Backscattering in the vicinity of a mode cutoff

Abstract

In a recent paper to this journal (Whitman A M et al 2003 Waves Random Media 13 269–86) we derived a set of coupled equations that describe the intermodal scattering of acoustic radiation in a duct whose speed of sound varies randomly in space and time. In the paper we were mainly interested in modes that were not near cutoff. Here we study the solution of these equations in the vicinity of the cutoff. We find that near cutoff almost all the energy is reflected back independent of the other duct parameters. In addition to presenting these results, we analyse the mathematical structure of the equations in these regions in order to elucidate the reason for this behaviour.     

Exact operator solutions to Euler hamiltonians

It is nearly impossible in general to solve exactly the quantum-mechanical Heisenberg equations of motion when these operator equations are non-linear. However, in this paper we show how to obtain exact closed-form solutions for the operators p(t) and q(t) for any Euler hamiltonian (one that be expressed a function of pq).     

Classification of static spherically symmetric perfect fluid space-times via conformal vector fields in f(T) gravity

In this paper, we classify static spherically symmetric (SS) perfect fluid space-times via conformal vector fields (CVFs) in f(T) gravity. For this analysis, we first explore static SS solutions by solving the Einstein field equations in f(T) gravity. Secondly, we implement a direct integration technique to classify the resulting solutions. During the classification, there arose 20 cases. Studying each case thoroughly, we came to know that in three cases the space-times under consideration admit proper CVFs in f(T) gravity. In one case, the space-time admits proper homothetic vector fields, whereas in the remaining 16 cases either the space-times become conformally flat or they admit Killing vector fields.     

The Cartesian analytical solutions for the N-dimensional compressible Navier–Stokes equations with density-dependent viscosity

In this paper, we prove the existence of general Cartesian vector solutions u = b(t) + A(t)x for the N-dimensional compressible Navier–Stokes equations with density-dependent viscosity, based on the matrix and curve integration theory. Two exact solutions are obtained by solving the reduced systems.     

Generalized Nonlocal Ginzburg-Landau Equations

In a previous paper we established a set of nonlocal Ginzburg-Landan equations near T_c. In this paper this set of equations is generalized to the cases well below T_c. the generalization is characterized by two new kernel functions which can be reduced to a similar form aa that obtained previously. The form factor resulted from first principle calculation is in good agreement with neutron scattering data.     

A discrete KdV equation hierarchy: continuous limit,diverse exact solutions and their asymptotic state analysis

In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized (m, 2N − m)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations.     

Dynamics of surface roughening in disordered media

In this paper the roughening of interfaces moving in inhomogeneous media is investigated by examining the corresponding stochastic differential equations using (i) numerical methods and (ii) dimensional analysis. We consider interface evolution equations where disorder is represented by quenched noise which can be both additive and multiplicative. Our main finding is that quenched noise leads to a new universality class as concerning the exponents δ and β describing respectively the spatial and temporal scaling of surface roughness. In particular, additive noise close to the pinning transition results in a behaviour with δ = 0.71 ± 0.08 and β = 0.61±0.06 up to a crossover time. These estimates are in very good agreement with the theoretical prediction and that we derive from a dimensional analysis of the equation. Furthermore, we argue that multiplicative noise is the appropriate choice to describe experiments where the interface between two flowing phases is considered. By numerically integrating the proposed equation we have obtained (i) surfaces remarkably similar to those observed in the experiments and (ii) a scaling of the surface width as a function of time with an exponent β = 0.65 being in an excellent agreement with the experimental value. In addition to the exponents we discuss other relevant features of the surfaces, including the scaling of the average velocity of the surface ν_a close to pinning and the non-trivial, power law distribution of waiting times and noise along the interface in the stationary regime.     

The algebraic Bethe ansatz for rational braid-monoid lattice models

In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_nand D_n Lie algebra and by the superalgebra Osp(n||2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvaluesof the transfer matrix associated to the B_n, C_n, D_n, Osp(2nt-1||2), Osp(2||2nt-2), Osp(2nt-2||2) and Osp(1||2n) models. The corresponding Bethe ansatz equations can be formulated in terms of the root structure of the underlying algebra.     

