ON THE Benjamin-Ono EQUATION AND ITS GENERALIZATION IN THE ATMOSPHERE

This paper deals with the nonlinear problems of the two-layer shallow water wave modelin the atmosphere by the multiple scale method and points out that a nonlinear Benjamin-Ono equation may be obtained if the meridional disturbance wind is weak. Furthermore, thealgebraic solitary waves and nonlinear periodic waves are also calculated and the breakup ofan algebraic solitary wave at the initial time into two is discussed. It is found that the waveform steepens in this process, which is similar to the triggering process of squall lines inthe atmosphere. On the other hand, we also point out that when the meridional disturbancewind is strong, we may obtain a modified Benjamin-Ono equation, i. e. the Benjamin-Ono-KDV equation.     

A THEORY OF BLOCKING FORMATION IN THE ATMOSPHERE

In this paper, a new theory of blocking formation was proposed. The nonlinear Schrdinger equation satisfied by nonlear barotropic Rossby waves for the weak shear zonal flow was obtained by using the WKB method. It was pointed out that when the Rossby wavenumbers sarisfied the relation: k/3相似文献   

Nonlinear Rossby Waves and Their Interactions (Ⅰ) ——Collision of Envelope Solitary Rossby Waves

By using the multiple-scale perturbation method a set of equations which describes two interacting nonlinear Rossby waves in the barotropic atmosphere is derived. The equations are used to study the collision of two envelope solitary Rossby waves. It is found that for a range of parameters, the collision interactions are envelope soliton-like in that the properties of the two envelope solitary waves change very little. For other parameters, new "inelastic" effects are observed, including speed changes, fission of envelope solitary waves and energy dispersion. It is also found that despite of the complexity of the interacting process, the energy of each wave is conserved.     

Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability

We describe a new type of solitary waves, which propagate in such a manner that the pulse periodically disappears from its original position and reemerges at a fixed distance. We find such jumping waves as solutions to a reaction-diffusion system with a subcritical short-wavelength instability. We demonstrate closely related solitary wave solutions in the quintic complex Ginzburg-Landau equation. We study the characteristics of and interactions between these solitary waves and the dynamics of related wave trains and standing waves.     

PERIODIC, SOLITARY AND DISCONTINUOUS PERIODIC SOLUTION OF NONLINEAR WAVES IN THE ATMOSPHERE AND THEIR EXISTENCE (Ⅱ)——ON THE POSSIBILITY OF TAYLOR EXPANSION, M CRITERION AND NONLINEAR WAVE SPEED FORMULAS

In this part, the nonlinear wave speed formulas are discussed. Because the nonlinear wave speed formulas are relative to wave form, we introduce a non-dimensional quantity M, which describes the nonlinear wave pattern and qualitatively determines the nonlinear degree. It is called M criterion. The wave speed formulas of the nonlinear Rossby wave and the nonlinear inertial gravity wave are also discussed. The wave speed of the former decreases with the growth of the amplitude but that of the latter is on the opposite. Furthermore we have also discussed the problems which must be taken note of in applying the Taylor expansion as we solve the approximate solution of nonlinear waves.     

Acoustofluidics 15: streaming with sound waves interacting with solid particles

In Part 15 of the tutorial series "Acoustofluidics-exploiting ultrasonic standing waves forces and acoustic streaming in microfluidic systems for cell and particle manipulation," we examine the interaction of acoustic fields with solid particles. The main focus here is the interaction of standing waves with spherical particles leading to streaming, together with some discussion on one non-spherical case. We begin with the classical problem of a particle at the velocity antinode of a standing wave, and then treat the problem of a sphere at the velocity node, followed by the intermediate situation of a particle between nodes. Finally, we discuss the effect of deviation from sphericity which brings about interesting fluid mechanics. The entire Focus article is devoted to the analysis of the nonlinear fluid mechanics by singular perturbation methods, and the study of the streaming phenomenon that ensues from the nonlinear interaction. With the intention of being instructive material, this tutorial cannot by any means be considered 'complete and comprehensive' owing to the complexity of the class of problems being covered herein.     

一种新的有机非线性光学晶体——L-精氨酸磷酸盐

近年来,在探索新的有机非线性光学晶体的工作中,对含有给电子或受电子基团的芳香族化合物已有广泛深入的研究,并已研制出像2,4-二硝基苯丙氨酸甲酯(MAP)等具有较大倍频系数的新的非线性光学晶体。但是,由于强的共轭效应使它们大π键各能级间的距离接近而使此类晶体无法应用于紫外区。     

On nonlinear waves in an elastic solid

We describe the nonlinear dispersive dissipative evolution of strain waves in a solid in the limiting condition B∼O(R/L), where B is the characteristic amplitude of the wave, L its wavelength and R the radius of a solid rod. We also provide conditions on dissipation and dispersion for the propagation of either shocks or solitary waves of permanent form.     

