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.

We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between ...

We consider the backreaction of the magnetic field on the magnetic dynamo coefficients and the role of boundary conditions in interpreting whether numerical evidence for suppression is dynamical. If a uniform field in a periodic box serves as the initial condition for modeling the backreaction on the turbulent EMF, then the magnitude of the turbulent EMF and thus the dynamo coefficient α, have ...

We present a new method to simulate repetitive ferromagnetic structures. This macro geometry approach combines treatment of short-range interactions (i.e. the exchange field) as for periodic boundary conditions with a specification of the arrangement of copies of the primary simulation cell in order to correctly include effects of the demagnetizing field. This method (i) solves a consistency pr...

A new theorem is applied to the Kuramoto-Sivashinsky equation with L-periodic boundary conditions, proving the existence of an asymptotically complete inertial manifold attracting all initial data. Combining this result with a new estimate of the size of the globally absorbing set yields an improved estimate of the dimension, N ∼ L.

We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f :R→ R is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant β > 0 such that u f (u) > 0 whenever |u| ≥ β. For such an equation we prove that ifN is an odd integer...

We study a linear fractional differential equation with a periodic boundary condition and give the explicit form of the solution and the corresponding Green’s function. Using some properties of the Green’s function we present some new comparison results.

The nonlinear eigenvalue problem of the differential equation ( |x′|p−2 x′ )′ + (λ+ c(t)) |x|p−2 x = 0, p > 1, with respect to the periodic boundary conditions: x(0) = x(T ), x′(0) = x′(T ), or to the antiperiodic boundary conditions: x(0) = −x(T ), x′(0) = −x′(T ) are considered. Various results on the set of eigenvalues concerning both problems are presented. Some estimates are given for the ...

We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of Þxed or free boundary curves in R, S and H. The algorithm makes no restriction on the genus and can handle singular triangulations. For a discrete harmonic map a conjugation process is presented leading in case of minimal surfaces additionally to instable solutions of the free boundary value problem fo...