Thermodynamic analysis of BaxK1 − xBiO3 using the Eliashberg theory

In order to understand the mechanism that gives rise to superconductivity in the ceramic superconductors of the type Ba_xK_{1 − x}BiO₃, we analyze the thermodynamic properties with the use of the Eliashberg equations. For these calculations we used the electron-phonon spectral density function ²(ω)F(ω), calculated by Shirai et al. [1] from first principles for two different K concentrations, x=0.5 and x=0.7.     

Infrared reflectivity and dielectric permeability of ultra-thin Cu and Al films

In this report we present an experimental investigation of the reflectivity (R) and the dielectric permeability () for Cu and Al ultra-thin films ranging in thickness from a few monolayers to 12 nm at infrared and visible wavelengths. The metal films were prepared by RF-sputtering on SiO₂ (glass) and Si substrates. IR reflectivity was measured at 9.2 μm, while was measured with the help of laser ellipsometer at a wavelength of 632.8 nm. Two types of oscillations on R(d) and (d) were discovered for two thickness regions determined by the critical thickness value d*. Oscillations at d<d* with periods near 0.3 nm for Al and Cu films were observed on R(d) and (d) due to quantum sized effects (QSEs). At d>d* (thickness between 6–12 nm) we discover a new type of strong oscillation of R(d) and (d) with an oscillating period of 0.2 nm. For thickness larger than 12 nm all the oscillations tend to disappear and R and behave almost as their volume values. A possible explanation for the appearance of these two kinds of oscillations is based on the introduction of the critical film thickness d*.     

Optimization of corrugated-QWIPs for large format, high quantum efficiency, and multi-color FPAs

Previously, we demonstrated a large format 1024 × 1024 corrugated quantum well infrared photodetector focal plane array (C-QWIP FPA). The FPA has a cutoff at 8.6 μm and is BLIP at 76 K with f/1.8 optics. The pixel had a shallow trapezoidal geometry that simplified processing but limited the quantum efficiency QE. In this paper, we will present two approaches to achieve a larger QE for the C-QWIPs. The first approach increases the size of the corrugations for more active volume and adopts a nearly triangular pixel geometry for larger light reflecting surfaces. With these improvements, QE is predicted to be about 35% for a pair of inclined sidewalls, which is more than twice the previous value. The second approach is to use Fabry–Perot resonant oscillations inside the corrugated cavities to enhance the vertical electric field strength. With this approach, a larger QE of 50% can be achieved within certain spectral regions without using either very thick active layers or anti-reflection coatings. The former approach has been adopted to produce two FPAs, and the preliminary experimental results will be discussed. In this paper, we also describe using voltage tunable detector materials to achieve multi-color capability for these FPAs.     

Spectra of quantum chains without the Yang-Baxter equation

We study one-dimensional reaction-diffusion models described by master equations and their associated two-state quantum hamiltonians. By choosing appropriate rates, the equations of motion decouple into certain subsets. We solve the first subset which has a close relation to the problem of lattice electrons in an electric field. In this way we obtain L(L − 1) + 1 energy levels of a quantum chain with L sites. The corresponding hamiltonian depends on seven parameters and does not look integrable using conventional methods. As an application, we compute the dynamical critical exponent of a new type of kinetic Ising model.     

弹体尾部轴对称干扰流场数值模拟

绕弹体的超声速气流与发动机喷流相互作用,在尾部形成复杂的干扰流场。本文用有限差分法求解全N-S方程,对这一复杂流场进行了数值模拟,得到了实验观察到的各种流场结构及其随喷口压力比的变化规律。外流M_∞=1.94,R_e∞=2.2×10⁵,喷流M_j=3.0,喷口压力比p_j/p_∞分别为1.03,0.527,0.15三种。差分算法为一种改进的Beam-Warming格式。计算底部压力和激波在喷流中心的反射位置与实验数据进行了比较,吻合较好。     

