUa°Y�eUa:@KJ��?5XJÍ5�M(@Ke�@KJLS��Ía:Y�S�@B7¸5�S\DF7°eUa:@��2JL@BS�@B7�e�SU@Ke�Y�h¤��Y�M"�?¨:eU5XeUDdY�72SB9H@�/ª8:/d9Ï�Év��:9ËvËw�9ËvB �#¥/ �Ý75�A2A2DFeUDdY�7N9o5�SQM(@B7�eUDFY�7:@BA�DF7�[E@B��eUDdY�7��E/ò¡E9Ð��Ï _��K5�7�«]@���Y�7�c�@B7?Dd@B7�eUTFf¼�?JUY�8�JL5�M"M(@BA�e�Y�«]@WV tYX Y�JLA2@KJ-DF75��K�K¨:JL5���f�/j>!Dd8�¨2JU@6¡mvkSUa:Y#3�S0a:YË3 S�@Kc�@KJL5�TmSU�Ía:@BM(@BSШ2SU@BAQDF7-Y�eUa:@KJÐS�eU¨2A2DF@BS���Y�M(�<5XJU@�34DdeUa=eUa:@6�2JU@BSU@B7�e!��Ï _SU�Ía:@BM(@BSK/�.�TdY�e�e�@BA�5XJU@��]@B5XC��2JU@BSLSU¨:JU@"M"5X8�7?DdeU¨2A:@"«]@Ba2DV72AeUa:@�Y#c�@KJLA:JLDFc�@B7 A:@Ke�Y�7?5XeUDdY�7°�µ5Xh�e�@KJ�JU@B5��La?DF7:8TFDFM�Dde���fm�KTd@�u¦TFDdC�@`�?¨?TFSU5XeUDdY�72Së�j5�Sp5¤hµ¨272��eUDdY�7�Y�hoJL@BTF5XeUDdc�@=M(@BSUa�S��<5��KDF7:8:9m3�a:@KJU@ 5¤JU@BTF5XeUDFc�@=M(@BSUa�S��?5��KDF728¤Y�hvX/©s)��Y�JUJU@BSU�­Y�7?A2S�e�Y�vKs��]Y�DF7�eUS4�]@KJ�� �  9N5�M(@BSUaS��?5��KDV7:8�Y�h6sm/òt���Y�JUJU@BS��]Y�72A2S4e�Y�¡Xs��]Y�DF7�eUS4�]@KJÔ� �  9N@KeU�X/OÇa:@�5�Tde�@KJL7?5XeUDdc�@(SU�La:@BM"@BS SUa:YË347¼5XJL@¤eUa2@¤�<Dd@B��@K3�DFS�@Q�?5XJL5X«]Y�TFDF�QM(@KeUa:YmA �µ.�.�I��4¨2S�@BA¼«Ef�G6Y�¨:JLTFDdY�¨:έ9­@Ke5�TS�Év��)#¥9ÈeUa:@�[:¨:�]@KJU«]@K@-TFDFM"DFe�@KJH5�72A�I¼DF72M"YEA¼TFDFM"DFe�@KJ4@�Î:5�M"DF7:@BA¼«Ef[Z`¨?DdJUC(�ÉvB �#¥9�5�7?A\eUa2@(JU@B��@B7�e=¨?72S��?TFDFeSU�Ía:@BM(@ÇY�hN.!5X�?5�Td@�Î:5�72A:JLDVSK9�@Ke�5�T�/S�ÉvËw®#¥/j;�@BSU¨2TdeUSÐh�Y�Jj«]Y�eUa"S�@B��Y�7?A"Y�JLA:@KJ���Ï _ ��E���Ï _ ¡)G���5�72A(eUa2DdJÍAQY�JÍA:@KJ��Ï _ ��E���Ï`_ �)G���M(@KeUa:YmA2S"5XJL@�SUa:Y#3�7N963�DdeUa�«]Y�eUa noYE�K5�TÇn�5|Î%>:JLDd@BA:JÍDF�La2S��µn�no>j�(5�7?A%;ÇYE@�>!DÉÎ �µ;�>j�SU�Ía:@BM(@BSK/ ;Ç@BSL¨2TdeUS4hlY�JHeUa:@�DF72DdeUDF5�To��Y�72A2DdeUDdY�7?S�Y�hj«]Y�eUa\eUa:@�$]Ï4PÁA:@Ke�Y�725XeUDdY�7 �µM"5XJLC�@BA*EM$NÏ4P�G��45�72A¼eUa:@�2JUY��<5X8�5XeUDF7:8"SUa:Ym�UC��µ5�TFT]Y�eUa2@KJ4��Ï _�JU@BSL¨2TdeUSÍ�65XJU@=5�TVS�Y"8�Ddc�@B7N/

Ï4@B5XJLTdf�5�TVToSU�Ía:@BM(@BS`5X�2�2JUY�5��Ía¼eUa:@¤��Y�JLJU@B��e`�­@B5XC)�?JU@BSUSU¨:JL@��µ5Xe 5X�2�2JUYËÎmDFM�5Xe�@BTdfP��Ðrq�qE9]�2JU@BA2DF��e�@BA\DF7�ÉvB��#��6h�Y�Jkc�@KJUf�Ì­7:@4JL@BS�Y�TF¨:eUDdY�7�Y�hoeUa2@ JU@B5���eUDdY�7�ZKY�7:@`Y�JÇ5(SUM"5�TVT?cX5�TF¨:@HY�h�eUa2@HJL@BTF5XeUDdc�@ M(@BSUa�S��?5��KDV7:8:/_Åj@KeeUa:@�eUa2DdJÍA\Y�JÍA:@KJ=��Ï _ÁSU�La:@BM"@BSK9o«]Y�eUa¼3�DdeUanon�> 5�7?A3�DdeUa;�>69N5XJU@"5X«?Td@�e�Y�5��Ía2Dd@Kc�@(eUa:@"��Y�JUJL@B��e �­@B5XC�2JU@BSLSU¨:JU@�3�DdeUa 5JL@BTF5XeUDdc�@BTdf���Y�5XJLS�@�JL@BS�Y�TF¨:eUDdY�7 ��JU@BTV5XeUDdc�@�M(@BSUa SU�?5��KDF7:8�Y�h�vX/©s��Í/ RHS"7:Y�e�@BA%DF7 [m@B��eUDdY�7�:/ò�E9ÈeUa:@�DF72DFeUDF5�To��Y�72A?DdeUDdY�7\Y�h�eUa:@Ù$]ÏHPÁA2@Ke�Y�725XeUDdY�7¼fEDF@BTFA2SH5�SUY�TF¨:eUDdY�7\hlY�J`�]@B5XC��?JU@BSUSU¨:JL@-eUa25Xe DFS`7:@B5XJLTFfDFA:@B7�eUDF�K5�T�e�Y4eUa25Xe0¨2SUDF728ÇeUa:@��?JUY��?5X8�5XeUDF7:8HSUa:Ym�UC���34DdeUa-54sm/òt7-¸A?DÉÑ­@KJL@B72��@�DF7-�]@B5XC �2JU@BSUSU¨2JU@j5Xe�eUa2@6��Y�5XJLSU@BS�e8�JLDFA�JU@BS�Y�TF¨2eUDdY�7<�Í/p�Ý7�hµ5���eK9]3�DdeUa�5�JU@BTF5XeUDFc�@QM(@BSUa¼S��?5��KDV7:8"Y�h�sm/òtE9]Y�J ¡Xs��]Y�DF7�eUS��]@KJR� �  9­5�TVTÈY�hjeUa:@¤��Ï _SU�Ía:@BM(@BS��µS�@B��Y�72A5�72A�eUa?DdJLA)Y�JLA2@KJë�ka25Ëc�@Q@BSUSU@B7�eUDF5�TVTdf)��Y�7�c�@KJU8�@B7?��@�DV7��]@B5XC)�2JU@BSUSL¨:JU@�923�a?DF�La�DVS�7:Y�e4e�JL¨:@h�Y�J�M(Y�S�eÇY�h0eUa:@=Y�eUa2@KJ4SU�Ía:@BM(@BSK/Åj@Ke-5�SQ7:Y�e�@BA�DF7�[E@B��eUDFY�7��:/ò¡E9�eUa2@"��Y�7�c�@KJU8�@BA�c|5�TV¨:@(Y�h�eUa2@(�­@B5XC¼�2JU@BSLSU¨:JU@(A:YE@BS 7:Y�e e�@BTFTÐeUa2@(3�a:Y�Td@S�e�Y�JUf3�DFeUa�JU@BS��]@B��e=e�Y�5�7 5��K�K¨:JL5Xe�@�JU@BS�Y�TF¨:eUDFY�7�Y�hkeUa2DFS=�K5�7:Y�7?DF�K5�TÐ�2JUY�«<Td@BM)/"�Ý7�>!Dd8�¨:JU@�¡�¡�eUa:@"�]@KJLDdYmA2SY�h!�2JU@BSUSL¨:JU@`Y�SU�KDFTFTV5XeUDdY�7�Y�«2eU5�DF7:@BA�«�f�eUa:@=A2DdÑ­@KJU@B7�eÇ��Ï _ SL�La:@BM(@BS45XJU@-��Y�M(�<5XJU@BAN9?5X8�5�DF7È923�DdeUa)DF7?�KTF¨2SUDdY�7Y�hp�K5�S�@BSQ3�DdeUaeUa:@Ï$NÏ4P�A:@Ke�Y�7?5XeUDdY�7�5�S-eUa:@�DF72DFeUDF5�T���Y�7?A2DdeUDdY�7N/�1�@KJU@�9�EÝ�]@KJLDdYmA�G�DFS=A:@�Ì­7:@BA�5�S=eUa:@�eUDFM(@«]@Ke¦36@K@B7�SU¨2�K��@BSLSUDdc�@ �2JU@BSLSU¨:JU@`�]@B5XCESpA?¨:JLDF7:8QeUa:@=TFDFM�Dde6��fm�KTd@ Y�SU�KDVTFTF5Xe�Y�JUf�«­@Ba?5BcmDdY�JkY�h�eUa:@=A2@Ke�Y�725XeUDdY�7N/j�Ý7eUa:@p�2JL@BS�@B7�eÐ��Y�M(�<¨:eU5XeUDdY�72SK9�eUa:@Ç5Bc�@KJL5X8�@4eUDFM(@k«]@Ke¦36@K@B7(eUa:@��|JLA(5�7?AQ��eUa"�­@B5XC¤5�72A�eUa:@p��eUa"5�7?A�t|eUa"�­@B5XCDFSj¨?S�@BA(e�YQA2@�Ì<7:@�EÝ�]@KJLDdYmA�Gm¢�eUa:@BSU@�e¦36Y-eUDVM(@BS�5XJU@45�Td365ËfES�3�DdeUa2DV7)v�-rY�h]@B5��La�Y�eUa:@KJ�h�Y�J�eUa2@���Y�M(�?¨:eU5XeUDFY�72S

vËw

Page 18: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

�]@KJUh�Y�JLM(@BA)a:@KJU@�/OÇa2@�A2DÉÑ]@KJU@B72��@BS(«]@Keg3�@K@B7 eUa:@�S�@B��Y�7?A%Y�JLA:@KJ�5�72A%eUa?DdJLA�Y�JLA:@KJ���Ï _ SU�Ía:@BM(@BS�5XJU@�M(Y�JU@¼5X�2�?5XJU@B7�e

