Two-Mode Wave Solutions to the Degasperis--Procesi Equation

By introducing a new type of solutions, called the multiple-mode wave solutions which can be expressed in nonlinear superposition of single-mode waves with different speeds, we investigate the two-mode wave solutions in Degasperis-Procesi equation and two cases are derived. The explicit expressions for the two-mode waves as well as the existence conditions are presented. It is shown that the two-mode waves may be the nonlinear combinations of many types of single-mode waves, such as periodic waves, solJtons, compactons, etc., and more complicated multiple-mode waves can be obtained if higher order or more single-mode waves are taken into consideration. It is pointed out that the two-mode wave solutions can be employed to display the typical mechanism of the interactions between different single-mode waves.     

Experimental study on the Stokes effect in disordered birefringent microstructure fibers

In this paper, a 120-fs pulse transmission experiment is carried out using disordered birefringent microstructure fibers with cladding ventages. Through this experiment, it is found for the first time that remarkable Stokes and anti-Stokes waves can also be produced when the central wavelength of the incident pulse is in the normal dispersion regime of the microstructure fiber. The generation of the two waves can be explained by the four-wave mixing phase matching theory. Properties of the two waves under the action of femtosecond laser pulses with different parameters are studied. The results show that the central wavelength of anti-Stokes waves and Stokes waves produced under the two orthogonal polarization states shift by 63 nm and 160 nm, respectively. The strengths and central positions of the two waves in birefringent fibers can be controlled by adjusting the phase match condition and the polarization directions of incident pulses.     

Reflection and refraction of waves in oscillatory media

This paper uses the two-dimensional Brusselator model to study reflection and refraction of chemical waves. It presents some boundary conditions of chemical waves, with which occurence of observed phenomena at interface as refraction and reflection of chemical waves can be interpreted. Moreover, the angle of reflection may be calculated by using the boundary conditions. It finds that reflection and refraction of chemical waves can occur simultaneously even if plane wave goes from a medium with higher speed to a medium with lower speed, provided the incident angle is larger than the critical angle.     

Elimination of spiral waves and spatiotemporal chaos by the pulse with a specific spatiotemporal configuration

Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this paper spiral waves and spatiotemporal chaos are successfully eliminated by the pulse with a very specific spatiotemporal configuration. The excited position D of spiral waves or spatiotemporal chaos is first recorded at an arbitrary time （to）. When the system at the domain D enters a recovering state, the external pulse is injected into the domain. If the intensity and the working time of the pulse are appropriate, spiral waves and spatiotemporal chaos can finally be eliminated because counter-directional waves can be generated by the pulse. There are two advantages in the method. One is that the tip can be quickly eliminated together with the body of spiral wave, and the other is that the injected pulse may be weak and the duration can be very short so that the original system is nearly not affected, which is important for practical applications.     

Electromagnetic backscattering from freak in （1＋1）-dimensional deep-water

To study the electromagnetic （EM） backscatter characteristics of freak waves at moderate incidence angles, we establish an EM backscattering model for freak waves in （1＋1）-dimensional deep water. The nonlinear interaction between freak waves and Bragg short waves is considered to be the basic hydrodynamic spectra modulation mechanism in the model. Numerical results suggest that the EM backscattering intensities of freak waves are less than those from the background sea surface at moderate incidence angles. The normalised radar cross sections （NRCSs） from freak waves are highly polarisation dependent, even at low incidence angles, which is different from the situation for normal sea waves; moreover, the NRCS of freak waves is more polarisation dependent than the background sea surface. NRCS discrepancies between freak waves and the background sea surface with using horizontal transmitting horizomtal （HH） polarisation are larger than those using vertical transmitting vertical （VV） polarisation, at moderate incident angles. NRCS discrepancies between freak waves and background sea surface decreases with the increase of incidence angle, in both HH and VV polarisation radars. As an application, in the synthetic-aperture radar （SAR） imaging of freak waves, we suggest that freak waves should have extremely low backscatter NRCSs for the freak wave facet with the strongest slope. Compared with the background sea surface, the freak waves should be darker in HH polarisation echo images than in VV echo images, in SAR images. Freak waves can be more easily detected from the background sea surface in HH polarisation images than in VV polarisation images. The possibility of detection of freak waves at low incidence angles is much higher than at high incidence angles.     

