Wave propagation in a 2D nonlinear structural acoustic waveguide using asymptotic expansions of wavenumbers

Nonlinear acoustic wave propagation in an infinite rectangular waveguide is investigated. The upper boundary of this waveguide is a nonlinear elastic plate, whereas the lower boundary is rigid. The fluid is assumed to be inviscid with zero mean flow. The focus is restricted to non-planar modes having finite amplitudes. The approximate solution to the acoustic velocity potential of an amplitude modulated pulse is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger equation (NLSE). The first objective here is to study the nonlinear term in the NLSE. The sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. Secondly, at other frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonics. This happens when the phase speeds of the waves match and the objective is to identify the frequencies of such interactions. For both the objectives, asymptotic coupled wavenumber expansions for the linear dispersion relation are required for an intermediate fluid loading. The novelty of this work lies in obtaining the asymptotic expansions and using them for predicting the sign change of the nonlinear term at various frequencies. It is found that when the coupled wavenumbers approach the uncoupled pressure-release wavenumbers, the amplitude modulation is stable. On the other hand, near the rigid-duct wavenumbers, the amplitude modulation is unstable. Also, as a further contribution, these wavenumber expansions are used to identify the frequencies of the higher harmonic interactions. And lastly, the solution for the amplitude modulation derived through the MMS is validated using these asymptotic expansions. (C) 2015 Elsevier Ltd. All rights reserved.

Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

Strain Gradient Effects on Deformation Strengthening Behavior of Particle Reinforced Metal Matrix Composites

Dislocation models with considering the mismatch of elastic modulus between matrix and reinforcing particles are used to determine the effective strain gradient \ita for particle reinforced metal matrix composites (MMCp) in the present research. Based on Taylor relation and the kinetics of dislocation multiplication, glide and annihilation, a strain gradient dependent constitutive equation is developed. By using this strain gradient-dependent constitutive equation, size-dependent deformation strengthening behavior is characterized. The results demonstrate that the smaller the particle size, the more excellent in the reinforcing effect. Some comparisons with the available experimental results demonstrate that the present approach is satisfactory.

p Dissipative operator

In this paper the authors prove that the generalized positive p selfadjoint (GPpS) operators in Banach space satisfy the generalized Schwarz inequality, solve the maximal dissipative extension representation of p dissipative operators in Banach space by using the inequality and introducing the generalized indefinite inner product (GIIP) space, and apply the result to a certain type of Schrodinger operator.

Dynamical symmetry of screened Coulomb potential and isotropic harmonic oscillator

It is shown that for the screened Coulomb potential and isotropic harmonic oscillator, there exists an infinite number of closed orbits for suitable angular momentum values. At the aphelion (perihelion) points of classical orbits, an extended Runge-Lenz vector for the screened Coulomb potential and an extended quadrupole tensor for the screened isotropic harmonic oscillator are still conserved. For the screened two-dimensional (2D) Coulomb potential and isotropic harmonic oscillator, the dynamical symmetries SO3 and SU(2) are still preserved at the aphelion (perihelion) points of classical orbits, respectively. For the screened 3D Coulomb potential, the dynamical symmetry SO4 is also preserved at the aphelion (perihelion) points of classical orbits. But for the screened 3D isotropic harmonic oscillator, the dynamical symmetry SU(2) is only preserved at the aphelion (perihelion) points of classical orbits in the eigencoordinate system. For the screened Coulomb potential and isotropic harmonic oscillator, only the energy (but not angular momentum) raising and lowering operators can be constructed from a factorization of the radial Schrodinger equation.

The effect of the surface tension on non-propagating solitary waves

In this paper, the effect of the surface tension is considered carefully in the study of non-propagating solitary waves. The parameter plane of the surface tension and the fluid depth is divided into three regions; in two of them a breather soliton can be produced. In literature the parameters of breather solitons are all in one of the parameter regions. The new region reported here has been confirmed by our experiments. In the third region, the theoretical solution is a kink soliton, but a kind of the non-propagating solitary wave similar to the breather soliton was found in our experiments besides the kink soliton.

Microscopic theory of chemical-reaction rate

In this paper we deduce the formulae for rate-constant of microreaction with high resolving power of energy from the time-dependent Schrdinger equation for the general case when there is a depression on the reaetional potential surface (when the depression is zero in depth, the case is reduced to that of Eyring). Based on the assumption that Bolzmann distribution is appropriate to the description of reactants, the formula for the constant of macrorate in a form similar to Eyring's is deduced and the expression for the coefficient of transmission is given. When there is no depression on the reactional potential surface and the coefficient of transmission does not seriously depend upon temperature, it is reduced to Eyring's. Thus Eyring's is a special case of the present work.