3�a:@B7Y�72@"��Y�72SUDFA:@KJÍS4eUa2@(�­@KJÍDdYEA¼Y�h6Y�SU�KDFTFTV5XeUDdY�7N/QO�a:@�eUa2DdJLA¼Y�JLA:@KJQSU�La:@BM"@BS=5XJU@"�KTd@B5XJLTFf\5X«?Td@�e�Y��?JU@BA2DF��eeUa:@(�]@KJLDdYmA¼M(Y�JU@"5��K�K¨:JL5Xe�@BTFf\h�Y�J=5�8�Ddc�@B7�M(@BSLa�S��?5��KDF7:8�eUa25�7��K5�7�eUa:@"S�@B��Y�72AY�JLA2@KJ=SU�La:@BM"@BSK/�Åj@Ke-5�TFTSU�Ía:@BM(@BS(��Y�7�c�@KJU8�@)e�Y¼5¼�]@KJLDdYmA�DF7 eUa:@�JL5�7:8�@�w�/ò���¼e�Y�w�/ò��w�h�Y�J(5�JL@BTF5XeUDdc�@�8�JLDFA�S��?5��KDF7:8\«]@BTdYË3�sm/ò¡���Y�JM(Y�JU@\eUa25�7 tXs��]Y�DF7�eUS"�]@KJC� �  �Í/ ��e�SUa:Y�¨?TFA «]@\7:Y�e�@BA eUa25Xe�eUa:@\72Y�72TFDF7:@B5XJ�S�eU5X«?DFTFDFe¦f 5�725�TdfmSUDFS�hlY�J�eUa:@7�y�v)�ò��A:@Ke�Y�725XeUDdY�7\«�f)��JU�]@B7�«]@B�UC0�ÉvB¡�#!�2JU@BA2DV��eUSÇ�]@KJLDdYmA2SkY�hÐY�SU�KDFTVTF5XeUDdY�7)Y�h�w�/ª�2vQY�J w�/ª��qE9NA:@K�]@B72A?DF7:8�Y�7eUa:@=�]@KJUeU¨2JU«?5XeUDdY�7�M(@KeUa:YmA�¨2SU@BAN/

>!Dd8�¨:JL@BS=¡mv"5�72A�>!Dd8�¨:JU@"¡�¡)SL¨:8�8�@BS�e eUa25Xe=Dde=DVSH72Y�e=5�A:@BÒ�¨?5Xe�@�9oh�Y�J-SUDd8�72SHY�hk��Y�7�c�@KJL8�@B72��@�9�e�Y\TdY�Y�C¼5Xe�]@B5XC��2JL@BSUSU¨:JU@�5�M(�?TVDdeU¨2A:@,¸)µ»¶)Ë´â DV7\cX5�TFDFA?5XeUDF7:8�5�7YËc�@KJLA:JÍDdc�@B7�A:@Ke�Y�725XeUDFY�7���Y�M(�?¨:eU5XeUDdY�7È/¤RHS SUa:Y#3�7�DF7eUa:@BS�@�Ì?8�¨2JU@BSK9j5¼M(@BSUa�S��?5��KDF728\3�a?DF�La 8�Ddc�@BS���Y�7�c�@KJL8�@B72��@�DF7 �]@B5XC��2JU@BSUSL¨:JU@�5�M"�?TFDdeU¨2A2@�M"5Bf�7:Y�e¤8�Ddc�@��Y�7�c�@KJU8�@B72��@)DF7�eUa2@��]@KJLDdYmAY�hpY�SU�KDFTFTV5XeUDdY�7N/��ge¤DFS=eUaE¨2SQSU¨:8�8�@BS�e�@BA�eUa25XeQeUa:@�M(Y�JL@�A:@BM"5�7?A2DF7:8���JLDFe�@KJLDdY�7Y�h-��Y�7�c�@KJU8�@B72��@�DV7%Y�SU�KDFTVTF5XeUDdY�7 �­@KJÍDdYEA SUa:Y�¨2TVA%«]@\¨2SU@BAN9�ÊÌËè¸pápá)Ê\59Ê9¶ºË]5�¶^2ªâM¸:_^28äàâ�ãMã3Íä�â�9`DF7 c|5�TVDFA25XeUDF7:87E¨2M(@KJLDF�K5�TNSL�La:@BM(@BS�«]@BDF7:8�e�@BS�e�@BA�¨?SUDF7:8�eUa:@"vKP Y#c�@KJLA:JLDFc�@B7�A:@Ke�Y�725XeUDdY�7��2JUY�«?TF@BM)/

` aÃ����ÆkJ"��´�M����ÂOÇa2@j�K5�7:Y�72DF�K5�T��2JUY�«?Td@BM Y�hmeUa:@�Y�7:@�u¦A2DFM(@B7?SUDdY�725�T�9K�<¨2TFSU5XeUDF728:9BYËc�@KJLA2JLDdc�@B7-A2@Ke�Y�725XeUDdY�7=3k5Bc�@63�DdeUa SLDF7:8�Td@

S�e�@K��JU@B5���eUDdY�7�CmDF7:@KeUDV�KS�a25�Sk«]@K@B7�S�eU¨2A2DF@BA�a:@KJL@H7E¨2M(@KJLDV�K5�TFTdf(¨2SUDF728Qa2Dd8�a�Y�JLA:@KJkJU@BSUY�TF¨:eUDdY�7���Ï _ SU�La:@BM"@BSK/R SUfES�e�@BM�5XeUDF��S�eU¨2A:f�Y�h4eUa:@�@�Ñ]@B��eUS(Y�hH��Y�M(�?¨:eU5XeUDdY�7?5�T6A2Y�M"5�DF7�SUDdZK@�9jJU@B5���eUDFY�7 ZKY�72@�JL@BS�Y�TF¨:eUDdY�7È9jDF72DdeUDF5�T��Y�72A2DFeUDdY�72SK9!5�72A�7�¨2M"@KJLDF�K5�T�M"@KeUa:YEA2Y�TdY�8�f�Y�7�A:@Ke�Y�725XeUDdY�7�3k5Bc�@�«]@Ba25BcmDdY�J�DFS=�]@KJUh�Y�JLM(@BAN/\R4�K�K¨:JÍ5���f�DF7eUa:@`JU@BS�Y�TV¨:eUDdY�7�Y�hoeUa:@`YËc�@KJÍA:JLDdc�@B7)A:@Ke�Y�7?5XeUDdY�7)DFS6hlY�¨?72A�e�Y¤«]@HJU@BÒE¨2DdJU@BA�«]Y�eUa)DF7�e�@KJÍM"SkY�hoeUa:@ M"5X8�7?DdeU¨2A:@Y�hoeUa2@H�]@B5XC"�?JU@BSUSU¨:JL@�«]@Ba2DF72A�eUa:@`365Ëc�@-5�Sk36@BTFT<5�SpDV7�eUa:@`�]@KJLDdYmA�Y�hÈY�SU�KDFTFTV5XeUDdY�7�DF7�eUa2@H3k5Bc�@�/��gepDFS�h�Y�¨272AeUa25XeK9È��Y�7�e�JL5XJUf¼e�Y)S�@Kc�@KJL5�TÐ�?¨2«?TFDFSUa2@BA)S�@KeUS Y�h�JL@BSU¨2TdeUSK9]5�JU@B5���eUDdY�7ZKY�7:@(JL@BS�Y�TF¨:eUDdY�7\Y�h�5Xe Td@B5�SUe ¡Xs��]Y�DF7�eUS�]@KJ�JL@B5���eUDdY�7�ZKY�7:@=a25�TdhÈTF@B7:8�eUa4� �  DFS�JL@BÒ�¨2DFJU@BA�h�Y�Jp5��K�K¨:JL5Xe�@ JU@BSUY�TF¨:eUDdY�7�Y�hoeUa:@ A:@Ke�Y�7?5XeUDdY�7�365Ëc�@=3�DdeUa�5�7YËc�@KJÍA:JLDdc�@`Y�hu7,yrv)�ò�E/6I�Y�JL@KYËc�@KJB9?DFe6DFS6h�Y�¨272A�eUa25XekeUa:@ S�@BTd@B��e�@BA)��Y�M(�<¨:eU5XeUDdY�725�T]A:Y�M"5�DV7�SUDFZK@`�K5�7)a?5Bc�@=5SUDd8�7?DÉÌ<�K5�7�eÇ@�Ñ­@B��e`Y�7\eUa:@Q5��K�K¨2JL5���f�Y�hÐeUa:@¤��Y�M(�?¨:eU5XeUDFY�7N/�RH7\5X�2�?JUYBÎ:DFM"5Xe�@¤M(@KeUa:YmA�h�Y�J4@BSUeUDFM"5XeUDF7:8�eUa:@JU@BÒE¨2DdJU@BA(��Y�M"�?¨:eU5XeUDdY�725�T<A:Y�M"5�DF7�SUDdZK@�9�«<5�S�@BA"Y�7�eUa:@�eUDFM"@Çe�Y-3�a?DF�La"5�7�5��K�K¨:JL5Xe�@HS�Y�TF¨:eUDdY�7�DFSÐJU@BÒE¨2DdJU@BAÈ9�DFS

