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.     

NONLINEAR GRAVITY INERTIAL WAVE OF TWO DIMENSIONS AND DISCUSSION OF THE POSSIBILITY OF SOLITARY WAVE''''S EXISTENCE

In this paper we discuss the problem of a nonlinear gravity inertial wave of twodimensions and the possibility of solitary wave's existence. First of all, the existingcondition and analytic solution expression of shallow water waves are obtained by theapplication of the qualitative method of O. D. Es. We find that when the problem is de-generated, some physical values produce the nonlinear solitary wave, while other physi-cal values will be unbounded, so we consider that the nonlinear solitary wave for thesystem does not exist. Then we introduce concepts of the generalized energy (i. e. pseu-do-energy): when the pseudo-energy produces the tiny change at acting on a special ex-ternal effect, there will be solitary waves in this system. Finally, we obtain the repre-sentative of the nonlinear solitary wave which is different from KdV equation.     

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.     

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   

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 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.     

Combustion waves in a model with chain branching reaction

In this paper the steady planar travelling waves in the adiabatic model with two-step chain branching reaction mechanism are investigated numerically. The properties of these solutions are demonstrated to have similarities with the properties of non-adiabatic combustion waves that is, there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. It is also shown that the model possesses a new type multiple travelling wave solutions (which we call wave trains) with complex structure of the profiles and varying speeds     

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.     

Polarographische Untersuchungen an Solochromviolett RS in Pufferlösungen in Abwesenheit und in Gegenwart oberflächenaktiver Stoffe (SAS)

The polarographic behaviour of solochrome violet RS is investigated in buffer solutions of varying pH in the absence and presence of surfactants (triton 100-X and dodecylbenzene-sulphonate). The reduction proceeds irreversibly along a single wave in acid solutions and two waves in alkaline ones. The electrode reaction corresponds to four electrons in media of pH<2.5 and pH>8.0; in media of pH 4 5.5 two electrons are consumed. In solution of pH 2.5 4 or 5.5–8.0, both reactions contribute in varying magnitudes. The addition ofSAS causes the inhibition of reduction beyond the 2-electrons stage in acid solutions; the polarograms comprise one wave in case ofDBS and two waves of equal height in presence of triton. In alkaline media the polarogram comprises three waves due to the splitting of the main reduction wave. The kinetic parameters of the electrode reaction are also determined.     

Wave-pinned filaments of scroll waves

Scroll waves are three-dimensional excitation patterns that rotate around one-dimensional space curves. Typically these filaments are closed loops or end at the system boundary. However, in excitable media with anomalous dispersion, filaments can be pinned to the wake of traveling wave pulses. This pinning is studied in experiments with the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction and a three-variable reaction-diffusion model. We show that wave-pinned filaments are related to the coexistence of rotating and translating wave defects in two dimensions. Filament pinning causes a continuous expansion of the total filament length. It can be ended by annihilating the pinning pulse in a frontal wave collision. Following such an annihilation, the filament connects itself to the system boundary. Its postannihilation shape that is initially the exposed rim of the scroll wave unwinds continuously over numerous rotation periods.     

The CuII−CuI−Cu0(Hg) system in the presence of benzotriazole: Part I. A polarographic investigation

A polarographic investigation of Cu^II electroreduction from solutions of benzotriazole (BTA) of pH from 1 to 3 at a dropping mercury electrode shows the presence of two successive adsorption waves of equal height (waves Ic and IIIc) due, respectively, to the formation and to the subsequent dissolution of an adsorbed film of a Cu^I compound. The dependence of the half-wave potential of wave IIIc, which is polarographically reversible, upon pH and BTA concentration indicates that the adsorbed film has the composition [Cu^I(BTA^?)], where BTA^? denotes the deprotonated anionic form of benzotriazole. Moreover, the maximum height of wave IIIc indicates that this film is one monolayer thick. A third cathodic wave (wave IIc), lying between waves Ic and IIIc, stems from the reduction to the metal state of the Cu^II ions diffusing from the bulk solution. Copper(0) oxidation at dropping amalgam electrodes in BTA solutions yields two successive adsorption waves (waves Ia and IIa). Wave Ia is due to the same electrode process, Cu⁰ (Hg)+BTA?Cu^I(BTA^?)+H⁺+e, responsible for the cathodic wave IIIc. On the other hand, wave IIa is due to the formation of roughly two adsorbed monolayers of [Cu^I(BTA^?)] upon that formed along wave Ia.     

