A modified warping operator based on BDRM theory in homogeneous shallow water

In this paper, a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode (BDRM) theory is presented. According to the BDRM theory, the contribution of the beam displacement and the time delay to the group velocity can be easily considered in a shallow water waveguide. A more accurate dispersion formula is derived by using the cycle distance formula to calculate the group velocity of normal modes. The derived dispersion formula can be applied to the homogeneous shallow water waveguide. Theoretically, the formula is related to the phase of the reflection coefficient and suitable for various bottom models. Furthermore, based on the derived dispersion relation, the modified warping operator is developed to obtain linear modal structures. For the Pekeris model, the formulae for the phase of the reflection coefficient are derived in this work. By taking account of the effect of the bottom attenuation on the reflection coefficient, the formula for the phase of the reflection coefficient including the bottom attenuation is obtained for the Pekeris model with a lossy bottom. Performance and accuracy of different formulae are evaluated and compared. The numerical simulations indicate that the derived dispersion formulae and the modified warping operator are more accurate.     

On the effect of the width of the scattering indicatrix on the dispersion of photon density waves in a strongly scattering medium

The dispersion of photon density waves in strongly scattering media with different widths of the scattering indicatrix is studied by the spherical harmonics method using approximations of various orders (up to the P ₇ approximation inclusive). It is shown that, beginning from the P ₃ approximation, the reduction in the velocity of photon density waves that is characteristic of the P ₁ approximation is eliminated and, independently of the width of the scattering indicatrix in the region of modulation frequencies exceeding 10¹⁰ Hz, the velocity of photon density waves asymptotically approaches the speed of light. Our study of the damping of photon density waves has shown that the formula obtained previously for the calculation of the damping coefficient (Imk(μ _s ^′ , ω)) as a function of the transport scattering coefficient and the velocity is valid at Imk ≤ μ_s (μ_s is the light scattering coefficient). The maximum growth in the damping coefficient of photon density waves with a further increase in the frequency is limited by the value of the light scattering coefficient Imk _max ≈ μ_s.     

Bound state poles of the form factors in eikonal approximation and infinite component wave equations

We investigate the form factor in eikonal approximation for the whole region of momentum transfer t in electrodynamics and in φ³ theory, and determine the poles in the time-like region below the threshold. A covariant mass formula is obtained similar to the one derived from four point functions in eikonal approximation. The mass formula does not become imaginary for large values of the coupling constant. The relation to positronium Regge trajectory and infinite component wave equations is discussed.     

Critical ultrasound attenuation in isotropic systems

Starting with a complete set of coupled Langevin equations for the hydrodynamic variables including the order parameter and the acoustic phonons, the critical sound dispersion relation is derived for models C and F. The final expression for the sound dispersion relation contains a quantity which can be interpreted as a frequency-dependent specific heat depending only on the critical degrees of freedom. The elimination of the phonons from the self-energy is justified in detail. Our microscopic result agrees with the phenomenological formula of Ferrell and Bhattarcharjee only in limiting cases. In general, as for instance for model F, it is more complicated than one could have anticipated on a phenomenological basis. For model C, the scaling function of the critical sound attenuation coefficient is calculated to two-loop order. Finally, it is shown that for model C with more than one order parameter component and model F the sound dispersion relation obtained at the critical point is also valid in the crossover region between the critical point and the coexistence region which is in a critical state due to the Goldstone modes.     

Tunneling migrational polarization in dielectrics

The effect of tunneling accompanying volume-charge relaxation is analyzed. The Fokker-Planck equation, in which tunneling transitions are taken into account in the diffusion coefficient and the mobility in the quasiclassical approximation for rectangular potential barriers, is derived from the condition of transitions of the relaxation oscillators between neighboring states. The distribution of the volume charge was found by solving simultaneously the Fokker-Planck and Poisson equations by the small-parameter method with auxiliary contacts on the electrodes. The region of non-Debye dispersion was determined by taking into account the tunneling of relaxation oscillators. Formulas for calculating the complex dielectric constant were derived.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 71–75, November, 1990.     

