Simulation studies of the scattering of a solitary wave by a mass impurity in a chain of nonlinear oscillators

We have simulated large amplitude motion in cyclic one-dimensional lattices of Morse potential oscillators with a mass impurity, and have observed an unexpected persistence of solitary wave behavior for which we are unable to discover a satisfactory explanation. In solitary wave motion as a function of cycle length and of initial energy, the most common feature of the dynamics is an initial energy plateau with regular oscillatory energy exchange between the solitary wave and other excitations of the lattice, followed by rapid decay. Some systems show no decay at all through 1000 impurity interactions, while others show no significant plateau before decaying. For some cycle lengths there are energy bands in which the solitary wave propagates indefinitely long, with small amplitude oscillatory exchange of energy with the lattice. No regularities were found.     

Asymptotic behavior of electron wave functions in disordered granular materials

For weakly localized electrons in disordered granular materials, the wave function decay length that determines the spatial decrease of the wave functions in the superlocalization mode is calculated. The dependence of the decay length on the energy and structural parameters of the system is established.     

Effect of the structurally damaged surface layer of an isotropic solid on Rayleigh wave dispersion and damping

The effect of the structurally damaged isotropic surface layer on the free surface of an isotropic solid on the Rayleigh wave propagation has been considered. The phase velocity dispersion and inverse Rayleigh wave decay length in the second order of vanishing with respect to the ratio of the structurally damaged layer thickness to the wavelength have been obtained in an analytical form. For the dispersion and the inverse wave decay length, the long-wave limit has been studied when the wavelength is much larger than the characteristic size of layer inhomogeneity. The inverse decay length has been calculated numerically.     

Description of two-proton radioactivity on the basis of methods of the quantum theory of ternary nuclear fission

The two-proton decay of spherical nuclei is investigated on the basis of the formalism developed in constructing the quantum-mechanical theory of ternary fission. The proposed method for determining the amplitudes of partial widths with respect to two-proton decay and the asymptotic behavior of the wave function for a decaying nucleus makes it possible to solve the problem of describing two-proton radioactivity without recourse to the traditionally used (in R-matrix approaches) cumbersome procedure of matching the internal and the external wave function for the decaying nucleus within the three-body formulation. In the diagonal approximation and with allowance for the properties of the potential describing the interaction of the products of two-proton decay, the structure of the wave function for the Cooper pair of two protons bound in the parent nucleus is analyzed, along with the behavior of the wave function describing the potential scattering of the products of binary decay, the coupling of decay channels being taken into account in this analysis.     

Control of Wave Propagation and Effect of Kerr Nonlinearity on Group Index

We use four-level atomic system and control the wave propagation via forbidden decay rate. The Raman gain process becomes dominant on electromagnetically induced transparency (EIT) medium by increasing the forbidden decay rate via increasing the number of atoms [G.S. Agarwal and T.N. Dey, Phys. Rev. A 74 (2005) 043805 and K. Harada, T. Kanbashi, and M. Mitsunaga, Phys. Rev. A 73 (2006) 013803]. The behavior of wave propagation is dramatically changed from normal (subluminal) to anomalous (superluminal) dispersion by increasing the forbidden decay rate. The system can also give a control over the group velocity of the light propagating through the medium via Kerr field.     

Control of Wave Propagation and Effect of Kerr Nonlinearity on Group Index

We use four-level atomic system and control the wave propagation via forbidden decay rate. The Raman gain process becomes dominant on electromagnetically induced transparency (EIT) medium by increasing the forbidden decay rate via increasing the number of atoms [G.S. Agarwal and T.N. Dey, Phys. Rev. A 74 (2005) 043805 and K. Harada, T. Kanbashi, and M. Mitsunaga, Phys. Rev. A 73 (2006) 013803]. The behavior of wave propagation is dramatically changed from normal (subluminal) to anomalous (superluminal) dispersion by increasing the forbidden decay rate. The system can also give a control over the group velocity of the light propagating through the medium via Kerr field.     

Electron spin decoherence in quantum dots due to interaction with nuclei

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei. The decay is caused by the spatial variation of the electron wave function within the dot, leading to a nonuniform hyperfine coupling A. We evaluate the spin correlation function and find that the decay is not exponential but rather power (inverse logarithm) lawlike. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by (planck)N/A, where N is the number of nuclei inside the dot, and the amplitude of precession decays to a finite value. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.     

Stress wave propagation in A1 single crystals

Transmitted wave profiles are presented for A1 single crystals that were loaded along crystallographic directions [100], [110] and [111] by a stress wave of the amplitude 1·85 GPa. The experiments were carried out with the Hopkinson Split Bar Technique. The observed wave profiles strongly depend on the specimen length. The constitutive relation of elastic-plastic-relaxing solid was proposed for the interpretation of obtained results. Mechanical properties can then be inferred by comparing observed rates of decay with theoretical models of stress relaxation.     