vB 

Page 19: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

A:@BSU��JÍDd«]@BAQDF7QeUa2DFS!S�eU¨?A:f<¢�eUa?DFS0@BS�eUDFM"5Xe�@ÇM"5Ëf-«]@k¨2S�@BA�DF7¤�2JU@BA2DV��eUDF7:8�JL@BÒ�¨2DFJU@BAQ��Y�M"�?¨:eU5XeUDdY�725�TmA:Y�M�5�DF7�SUDdZK@5Q�2JLDdY�JLD¥9�5�72A��K5�7�JL@BSU¨2Tde6DF7�SU¨2«?S�eU5�7�eUDF5�T?��Y�M(�<¨:eU5XeUDdY�725�T]SU5ËcEDF728�SK/!��72DFeUDF5�T?��Y�72A?DdeUDdY�72S�DF7"eUa:@`��Y�M(�?¨2eU5XeUDdY�7��eUa:@(�2JLY��?5X8�5XeUDF7:8B$]ÏHP A:@Ke�Y�725XeUDdY�7cmSK/¤eUa:@��2JUY��?5X8�5XeUDF728�SLa:YE�LC\3k5Bc�@#�Í903�a:@B7S�@BTF@B��e�@BA�5X�2�2JUY��?JLDF5Xe�@BTdf�95XJU@(S�@K@B7�e�Y�fmDd@BTFA¼@BSUS�@B7�eUDF5�TFTFf�eUa:@(SU5�M(@�JU@BSU¨?TdeUSHhlY�J=TFDVM"Dde4��fm�KTd@�«]@Ba25BcmDdY�J`Y�h�eUa2@¤�<¨2TFSU5XeUDF728�A:@Ke�Y�7?5XeUDdY�7N/>!DF725�TFTFf�9�Dde¤DFS-A:@BM"Y�72S�e�JL5Xe�@BA eUa25Xe-eUa?DdJLA�Y�JÍA:@KJQ��Ï`_ M(@KeUa:YmA2SK90@BDdeUa:@KJQ3�DdeUa�n�no> Y�J�;�>¸SU�La:@BM"@BSK9j5XJU@5X«?Td@He�Y(JU@BS�Y�TFc�@H«]Y�eUa��]@B5XC"�2JU@BSLSU¨:JU@BS65�72A��]@KJLDdYmA2S�Y�h�Y�SU�KDFTFTV5XeUDdY�72S�c�@KJUf�5��K�K¨:JÍ5Xe�@BTdf�9:3�DdeUa���Y�5XJLS�@KJ�SU�?5XeUDF5�TJU@BS�Y�TV¨:eUDdY�7�eUa25�7�DVSkJU@BÒ�¨?DdJU@BA)DF7�Y�eUa:@KJHSU�La2@BM(@BSK/

b ¿�ÆUcz�P��d JMLk�KZ[L%N L%�HÃ]ÂOÇa?DFSj36Y�JUC"a25�S6«]@K@B7�SU¨2�2�]Y�JUe�@BA�5Xekb`ipnoR «Ef"eUa:@`_R¯���@4Y�h�Ï45Ëc|5�T];Ç@BSU@B5XJL�La�¨272A2@KJÄ¡HJL5�7�eUSkÏ4s�s�s:v��Xu

q�wËuLvëu¦s�s�¡�w 5�72A Ï4s�s�s:v��Xugq�wËuLvëu¦s�q��� E9¤34DdeUa PHJB/±/�@B7 I\5�SUe�@KJLS�5�S)e�@B�Ía272DF�K5�T=M"Y�72Dde�Y�JB9H5�72A «�f ÏHR`[mRPHJUfmA:@B7%>!TFDd8�a�e";Ç@BS�@B5XJÍ�La°ik@B7�e�@KJ�¨272A:@KJC¡HJÍ5�7�e�Ï iÇi�ug¡#ug��w#�:9p34DdeUa%PHJB/°[Ee�@K�<a:@B7 i6Y�JLA25�5�S�e�@B�La27?DF�K5�TM(Y�72DFe�Y�JB/"PHJB/�O /ÈP¤/oRHSUTF5�M.&©S 3�Y�JLC5XeQnÈY�S-RHTF5�M(Y�S-Ï45XeUDdY�7?5�Tjno5X«]Y�JL5Xe�Y�JUf3k5�S=�]@KJUh�Y�JLM(@BA�¨27?A:@KJ eUa:@5�¨2S��<DF��@BSpY�h0eUa:@-bH72Dde�@BA�[EeU5Xe�@BS4P4@K�<5XJUeUM(@B7�e�Y�h!��7:@KJU8�f�/

e ³ Lgf LjÄ�L%��ÆDLj³ L"f L�Ä�L%��ÆDLjÂ�Év3#(ipa25X�?M"5�7N9�PQ/©n�/d9uEL_ 7"eUa:@H;�5Xe�@�Y�hÈ�jÎE�<TdY�SUDdY�7(DF7Ï¡`5�S�@BS�Gm9�h�i�Ê¥µ»¶5ãI6kj0¸ ¹l6F9��ÐY�T�/���w�9]vB �q�qE9:�2�È/�qXs|uLvKsX�:/�ª¡�#�^�Y�¨:8�@KeK9m�Ç/d9�EL_ 7"eUa:@�.�JUY��?5X8�5XeUDdY�7�Y�hoika:@BM"DF�K5�T?;Ç@B5���eUDdY�72S�DF7C¡`5�SU@BS�Gm9EmQ6<á�â0j0¸+5Mi¨âæÉ�¸+59Ê\n Ídâ3ã0h ͨäàâ�ãâ�5po�2728µ¾Ê\n ÍdâMâ3ãë92�ÐY�T�/ovX9�vBqXs�tE9<�2�o/:�|��wËu¥��¡�tE9N��Y�7�eUDF7E¨:@BA�DF7��ÐY�T�/­¡E9ovBqXs��E9?�2�o/?t#ug �tE/�ª��#�^�Y�¨:8�@KeK9?��/d9%E�I�@B�K5�7?DFÒ�¨2@-A:@BSp@�Îm�?TdY�SUDFh�S�Gm9�h[¸)ä"Ê¥ãIqWrS·�5�¸sLºâ�t�¶)ÊÌË(âu5wvkÊ̵ ãÍ9ovBqmvËw�/� �)#K$]@BT'&©A:YËcmDF�ÍaN9��Ý5m9�GH/d9uEL_ 7(eUa:@�OÇa2@KY�JUf�Y�h­eUa2@�.jJUY��<5X8�5XeUDdY�7"Y�hNPH@Ke�Y�725XeUDdY�7�DF7Ù¡`5�S�@KY�¨?Sk[EfmS�e�@BM"SMGm9�x>iy6

z�_®ã{2E6�|8âM¶)äu64v%ÊB}�6F9?�ÐY�T�/ovKsm9ovBq|��sm9<�2�È/?t|��¡#ugt��� E/�ªt�#Qc�Y�7�Ï4@B¨2M"5�727È9m^2/d9_E�O�a:@KY�JUf"Y�hoPH@Ke�Y�725XeUDFY�7,/�5Bc�@BS�Gm9~m¨¶:i�Ë���¶ºË��£âæͨÉK¸ºË�Ë1�P�D¶)µÌµ»âM·�5aâ�á��B¶)ä_®ãë9m�ÐY�T�/�E9�vBq|��¡E/