Transmission of Correlated Gaussian Packets Through a Delta-Potential

We study the evolution of the most general initial Gaussian packet with nonzero correlation coefficient between the coordinate and momentum operators in the presence of a repulsive delta-potential barrier, using the known exact propagator of the time-dependent Schrödinger equation. For the initial packet localized far enough from the barrier, we define the transmission coefficient as the probability of discovering the particle in the whole semi-axis on the other side of the barrier. It appears that the asymptotical transmission coefficient (calculated in the large time limit) depends on two dimensionless parameters: the normalized ratio of the potential strength to the initial mean value of momentum and the ratio of the initial momentum dispersion to the initial mean value of momentum. For small values of the second parameter, the result is reduced to the well-known formula for the transparency of the delta barrier, obtained in the plane-wave approximation by solving the stationary Schrödinger equation. For large values of the second parameter, the transmission coefficient can be much larger than that calculated in the plane-wave approximation. For a fixed initial spread of the packet in the coordinate space, the initial correlation coefficient influences the transparency of the barrier only indirectly, through the increase in the initial momentum dispersion.     

Surface plasmons and the extreme anomalous skin effect

We have derived a simple formula for the dispersion relation of surface plasmons on metals in the extreme anomalous skin effect region. Comparisons of this theory with the usual local dielectric theory is made for Cu, Ag, Au, Sn, and Pb. The two theories can be more than two orders of magnitude different in their predictions of propagation lengths, depending on the temperature.     

Interatomic dispersion dipole

A new formula is derived for the coefficient D ₇ of the leading term in R ^-7 for the electric dipole moment of two atoms in S-states at a large distance R apart. An approximation is proposed which leads to a simple formula for D ₇ involving mainly accessible atomic properties. The approximation is checked for scaled hydrogen atoms and is accurate to about one per cent.     

Luminescence in epitaxial Er-doped LiNbO3 films

Epitaxial Er-doped LiNbO3 films were pulsed-laser-deposited onto c-cut sapphire. Wavelength dispersion of the refractive index and the extinction coefficient was obtained by fitting the experimental transmittance spectrum to the Swanepoel formula and microscopic theory, which accounts for two resonance transitions in the electric dipole approximation. Strong room temperature luminescence was observed under 514.5 nm Ar-laser pumping. Two-lifetime (3.0 and 6.0 ms) luminescent decay is characteristic for the lasing 4I13/2→4I15/2 transition in Er:LiNbO3 films.     

Temperature dependence of optical absorption for the visible region in transparent conducting oxides

We study theoretically the temperature dependence of the optical-absorption coefficient, for the visible region, in thin films of transparent conducting oxides by using the well-known Varshni approach relative to optical band-gap energy. Zero absorption is considered and an approximate formula for the coefficient of visible absorption is derived when photon energy is near the band-gap energy, that is, when absorption is negligible.     

Estimation of the Axial Dispersion Effect on Supercritical Fluid Extraction from Bidisperse Packed Beds

The general hydrodynamic equations of a mathematical model for supercritical fluid extraction are derived within the framework of the continuum mechanics approach. The shrinking core concept is used to describe the mass transfer on the solid-liquid interface. The complete system of macroscopic differential mass-balance equations is reduced to a one-dimensional approximation and accounts for the axial dispersion effect. Correlation formulas available in the literature are used to calculate the axial dispersion coefficient for the conditions of supercritical CO₂ filtration. The effect of axial dispersion on the characteristics of the macroscopic process is analyzed for the typical laboratory-scale extraction conditions in the framework of the suggested model. The numerical simulations demonstrate that the difference between the values of the current mass of accumulated extract calculated in terms of the complete approach, which accounts for the axial dispersion, and the one related to the simplified model (in which the axial dispersion is neglected), is less than 10%. The same comparison is made for the outlet concentrations of the target compounds; the difference reaches 200%.     

On the theory of hall conductivity in disordered systems

A general formula for the Hall conductivity, which is exact in the one-particle approximation, has been obtained. Making use of this formula, the Hall coefficient for small polarons has been calculated.     

