Persistent random walk of cells involving anomalous effects and random death.

@article{Fedotov2015PersistentRW,
  title={Persistent random walk of cells involving anomalous effects and random death.},
  author={Sergei Fedotov and Abby Tan and Andrey Yu. Zubarev},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2015},
  volume={91 4},
  pages={
          042124
        }
}
The purpose of this paper is to implement a random death process into a persistent random walk model which produces sub-ballistic superdiffusion (Lévy walk). We develop a stochastic two-velocity jump model of cell motility for which the switching rate depends upon the time which the cell has spent moving in one direction. It is assumed that the switching rate is a decreasing function of residence (running) time. This assumption leads to the power law for the velocity switching time distribution… 

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References

SHOWING 1-10 OF 108 REFERENCES
Random death process for the regularization of subdiffusive fractional equations.
TLDR
The inclusion of the random death process in the random walk scheme is proposed, which is quite natural for biological applications including morphogen gradient formation and shows that this equation is structurally stable against spatial variations of the anomalous exponent.
Fluid limit of the continuous-time random walk with general Lévy jump distribution functions.
TLDR
The continuous time random walk (CTRW) is a natural generalization of the Brownian random walk that allows the incorporation of waiting time distributions psi(t) and general jump distribution functions eta(x) and an integrodifferential equation describing the dynamics in the fluid limit is considered.
Non-homogeneous random walks, subdiffusive migration of cells and anomalous chemotaxis
TLDR
The criteria under which the anomalous aggregation of cells takes place in the semi-infinite domain is found and the structural instability of fractional subdiffusive equation is shown with respect to the partial variations of anomalous exponent.
Continuous Time Random Walks with Reactions Forcing and Trapping
One of the central results in Einstein’s theory of Brownian motion is that the mean square displacement of a randomly moving Brownian particle scales linearly with time. Over the past few decades
Front propagation in reaction-dispersal models with finite jump speed.
TLDR
The continuous-time random walk and the Hamilton-Jacobi method are used to reach analytical expressions for the speed of traveling fronts in reaction-dispersal models and the possibility that several particle speeds are allowed, so different dispersal mechanisms can be considered simultaneously.
FRACTIONAL DIFFUSION AND LEVY STABLE PROCESSES
Anomalous diffusion in which the mean square distance between diffusing quantities increases faster than linearly in ‘‘time’’ has been observed in all manner of physical and biological systems from
Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous-time random walks.
TLDR
A more general derivation valid under less stringent constraints than those found in the current literature is presented, e.g., for location-independent exponential evanescence.
Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
TLDR
The question arises as to whether aggregation is possible under suitable hypotheses on the transition rules and the production of a control species that modulates the transition rates of the myxobacteria.
Towards deterministic equations for Lévy walks: the fractional material derivative.
  • I. Sokolov, R. Metzler
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
TLDR
A generalized dynamical formulation is derived for Lévy walks, in which the fractional equivalent of the material derivative occurs, which is expected to be useful for the dynamical formulations of LÉvy walks in an external force field or in phase space.
...
...