Up to now, the analytical calculation has been made only when the magnets own parallel magnetization directions. We have succeeded in two new results of first importance for the analytical calculation: the torque between two magnets, and the force components and torque when the magnetization directions are perpendicular. The last result allows the analytical calculation of the interactions when...

A standard approach for solving linear partial differential equations is to split the solution into a homogeneous solution and a particular solution. Motivated by the method of fundamental solutions for solving homogeneous equations, we propose the similar approach using the method of particular solutions for solving linear inhomogeneous differential equations without the need of finding the ho...

We propose a conceptually new method for solving nonlinear inverse scattering problems (ISPs). The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant mathematical formalism. We formulate the ISP as a problem whose goal is to determine an unknown and, generally, nonlocal interaction potential V from external scattering data. We then utilize the one...

The ability of grains to rotate can play a crucial role on the collective behavior of granular media. It has been observed in computer simulations that imposing a torque at the contacts modifies the force chains, making support chains less important. In this work we investigate the effect of a gradual hindering of the grains rotations on the so-called critical state of soil mechanics. The criti...

We present an enhanced moment-closure approximation to the finiteextensiblenonlinear-elastic (FENE) models of polymeric fluids. This new moment-closure method involves the perturbation of the equilibrium probability distribution function (PDF), which takes into account of the drastic split into two spikes and centralized behavior under the large macroscopic flow effects. The resulting macroscop...

By representing a system of budget shares as an approximate factor model we determine its rank, i.e. the number of common functional forms, or factors and we estimate a base of the factor space by means of approximate principal components. We assume that the extracted factors span the same space of basic Engel curves representing the fundamental forces driving consumers’ behaviour. We identify ...

Robustness in control systems is without doubt a property as important as stability; it is the property by which a system preserves an acceptable behavior under uncertainty, external disturbances, measurement noise, etc. Generally speaking, uncertainty and disturbances may take different forms and meanings, especially for the theoretician and for the practitioner. Uncertainty may stem from impr...

We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra. As applications, we compute Shimura curve parametrizations of elliptic curves over a totally real field, including the image of CM points, and equations for Shimura curves.

In the spirit of previous papers, but using more general field configurations, the non-linear O(3) model in (2+1)-D, modified by the addition of both a potential-like term and a Skyrme-like term, is considered. The instanton solutions are numerically evolved in time and some of their stability properties studied. They are found to be stable, and a repulsive force is seen to exist among them. Th...

The useful and efficient method of Finite Element (FEM) has a drawback for dynamic analysis of complex structures, especially in the medium and high frequency range. To overcome this fundamental difficulty, application of Statistical Energy Analysis (SEA) and power flow technique has been suggested. As the SEA is based on the average response of structure and statistical properties of its reson...