vBq

Page 20: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

�ª��#¤PHYE@KJLDF7:8:9ª/�/d9%EL_`7�P4@Ke�Y�7?5XeUDdY�7\.�JUYm��@BSUS�@BSÇDF7B¡ 5�S�@BS�Gm9Eo�Ë�Ë�6Uh�i�½�ãu6F9?�ÐY�T�/2���E9ovBq|���E9­�2�È/m��¡mvëu¥�����E/�©w®#¤G6Y�¨:JÍTFDdY�¨mÎ]9�R-/d9 I\5�3UA25m9 RQ/ò^:/d9 E�OÇa:@KY�JU@KeUDV�K5�T�5�72A Ï4¨2M"@KJLDF�K5�T�[Ee�JL¨2��eU¨2JU@ h�Y�J bH72S�eU5X«?Td@rOp36YXuP`DFM"@B72SUDdY�725�T]PH@Ke�Y�725XeUDdY�7?S�Gm9��D¶)ÉÙ¼æÍ�ãI59Ê9¶ºË(¸)Ë8áWv%µ�¸ºÉ�âK9?�ÐY�T�/?qXsm90vBq�q�¡E9?�2�o/?¡mv�vëug¡�¡�qE/�ª �#£/ DFTFTVDF5�M"SK9�P¤/mÏ-/d9mGk5�¨�36@B72SK9:n�9�5�72A)_HJL5�7N9m�Ç/:[­/d9_E�P4@KeU5�DVTd@BA�[Ee�JL¨2��eU¨:JL@�5�72A�.jJUY��?5X8�5XeUDFY�7�Y�hÈO�a:JU@K@�uP`DFM"@B72SUDdY�725�T�P4@Ke�Y�7?5XeUDdY�72S�Gm9S|4�¢âæË�59½s�{�8Ê'J�5Mi��d½)É�2¨¶5ã3ʥͨÉ��M�"Ë�5%6���¶ºË]�D¶)ÉÙ¼�ÍãH59Ê'¶)Ë294vBq�q��E9j�2�È/!¡�q�qmvëu¡�q�q� E/�ªq�#(ip5�M(�2«]@BTFT�9�iH/d9º/�YEYEA2a2@B5�AN9�P¤/ / /d9uE�OÇa:@k��8�72DdeUDdY�7¤Y�h<¡`5�S�@BSЫEfQ5�7(�jÎE�?TFY�SUDdY�7£/�5Bc�@�/�.!5XJUeÐ�ë/�ik5XJU«]Y�7I\Y�7:YËÎmDFA2@-5�72A)14fEA:JLY�8�@B7�I¼DÉÎEeU¨2JU@BS�Gm9>m160�4i¨â�ÉW6p�´¶®·�6V9ovBq�¡�w�9<�?�È/NvBt�wX¡#uLvBt�wX E/�ÉvKs5#¤��JU�]@B7�«]@B�LC<9<^2/ò^:/d9%EL[meU5X«?DFTFDdegf�Y�h�[me�@B5�A:f�u�[meU5Xe�@¤��Ò�¨2DVTFDd«2JLDV¨2M PH@Ke�Y�725XeUDdY�72SMGm9Uh�ih½5ã"Ê'·�㣶 å�v%µ ͨÊ'á5ãÍ9<�ÐY�T�/tE9�vBq���¡E9?�2�È/?�XsX�Xug�mv��:/�Év�v3#¤��JU�]@B7�«]@B�LC<92^:/ò^2/d9%EL[EeU5X«?DVTFDde¦f�Y�h��ÝA:@B5�TFDFZK@BA�_`7:@�u¦;Ç@B5���eUDFY�7�PH@Ke�Y�725XeUDdY�72S�Gm9>h�ih½5ã3Ê9·æ㣶 å�v%µ ͨÊ'á5ãÍ9<�ÐY�T�/<w�9vBq��|�:9<�2�È/?�� |�Xug��q��E/�ÉvB¡�#¤��JU�]@B7�«]@B�LC<9�^2/ò^:/d9zE�Ï4Y�72TFDF72@B5XJ�O�a:@KY�JUf�Y�hHb472SUeU5X«?Td@�_`7:@�u¦P`DFM(@B7?SUDdY�725�T�P4@Ke�Y�7?5XeUDdY�72S�Gm9�h�ih½5ã3Ê9·æã,¶ åv%µ¾Í¨Ê9á5ãë92�ÐY�T�/ovKsm90vBq���w�9?�2�o/?¡�w#�Xug¡� � E/�ÉvB��#¤>!DF�LC�@Ke�eK9</�/d9�/�Y�YmAN9�/ / /�/d9SE�>!TdYË3Áip5�TF�K¨2TF5XeUDdY�7?S�h�Y�J .�¨2TFSL5XeUDF7:8�_`72@�u¦PHDVM(@B72SUDdY�7?5�ToPH@Ke�Y�725XeUDdY�72SMGm9h�ih½5ã"Ê'·�㣶 åFvkµ¾Í¨Ê9á)ãÍ92�ÐY�T�/­qE9ovBq����E9?�2�o/?qXs��#ugqmvB�E/�Év��)#¤G6Y�¨:JÍTFDdY�¨mÎ]9�RQ/d9EI¼5�3�A?5m9ERQ/ò^:/d9m;ÇY#f�e�«?¨2JLAN9��¤/d9_E�OÇa:@KY�JU@KeUDF�K5�T­5�72A�Ï4¨2M"@KJLDF�K5�T­[me�JL¨2��eU¨:JU@�hlY�J6b472SUeU5X«?Td@_ 7:@�u¦P`DFM(@B72SUDFY�725�TÇPH@Ke�Y�725XeUDdY�72SMGm9��Q��o�j m¨¶ºÍä3Ë8¸)µÔ¶ å�o�272´µ Ê�â�á�j(¸+5Mi¨â�É�¸+59Ê'·�ãë9��ÐY�T�/ptmvX9-vBq�qmvX9H�2�È/�Xs��#ug�|���E/�ÉvBt�#¤no@K@�921-/ª�ë/d9<[Ee�@K3k5XJUeK92P¤/ [­/d9kELik5�TF�K¨?TF5XeUDdY�7�Y�h�n�DF7:@B5XJpPH@Ke�Y�725XeUDdY�7\[EeU5X«<DFTFDdegf<��_`7:@�u¦P`DFM"@B72SUDdY�725�T<�Ý72S�eU5|u«<DFTFDdegf"Y�hÐ.�TF5�7:@=PH@Ke�Y�725XeUDFY�7�Gm9~mª¶)ͨä"Ë´¸)µ�¶ å�v%µ¾Í¨Ê9áWjFâ�·Ii¨¸)Ë�Ê'·�ãÍ9:�ÐY�T¥/<¡mvB�E9�vBq�qXsm9­�2�È/NvKs��#uLvB��¡E/�ÉvB��#(ipTF5BcmDF7N9­.�/d9N14@�9Nnj/d9 EL[EeU5X«?DFTVDde¦f)5�72A¼Ï�Y�7?TFDF7:@B5XJ`PHfE725�M�DF�KS�Y�hk_`7:@�u¦P`DFM(@B72SLDdY�725�T�_Hc�@KJÍA:JLDdc�@B7¼PH@Ke�YXu7?5XeUDdY�72SÇDF7B¡ 5�S�@BS�Gm9~mª¶)ͨä3Ë8¸)µ�¶ åFvkµ¾Í¨Ê9á�jFâ�·Ii¨¸)Ë�Ê'·�ãÍ9?�ÐY�T�/<�Xs��E9�vBq�q��E9<�2�È/?��t��#ug��wX E/

¡Xs

Page 21: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

�ÉvËw®#¤.!5X�?5�TF@�Îm5�72A2JLDFSK9mI�/ª�¤/d9?no@KY�725XJLAN92RQ/d92P`DFM(Y�eU5XCmDFSK92.0/©�Ç/d9%E�bH72S��<TFDdeÇ[m�La:@BM"@BSphlY�JÇ14fE�­@KJL«­Y�TVDF�Hi6Y�7?S�@KJ�ucX5XeUDdY�7�no5Ë3�Sk3�DdeUa)[EY�¨:JÍ��@HO�@KJLM"SkDF7)_`7:@=[E�?5���@`P`DFM(@B72SUDFY�7�Gm9�mª¶)ͨä3Ë8¸)µ�¶ åW�D¶)É�28Í15�¸+59Ê'¶)Ë8¸)µEh�ih½5ã"Ê'·�ãë9�ÐY�T¥/ovB�|�:9�vBq�q�w�9<�2�È/?�mvëug�mvX/�ÉvB �#�Z ¨2DdJUC­9�^:/ò^2/d9KEM¡HYEA?¨27:YËc�u¦O�f��]@\[m�Ía:@BM(@BS�R4�2�?TVDd@BA�e�Y PH@Ke�Y�725XeUDdY�7°>!TdYË3�SMGm9��D¶)ÉÙ¼æÍ�ãI59Ê9¶ºË°Ê¥Ë��ÔÊ»¹sil��72ªâMâMáWvkµ»¶s�_ãë9�vBq�q|�:9­�2�È/2t�wXt#ugt�q��E/�ÉvBq�#¤1H5XJUe�@B7N9�RQ/d9E_`SLa:@KJÐ[]/�^2/d9���7:8�ÒE¨2DFSUeK9XGH/��Ç/d9�5�7?A(ipa25XC�JÍ5BcX5XJUeUa�f�9m[­/|;-/d9<EL[EY�M(@p;Ç@BSL¨2TdeUS0Y�7�b472DFhlY�JLM�Tdf1HDd8�amu�_`JLA:@KJ�RH�K�K¨:JL5Xe�@Ç��SUS�@B7�eUDF5�TFTdf Ï4Y�7:Y�SU�KDFTVTF5Xe�Y�JUf¤[m�Ía:@BM(@BS�Gm9�mQ6Qo�2�28µ'6���ͨÉÙâ�äu6yj(¸+5Miy6V9��ÐY�T�/�¡E9��|��wËu��w�w�90vBq� ��E/�ª¡Xs5#([:a�¨N9=iH/ /�/�5�72A¸_`SLa:@KJB9-[­/d9,E��D¯��KDF@B7�e)�ÝM(�?Td@BM"@B7�eU5XeUDdY�7 Y�h¤��SUS�@B7�eUDF5�TFTdf°Ï�Y�7mu�_ SU�KDFTFTF5Xe�Y�JLf [ma:Ym�UCip5X�2eU¨:JLDF728([m�Ía:@BM(@BS��U� Gm9>mª¶)ͨä3Ë8¸)µu¶àå<�D¶)É�28Í15�¸+59Ê'¶)Ë8¸)µUh�ih½5ã3Ê9·æãÍ92�ÐY�T�/­ ��E9�vBq� �qE9?�?�È/?��¡#u�wX E/�ª¡mv3#¤>2@BA:CEDF3=9:;=/©.0/d9:I�@KJUJÍDFM"5�7N9mGH/d92P4Y�7?5XeK9?;=/d9:5�72A�_`SUa2@KJB9:[]/d9_E�O�a:@H.0@B7E¨2TdeUDFM�5Xe�@=[:�La:@BM(@`h�Y�J�[EfESUe�@BM"SY�h`i6Y�72S�@KJUcX5XeUDdY�7�no5Ë3�SK��>!DF72DFe�@�P`DÉÑ­@KJL@B72��@)��Ï _�3�DFeUa�I¼5XJLÒ�¨?DF725¨&©S¤>0TV¨mÎ�[E�?TFDFe�eUDF7:8pGm9"hÄäà¶�¹ºä�â3ã"ãÏÊÌË��ͨÉÙâ�ä3Ê9·"¸)µw�´¶)µ¾Í159Ê9¶)Ë�ã�¶àå�hS¸)äI59Ê9¸ºµ4t�Ê �RâæäàâæË�59Ê9¸ºµUzPnæÍ�¸+59Ê'¶)˪ãë9È@BA2Dde�@BA«Ef\I /È145Xh�@KZ�9�R4JL5��Ía:Y�7N9o>:JÍ5�72��@�9^�¨2Tdf�9NvBq�q� �ª¡�¡�#¤>2@BA:CEDF3=92;=/©.0/d9?I\@KJUJLDFM�5�7N92GH/d9­_`SUa:@KJË9<[­/d9kE�14DF8�a�5��K�K¨:JL5���f�7E¨2M(@KJLDV�K5�TNM(@KeUa:YmA2Sph�Y�JÇeUa:@KJLM"5�TVTdf��]@KJ�uh�@B��e�8�5�S�Ê?Y#3�Sj3�DFeUa"�La:@BM�DFS�e�JUf¨Gm9�mª¶)ͨä"Ë´¸)µ�¶àåS�D¶)É�28Í15�¸+59Ê'¶)Ë8¸)µ�h�ih½5ã"Ê'·�ãë9��ÐY�T�/­vB��¡E9mÏ4Y:/E¡E9E�2��vËwXt#uLvBqXsm9vBq�q�w�/�ª¡���#¤G6JUY#3�7N9�.0/|ÏQ/d9�G6f�JÍ7:@�9h¡¤/|P¤/d9�5�72A¤1HDF72A2M"5XJÍSUaN9#RQ/�iH/8EÝ�4_`P`���XR�cX5XJLDF5X«<Td@���YE@�¯��KDd@B7�ej_ PH�S�Y�TFc�@KJMGm9�1��o�j�m164�´·æÊ�â�Ë�59Ê �¢·���5�¸+59Ê¥ãH59Ê'·M¸ºµ��D¶)É�28Í159ÊÌË�¹�vKsm92�2�È/ÈvKs��� #uLvKs�tmvX9ÐvBq� �qE/�ª¡|�)#¤143k5�7:8:9�.0/d9�EL[:DFMQ¨?TF5XeUDdY�72SHY�hÇ_`7:@�u¦P`DFM(@B72SLDdY�725�T!.�¨2TVSU5XeUDF7:8)PH@Ke�Y�725XeUDdY�72S=3�DdeUa�P`DÉÑ]@KJU@B7�eQnÈ@Kc�@BTFS Y�hÏH¨2M(@KJÍDF�K5�TN;Ç@BS�Y�TV¨:eUDdY�7�G��0�U ~o¡zÄ˹ºÊÌË´âMâæä"ÊÌË�¹W¢Sâ$2¨¶)äI5o��ÏÔ¡4u¦s�s|ug¡mvB¡E9NPH@B��@BM-«]@KJB90vBq�q� E/�ª¡�t�#¤��7:8�ÒE¨2DFS�eK9ÇGH/d9=[�3ÝY�8�JL@B7N9�GH/d9CE�;�Y�«?¨2S�e)P`DÉÑ]@KJU@B72��@R��2�?JUYBÎ:DFM"5XeUDdY�7?S�Y�h([EeUDÉѸDF7�cEDVSU�KDFA PH@Ke�Y�725XeUDFY�7/�5Ëc�@BS�Gm9����U 4o£�Uo�j¤¢Sâ$2¨¶)äI5µ9<�ÐY�T�/­qmvëu¦s��E9�vBq�qmvX/

