Related papers: Point Forces in Elasticity Equation and Their Alte…
We consider a mathematical model for wound contraction, which is based on solving a momentum balance under the assumptions of isotropy, homogeneity, Hooke's Law, infinitesimal strain theory and point forces exerted by cells. However, point…
For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the Dirac Delta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller…
Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells,…
Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux…
In this article we consider regularizations of the Dirac delta distribution with applications to prototypical elliptic and hyperbolic partial differential equations (PDEs). We study the convergence of a sequence of distributions…
We develop an unfitted compatible finite element discretisation for the Darcy problem based on $H(\mathrm{div})$-conforming flux spaces and discontinuous pressure spaces. The method is designed to preserve pointwise discrete mass…
The laws of friction are reasonably well understood for the case of blocks in contact with rough plane surfaces. However, as far as bodies with circular sections are concerned, the physics of friction becomes more involving and it is not…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
We consider the system of two material points that interact by elastic forces according to Hooke's law and their motion is restricted to certain curves lying on the plane. The nonintegrability of this system and idea of the proof are…
Living cells respond to mechanical changes in the matrix surrounding them by applying contractile forces that are in turn transmitted to distant cells. We calculate the mechanical work that each cell performs in order to deform the matrix,…
A number of problems arise when long-range forces, such as those governed by Bessel functions, are used in particle-particle simulations. If a simple cut-off for the interaction is used, the system may find an equilibrium configuration at…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the…
We give a description of cell diffusion in a soft tissue, paying special attention to the coupling of force, matter, and microforce balance laws through a suitable dissipation principle. To this end, we cast our framework into a multi-level…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
Motivated by the long-debated question about the internal stability of the electron, the force densities acting on the charge density of the 1s electron in the H atom are investigated. The problem is mapped onto the canonical formalism for…
We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework…
We study slender, helical elastic rods subject to distributed forces and moments. Focussing on the case when the helix axis remains straight, we employ the method of multiple scales to systematically derive an 'equivalent-rod' theory from…
For various species of biological cells, experimental observations indicate the existence of universal distributions of the cellular size, scaling relations between the cell-size moments and simple rules for the cell-size control. We…
For many biological systems that involve elastic structures immersed in fluid, small length scales mean that inertial effects are also small, and the fluid obeys the Stokes equations. One way to solve the model equations representing such…