Transverse magnetic scattering of two incident plane waves by a dielectric coated cylindrical reflector

Scattering characteristics of two plane waves are investigated for a circular cylinder covered by a dielectric substance. Fields are assumed to be transverse magnetic (TM) and represented in an exponential series form. The diffracted radiations are found by applying the boundary conditions to the wave functions. The wave transformation method and the orthogonality of the exponential functions are respectively employed to obtain an infinite series in the solution. Numerical results are evaluated by reducing the infinite series to a finite number of terms and comparing estimates with the single plane wave scattering situation.     

A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method

In this Letter, we considered a numerical treatment for the solution of the hydromagnetic peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube using Adomian decomposition method and a modified form of this method. The axial velocity is obtained in a closed form. Comparison is made between the results obtained by only three terms of Adomian series with those obtained previously by perturbation technique. It is observed that only few terms of the series expansion are required to obtain the numerical solution with good accuracy.     

Fractional Cattaneo heat equation in a semi-infinite medium

To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.     

Oscillator rule of the trap activation energies in NaCl crystals

The energy spectra of traps in NaCl crystals have been studied in detail by the method of thermoluminescence. Crystals of NaCl were undoped but treated thermally in different ways. The activation energies of traps form a single oscillator series, E _n =ℏω _TL (n+1/2), ℏω _TL =903 cm^-1. Contrary to other previously studied crystals with complex lattices, the corresponding line ℏω _Ram =ℏω _TL was not found in Raman spectra of NaCl. It is assumed that the oscillator rule is governed by the polaron nature of traps. The trap activation energy is determined by the vibration level from which the transition of the charge carrier to the excited luminescence centre is made possible and depends on the distance between these centres.     

Thermal activation of current in an inhomogeneous Schottky diode with a Gaussian distribution of barrier height

This paper investigates the thermal activation behaviour of current in an inhomogeneous Schottky diode with a Gaussian distribution of barrier height by numerical simulation. The analytical Gaussian distribution model predicted that the I--V--T curves may intersect with the possibility of the negative thermal activation of current, but may be contradictory to the thermionic emission mechanism in a Schottky diode. It shows that the cause of the unphysical phenomenon is related to the incorrect calculation of current across very low barriers. It proposes that junction voltage V_j, excluding the voltage drop across series resistance from the external bias, is a crucial parameter for correct calculation of the current across very low barriers. For correctly employing the thermionic emission model, V_j needs to be smaller than the barrier height Ф. With proper scheme of series resistance connection where the condition of V_j > Ф is guaranteed, I--V--T curves of an inhomogeneous Schottky diode with a Gaussian distribution of barrier height have been simulated, which demonstrate normal thermal activation. Although the calculated results exclude the intersecting possibility of I--V--T curves with an assumption of temperature-independent series resistance, it shows that the intersecting is possible when the series resistance has a positive temperature coefficient. Finally, the comparison of our numerical and analytical results indicates that the analytical Gaussian distribution model is valid and accurate in analysing I--V--T curves only for small barrier height inhomogeneity.     

Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy

It is well-known that the finite-gap solutions of the KdV equationcan be generated by its recursion operator.We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to alower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depictedby a series of ordinary differential equations (ODEs), which may be gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies. The key is a special form of Lax pair for the AKNS hierarchy. It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.     

Miscibility studies of disc-like molecules

The total miscibility method is applied to study the recently discovered mesophases of disc-like molecules, benzene-hexa-n-alkanoates. These compounds do not form continuous solid solutions, but are totally miscible in the liquid and mesomorphic states. The virtual mesophase-isotropic transition temperature for the hexanoate compound derived from the miscibility diagram is in excellent accord with that obtained from the previously reported pressure-temperature phase diagram. With simplifying assumptions, it is possible to predict with acceptable reliability the isobaric binary phase diagrams of any two members of the series. The real and virtual mesophase-liquid transition temperatures are linear functions of the molecular weight. On the other hand, a plot of the crystal-liquid transition temperatures versus the molecular weight exhibits a minimum. Total miscibility in the mesomorphic state is not observed for two members of different discogenic series, but the existence of different mesophase types is not proved. Lyotropic mesomorphism for a disc-like mesophase is established.     

Analogs of Bohr-Sommerfeld-Maslov quantization conditions on Riemann surfaces and spectral series of nonself-adjoint operators

In the paper, the semiclassical asymptotic behavior of the eigenvalues of some nonself-adjoint operators important for applications is studied (for the Sturm-Liouville operator with complex potential and the operator of induction). It turns out that the asymptotic behavior can be calculated using the quantization conditions, which can be represented as the condition that the integrals of a holomorphic form over the cycles on the corresponding complex Lagrangian manifold, which is a Riemann surface of constant energy, are integers. In contrast to the real case (the Bohr-Sommerfeld-Maslov formulas), to calculate a chosen spectral series, it is sufficient to assume that the integral over only one of the cycles takes integer values, and different cycles determine different series.     

Modified geometric optics: Accounting for exponentially small scattered fields

We propose a modified geometrical-optics approximation (MGO). It is based on the solution of the Helmholtz equation in the form of a series in which the main term describes the zero-order geometrical-optics approximation. The proposed method allows one to take into account an exponentially small backscattering in smoothly inhomogeneous media and thus improves the geometrical-optics approximation. In the case of forward scattering, the solution obtained is reduced to the conventional geometrical-optics series over negative powers of the wavenumber. We estimate the backscattering using the perturbation technique for rays and determine the conditions under which the backscattered field agrees with the Born approximation of scattering theory. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 2, pp. 106–114, January 2000.     

