Related papers: Nonlinear multidomain model for nerve bundles with…
Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present…
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate…
Real-world machine learning applications often involve deploying neural networks to domains that are not seen in the training time. Hence, we need to understand the extrapolation of nonlinear models -- under what conditions on the…
A single axon can generate branches connecting with plenty synaptic targets. Process of branching is very important for making connections in central nervous system. The interstitial branching along primary axon shaft occurs during nervous…
We propose a mechanism for mechanical regulation at the membrane of living cells, based on the exchange of membrane area between the cell membrane and a membrane reservoir. The reservoir is composed of invaginated membrane microdomains…
Within the framework of the Landau-Ginzburg-Devonshire approach we explore the impact of elastic anisotropy, electrostriction, flexoelectric couplings, and mismatch strain on the domain structure morphology in ferroelectric core-shell…
Using a new scheme of the derivation of the non-linear $\sigma$-model we consider the electron motion in a random magnetic field (RMF) in two dimensions. The derivation is based on writing quasiclassical equations and representing their…
Mode-division multiplexing (MDM) is seen as a possible solution to satisfy the rising capacity demands of optical communication networks. To make MDM a success, fibers supporting the propagation of a huge number of modes are of interest.…
Myosin motor proteins drive vigorous steady-state fluctuations in the actin cytoskeleton of cells. Endogenous embedded semiflexible filaments such as microtubules, or added filaments such as single-walled carbon nanotubes are used as novel…
We investigate nonlinear magnetoelastic wave dynamics and electrically tunable soliton excitations in hexagonal multiferroic media. By varying the magnetoelastic coupling strength and using a coupled magnetoelastic-ferroelectric continuum…
We construct a nonlinear $\sigma$ model to describe a system of non-interacting electrons propagating in the presence of random magnetic flux. We find a term describing the long ranged logarithmic interaction between the topological density…
This paper deals with the mathematical modelling of signal propagation in nerve fibres. Due to the complexity of the processes where electrical, mechanical, and thermal effects are coupled, a phenomenological approach helps to build…
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function which can interpolate between the two limiting cases of load redistribution, the global and the local load sharing…
Nonlinear reaction-diffusion systems admit a wide variety of spatiotemporal patterns or structures. In this lecture, we point out that there is certain advantage in studying discrete arrays, namely cellular neural/nonlinear networks (CNNs),…
Collective behavior of proteins on biomembranes is usually studied within the spontaneous curvature model. Here we consider an alternative phenomenological approach, which accounts consistently for partial ordering of proteins as well as…
Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic constants,…
The Hubbard model is a prototype for strongly correlated electrons in condensed matter, for molecules and fermions or bosons in optical lattices. While the equilibrium properties of these systems have been studied in detail, the excitation…
We study a model of contraction-based cell motility inside a microchannel to investigate the regulation of cell polarization and motion by the mechanical resistance of the environment. A positive feedback between the asymmetry of the…
We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically-coupled pendulums without any restrictions to their amplitudes (excluding a vicinity of $\pi$). Although this…