maximum power: and atwood’s machine by: g.h. boyle 4 th oct canussee 2015 screen shot from mpplab...

Maximum Power:

And Atwood’s MachineBy: G.H. Boyle

4th OctCANUSSEE 2015

Screen shot from MppLab I

Downloadable at orrery-software.webs.com

Challenging the Veracity of the Maximum Power

Concept

Situate My InterestSustainability of the Co-evolving Global

Ecological and Global Economic SystemsSelf-Organizing (Autocatalytic) Systems

Conditions that Govern/Compel/Constrain self-organizing behaviour

The Maximum Power Principle (MPP)The Maximum Entropy Production Principle (MEPP)

Ecological System Economic System

SAME PLANET – DIFFERENT WORLDS?!?

Agenda

A. A restatement of the MPPB. Insights From Atwood’s MachineC. Agent-Based Computer Model

MppLab I and Evolving Trophic websD. Concluding Thoughts

Agenda



A001

A Restatement of the Lotka/OdumMaximum Power Principle (MPP)

Why a “Restatement”?• In a variety of writings, the

presentation of the MPP is either fragmentary, or qualified.

A002

• I could not find any clear set of hypotheses that were:• Falsifiable• Comprehensive; and• Fully general.

Essential for Model

Building


MPP#1 – ALL PERSISTENT AUTOCATALYTIC SYSTEMS ARE CHARACTERISED BY ENERGY FLUXES THROUGH ENERGY STORES, AND PERSISTENT ENERGY PATHWAYS THROUGH WHICH ENERGY FLOWS FROM STORE TO STORE

MPP#2 – ALL CATEGORIES OF PERSISTENT STORE-TO-STORE ENERGY TRANSFER MECHANISMS WITHIN PERSISTENT ENERGY PATHWAYS ARE CHARACTERIZED BY STRICTLY CONCAVE POWER-EFFICIENCY FUNCTIONS

MPP#3 – ALL PERSISTENT AUTOCATALYTIC SYSTEMS EVOLVE TO CAPTURE AND CONSUME ENERGY AT MAXIMUM POWER AND AT SOME INTERMEDIATE EFFICIENCY

A003


MPP#1 – ALL AUTOCATALYTIC SYSTEMS ARE CHARACTERISED BY ENERGY FLUXES THROUGH ENERGY STORES, AND PERSISTENT ENERGY PATHWAYS THROUGH WHICH ENERGY FLOWS FROM STORE TO STORE

Solar Systems

Metabolic Systems

Ecological Systems

Economic Systems

A004Sources: kidcyber.com.au; manet.illinois.edu; Mark David Thompson, Lawrence Livermore National Lab

AUTOCATALYTIC

SYSTEM


SINKEnergy Store

Type #1Energy Store

Type #2SOURCE

A005

MPP#1 – ALL PERSISTENT AUTOCATALYTIC SYSTEMS ARE CHARACTERISED BY ENERGY FLUXES THROUGH ENERGY STORES, AND PERSISTENT ENERGY PATHWAYS THAT TRANSFER ENERGY FROM STORE TO STORE.


A005A

MPP#1 – ALL PERSISTENT AUTOCATALYTIC SYSTEMS ARE CHARACTERISED BY ENERGY FLUXES THROUGH ENERGY STORES, AND PERSISTENT ENERGY PATHWAYS THAT TRANSFER ENERGY FROM STORE TO STORE.

Energy Store Type #1




A PERSISTENT RENEWABLE PATHWAY OF STORES THROUGH WHICH ENERGY FLOWS.


MPP#2 – ALL CATEGORIES OF PERSISTENT STORE-TO-STORE ENERGY TRANSFER MECHANISMS WITHIN PERSISTENT ENERGY PATHWAYS ARE CHARACTERIZED BY STRICTLY CONCAVE POWER-EFFICIENCY FUNCTIONS.





A006

0.50Po

wer

Efficiency

0.50Pow

er

Efficiency


EXAMPLE FROM ATWOOD’S MACHINE:

Factor varies with efficiency

Constant Factor

Key ShapeStrictly Concave

Useful Power

MPP#2 – ALL CATEGORIES OF PERSISTENT STORE-TO-STORE ENERGY TRANSFER MECHANISMS WITHIN PERSISTENT ENERGY PATHWAYS ARE CHARACTERIZED BY STRICTLY CONCAVE POWER-EFFICIENCY FUNCTIONS.

A007

P – A Family of Strictly Concave Zero-Bounded Functions on the Unit Interval

Where:1 A 51 B 50 C 51 D 5Showing the first 50

of 750 functions in this part of the

family.

