Modulated Wave Packets Research Articles

Molecular dynamics simulation of heat pulse propagation in single-wall carbon nanotubes

The propagation of heat pulses in zigzag and armchair double wall nanotubes (DWNTs) has been investigated using molecular dynamics simulations. It is found that the leading heat wave packets in zigzag $(9,0)∕(18,0)$ and armchair $(5,5)∕(10,10)$ DWNTs move with the speed of longitudinal acoustic (LA) phonon modes. The intensities of the leading heat wave packets in outer and inner shells in DWNTs were found to be five to seven times larger than that of the corresponding single wall nanotubes (SWNTs). The heat energy carried by the leading heat wave packets in zigzag DWNT was about four and five times more than those in armchair DWNT shells. Within the leading LA wave packet, the strain in the inner shell of the DWNTs is stronger than the strain in the outer shell and considerably larger than strain in the corresponding SWNTs. The regions with the largest strain coincide with the regions of high kinetic temperatures within the LA mode wave packets. The higher energy of the LA mode waves in DWNT shells compared to SWNT is attributed to the presence of higher strain fields in DWNTs compared to individual SWNTs. The higher strain in the inner shell of DWNT compared to the outer shell accounts for the three to five times higher kinetic energy of leading wave packets in inner shells compared to those in outer shells. The induced strain fields in zigzag DWNT are distributed over a wider region compared to armchair DWNT, and the strains in inner and outer shells of zigzag DWNT are out phase by 180\ifmmode^\circ\else\textdegree\fi{}.

A cylindrical Davey–Stewartson equation for a modulated cylindrical wave packet

The modulation of a dust-ion acoustic wave (DIAW) in dusty plasmas with the combined effects of bounded cylindrical geometry and the transverse perturbation are studied. By using the standard reductive perturbation method, a cylindrical Davey–Stewartson (CDS) equation is obtained for the first time. The modulational instability of the DIAW described by the CDS equation is investigated. A new explicit criterion for the modulational instability of the DIAW described by the CDS is obtained. It is shown that the present instability criterion is different from that obtained in a standard nonlinear Schrödinger equation (NLSE), a Davey–Stewartson equation, or a cylindrically symmetric NLSE, and a wider parameter domain for modulational instability exists.

Theoretical and numerical studies of density modulated whistlers

Recently, observations from laboratory experiments, which are relevant to space observations as well, have conclusively revealed the amplitude modulation of whistlers by low‐frequency perturbations. Our objective here is to present theoretical and simulation studies of amplitude modulated whistler packets on account of their interaction with background low‐frequency density perturbations that are reinforced by the whistler ponderomotive force. Specifically, we show that nonlinear interactions between whistlers and finite amplitude density perturbations are governed by a nonlinear Schrödinger equation for the modulated whistlers, and a set of equations for arbitrary large amplitude density perturbations in the presence of the whistler ponderomotive force. The governing equations are solved numerically to show the existence of large scale density perturbations that are self‐consistently created by localized modulated whistler wavepackets. Our numerical results are found to be in good agreement with experimental results, as well as have relevance to observations from magnetized space plasmas.

Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering

Abstract A proposal is made for the creation of macroscopic quantum states of collective atomic-ensemble variables by the use of stimulated Raman scattering (SRS), followed by conditional optical measurement. After the completion of the SRS process, one is able to reverse the process and to return all the atoms to their ground states in such a way that reads out an arbitrary quantum state of the collective atomic field and writes this state onto the outgoing optical field. This scheme can be used for the creation of entanglement between two distant atomic ensembles. The quantum analysis of the SRS process treats one-dimensional spatial-temporal propagation accurately. Remarkably, it is found that this multimode problem can be simplified to a two-mode problem involving spatial-temporal wave-packet modes of the optical and atomic collective fields. This improves the understanding of the entanglement created in this system.

Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering

A proposal is made for the creation of macroscopic quantum states of collective atomic-ensemble variables by the use of stimulated Raman scattering (SRS), followed by conditional optical measurement. After the completion of the SRS process, one is able to reverse the process and to return all the atoms to their ground states in such a way that reads out an arbitrary quantum state of the collective atomic field and writes this state onto the outgoing optical field. This scheme can be used for the creation of entanglement between two distant atomic ensembles. The quantum analysis of the SRS process treats one-dimensional spatial-temporal propagation accurately. Remarkably, it is found that this multimode problem can be simplified to a two-mode problem involving spatial-temporal wave-packet modes of the optical and atomic collective fields. This improves the understanding of the entanglement created in this system.

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 Schrödinger-type equation, may lead to propagating localized envelope structures whose exact forms are presented and discussed. Explicit suggestions for experimental investigations are put forward.

Modulated Wave Packets and Envelope Solitary Structures in Complex Plasmas

A theoretical study is presented of the nonlinear amplitude modulation of waves propagating in unmagnetized plasmas contaminated by charged dust particles. Distinct well-known dusty plasma modes are explicitly considered, namely, the dust-acoustic wave, the dust-ion acoustic wave, and transverse dust-lattice waves. Using a multiple-scale technique, a nonlinear Schrodinger-type equation is derived, describing the evolution of the wave amplitude. A stability analysis reveals the possibility for modulational instability to occur, possibly leading to the formation of different types of envelope-localized excitations (solitary waves), under conditions which depend on the wave dispersion laws and intrinsic dusty plasma parameters.

Modulational instability of two colliding whistlers

It is shown that the dynamics of two colliding whistlers is governed by a pair of coupled nonlinear Schrödinger equations. The latter exhibit a modulational instability of constant amplitude whistlers that are nonlinearly interacting through quasistationary density perturbations created by the combined action of the ponderomotive forces of two whistlers. It has been found that the growth rate of the modulational instability increases with the intensity of any of the colliding whistlers, but decreases with the wave number per unit length of the modulated wave packet.

Perturbation Methods for Differential Equations

Perturbation Methods for Differential Equations

Dynamics of two-mode radiation in optical waveguides with strong mode coupling

Amplitude equations, as well as the effective dispersion and nonlinearity parameters, which define the dynamics of a wave packet formed by two strongly coupled modes, are derived with allowance for the frequency dependence of the linear mode coupling coefficient. These equations are used to study the onset of the modulation instability of the two-mode wave packet, soliton-like pulses, and compression modes. Unlike single-mode systems, the last two effects in optical waveguides may arise for both a negative and positive disper-sion of the waveguide material.

Weakly two-dimensional modulated wave packet in dusty plasmas

The higher order transverse perturbations for modulated wave packets in a dusty plasma are investigated. A Davey–Stewartson equation is obtained for this system. The instability for small amplitude linear transverse perturbations are investigated.

Nonlinear coupling between two colliding modulated upper-hybrid wave packets

The nonlinear interaction between two colliding modulated upper-hybrid wave packets has been considered, taking into account their coupling with quasi-stationary density perturbations reinforced by the ponderomotive forces of the upper-hybrid waves. It is found that this interaction is governed by two coupled cubic Schrödinger equations. The normal mode analysis of the latter reveals that positive (negative) group dispersive colliding wave packets are modulationally unstable (stable).

Ultrafast structural dynamics in electronically excited solid neon. I. Real-time probing of the electronic bubble formation

The dynamics of electron ``bubble'' formation upon excitation of the $A(3s\ensuremath{\sigma})$ Rydberg orbital of NO in solid Ne was investigated by means of conventional spectroscopy and femtosecond pump-probe spectroscopy. The femtosecond pump pulse initiates the formation of a bubble by the expansion of the Ne atoms surrounding the NO impurity, generating a wave packet of intermolecular NO-matrix modes. The dynamics exhibits a first peak due to the sampling of the initial expansion of the bubble followed by at least one oscillation of the bubble boundaries, which occurs \ensuremath{\sim}1.3 ps after the start of the dynamics and is significantly broader than the first peak. The whole process of bubble formation and stabilization is over by 2--3 ps in which 0.54 eV are released into the lattice. This suggests a sudden, probably shock-wave-like, emission of energy into the lattice. We directly extract in a first approximation the time dependence of the bubble radius from the pump-probe transients. This trajectory is used to simulate the experimental data with good agreement. Paradoxically, even though solid Ne is a lighter solid, the overall dynamics (expansion and recurrence) are slower than for the heavier argon solid.

