Related papers: Electromagnetic space-time crystals. II. Fractal c…
We consider a two-dimensional layer of dipolar particles in the regime of strong dipole moments. Here we can describe the system using classical methods and determine the crystal structure that minimizes the total energy. The dipoles are…
Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…
Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics…
We study boundary element methods for time-harmonic scattering in $\mathbb{R}^n$ ($n=2,3$) by a fractal planar screen, assumed to be a non-empty bounded subset $\Gamma$ of the hyperplane $\Gamma_\infty=\mathbb{R}^{n-1}\times \{0\}$. We…
We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth condition. In $\mathbb R^{3+1}$ we obtain the sharp estimate and in higher dimensions improve the previous results.
A formalism in terms of Hertz potentials is presented describing sum-frequency generation in a uniaxial non-linear crystal. A scheme is proposed consisting in aligning the side-walk propagation of extraordinary waves in combination with…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
By means of the offered analytical method the determinant relation for a phase velocities of elastic waves for an arbitrary propagation directions in a piezoelectric crystal are received. The phase velocities of three normal elastic waves…
The fractal cosmological model which accounts for observable fractal properties of the Universe's large-scale structure is constructed. In this framework these properties are consequences of the rotary symmetry of charged scalar meson…
Analysis on fractals is a growing field, with hints of potential for widespread applicability across all of STEM. One of the most heavily researched type of fractals are the nested fractals, fractal shapes defined by virtue of being made of…
Point-form relativistic quantum mechanics is used to derive an expression for the electromagnetic form factor of a pseudoscalar meson for space-like momentum transfers. The elastic scattering of an electron by a confined quark-antiquark…
This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…
Rayleigh waves are considered for crystals possessing at least one plane of symmetry. The secular equation is established explicitly for surface waves propagating in any direction of the plane of symmetry, using two different methods. This…
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In…
Analytic representation formulas and power series are developed describing the band structure inside non-magnetic periodic photonic three-dimensional crystals made from high dielectric contrast inclusions. Central to this approach is the…
We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary…
Analytic first and second derivatives of the energy are developed for the fragment molecular orbital method interfaced with molecular mechanics in the electrostatic embedding scheme at the level of Hartree-Fock and density functional…
Accurate analytic approximations are developed for the band gap boundaries and surface waves of a 1D photonic crystal, making use of the semiclassical theory recently developed by the authors: [Phys. Rev. E {69} (2004) 016612 and {70}…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have been found to describe and model many systems in nature, in particular fluid mechanics and geophysical related geometrical objects, like the convective boundary…