相关论文: Capillary Network, Cancer and Kleiber Law

Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states,…

A simple model of two-phase flow in porous media is presented. A connection is made to statistical mechanics by applying capillary power as a constraint. Stochastic sampling is then used to test the validity of this approach. Good agreement…

The paper studies a higher-order diffusion model of Maxwell-Stefan kind. The model is based upon higher-order moment equations of kinetic theory of mixtures, which include viscous dissipation in the model. Governing equations are analyzed…

A macroscopic model of the tumor Gompertzian growth is proposed. This approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor factors.…

We consider weak solutions to a problem modeling tumor growth. Under certain conditions on the initial data, solutions can be obtained by passing to the stiff (incompressible) limit in a porous medium type problem with a Lotka-Volterra…

Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of…

When modeling of tumor-driven angiogenesis, a major source of analytical and computational complexity is the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the…

We introduce a multi-species diffuse interface model for tumor growth, characterized by its incorporation of essential features related to chemotaxis, angiogenesis and proliferation mechanisms. We establish the weak well-posedness of the…

A recently proposed single progenitor cell model for skin cell proliferation [Clayton et al., Nature v446, 185 (2007)] is extended to incorporate homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can…

Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…

Generalization of the Kac integral and Kac method for paths measure based on the Levy distribution has been used to derive fractional diffusion equation. Application to nonlinear fractional Ginzburg-Landau equation is discussed.

Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used…

Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn-Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models.…

Existing approaches to modeling the dynamics of brain tumor growth, specifically glioma, employ biologically inspired models of cell diffusion, using image data to estimate the associated parameters. In this work, we propose an alternative…

We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…

Based on the Kraus-form solution to the master equation describing diffusion we develop an integral form solution by using the method of integration within ordered product of operators, i.e., the evolution law of density operator in…

Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles…

Understanding the cosmic ray (CR) ionization rate is crucial in order to simulate the dynamics of, and interpret the chemical species observed in molecular clouds. Calculating the CR ionization rate requires both accurate knowledge of the…

We demonstrate the validity of Murray's law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with…

We consider a generalised diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyse the probability distribution functions and we derive the mean squared displacement in $x$ and $y$ directions.…