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1.
Formally exact expressions have been derived for the response to a spin-dependent non-local pseudopotential and for the ion-ion interaction in a spin-polarized electron gas. These expressions have been compared to previously used expressions for these quantities and have been found to differ in several important ways. The improved expressions will make possible a quantitative investigation of the influence of a magnetic field on lattice properties of simple metals. 相似文献
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Muhammad Taher Abuelma'atti 《International Journal of Infrared and Millimeter Waves》1993,14(6):1299-1310
In this paper a simple mathematical model is presented for the inherent resistive nonlinearity of a Josephson junction. By incorporating this model in the RSJ model of the Josephson junction, series expressions are obtained for the harmonic and intermodulation performance of Josephson junctions irradiated by multisinusoidal signals. Special cases are considered where the series expressions can be reduced to simple analytical expressions. 相似文献
4.
J.R Chelikowsky 《Solid State Communications》1980,33(12):1201-1204
Local density expressions provide a simple and flexible means of calculating kinetic energies. Recently it has been ascertained that such expressions can be quite accurate (to within 1%) in obtaining the total kinetic energy of an atomic system. However, we shall demonstrate that local density kinetic energy expressions, as presently formulated, are not appropriate for molecular or solid state calculations. In particular, these expressions do not properly describe trends appropriate for valence electron charge density configurations. 相似文献
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Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting
of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions,
we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and
our expressions can be used to easily determine membrane parameters from experimentally obtained shapes. 相似文献
7.
We obtained basic analytical expressions for the efficiency of the second harmonic in nonlinear crystals with a regular domain
structure; in these expressions we took into account the angular divergence of the laser beam. The calculation was done in
the geometric-optics approximation of the given field of laser radiation. We show that the expressions obtained are similar
to the corresponding expressions for homogeneous nonlinear crystals.
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 134–138, January–February, 2000. 相似文献
8.
General expressions are obtained for the scattering of neutrons from molecular solids with the exchange of m-quanta. Explicit expressions are obtained for the total cross section, when both the phonon and the torson modes are given by the Einstein distribution functions. The expressions can be readily utilized to understand neutron scattering from a molecular crystal. 相似文献
9.
An adjoint perturbative method is used to derive expressions for the first- through third-order derivatives of a pressure field with respect to sound speed, density, and frequency, for the restricted case of a laterally homogenous waveguide in which environmental parameters are only a function of depth. By using a normal-mode Green's function, the three-dimensional spatial correlation required by the standard acoustic adjoint equation can be reduced to a set of one-dimensional depth integrals. The resulting expressions for the first-order derivative are similar to those obtained by previous perturbative approaches based on the depth-separated wave equation, but the approach followed here permits straightforward extension to higher-order derivatives. Explicit evaluations of the expressions for a representative shallow-water waveguide model are in excellent agreement with numerical finite-difference computations. An analysis of the expressions as a function of source-receiver range finds the contributions to the mode amplitude derivatives to be non-negligible at ranges less than a few modal interference lengths, for parameters associated with the ocean bottom. Therefore, linear perturbative inversion methods that perturb only horizontal wavenumbers and not mode amplitudes should either be used with caution or modified to incorporate the expressions presented here. 相似文献
10.
In this paper, closed-form expressions for the mobility of the circumferential modes in an infinite in-vacuo thin-walled pipe are derived in terms of the axial wave receptances for each mode. These expressions are valid below the ring frequency. By using simplified expressions for the wavenumbers, low-frequency approximations for the point and transfer mobilities are also derived. These new mobility expressions are validated experimentally, and are used to examine the dynamic behaviour of an in-vacuo pipe. 相似文献
11.
Cynthia Y. Young Aaron J. Masino Fredrick E. Thomas Christopher J. Subich 《Waves in Random and Complex Media》2004,14(1):75-96
The Rytov perturbation method can be used to derive analytic expressions governing statistical quantities of an optical wave propagating through the Earth's atmosphere. It is generally accepted that the validity of these expressions is restricted to the weak fluctuation regime, and that the wave structure function for plane and spherical waves obtained via the Rytov method is valid in all fluctuation regimes, for sufficiently small separation distances. Data from experimental results for the wave structure function as a function of the fluctuation strength for a fixed value of the separation distance indicate that the Rytov method does not accurately model the behaviour of the wave structure function in moderate to strong fluctuation regimes. This is similar to what is observed for the scintillation index. Recently, however, it was shown that the integral definition of the scintillation index obtained via the Rytov perturbation yields analytic expressions that are valid in all fluctuation regimes when a filter function is applied to the atmospheric spectrum. The underlying physical theory is that as the wave propagates, intermediate refractive index scale sizes fail to refract or diffract the beam. Hence, these scale sizes do not contribute to the scintillation index. In this paper, we investigate the results of applying this concept to the wave structure function. Specifically, we apply a filter function to the atmospheric spectrum and develop analytic expressions for the wave structure function for plane, spherical and Gaussian beam waves using the Rytov perturbation method. It is shown that in weak fluctuations these expressions yield similar results to standard expressions obtained where no filter function is applied. However, in moderate to strong fluctuations, these new expressions predict a decrease in the value of the wave structure function as compared to the standard expressions, following the trend of the experimental data presented by Gurvich.
(Some figures in this article are in colour only in the electronic version) 相似文献
(Some figures in this article are in colour only in the electronic version) 相似文献
12.
