where u can be interpreted as the velocity field of an incompressible fluid motion, and p is then the associated pressure, the constant μ is the viscosity coefficient of the fluid. For simplicity, we consider homogenous Dirichlet boundary condition for the velocity, i.e. u|∂Ω = 0 and μ = 1. The conditions for the well posedness is known as inf-sup condition or Ladyzhenskaya-Babuška-Breezi (LBB)...

preprint numerics no. 1/2006 norwegian university of science and technology trondheim, norway The cubic nonlinear Schrödinger (nls) equation with periodic boundary conditions is solvable using Inverse Spectral Theory. The " nonlinear " spectrum of the associated Lax pair reveals topological properties of the nls phase space that are difficult to assess by other means. In this paper we use the i...

(1)  ut −∆u = f in Ω× (0, T ), u = 0 on ∂Ω× (0, T ), u(·, 0) = u0 in Ω. Here u = u(x, t) is a function of spatial variable x ∈ Ω and time variable t ∈ (0, T ). The Laplace differential operator ∆ is taking with respect to the spatial variable. For the simplicity of exposition, we consider only homogenous Dirichlet boundary condition and comment on the adaptation to Neumann and other type of b...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

It is shown that certain natural maps between the ideal, Gromov, and end boundaries of a complete CAT(0) space can fail to be either injective or surjective. Additionally the natural map from the Gromov boundary to the end boundary of a complete CAT(−1) space can fail to be either injective or surjective.

We solve the spectrum of quantum spin chains based on representations of the TemperleyLieb algebra associated with the quantum groups Uq(Xn) for Xn = A1, Bn, Cn and Dn. The tool is a modified version of the coordinate Bethe Ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up ...

In this paper we consider the (2D and 3D) exterior problem for the non homogeneous wave equation, with a Dirichlet boundary condition and non homogeneous initial conditions. First we derive two alternative boundary integral equation formulations to solve the problem. Then we propose a numerical approach for the computation of the extra “volume” integrals generated by the initial data. Finally, ...

The hard square model in statistical mechanics has been investigated for the case when the activity z is −1. For cyclic boundary conditions, the characteristic polynomial of the transfer matrix has an intriguingly simple structure, all the eigenvalues x being zero, roots of unity, or solutions of x 3 = 4 cos 2 (πm/N). Here we tabulate the results for lattices of up to 12 columns with cyclic or ...

We study dynamical aspects of the q-state Potts model on an n × n box at its critical βc(q). Heat-bath Glauber dynamics and cluster dynamics such as Swendsen–Wang (that circumvent low-temperature bottlenecks) are all expected to undergo “critical slowdowns” in the presence of periodic boundary conditions: the inverse spectral gap, which in the subcritical regime is O(1), should at criticality b...

Using Monte Carlo techniques, the critical Binder cumulant U∗ of isotropic nearest–neighbour Ising models on square and triangular lattices is studied. For rectangular shapes, employing periodic boundary conditions, U∗ is found to show the same dependence on the aspect ratio for both lattice types. Similarly, applying free boundary conditions for systems with square as well as circular shapes f...