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Cell migration is closely linked to cell shape, yet cell size is often assumed to remain constant. This assumption is challenged by recent experiments showing that cells undergo volume loss during spreading and swelling upon activation,…
The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions…
We define and study the Cauchy problem for a 1-D nonlinear Dirac equation with nonlinearities concentrated at one point. Global well-posedness is provided and conservation laws for mass and energy are shown. Several examples, including…
The framework of this article is cell motility modeling. Approximating cells as rigid spheres we take into account for both non-penetration and adhesions forces. Adhesions are modeled as a memory-like microscopic elastic forces. This leads…
The deformation and stress distribution in a stretched thin neo-Hookean circular membrane with a hole at its center are analyzed within the framework of finite deformation elasticity. Initially, we derive a simple form for the differential…
For the first time the phenomenon of cellular structure coarsening are consistently analysed from the positions of kinetic, hydrodynamic and stochastodynamic theories of nonequilibrium statistical systems. Thereby micro-, meso- and…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
In this work, we consider parabolic models with dynamic boundary conditions and parabolic bulk-surface problems in 3D. Such partial differential equations based models describe phenomena that happen both on the surface and in the…
Connecting cell behavior to tissue shape and mechanics is a key challenge in the physics of morphogenesis. Cytoskeletal turnover precludes a fixed reference state, and tensions are actively generated independently of strain; so conventional…
Dealing with variational formulations of second order elliptic problems with discontinuous coefficients, we recall a single field minimization problem of an extended functional presented by Bevilacqua et al (1974), which we associate with…
In this work we propose an extension to the analytical one-dimensional model proposed by E. Gnecco (Phys. Rev. Lett. 84:1172) to describe friction. Our model includes normal forces and the dependence with the angular direction of movement…
We present a systematic investigation of the distribution of normal forces at the boundaries of static packings of spheres. A new method for the efficient construction of large hexagonal-close-packed crystals is introduced and used to study…
We suggest an alternative mathematical model for the electron in dimension 1+2. We think of our (1+2)-dimensional spacetime as an elastic continuum whose material points can experience no displacements, only rotations. This framework is a…
This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard…
In the frame of the Boltzmann equation, wall-bounded flows of rarefied gases require the implementation of boundary conditions at the kinetic level. Such boundary conditions induce a discontinuity in the distribution function with respect…
In three dimensional toroidal domains without symmetry, the standard magnetohydrodynamic (MHD) equilibrium model used for magnetic confinement fusion does not generally support smooth solutions. Instead, solutions have singular plasma…
We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} ({\bPsi} \Psi)^{\kappa+1}$ in the presence of various external electromagnetic fields. Starting from the exact…
We study cell count moments up to fifth order of the distributions of haloes, of halo substructures as a proxy for galaxies, and of mass in the context of the halo model and compare theoretical predictions to the results of numerical…
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…
We generalise a hybridized discontinuous Galerkin method for incompressible flow problems to non-affine cells, showing that with a suitable element mapping the generalised method preserves a key invariance property that eludes most methods,…