The parametrically modified sine-Gordon equation: spectral properties, collisions, resonances and their connection to integrability

In this work, we revisit kinks and their interactions in the parametrically modified sine-Gordon (pmsG) equation. The central motivating question of our work is the following: what is the mechanism which in the absence of internal modes generates phonon radiation and causes the inelasticity of collisions in a near-integrable system? We do not give a complete answer to this question but rather we study a case example where we examine the penetration of an internal mode into the phonon band, and identify its consequences in the spectrum, the shape of the eigenfunctions and resonances of the spectrum with an external ac drive. In particular, by studying the linear spectrum around the kink solution we show that in the absence of the internal mode, some odd phonon modes can act as a localized wavepacket of modes depending on the parameter r of the potential. We also show by using the phenomenological theory developed in [Physica D 9 (1983) 1] that these modes are related to the quasi-resonance process and bound states suggested in [Physica D 9 (1983) 33], hence during the collision process the energy of the translational modes goes directly to the “localized” phonons. Finally, we investigate another problem for which these “localized” phonon modes also act as internal modes do. In particular, we study the resonance phenomena (related with either the internal mode or with the phonon modes) that appear in this system when it is subject to external ac drive. We attempt to connect such properties of the phonons (as well as properties of the internal modes) to the non-integrability of the model for r≠0.

Flow dissipation effects in a nonlinear nematic fiber.

Dissipative effects due to the presence of hydrodynamic flow in a cylindrical fiber whose cladding is an initially quiescent incompressible nematic liquid crystal are analyzed. An analytic and iterative solution of the nematodynamic equations coupled to the Maxwell's equations describing the propagation of a narrow wave packet of transverse magnetic modes is provided. We derive a generalized nonlinear Schröedinger equation for the amplitude of this propagating wave packet that takes into account the dissipation in the nematic's reorientation and the hydrodynamical effects. For the solitonlike solution of this equation we find that the penetration length and the real part of the nonlinear refraction index increase by a factor of 1.75, with respect to those values obtained in the absence of hydrodynamical flow. The imaginary part remains unaltered.

Nonlinear mechanism of tsunami wave generation by atmospheric disturbances

Abstract. The problem of tsunami wave generation by variable meteo-conditions is discussed. The simplified linear and nonlinear shallow water models are derived, and their analytical solutions for a basin of constant depth are discussed. The shallow-water model describes well the properties of the generated tsunami waves for all regimes, except the resonance case. The nonlinear-dispersive model based on the forced Korteweg-de Vries equation is developed to describe the resonant mechanism of the tsunami wave generation by the atmospheric disturbances moving with near-critical speed (long wave speed). Some analytical solutions of the nonlinear dispersive model are obtained. They illustrate the different regimes of soliton generation and the focusing of frequency modulated wave packets.

Parametric decay to lower hybrid waves as a source of modulated Langmuir waves in the topside ionosphere

Langmuir emissions generated by electron beams in space plasmas usually appear as chains of strongly modulated wave packets. In this paper, we present a quantitative analysis of three‐wave interaction between Langmuir and lower hybrid waves, L1 ↔ L2+LH, which explains many details of recent Freja observations in the topside ionosphere. The packet‐like waveforms are generated as the beating of several Langmuir modes. The primary Langmuir mode (L1) is produced by beam‐plasma instability, and the other modes are produced as a result of parametric decay to secondary Langmuir waves (L2) and lower hybrid modes (LH). We show that the decay instability has a very low threshold and high growth rate. The limited transverse dimensions of electron beams in the polar ionosphere cause radiation losses from the beam region which influence spectra of the beam‐plasma and parametric instabilities.