Electromagnetic backscattering from freak waves in(1+1)-dimensional deep-water

To study the electromagnetic (EM) backscatter characteristics of freak waves at moderate incidence angles, we establish an EM backscattering model for freak waves in (1+1)-dimensional deep water. The nonlinear interaction between freak waves and Bragg short waves is considered to be the basic hydrodynamic spectra modulation mechanism in the model. Numerical results suggest that the EM backscattering intensities of freak waves are less than those from the background sea surface at moderate incidence angles. The normalised radar cross sections (NRCSs) from freak waves are highly polarisation dependent, even at low incidence angles, which is different from the situation for normal sea waves; moreover, the NRCS of freak waves is more polarisation dependent than the background sea surface. NRCS discrepancies between freak waves and the background sea surface with using horizontal transmitting horizomtal (HH) polarisation are larger than those with using vertical transmitting vertical (VV) polarisation, at moderate incident angles. NRCS discrepancies between freak waves and background sea surface decreases with the increase of incidence angle, in both HH and VV polarisation radars. As an application, in the synthetic-aperture radar (SAR) imaging of freak waves, we suggest that freak waves should have extremely low backscatter NRCSs for the freak wave facet with the strongest slope. Compared with the background sea surface, the freak waves should be darker in HH polarisation echo images than in VV echo images, in SAR images. Freak waves can be more easily detected from the background sea surface in HH polarisation images than in VV polarisation images. The possibility of detection of freak waves at low incidence angles is much higher than at high incidence angles.     

Propagation of Cylindrical Waves in Media of Time-Dependent Permittivity

We present the propagation of cylindrical waves in the media whose permittivity varies with time abruptly or continuously. By the method of variable separation, we derive the general expression of electric field of TM-polarized waves in two-dimensional space with excitation of any point at any time. With this expression,the solution for a spatially and temporally distributed source can be obtained theoretically. The focusing of reflected waves in the cross section is shown when the media undergoes a sudden or continuous change. The wave propagation in time-invariant media can be considered as a special case of the media under exponential variance.     

Topological Constraints on Scroll and Spiral Waves in Excitable Media

A conservation equation for topological charges of phase singularities （scroll and spiral waves） in excitable media is given. It provides some topological properties of scroll （spiral） waves： for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.     

Exciting rogue waves,breathers, and solitons in coherent atomic media

We propose a scheme that excites rogue waves via electromagnetically induced transparency(EIT), which can also excite breathers and solitons. The system is a resonant Λ-type atomic ensemble. Under EIT conditions, the envelope equation of the probe field can be reduced to several different models, such as the saturable nonlinear Schr?dinger equation(SNLSE), and SNLSE with the trapping potential provided by a far-detuned laser field or a magnetic field. In this scheme, rogue waves can be generated by different initial pulses, such as the Gaussian wave with(or without) the uniform background. The scheme can be used to obtain rogue waves,breathers and solitons. We show the existence regions of rogue waves, breathers, and solitons as the function of the amplitude and width of the initial pulse. The novelty of our paper is that, we not only show rogue waves in the integrable system numerically, but also present the method to generate and control rogue waves in the non-integrable system.     

Generation of sub-half-wavelength micro-optical traps by dichroic evanescent standing waves

The bi-dimensional optical lattices formed by several sets of laser evanescent standing waves propagating at the surface of a dielectric prism are investigated. The characteristics of the optical traps including their depths and the sizes are analysed. It is shown that the micro-optical lattice with a sub-half-wavelength size can be achieved by the interference of the selected evanescent waves. The scheme together with the recently developed atomic chip may be used for atomic quantum manipulation.     

Unconventional Hamilton-type variational principles for analytical mechanics

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the un-conventional Hamilton-type variational principles of holonomic conservative system in analytical mechanics can be established systematically. This unconventional Hamilton-type variational principle can fully characterize the initial-value problem of analytical mechanics, so that it is an important innovation for the Hamilton-type variational principle. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for analytical mechanics in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work of holonomic conservative system in analytical mechanics, but also to derive systematically the complementary functionals for three-field and two-field unconventional variational principles, and the functional for the one-field one by the generalized Legendre transformation given in this paper. Further, with this new approach, the intrinsic relationship among various principles can be explained clearly. Meanwhile, the unconventional Hamilton-type variational principles of nonholonomic conservative system in analytical mechanics can also be established systematically in this paper.     

Interaction region of magnon-mediated spin torques and novel magnetic states

We determine the region in which the magnon-mediated spin torques exist. This region can be controlled by the spin waves. In terms of stability analysis of magnetization dynamics based on the spin-wave background, we obtain the instability conditions of spin waves. With these results, we find the relationship between unstable regions and the formation of Akhmediev breather, Kuznetsov–Ma breather and rogue waves. We establish the phase diagram of some novel magnetic excitaions.     

Actual Tropical Waves Identified by the Wavenumber-Frequency Spectrum Analysis during Boreal Summer

Based on daily satellite-observed outgoing longwave radiation （OLR） data, the tropical intraseasonal oscillation （ISO） associated with the Asian summer monsoon is found to be dominant during the 2005 summer. Such an ISO along with other tropical waves are identified using a wavenumber-frequency spectrum analysis. Some of Significant spectral peaks coincide well with the dispersion curves of the equatorially trapped wave modes from shallow＇water theory, with various equivalent depths of 12-200 m, suggesting that actual tropical waves can be detected from observational data. Although the formation mechanism of the ISO is more complicated than those of other tropical waves with higher frequencies, significant spectral peaks that correspond to the ISO with a period of 30-60 days distinctly appear in the OLR spectra. The selective wavenumber-frequency filtering of OLR data is thus performed to isolate the ISO, Kelvin and equatoriai Rossby waves, and the properties and signatures of such tropical waves that control tropical atmospheric variability for the 2005 summer are clearly identified.     