Spatiotemporal chaos arising from standing waves in a reaction-diffusion system with cross-diffusion

We show that quasi-standing wave patterns appear in the two-variable Oregonator model of the Belousov-Zhabotinsky reaction when a cross-diffusion term is added, no wave instability is required in this case. These standing waves have a frequency that is half the frequency of bulk oscillations displayed in the absence of diffusive coupling. The standing wave patterns show a dependence on the systems size. Regular standing waves can be observed for small systems, when the system size is an integer multiple of half the wavelength. For intermediate sizes, irregular patterns are observed. For large sizes, the system shows an irregular state of spatiotemporal chaos, where standing waves drift, merge, and split, and also phase slips may occur.     

A quasicontinuum approximation for solitons in an atomic chain

An accurate approximation is derived for solitary wave motion in a one-dimensional oscillator chain. Analysis shows that waves exist, travelling faster than sound, whenever the repulsive wall of the potential is anharmonic. The waves carry considerable momentum and potential energy but relatively little kinetic energy.     

ON NONLINEAR GRAVITY TRAVELLING WAVE

In this paper, a two--layer model with dispersive and dissipative effects but without Co-?iolis effect is investigated. It is proved that in the model, under certain parameter condi-tions, there exists monotone travelling wave as well as oscillation travelling wave in additionto the nonlinear periodic solution and solitary wave. The conditions for their existence areprovided. It is particularly pointed out that the pattern of the oscillation travelling wave issimilar to that of the pressure upwelling wave of a squall line which passes certain region.     

Elimination of Anti-spiral Waves by Local Inhomogeneity in Oscillatory Systems

Anti-spiral waves are controlled in an oscillatory system by using a local inhomogeneity. The inhomogeneity acts as a wave source, and gives rise to the propagating plane waves. It is found that there is a critical pacemaking domain size below which no wave will be created at all. Two types of ordered waves (target waves and traveling waves) are created depending on the geometry of the local inhomogeneity. The competition between the anti-spiral waves and the ordered waves is discussed. Two different competition mechanisms were observed, which are related to the ordered waves obtained from different local inhomogeneities. It is found that traveling waves with either lower frequency or higher frequency can both eliminate the anti-spiral waves, while only the target waves with lower absolute value of frequency can eliminate the anti-spiral waves.This method also applies to outwardly rotating spiral waves. The control mechanism is intuitively explained and the control method is easily operative.     

General Solutions to Some Types of Solitons in the Atmosphere

In terms of the Bargmann potential technique the problem of solutions to atmospheric solitary waves is investigated with the derivation of the solutions and their dispersion relations of such solitary waves as of inertial, internal gravity and Rossby modes, and some further appreciation and significant outcome have been achieved.     

Reaction-diffusion travelling waves in the acidic nitrate-ferroin reaction

A two-variable model proposed for the acidic nitrate-ferroin reaction is considered in the reaction-diffusion context. An initial-value problem in which an amount of nitrate is introduced locally into ferroin at uniform concentration is treated both analytically and numerically. It is shown that the large time structure is a reaction-diffusion travelling wave of permanent form propagating with constant speed. This asymptotic wave speed is shown to be the minimum possible wave speed and the asymptotic approach to this value is estimated. Properties of the permanent-form travelling waves are derived and solutions valid for small and large values of a parameter , involved in the kinetic mechanism, are obtained.     

The effect of Lewis number variation on combustion waves in a model with chain-branching reaction

In this paper we investigate the linear stability and properties of the travelling premixed combustion waves in a model with two-step chain-branching reaction mechanism in the adiabatic limit in one spatial dimension. It is shown that the Lewis number for fuel has a significant effect on the properties and stability of premixed flames, whereas the Lewis number for the radicals has only quantitative (but not qualitative) effect on the combustion waves. We demonstrate that when the Lewis number for fuel is less than unity the flame speed is unique and is a monotonically decreasing function of the dimensionless activation energy. The combustion wave is stable and exhibits extinction for finite values of activation energy as the flame speed decreases to zero. For fuel Lewis number greater than unity the flame speed is a double-valued function. The slow solution branch is shown to be unstable whereas the fast solution branch is either stable or exhibits the onset of pulsating instabilities via the Hopf bifurcation. The evolution of these instabilities leads to flame extinction.     

Interfacial Wave Motions Due to Marangoni Instability

Collisions and reflections of solitary waves and (periodic) wave trains driven by surface tension gradients (Marangoni stresses) exhibit a wealth of astonishing features. Depending on the angle between the incoming wave crests, the outgoing waves show in their trajectories after collision negative phase shift for small enough angles, no phase shift at about pi/2 and hence no appreciable change in their trajectories, or positive phase shift, accompanied by the appearance of a phase-locked third wave or Mach-Russell stem at wider crossing angles. Synchronous wave collisions exhibit regular but complex dynamic network patterns whose formation and dependence on the size and the shape of the container are discussed. Although wave reflections share some of these features, corresponding apparently to the outcome of the virtual collision of a wave with its mirror image, there are significant differences that are described here. Copyright 2001 Academic Press.     