¡mv

Page 22: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0

10

20

30

40

50

60

70

80

71 72 73 74 75 76 77

Pre

ssur

x

>!Dd8�¨:JU@ vX�°[m�?5XeUDF5�TH�2JU@BSUSL¨:JU@�A2DFS�e�JÍDd«?¨:eUDdY�7 5Xe���Y�M(�?¨2eU5XeUDdY�725�T eUDFM"@¦/0y sm9`hlY�J�eUa:@�DF72DdeUDV5�T4��Y�72A?DdeUDdY�7JU@K�2JL@BS�@B7�eUDV7:8(eUa:@ YËc�@KJÍA:JLDdc�@B76$]Ï4PrA:@Ke�Y�7?5XeUDdY�7�3�DFeUa.76y�vX/ò�E/

¡�¡

Page 23: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 10 20 30 40 50 60 70 80Time

50

60

70

80

90

100

110

120

Glo

balM

axim

um

Pre

ssu

re

�FÖ� ÈÔ0è©âëý|ÖÍèEàËÕ¥ÚÝê�ê�Ø#Õ¥Ú0áÇÖ¨§Ëç©áÇÖ

0 10 20 30 40 50 60 70 80Time

50

60

70

80

90

100

110

120

Loca

lMax

imum

Pre

ssur

e

�dý) ���âKå�ÖLèEà#Õ¥Ú�ê�ê�Ø#Õ¥ÚÐáÇÖ¨§Ëç©áÇÖ>!Dd8�¨:JU@Ç¡E�!.�TdY�eUS!Y�h!�µ5���eUa:@p8�TdY�«?5�TE�2JL@BSUSU¨:JU@kM"5|Î:DFM"5`5�72A���«­�oeUa:@ÇTFYE�K5�TE�2JU@BSLSU¨:JU@kM"5|Î:DFM"5(�µDF7¤eUa:@pcmDF�KDF72DdegfY�hÇeUa:@�SUa:Ym�UC�hlJUY�7�eÍ�-5�S¤5\hµ¨272��eUDdY�7 Y�hÇeUDFM(@�/*ELikTFDd�?�?DF7:8pG�Y�hÇeUa2@��2JL@BSUSU¨:JU@��2JUYXÌ<TF@"YE�K�K¨2JLS¤3�a:@B7 8�TdY�«?5�TM"5|Î:DFM"5(5XJU@-�?TdY�e�e�@BAN/ ¡��

Page 24: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 50 100 150 200 250Time

50

60

70

80

90

100

110

120

Sh

ock

Pre

ssur

e

>!Dd8�¨:JU@=�E�j.�JU@BSUSU¨:JL@H«]@Ba2DV72A"eUa:@ SUa2YE�LC�h�JUY�7�ek5�Sp5�hµ¨272��eUDFY�7�Y�h�eUDFM(@`h�Y�JpeUa:@ YËc�@KJLA2JLDdc�@B7)A:@Ke�Y�725XeUDFY�7�3�DdeUa76y�vX/ò�E9?¨2SUDF728�¡Xs¤8�JLDFA��]Y�DF7�eUS6�­@KJ ���  9m5�7?A�3�DdeUa�5���Y�M(�?¨:eU5XeUDdY�7?5�TNA:Y�M"5�DF7�SUDdZK@`Y�h6vKsº�K�  &©SK/jO�a:@ DF72DdeUDF5�T��Y�72A2DFeUDdY�72Sp��Y�JUJU@BSU�­Y�7?A�e�Y"eUa:@=�2JLY��?5X8�5XeUDF7:8"SUa2YE�LC�3k5Bc�@�/

¡|�

Page 25: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 50 100 150 200 250Time

50

60

70

80

90

100

110

120

Sh

ock

Pre

ssur

e

>!Dd8�¨:JU@`�:�j.�JU@BSUSU¨:JL@H«]@Ba2DV72A"eUa:@ SUa2YE�LC�h�JUY�7�ek5�Sp5�hµ¨272��eUDFY�7�Y�h�eUDFM(@`h�Y�JpeUa:@ YËc�@KJLA2JLDdc�@B7)A:@Ke�Y�725XeUDFY�7�3�DdeUa76y�vX/ò�E9?¨2SUDF728�¡Xs¤8�JLDFA��]Y�DF7�eUS6�­@KJ ���  9m5�7?A�3�DdeUa�5���Y�M(�?¨:eU5XeUDdY�7?5�TNA:Y�M"5�DF7�SUDdZK@`Y�h!tXsº�K�  &©SK/jO�a:@ DF72DdeUDF5�T��Y�72A2DFeUDdY�72Sp��Y�JUJU@BSU�­Y�7?A�e�Y"eUa:@=�2JLY��?5X8�5XeUDF7:8"SUa2YE�LC�3k5Bc�@�/

¡�t

Page 26: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

D = 8.6

t

x

L2.4

L8.6

L8.6

+

L

u + c = 11

∆V = 2.4

L2.4

0 11 L2.4

First point thrown out

>!Dd8�¨:JU@¤tE�6Ï4Y�7mu¦A2DFM"@B72SUDdY�725�T�Î � /ÇA2DV5X8�JL5�M�Y�hÐeUa:@Q�2JUY��?5X8�5XeUDF728�SUa:Ym�UC�h�JUY�7�e��µS��]@K@BAB-Vy  �ò���Ç5�72A�eUa:@�2JUY��<5X8�5XeUDF7:8 � vFÆH365Ëc�@��µS��]@K@BA � vFÆSyrv�vË�63�a2DV�La�@BM"5�725Xe�@BS�hlJUY�MÑÎ,y s(5XepeUa:@ eUDFM"@���,X �ò�(5Xep3�a2DV�LaA25XeU5�a25Bc�@¤«]@K8�¨27)e�Y�«]@=@BTVDFM"DF725Xe�@BA�h�JUY�M eUa:@Q��Y�M(�<¨:eU5XeUDdY�725�T�A:Y�M"5�DF7N/6�j5�TF¨:@BS4a:@KJU@-��Y�JLJU@BS��]Y�72A�e�Y�eUa:@YËc�@KJÍA:JLDdc�@£7,yrv)�ò�E/

¡��

Page 27: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300 350 400

x

u+c characteristic locationshock front location

>!Dd8�¨:JU@p�E�!Ï�Y�7mu¦A?DFM(@B72SUDFY�725�TpÎ � /0A2DF5X8�JL5�MrSUa:Y#3�DF7:84eUa:@k�2JUY��?5X8�5XeUDV7:8HSLa:YE�LC1.|A2@Ke�Y�725XeUDdY�7(h�JUY�7�ek�µDF7?DdeUDF5Xe�@BA5XeKÎ*y wXt��¤5�72A�eUa:@�5���eU¨?5�Tk�2JUY��?5X8�5XeUDF728 � v°Æ�365Ëc�@ ��@BM"5�725XeUDV7:8hlJUY�MêÎÃy s��Í9�h�Y�J(eUa:@�YËc�@KJLA:JÍDdc�@B7A:@Ke�Y�725XeUDFY�7)3�DdeUa,7 y�vX/ò�E/�OÇa2@`��Y�M"�?¨:eU5XeUDdY�7�a2@KJU@ ¨2S�@BSp5"t|eUa)Y�JLA2@KJÇ��Ï _rSU�La2@BM(@ 3�DdeUa)¡Xs(8�JLDVA��]Y�DF7�eUS�]@KJS� �  5�72A�3�DdeUa)7:Y(@BTFDVM"DF725XeUDdY�7�Y�h!A25XeU5(h�JUY�M�eUa:@Q��Y�M(�?¨:eU5XeUDdY�7?5�TÈA:Y�M"5�DF7È/

