Travelling Wave Solution of Korteweg-de Vries-Burger's Equation

An attempt has been made to obtain exact analytical travelling wave solution of Korteweg-de Vries-Burger's (KdVB) equation by the so-called tanh-method. This equation can be derived for dust ion acoustic shocks by using reduction perturbation method. It is found that an exact solution of the KdVB equation is obtained by tanh-method, provided the parameters involved satisfy a constraint relation. However a special exact analytical solution can be obtained where no such restriction is necessary. This solution has the structure of a shock wave. Numerical solution is also obtained for travelling wave with or without the assumption of the constraint relation. We have also found a singular solution in terms of cosech and coth functions.     

Robust feed-back control of travelling waves in a class of reaction-diffusion distributed biological systems

Reaction-Diffusion (RD) mechanisms can describe many biological phenomena such as neuron firing in the brain, the heartbeat, cellular organization activities or even biological disorders such as fibrillation. The FitzHugh-Nagumo (FHN) model is a particular case of RD systems. It is able to capture the key features of many biological processes and since it is relatively simple it has been widely employed during recent years. Some examples of its predictive capabilities include the representation of the normal behavior of some physiological phenomena, related to a travelling plane wave, as well as biological disorders associated with spiral or irregular fronts. The objective of this work is to design a control law that is able to stabilize complex behaviors (travelling plane wave) in biological systems using the FHN model as a case study. Since, in biological systems there usually exists a lack of detailed information on the system structure, our control law will be designed to be robust, i.e., it must be able to reach the predefined reference regardless the presence of structural uncertainties. To this purpose, we will extend some classical results on the finite-dimensional robust control theory to RD systems by means of order reduction techniques, in particular the Proper Orthogonal Decomposition method.     

Large-eddy simulation of the generation and propagation of internal solitary waves

A modified large-eddy simulation model,the dynamic coherent eddy model(DCEM)is employed to simulate the generation and propagation of internal solitary waves(ISWs)of both depression and elevation type,with wave amplitudes ranging from small,medium to large scales.The simulation results agree well with the existing experimental data.The generation process of ISWs is successfully captured by the DCEM method.Shear instabilities and diapycnal mixing in the initial wave generation phase are observed.The dissipation rate is not equal at different locations of an ISW.ISW-induced velocity field is analyzed in the present study.The structure of the bottom boundary layer(BBL)of internal wave packets is found to be different from that of a single ISW.A reverse boundary jet instead of a separation bubble exists behind the leading internal wave while separation bubbles appear in other parts of the wave-induced velocity field.The boundary jet flow resulting from the adverse pressure gradients has distinctive dynamics compared with free shear jets.     

Experimental study of solitary waves in a nonlinear transmission line

Several properties of solitary waves were measured on a nonlinear transmission line. These include the transition from a linear dispersive response into a solitary wave response as the amplitude of a narrow voltage impulse is increased, and an observation of the recurrence phenomena of solitary waves. Supported in part by the National Science Foundation.     

Nonlinear coupling of waves in a plasma in a strong dissipation limit

We study the nonlinear resonant coupling of two waves in a plasma for strong dissipation. We show that the corresponding system of differential equations has a saddle-focus fixed point and study its stable and unstable manifolds. The results we obtain suggest that the stochasticity which is numerically observed might be due to the existence of a spiral-type strange attractor.     

Promotion of partial oxidation of methanol over thin Pt and Pd film catalysts by resonance oscillation of acoustic waves

The thickness extension mode resonance oscillation (TERO) of bulk acoustic waves generated on z-cut LiNbO₃ by rf electric power was employed to the catalytic oxidation of methanol over thin Pt and Pd film catalysts deposited. Both the catalysts produced formaldehyde, methyl formate, and carbon dioxide as carbon-containing products in the gas phase. The TERO considerably increased the selectivity for formaldehyde production on Pt at a moderate rf power, indicating the ability of promoting the partial oxidation of methanol, whereas a small and monotonous decrease in the selectivity of the reaction on Pd occurred with power. The different TERO effects on the selectivity are discussed.     

Motion of spiral waves in the complex Ginzburg-Landau equation

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the centres are found which vary depending on the order of magnitude of the separation of the centres. In particular, the direction of the interaction changes from along the line of centres to perpendicular to the line of centres as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wavenumber and frequency are determined. These depend on the positions of the centres of the spirals, and so evolve slowly as the spirals move.     

