Diffusion of active particles with stochastic torques modeled asα-stable noise

Abstract

We investigate the stochastic dynamics of an active particle moving at a constant speed under the influence of a fluctuating torque. In our model the angular velocity is generated by a constant torque and random fluctuations described as a Lévy-stable noise. Two situations are investigated.First, we study white Lévy noise where the constant speed and the angular noise generate a persistent motion characterized by the persistence time τ D . At this time scale the crossover from ballistic to normal diffusive behavior is observed. The corresponding diffusion coefficient can be obtained analytically for the whole class of symmetric α-stable noises. As typical for models with noise-driven angular dynamics, the diffusion coefficient depends non-monotonously on the angular noise intensity. As second example, we study angular noise as described by an OrnsteinUhlenbeck process with correlation time τ c driven by the Cauchy white noise. We discuss the asymptotic diffusive properties of this model and obtain the same analytical expression for the diffusion coefficient as in the first case which is thus independent on τ c . Remarkably, for τ c > τ D the crossover from a non-Gaussian to a Gaussian distribution of displacements takes place at a time τ G which can be considerably larger than the persistence time τ D .

Search and return model for stochastic path integrators

“…The colored symbols are obtained from simulations according to equations (22), with the definition of the position angle β, given by (2). The black dashed lines correspond to equation (32). The approximations (32) fit the simulation results well for the small noise intensity σ 2 = 0.01.…”

Nonlinear friction in underdamped anharmonic stochastic oscillators

“…is a nonmonotonous function of v. Clearly, such a nonlinear friction only dissipate energy, i.e., it does not lead to the active Lévy motion [70,71]. In Ref.…”

Eliminating inertia in a stochastic model of a micro-swimmer with constant speed

“…Thus, as assumed in the model, the acceleration acts perpendicular to the velocity. We note that both vector components have the same acting noise at time t [49,50,52]. Applying the Stratonovich calculus gives for the increments of both velocity components v x (t) = v 0 cos(φ(t)) and v y (t) = v 0 sin(φ(t)) in lowest order in dW t and dt…”

“…A similar systematic reduction procedure in case of ABPs is nowadays still missing. Here, we fill this gap for the simple case of a micro-swimmer with constant speed as studied in [48][49][50][51][52][53][54][55][56][57][58][59] and in many other applications. We will proceed in a similar way as it is presented in Sec.…”