Electromagnetic wave propagation at the interface between two polar semiconductors

The interface between two polar semiconductors can support three types of phonon-plasmon-polariton modes propagating in three well-defined frequency windows ??1?[min(?1,?3),?R1], ??2?[max(?2,?4),?R2], and ??3?[min(?2,?4),?R3]. The limiting frequencies ?1,2,3,4 are defined by ?1(?)=0, ?2(?)=0, and ?R1,2,3 by ?1(?)+?2(?)=0, where ?i(?) are dielectric functions of the two media with i=1,2. The dispersion, decay distances, and polarization of the three modes are discussed. The variation of the limiting frequencies with the interface plasma parameter ???p22/?p12 reveals an interesting feature in the dispersion characteristics of these modes. For the interfaces for which the bulk coupled phonon-plasmon frequencies of medium 1 are greater than the LO frequency or are less than the TO frequency of medium 2, there exist two values of ?=?1 and ?2(

Experimental studies and phase field modeling of microstructure evolution during solidification with electromagnetic stirring

Thixocasting requires manufacturing of billets with non-dendritic microstructure. Aluminum alloy A356 billets were produced by rheocasting in a mould placed inside a linear electromagnetic stirrer. Subsequent heat treatment was used to produce a transition from rosette to globular microstructure. The current and the duration of stirring were explored as control parameters. Simultaneous induction heating of the billet during stirring was quantified using experimentally determined thermal profiles. The effect of processing parameters on the dendrite fragmentation was discussed. Corresponding computational modeling of the process was performed using phase-field modeling of alloy solidification in order to gain insight into the process of morphological changes of a solid during this process. A non-isothermal alloy solidification model was used for simulations. The morphological evolution under such imposed thermal cycles was simulated and compared with experimentally determined one. Suitable scaling using the thermosolutal diffusion distances was used to overcome computational difficulties in quantitative comparison at system scale. The results were interpreted in the light of existing theories of microstructure refinement and globularisation.

Hydromagnetic surface waves in a compressible medium

The dispersive characteristic of hydromagnetic surface waves along a plasma-plasma interface when the upper fluid moves with a uniform velocity is discussed. The region of propagation of these waves is shifted above or below depending on whether the basic velocity (uniform)Ugl0.

Propagation of quasi-simple waves in a compressible rotating atmosphere

A class of self-propagating linear and nonlinear travelling wave solutions for compressible rotating fluid is studied using both numerical and analytical techiques. It is shown that, in general, a three dimensional linear wave is not periodic. However, for some range of wave numbers depending on rotation, horizontally propagating waves are periodic. When the rotation ohgr is equal to $$\sqrt {(\gamma - 1)/(4\gamma )}$$ , all horizontal waves are periodic. Here, gamma is the ratio of specific heats. The analytical study is based on phase space analysis. It reveals that the quasi-simple waves are periodic only in some plane, even when the propagation is horizontal, in contrast to the case of non-rotating flows for which there is a single parameter family of periodic solutions provided the waves propagate horizontally. A classification of the singular points of the governing differential equations for quasi-simple waves is also appended.

Solution of a Boundary-Value Problem associated with Diffraction of Water Waves by a Nearly Vertical Barrier

An exact solution is derived for a boundary-value problem for Laplace's equation which is a generalization of the one occurring in the course of solution of the problem of diffraction of surface water waves by a nearly vertical submerged barrier. The method of solution involves the use of complex function theory, the Schwarz reflection principle, and reduction to a system of two uncoupled Riemann-Hilbert problems. Known results, representing the reflection and transmission coefficients of the water wave problem involving a nearly vertical barrier, are derived in terms of the shape function.

