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Simulating Model G neutral particle in a G, X, Y gradients

Simulating Model G neutral particle in a G, X, Y gradients with python

See @ https://github.com/bjdarrer/particle_in_gradient_slope50_100s_1e_gxygradients_3j

1. Model G 1D particle in gradient with G- (slope -1/50), X- (slope 0.0), and Y- (slope 0.0) gradients – 3e

Model G 1D particle in gradient – 3e

2. Model G 1D particle in gradient with G- (slope 0), X- (slope – 1/50), and Y- (slope 0) gradients – 3f

Model G 1D particle in gradient – 3f

3. Model G 1D particle in gradient with G- (slope 0), X- (slope – 1/30), and Y- (slope 0) gradients – 3g

Model G 1D particle in gradient – 3g

4. Model G 1D particle in gradient with G- (slope 0), X- (slope 0), and Y- (slope +1/30) gradients – 3h

Model G 1D particle in gradient – 3h

5. Model G 1D particle in gradient with G- (slope 0), X- (slope 0), and Y- (slope +1/20) gradients – 3i

Model G 1D particle in gradient – 3i

6. Model G 1D particle in gradient with G- (slope 0), X- (slope 0), and Y- (slope +1/26) gradients – 3j

Model G 1D particle in gradient – 3j

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Simulating Model G neutral particle in a G gradient with python, continued…

Simulating Model G neutral particle in a G gradient with python. G gradient = -1/50

Simulating Model G neutral particle in a G gradient with python. G gradient = -1/100

Simulating Model G neutral particle in a G gradient with python. G gradient = -1/10

Simulating Model G neutral particle in a G gradient with python. G gradient = -1/5 — no. 1

Simulating Model G neutral particle in a G gradient with python. G gradient = -1/5 — no. 2

Simulating Model G neutral particle in a G gradient with python. G gradient = -1/5 — no. 3

Simulating Model G neutral particle in a G gradient with python. G gradient = -1/5 — no. 4

Simulating Model G neutral particle in a G gradient with python. G gradient = -1/5 — no. 5

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Model G Research Group

Hi Everyone,

We have a new forum in “Model G Research Group” on a server. Please send email to me, Brendan with brendan.darrer.12@ucl.ac.uk, if you want to join.

Brendan

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Vector velocity field of a 3d soliton particle (Model G) using cones as vectors

Here are some videos attempting to model the vector velocity field of a 3d soliton particle (Model G) using cones as vectors. See @ https://plotly.com/python/cone-plot/ . As you can see this may be not how it should look like, but in the cone plot you can see where the particle starts to form as the cone shapes change dramatically. The 3d array that each time segment produces for the video of n = 200 time slots, is converted into a .csv file of 7,270,400 lines and each 325 MB, that is replaced on each loop of the code, and later sewn together to make the video with ffmpeg.

Below are the Model G code changes for 3d particle video, 3d vector velocity cone video and 3d yaml files, see:

https://github.com/bjdarrer/tf2-model-g/blob/master/backups/render_video____nucleation_3D______1_seed__y0_x0____n200_R20_res160pVD10_OS1_ST10___with_cone_velocity_vector_242__7-12-2022__3.py?fbclid=IwAR3GTKfPX4M-sReaoKmrlDb_HEvervGs8E6SQrMufDs2EeaPfkpael4rPkU#L689

https://github.com/bjdarrer/tf2-model-g/blob/master/backups/fluid_model_g______nucleation_3D______1_seed__y0_x0____n200_R20_res160pVD10_OS1_ST10___with_cone_velocity_vector_242__7-12-2022__3.py?fbclid=IwAR1cuRFZj7RXaahASLjXTbU0yYz4XWV7Qy513hQQPb97N8sfKiMlTyBcFMg#L312

https://github.com/bjdarrer/tf2-model-g/blob/master/backups/nucleation_3D______1_seed__y0_x0____n200_R20_res160pVD10_OS1_ST10___with_cone_velocity_vector_242__7-12-2022__3.yaml?fbclid=IwAR3TvcumfD_6UUtibZYECp4-r-J5O8m77csUHJwqh2cWS5ygOKsQ9Na6ek8

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Papers on the Brusselator – early and recent

Model G is based on the Brusselator adding an extra G component. To understand Model G better we need to look at the Brusselator and how it was derived. See these papers below. N.B. sorry I can’t upload them to this site at the moment. Working on it. Brendan

Paper 1:

BULLETIN OF MATHEMATICAL BIOLOGY VOLUME 37 1975

BIFURCATION ANALYSIS OF NONLINEAR REACTION – DIFFUSION EQUATIONS–I. EVOLUTION EQUATIONS AND THE STEADY STATE SOLUTIONS

J. F. G. Auchmuty
Department of Mathematics,
Indiana University,
Bloomington, Indiana 47401
and
G. Nicolis
Faculty des Sciences,
Universite Libre de Bruxelles,
Belgium

https://www.researchgate.net/publication/242968205_Bifurcation_analysis_of_nonlinear_reaction-diffusion_equations-I_Evolution_equations_and_the_steady_state_solutions

Paper 2

BULLETIN OF MATHEMATICAL BIOLOGY VOLUME 37 1975

BIFURCATION ANALYSIS OF NONLINEAR REACTION-DIFFUSION EQUATIONS–II. STEADY STATE SOLUTIONS AND COMPARISON WITH NUMERICAL SIMULATIONS

M. Herschkowitz-Kaufman
Faeulte des Sciences,
Universite Libre de Bruxelles
Belgium

Paper 3

CHAOS 27, 104617 (2017)

Dissipative structures: From reaction-diffusion to chemo-hydrodynamic patterns

M. A. Budroni and A. De Wit

Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Theorique,
Universite libre de Bruxelles (ULB), CP 231 – Campus Plaine, 1050 Brussels, Belgium

https://nlpc.ulb.be/pdf/17.Budroni_CHAOS_Prigogine.pdf