We study the averaged mean curvature flow, also called the volume preserving mean curvature flow, in the particular setting of axisymmetric surfaces embedded in R3 satisfying periodic boundary conditions. We establish analytic well–posedness of the flow within the space of little-Hölder continuous surfaces, given rough initial data. We also establish dynamic properties of equilibria, including ...

This paper describes sharp inequalities for the trace of Sobolev functions on the boundary of a bounded region Ω ⊂ R . The inequalities bound (semi-)norms of the boundary trace by certain norms of the function and its gradient on the region and two specific constants kρ and kΩ associated with the domain and a weight function. These inequalities are sharp in that there are functions for which eq...

In this work, simple exact results are presented for summations in two-particle potential with long-range interactions. Polygamma function is used to evaluate summations. Results are found when a periodic media is consider. Periodic boundary conditions are applied by symmetric repetitions of a central cell. Contributions over all space are used in the problem. The potential depends strongly on ...

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.