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Levy walk is a fundamental model with applications ranging from quantum physics to paths of animal foraging. Taking animal foraging as an example, a natural idea that comes to ones mind is to introduce the multiple internal states for dealing with the dependence of the PDF of waiting time on the energy of the animal and richness of the food at a particular location, etc; the framework can also be used to model the moving trajectories of smart animals without returning to the directions or locations which they come from immediately. After building the Levy walk model with multiple internal states and deriving the governing equation of the distribution of the positions of the particles, some applications are discussed with specific transition matrices. The type of diffusion for non-immediately-repeating L{e}vy walk is uncovered, and the distribution and average of first passage time are numerically simulated.
Integral transform method (Fourier or Laplace transform, etc) is more often effective to do the theoretical analysis for the stochastic processes. However, for the time-space coupled cases, e.g., Levy walk or nonlinear cases, integral transform metho
Levy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of animals, humans, r
Levy walks define a fundamental concept in random walk theory which allows one to model diffusive spreading that is faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a diffusion e
We demonstrate the phenomenon of cumulative inertia in intracellular transport involving multiple motor proteins in human epithelial cells by measuring the empirical survival probability of cargoes on the microtubule and their detachment rates. We fo
A stochastic process with movement, return, and rest phases is considered in this paper. For the movement phase, the particles move following the dynamics of Gaussian process or ballistic type of Levy walk, and the time of each movement is random. Fo