Prefusion and postfusion states of the biological fusion process between lipid bilayer vesicle membranes are studied in this paper. Based on the Helfrich-type continuum theory, a diffuse interface model is developed which describes the phase changes on the deformable vesicles via a scalar phase field function, and incorporates the adhesion effect between the different phases of the vesicles thr...

We analyze radially symmetric bumps in a two-dimensional piecewise-smooth neural field model with synaptic depression. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activ...

In this paper we review recent developments in blending methods for atomistic-to-continuum (AtC) coupling in material statics problems. Such methods tie together atomistic and continuum models by using a bridge domain that connects the two models. There are several reasons why AtC coupling methods (of which blending methods are a subset) are important and have been subject to an increased inter...

The peridynamic model is a framework for continuum mechanics based on the idea that pairs of particles exert forces on each other across a finite distance. The equation of motion in the peridynamic model is an integro-differential equation. In this paper, a notion of a peridynamic stress tensor derived from nonlocal interactions is defined. At any point in the body, this stress tensor is obtain...

An active conducting medium is one where the resistance (conductance) of the medium is modified by the current (flow) and in turn modifies the flow, so that the classical linear laws relating current and resistance, e.g., Ohm's law or Darcy's law, are modified over time as the system itself evolves. We consider a minimal model for this feedback coupling in terms of two parameters that character...

We construct a Q = 1 supersymmetry and U(1)5 global symmetry preserving deformation of the type IIB matrix model. This model, without orbifold projection, serves as a nonperturbative regularization forN = 4 supersymmetric Yang-Mills theory in four Euclidean dimensions. Upon deformation, the eigenvalues of the bosonic matrices are forced to reside on the surface of a hypertorus. We explicitly sh...

In this paper we introduce a simple continuum model for swarming of organisms in which there is a nonlocal aggregation term with an asymmetric sensing kernel countered by a nonlinear diffusion. The model can be thought of as capturing the dynamics of organisms that aggregate responding to visual cues and whose field of vision is predominantly in the direction of motion. The model has a variety ...

Nonlocal continua have been proposed to offer a more realistic model for the electrostatic response of solutions such as the electrolyte solvents prominent in biology and electrochemistry. In this work, we review three nonlocal models based on the Landau–Ginzburg framework which have been proposed but not directly compared previously, due to different expressions of the nonlocal constitutive re...

*Correspondence: [email protected] School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, P.R. China Abstract This paper studies the spectral problem of a class of fractional differential equations from nonlocal continuummechanics. By applying the spectral theory of compact self-adjoint operators in Hilbert spaces, we show that the spectrum of this problem consists of ...

An algorithm is developed for performing calculations for the nonlocal electrostatic solvation theory of an ion in a cavity, accounting for electrostatic boundary conditions. The latter implies an induced charge distribution on the cavity surface as well as an induced volume charge distribution in the medium. This approach is validated by a variational derivation which also provides a general e...