Nonharmonic transverse vibration of the H-bonded molecules and the THz spectra in ice and water

A nonlinear equation of motion is found for the dimer comprising two charged H2O molecules. The THz dielectric response to nonharmonic vibration of a nonrigid dipole, forming the hydrogen bond (HB), is found in the direction transverse to this bond. An explicit expression is derived for the autocorrelator that governs the spectrum generated by transverse vibration (TV) of such a dipole. This expression is obtained by analytical solution of the truncated set of recurrence equations. The far infrared (FIR) spectra of ice at the temperature - 7 degrees C are calculated. The wideband, in the wavenumber (frequency) v range 0... 100.0 cm(-1), spectra are obtained for liquid water at room temperature and for supercooled water at -5.6 degrees C. All spectra are represented in terms of the complex permittivity epsilon(v) and the absorption coefficient alpha(v). The obtained analytical formula for epsilon comprises the term epsilon(perpendicular to) pertinent to the studied TV mechanism with three additional terms Delta epsilon(q), Delta epsilon(mu), and epsilon(or) arising, respectively, from: elastic harmonic vibration of charged molecules along the H-bond; elastic reorientation of HB permanent dipoles; and rather free libration of permanent dipoles in 'defects' of water/ice structure. The suggested TV-dielectric relaxation mechanism allows us: (a) to remove the THz 'deficit' of loss epsilon" inherent in previous theoretical studies; (b) to explain the THz loss and absorption spectra in supercooled (SC) water; and (c) to describe, in agreement with the experiment, the low- and high-frequency tails of the two bands of ice H2O located in the range 10...300 cm(-1). Specific THz dielectric properties of SC water are ascribed to association of water molecules, revealed in our study by transverse vibration of HB charged molecules. (C) 2006 Published by Elsevier B.V.

Statistical theory of finite Fermi systems with chaotic excited eigenstates

A theory of strongly interacting Fermi systems of a few particles is developed. At high excit at ion energies (a few times the single-parti cle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-part icle basis st at es by the residual two- body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-part icle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variable s such as t emperature in an isolated microscopic Fermi system of a few particles.

Simulation of Distributed Contact in String Instruments: a Modal Expansion Approach

Impactive contact between a vibrating string and a barrier is a strongly nonlinear phenomenon that presents several challenges in the design of numerical models for simulation and sound synthesis of musical string instruments. These are addressed here by applying Hamiltonian methods to incorporate distributed contact forces into a modal framework for discrete-time simulation of the dynamics of a stiff, damped string. The resulting algorithms have spectral accuracy, are unconditionally stable, and require solving a multivariate nonlinear equation that is guaranteed to have a unique solution. Exemplifying results are presented and discussed in terms of accuracy, convergence, and spurious high-frequency oscillations.

Modeling relativistic soliton interactions in overdense plasmas: A perturbed nonlinear Schrodinger equation framework

We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrodinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrodinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.

Fully nonlinear ion-sound waves in a dense Fermi magnetoplasma

The nonlinear propagation of ion-sound waves in a collisionless dense electron-ion magnetoplasma is investigated. The inertialess electrons are assumed to follow a non-Boltzmann distribution due to the pressure for the Fermi plasma and the ions are described by the hydrodynamic (HD) equations. An energy balance-like equation involving a new Sagdeev-type pseudo-potential is derived in the presence of the quantum statistical effects. Numerical calculations reveal that the profiles of the Sagdeev-like potential and the ion-sound density excitations are significantly affected by the wave direction cosine and the Mach number. The present studies might be helpful to understand the excitation of nonlinear ion-sound waves in dense plasmas such as those in superdense white dwarfs and neutron stars as well as in intense laser-solid density plasma experiments.

Nonlinear dynamics and solitons in Debye bi-crystals

The nonlinear dynamics of longitudinal dust lattice waves propagating in a dusty plasma bi-crystal is investigated. A “diatomic”-like one-dimensional dust lattice configuration is considered, consisting of two distinct dust grain species with different charges and masses. Two different frequency dispersion modes are obtained in the linear limit, namely, an optical and an acoustic wave dispersion branch. Nonlinear solitary wave solutions are shown to exist in both branches, by considering the continuum limit for lattice excitations in different nonlinear potential regimes. For this purpose, a generalized Boussinesq and an extended Korteweg de Vries equation is derived, for the acoustic mode excitations, and their exact soliton solutions are provided and compared. For the optic mode, a nonlinear Schrödinger-type equation is obtained, which is shown to possess bright- (dark-) type envelope soliton solutions in the long (short, respectively) wavelength range. Optic-type longitudinal wavepackets are shown to be generally unstable in the continuum limit, though this is shown not to be the rule in the general (discrete) case.

