相关论文: Differential approach to on-shell scalar products …
In this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the…
We present numerical results for the six-vertex model with a variety of boundary conditions. Adapting an algorithm proposed by Allison and Reshetikhin for domain wall boundary conditions, we examine some modifications of these boundary…
This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The model's partition function is shown to obey a system of PDEs resembling the celebrated…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
We discuss the influence of boundary conditions on the continuum limit of the six-vertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences…
We consider nonlinear viscoelastic materials of differential type and for some special models we derive exact solutions of initial boundary value problems. These exact solutions are used to investigate the reasons of non-existence of global…
Several models for the pricing of derivative securities in illiquid markets are discussed. A typical type of nonlinear partial differential equations arising from these investigation is studied. The scaling properties of these equations are…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
In this paper, we propose simple numerical algorithms for partial differential equations (PDEs) defined on closed, smooth surfaces (or curves). In particular, we consider PDEs that originate from variational principles defined on the…
The partition function of the six-vertex model on a square lattice with domain wall boundary conditions (DWBC) is rewritten as a hermitean one-matrix model or a discretized version of it (similar to sums over Young diagrams), depending on…
We consider distributions on $\R^n\setminus{0}$ which satisfy a given set of partial differential equations and provide criteria for the existence of extensions to $\R^n$ that satisfy the same set of equations on $\R^n$. We use the results…
In this paper we study a new class of shell models, defined in terms of two complex dynamical variables per shell, transporting positive and negative helicity respectively. The dynamical equations are derived from a decomposition into…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
The interplay between off-shell and on-shell unfolded systems is analysed. The formulation of invariant constraints that put an off-shell system on shell is developed by adding new variables and derivation in the target space, that extends…
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the…
The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a…
We consider the enumeration of states in the Brubaker-Bump-Friedberg six-vertex model, whose boundary conditions are determined by an integer partition. In general, we find the number of states is a polynomial in the largest part of the…
We consider the five-vertex model on a rectangular domain of the square lattice, with the so-called `scalar-product' boundary conditions. We address the evaluation of the free-energy density of the model in the scaling limit, that is when…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to…