ECHO STRUCTURE OF SOUND SCATTERING BY A FINITE ELASTIC CYLINDER IN WATER

In this paper the echo structure of short pulse from finite solid elastic circular cylinder is investigated.Itis emphasized that in the case of oblique incidence the echoes still include two kinds of scattering wave:(1).Geometrical scattering waves,namely corner waves.(2).Elastic scattering waves,i.e.waves related with theelasticity of cylinder.The geometrical scattering waves are the waves reflected form the discontinuities ofcylinder,and essentially independent of the material of cylind.Using Kirchhoff approximation therepresentation of corner waves from rigid cylinder has been derived.In the case of oblique incidence theelastic scattering waves differ from the circumferential waves for an infinite cylinder.Two sorts of echoescaused by the reradiation of elastic surface wave have been obeerved in experiments;the radial surfacebackscattering wave and the longitudinal surface backscattering wave,They can be identified according to the arriving time and appearing angle,and the results of a comparable obse     

ULF Waves Associated with Solar Wind Deceleration in the Earth＇s Foreshock

Characteristics of ULF waves associated with the solar wind deceleration in the Earth＇s foreshock on 6-7 April 2003 is studied using the wave telescope technique. In the satellite frame, the ULF waves are the left-handed polarized and quasi anti-parallel propagating mode, with a power peak at about 18.63mHz. The wave vector in the GSE coordinates is estimated to be k = （-4.29, 2.28, 1.21）×10^-4 km^-1, In the solar wind frame, the frequency of waves becomes - 9.39 mHz after the Doppler shift correction. The propagation direction of the waves is thus reversed and correspondingly the polarization of the waves becomes right-handed. The above-mentioned characteristics of the ULF waves in the solar wind frame indicate that the ULF waves associated with the solar wind deceleration are the Alfven-whistler waves, which have been frequently reported in both the observations and computer simulations.     

A STUDY OF THE SOUND REFLECTION FROM POROUS MATERIAL BY IMPULSE METHOD

This paper presents a study of the reflection of sound pulse from porous material when the im-pulse sound source and receiver are located on a line perpendicular to the surface of the material.The transfer functions of reflected sound waves were calculated from the experimental incident and thereflected sound pulses by use of DFT.The impulse response of reflected sound waves can be calculatedtheoretically under the assumption of idealized porous material.Both local reacting and extendedreacting materials were taken into account in the calculations. comparison of the calculationsfor spherical waves and plane waves provides a measure of the effect of spherical waves on thetransfer function of reflected sound waves.For a layer of porous material the reflections in thematerial are studied.     

The effect of cellular aging on the dynamics of spiral waves

Cellular aging can result in deterioration of electrical coupling, the extension of the action potential duration, and lower excitability of the cell. Those factors are introduced into the Greenberg–Hastings cellular automaton model and the effects of the cellular aging on the dynamics of spiral waves are studied. The numerical results show that a 50% reduction of the coupling strength of aging cells has a little influence on spiral waves. If the coupling strength of aging cells equals zero, the ability for the medium to maintain spiral waves will be reduced by approximately 50% when the aging cell ratio increases from 0 to 0.5, where the reduction of cell excitability plays a major role in inducing disappearance of spiral waves. When the relevant parameters are properly chosen, the cellular aging can lead to the meandering of spiral waves,the emergence of the binary spiral waves, and even the disappearance of spiral waves via the stopping rotation or shrinkage of wave. Physical mechanisms of the above phenomena are analyzed briefly.     

Singular Wave Solutions of Two Integrable Generalized KdV Equations

We present some singular wave solutions such as multi-peaked periodic waves, multi-peaked kink waves, multi-peaked peakons as well as kink-compactons, associated with singular curves of generalized KdV equation and modified KdV equation. When a trajectory intersects with the singular curve, it may be divided into segments. Different combinations of these segments may lead to different singular wave solutions, while at the intersection points, peaks on the waves can be observed.     

Response of Charged Particles in a Storage Ring to Gravitational Waves

The influence of gravitational waves on the charged particles in a storage ring is studied. It shows that the gravitational waves might be directly detected by monitoring the motion of charged particles in a storage ring. The angular velocity of the charged particles is continually adjustable by changing the initial energy of particles and the strength of the magnetic field. This feature is very useful for finding the gravitational waves with different frequencies.     

Some basic principles in dynamic theory of viscoelastic materials with voids

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo, some basic principles in the dynamic theory of viscoelastic materials with voids can be estab- lished systematically. In this paper, an important integral relation in terms of con- volutions is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem, but also to derive systemati- cally the complementary functionals for the eight-field, six-field, four-field simpli- fied Gurtin-type variational principles and the potential energy-functional for the two-field one in the dynamic theory of viscoelastic materials with voids by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.