Nonlinear excitations in electron-positron-ion plasmas in accretion disks of active galactic nuclei

The propagation of acoustic nonlinear excitations in an electron-positron-ion (e-p-i) plasma composed of warm electrons and positrons, as well as hot ions, has been investigated by adopting a two-dimensional cylindrical geometry. The electrons and positrons are modeled by hydrodynamic fluid equations, while the ions are assumed to follow a temperature-parametrized Boltzmann distribution (the fixed ion model is recovered in the appropriate limit). This situation applies in the accretion disk near a black hole in active galactic nuclei, where the ion temperature may be as high as 3 to 300 times that of the electrons. Using a reductive perturbation technique, a cylindrical Kadomtsev-Petviashvili equation is derived and its exact soliton solutions are presented. Furthermore, real situations in which the strength of the nonlinearity may be weak are considered, so that higher-order nonlinearity plays an important role. Accordingly, an extended cylindrical Kadomtsev-Petviashvili equation is derived, which admits both soliton and double-layer solutions. The characteristics of the nonlinear excitations obtained are investigated in detail

Ion-acoustic waves in a plasma consisting of adiabatic warm ions, non-isothermal electrons and a weakly relativistic electron beam: linear and higher-order nonlinear effects

The nonlinear propagation of finite amplitude ion acoustic solitary waves in a plasma consisting of adiabatic warm ions, nonisothermal electrons, and a weakly relativistic electron beam is studied via a two-fluid model. A multiple scales technique is employed to investigate the nonlinear regime. The existence of the electron beam gives rise to four linear ion acoustic modes, which propagate at different phase speeds. The numerical analysis shows that the propagation speed of two of these modes may become complex-valued (i.e., waves cannot occur) under conditions which depend on values of the beam-to-background-electron density ratio , the ion-to-free-electron temperature ratio , and the electron beam velocity v0; the remaining two modes remain real in all cases. The basic set of fluid equations are reduced to a Schamel-type equation and a linear inhomogeneous equation for the first and second-order potential perturbations, respectively. Stationary solutions of the coupled equations are derived using a renormalization method. Higher-order nonlinearity is thus shown to modify the solitary wave amplitude and may also deform its shape, even possibly transforming a simple pulse into a W-type curve for one of the modes. The dependence of the excitation amplitude and of the higher-order nonlinearity potential correction on the parameters , , and v0 is numerically investigated.

Parametric study of nonlinear electrostatic waves in two-dimensional quantum dusty plasmas

The nonlinear properties of two-dimensional cylindrical quantum dust-ion-acoustic (QDIA) and quantum dust-acoustic (QDA) waves are studied in a collisionless, unmagnetized and dense (quantum) dusty plasma. For this purpose, the reductive perturbation technique is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining the cylindrical Kadomtsev–Petviashvili (CKP) equations. The effects of quantum diffraction, as well as quantum statistical and geometric effects on the profiles of QDIA and QDA solitary waves are examined. It is found that the amplitudes and widths of the nonplanar QDIA and QDA waves are significantly affected by the quantum electron tunneling effect. The addition of a dust component to a quantum plasma is seen to affect the propagation characteristics of localized QDIA excitations. In the case of low-frequency QDA waves, this effect is even stronger, since the actual form of the potential solitary waves, in fact, depends on the dust charge polarity (positive/negative) itself (allowing for positive/negative potential forms, respectively). The relevance of the present investigation to metallic nanostructures is highlighted.

Linear and nonlinear properties of Rao-dust-Alfven waves in magnetized plasmas

The linear and nonlinear properties of the Rao-dust-magnetohydrodynamic (R-D-MHD) waves in a dusty magnetoplasma are studied. By employing the inertialess electron equation of motion, inertial ion equation of motion, Ampere's law, Faraday's law, and the continuity equation in a plasma with immobile charged dust grains, the linear and nonlinear propagation of two-dimensional R-D-MHD waves are investigated. In the linear regime, the existence of immobile dust grains produces the Rao cutoff frequency, which is proportional to the dust charge density and the ion gyrofrequency. On the other hand, the dynamics of amplitude modulated R-D-MHD waves is governed by the cubic nonlinear Schrodinger equation. The latter has been derived by using the reductive perturbation technique and the two-timescale analysis which accounts for the harmonic generation nonlinearity in plasmas. The stability of the modulated wave envelope against non-resonant perturbations is studied. Finally, the possibility of localized envelope excitations is discussed. (C) 2004 American Institute of Physics.

Weakly nonlinear vertical dust grain oscillations in dusty plasma crystals in the presence of a magnetic field

The weakly nonlinear regime of transverse paramagnetic dust grain oscillations in dusty (complex) plasma crystals is discussed. The nonlinearity, which is related to the sheath electric/magnetic field(s) and to the intergrain (electrostatic/magnetic dipole) interactions, is shown to lead to the generation of phase harmonics and, in the case of propagating transverse dust-lattice modes, to the modulational instability of the carrier wave due to self-interaction. The stability profile depends explicitly on the form of the electric and magnetic fields in the plasma sheath. The long term evolution of the modulated wave packet, which is described by a nonlinear Schrodinger-type equation, may lead to propagating localized envelope structures whose exact forms are presented and discussed. Explicit suggestions for experimental investigations are put forward. (C) 2004 American Institute of Physics.

Nonlinear compressional electromagnetic ion-cyclotron wavepackets in space plasmas

The parametric coupling between large amplitude magnetic field-aligned circularly polarized electromagnetic ion-cyclotron (EMIC) waves and ponderomotively driven ion-acoustic perturbations in magnetized space plasmas is considered. A cubic nonlinear Schrodinger equation for the modulated EMIC wave envelope is derived, and then solved analytically. The modulated EMIC waves are found to be stable (unstable) against ion-acoustic density perturbations, in the subsonic (supersonic, respectively) case, and they may propagate as "supersonic bright" ("subsonic dark", i.e. "black" or "grey") type envelope solitons, i.e. electric field pulses (holes, voids), associated with (co-propagating) density humps. Explicit bright and dark (black/grey) envelope excitation profiles are presented, and the relevance of our investigation to space plasmas is discussed.