An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are u...

I present a calculation of the interfacial width within the capillary wave (Gaussian) approximation. The calculation is done on rectangular lattices of size L1 times L2, with periodic boundary conditions.

The nonlinear differential equation x" = f(t, x(t)), f being 22T-periodic in t, is considered for the existence of 27T-periodic solutions. The equation is reduced to an equivalent system of two Hammerstein equations. The case of nonlinear perturbation at resonance is also discussed.

Let Wn be a random walk on the locally free group with m generators subject to periodic boundary conditions, and let T (Wn) be the set of removable elements. We prove that limn→∞ E(#T (Wn)) m ≤ 0.32893 for m ≥ 4. This result disproves a conjecture (due to Vershik et. al. [3]) that the limit tends to 1 3 as m → ∞.

In this paper, we consider one-dimensional attractor of a non-autonomous second order strongly damped lattice system with periodic driving force under Neumann boundary condition or periodic boundary condition. We obtain the existence of a global attractor and prove this attractor is homeomorphic to the circle.