219 research outputs found
Maxwell Equations in Complex Form of Majorana - Oppenheimer, Solutions with Cylindric Symmetry in Riemann S_{3} and Lobachevsky H_{3} Spaces
Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in
Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian
space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock -
Ivanenko. In this approach, the Maxwell equations are solved exactly on the
background of static cosmological Einstein model, parameterized by special
cylindrical coordinates and realized as a Riemann space of constant positive
curvature. A discrete frequency spectrum for electromagnetic modes depending on
the curvature radius of space and three parameters is found, and corresponding
basis electromagnetic solutions have been constructed explicitly. In the case
of elliptical model a part of the constructed solutions should be rejected by
continuity considerations. Similar treatment is given for Maxwell equations in
hyperbolic Lobachevsky model, the complete basis of electromagnetic solutions
in corresponding cylindrical coordinates has been constructed as well, no
quantization of frequencies of electromagnetic modes arises.Comment: 39 page
Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell
electrodynamics in vacuum is investigated within the matrix formalism. The
matrix form of electrodynamics includes three real 4 \times 4 matrices. Within
the squaring procedure we construct four formal solutions of the Maxwell
equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem
of separating physical electromagnetic waves in the linear space
\lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3}
is investigated, several particular cases, plane waves and cylindrical waves,
are considered in detail.Comment: 26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk,
Belaru
Field theory of massive and massless vector particles in the Duffin - Kemmer - Petiau formalism
Field theory of massive and massless vector particles is considered in the
first-order formalism. The Hamiltonian form of equations is obtained after the
exclusion of non-dynamical components. We obtain the canonical and symmetrical
Belinfante energy-momentum tensors and their nonzero traces. We note that the
dilatation symmetry is broken in the massive case but in the massless case the
modified dilatation current is conserved. The canonical quantization is
performed and the propagator of the massive fields is found in the Duffin -
Kemmer - Petiau formalism.Comment: 20 pages, typos corrected, a reference added, journal version,
accepted in Int.J.Mod.Phys.
The Coulomb-Oscillator Relation on n-Dimensional Spheres and Hyperboloids
In this paper we establish a relation between Coulomb and oscillator systems
on -dimensional spheres and hyperboloids for . We show that, as in
Euclidean space, the quasiradial equation for the dimensional Coulomb
problem coincides with the -dimensional quasiradial oscillator equation on
spheres and hyperboloids. Using the solution of the Schr\"odinger equation for
the oscillator system, we construct the energy spectrum and wave functions for
the Coulomb problem.Comment: 15 pages, LaTe
Two-body quantum mechanical problem on spheres
The quantum mechanical two-body problem with a central interaction on the
sphere is considered. Using recent results in representation
theory an ordinary differential equation for some energy levels is found. For
several interactive potentials these energy levels are calculated in explicit
form.Comment: 41 pages, no figures, typos corrected; appendix D was adde
Influence of the initial chemical conditions on the rational design of silica particles
The influence of the water content in the initial composition on the size of silica particles produced using the Stöber process is well known. We have shown that there are three morphological regimes defined by compositional boundaries. At low water levels (below stoichiometric ratio of water:tetraethoxysilane), very high surface area and aggregated structures are formed; at high water content (>40 wt%) similar structures are also seen. Between these two boundary conditions, discrete particles are formed whose size are dictated by the water content. Within the compositional regime that enables the classical Stöber silica, the structural evolution shows a more rapid attainment of final particle size than the rate of formation of silica supporting the monomer addition hypothesis. The clearer understanding of the role of the initial composition on the output of this synthesis method will be of considerable use for the establishment of reliable reproducible silica production for future industrial adoption
Facile control of silica nanoparticles using a novel solvent varying method for the fabrication of artificial opal photonic crystals
In this work, the Stöber process was applied to produce uniform silica nanoparticles (SNPs) in the meso-scale size range. The novel aspect of this work was to control the produced silica particle size by only varying the volume of the solvent ethanol used, whilst fixing the other reaction conditions. Using this one-step Stöber-based solvent varying (SV) method, seven batches of SNPs with target diameters ranging from 70 to 400 nm were repeatedly reproduced, and the size distribution in terms of the polydispersity index (PDI) was well maintained (within 0.1). An exponential equation was used to fit the relationship between the particle diameter and ethanol volume. This equation allows the prediction of the amount of ethanol required in order to produce particles of any target diameter within this size range. In addition, it was found that the reaction was completed in approximately 2 h for all batches regardless of the volume of ethanol. Structurally coloured artificial opal photonic crystals (PCs) were fabricated from the prepared SNPs by self-assembly under gravity sedimentation
Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
We propose the integrable (pseudo)spherical generalization of the
four-dimensional anisotropic oscillator with additional nonlinear potential.
Performing its Kustaanheimo-Stiefel transformation we then obtain the
pseudospherical generalization of the MICZ-Kepler system with linear and
potential terms. We also present the generalization of the
parabolic coordinates, in which this system admits the separation of variables.
Finally, we get the spherical analog of the presented MICZ-Kepler-like system.Comment: 7 page
Crystal Field and Dzyaloshinsky-Moriya Interaction in orbitally ordered La_{0.95}Sr_{0.05}MnO_3: An ESR Study
We present a comprehensive analysis of Dzyaloshinsky-Moriya interaction and
crystal-field parameters using the angular dependence of the paramagnetic
resonance shift and linewidth in single crystals of La_{0.95}Sr_{0.05}MnO_3
within the orthorhombic Jahn-Teller distorted phase. The Dzyaloshinsky-Moriya
interaction (~ 1K) results from the tilting of the MnO_6 octahedra against each
other. The crystal-field parameters D and E are found to be of comparable
magnitude (~ 1K) with D ~= -E. This indicates a strong mixing of the |3z^2-r^2>
and |x^2-y^2> states for the real orbital configuration.Comment: 12 pages, 6 figure
Hadron Energy Reconstruction for the ATLAS Calorimetry in the Framework of the Non-parametrical Method
This paper discusses hadron energy reconstruction for the ATLAS barrel
prototype combined calorimeter (consisting of a lead-liquid argon
electromagnetic part and an iron-scintillator hadronic part) in the framework
of the non-parametrical method. The non-parametrical method utilizes only the
known ratios and the electron calibration constants and does not require
the determination of any parameters by a minimization technique. Thus, this
technique lends itself to an easy use in a first level trigger. The
reconstructed mean values of the hadron energies are within of the
true values and the fractional energy resolution is . The value of the ratio
obtained for the electromagnetic compartment of the combined calorimeter is
and agrees with the prediction that for this
electromagnetic calorimeter. Results of a study of the longitudinal hadronic
shower development are also presented. The data have been taken in the H8 beam
line of the CERN SPS using pions of energies from 10 to 300 GeV.Comment: 33 pages, 13 figures, Will be published in NIM
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