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- Vicenç Méndez, Joaquim Fort, Horacio G Rotstein, Sergei Fedotov
- Physical review. E, Statistical, nonlinear, and…
- 2003

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic… (More)

- Sergei Fedotov, Steven Falconer
- Physical review. E, Statistical, nonlinear, and…
- 2012

We derive the fractional master equation with space-dependent anomalous exponent. We analyze the asymptotic behavior of the corresponding lattice model both analytically and by Monte Carlo simulation. We show that the subdiffusive fractional equations with constant anomalous exponent μ in a bounded domain [0,L] are not structurally stable with respect to… (More)

- Sergei Fedotov, Vicenç Méndez
- Physical review letters
- 2008

Motivated by the experiments [Santamaria, Neuron 52, 635 (2006)10.1016/j.neuron.2006.10.025] that indicated the possibility of subdiffusive transport of molecules along dendrites of cerebellar Purkinje cells, we develop a mesoscopic model for transport and chemical reactions of particles in spiny dendrites. The communication between spines and a parent… (More)

- Sergei Fedotov, Alexander Iomin
- Physical review letters
- 2007

We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW), we formulate a system of the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration. The transport process is formulated… (More)

- Sergei Fedotov, David Moss, Daniel Campos
- Physical review. E, Statistical, nonlinear, and…
- 2008

We present a stochastic two-population model that describes the migration and growth of semisedentary foragers and sedentary farmers along a river valley during the Neolithic transition. The main idea is that random migration and transition from a sedentary to a foraging way of life, and backwards, is strongly coupled with the local crop production and… (More)

- S Fedotov
- Physical review letters
- 2001

We studied the propagation of traveling fronts into an unstable state of the reaction-transport systems involving integral transport. By using a hyperbolic scaling procedure and singular perturbation techniques, we determined a Hamiltonian structure of reaction-transport equations. This structure allowed us to derive asymptotic formulas for the propagation… (More)

- Sergei Fedotov
- Physical review. E, Statistical, nonlinear, and…
- 2010

The main aim of the paper is to incorporate the nonlinear kinetic term into non-Markovian transport equations described by a continuous time random walk (CTRW) with nonexponential waiting time distributions. We consider three different CTRW models with reactions. We derive nonlinear Master equations for the mesoscopic density of reacting particles… (More)

- Sergei Fedotov
- 1998

A new asymptotic method is presented for the analysis of the traveling waves in the onedimensional reaction-diffusion system with the diffusion with a finite velocity and KolmogorovPetrovskii-Piskunov kinetics. The analysis makes use of the path-integral approach, scaling procedure and the singular perturbation techniques involving the large deviations… (More)

- Sergei Fedotov, Alexander Iomin
- Physical review. E, Statistical, nonlinear, and…
- 2008

The proliferation and migration dichotomy of the tumor cell invasion is examined within a two-component continuous time random walk (CTRW) model. The balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration are derived. The transport of tumor cells is formulated in terms of the CTRW with an… (More)

- Sergei Fedotov, Alexander Iomin, Lev Ryashko
- Physical review. E, Statistical, nonlinear, and…
- 2011

Proliferation and migration dichotomy of the tumor cell invasion is examined within two non-Markovian models. We consider the tumor spheroid, which consists of the tumor core with a high density of cells and the outer invasive zone. We distinguish two different regions of the outer invasive zone and develop models for both zones. In model I we analyze the… (More)