The physics in the auroral dynamo regions and auroral particle acceleration

Auroral particle acceleration requires an energy flux flowing into the acceleration region and the subsequent development of parallel electric fields. Auroral arcs are often very dynamic, and even in cases when a quasi-steady arc is formed, the question arises of how the system evolved to this quasi-steady state. Existing theories of auroral current generation and the formation of parallel electric fields mostly consider such a steady situation, limiting their ability to describe the dynamics of the system. Since the energy necessary to power auroral particle acceleration is related to the auroral current system, the generation of field-aligned currents (FAC) and auroral particle acceleration are closely coupled. Thus, in order to understand the dynamics of auroral particle acceleration, the physics in the auroral dynamo region must also be considered. Construction of such a dynamical theory of the auroral current system requires that the time-dependent generation of field-aligned currents (∂J|/∂t) and the dynamics of the generation of parallel electric fields (∂E|/∂t) and parallel potential drops must be the primary considerations.The time-dependent generation of FAC filaments can occur as a result of the interaction of the MHD fast mode wave packets and a current sheet, either at the magnetopause or in the plasma sheet. In this process, a shear Alfvén wave can be generated in a discrete form as shear Alfvén wave packets. Although a single shear Alfvén wave packet can propagate without distortion or nonlinear interaction, the interaction of incident and reflected shear mode wave packets in the auroral acceleration region can release the kinetic and/or magnetic energy carried by the wave packets. Either solitary waves accompanied by a charge condensation (charge hole) or a net parallel potential drop may be formed, depending on the polarizations of the interacting wave packets. In order to produce FAC filaments and parallel electric fields by the wave packet interaction, a localized breakdown of the frozen-in condition is necessary. The electron inertial term is a natural candidate to break the frozen-in condition locally.

Langmuir wave structures registered by FREJA: analysis and modeling

A large set of observations of Langmuir emissions generated by super-thermal electron beams in the topside polar ionosphere has been obtained during the recent FREJA mission. Langmuir emissions appeared as a chain of strongly modulated wave packets; in many cases the packet envelopes were modulated periodically. In present report we suggest the theory which explains these observations. We suggest that packet-like waveforms are the beatings of several Langmuir modes. One of modes (the primary mode) appears as a result of beam-plasma instability, other modes — as a result of parametric decay of primary mode to the secondary Langmuir wave and lower-hybrid wave (or as a result of decay cascade). We present the quantitative theory of three-wave interaction L→L+LH which explain many details of FREJA observations.

Kelvin‐Helmholtz instability on the magnetospheric flanks: An absolute and convective instability approach

In this paper, an absolute and convective instability approach to the Kelvin‐Helmholtz instability of magnetospheric surface and body/waveguide modes is presented. Rather than considering normal modes individually, the development of localized wavepackets is considered. It is shown that the time asymptotic behavior of such a wavepacket is determined by the double roots of the dispersion relation and that each double root may be identified with a normal mode, for our particular system. The dominant behavior in any reference frame is given by the double root with the largest growth rate. We consider the absolute or convective nature of the instability in the rest frame of the magnetosphere and deduce that in this reference frame wavepackets may only be absolutely unstable (growing at any fixed point in space at large time) close to the nose of the magnetosphere and are convectively unstable (moving away so that at large time there is no disturbance at any fixed point) elsewhere. The e‐folding lengths of fast surface mode wavepackets are found to be small but increase around the flanks (these will become nonlinear and lead to the broadening of the low‐latitude boundary layer in agreement with previous studies) [Manuel and Samson, 1993]. Fast body modes will e‐fold only once as they convect around the flanks, so would be expected to remain linear in this region. Slow‐mode wavepackets are also studied and are found to have very large e‐folding lengths, so that their growth on the flanks will be negligible. The results are compared to a numerical simulation and excellent agreement is obtained.