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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)
The mapping of the nonlinear Schrödinger equation with a random potential on the Fokker-Planck equation is used to calculate the localization length of its stationary states. The asymptotic growth rates of the moments of the wave function and its derivative for the linear Schrödinger equation in a random potential are computed analytically, and resummation(More)
For the nonlinear Schrödinger equation (NLSE), in the presence of disorder, exponentially localized stationary states are found. We demonstrate analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation. The analysis makes use of the(More)
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)
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)
We study specific properties of particles transport by exploring an exact solvable model, a so-called comb structure, where diffusive transport of particles leads to subdiffusion. A performance of the Lévy-like process enriches this transport phenomenon. It is shown that an inhomogeneous convection flow is a mechanism for the realization of the Lévy-like(More)
  • A Iomin
  • 2012
A toy model for glioma treatment by a radio frequency electric field is suggested. This low-intensity, intermediate-frequency alternating electric field is known as the tumor-treating field (TTF). In the framework of this model the efficiency of this TTF is estimated, and the interplay between the TTF and the migration-proliferation dichotomy of cancer(More)
It is shown that the Weyl fractional derivative can quantize an open system. A fractional kicked rotor is studied in the framework of the fractional Schrödinger equation. The system is described by the non-Hermitian Hamiltonian by virtue of the Weyl fractional derivative. Violation of space symmetry leads to acceleration of the orbital momentum. Quantum(More)