¡�w

Page 28: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85Time

50

60

70

80

90

100

110

120

130

140

Sh

ock

Pre

ssur

e

Note: Solid line is exact solution

>!Dd8�¨:JU@�w��!.jJU@BSLSU¨:JU@6«]@Ba2DF72A-eUa:@ÇSUa:Ym�UCQhlJUY�7�eÐ5�SÐ5`h�¨?72��eUDdY�7¤Y�h?eUDFM"@6h�Y�JÐeUa:@kYËc�@KJÍA:JLDdc�@B7"A2@Ke�Y�725XeUDdY�7�3�DdeUaK7yÁvX/ò�E9?¨2SUDV7:8¤¡Xs�8�JLDVA��]Y�DF7�eUS6�­@KJÄ� �  9:5�72A�3�DFeUa�5(��Y�M(�<¨:eU5XeUDdY�725�T]A:Y�M"5�DV7�SUDFZK@HY�h!�)� �  &©SK/jO�a:@`�|JÍA�Y�JÍA:@KJ��Ï _rM(@KeUa2YEA)DFSp¨?S�@BA�3�DdeUa�eUa:@=n�no>�SU�La2@BM(@�/6i6Y�M(�<5XJLDFS�Y�7)DFSpM�5�A:@ 3�DdeUa�eUa:@.EÝ@�Î:5���e�G�S�Y�TV¨:eUDdY�7N9m3�a2DV�LaJU@KeU5�DF7?S4@Kc�@KJLf¼SUDV7:8�Td@�7:YEA2@Q«]@Ba2DF7?A�eUa:@(SUa2YE�LC</¤OÇa:@�DF72DdeUDF5�T0��Y�72A2DFeUDdY�72SH��Y�JUJU@BS��]Y�72A¼e�Y)eUa:@��2JUY��<5X8�5XeUDF7:8SUa:Ym�UC�3k5Bc�@�/

¡� 

Page 29: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85Time

50

60

70

80

90

100

110

120

Sh

ock

Pre

ssur

e

Note: Solid line is exact solution

>!Dd8�¨:JU@Ç E�!.jJU@BSLSU¨:JU@6«]@Ba2DF72A-eUa:@ÇSUa:Ym�UCQhlJUY�7�eÐ5�SÐ5`h�¨?72��eUDdY�7¤Y�h?eUDFM"@6h�Y�JÐeUa:@kYËc�@KJÍA:JLDdc�@B7"A2@Ke�Y�725XeUDdY�7�3�DdeUaK7yÁvX/ò�E9?¨2SUDV7:8¤¡Xs�8�JLDVA��]Y�DF7�eUS6�­@KJÄ� �  9:5�72A�3�DFeUa�5(��Y�M(�<¨:eU5XeUDdY�725�T]A:Y�M"5�DV7�SUDFZK@HY�h!t)� �  &©SK/jO�a:@`�|JÍA�Y�JÍA:@KJ��Ï _rM(@KeUa2YEA)DFSp¨?S�@BA�3�DdeUa�eUa:@=n�no>�SU�La2@BM(@�/6i6Y�M(�<5XJLDFS�Y�7)DFSpM�5�A:@ 3�DdeUa�eUa:@.EÝ@�Î:5���e�G�S�Y�TV¨:eUDdY�7N9m3�a2DV�LaJU@KeU5�DF7?S4@Kc�@KJLf¼SUDV7:8�Td@�7:YEA2@Q«]@Ba2DF7?A�eUa:@(SUa2YE�LC</¤OÇa:@�DF72DdeUDF5�T0��Y�72A2DFeUDdY�72SH��Y�JUJU@BS��]Y�72A¼e�Y)eUa:@��2JUY��<5X8�5XeUDF7:8SUa:Ym�UC�3k5Bc�@�/

¡�q

Page 30: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85Time

50

60

70

80

90

100

110

120

Sh

ock

Pre

ssur

e

Note: Solid line is exact solution

>!Dd8�¨:JU@ÇqE�!.jJU@BSLSU¨:JU@6«]@Ba2DF72A-eUa:@ÇSUa:Ym�UCQhlJUY�7�eÐ5�SÐ5`h�¨?72��eUDdY�7¤Y�h?eUDFM"@6h�Y�JÐeUa:@kYËc�@KJÍA:JLDdc�@B7"A2@Ke�Y�725XeUDdY�7�3�DdeUaK7y vX/ò�E9m¨2SUDV7:8=¡Xs=8�JLDFA"�­Y�DV7�eUSÐ�]@KJ%� �  9E5�72A"3�DdeUa"5=��Y�M"�?¨:eU5XeUDdY�725�T<A:Y�M"5�DF7�SUDdZK@ÇY�hÐvKsº� �  &©SB/!O�a:@4�|JLA(Y�JÍA:@KJ��Ï _rM(@KeUa2YEA)DFSp¨?S�@BA�3�DdeUa�eUa:@=n�no>�SU�La2@BM(@�/6i6Y�M(�<5XJLDFS�Y�7)DFSpM�5�A:@ 3�DdeUa�eUa:@.EÝ@�Î:5���e�G�S�Y�TV¨:eUDdY�7N9m3�a2DV�LaJU@KeU5�DF7?S4@Kc�@KJLf¼SUDV7:8�Td@�7:YEA2@Q«]@Ba2DF7?A�eUa:@(SUa2YE�LC</¤OÇa:@�DF72DdeUDF5�T0��Y�72A2DFeUDdY�72SH��Y�JUJU@BS��]Y�72A¼e�Y)eUa:@��2JUY��<5X8�5XeUDF7:8SUa:Ym�UC�3k5Bc�@�/

�Xs

Page 31: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85Time

50

60

70

80

90

100

110

120

Sh

ock

Pre

ssur

e

Note: Solid line is exact solution

>!Dd8�¨:JU@QvKsm�!.�JU@BSUSU¨2JU@Ç«]@Ba2DF72A¤eUa:@HSUa:Ym�UC�h�JUY�7�e�5�S�5-h�¨27?��eUDdY�7�Y�hNeUDFM(@Çh�Y�J�eUa2@ÇYËc�@KJLA2JLDdc�@B7�A:@Ke�Y�725XeUDdY�7�3�DdeUa7Ùy vX/ò�E9�¨2SUDF7:8�¡Xs�8�JLDFA �]Y�DF7�eUSÈ�]@KJ�� �  9|5�7?A=3�DdeUa-5���Y�M(�?¨2eU5XeUDdY�725�TEA:Y�M"5�DF7=SLDdZK@jY�h?tXsº� �  &©SB/0OÇa2@��|JLA=Y�JÍA:@KJ��Ï _rM(@KeUa2YEA)DFSp¨?S�@BA�3�DdeUa�eUa:@=n�no>�SU�La2@BM(@�/6i6Y�M(�<5XJLDFS�Y�7)DFSpM�5�A:@ 3�DdeUa�eUa:@.EÝ@�Î:5���e�G�S�Y�TV¨:eUDdY�7N9m3�a2DV�LaJU@KeU5�DF7?S4@Kc�@KJLf¼SUDV7:8�Td@�7:YEA2@Q«]@Ba2DF7?A�eUa:@(SUa2YE�LC</¤OÇa:@�DF72DdeUDF5�T0��Y�72A2DFeUDdY�72SH��Y�JUJU@BS��]Y�72A¼e�Y)eUa:@��2JUY��<5X8�5XeUDF7:8SUa:Ym�UC�3k5Bc�@�/

�mv

Page 32: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85Time

50

60

70

80

90

100

110

120

Sh

ock

Pre

ssur

e

Note: Solid line is exact solution

>!Dd8�¨:JU@Qv�vX�!.�JU@BSUSU¨2JU@Ç«]@Ba2DF72A¤eUa:@HSUa:Ym�UC�h�JUY�7�e�5�S�5-h�¨27?��eUDdY�7�Y�hNeUDFM(@Çh�Y�J�eUa2@ÇYËc�@KJLA2JLDdc�@B7�A:@Ke�Y�725XeUDdY�7�3�DdeUa7Ùy vX/ò�E9�¨2SUDF7:8�¡Xs�8�JLDFA �]Y�DF7�eUSÈ�]@KJ�� �  9|5�7?A=3�DdeUa-5���Y�M(�?¨2eU5XeUDdY�725�TEA:Y�M"5�DF7=SLDdZK@jY�h<wXt)� �  &©SB/0OÇa2@��|JLA=Y�JÍA:@KJ��Ï _rM(@KeUa2YEA)DFSp¨?S�@BA�3�DdeUa�eUa:@=n�no>�SU�La2@BM(@�/6i6Y�M(�<5XJLDFS�Y�7)DFSpM�5�A:@ 3�DdeUa�eUa:@.EÝ@�Î:5���e�G�S�Y�TV¨:eUDdY�7N9m3�a2DV�LaJU@KeU5�DF7?S4@Kc�@KJLf¼SUDV7:8�Td@�7:YEA2@Q«]@Ba2DF7?A�eUa:@(SUa2YE�LC</¤OÇa:@�DF72DdeUDF5�T0��Y�72A2DFeUDdY�72SH��Y�JUJU@BS��]Y�72A¼e�Y)eUa:@��2JUY��<5X8�5XeUDF7:8SUa:Ym�UC�3k5Bc�@�/