A mathematical analysis of nonlinear waves in a fluid filled visco-elastic tube

Our investigations in this paper are centred around the mathematical analysis of a ldquomodal waverdquo problem. We have considered the axisymmetric flow of an inviscid liquid in a thinwalled viscoelastic tube under certain simplifying assumptions. We have first derived the propagation space equations in the long wave limit and also given a general procedure to derive these equations for arbitrary wave length, when the flow is irrotational. We have used the method of operators of multiple scales to derive the nonlinear Schrödinger equation governing the modulation of periodic waves and we have elaborated on the ldquolong modulated wavesrdquo and the ldquomodulated long wavesrdquo. We have also examined the existence and stability of Stokes waves in this system. This is followed by a discussion of the progressive wave solutions of the long wave equations. One of the most important results of our paper is that the propagation space equations are no longer partial differential equations but they are in terms of pseudo-differential operators.Die vorliegenden Untersuchungen beziehen sich auf die mathematische Behandlung des ldquorModalwellenrdquo-Problems. Die achsensymmetrische Strömung einer nichtviskosen Flüssigkeit in einem dünnwandigen viskoelastischen Rohr, unter bestimmten vereinfachenden Annahmen, wird betrachtet. Zuerst werden die Gleichungen des Ausbreitungsraumes im Langwellenbereich abgeleitet und eine allgemeine Methode zur Herleitung dieser Gleichungen für beliebige Wellenlängen bei nichtrotierender Strömung angegeben. Eine Operatorenmethode mit multiplem Maßstab wird verwendet zur Herleitung der nichtlinearen Schrödinger-Gleichung für die Modulation der periodischen Wellen, und die ldquorlangmodulierten Wellenrdquo sowie die ldquormodulierten Langwellenrdquo werden aufgezeigt. Weiters wird die Existenz und die Stabilität der Stokes-Wellen im System untersucht. Anschließend werden die progressiven Wellenlösungen der Langwellengleichungen diskutiert. Eines der wichtigsten Ergebnisse dieser Arbeit ist, daß die Gleichungen des Ausbreitungsraumes keine partiellen Differentialgleichungen mehr sind, sondern Ausdrücke von Pseudo-Differentialoperatoren.

Long waves in inviscid compressible atmospheres: Isothermal atmosphere

Solitary waves and cnoidal waves have been found in an adiabatic compressible atmosphere which, under ambient conditions, has winds, and is isothermal. The theory is illustrated with an example for which the background wind is linearly increasing. It is found that the number of possible critical speeds of the flow depends crucially on whether the Richardson number is greater or less than one‐fourth.

Ion-acoustic solutions and shock waves in multicomponent plasmas

The present investigation of ion-acoustic waves is based on the study of the nonlinearity of plasma waves in a dispersive medium. Here the authors study ion-acoustic solitary waves in a warm ion plasma with non-isothermal electrons and then the results for solitary waves in a plasma with isothermal electrons are obtained. Incorporating the previous results obtained from the solitary wave solutions, the authors generalize the effect of negative ions on ion-acoustic waves in plasmas consisting of either a warm or cold ion species. A reflection phenomenon of ions in these waves is also studied. These results can be generalized, but the discussion is limited to a particular model of the plasma.

Long waves in inviscid compressible atmospheres: Isothermal atmosphere

Solitary waves and cnoidal waves have been found in an adiabatic compressible atmosphere which, under ambient conditions, has winds, and is isothermal. The theory is illustrated with an example for which the background wind is linearly increasing. It is found that the number of possible critical speeds of the flow depends crucially on whether the Richardson number is greater or less than one‐fourth.

Alfvén waves in inhomogeneous magnetic fields: An integrodifferential equation formulation

An integrodifferential formulation for the equation governing the Alfvén waves in inhomogeneous magnetic fields is shown to be similar to the polyvibrating equation of Mangeron. Exploiting this similarity, a time‐dependent solution for smooth initial conditions is constructed. The important feature of this solution is that it separates the parts giving the Alfvén wave oscillations of each layer of plasma and the interaction of these oscillations representing the phase mixing.

Resonant absorption of Alfven waves and the associated phenomenon of magnetic reconnection

It is proposed that the mathematical analysis of the Alfven wave equation in inhomogeneous magnetic fields which explain the resonance absorption of Alfven surface waves near a resonant layer can also be used to show that the magnetic reconnection process can arise near the zero-frequency resonant layer driven by VLF Alfven surface waves. It is suggested that the associated phenomena of resonant absorption and magnetic reconnection can account for the recent observations of intense magnetic activity in the long-period geomagnetic micropulsation range, at cusp latitudes, during flux transfer events.

On the Existence of Hydromagnetic Interface Waves in a Structured Atmosphere

The conditions under which the hydromagnetic interface waves can exist at a magnetic interface is deduced. Using these conditions, it is shown that a slow interface wave with a phase velocity about 5Km/s and a fast interface wave with a phase velocity 6.5 to 8km/s at the photospheric level can exist.