The Laplace-Green's function methods of Paper I are extended to describe polymers confined in interacting, impenetrable cylindrical geometries, whose treatment is far more challenging than the slit and box geometries considered in Paper I. The general methods are illustrated with calculations (as a function of the polymer-surface interaction) of the free energy of confinement, the radial densit...

This paper discusses the multiscale method for the time-dependent Maxwell’s equations with memory effects in composite materials. The main difficulty is that one cannot use the usual multiscale asymptotic method (cf. [25, 4]) to solve this problem, due to the complication of the memory terms. The key steps addressed in this paper are to transfer the original integrodifferential equations to the...

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

The inverse problem of estimating dielectric constants of explosives using boundary measurements of one component of the scattered electric field is addressed. It is formulated as a coefficient inverse problem for a hyperbolic differential equation. After applying the Laplace transform, a new cost functional is constructed and a variational problem is formulated. The key feature of this functio...

Determining the shape of an inclusion within a conducting medium from voltage and current measurements on the accessible boundary of the medium can be modeled as an inverse boundary value problem for the Laplace equation. We present a solution method for such an inverse boundary value problem with a generalized impedance boundary condition on the inclusion via boundary integral equations. Both ...

concrete deformation due to temperature and moisture condition will always develop simultaneously and interactively. the environmentally (hygral and thermally) induced stress and deformation are essential to concrete durability. to simulate the deformation of concrete caused by the coupling effect of temperature and moisture, a numerical simulation approach is proposed comprising analytical pro...