��¡

Page 33: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

40

50

60

70

80

90

100

110

120

0 20 40 60 80 100 120

5L1/2Exact

>!Dd8�¨:JU@QvB¡E�!.�JU@BSUSU¨2JU@Ç«]@Ba2DF72A¤eUa:@HSUa:Ym�UC�h�JUY�7�e�5�S�5-h�¨27?��eUDdY�7�Y�hNeUDFM(@Çh�Y�J�eUa2@ÇYËc�@KJLA2JLDdc�@B7�A:@Ke�Y�725XeUDdY�7�3�DdeUa74y�vX/òtE9�¨2SUDV7:8H¡Xs`8�JLDVAQ�]Y�DF7�eUS0�]@KJ_� �  9�5�72A�3�DdeUa¤5 ��Y�M(�?¨2eU5XeUDdY�725�T:A:Y�M"5�DV7¤SLDdZK@�Y�hNt)� �  &©SB/0OÇa2@p�|JÍAQY�JÍA:@KJ��Ï _rM(@KeUa2YEA)DFSp¨?S�@BA�3�DdeUa�eUa:@=n�no>�SU�La2@BM(@�/6i6Y�M(�<5XJLDFS�Y�7)DFSpM�5�A:@ 3�DdeUa�eUa:@.EÝ@�Î:5���e�G�S�Y�TV¨:eUDdY�7N9m3�a2DV�LaJU@KeU5�DF7?S4@Kc�@KJLf¼SUDV7:8�Td@�7:YEA2@Q«]@Ba2DF7?A�eUa:@(SUa2YE�LC</¤OÇa:@�DF72DdeUDF5�T0��Y�72A2DFeUDdY�72SH��Y�JUJU@BS��]Y�72A¼e�Y)eUa:@��2JUY��<5X8�5XeUDF7:8SUa:Ym�UC�3k5Bc�@�/

���

Page 34: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

40

50

60

70

80

90

100

110

120

0 20 40 60 80 100 120

10L1/2Exact

>!Dd8�¨:JU@QvB�E�!.�JU@BSUSU¨2JU@Ç«]@Ba2DF72A¤eUa:@HSUa:Ym�UC�h�JUY�7�e�5�S�5-h�¨27?��eUDdY�7�Y�hNeUDFM(@Çh�Y�J�eUa2@ÇYËc�@KJLA2JLDdc�@B7�A:@Ke�Y�725XeUDdY�7�3�DdeUa7Ùy vX/òtE9�¨2SUDF7:8�¡Xs�8�JLDFA �]Y�DF7�eUSÈ�]@KJ�� �  9|5�7?A=3�DdeUa-5���Y�M(�?¨2eU5XeUDdY�725�TEA:Y�M"5�DF7=SLDdZK@jY�hÈvKsº� �  &©SB/0OÇa2@��|JLA=Y�JÍA:@KJ��Ï _rM(@KeUa2YEA)DFSp¨?S�@BA�3�DdeUa�eUa:@=n�no>�SU�La2@BM(@�/6i6Y�M(�<5XJLDFS�Y�7)DFSpM�5�A:@ 3�DdeUa�eUa:@.EÝ@�Î:5���e�G�S�Y�TV¨:eUDdY�7N9m3�a2DV�LaJU@KeU5�DF7?S4@Kc�@KJLf¼SUDV7:8�Td@�7:YEA2@Q«]@Ba2DF7?A�eUa:@(SUa2YE�LC</¤OÇa:@�DF72DdeUDF5�T0��Y�72A2DFeUDdY�72SH��Y�JUJU@BS��]Y�72A¼e�Y)eUa:@��2JUY��<5X8�5XeUDF7:8SUa:Ym�UC�3k5Bc�@�/

�|�

Page 35: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

40

50

60

70

80

90

100

110

120

0 20 40 60 80 100 120

50L1/2Exact

>!Dd8�¨:JU@Qv��:�!.�JU@BSUSU¨2JU@Ç«]@Ba2DF72A¤eUa:@HSUa:Ym�UC�h�JUY�7�e�5�S�5-h�¨27?��eUDdY�7�Y�hNeUDFM(@Çh�Y�J�eUa2@ÇYËc�@KJLA2JLDdc�@B7�A:@Ke�Y�725XeUDdY�7�3�DdeUa7Ùy vX/òtE9�¨2SUDF7:8�¡Xs�8�JLDFA �]Y�DF7�eUSÈ�]@KJ�� �  9|5�7?A=3�DdeUa-5���Y�M(�?¨2eU5XeUDdY�725�TEA:Y�M"5�DF7=SLDdZK@jY�h?tXsº� �  &©SB/0OÇa2@��|JLA=Y�JÍA:@KJ��Ï _rM(@KeUa2YEA)DFSp¨?S�@BA�3�DdeUa�eUa:@=n�no>�SU�La2@BM(@�/6i6Y�M(�<5XJLDFS�Y�7)DFSpM�5�A:@ 3�DdeUa�eUa:@.EÝ@�Î:5���e�G�S�Y�TV¨:eUDdY�7N9m3�a2DV�LaJU@KeU5�DF7?S4@Kc�@KJLf¼SUDV7:8�Td@�7:YEA2@Q«]@Ba2DF7?A�eUa:@(SUa2YE�LC</¤OÇa:@�DF72DdeUDF5�T0��Y�72A2DFeUDdY�72SH��Y�JUJU@BS��]Y�72A¼e�Y)eUa:@��2JUY��<5X8�5XeUDF7:8SUa:Ym�UC�3k5Bc�@�/

��t

Page 36: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 10 20 30 40Time

50

60

70

80

90

100

110

120

Sh

ock

Pre

ssur

e

Dotted Line: 5 Points per Half-Reaction LengthSolid Line: 80 Points per Half-Reaction Length

>!Dd8�¨:JU@QvBtE�!.�JU@BSUSU¨2JU@Ç«]@Ba2DF72A¤eUa:@HSUa:Ym�UC�h�JUY�7�e�5�S�5-h�¨27?��eUDdY�7�Y�hNeUDFM(@Çh�Y�J�eUa2@ÇYËc�@KJLA2JLDdc�@B7�A:@Ke�Y�725XeUDdY�7�3�DdeUa7Èy vX/ò�E9!¨?SUDF7:8�t�8�JLDFA��]Y�DF7�eUS=�]@KJz� �  9Ð5�72A�3�DdeUa�5\��Y�M(�?¨:eU5XeUDFY�725�T�A:Y�M�5�DF7�SUDdZK@�Y�h4wXt)� �  &©SK/)OÇa:@��|JLAY�JLA:@KJj��Ï`_ M(@KeUa:YmA(DFSШ2S�@BA�3�DFeUa�eUa:@Çnon�>¼SL�La:@BM(@�/�i6Y�M"�?5XJLDFS�Y�7(DVS0M�5�A:@p3�DdeUa�eUa:@p«<5�S�@BTFDF7:@k�K5�S�@Ç34a:@KJU@ Xs(8�JLDVA��­Y�DV7�eUSp�]@KJS� �  DFSp¨2S�@BAN/jO�a:@=DF72DdeUDV5�T<��Y�72A?DdeUDdY�72Sp��Y�JUJL@BS��]Y�72A�e�Y�eUa:@ �?JUY��?5X8�5XeUDF7:8"SLa:YE�LC�365Ëc�@�/

���

Page 37: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 10 20 30 40Time

50

60

70

80

90

100

110

120

Sh

ock

Pre

ssur

e

Dotted Line: 10 Points per Half-Reaction LengthSolid Line: 80 Points per Half-Reaction Length

>!Dd8�¨:JU@QvB�E�!.�JU@BSUSU¨2JU@Ç«]@Ba2DF72A¤eUa:@HSUa:Ym�UC�h�JUY�7�e�5�S�5-h�¨27?��eUDdY�7�Y�hNeUDFM(@Çh�Y�J�eUa2@ÇYËc�@KJLA2JLDdc�@B7�A:@Ke�Y�725XeUDdY�7�3�DdeUa7 y vX/ò�E9�¨2SUDV7:8¼vKs�8�JÍDFA¼�­Y�DV7�eUSH�]@KJÔ� �  9È5�72A3�DFeUa¼5���Y�M(�<¨:eU5XeUDdY�725�TÐA:Y�M�5�DF7SUDdZK@�Y�hpwXt)� �  &©SK/�OÇa:@(�|JLAY�JLA:@KJj��Ï`_ M(@KeUa:YmA(DFSШ2S�@BA�3�DFeUa�eUa:@Çnon�>¼SL�La:@BM(@�/�i6Y�M"�?5XJLDFS�Y�7(DVS0M�5�A:@p3�DdeUa�eUa:@p«<5�S�@BTFDF7:@k�K5�S�@Ç34a:@KJU@ Xs(8�JLDVA��­Y�DV7�eUSp�]@KJS� �  DFSp¨2S�@BAN/jO�a:@=DF72DdeUDV5�T<��Y�72A?DdeUDdY�72Sp��Y�JUJL@BS��]Y�72A�e�Y�eUa:@ �?JUY��?5X8�5XeUDF7:8"SLa:YE�LC�365Ëc�@�/

��w

Page 38: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 10 20 30 40Time

50

60

70

80

90

100

110

120

Sh

ock

Pre

ssur

e

Dotted Line: 20 Points per Half-Reaction LengthSolid Line: 80 Points per Half-Reaction Length

>!Dd8�¨:JU@QvËw��!.�JU@BSUSU¨2JU@Ç«]@Ba2DF72A¤eUa:@HSUa:Ym�UC�h�JUY�7�e�5�S�5-h�¨27?��eUDdY�7�Y�hNeUDFM(@Çh�Y�J�eUa2@ÇYËc�@KJLA2JLDdc�@B7�A:@Ke�Y�725XeUDdY�7�3�DdeUa7 y vX/ò�E9�¨2SUDV7:8�¡Xs�8�JÍDFA¼�­Y�DV7�eUSH�]@KJÔ� �  9È5�72A3�DFeUa¼5���Y�M(�<¨:eU5XeUDdY�725�TÐA:Y�M�5�DF7SUDdZK@�Y�hpwXt)� �  &©SK/�OÇa:@(�|JLAY�JLA:@KJj��Ï`_ M(@KeUa:YmA(DFSШ2S�@BA�3�DFeUa�eUa:@Çnon�>¼SL�La:@BM(@�/�i6Y�M"�?5XJLDFS�Y�7(DVS0M�5�A:@p3�DdeUa�eUa:@p«<5�S�@BTFDF7:@k�K5�S�@Ç34a:@KJU@ Xs(8�JLDVA��­Y�DV7�eUSp�]@KJS� �  DFSp¨2S�@BAN/jO�a:@=DF72DdeUDV5�T<��Y�72A?DdeUDdY�72Sp��Y�JUJL@BS��]Y�72A�e�Y�eUa:@ �?JUY��?5X8�5XeUDF7:8"SLa:YE�LC�365Ëc�@�/

