Trajectories of Deformable Self-Propelled Particles

evolution time

parameters:

γ

κ

a

b

initial conditions:

v

0

ϕ

0

s

0

θ

0

ellipse parameters:

size

number

One of the simplest models for a deformable self-propelled particle based on symmetry arguments is given by the following equations:



v

(t)=γv(t)-

2

v(t)

v(t)-a



S

(t).v(t)



^

S

(t)=-κ



S

(t)+bv(t)⊗v(t)+

1

2

v(t)

v(t)={v(t)cos(ϕ(t)),v(t)sin(ϕ(t))}



S

(t)=s(t)n(t)⊗n(t)-

1

2

n(t)={cos(θ(t)),sin(θ(t))}

Here

v(t)

is the velocity of the particle,

n(t)

is the vector of the half-axes of the particle, which is assumed to be shaped like an ellipse, and

s(t)

describes the deviation of the shape from a circle.