非传播孤立波的数值模拟

非传播孤立波是近年来由中国学者发现的一种独特的孤立水波。本文通过数值求解非传播孤立波目前公认的控制方程-Miles导出的一个带共轭项的非线性立方Schrodinger方程，对非传播孤立波进行数值模拟。本文针对非传播孤立波的各种性质，作了大量的数值计算工作，并与实验观察的现象及人们对非传播孤立波的理论研究结果进行了比较和分析。为了得到稳定的非传播孤立波，本文讨论了Miles方程中的线性阻尼系数a的值，计算表明，线性阻尼a对能否形成稳定的非传播孤立波影响很大，在某些情况下，Laedke等人提出的Miles方程的非传播孤立波解的稳定性条件与我们对Miles方程的数值模拟的结果相当一致，a可在满足稳定性条件的区间内取值，但也发现在某些情况下Laedke等人的稳定性条件与我们的数值模拟不完全符合，证明Laedke等人关于非传播孤立波的稳定性条件只是一个必要条件，而不是充分条件。本文研究了两个非传播孤立波的相互作用，数值模拟表明，两个波的作用模式依赖于系统的参数，只有适当大小的外驱动频率和振幅及线性阻尼a可算出两个非传播孤立波周而复始的相互作用现象来，参数不合适时，两个波可能最终合并为一个非传播孤立波而不再分离，也可能彼此不发生作用，保持各自的独立。对不同的初始扰动及其演化的计算表明，要形成单个稳定的非传播孤立波，则初始扰动必须适当，否则扰动可能消失或发展成多个孤立波。关于形成非传播孤立波所需的外驱动条件，计算结果表明，只有适当大小的外驱动频率和振幅可形成稳定的非传播孤立波，数值结果可以描述驱动频率的上限和驱动振幅的上下限，但无法描述驱动频率的下限。我们的数值模拟工作说明Miles方程确实较好的描述了非传播孤立波的物理模型，该方程可以解释许多关于非传播孤立波的物理特性。但Miles方程无法对非传播孤立波的某些实验现象作出解释，因而有待于进一步研究改进。

Oscillatory integral operators related to pointwise convergence of Schrödinger operators

In this thesis we consider smooth analogues of operators studied in connection with the pointwise convergence of the solution, u(x,t), (x,t) ∈ ℝ^n x ℝ, of the free Schrodinger equation to the given initial data. Such operators are interesting examples of oscillatory integral operators with degenerate phase functions, and we develop strategies to capture the oscillations and obtain sharp L^2 → L^2 bounds. We then consider, for fixed smooth t(x), the restriction of u to the surface (x,t(x)). We find that u(x,t(x)) ∈ L^2(D^n) when the initial data is in a suitable L^2-Sobolev space H^8 (ℝ^n), where s depends on conditions on t.

A scaling law of photoionization in ultrashort pulses

By means of the numerical solution of time-dependant Schrodinger equation, we verify a scaling law of photoionization in ultrashort pulses. We find that for a given carrier-envelope phase and duration of the pulse, identical photoionizations are obtained provided that when the central frequency of the pulse is enlarged by k times, the atomic binding potential is enlarged by k times, and the laser intensity is enlarged by k(3) times. The scaling law allows us to reach a significant control over direction of photoemission and offers exciting prospects of reaching similar physical processes in different interacting systems which constitutes a novel kind of coherent control.

脉冲啁啾对于阿秒脉冲的影响

采用单电子近似和软核势模型，通过数值求解一维含时薛定谔方程，理论研究了当脉冲分别带有正、负啁啾的情况下所产生的阿秒脉冲，分析了不同脉冲啁啾特性对阿秒脉冲的强度和宽度的影响，研究结果表明，无论是正啁啾还是负啁啾，随着啁啾量的增加，都将使激光脉冲由产生单个阿秒脉冲趋向于产生阿秒脉冲链，正啁啾和负啁啾对于阿秒脉冲宽度的影响是不同的，负啁啾对于阿秒脉冲宽度影响很小，适当的负啁啾有利于缩小阿秒脉冲的宽度；而正啁啾脉冲产生的阿秒脉冲较无啁啾时展宽，且随着啁啾量的增加，其阿秒脉冲宽度迅速增大。

极紫外阿秒脉冲在高次谐波产生过程中引起的非偶极效应

当红外强激光和极紫外（XUV）阿秒脉冲共同作用于原子分子时，电离出去的电子通常会吸收和辐射激光光子而发生能量扩展．讨论了由于XUV阿秒脉冲的短波长与扩展后的电子波包尺度可相比拟时在高次谐波产生过程中引起的非偶极效应．采用彤作为模型分子，并把分子轴置于激光场的传播方向，通过解二维含时薛定谔方程并比较考虑非偶极效应和采用偶极近似两种方法计算得到的结果，两者相比，前者的谐波强度降低，谐波频率向低级次稍有移动，电子能谱的能带内出现了更多的光电子峰．在相同的光电子能量处，两种方法计算得到的信号强度相差2—5倍．并且

Nonlinear X-wave formation and conical emission at different powers of a femtosecond laser pulse in water

Nonlinear X-wave formation at different pulse powers in water is simulated using the standard model of nonlinear Schrodinger equation (NLSE). It is shown that in near field X-shape originally emerges from the interplay between radial diffraction and optical Kerr effect. At relatively low power group-velocity dispersion (GVD) arrests the collapse and leads to pulse splitting on axis. With high enough power, multi-photon ionization (NIPI) and multi-photon absorption (MPA) play great importance in arresting the collapse. The tailing part of pulse is first defocused by MPI and then refocuses. Pulse splitting on axis is a manifestation of this process. Double X-wave forms when the split sub-pulses are self-focusing. In the far field, the character of the central X structure of conical emission (CE) is directly related to the single or double X-shape in the near field. (c) 2007 Elsevier B.V. All rights reserved.

Embedding quantum simulators

79 p.

One-dimensional potential for image-potential states on graphene

In the framework of dielectric theory, the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-potential states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by numerically solving the one-dimensional Schrodinger equation. The imagepotential state wave functions accumulate most of their probability outside the slab. We find that the random phase approximation (RPA) for the nonlocal dielectric function yields a superior description for the potential inside the slab, but a simple Fermi-Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters: the slab width and the electronic density. The theoretical calculations are compared with experimental results for the work function and image-potential states obtained by two-photon photoemission.