The Heisenberg XXZ model is a chain model with nearest-neighbor interactions. Its thermodynamics is exactly obtained via Bethe ansatz. Recently, we developed a method to derive the hightemperature expansion of the grand potential per site of translationally invariant chain models, with periodic boundary conditions. Here we apply this approach to the XXZ model with periodic boundary conditions f...

We investigate the exploration problem of a short-sighted mobile robot moving about in an unknown cellular room. In order to explore a cell, the robot must enter it. Once inside, the robot knows which of the 4 adjacent cells exist and which are boundary edges. The robot starts from a specified cell adjacent to the room’s outer wall; it visits each cell, and returns to the start. Our interest is...

Vehicles accelerating from a high density region in a two lanes system selforganize to a throughput which is equivalent to the the maximum throughput of a closed system with periodic boundary conditions. This holds for both a symmetric and asymmetric set of rules deening the exchange and interactions of the two lanes.

Transparent boundary conditions (TBCs) for general Schrr odinger{ type equations on a bounded domain can be derived explicitly under the assumption that the given potential V is constant on the exterior of that domain. In 1D these boundary conditions are non{local in time (of memory type). Existing discretizations of these TBCs have accuracy problems and render the overall Crank{Nicolson nite d...

When can a given finite region consisting of cells in a regular lattice (triangular, square, or hexagonal) in [w’ be perfectly tiled by tiles drawn from a finite set of tile shapes? This paper gives necessary conditions for the existence of such tilings using boundary inuariants, which are combinatorial group-theoretic invariants associated to the boundaries of the tile shapes and the regions t...

The formalism of Greensite for treating the spacetime signature as a dynamical degree of freedom induced by quantum fields is considered, for spacetimes with nontrivial topology of the kind R ×T1, for varying D. It is shown that a dynamical origin for the Lorentzian signature is possible in the five-dimensional space R × T with small torus radius (periodic boundary conditions), as well as in fo...

The existence and Hausdorff dimension of the global attractor for discretization of a damped wave equation with the periodic nonlinearity under the periodic boundary conditions are studied for any space dimension. The obtained Hausdorff dimension is independent of the mesh sizes and the space dimension and remains small for large damping, which conforms to the physics.

The integrability of the one-dimensional long range supersymmetric t-J model has previously been established for both open systems and those closed by periodic boundary conditions through explicit construction of its integrals of motion. Recently the system has been extended to include the effect of magnetic flux, which gives rise to a closed chain with twisted boundary conditions. While the t-...

In this article, Adomian decomposition method is successfully applied to find an approximate analytical solution of a Stefan problem subject to periodic boundary condition. By using initial and boundary conditions, the explicit solutions of the temperature distribution and the position of moving interface are evaluated and numerical results are depicted graphically. The method performs extremel...

Asymptotics and functional form of correlators in the XX-spin chain of finite length. Abstract We verify the functional form of the asymptotics of the spin-spin equal-time correlation function for the XX-chain, predicted by the hypothesis of conformal invariance at large distances and by the bosonization procedure. We point out that bosonization pocedure also predicts the functional form of the...