SAR图像中机场跑道自动检测方法研究

跑道检测通常由边缘检测和霍夫变换2个步骤组成.由于SAR图像中存在大量斑点噪声,使得边缘检测中存在大量虚假边缘,增加了霍夫变换的时间,降低了跑道检测的准确度,提出一种基于区域分割和距离变换的SAR图像中机场跑道自动检测的新方法.采用基于统计信息的方法增强跑道一背景的对比度,然后用二维直方图阈值分割方法分割图像,再通过距离变换对跑道一背景二值图进行处理,得到跑道中心线的大致分布,最后采用局部空间霍夫变换得到跑道参数.实验结果表明:该方法能够可靠检测出跑道,运算速度满足实时性要求.     

Incredible negative values of effective electromechanical coupling coefficient for surface acoustic waves in piezoelectrics

The extraordinary case of increase in velocity of surface acoustic waves (SAW) caused by electrical shorting of the surface of the superstrong piezoelectric crystal potassium niobate, KNbO3, is numerically found. The explanation of this effect is based on considering SAWs as coupled Rayleigh and Bleustein-Gulyaev modes. A general procedure of approximate decoupling of the modes is suggested for piezoelectric crystals of arbitrary anisotropy. The effect under study takes place when the phase velocity of uncoupled sagittally polarized Rayleigh waves is intermediate between the phase velocities of uncoupled shear-horizontal Bleustein Gulyaev waves at the free and metallized surfaces. In this case, the metallization of the surface by an infinitely thin layer may cause a crossover of the velocity curves of the uncoupled waves. The presence of the mode coupling results in splitting of the curves with transition from one uncoupled branch to the other. This transition is responsible for the increase in SAW velocity, which appears to be greater than its common decrease produced by electrical shorting of the substrate surface.     

Diffraction of spherical waves at an annular aperture in the use of the boundary diffraction wave theory: A comparison of different diffraction integral approaches

The integral expression for divergent spherical waves diffracted at an annular aperture is derived based on the theory of the boundary diffraction wave. The expressions for divergent spherical waves diffracted at a circular aperture and a disk, and the axial field are treated as the special cases of our general one. Numerical calculation results for axial and transversal intensity distributions are given to compare our results with the Kirchhoff diffraction integral, first and second Rayleigh diffraction integrals. As expected, our results are in agreement with those in the use of the Kirchhoff diffraction integral, but the computer time is reduced greatly by using the boundary diffraction wave theory. The four diffraction formulae are shown to be consistent for axial and transversal intensity distributions, if the source and observation points are positioned equally from the aperture, or the observation point is located enough far from the aperture. Otherwise, the mean value of the first and second Rayleigh diffraction integrals is equal to the result of the boundary diffraction wave theory.     

The influence of the benthic frontal zone on acoustic wave propagation in the ocean and evaluation of the possibilities of its ray tomography

The specificity of ray trajectories in the presence of a benthic front, which is the boundary between the Antarctic deep and bottom waters, has been considered. Deep-water “noncanonical” caustic surfaces confined to the front have been found. The ability to reconstruct a sound velocity profile in the benthic frontal zone has been evaluated using methods of ray tomography in the ocean. A possible reconstruction of the profile using a horizontal displacement of the receiving antenna or transmitter at relatively small depths has been shown. Original Russian Text ? V.S. Ivanov, P.N. Kravchun, 2009, published in Vestnik Moskovskogo Universiteta. Fizika, 2009, No. 2, pp. 92–97.     

Solitary density waves in the strongly coupled one component Coulomb particle structures as experimental support of the general versatility of the caustic theory

In this paper we demonstrate that generation of the solitary density wave in the strongly coupled one component Coulomb system of particles confined in a long quadrupole electrodynamic Paul trap is possible, when the energy losses due to air viscosity can be compensated by the energy contribution of the altering electric fields of the trap. Results of this paper allow to identify observed solitary waves as the caustics (according to definition of the book “Catastrophe Theory” by V. I. Arnold) and can be considered as the new experimental support of the general versatility of the caustic theory in describing different physical phenomena not only in collisionless systems of particles but also when interparticle interaction and interaction with external fields in viscous media are strong.     

Modulational instability of dust acoustic waves in a dusty plasma with nonthermal electrons and ions

Effects of nonadiabaticity of variable dust charge, dust fluid temperature, trapped electrons as well as nonisothermality of ions on the amplitude modulation of dust acoustic waves in an unmagnetized dusty plasma are investigated. A modified nonlinear Schr?dinger equation (NLSE) is obtained by the standard reductive perturbation technique and is solved numerically by the split-step Fourier method. The modulational instability and the envelope solitary wave structure are found to be modified somewhat by the effects of nonthermally distributed ions and trapped electrons.