Langevin-like equation with colored noise

Consider a stochastic differential equation of the form of a Langevin equation, but in which the noise source is not white. If it is nearly white, i.e., its autocorrelation time is short, a systematic approximation method is known. It leads to a Fokker-Planck equation with successive higher order corrections. To obtain the coefficients more explicitly, a secondary expansion may be employed. The validity of the resulting double series approximation is discussed and confronted with the various results given in the literature. In addition, an alternative approximation method is obtained using the technique for eliminating fast variables. It produces the same terms in a different sequence.     

A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions

Free vibration analysis of truncated conical shells with general elastic boundary conditions is presented in this paper. An accurate modified Fourier series solution is developed, in which, regardless of the boundary conditions, each displacement of the conical shell is invariantly expressed as a new form of improved series expansions composed of a standard Fourier series and closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series expansion. All the expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh–Ritz method. By using the present method, conical shells with arbitrary boundary conditions including all classical and elastic end restraints can be solved in a unified form. The accuracy and convergence of the current approach are validated by numerical examples and comparison with FEM results and those from the literature, and excellent accuracy is demonstrated. Comprehensive studies on the effects of elastic restraint parameters, semi-vertex angle and the ratio of length to radius are also reported. Some new results are presented for cases with elastic boundary restraints which may serve as benchmark solution for future researches.     

Representation of the Helmholtz equation solution in the form of a series based on backscattering multiplicity

The representation of the Helmholtz equation solution in the form of a series based on backscattering multiplicity is considered. New methods for calculating wave fields propagating in inhomogeneous media, which have been developed on the basis of this series, are presented. The results that have been obtained using these new methods are briefly described.     

A broadband planar acoustic metamaterial lens

Based on quasi-conformal mapping approach, we propose a two-dimensional broadband and low-loss planar lens in the acoustic regime, which can be realized using gradient-index sub-wavelength artificial structures with hard boundary. In this design, QCM is employed in the acoustic regime to convert a parabolic form into a planar one, which makes the resultant material approximately isotropic through minimizing the anisotropic factor. It is found that the planar lens can show the same performance as its parabolic counterparts over a broadband range of frequency. Moreover, the lens is fabricated via 3D printing technology and measured experimentally, which gives identical results with the theoretical prediction. The proposed technique could be extended to realize different acoustic devices and applied for a series of practical applications.     

Multiple scattering in dilute systems

Multiple scattering in the limit in which the constituent scatterers are far removed from each other is studied. It is seen how this situation leads, in the Watson multiple-scattering series, to the dominance of on-shell propagation between the constituents. It also yields a version of the Glauber multiple-scattering theory in which no assumption is made to the effect that the individual projectile-constituent scattering amplitudes are eikonal in form. This approach allows for the immediate extraction of Fresnel corrections to the Glauber result and explains several apparent contradictions as to the relationship between the Watson multiple-scattering series approximated with on-shell propagation only and the Glauber theory.     

The probability distribution associated with the dichotomic Markov process

We have calculated the probability distribution function for the dichotomic Markov process using the work of Pomraning [Linear kinetic theory and particle transport in stochastic mixtures. Singapore: World Scientific; 1991] and have studied the rate of convergence to this exact form as the number of terms in a series approximation is increased. Each term in the series involves an additional stochastic moment in the hierarchy of moments. It is observed that convergence is fast near the source but, as the distance from the source increases, more and more moments are required to obtain a specified accuracy.     

Renormalization group functions for two-dimensional phase transitions: To the problem of singular contributions

According to the available publications, the field theoretical renormalization group approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This property is associated with the existence of nonanalytic contributions in the renormalization group functions. The situation is analyzed in this work using a new algorithm for summing divergent series that makes it possible to determine the dependence of the results for the critical exponents on the expansion coefficients for the renormalization group functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonic sections or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in the renormalization group functions.     

载流子在金属/聚对苯乙炔/金属结构中注入及输运的动力学研究

采用紧束缚的Su-Schrieffer-Heeger模型,利用非绝热动力学方法研究了载流子在金属/聚对苯乙炔(poly(p-phenylene vinylene,简记为PPV))/金属三明治结构中注入与输运的动力学过程.发现由于强的电子-晶格相互作用,注入的电荷在PPV链中形成波包,波包的形成与施加在金属电极上的偏压、PPV链上的电场强度及金属电极与PPV之间的界面耦合强度密切相关.在无外电场的情况下,当偏压达到临界值时电荷能够从金属电极注入到PPV链中并形成波包.随着电场强度的增大,波包能 关键词： 金属/聚对苯乙炔/金属结构 载流子输运 波包     

Irreducibility and Compositeness in q-Deformed Harmonic Oscillator Algebras

A study of the reducibility of the Fock space representation of the q-deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is carried out by using the properties of the Gauss polynomials. When the deformation parameter is a root of unity, an interesting result comes out in the form of a reducibility scheme for the space representation which is based on the classification of the primitive or nonprimitive character of the deformation parameter. An application is carried out for a q-deformed harmonic oscillator Hamiltonian, to which the reducibility scheme is explicitly applied.On leave from     

Representation of the Helmholtz equation solution in the form of a series based on backscattering multiplicity

Abstract

The representation of the Helmholtz equation solution in the form of a series based on backscattering multiplicity is considered. New methods for calculating wave fields propagating in inhomogeneous media, which have been developed on the basis of this series, are presented. The results that have been obtained using these new methods are briefly described.     

Theoretical calculations of the temperature dependence of the electrical and thermal conductivities of liquid gallium

The electrical and thermal resistivities of liquid gallium are calculated over a range of temperatures above the melting point using the solutions of the Boltzmann equation. The experimental x-ray structure factor of Waseda and the form factor derived using the Heine-Abarenkov model potential are used in these calculations. The ratio of the electrical and thermal conductivities is calculated and compared to experimental values and to the theoretical Lorenz number.