A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis

A nonlocal Boussinesq equation is deduced from the local one by using consistent correlated bang method. To study various exact solutions of the nonlocal Boussinesq equation, it is converted into two local equations which contain the local Boussinesq equation. From the N-soliton solutions of the local Boussinesq equation, the N-soliton solutions of the nonlocal Boussinesq equation are obtained, among which the (N=2,3,4)-soliton solutions are analyzed with graphs. Some periodic and traveling solutions of the nonlocal Boussinesq equation are derived directly from the known solutions of the local Boussinesq equation. Symmetry reduction solutions of the nonlocal Boussinesq equation are also obtained by using the classical Lie symmetry method.     

Shock wave propagation through a model one dimensional heterogeneous medium

We study the problem of impact-induced shock wave propagation through a model one-dimensional heterogeneous medium. This medium is made of a model material with spatially varying parameters such that it is heterogeneous to shock waves but homogeneous to elastic waves. Using the jump conditions and maximal dissipation criteria, we obtain the exact solution to the shock propagation problem. We use it to study how the nature of the heterogeneity changes material response, the structure of the shock front and the dissipation.     

Mechanics of the implosion of cylindrical shells in a confining tube

A fundamental experimental investigation, with corresponding computational simulations, was conducted to understand the physical mechanisms of implosions of cylindrical shells occurring within a tubular confining space which has a limited potential energy reservoir. In particular, attention was focused on studying the generation of pressure waves from the implosion, the interaction of the pressure waves with the confining tube walls and end caps, and the collapse mechanisms of the implodable volume. Experiments were conducted with three implodable volume geometries which had similar critical collapse pressures. The implodable volumes were aluminum 6061-T6 cylindrical tubing and were placed concentrically within the confining tube. Pressure histories recorded along the length of the confining tube during the experiments were utilized to analytically evaluate the deformation of the implodable volume using fluid–structure coupled deformation models. Computational simulations were conducted using a coupled Eulerian–Lagrangian scheme to explicitly model the implosion process of the tubes along with the resulting compressible fluid flow. The numerical model developed in this study is shown to have high correlation with the experimental results and will serve as a predictive tool for the simulation of the implosion of different cylindrical geometries as well as various tube-in-tube implosion configurations. The experimental results show that the limited hydrostatic potential energy available in a confined environment, as compared to a free field, significantly influences the implosion process. The wall velocities of the implodable volume during the collapse, as well as the extent of the collapse progression, are largely affected by the sudden decrease in the available hydrostatic potential energy. This energy is shown to be partially transformed into elasto-plastic strain energy absorbed in the deformation of the implodable volume, as well as the kinetic energy of the water during the implosion process. Experiments also show that the extent of the collapse progression of an implodable volume can potentially be inhibited within a closed environment, which can lead to the arresting of an implosion event prior to completion for larger implodable volumes. The pressure waves generated during collapse comprise of waves emitted due to the impact of the implodable volume walls, the arrest of rushing water and contact propagation along the walls. These processes later evolve into water hammer type axial wave behavior.     

Effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces

The effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces are studied in this paper. First, the secular equations in the traverse isotropic piezoelectric half space are derived from the general dynamic equation with initial stress taken into consideration. Then, the interface conditions that displacement, stress, electric potential, and electric displacement are continuous across interface are required to be satisfied by three sets of coupled waves, namely, quasi-longitudinal wave, quasi-transverse wave and the electric–acoustic wave. The algebraic equations resulting from the interface conditions are solved to obtain the amplitude ratio of various waves and furthermore the energy reflection and transmission coefficients of various waves. The numerical results are shown graphically and the effects of initial stress are discussed.     

Nano-structured Fabry–Pérot resonators in neutron optics & tunneling of neutron wave-particles

Correlated to the quantum mechanics wave-particle duality, the optical analogy between electromagnetic waves and cold neutrons manifests itself through several interference phenomena particularly the so called Frustrated Total Reflection i.e., the tunneling process in Fabry–Pérot nano-structured cavities. Prominent resonant situations offered by this configuration allow the attainment of numerous fundamental investigations and surface-interface studies as well as to devise new kinds of neutron optics devices. This review contribution reports such possibilities in addition to the recently observed peculiar Goos–Hänchen longitudinal shift of neutron wave-particles which was predicted by Sir Isaac Newton as early as 1730.     

