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N UMERICAL S IMULATIONS Motolani Olarinre Ivana Seric Mandeep Singh

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I NTRODUCTION

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M ETHOD AND BC S

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N UMERICAL R ESULTS Types of wave profiles: -Traveling wave solution -Convective instability -Absolute instability Figure: Flow down the vertical plane (t=10). From top to bottom, N=16, 22, 27.

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S TABLE TRAVELING WAVE SOLUTION

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Flow down the vertical plane (N=16). From top to bottom, t=0, 40, 80, 120.

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C ONVECTIVE INSTABILITY Figure: N=22, flow down the vertical. From top to bottom, t=0, 40, 80, 120.

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C ONVECTIVE INSTABILITY

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A BSOLUTE INSTABILITY Figure: N=27, absolute instability. From top to bottom, t=0, 40, 80, 120.

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A BSOLUTE INSTABILITY

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S PEED OF THE LEFT BOUNDARY NumLSANumLSA 18.617.7925.4325.44 24.424.1330.630.46

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NUMERICS

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F INITE D IFFERENCE D ISCRETIZATION P ROCEDURE

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O UR S IMULATIONS We ran simulations in FORTRAN using the following parameters: C = 1, B = 0, N = 10, U = 1, b = 0.1, beta = 1. These parameters indicate a liquid crystal flowing down a vertical surface (90 degree angle) The output from our simulations were plotted and analyzed using MATLAB

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We ran simulations for two distinct cases: Constant Flux: Uses a semi-infinite hyperbolic tangent profile for its initial condition. Simulates a case where an infinite volume of liquid is flowing. Constant Volume: Uses a square hyperbolic tangent profile for its initial condition. Simulates a case where a drop is flowing. O UR S IMULATIONS

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G ROWTH R ATE A NALYSIS

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80.7854 100.6283 120.5236 140.4488 160.3927 180.3491 200.3142

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G ROWTH R ATE A NALYSIS