Related papers: Exact Solution of an One Dimensional Deterministic…
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
We study the steady state of the abelian sandpile models with stochastic toppling rules. The particle addition operators commute with each other, but in general these operators need not be diagonalizable. We use their abelian algebra to…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
We investigate the properties of a two-state sandpile model subjected to a confining potential in two dimensions. From the microdynamical description, we derive a diffusion equation, and find a stationary solution for the case of a…
We present a procedure to calculate 1/d corrections to the two-particle properties around the infinite dimensional dynamical mean field limit. Our method is based on a modified version of the scheme of Ref. onlinecite{SchillerIngersent}}.…
In this paper we use fixed point tilings to answer a question posed by Michael Hochman and show that every one-dimensional effectively closed subshift can be implemented by a local rule in two dimensions. The proof uses the fixed-point…
Geometric model fitting is a fundamental research topic in computer vision and it aims to fit and segment multiple-structure data. In this paper, we propose a novel superpixel-guided two-view geometric model fitting method (called SDF),…
A review of a recent method is presented to construct certain exact solutions to the focusing nonlinear Schr\"odinger equation on the line with a cubic nonlinearity. With motivation by the inverse scattering transform and help from the…
We perform large scale numerical simulations of a directed version of the two-state stochastic sandpile model. Numerical results show that this stochastic model defines a new universality class with respect to the Abelian directed sandpile.…
This paper concerns exact differential equations. First, I define two types of functions which I have named Basic Function of Type One and Basic Function of Type Two. I then derive the property and theorems of these functions. Finally, by…
This survey is an extended version of lectures given at the Cornell Probability Summer School 2013. The fundamental facts about the Abelian sandpile model on a finite graph and its connections to related models are presented. We discuss…
A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is…
We introduce here a simple finite-dimensional feedback control scheme for stabilizing solutions of infinite-dimensional dissipative evolution equations, such as reaction-diffusion systems, the Navier-Stokes equations and the…
By using a decomposition of the transfer matrix of the two dimensional $q$-state Potts Model to $V^{\prime}_1$ and $V_2$ its determinant is calculated. Our result is a proof for a conjectured formula by Chang and Shrock in [14].
In this paper we present a method for deriving effective one-dimensional models based on the matrix product state formalism. It exploits translational invariance to work directly in the thermodynamic limit. We show, how a representation of…
We consider one-dimensional and two-dimensional models of the stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and…
We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations \cite{Borchardt:2015rxa}. The advantages of our method are illustrated with the help of…
The $A^{(1)}_{n-1}$ trigonometric vertex model with {\it generic non-diagonal} boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the…
We propose a numerical method to estimate one-point functions and the free-energy density of conformal field theories at finite temperature by solving the Kubo-Martin-Schwinger condition for the two-point functions of identical scalars. We…