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Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…
The system under study is a reaction-diffusion equation in a horizontal strip, coupled to a diffusion equation on its upper boundary via an exchange condition of the Robin type. This class of models was introduced by H. Berestycki, L. Rossi…
Flowing blood displays a phenomenon called margination, in which leukocytes and platelets are preferentially found near blood vessel walls, while erythrocytes are depleted from these regions. Here margination is investigated using direct…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
The inhomogeneous cooling state describing the hydrodynamic behavior of a freely evolving granular gas strongly confined between two parallel plates is studied, using a Boltzmann kinetic equation derived recently. By extending the idea of…
We investigate the radiative heat transfer and spatial distributions of stationary temperatures in periodic many-body systems composed of alternating slabs of two different materials. We show that temperature distributions exhibit an…
Two-length-scale pair potentials arise ubiquitously in condensed matter theory as effective interparticle interactions in molecular, metallic and soft matter systems. The existence of two different bond lengths generated by the shape of…
A unifying framework to describe dense flows of dry, deformable grains is proposed. Perturbative analysis of a granular temperature equation describing flows with contact stresses, supported by the recovery of the nonlocal granular fluidity…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
The combination of protrusions and retractions in the movement of polarized cells leads to understand the effect of possible synchronisation between the two ends of the cells. This synchronisation, in turn, could lead to different dynamics…
Some microbes appear to be able to metabolize in glacial ice or permafrost. The rate depends on temperature, nutrient level, and bioelement availability, among other factors. I have developed a plausible argument that they do this while…
Blood system functions are very diverse and important for most processes in human organism. One of its primary functions is matter transport among different parts of the organism including tissue supplying with oxygen, carbon dioxide…
A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional,…
Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…
Heat transfer to a granular flow is comprised of two resistances in series: near the wall and within the bulk particle bed, neither of which is well understood due to the lack of experimental probes to separate their respective…
We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic…
A description in terms of transition rates among cells is used to analyze self-diffusion of hard spheres in the fluid phase. Cell size is assumed much larger than the mean free path. Transition state theory is used to obtain an equation…
Observation of coronal EUV spectral lines sensitive to different temperatures offers an opportunity to evaluate the thermal structure and flows in flaring atmospheres. This can be used to estimate the partitioning between the thermal and…