相关论文: Dendrites and conformal symmetry

The cable equation describes the voltage in a straight cylindrical cable, this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some…

The cable equation is a second order, parabolic, partial differential equation that describes the evolution of voltage in the dendrite of a neuron. Here we look at the various ways in which lambda(space constant/ variable space…

In this paper we consider the Schr\"odinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schr\"odinger equation with…

Mesoscopic systems and large molecules are often modeled by graphs of one-dimensional wires, connected at vertices. In this paper we discuss the solutions of the Schr\"odinger equation on such graphs, which have been named "quantum…

Signal propagation in neuronal dendrites represents the basis for interneuron communication and information processing in the brain. Here we take into account charge inhomogeneities arising in the vicinity of ion channels in cytoplasm and…

We propose a simple graphical approach to steady state solutions of the cable equation for a general model of dendritic tree with tapering. A simple case of transient solutions is also briefly discussed.

The Schr\"odinger equation is universally accepted due to its excellent predictions aligning with observed results within its defined conditions. Nevertheless, it does not seem to possess the simplicity of fundamental laws, such as Newton's…

We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide…

The essence of the potential algebra concept [3] is that quantum mechanical free motions of scalar particles on curved surfaces of given isometry algebras can be mapped on 1D Schroedinger equations with particular potentials. As long as the…

According to classical non-relativistic Schr\"odinger equation, any local perturbation of wave function instantaneously affects all infinite region, because this equation is of parabolic type, and its solutions demonstrate infinite speed of…

A theory for conduction electron scattering by inhomogeneous crystal lattice strains is developed, based on the differential geometric treatment of deformations in solids. The resulting fully covariant Schr\"odinger equation shows that the…

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as…

The Derivative Nonlinear Schr\"odinger equation is an $L^2$-critical nonlinear dispersive equation model for Alfv\'en waves in space plasmas. Recent numerical studies on an $L^2$-supercritical extension of this equation provide evidence of…

For the first time, a nonlinear Schr\"odinger equation of the general form is considered, depending on time and two spatial variables, the potential and dispersion of which are specified by two arbitrary functions. This equation naturally…

Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schr\"odinger equation with a quintic nonlinearity. These patterns include bright pulses, fronts and dark solitons. The evolution of the wave…

Electronic transport through a material depends on the response to local perturbations induced by defects or impurities in the material. The scattering processes can be described in terms of phase shifts and corresponding cross sections.…

We analyze the matter wave transmission above a step potential within the framework of the cubic-nonlinear Schr\"odinger equation. We present a comprehensive analysis of the corresponding stationary problem based on an exact second-order…

The discrete Schr\"odinger equation on a two-dimensional honeycomb lattice is a fundamental tight-binding approximation model that describes the propagation of waves on graphene. For free evolution, we first show that the degenerate…

Schr\"odinger connections are a special class of affine connections, which despite being metric incompatible, preserve length of vectors under autoparallel transport. In the present paper, we introduce a novel coordinate-free formulation of…

We study symmetry properties of the Schr\"odinger equation with the potential as a new dependent variable, i.e., the transformations which do not change the form of the class of equations. We also consider systems of the Schr\"odinger…