We prove that a certain finite difference scheme converges to the weak solution of the Cauchy problem on a finite interval with periodic boundary conditions for the Camassa– Holm equation ut−uxxt +3uux−2uxuxx−uuxxx = 0 with initial data u|t=0 = u0 ∈ H1([0, 1]). Here it is assumed that u0 − u′′ 0 ≥ 0 and in this case, the solution is unique, globally defined, and energy preserving.

Let f , U and C represent, respectively, the free energy, the internal energy and the specific heat of the critical Ising model on the square M×N lattice with periodic boundary conditions, and f∞ represents f as M,N → ∞. We find that f , U and C can be written as: N(f −f∞) = ∑ ∞ i=1 fi/N 2i−1, U = − √ 2+ ∑ ∞ i=1 ui/N 2i−1 and C = 8 π lnN+ ∑ ∞ i=0 ci/N i andNf and U are well-defined odd function...

Taking the isotropic limit ∆ → 1 in a recent representation theoretic construction of Baxter’s Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX model. We show that quasi-periodic boundary conditions are needed to ensure convergence of the Q-operator construction and derive a quantum Wronskian relation which implies two different sets of Bet...

We show that the Markov semigroups generated by a large class of singular stochastic PDEs satisfy the strong Feller property. These include for example the KPZ equation and the dynamical Φ3 model. As a corollary, we prove that the Brownian bridge measure is the unique invariant measure for the KPZ equation with periodic boundary conditions.

In this paper, we prove the existence of solutions for impulsive fractional differential inclusions with anti-periodic boundary conditions by applying Bohnenblust-Karlin’s fixed point

The N-particle partition function of a one-dimensional δ-function bose gas is calculated explicitly using only the periodic boundary condition (the Bethe ansatz equation). The N-particles cluster integrals are shown to be the same as those by the thermal Bethe ansatz method.

We present a model for nonlocal diffusion with Dirichlet boundary conditions in a bounded smooth domain. We prove that solutions of properly re-scaled non local problems approximate uniformly the solution of the corresponding Dirichlet problem for the classical heat equation.

To make the ππ state with non-zero relative momentum as the leading exponential, we impose anti-periodic boundary condition on the pion, which is implemented by imposing G-parity or H-parity on the quark fields at the boundary. With this, we calculate the I = 2 ππ phase shift from lattice simulation by using Lüscher's formula.

In this study, an analytical modeling of two dimensional heat conduction in a hollow sphere, subjected to time dependent periodic boundary condition at the inner and the outer surfaces, is performed. The thermo physical properties of the material are assumed to be isotropic and homogenous. Also, the effects of the temperature oscillations frequency on the boundaries, the thickness variation of ...

We consider the ground states of the ferromagnetic XXZ chain with spin up boundary conditions in sectors with a fixed number of down spins. This forces the existence of a droplet of down spins in the system. We find the exact energy and the states that describe these droplets in the limit of an infinite number of down spins. We also prove that the droplet states, which were known to be separate...