To determine the deformation of a body from the system of differential equations governing its thermo-mechanical deformations, we need side conditions such as boundary conditions. The most frequently employed boundary conditions are those of place and/or traction in a purely mechanical problem and of temperature and/or heat flux in a thermal problem. These and other more familiar mechanical bou...

A review is presented of some recent progress in spectral geometry on manifolds with boundary: local boundary-value problems where the boundary operator includes the effect of tangential derivatives; application of conformal variations and other functorial methods to the evaluation of heat-kernel coefficients; conditions for strong ellipticity of the boundary-value problem; fourth-order operato...

non-fourier heat transfer analysis of functionally graded (fg) spherical shells subjected to the radiative-convective boundary conditions at their inner and outer surfaces are presented. it is assumed that the material properties have continuous variations along the thickness direction. the incremental differential quadrature method (idqm) as an accurate and computationally efficient numerical ...

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 ...

For one-dimensional p-Laplacian with weights in Lγ : L 0, 1 ,R 1 ≤ γ ≤ ∞ balls, we are interested in the extremal values of the mth positive half-eigenvalues associated with Dirichlet, Neumann, and generalized periodic boundary conditions, respectively. It will be shown that the extremal value problems for half-eigenvalues are equivalent to those for eigenvalues, and all these extremal values a...

Immersing a physical system in a heat bath results in the fields acquiring different properties according to their statistics. E.g., finite-temperature bosonic fields obey periodic boundary conditions, while fermionic fields satisfy antiperiodic b.c.’s. Such a distinction can be seen also at the level of the Green’s functions. Depending on the field’s statistics, thermal propagators obey either...

The Cauchy problem for the 2D Boussinesq system with periodic boundary conditions is studied. The global existence and uniqueness of a solution with initial data (u(0), θ(0)) ∈ Φ(α) is established, where Φ(α) is the space of functions the kth Fourier coefficients of which decay at infinity as 1 |k|α , α > 2. It is proved that the solution becomes analytic at any positive time. Bibliography: 10 ...