Nonlinear Wave Propagation in a Disordered Medium

In this paper we consider the problem of solitary wave propagation in a weakly disordered potential. Through a series of careful numerical experiments we have observed behavior which is in agreement with the theoretical predictions of Kivshar et al., Bronski, and Gamier. In particular we observe numerically the existence of two regimes of propagation. In the first regime the mass of the solitary wave decays exponentially, while the velocity of the solitary wave approaches a constant. This exponential decay is what one would expect from known results in the theory of localization for the linear Schrödinger equation. In the second regime, where nonlinear effects dominate, we observe the anomalous behavior which was originally predicted by Kivshar et al. In this regime the mass of the solitary wave approaches a constant, while the velocity of the solitary wave displays an anomalously slow decay. For sufficiently small velocities (when the theory is no longer valid) we observe phenomena of total reflection and trapping.     

Experimental determination of the neutron channeling length in a planar waveguide

In neutron waveguides, the neutron wave is confined inside the guiding layer of the structure and can escape from the layer edge as a microbeam. The channeling within the guiding layer is accompanied by an exponential decay of the neutron wave function density inside the waveguide. Here, we report direct determination of the corresponding decay constant, termed the neutron channeling length. For this, we measured the microbeam intensity as a function of the length of a neutron absorbing layer of variable length placed onto the surface of a waveguide structure. Such planar neutron waveguides transform a conventional neutron beam into an extremely narrow but slightly divergent microbeam, which can be used for the investigation of nanostructures with submicron spatial resolution.     

Decay of turbulence in pipe flow

A novel experiment has been devised which provides direct evidence for critical point behavior in the longstanding problem of the transition to turbulence in a pipe. The novelty lies in the quenching of turbulence by reducing the Reynolds number and observing the decay of disordered motion. Divergence of the time scales implies underlying deterministic dynamics which are analogous to those found in boundary crises in dynamical systems. A modulated wave packet emerges from the long term transients and this coherent state provides evidence for connections with recent theoretical developments.     

Multi-scale homogenization-based modeling of semi-crystalline polymers

This paper presents a finite-strain, multi-scale constitutive model for semi-crystalline polymers, accounting explicitly for the current state and evolution of the underlying crystallographic, lamellar and morphological texture. Specifically, a semi-crystalline polymer is modeled as a two-scale composite, assumed to be, at the larger length scale, an aggregate of randomly distributed grains that, at the smaller length scale, are made up of alternating layers of an amorphous and a crystalline phase. The model incorporates finite elasticity for the amorphous phase and crystallographic hardening for the crystalline phase. The instantaneous effective response of this composite is determined by means of multi-scale homogenization methods, consisting in the use of a “linear comparison composite” (LCC) with the same internal structure as the actual nonlinear composite, with local properties that are optimally chosen via suitably designed variational principles. The effective properties of the resulting two-scale LCC are obtained through a “sequential” homogenization procedure, involving the exact solution for the effective behavior of the lamellar grains and a self-consistent estimate for the aggregate. The latter results are also used to establish evolution laws for the appropriate internal variables in the material. The predictions of the model for the macroscopic response and texture evolution in high-density polyethylene are confronted with available experimental results and compared with those of earlier models.     

Linear mechanism of surface gravity wave generation in horizontally sheared flow

An analysis is presented of a linear mechanism of surface gravity wave generation in a horizontally sheared flow in a fluid layer with free boundary. A free-surface flow of this type is found to be algebraically unstable. The development of instability leads to the formation of surface gravity waves whose amplitude grows with time according to a power law. Flow stability is analyzed by using a nonmodal approach in which the behavior of a spatial Fourier harmonic of a disturbance is considered in a semi-Lagrangian frame of reference moving with the flow. Shear-flow disturbances are divided into two classes (wave and vortex disturbances) depending on the value of potential vorticity. It is shown that vortex disturbances decay with time while the energy of wave disturbances increases indefinitely. Transformation of vortex disturbances into wave ones under strong shear is described.     

Microphase separation in a melt of graft copolymers formed by blocks with different grafting densities

The weak-segregation phase behavior of a monodisperse melt of a binary graft copolymer the macromolecules of which consist of two blocks with different densities of grafting of side chains is investigated. The length of the side chains in each block is assumed to be the same. Analysis of the structure factor of the system indicates the possibility of formation of two-scale structures in the melt. The realized scales differ significantly from each other and correspond to a phase separation between the blocks and between the monomeric units that form the repeating fragment of the graft copolymer. Classification diagrams are constructed, which describe the scale of the structures formed in the melt at different values of the parameters of the chemical structure of the macromolecules.     

