Cutoff for General Spin Systems with Arbitrary Boundary Conditions

Cutoff for General Spin Systems with Arbitrary Boundary Conditions

The cutoff phenomenon describes a sharp transition in the convergence of a Markov chain to equilibrium. In recent work, the authors established cutoff and its location for the stochastic Ising model on the d-dimensional torus (Z/nZ) for any d ≥ 1. The proof used the symmetric structure of the torus and monotonicity in an essential way. Here we enhance the framework and extend it to general geom...

On decay of correlations for unbounded spin systems with arbitrary boundary conditions

We propose a method based on cluster expansion to study the truncated correlations of unbounded spin systems uniformly in the boundary condition and in a possible external eld. By this method we study the spin-spin truncated correlations of various systems, including the case of innnite range simply integrable interactions, and we show how suitable boundary conditions and/or external elds may i...

Bending Analysis of Laminated Composite Plates with Arbitrary Boundary Conditions

It is well known that for laminated composite plates a Levy-type solution exists only for cross-ply and antisymmetric angle-ply laminates. Numerous investigators have used the Levy method to solve the governing equations of various equivalent single-layer plate theories. It is the intension of the present study to introduce a method for analytical solutions of laminated composite plates with ar...

Subelliptic boundary conditions for Spin

The ∂̄-Neumann problem has served as the technical foundation and a source of inspiration for research in several complex variables since the seminal work of Spencer, Kohn and Nirenberg. In this note we describe a generalization of these boundary conditions to Spin C -manifolds whose boundaries satisfy appropriate convexity conditions. Our results demonstrate the remarkable robustness of the ∂̄Ne...

Analysis of Free Vibration of Triangular Plates with Non-Uniform Linear Thickness and Arbitrary Boundary Conditions