The one particle theory of periodic point interactions

We solve explicitly and without approximation the problem of a quantum-mechanical particle inR ³ subjected to point interactions that are periodic inR ³ with periodicity of the typeZ, Z ², andZ ³. In the first case we get a model of an infinite straight polymer, in the second case we get a model of a monomolecular layer and in the third case we get a model of a crystal. In all three cases the unit cell of the Bravais lattice is allowed to contain any finite number of interaction sites (atomes), placed arbitrarily and with arbitrary interaction strength. In the case: one interaction site per unit cell we find explicit formulas for the resonance bands and energy bands and their corresponding wavefunctions.     

Hydrodynamic interactions in self similar structures, such as polymers

We study the hydrodynamic properties of polymers and more generally self-similar structures using a new recursion model. The hydrodynamic interaction between monomers is modeled by the standard Green's function of Stokes flow in which an ultrametric distance is substituted for the usual Euclidean distance. This leads to a model where the long-range hydrodynamic interactions and the long-range correlations of the polymer conformation can both be accounted for and yet allow for analytical solutions. We explore the asymptotic as well as the finite size corrections to the scaling behavior with this model. In order to compare the results of the present scheme with more conventional techniques a generalized version of the existing mean field results by Kirkwood and Riseman for the hydrodynamic drag is introduced. Received 26 August 1998 and Received in final form 7 December 1998     

三种同轴双波纹周期慢波结构对比研究

利用Fourier级数展开法,给出了任意几何结构的表达式的求解方法.通过数值计算,对比分析了余弦、梯形和矩形波纹慢波结构(slow-wave structure,SWS)的色散特性.根据S参数理论,研究了这三种SWS纵向模式选择的特性,提出了在同轴慢波器件中加入同轴引出结构,可减少所需SWS周期数,不但使器件结构更为紧凑,还可避免纵模竞争从而提高器件效率、稳定产生微波频率.进一步通过KARAT 2.5维全电磁粒子模拟程序,探讨了分别采用三种SWS的相对论返波振荡器(backward-wave oscillator,BWO)的束-波作用的物理过程,设计了一种紧凑型、吉瓦级、同轴L波段BWO,分析了不同形状SWS的选取原则.在此基础上,开展了初步实验研究：在二极管电压为670 kV,电子束流为107 kA,引导磁场为075 T的条件下,输出微波峰值功率约为102 GW,微波波形半高宽为22 ns,功率转换效率约为142%,频率为161 GHz. 关键词： 同轴慢波结构 相对论返波振荡器 色散特性 高功率微波     

三种同轴双波纹周期慢波结构对比研究

利用Fourier级数展开法,给出了任意几何结构的表达式的求解方法.通过数值计算,对比分析了余弦、梯形和矩形波纹慢波结构(slow-wave structure,SWS)的色散特性.根据S参数理论,研究了这三种SWS纵向模式选择的特性,提出了在同轴慢波器件中加入同轴引出结构,可减少所需SWS周期数,不但使器件结构更为紧凑,还可避免纵模竞争从而提高器件效率、稳定产生微波频率.进一步通过KARAT 2.5维全电磁粒子模拟程序,探讨了分别采用三种SWS的相对论返波振荡器(backward-wave oscillator,BWO)的束-波作用的物理过程,设计了一种紧凑型、吉瓦级、同轴L波段BWO,分析了不同形状SWS的选取原则.在此基础上,开展了初步实验研究：在二极管电压为670 kV,电子束流为107 kA,引导磁场为075 T的条件下,输出微波峰值功率约为102 GW,微波波形半高宽为22 ns,功率转换效率约为142%,频率为161 GHz.     

Evidence for the production of a new particle in neutrino interactions

We present here evidence, based on 5 events recorded in cosmic ray experiments deep underground, for the production of new, massive (? 2 GeV) and long lived (τ ～^?9 sec) particles in neutrino with rock nuclei.     

Flow acoustics in periodic structures

A recent paper [A.A. Krokhin, J. Arriaga, L.N. Gumen, Speed of sound in periodic elastic composites, Phys. Rev. Lett. 91 (2004) 264302-1-4] addresses the speed of sound in periodic elastic composites (phononic crystals) with particular emphasis to the case where air bubbles are present in water and arranged periodically. In such periodically arranged mixtures, the well-known phenomena of the drop of the speed of sound may occur and applications related to, e.g., sound-beam focusing and acoustic surgery are possible [F. Cervera, L. Sanchez, J.V. Sanchez-Perez, R. Martinez-Sala, C. Rubio, F. Meseguer, C. Lopez, D. Caballero, J. Sanchez-Dehesa, Phys. Rev. Lett. 88 (2002) 023902]. In this paper, the analysis is extended theoretically to include cases where a background flow in a periodic structure is maintained. Calculations of dispersion relations and group velocities are presented in cases with one- and two-dimensional material periodicity for background flow values in the range: 0-1m/s. Materials considered in the calculations are periodic water-air mixtures. It is shown that acoustic waves couple to the group velocities only if the (acoustic) wave vector has a component along the background flow velocity direction.     