Non-threshold (F, Dp) bound states

In the previous paper [hep-th/9904112], we argued that there exist BPS bound states of Dp branes carrying certain units of quantized constant electric field for every p (with 1 p 8). Each of these bound states preserves one half of the spacetime supersymmetries. In this paper, we construct these bound state configurations explicitly for 2 p 7 from Schwarz's (m, n)-string or (F, D1) bound state in type IIB string theory by T-dualities along the transverse directions. We calculate the charge per of (p − 1)-dimensional area for F-strings in (F,Dp) and the tension for each of these bound states. The results agree precisely with those obtained previously from the worldvolume study. We study the decoupling limit for the (F, D3) bound state and find that Maldacena's AdS₅/CFT₄ correspondence may hold true even with respect to this bound state but now with an effective string coupling rather than the usual string coupling. This coupling is quantized and can be independent of the usual string coupling in a certain limit.     

Constant scalar curvature and warped product globally null manifolds

This paper deals with the curvature properties of a class of globally null manifolds (M,g) which admit a global null vector field and a complete Riemannian hypersurface. Using the warped product technique we study the fundamental problem of finding a warped function such that the degenerate metric g admits a constant scalar curvature on M. Our work has an interplay with the static vacuum solutions of the Einstein equations of general relativity.     

New exact solutions to the Eddington-inspired-Born-Infeld equations for a relativistic perfect fluid in a Bianchi type I spacetime

We consider a Bianchi type I physical metric g, an auxiliary metric q and a density matter ρ in Eddington-inspired-Born-Infeld theory. We first derive a system of second order nonlinear ordinary differential equations. Then, by a suitable change of variables, we arrive at a system of first order nonlinear ordinary differential equations. Using both the solution-tube concept for the first order nonlinear ordinary differential equations and the nonlinear analysis tools such as the Arzelá–Ascoli theorem, we prove an existence result for the nonlinear system obtained. The resolution of this last system allows us to obtain new exact solutions for the model considered. Finally, by studying the asymptotic behaviour of the exact solutions obtained, we conclude that this solution is the counterpart of the Friedman–Lemaître–Robertson–Walker spacetime in Eddington-inspired-Born-Infeld theory.     

左手材料阶跃型光纤的模场特性

从Maxwell方程组出发,讨论纤芯为左手材料,包层为右手材料阶跃型光纤,推导了矢量解的场方程.经过数学计算,求得了左手材料阶跃型光纤矢量解的特征方程.根据矢量模的分类,找到了TE模、TM模、HE模和EH模的特征方程.根据各模的特征方程,并且与右手材料光纤相关的特征方程,在靠近截止和远离截止两种情况下进行了比较,得到了左手材料光纤的某些奇异特性.     

三种湍流模式数值模拟直角弯管内三维分离流动的比较

采用有限体积法数值离散雷诺时均Navier Stokes方程,模拟了方形截面90°大曲率弯曲管道内的三维湍流流动.用3种湍流模式(标准k-ε湍流模式、RNG k-ε湍流模式、Realizable k-ε湍流模式)求解该问题.给出了数学模型和计算结果,并与实验数据进行了比较.结果表明,采用RNG k-ε湍流模式并结合两层壁面模型的处理,能有效准确地求解强曲率影响的管道内及近壁区湍流的流动.     

The Maxwell-Vlasov equations as a continuous hamiltonian system

The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion.     

Fluctuation-regularized front propagation dynamics in reaction-diffusion systems

We introduce and study a new class of fronts in finite particle-number reaction-diffusion systems, corresponding to propagating up a reaction-rate gradient. We show that these systems have no traditional mean-field limit, as the nature of the long-time front solution in the stochastic process differs essentially from that obtained by solving the mean-field deterministic reaction-diffusion equations. Instead, one can incorporate some aspects of the fluctuations via introducing a density cutoff. Using this method, we derive analytic expressions for the front velocity dependence on bulk particle density and show self-consistently why this cutoff approach can get the correct leading-order physics.