A008

Partial Parameter Space

750 MembersFamily Template

P – A Family – Known Members

Atwood’s Machine

MT Constant(2,1,3,2)

MH Constant(2,1,1,2)

Jacobi’s Law – Rint Constant (1,1,0,1)

Family Template(A,B,C,D)

A009


MPP#3 – ALL AUTOCATALYTIC SYSTEMS EVOLVE TO CAPTURE AND CONSUME ENERGY AT MAXIMUM POWER AND AT SOME INTERMEDIATE EFFICIENCY

TWO ASSOCIATED AND DEPENDENT INFERENCES:a) Persistent energy stores, persistent energy transfer

mechanisms and pathways will all co-evolve.b) The system under constraint will expand scope to access

available:i. Sources of energy,ii. Sources of mass,iii. Sources of capital.

A010


INFERENCE 3a: Evolution of energy pathways occurs through co-evolution of the energy stores and the energy transfer mechanisms.



Prey Predator

A011

Energy Transfer

Mechanism


Mutation

Evolution of an Energy Transfer MechanismTypes of “Adaptive” Mutation

Original transfer

More power, more efficient

Organism Type #1

Organism Type #2a

Organism Type #1

Organism Type #2b

Mutation

Organism Type #1

Organism Type #3a

Organism Type #1

Organism Type #3b

Prey Predator

Prey Predator

Original transfer

More power, less efficient

A012

Evolution of an Energy Transfer

X

Energy pathways with more effective energy transfer mechanisms out-compete those with less effective energy transfer mechanisms, and so, the energy transfer mechanisms themselves evolve along a trajectory towards maximum power.

A013

Pow

er

Efficiency


INFERENCE 3b: If some available but untapped source of energy, mass or capital exists, the system will evolve mechanisms to tap into that source, and thereby increase the flux of energy.

E.g. plants and animals move from sea to land.

E.g. populations live on the edge of starvation, having barely enough food, but when food arrives, the population grows.

E.g. mankind learns to tap into metals, minerals and fossil fuels, and to harness natural, human and intellectual capital. A014



MY GOAL: • I attempted to produce a counter-example to

hypothesis MPP#3, and thereby falsify this hypothesis.

• That is, – I constructed a simple model of a persistent self-

organizing trophic web (in compliance with MPP#1); – I ensured that all energy transfer mechanisms were

strictly concave (in compliance with MPP#2), and – I wanted to see whether the system would evolve to

function at maximum power.

A014

Agenda



B001

Introducing Atwood’s Machine

ORIGINAL DESIGN

• Sir Isaac Newton• Principia Mathematica (1687)• Laws of motion

• George Atwood• English Mathematician• Invented machine in 1784• Study Newtonian Motion

B002

One Pulley

Introducing Atwood’s Machine MY DESIGN• Two Pulleys• Two masses– MH = Heavy mass– ML = Light mass

• D = Distance to Floor• Release pin• g = acc. due to gravity

LINKABLE HALVES OF OPEN ATWOOD MACHINES

B003

POTENTIAL

KINETIC

Operation of Atwood’s Machine

ML

D

FLOOR

DMH

WASTE HEAT

B004


ML

D

FLOOR

DMH

B005

POTENTIAL

KINETIC


ML

D

FLOOR

DMH

B006

POTENTIAL

KINETIC


ML

D

FLOOR

D

MH

B007

POTENTIAL

KINETIC


MLD

FLOOR

D

MH

B008

POTENTIAL

KINETIC


ML D

FLOOR

D

MH

B009

POTENTIAL

KINETIC


MLD

FLOOR

D

MH

B010

POTENTIAL

KINETIC


ML

D

FLOOR

D

MH

B011

POTENTIAL

KINETIC


ML

D

FLOOR

D

MH

B012

FLOORWASTE HEAT


ML

D

D

MH

B013

FLOORWASTE HEAT


ML

D

D

MH

B014

FLOORWASTE HEAT


ML

D

D

MH

B015

FLOORWASTE HEAT


ML

D

D

MH

B016


ML

D

FLOOR

D

MH

WASTE HEAT

B017


ML

D

FLOOR

D

MH

WASTE HEAT

B018


ML

D

FLOOR

D

MH

B019

“USEFUL Power” of Persistent Energy TransfersPU = EU/T =

PU is zero when ML = zero. PU is zero when MD = 0 (i.e. ML = MH).

Some Universal Concepts for Persistent Energy Transfers

Drop Time (duration)T = =

T is infinite when MD = 0 (i.e. ML = MH).

MT=Sum; MD=Difference

Efficiency of Persistent Energy Transfers = EU/ET =

varies between zero and one as ML varies from zero to MH.

B023

P

ower

0 ML MH

Power as a Function of EfficiencyAtwood’s Machine

MT Constant

MH Constant

ML Constant

0.50

0.62

PERSISTENT

B025Po

wer

Efficiency

Pow

er

Efficiency

Pow

er

Efficiency

Agenda



C001

Test of MPP#3 – MppLab I

X But, I, personally, do not understand organic chemistry sufficiently well. I do not know how to model energy transfers associated with gestation or digestion.