�� 

Page 39: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

0 10 20 30 40Time

50

60

70

80

90

100

110

120

Sh

ock

Pre

ssur

e

Dotted Line: 40 Points per Half-Reaction LengthSolid Line: 80 Points per Half-Reaction Length

>!Dd8�¨:JU@QvB E�!.�JU@BSUSU¨2JU@Ç«]@Ba2DF72A¤eUa:@HSUa:Ym�UC�h�JUY�7�e�5�S�5-h�¨27?��eUDdY�7�Y�hNeUDFM(@Çh�Y�J�eUa2@ÇYËc�@KJLA2JLDdc�@B7�A:@Ke�Y�725XeUDdY�7�3�DdeUa7 y vX/ò�E9�¨2SUDV7:8���s�8�JÍDFA¼�­Y�DV7�eUSH�]@KJÔ� �  9È5�72A3�DFeUa¼5���Y�M(�<¨:eU5XeUDdY�725�TÐA:Y�M�5�DF7SUDdZK@�Y�hpwXt)� �  &©SK/�OÇa:@(�|JLAY�JLA:@KJj��Ï`_ M(@KeUa:YmA(DFSШ2S�@BA�3�DFeUa�eUa:@Çnon�>¼SL�La:@BM(@�/�i6Y�M"�?5XJLDFS�Y�7(DVS0M�5�A:@p3�DdeUa�eUa:@p«<5�S�@BTFDF7:@k�K5�S�@Ç34a:@KJU@ Xs(8�JLDVA��­Y�DV7�eUSp�]@KJS� �  DFSp¨2S�@BAN/jO�a:@=DF72DdeUDV5�T<��Y�72A?DdeUDdY�72Sp��Y�JUJL@BS��]Y�72A�e�Y�eUa:@ �?JUY��?5X8�5XeUDF7:8"SLa:YE�LC�365Ëc�@�/

��q

Page 40: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

50

60

70

80

90

100

110

120

0 10 20 30 40

Sho

ck P

ress

ure

ª

Time

>!Dd8�¨:JU@�vBqE�).jJL@BSUSU¨:JU@�«]@Ba2DF7?A�eUa:@�SUa2YE�LC�h�JUY�7�e"5�S(5hµ¨272��eUDFY�7 Y�hHeUDFM(@�h�Y�J(eUa:@�YËc�@KJLA2JLDdc�@B7%A:@Ke�Y�7?5XeUDdY�73�DdeUa�7(y vX/ò�E9]¨?SUDF7:8�vKs�8�JLDFA��­Y�DV7�eUS��­@KJR� �  9]5�72A�3�DFeUa�5���Y�M(�?¨:eU5XeUDdY�7?5�ToA:Y�M"5�DV7�SUDdZK@QY�h�wXt)� �  &©SB/ÇOÇa:@�|JLA�Y�JLA:@KJ(��Ï`_ M(@KeUa2YEA�DFS�¨2S�@BA 3�DdeUa�eUa:@)n�no>¸SL�La:@BM(@�/�OÇa:@�DF72DdeUDV5�T���Y�72A2DFeUDdY�72S¤��Y�JUJU@BS��]Y�72A e�Y�eUa:@�2JUY��<5X8�5XeUDF7:8C$]ÏHP A:@Ke�Y�725XeUDdY�7 �µ>0DF8�¨:JU@�vË�Í/

��s

Page 41: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

50

60

70

80

90

100

110

120

0 10 20 30 40

Sho

ck P

ress

ure

ª

Time

>!Dd8�¨:JU@�¡Xsm�).jJL@BSUSU¨:JU@�«]@Ba2DF7?A�eUa:@�SUa2YE�LC�h�JUY�7�e"5�S(5hµ¨272��eUDFY�7 Y�hHeUDFM(@�h�Y�J(eUa:@�YËc�@KJLA2JLDdc�@B7%A:@Ke�Y�7?5XeUDdY�73�DdeUa�7(y vX/ò�E9]¨?SUDF7:8(��s�8�JLDFA��­Y�DV7�eUS��­@KJR� �  9]5�72A�3�DFeUa�5���Y�M(�?¨:eU5XeUDdY�7?5�ToA:Y�M"5�DV7�SUDdZK@QY�h�wXt)� �  &©SB/ÇOÇa:@�|JLA�Y�JLA:@KJ(��Ï`_ M(@KeUa2YEA�DFS�¨2S�@BA 3�DdeUa�eUa:@)n�no>¸SL�La:@BM(@�/�OÇa:@�DF72DdeUDV5�T���Y�72A2DFeUDdY�72S¤��Y�JUJU@BS��]Y�72A e�Y�eUa:@�2JUY��<5X8�5XeUDF7:8C$]ÏHP A:@Ke�Y�725XeUDdY�7 �µ>0DF8�¨:JU@�vË�Í/

�2v

Page 42: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

« ¬­ ®¯ °± ²³ ´µ ¶· ¸¹ º» ¼½ ¾¿ ¿À Á Á à ÂÄ Å ÆÇ È ÉÊ Ë Ì

Í Î Ï Ð Ñ Ò Ó Ô Õ Ö × Ø Ù ÚÛ Ü Ý Þ ß à á Ü â Ü ã ä å æ Þ ç à è é

ê ëìíê îëïïðîë ñ ò ó ô õ ö ö ÷ õ ø ò ù

ú û ü ý þ ÿ û ü � � � � þ � � � � � � �

� � � � �� � � � � � �

� � � � � � � � � � ! " � # $ � % $ $ & � ' � ( $ �

) * + , - . /

0 1 2 3 4 5 5 6

7 8 9 : ; < = > > ? @ A B 9 C D E F G 9 D 9 H I :

>!Dd8�¨:JU@k¡mvX�0.0@B5XCQ�2JU@BSUSU¨2JU@j«]@Ba2DF72A=eUa:@6SLa:YE�LC=h�JUY�7�e0h�Y�J0eUa2@6SU¨?S�eU5�DF7:@BA-�?¨2TFSU5XeUDV7:8�A:@Ke�Y�725XeUDFY�7¤5�S!54h�¨?72��eUDdY�7Y�h0JU@BTF5XeUDdc�@ M(@BSUa)SU�?5��KDF7:8���y vKsA.¤7:Y:/�8�JLDFA��]Y�DF7�eUS6�]@KJS� �  �Í9:h�Y�J�76y vX/ò�E/6i6Y�M(�<5XJLDFS�Y�7�DFSpM"5�A2@`5�M"Y�7:87E¨2M(@KJLDF�K5�T?SU�La:@BM"@BS6¨?S�@BA�DF7"�2JLDdY�J�SUeU¨2A2Dd@BS�5�72A"eUa:@4�2JU@BS�@B7�e���Ï`_ SU�La2@BM(@BSK/jOÇa:@H7:Y�eU5XeUDdY�7+EM$]ÏHPRG-JU@Kh�@KJLSe�Y(eUa:@£$]ÏHPrA:@Ke�Y�725XeUDdY�7�5�SkeUa:@=DF72DdeUDV5�T<��Y�72A?DdeUDdY�7N¢m3�DdeUa2Y�¨:e�eUa?DFSp7:Y�eU5XeUDdY�7)h�Y�JÇ��Ï _�SU�Ía:@BM(@BSK92eUa2@=DF72DdeUDF5�T��Y�72A2DFeUDdY�72Sp��Y�JUJU@BSU�­Y�7?A2Ske�Y"eUa:@=�?JUY��?5X8�5XeUDF7:8"SLa:YE�LC</

��¡

Page 43: Stanford Universityphysbam.stanford.edu/~fedkiw/papers/cam1999-12.pdf · 2000-06-16 · Y 7mÌ?8 ¨:JÍ5XeUDdY 72S¤YËc @KJ"eUa2@ f @B5XJÍS. ©w 9Í # ¥/ 0/ a2DFTd@ JU@B @B7 e

J K L M

N O P Q

R S T U

V W X Y

Z [ \ ]

^ _ ` `

a b c d

e f g h

i j i k

l m l n

o p o q r s t u v w x y z { | } ~ � � � �� � � � � � � � � � � � � � � � � � �

� ��� �

� � � � � � �

�   ¡ ¢ £ ¤ ¤ ¥¦ § ¨ © ª « « ¬­ ® ¯ ° ± ² ² ³ ± ´ ® µ¶ · ¸ ¹ º » ¼

>!Dd8�¨:JU@¡�¡E��.�@KJÍDdYEA Y�h=eUDFM(@�«­@Keg3�@K@B7 SU¨?�K��@BSUSUDdc�@\�2JU@BSUSU¨2JU@��]@B5XCES�h�Y�J�eUa:@\�?¨2TFSL5XeUDF7:8�A:@Ke�Y�725XeUDFY�7 5�S�5hµ¨272��eUDdY�7(Y�h]JU@BTV5XeUDdc�@�M(@BSUa�S��?5��KDF7:8���y vKsS.`72Y:/Ð8�JLDFA��]Y�DF7�eUSÐ�]@KJ%� �  �Í9EhlY�J¢7�yrvX/ò�E/6i6Y�M(�<5XJLDFS�Y�7(DFS�M"5�A:@5�M(Y�7:8¤eUa:@H�2JU@BS�@B7�ek��Ï _¸SL�La:@BM(@BSB/jOÇa:@`7:Y�eU5XeUDdY�7 EM$]ÏHPRG¤JU@Kh�@KJLS�e�Y�eUa:@Ô$NÏ4P A:@Ke�Y�725XeUDdY�7�5�S6eUa:@`DF72DdeUDF5�T��Y�72A2DFeUDdY�7N¢m3�DdeUa:Y�¨2epeUa2DFSp7:Y�eU5XeUDdY�7È92eUa:@=DF72DFeUDF5�T]��Y�72A2DdeUDdY�7?Sp��Y�JUJU@BS��]Y�72A2Ske�Y�eUa:@ �2JUY��?5X8�5XeUDV7:8�SUa:Ym�UC­/

���