1,720,991 research outputs found
Run-and-tumble motion in one dimension with space-dependent speed
No full textWe consider a particle performing run-and-tumble dynamics with space-dependent speed. The model has biological relevance as it describes motile bacteria or cells in heterogeneous environments. We give exact expression for the probability density function in the case of free motion in unbounded space. We then analyze the case of a particle moving in a confined interval in the presence of partially absorbing boundaries, reporting the probability density in the Laplace (time) domain and the mean time to absorption. We also discuss the relaxation to the steady state in the case of confinement with reflecting boundaries and drift effects due to direction-dependent tumbling rates, modeling taxis phenomena of cells. The case of diffusive particles with spatially variable diffusivity is obtained as a limiting case
On fractional Cattaneo equation with partially reflecting boundaries
No full textIn this paper we study the time-fractional Cattaneo equation in a bounded domain with semi-reflecting conditions. In particular, we are able to find the Laplace transform of the probability density function of the absorption time and therefore the mean-time to absorption. We show the crucial role of the time-fractional formulation. Indeed, in this case we have that the mean-time to absorption diverges due to the fact that the generalized Cattaneo equation is based on the application of integral operators with a long-tail memory kernel. We also consider the time-fractional diffusion and wave limits behaviour, recovering some previous results obtained in the literature. Finally, a section is devoted to the generalized Cattaneo equation in unbounded domain. In this case we are able to discuss the characterization of the mean square displacement for short times and asymptotically by using the Fourier-Laplace transform of the solution
Probability distributions for the run-and-tumble models with variable speed and tumbling rate
No full textIn this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity and changing direction at instants distributed according to a non-stationary Poisson distribution with rate . We show that, under suitable assumptions, we are able to find the exact form of the probability distribution. We also consider the space-fractional counterpart of this model, finding the characteristic function of the related process. A conclusive discussion is devoted to the potential applications to run-and-tumble models
Self-Sustained Density Oscillations of Swimming Bacteria Confined in Microchambers
No full textWe numerically study the dynamics of run-and-tumble particles confined in two chambers connected by thin channels. Two dominant dynamical behaviors emerge: (i) an oscillatory pumping state, in which particles periodically fill the two vessels, and (ii) a circulating flow state, dynamically maintaining a near constant population level in the containers when connected by two channels. We demonstrate that the oscillatory behavior arises from the combination of a narrow channel, preventing bacteria reorientation, and a density-dependent motility inside the chambers
Generalized model of blockage in particulate flow limited by channel carrying capacity
No full textWe investigate stochastic models of particles entering a channel with a random time distribution. When the number of particles present in the channel exceeds a critical value N, a blockage occurs and the particle flux is definitively interrupted. By introducing an integral representation of the n-particle survival probabilities, we obtain exact expressions for the survival probability, the distribution of the number of particles that pass before failure, the instantaneous flux of exiting particles, and their time correlation. We generalize previous results for N = 2 to an arbitrary distribution of entry times and obtain exact solutions for N = 3 for a Poisson distribution and partial results for N >= 4
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