I understand Newtonian mechanics. I know how to model Darwinian

evolution of organisms.

MY PERSONAL DILEMMA

C002


How, then, can I model evolving energy pathways through which energy flows store-to-store, if I cannot actually model the energy transfer mechanisms between stores?

MY PERSONAL DILEMMA

C003


A. Assume that hypotheses MPP#1 & MPP#2 are correct;

B. Choose a known concave power-efficiency relation (say, an AM-associated curve); and

C. Model the biological energy transfer mechanisms using that proxy AM energy transfer mechanism.

MY PERSONAL SOLUTION

C004

Test of MPP#3 – MPPLab IA “Wizard of Oz” Thought Experiment

• Imagine the energy stores are organisms that:– receive energy (at birth, or in their food), – use it for metabolic activities, and then – transfer remaining energy to other organisms via

birth, or predation.• Call these imaginary organisms HOAMs.• Assume the energy transfers between

HOAMs have analogous dynamics to those of the AM’s energy transfers.

C005


HOAMs model organisms which move, feed, and reproduce with mutation, or die as prey.

The HOAMs model:• autotrophs (plants),

getting energy from the Sun, and • heterotrophs

(animals) getting energy by eating plants and other animals

C014


C015


They model:• daisies growing

(green) or being eaten (purple), and • animals hunting

(red), eating (yellow) or being eaten (purple)

C016


Constraint #3 – Heterotrophic agents cannot attack any agent with an AM-gene larger than four times its own AM-gene.

MODEL DESIGN ISSUES: THREE CONSTRAINTS

C017

Definition – The AM-gene is a proxy for mass to be used in any transient OAM formed.

Constraint #1 – The population of autotrophs is held constant at about 1,000.Constraint #2 – The AM-gene for autotrophic agents is set to 128 and held constant.


C018


C019


C020


C021


Histogram of AM-genes (i.e. pseudo-mass) of HOAMs.

C022



C023



Detail from Histogram.

C024



Detail from Histogram.

Histogram of Efficiency of OAMs.

C025


NOTE THAT, IN THIS VIDEO, ENERGY FLOWS:• FROM SUN (ON THE RIGHT) • THROUGH PLANTS, • TOWARDS THE APEX PREDATORS (ON THE LEFT).

C025





Apex Predators Plants

OmnivoresCarnivores

Test of MPP#3 – MppLab INOTE THAT, IN THIS VIDEO, THERE IS EVOLUTIONARY PRESSURE ON THE GENES RIGHT TO LEFT:• Organisms on the right have fewer food choices• Organisms on the left have more food choices• So the left-most can multiply more quickly

C025


Show Video 01An Operating Trophic Web

C026

Test of MPP#3 – MppLab IWhile the individual OAMs have varied efficiency, the trophic web, as a whole, has efficiency of 0.5, or Maximum Power.

Tick

275

0

C027

Pow

er

Efficiency


Demonstrated: • A persistent autocatalytic system (MPP#1)• in which all energy transfers are

characterized by strictly concave power-efficiency curves (MPP#2)

• evolved to form a system in which average efficiency of all predations is at point of Maximum Power ( = 0.5; MPP#3)

• in agreement with hypothesis MPP#3.C030

My attempt to falsify MPP#3 failed.

Agenda



D001

The Maximum Power Principle (MPP)

If we look carefully, we can see evidence of the MPP at work in

the World all around us.Lotka and Odum both believed that the MPP should be a candidate for the fourth law of thermodynamics.

D002All Just Hokum?

The Maximum Power Principle (MPP)It required about 150 years (1800-1950)

for the details of the first law (conservation of energy) to be worked out.

The second law (re entropy) has been undergoing development and change

since 1825, and is still evolving.

D003

The Maximum Power Principle (MPP)This proposed “fourth law” candidate, the MPP, was first described in 1922 –

it is still a very young concept.

Developments in empirical research techniques, and in computer modeling

techniques, make the MPP concepts much more accessible to researchers

now.D004

Other Related Phenomena

• Carnot’s Theorem• Onsager’s Reciprocal Relations• Jacobi’s Law (Maximum Power Transfer

Theorem)• Curzon-Ahlborn Engine (Efficiency of a Carnot

Engine at Maximum Power Output)• Law of Diminishing Marginal Returns

D005

Opportunity for Serious Research

D006

This is THE LINK that we most desperately need to understand at this moment in history.

The MPP spans the conceptual gap between co-evolving systems such as the global ecological

system and the global economic system.

MPP

QUESTIONS?

maximum power: and atwood’s machine by: g.h. boyle 4 th oct canussee 2015 screen shot from mpplab...

Documents