Related papers: On the influence of uniform singularity distributi…
The three-dimensional potential equation, motivated by representations of quantum mechanics, is investigated in four different scenarios: (i) In the usual Euclidean space $\mathbb{E}_{3}$ where the potential is singular but invariant under…
The one-loop effective potential calculated for a generic model that originates from 5-dimensional theory reduced down to 4 dimensions is considered. The cut-off and dimensional regularization schemes are discussed and compared. It is…
We study the isoperimetric problem in product spaces equipped with the uniform distance. Our main result is a characterization of isoperimetric inequalities which, when satisfied on a space, are still valid for the product spaces, up a to a…
We report on systematic measurements of the distribution of normal forces exerted by granular material under uniaxial compression onto the interior surfaces of a confining vessel. Our experiments on three-dimensional, random packings of…
The electrostatic force on a spherical particle near a planar surface is calculated for the cases of a uniform electric field applied in either normal or tangential direction to the surface. The particle and suspending media are assumed to…
A method for taking into account the long-range potential of atoms in the framework of the hard-sphere model is proposed. It is shown that thermodynamic quantities can be represented as a sum of three contribution: that of an ideal gas, the…
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space R^{m+1} was constructed recently, including a higher dimensional analogue of the logarithmic function in the complex…
We present several closed-form expressions of useful mass distributions. These include the potentials and accelerations of circular rings and arcs, the potentials of uniform density rings and arcs at arbitrary eccentricities, and the…
We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the…
In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete…
We present a systematic investigation of the distribution of normal forces at the boundaries of static packings of spheres. A new method for the efficient construction of large hexagonal-close-packed crystals is introduced and used to study…
This paper derives a finite-strain plate theory consistent with the principle of stationary three-dimensional (3-D) potential energy under general loadings with a third-order error. Staring from the 3-D nonlinear elasticity (with both…
This paper presents a study of acoustic scattering by a cylinder of either infinite or finite length near a flat pressure-release surface. A novel self-consistent method is developed to describe the multiple scattering interactions between…
This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for…
For problems with multiple bodies, the current integral approach needs the use of auxiliary potential functions in order to have an individual force formula for each body. While the singularity approach, based on an extension of the…
An integral equation-based numerical method for scattering from multi-dielectric cylinders is presented. Electromagnetic fields are represented via layer potentials in terms of surface densities with physical interpretations. The existence…
We derive the closed form solutions for the surface area, the capacitance and the demagnetizing factors of the ellipsoid immersed in the Euclidean space R^3. The exact solutions for the above geometrical and physical properties of the…
We use an exact solution of the elastic membrane shape equation, representing the curvature, which will serve as a quantum potential in the quantum mechanical two dimensional Schrodinger equation for a (quasi-) particle on the surface of…
We investigate the distribution of rational points on singular cubic surfaces, whose coordinates have few prime factors. The key tools used are universal torsors, the circle method and results on linear equations in primes.
In a wide class of potentials the exact asymptotic dependence on finite distance R from scattering center is established for outgoing differential flux. It is shown how this dependence is eliminated by integration over solid angle for total…