Structural order for one-scale and two-scale potentials

We perform molecular dynamics simulations to investigate the relationship between structural order and waterlike dynamic and thermodynamic anomalies in spherically symmetric potentials having either one or two characteristic length scales. Structural order is characterized by translational and orientational order parameters. We find that (i) dynamic and thermodynamic anomalies exist for both one-scale and two-scale ramp potentials, and (ii) waterlike structural order anomalies exist only for the two-scale ramp potential. Our findings suggest that the waterlike relationship between structural order and anomalies is related to the presence of two different length scales in the potential.     

Determination of the threshold intensity of a laser beam for exciting stimulated Mandelstam-Brillouin scattering in the atmosphere

Stimulated Mandelstam-Brillouin scattering at small angles is considered in the case of a powerful laser beam propagating in the static mode in an unbounded medium. In contrast to the pulse mode, a hypersonic wave can be formed not only in the backward direction, but also in the forward direction at small angles. In this work, the latter case is considered as having the smallest value of the threshold intensity. It is shown that finite dimensions of the beam significantly change the excitation conditions for a scattered radiation owing to the mismatch of the wave triplet due to diffraction effects. Determination of the threshold intensity is shown to be possible using the well-known expressions for a plane wave only if the Fresnel number of the beam on the path the length of which is equal to the distance of the optical wave decay due to absorption in the medium is much larger than unity. Moreover, a large number of decay distances of the hypersonic wave must fall on the beam radius. When these conditions are not satisfied, the threshold intensity increases as compared to the plane wave.     

冲击加载下20钢中弹性前驱波衰减与应力松弛行为实验研究

 通过改变样品厚度，对平面冲击加载下20钢的弹性前驱波的波幅衰减和应力松弛进行了实验研究。采用激光速度干涉测速仪（VISAR）实测了样品后自由面速度历史，采样频率达到1 ns，保证了实验结果的准确性。实验结果显示：Hugoniot弹性极限随着传播距离呈指数衰减，在所研究的样品厚度范围内，Hugoniot弹性极限减小了44%；应力松弛行为和弹性前驱波的上升沿时间也依赖于传播距离；冲击加载的强度对材料动态屈服行为的影响很小。     

Decay of solitons in an isotropic collisionless quasineutral plasma with isothermal pressure

Soliton-type solutions of the complete unreduced system of transport equations describing the plane-parallel motions of an isotropic collisionless quasineutral plasma in a magnetic field with constant ion and electron temperatures are studied. The regions of the physical parameters for fast and slow magnetosonic branches, where solitons and generalized solitary waves—nonlocal soliton structures in the form of a soliton “core” with asymptotic behavior at infinity in the form of a periodic low-amplitude wave—exist, are determined. In the range of parameters where solitons are replaced by generalized solitary waves, soliton-like disturbances are subjected to decay whose mechanisms are qualitatively different for slow and fast magnetosonic waves. A specific feature of the decay of such disturbances for fast magnetosonic waves is that the energy of the disturbance decreases primarily as a result of the quasistationary emission of a resonant periodic wave of the same nature. Similar disturbances in the form of a soliton core of a slow magnetosonic generalized solitary wave essentially do not emit resonant modes on the Alfvén branch but they lose energy quite rapidly because of continuous emission of a slow magnetosonic wave. Possible types of shocks which are formed by two types of existing soliton solutions (solitons and generalized solitary waves) are examined in the context of such solutions.     

Structural states and specific features of the deformation behavior of metals and alloys with mixed nano-and micrograin structure

A classification of the structural states of materials with a mixed nano-and microcrystalline structure is proposed. Theoretical analysis of the structural mechanisms and peculiarities of plastic flow of singlephase and two-phase nanostructured metals and alloys with a bimodal size distribution of grains and phases is performed. The effect of grain-boundary and dislocation mechanisms of plastic flow on the specific features of the deformation behavior and plasticity of nanocrystalline materials is analyzed. A microstructural model of strain hardening of a material with two-scale nano-and micrograin structure is proposed and the condition for the loss of plastic flow stability of such a material is investigated. The dependence of the yield strength and uniform strain of nanocrystalline materials with a two-scale structure on the grain size and the ratio of the volume fractions of the nano-and microstructural components is calculated.     

Electromagnetic scattering model of the Kelvin wake and turbulent wake by a moving ship

Taking the attenuation character of the Kelvin wake and the limitation of the traditional two-scale method into account, the practical electromagnetic (EM) scattering model of the Kelvin wake is obtained by using a facet-based model; and for a turbulent ship wake, it is produced by dealing with the wave energy loss rate due to turbulence with the width of turbulent wake closely following a moving ship. The volume scattering theory of foam or bubbles, by using the vector radiation transfer equation, is introduced to modify the traditional two-scale method, a special method for the EM scattering of a turbulent wake, which brings the scattering of ship wakes into better agreement with the real situation.