Model Equations for Interacting Quasi-Particles

In a special parameter-range it is possible to derive simple equations of motions for quasi-particles in a three-component reaction-diffusion-model. The state of each particle is characterized by its location p and some internal degree of freedom a, which is basically proportional to the propagation speed.  For the temporal evolution we can derive the system of ordinary differential equations

Wechselwirkungsmodell

The sums reflect the interaction processes between distinct particles i and j. As bifurcation parameter we have used the time constant . The speed of a single moving solution can easily be obtained from the above equations and depends like

from . The Applet below can numerically solve the equations of motion.
 

 

 Instructions

You can use the mouse to add new objects. A click on an existing object will remove it.

The bifurcationparameter  changes the speed of the solutions and depending on  different phenomena occur. The bifurcation point for the onset of propagation is at 3.33 . The time-constant ht will change the speed of the simulation and can be adjusted for convenience. 

Additionally it is possible to change the shape of the domain and the interaction potential between the particles using the buttons below.
 
Possible domains:

Rect: Quadrate domain with no-flux boundaries (The boundaries act like mirrors)
Disc: Disc-shaped domain with no-flux boundaries
Zykl: Quadrate domain with periodical boundaries

Interaction law:

Rep:  The interaction is repulsive
Osz:  Oscillatory interaction law: There exist certain distances which lead to an attraction.
 
 

Author: C. P. Schenk (16.06.1999)

Last change by Andreas W. Liehr (01.06.2000)


 
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