Related papers: Two boundary model for freezing front propagation …
In a real system the heating is nonuniform and a second-order phase transition into a broken symmetry phase occurs by propagation of the temperature front. Two parameters, the cooling rate $\tau_Q$ and the velocity $v_T$ of the transition…
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
It has been found the exact solutions for nonstationary distribution of the temperature in the liquid ring with two viscosities and two free boundaries of the ring.
A theory of temperature dynamics in many-body systems driven by time-dependent external sources is introduced. The formalism based on the combination of the perturbation theory and the fluctuational-electrodynamics approach in many-body…
A complete thermodynamical analysis for a blood model, based on mixture theory, is performed. The model is developed considering the blood as a suspension of red blood cells (solid component) in the plasma (fluid component), and taking into…
Demixing of binary fluids subjected to slow temperature ramps shows repeated waves of nucleation which arise as a consequence of the competition between generation of supersaturation by the temperature ramp and relaxation of supersaturation…
One of the main characteristics of blood coagulation is the speed of clot growth. This parameter strongly depends on the speed of propagation of the thrombin concentration in blood plasma. In the current work we consider mathematical model…
Mechanical signaling plays a key role in biological processes like embryo development and cancer growth. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful…
The use of nanoparticles for targeted drug delivery, especially in diseased arteries, is a novel procedure. We are incorporating nanoparticles into blood vessels using a catheter, which could potentially deliver drugs precisely to affected…
The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…
The problem of front propagation in a stirred medium is addressed in the case of cellular flows in three different regimes: slow reaction, fast reaction and geometrical optics limit. It is well known that a consequence of stirring is the…
The incredible thermo-mechanical properties of biological materials arise from the microscopic scale due to a complex hierarchical mechanism, regulated by microinstabilities at the molecular level. The description of such complex structures…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
An approximate theory is presented describing the propagation of the ice-water front that develops in droplets of water that are deposited on a planar surface at a temperature below the melting point of ice. A calculation based on this…
Self-regulation of living tissue as an example of self-organization phenomena in hierarchical systems of biological, ecological, and social nature is under consideration. The characteristic feature of these systems is the absence of any…
In the present monograph we formulate a simple model for heat transfer in living tissue with self - regulation. The initial point of the model is the governing equations describing heat transfer in living tissue at the mesoscopic level,…
In contrast to the infinite chain, the low-temperature expansion of a one-dimensional free-field Ising model has a strong dependence on boundary conditions. I derive explicit formula for the leading term of the expansion both under open and…