Wave attenuation in periodic structures

A periodic structure acts as a filter for traveling waves of any kind whether they be electromagnetic, acoustic, bending or anything else. This principle has been used to reduce the vibration level in one part of a structure when it is excited at another. For example, certain frequencies from engine excitation can be attenuated in the cabin of an aircraft. In this paper we report analytical methods for predicting the attenuation of bending waves in a dissipationless beam with flexible ribs attached to it. The insertion loss (attenuation) spectra for a wide frequency range are then compared with measured results for test structures with 1 to 15 ribs attached. Some preliminary work was also done on the effect of rib spacing. The width of the attenuation band increased with increasing number of ribs with seven ribs giving almost as wide a band as it had for the infinitely long periodic beam. Since the structure has no dissipation, the attenuation is due solely to interference effects of multiple reflections.     

Hydrodynamic model for particle size segregation in granular media

We present a hydrodynamic theoretical model for “Brazil nut” size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. We propose a new mechanism for this particle size-segregation due to buoyant forces caused by density variations which come from differences in the local “granular temperature”. The mobility of the particles is modified by the energy dissipation due to inelastic collisions and this leads to a different behavior from what one would expect for an elastic system. Using our model we can explain the size ratio dependence of the upward velocity.     

Focusing-to-defocusing crossover in nonlinear periodic structures

We demonstrate experimentally a transition from nonlinear beam trapping to defocusing in a two-dimensional periodic photonic structures by varying the modulation depth of the lattice. The observed effect illustrates the fundamental crossover from discrete to cw transport mechanisms. At the threshold modulation, the output beam is highly sensitive to refractive index and power variations, which can be potentially applied for high-sensitivity refractive index or temperature sensing.     

Epitaxial periodic p-n structures in PbS

The electrical and photoelectrical properites of periodic p-n structures in an epitaxial film of PbS are studied. The plane of the junctions is perpendicular to the plane of the film. The possibility of using such structures in the photodiode mode as low inertia detectors of IR radiation is shown. Qualitative agreement of the dark characteristics (volt-ampere curve, temperature dependence of resistance) of the p-n structure and photosensitive polycrystalline films was noted. This confirms the hypothesis that in sensitization of polycrystalline films, barriers of the p-n junction type are formed.     

The surface layer on a ferromagnetic. The energy of some periodic domain structures

Explicit solutions are found for a number of special cases of the potential problem of periodic charge distribution. The effect of uneven distribution of the charges of a Bloch wall on the magnetostatic energy is studied, the effective width of the Bloch wall is determined, an analytical expression is found for this distribution of poles and finally the effective height of the surface layer is also determined. An expression is derived for the orientation of the vectors of magnetization in the surface layer with respect to the easy directions of magnetization. The stability of the basic domain structure up to an inclination of 6°of the plane under observation to the direction of easy magnetization and the dimensions of the domains in periodic closure structures follow from the calculations.

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Deterministic weak localization in periodic structures

In some perfect periodic structures classical motion exhibits deterministic diffusion. For such systems we present the weak localization theory. As a manifestation for the velocity autocorrelation function a universal power law decay is predicted to appear at four Ehrenfest times. This deterministic weak localization is robust against weak quenched disorders, which may be confirmed by coherent backscattering measurements of periodic photonic crystals.     

Quantum electrodynamics in three-dimensionally periodic structures

Abstract

Recently, the possibility of obtaining ISE in spectral bands of forbidden light propagation (photonic bandgaps) has been suggested by Yablonovitch.¹ These bandgaps are spectral regions admitting only complex wavevectors k (evanescent waves) in any direction, and boundecl by frequencies ω_max((min) at which the dispersion curve ω(k) becomes discontinuous. Because they are associated with definite k (band edges), such hndgaps are delocalized in space, i.e., they inhibit spontaneous emission independently of t.he spatial distribution of emitters in the system. The systems that have been proposed¹ for the demonstration of bandgaps are dielectric superlattices that exhibit strong three-dimensional (3D) periodic moclulations of the dielectric index with a period comparable to half the emission wavelength.     

Wave dispersion in periodic post-buckled structures

Wave propagation in pinned-supported, post-buckled beams can be described with the Korteweg de Vries (KdV) equation. Finite-element simulations however show that the KdV is applicable only to post-buckled beams with strong pre-compression. For weak and moderate pre-stress, a dispersive front is present and it is the aim of the current paper to analyze sources of dispersion beyond periodicity given three support types: guided, pinned, and free. Bloch theorem and a transfer-matrix method are employed to obtain numerical dispersion relations and characteristic wave modes, which are used to analyze the effects of pre-stress, initial curvature, and the influence of support types. Additionally, a new method is proposed to obtain a semi-analytical dispersion equation for the acoustic branch. Powers of frequency and the propagation constant are explicitly expressed and their coefficients are based on stiffness and mass-matrix components obtained from finite elements. This allows a physical interpretation of the dispersion sources, based on which, equivalent mass–spring models of post-buckled beam are proposed. It is found that mass and stiffness coupling are significant dispersion sources. In the present paper, a reduced form of Bloch theorem is presented exploiting glide-reflection symmetries, reducing the size of the unit cell and allowing an easier representation and interpretation of results.