相关论文: On the first bifurcation point for a free boundary…
Herewith we discuss a network model of the ferroptosis avascular and vascular tumor growth based on our previous proposed framework. Chiefly, ferroptosis should be viewed as a first order phase transition characterized by a supercritical…
Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating from its environment. Depending on the…
We consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our…
Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in…
The appearance of detached recirculation regions in wakes with base bleed determines the aerodynamic properties of many natural organisms and technological applications. In this work we introduce an analytical model which captures certain…
We introduce a 2D free boundary problem with nonlinear diffusion that models a living cell moving on a substrate. We prove that this nonlinearity results in a qualitative of solution behavior compared to the linear diffusion case (Rybalko…
This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform…
Analytical expressions for coordinates of stationary points and conditions for their existence in the ABC flow are received. The type of the stationary points is shown analytically to be saddle-node. Exact expressions for eigenvalues and…
Phase separation, i.e., the coexistence of two different phases, is observed in many systems away from the coexistence curve of a first-order transition, leading to a stable heterogeneous phase or region. Examples include various quantum…
We consider the steady states of a gas between two parallel plates that is ionized by a strong electric field so as to create a plasma. There can be a cascade of electrons due both to the electrons colliding with the gas molecules and to…
The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…
A phase field crystal model is used to investigate the mechanisms of formation and growth of early clusters in quenched/aged dilute binary alloys, a phenomenon typically outside the scope of molecular dynamics time scales. We show that…
The bifurcation diagram for a vibro-fluidized granular gas in N connected compartments is constructed and discussed. At vigorous driving, the uniform distribution (in which the gas is equi-partitioned over the compartments) is stable. But…
Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed…
Arterial deformations arise in blood flow when surrounding tissue invades the space available for a blood vessel to maintain its circular cross section, the most immediate effects being a reduction in blood flow and redistribution of shear…
We present a numerical study of a two-lane version of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally-imposed…
We study a bulk-surface coupled system that describes the processes of lipid-phase separation and lipid-cholesterol interaction on cell membranes, in which cholesterol exchange between cytosol and cell membrane is also incorporated. The PDE…
Phase separation can drive spatial organization of multicomponent mixtures. For instance in developing animal embryos, effective phase separation descriptions have been used to account for the spatial organization of different tissue types.…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
We investigate the theoretical nonlinear response, Hessian stability, and possible wrinkling behaviour of a voltage-activated dielectric plate immersed in a tank filled with silicone oil. Fixed rigid electrodes are placed on the top and…