On evolution of non-linear waves in polytropic reacting gases

In this paper we have studied the behavior of wave motion as propagating wavelets and their culmination into shock waves in polytropic reacting gases with same \(\gamma \)-law. An expansion wave resulting from the action of receding piston has been considered and the solution to this problem has been obtained. The propagation of weak waves has been considered and the flow variables in the region bounded by the piston and the characteristic wave front have been found out. The expansive action of a receding piston undergoing an abrupt change in velocity has been discussed. Central expansion fan and shock fronts have been studied and the solutions up to first order in the physical plane have been obtained. The effects of reaction mechanism on the solutions have been analyzed in each case.     

Acousto-spinodal decomposition of compressible polymer solutions: early stage analysis

The structure and dynamics of early stage kinetics of pressure-induced phase separation of compressible polymer solutions via spinodal decomposition is analyzed using a linear Euler-Cahn-Hilliard model and the modified Sanchez Lacombe equation of state. The integrated density wave and Cahn-Hilliard equations combine the kinetic and structural characteristics of spinodal decomposition with density waves arising from pressure-induced couplings. When mass transfer rate is slower that acoustic waves, concentration gradients generate density waves that cycle back into the spinodal decomposition dynamics, resulting in oscillatory demixing. The wave attenuation increases with increasing mass transfer rates eventually leading to nonoscillatory spinodal demixing. The novel aspects of acousto-spinodal decomposition arise from the coexistence of stable oscillatory density dynamics and the unstable monotonic concentration dynamics. Scaling laws for structure and dynamics indicate deviations from incompressible behavior, with a significant slowing down of demixing due to couplings with density waves. Partial structure factors for density and density-concentration reflect the oscillatory nature of acousto-spinodal modes at lower wave vectors, while the single maximum at a constant wave vector reflects the presence of a dominant mode in the linear regime. The computed total structure factor is in qualitative agreement with experimental data for a similar polymer solution.     

Acoustic resonances in microfluidic chips: full-image micro-PIV experiments and numerical simulations

We show that full-image micro-PIV analysis in combination with images of transient particle motion is a powerful tool for experimental studies of acoustic radiation forces and acoustic streaming in microfluidic chambers under piezo-actuation in the MHz range. The measured steady-state motion of both large 5 microm and small 1 microm particles can be understood in terms of the acoustic eigenmodes or standing ultra-sound waves in the given experimental microsystems. This interpretation is supported by numerical solutions of the corresponding acoustic wave equation.     

Polarography of B(12) coenzyme

The polarography of B(12) coenzyme (5,6-dimethylbenzimidazolylcobamide, DBC coenzyme) has been investigated at the dropping mercury electrode. Exposure of solutions of the coenzyme to light and then to oxygen give polarograms comparable to those of B(12r) and hydroxocobalamin (B(12a)) respectively. At pH 11.6 the coenzyme gives two reduction waves, at -1.43 and -1.62 V vs. the S.C.E.; in less basic solutions the two waves merge to give one multielectron wave.     

Electrochemical reduction of 4-thienylquinazoline in dimethylformamide

Electrochemical reduction of 4-thienylquinazoline (4-TQ) at the dropping mercury electrode in dimethylformamide solutions containing 0.1 M tetrabutyl ammonium iodide supporting electrolyte gave two well-defined diffusion-controlled waves. The first wave was found to be quasi-reversible and the second irreversible, on the basis of the usual criteria. The controlled potential electrolysis experiments carried out at the limiting regions of the frist and the total waves of 4-TQ yielded the same number of electrons, namely two, in both cases. Mechanisms corresponding to the total wave and the first wave were proposed based on the results obtained.     

The Polarographic Behaviour of Some Arylidene Benzoic Hydrazide Derivatives and Substituent Effect

The polarographic reduction of some arylidene derivatives of benzoic hydrazide are investigated at the DME. The polarograms in solutions of pH≤8 consist of a single wave corresponding to 4 electrons in acid media and 2 electrons in alkaline ones. The wave splite into two daughter waves in media of pH≥10, the more negative wave increases in height at the expense of ihe original one with rise of pH. The reduction waves are essentially diffusion controlled with one proton and two electrons in the rate determining step. The electrode reaction is discussed and the important kinetic parameters are determined.     

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.