Related papers: Boundary dynamics and multiple reflection expansio…
A review is presented of some recent progress in spectral geometry on manifolds with boundary: local boundary-value problems where the boundary operator includes the effect of tangential derivatives; application of conformal variations and…
We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered - one…
We consider a one-dimensional exclusion dynamics in mild contact with boundary reservoirs. In the diffusive scale, the particles' density evolves as the solution of the heat equation with non-linear Robin boundary conditions. For…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
We consider a boundary-value problem for the second order elliptic differential operator with rapidly oscillating coefficients in a domain $\Omega_{\epsilon}$ that is $\epsilon-$periodically perforated by small holes. The holes are divided…
We prove geometric upper bounds for the Poincar\'e and Logarithmic Sobolev constants for Brownian motion on manifolds with sticky reflecting boundary diffusion i.e. extended Wentzell-type boundary condition under general curvature…
We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere…
We present an integrable Hamiltonian which describes the sinh-Gordon model on the half line coupled to a non-linear oscillator at the boundary. We explain how we apply Sklyanin's formalism to a dynamical reflection matrix to obtain this…
This article provides a functional analytical framework for boundary integral equations of the heat equation in time-dependent domains. More specifically, we consider a non-cylindrical domain in space-time that is the $C^2$-diffeomorphic…
We investigate how dynamic correlations of hard-core bosonic excitation at finite temperature are affected by additional interactions besides the hard-core repulsion which prevents them from occupying the same site. We focus especially on…
In this note, we demonstrated for the first time that one can derive an expression for the effective diffusion coefficient, equal to the Lifson-Jackson formula, using a subsequent homogenization of the 1D reaction-diffusion-advection…
Consider a finite system of diffusing particles coupled through a reactive boundary. Each particle is reflected, but may react with the boundary according to a killing mechanism which depends on the current reactivity of the boundary and…
We explore boundary scattering in the sine-Gordon model with a non-integrable family of Robin boundary conditions. The soliton content of the field after collision is analysed using a numerical implementation of the direct scattering…
We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the…
We reconsider four-dimensional scalar field theory in presence of Robin boundary conditions on two parallel plates. These boundary conditions are directly imposed in the path integral definition of the theory via auxiliary fields living on…
The investigation of boundary breather states of the sinh-Gordon model restricted to a half-line is revisited. Properties of the classical boundary breathers for the two-parameter family of integrable boundary conditions are reviewed and…
The results on the heat kernel expansion for the electromagnetic field in the background of dielectric media are briefly reviewed. The common approaches to the calculation of the heat kernel coefficients are discussed from the viewpoint of…
We generalize to multi-commutators the usual Lieb-Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expansions) in order to estimate…
We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been…
The boundary integral method is extended to derive closed integro-differential equations applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp…