相关论文: Constrained Nonlinear and Mixed Effects Differenti…

The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…

Rod-shaped particles embedded in certain matrices have been reported to exhibit an increase in their center of mass diffusivity upon increasing the matrix density. This increase has been considered to be caused by a kinetic constraint in…

This work puts forth a new optimal design formulation for planar elastic membranes. The goal is to minimize the membrane's compliance through choosing the material distribution described by a positive Radon measure. The deformation of the…

Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…

We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface…

A self-consistent model is presented for performing steady-state fully kinetic Particle-in-Cell simulations of magnetised plasma plumes. An energy-based electron reflection prevents the numerical pump instability associated with a typical…

Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. In this paper, we present a new optimization-based method for sampling…

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…

Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is…

Separation is a crucial step in the analysis of living microparticles. In particular, the selective microseparation of phytoplankton by size and shape remains an open problem, even though these criteria are essential for their gender and/or…

Using a perturbative approach, an evolution equation for the space charge density, correct up to the third order, is deduced for arbitrary initial density profiles of the electron and ion fluids in a cold nonrelativistic plasma. The…

We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…

We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…

Experimental studies of cell motility in culture have shown that under adequate conditions these living organisms possess the ability to organize themselves into complex structures. Such structures may exhibit a synergy that greatly…

Energy transfer among various spectral components of fluctuating physical parameters in plasma occurs due to the nonlinear interactions, but these effects are typically not captured by the traditional linear spectral methods. Plasma density…

Unequal partitioning of the molecular content at cell division has been shown to be a source of heterogeneity in a cell population. We propose to model this phenomenon with the help of a scalar, nonlinear impulsive differential equation…

A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a…

Power distribution networks, especially in North America, are often unbalanced but are designed to keep unbalance levels within the limits specified by IEEE, IEC, and NEMA standards. However, rapid integration of unbalanced devices, such as…

One important development in interaction potential models, or atomistic force fields, for molecular simulation is the inclusion of explicit polarisation, which represents the induction effects of charged or polar molecules on polarisable…

For the purpose of maximizing the spread of influence caused by a certain small number k of nodes in a social network, we are asked to find a k-subset of nodes (i.e., a seed set) with the best capacity to influence the nodes not in it. This…