Three simple analytic expressions satisfying the
limitation condition at low densities for the radial distribution function of
hard spheres are developed in terms of a polynomial expansion of nonlinear
base functions and the Carnahan--Starling equation of state. The simplicity
and precision for these expressions are superior to the well-known
Percus--Yevick expression. The coefficients contained in these expressions
have been determined by fitting the Monte Carlo data for the first
coordination shell, and by fitting both the Monte Carlo data and the
numerical results of Percus-Yevick expression for the second coordination
shell. One of the expressions has been applied to develop an analytic
equation of state for the square-well fluid, and the numerical results are in
good agreement with the computer simulation data. 相似文献
13.
John Lekner 《Journal of Electrostatics》2011,69(5):435-441
Exact series expressions are obtained for the longitudinal and transverse polarizabilities of a system of two conducting spheres, for arbitrary sphere radii and separation. In the important case of close approach, where the exact series converge slowly, approximate analytical expressions are obtained. These analytical expressions become more accurate as the distance between the spheres gets small compared to the sphere radii, and reduce to the known analytic values at sphere contact. 相似文献
14.
S. Mudaliar 《Waves in Random and Complex Media》2000,10(1):117-134
Analytic expressions are derived for the normalized radar cross sections (NRCS) of a random medium layer. These are calculated from the first-order solutions for diffuse intensities which are based on a multiple-scattering wave theoretical analysis. The permittivity fluctuations are assumed to be small and to obey stationary Gaussian statistics. On studying the expressions for the NRCS, some of their characteristics are pointed out. Three different correlation functions are considered and expressions for the coherent propagation constants are provided. Numerical examples are used to verify theoretical results and highlight some interesting characteristics of NRCS. 相似文献
15.
The results of analytical modeling of the resonant excitation of evanescent harmonics in a medium formed by parallel metallic
nanorods taking into account the spatial dispersion are presented. Analytical expressions are derived for the reflection and
transmission coefficients, as well as for the amplitudes of electromagnetic waves inside the medium. These expressions are
compared to similar expressions that were previously obtained using a local model of an ultimately anisotropic material without
taking into account the spatial dispersion. The obtained expressions are simplified for various partial cases, including the
superresolution imaging of a source that is located at a considerable distance from the metamaterial layer. A layer of a medium
composed from finitesized wires is numerically simulated and it is demonstrated that, due to the effect of resonant excitation
of evanescent spatial harmonics in the layer, subwavelength details of an object that is considerably distant from the layer
can be distinguished inside of the layer. 相似文献
16.
A new method of calculating the orbital angular momentum spectra of Laguerre-Gaussian beams in channels with atmospheric turbulence
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Studying orbital angular momentum(OAM) spectra is important for analyzing crosstalk in free-space optical(FSO)communication systems. This work offers a new method of simplifying the expressions for the OAM spectra of Laguerre-Gaussian(LG) beams under both weak/medium and strong atmospheric turbulences. We propose fixing the radius to the extreme point of the intensity distribution, review the expression for the OAM spectrum under weak/medium turbulence,derive the OAM spectrum expression for an LG beam under strong turbulence, and simplify both of them to concise forms.Then, we investigate the accuracy of the simplified expressions through simulations. We find that the simplified expressions permit accurate calculation of the OAM spectrum for large transmitted OAM numbers under any type of turbulence. Finally,we use the simplified expressions to analytically address the broadening of the OAM spectrum caused by atmospheric turbulence. This work should contribute to the concise theoretical derivation of analytical expressions for OAM channel matrices for FSO-OAM communications and the analytical study of the laws governing OAM spectra. 相似文献
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Joseph R. Lakowicz Henryk Cherek Józef Kuśba Ignacy Gryczynski Michael L. Johnson 《Journal of fluorescence》1993,3(2):103-116
This didactic paper summarizes the mathematical expressions needed for analysis of fluorescence anisotropy decays from polarized frequency-domain fluorescence data. The observed values are the phase angle difference between the polarized components of the emission and the modulated anisotropy, which is the ratio of the polarized and amplitude-modulated components of the emission. This procedure requires a separate measurement of the intensity decay of the total emission. The expressions are suitable for any number of exponential components in both the intensity decay and the anisotropy decay. The formalism is generalized for global analysis of anisotropy decays measured at different excitation wavelengths and for different intensity decay times as the result of quenching. Additionally, we describe the expressions required for associated anisotropy decays, that is, anisotropy decays where each correlation time is associated with a decay time present in the anisotropy decay. And finally, we present expressions appropriate for distributions of correlation times. This article should serve as a reference for researchers using frequency-domain fluorometry. 相似文献
19.
A.L. Crosbie J.B. Farrell 《Journal of Quantitative Spectroscopy & Radiative Transfer》1984,31(5):397-416
Exact expressions for the source function, flux, and scattered intensity normal to the surface are developed in cylindrical coordinates for a three-dimensional, absorbing, emitting, isotropically scattering medium exposed to both diffuse and collimated radiation. Simplifications of these expressions for certain important geometries and uniform loading are presented. Also, superposition of these equations and radiative equilibrium are discussed. The generalized three-dimensional equations are shown to reduce to the familiar one-dimensional results. Also, the equations for a strongly anisotropic phase function which is made up of a spike in the forward direction superimposed on an otherwise isotropic phase function are expressed in terms of the isotropic expressions. 相似文献
20.
The density of eigenvalues of a potential well is calculated in an asymptotic expansion for large geometrical size. Explicit, readily calculable expressions are obtained for volume and surface contributions. The resulting expressions are numerically applied to the case of a spherical Woods-Saxon well. 相似文献