Righi-Leduc effect in a quantizing magnetic field

The Righi-Leduc effect in semiconductors with a Kane dispersion law in the presence of strong, quantizing, magnetic fields is studied theoretically. The explicit form of the dependence on the magnetic field, temperature, and concentration in arbitrary quantizing magnetic fields is established for semiconductors with a nondegenerate electron gas in the approximation of small nonparabolicity. A simple formula that is applicable for all strong magnetic fields, including quantizing fields, is derived for the Righi-Leduc coefficient in the case of strongly degenerate semiconductors with an arbitrary nonparabolic band. It is shown that in order to determine the photon part of the thermal conductivity ,ph directly from experiment it is best to employ samples with a nondegenerate electron gas in strong, but nonquantizing, magnetic fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 102–107, July, 1988.     

Transmission of light through a random small-angle scattering medium

A theory of random small-angle scattering is presented. The photon dispersion partial differential equation is derived and the dispersion coefficient characterizing the medium is introduced. The equation is solved for a spatial impulse. The modulation transfer function and the contrast loss are derived as a funcion of spatial frequency, dispersion coefficient, and object-to-image distance. The limitation on resolution is shown by an indeterminancy relation based on the dispersion coefficient. The dispersion angle (rms value of scattering angle) is calculated as an example.     

声子色散对量子点中弱耦合磁极化子声子平均数的影响

利用线性组合算符和幺正变换相结合的方法,研究了声子色散对抛物量子点中弱耦合磁极化子电子周围光学声子平均数的影响。计及纵光学（ LO）声子色散,在抛物近似下导出了基态能量与量子点有效受限长度、声子色散系数、回旋共振频率以及电子－声子耦合常数之间的关系,电子周围光学声子平均数与声子色散系数以及电子－声子耦合常数的关系。数值计算结果表明在弱耦合情况下抛物量子点中磁极化子的基态能量随声子色散系数的增大而减小;电子周围光学声子平均数随声子色散系数增大而增大,随电子－声子耦合常数的增大而增大。     

声子色散对量子点中弱耦合磁极化子声子平均数的影响

利用线性组合算符和幺正变换相结合的方法,研究了声子色散对抛物量子点中弱耦合磁极化子电子周围光学声子平均数的影响．计及纵光学(LO)声子色散,在抛物近似下导出了基态能量与量子点有效受限长度、声子色散系数、回旋共振频率以及电子-声子耦合常数之间的关系,电子周围光学声子平均数与声子色散系数以及电子-声子耦合常数的关系．数值计算结果表明在弱耦合情况下抛物量子点中磁极化子的基态能量随声子色散系数的增大而减小;电子周围光学声子平均数随声子色散系数增大而增大,随电子-声子耦合常数的增大而增大．     

声子色散对量子点中弱耦合磁极化子性质的影响(英文)

利用线性组合算符和幺正变换的方法,研究声子色散对磁场中抛物量子点弱耦合磁极化子性质的影响.计及LO声子色散,在抛物近似下导出了基态能量与量子点有效受限长度、声子色散系数、磁场强度以及耦合强度之间的关系.我们可以得到在弱耦合情况下抛物量子点中磁极化子的基态能量E0随量子点有效受限长度l0、电子声子耦合常数α和声子色散系数γ的增大而减小,随磁场回旋频率ωc增大而增大.自陷能Eotr随声子色散系数γ增大而增大.     

The validity range of the dipole approximation for a dielectric mixture

This paper investigates the validity range of the dipole approximation for a dielectric mixture with spherical inclusions through electric field analyses according to a new criterion: if the maximum perturbation on an arbitrarily selected sphere surface caused by the interactions among spheres is less than a given allowable error, the dipole approximation is considered acceptable. Based on the dipole-enhanced dipole approximation previously presented by us, a theoretical formula for calculating the validity range of the dipole approximation is derived. It shows that the validity range depends on three parameters, the dielectric mismatch, the volume fraction of inclusions, and the allowable error. The calculated results by this formula are compared with those numerically obtained by the FEM. The good agreement between them indicates the credibleness of this formula.     

空间分辨漫反射的一阶散射参量灵敏度

以输运理论的P3近似为基础,推导了空间分辨漫反射的一阶散射参量灵敏度的解析表示,并进行了数值分析,比较了散射参量对P3近似和漫射近似漫反射的影响.结果表明:在距光源两个输运平均自由程以内,该灵敏度与相应于漫射近似的灵敏度差别较为明显;距离光源约四个输运平均自由程附近,该灵敏度等于零,并且与光源之距与相应于漫射近似情况也...