Search results for "Equations"
showing 10 items of 955 documents
Quantitative prediction of effective material properties of heterogeneous media
1999
Effective electrical conductivity and electrical permittivity of water-saturated natural sandstones are evaluated on the basis of local porosity theory (LPT). In contrast to earlier methods, which characterize the underlying microstructure only through the volume fraction, LPT incorporates geometric information about the stochastic microstructure in terms of local porosity distribution and local percolation probabilities. We compare the prediction of LPT and of traditional effective medium theory with the exact results. The exact results for the conductivity and permittivity are obtained by solving the microscopic mixed boundary value problem for the Maxwell equations in the quasistatic app…
Spectral theory of a Neumann-Poincare-type operator and analysis of cloaking due to anomalous localized resonance
2011
The aim of this paper is to give a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a layer of plasmonic material. Using layer potentials and symmetrization techniques, we give a necessary and sufficient condition on the fixed source term for electromagnetic power dissipation to blow up as the loss parameter of the plasmonic material goes to zero. This condition is written in terms of the Newtonian potential of the source term. In the case of concentric disks, we make the condition even more explicit. Using the condition, we are able to show that for any source supported outside a cr…
Eine Bemerkung zur Frage der Verwendung Lagrangescher Koordinaten in der Physik nichtlinearer Schwingungen
1958
For the Cartesian coordinates of the elements of a vibrating string, which are introduced as functions of time and a parameter (similar to the Lagrangean method in hydrodynamics), a general, non-linear system of differential equations is offered. The behaviour of the freely vibrating string corresponding to this system agrees, approximately, with the behaviour of a string put in motion in a certain way, which string, if moving freely, would act according to the linear differential equation of the elementary theory.
Experimental and Theoretical Study of Bi2O2Se Under Compression
2018
[EN] We report a joint experimental and theoretical study of the structural, vibrational, elastic, optical, and electronic properties of the layered high-mobility semiconductor Bi2O2Se at high pressure. A good agreement between experiments and ab initio calculations is observed for the equation of state, the pressure coefficients of the Raman-active modes and the bandgap of the material. In particular, a detailed description of the vibrational properties is provided. Unlike other Sillen-type compounds which undergo a tetragonal to collapsed tetragonal pressure-induced phase transition at relatively low pressures, Bi2O2Se shows a remarkable structural stability up to 30 GPa; however, our res…
Water-Hydrophobic Zeolite Systems
2012
Water intrusion-extrusion in hydrophobic microporous AFI, IFR, MTW and TON pure silica zeolites (zeosils) has been investigated through molecular dynamics (MD) simulations. It was found that intruded water volumes correlate with the free volume of the zeosil unit cells. Calculated adsorption isotherms allowed us to estimate the amounts of water intruded, and deviations from experiments (lower experimental with respect to calculated intrusion pressures) have been;explained in terms of connectivity defects in the synthesized materials. Water phase transitions in defectless zeosils occur in a narrow range at high pressure. On the basis of a simple model, we derived a thermodynamic equation tha…
Nonlinear Analysis of Phase-locked Loop-Based Circuits
2013
Main problems of simulation and mathematical modeling of high-frequency signals for analog Costas loop and for analog phase-locked loop (PLL) are considered. Two approachers which allow to solve these problems are considered. In the first approach, nonlinear models of classical PLL and classical Costas loop are considered. In the second approach, engineering solutions for this problems are described. Nonlinear differential equations are derived for both approaches.
Phononic heat transport in the transient regime: An analytic solution
2016
We investigate the time-resolved quantum transport properties of phonons in arbitrary harmonic systems connected to phonon baths at different temperatures. We obtain a closed analytic expression of the time-dependent one-particle reduced density matrix by explicitly solving the equations of motion for the nonequilibrium Green's function. This is achieved through a well-controlled approximation of the frequency-dependent bath self-energy. Our result allows for exploring transient oscillations and relaxation times of local heat currents, and correctly reduces to an earlier known result in the steady-state limit. We apply the formalism to atomic chains, and benchmark the validity of the approx…
Automated Stress Separation Along Stress Trajectories
2007
A procedure for the separation of principal stresses in automated photoelasticity is presented. It is based on the integration of indefinite equations of equilibrium along stress trajectories, also known as Lame-Maxwell equations. A new algorithm for precise and reliable stress trajectory calculation, which is an essential feature of the procedure, has also been developed. Automated stress separation is carried out along stress trajectories starting from free boundaries. Experimental tests were performed on a disc in diametral compression and on a ring with internally applied pressure. Full-field principal stress values were obtained and results were compared with those from the theory of e…
Determining the optical properties of adsorbate covered surfaces by dichroism in VUV-photoemission
1999
The dichroic effects of photoemission excited by polarised light depend on the angle of photon incidence. Measurements of the difference in the angle-resolved photoemission intensities from Cs 5p semi-corelevels excited by photons of opposite helicity, or of orthogonal linear polarisation are reported. It was thought that the dependence of dichroism on the angle of incidence cannot be described using equations omitting metal optics. A complete consideration of the vector potential of the exciting light is needed, including the phase shift between it's parallel and perpendicular components. The phase shift is produced by the complex index of refraction. Using the Fresnel equations for struct…
A quantum group for the Einstein's equations
2011
In this paper, we expose the construction of a possible, simple matrix quantum group structure (according to Woronowicz), related to elementary formal aspects of the Einstein field equations of General Relativity, and their possible symmetries.