This paper presents a method for inverting ground penetrating radargrams in terms of one-dimensional profiles. We resort to a special type of linearization of the damped E-field wave equation to solve the inverse problem. The numerical algorithm for the inversion is iterative and requires the solution of several forward problems, which we evaluate using the matrix propagation approach. Analytic...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

The phase behavior of Ising spin fluids is studied in the presence of an external magnetic field with the integral equation method. The calculations are performed on the basis of a soft mean spherical approximation using an efficient algorithm for solving the coupled set of the Ornstein-Zernike equations, the closure relations, and the external field constraint. The phase diagrams are obtained ...

Fe3O4 nanofluid fully developed forced convection inside a copper tube is empirically investigated under the effect of a magnetic field. All of the investigations are performed under laminar flow regime (670≤Re≤1700) and thermal boundary conditions of the tube with uniform thermal flux. The tube is under the effect of a magnetic field in certain points. This research aims to study the effect of...

Transverse magnetic (TM) scattering of an electromagnetic wave from a periodic dielectric diffraction grating can mathematically be described by a volume integral equation. This volume integral equation, however, in general fails to feature a weakly singular integral operator. Nevertheless, after a suitable periodization, the involved integral operator can be efficiently evaluated on trigonomet...

The scattering of a time-harmonic E-wave by a dielectric cylinder is solved by a single integral equation. Two alternatives are investigated to derive such a single integral equation. Interest is focused on the fields inside the dielectric. In this case the integral equation has only the incident electric field as its source term.

A field theoretic renormalization group method is presented which is capable of dealing with crossover problems associated with a change in the upper critical dimension. The method leads to flow functions for the parameters and coupling constants of the model which depend on the set of parameters which characterize the fixed point landscape of the underlying problem. Similar to Nelson’s traject...