Voltammetric behavior of tertiary butyl bromide at mercury electrodes in dimethylformamide

Polarograms for t-butyl bromide in dimethylformamide containing tetramethylammonium perchlorate exhibit two waves which signal stepwise reduction of the starting material to the t-butyl radical and the t-butyl carbanion. Cyclic voltammograms obtained with a hanging mercury drop and at a scan rate of 50 mV s^?1 confirm that the alkyl bromide undergoes stepwise reduction; but the height of the second peak is abnormally small, indicating that t-butyl radicals engage in combination and disproportionation. At a faster scan rate (500 mV s^?1), the first wave nearly merges with the second wave. At all scan rates, two pairs of anodic-cathodic waves, associated with reversible bromide-assisted oxidation of mercury, appear at positive potentials. In addition, another set of anodic-cathodic waves is seen if the potential is scanned rapidly to a value at which the t-butyl carbanion is generated; this set of waves might be related to the formation of trimethylammonium methylide (produced when the tetramethylammonium cation donates a proton to the t-butyl carbanion). Although this latter set of waves is eliminated by addition of a proton donor (diethyl malonate) to the system, the anion of diethyl malonate is itself involved in the appearance of yet another pair of anodic-cathodic waves.     

THEORETICAL AND COMPUTATIONAL INVESTIGATIONS OF NONLINEAR WAVE PROPAGATIONS IN ARTERIES (Ⅰ)——A THEORETICAL MODEL OF NONLINEAR PULSE WAVE PROPAGATIONS

In this paper, a new theoretical model of nonlinear wave propagations in arteries with surrounding tissues was put forward. The equations of motion for the blood vessels and their peripheral tissues as a system have been derived. These equations were expressed in terms of the stresses of the vessel wall and fluid, and the geometry of the blood vessel. They can be used to solve numerically the problems for the propagations of nonlinear pulse waves in arteries together with the momentum and continuity equations of incompressible-viscous flow, as well as the constitutive equations of fluid and vessel wall. The numerical solutions can involve pressure, velocities and flowrate of the blood flow, as well as displacements, velocities and stresses of the vessel wall. These physical variables of propagations of pulse waves in arteries are all of significance physiologically and clinically.     

An efficient nonlinear programming strategy for PCA models with incomplete data sets

Processing plants can produce large amounts of data that process engineers use for analysis, monitoring, or control. Principal component analysis (PCA) is well suited to analyze large amounts of (possibly) correlated data, and for reducing the dimensionality of the variable space. Failing online sensors, lost historical data, or missing experiments can lead to data sets that have missing values where the current methods for obtaining the PCA model parameters may give questionable results due to the properties of the estimated parameters. This paper proposes a method based on nonlinear programming (NLP) techniques to obtain the parameters of PCA models in the presence of incomplete data sets. We show the relationship that exists between the nonlinear iterative partial least squares (NIPALS) algorithm and the optimality conditions of the squared residuals minimization problem, and how this leads to the modified NIPALS used for the missing value problem. Moreover, we compare the current NIPALS‐based methods with the proposed NLP with a simulation example and an industrial case study, and show how the latter is better suited when there are large amounts of missing values. The solutions obtained with the NLP and the iterative algorithm (IA) are very similar. However when using the NLP‐based method, the loadings and scores are guaranteed to be orthogonal, and the scores will have zero mean. The latter is emphasized in the industrial case study. Also, with the industrial data used here we are able to show that the models obtained with the NLP were easier to interpret. Moreover, when using the NLP many fewer iterations were required to obtain them. Copyright © 2010 John Wiley & Sons, Ltd.     

Instability of a two-layer thin liquid film with surfactants: Dewetting waves

Dewetting dynamics of a liquid film composed of two superposed ultra-thin layers of immiscible liquids resting on a solid substrate is investigated in the case when surfactants are present at the liquid-liquid interface. Two cases are considered: insoluble surfactant and surfactant soluble in the lower liquid. The dependence of Hamaker constants on the surfactant concentration is taken into account. A system of three strongly nonlinear evolution equations describing large (comparable to the layer thicknesses), long-wave perturbations of the liquid-liquid and liquid-gas interfaces, as well as the surfactant concentration, is derived for each case in the lubrication approximation. The linear stability analysis shows that in the presence of surfactants, oscillatory dewetting instability can occur. Numerical simulations of this system of nonlinear evolution equations are performed. It is found that in the case of oscillatory instabilities, the system exhibits either standing or traveling "dewetting waves." The weakly nonlinear analysis explains this phenomenon.