The quantum effects of the spin and the Bohm potential in the oblique propagation of magnetosonic waves

We study the quantum corrections to the oblique propagation of the magnetosonic waves in a warm quantum magnetoplasma composed by mobile ions and electrons. We use a fluid formalism to include quantum corrections due to the Bohm potential and to the spin magnetization energy of electrons. The effects of both quantum corrections are shown in the dispersion relation for perpendicular, parallel and oblique propagation. We find that the quantum contributions to the low frequency depend on the type in the oblique propagation with respect to the background magnetic field. The relevance in astrophysical scenarios is exemplified.     

Localized nonlinear vector matter waves in two-component Bose–Einstein condensates with spatially modulated nonlinearities

Exact localized nonlinear vector matter waves in the form of soliton–soliton and vortex–vortex pairs in two-component Bose–Einstein condensates with spatially modulated nonlinearity coefficients and harmonic trapping potentials are reported. It is shown that there exists an infinite number of exact vector pairs sharing the same chemical potential with soliton–soliton ones for odd integer n while vortex–vortex ones for even integer n  . The stability of the vector pairs found is investigated by means of direct numerical simulations and a linear stability analysis; the results show that the stable vortex–vortex pairs (±l,±l)$(\pm l,\pm l)$ with large topological charges can be supported by the spatially modulated interaction when the harmonic trapping potential is presented in this system.     

Nonlinear analysis of traffic flow on a gradient highway

We investigate the slope effects upon traffic flow on a single lane gradient (uphill/downhill) highway analytically and numerically. The stability condition, neutral stability condition and instability condition are obtained by the use of linear stability theory. It is found that stability of traffic flow on the gradient varies with the slopes. The Burgers, Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations are derived to describe the triangular shock waves, soliton waves and kink-antikink waves in the stable, meta-stable and unstable region respectively. A series of simulations are carried out to reproduce the triangular shock waves, kink-antikink waves and soliton waves. Results show that amplitudes of the triangular shock waves and kink-antikink waves vary with the slopes, the soliton wave appears in an upward form when the average headway is less than the safety distance and a downward form when the average headway is more than the safety distance. Moreover both the kink-antikink waves and the solitary waves propagate backwards. The numerical simulation shows a good agreement with the analytical result.     

Can stochastic resonance and coherence resonance describe CDW dynamics in quasi-one dimensional conductors?

Stochastic resonance (SR) in nonlinear systems is a counterintuitive concept in which a weak periodic signal and noise cooperate and give rise to a maximum in the signal-to-noise ratio at the output of the system when the noise is tuned to a certain value. In the coherence resonance phenomenon (CR), there is no deterministic signal to be enhanced. Intrinsic oscillations are present as transients. Adding an optimum noise turns transients into coherent ones. We discuss the possible application of SR and CR concepts to CDW dynamics in quasi-one dimensional conductors. We show in a preliminary experiment that addition of white noise can modify the behavior of the CDW in the quasi-one dimensional conductor K_0.30MoO₃.     

Charge density waves in nanocrystalline thin films of blue bronze K0.3MoO3

Thin granular films of charge density wave (CDW) system K_0.3MoO₃ were prepared by pulsed laser deposition and investigated by various standard characterization methods such as GI-XRD, electric transport, TOF-ERDA, AFM and UV–visible spectroscopy. While all these methods indicate that the thin films consist of nanometer grains of K_0.3MoO₃, it is only the non-destructive femtosecond time-resolved spectroscopy (fsTRS) that demonstrates the charge density wave nature of the ground state and therefore proves directly the presence of K_0.3MoO₃. Furthermore, the comparison of the fsTRS data obtained in thin films and in single crystals shows the reduction of the charge density wave transition temperature and of the photoinduced signal strength in granular thin films with respect to single crystals, which is attributed to the granularity and crystal growth morphology. Our results establish fsTRS technique as the essential tool for the detection and characterization of complex ground states in nano-sized systems.