Nonlinear theory of dust lattice mode coupling in dust crystals

Quasi-crystals formed by charged mesoscopic dust grains (dust lattices), observed since hardly a decade ago, are an exciting paradigm of a nonlinear chain. In laboratory discharge experiments, these quasi-lattices are formed spontaneously in the sheath region near a negative electrode, usually at a levitated horizontal equilibrium configuration where gravity is balanced by an electric field. It is long known (and experimentally confirmed) that dust-lattices support linear oscillations, in the longitudinal (acoustic mode) as well as in the transverse, in plane (acoustic-) or off-plane (optic-like mode) directions. Either due to the (typically Yukawa type) electrostatic inter-grain interaction forces or to the (intrinsically nonlinear) sheath environment, nonlinearity is expected to play an important role in the dynamics of these lattices. Furthermore, the coupling between the different modes may induce coupled nonlinear modes. Despite this evidence, the elucidation of the nonlinear mechanisms governing dust crystals is in a rather preliminary stage. In this study, we derive a set of (coupled) discrete equations of motion for longitudinal and transverse (out-of-plane) motion in a one dimensional model chain of charged dust grains. In a continuum approximation, i.e. assuming a variation scale which is larger than the lattice constant, one obtains a set of coupled modified Boussinesq-like equations. Different nonlinear solutions of the coupled system are discussed, based on localized travelling wave ansatze and on coupled equations for the envelopes of co-propagating quasi-linear waves.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Modulated envelope localized wavepackets associated with electrostatic plasma waves

The nonlinear amplitude modulation of known electrostatic plasma modes is examined in a generic manner, by applying a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The moderately nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrodinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright- (pulses) or dark- (holes, voids) type, whose characteristics (maximum amplitude, width) depend on intrinsic plasma parameters. Effects like amplitude perturbation obliqueness, finite temperature and defect (dust) concetration are explicitly considered. The relevance with similar highly localized modulated wave structures observed during recent satellite missions is discussed.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Modulated dust-acoustic wave packets in a plasma with non-isothermal electrons and ions

Nonlinear self-modulation of the dust acoustic waves is studied, in the presence of non-thermal (non-Maxwellian) ion and electron populations. By employing a multiple scale technique, a nonlinear Schrodinger-type equation (NLSE) is derived for the wave amplitude. The influence of non-thermality, in addition to obliqueness (between the propagation and modulation directions), on the conditions for modulational instability to occur is discussed. Different types of localized solutions (envelope excitations) which may possibly occur are discussed, and the dependence of their characteristics on physical parameters is traced. The ion deviation from a Maxwellian distribution comes out to be more important than the electron analogous deviation alone. Both yield a de-stabilizing effect on (the amplitude of) DAWs propagating in a dusty plasma with negative dust grains. The opposite effect, namely a tendency towards amplitude stabilization, is found for the case of positively charged dust presence in the plasma.Comment: To appear in Journal of Plasma Physics (2004

Theory of solitary waves in complex plasma lattices

A comprehensive analytical theory for nonlinear excitations related to horizontal (longitudinal, acoustic mode) as well as vertical (transverse, optical mode) motion of charged dust grains in a dust crystal is presented. Different types of localized excitations, similar to those well known in solid state physics, are reviewed and conditions for their occurrence and characteristics in dusty plasma crystals are discussed. By employing a continuum approximation (i.e. assuming a long variation scale, with respect to the inter-particle distance) a dust crystal is shown to support nonlinear kink-shaped supersonic solitary excitations, associated with longitudinal dust grain displacement, as well as modulated envelope localized modes associated with either longitudinal or transverse oscillations. Although a one-dimensional crystal is considered for simplicity, the results in principle apply to a two-dimensional lattice if certain conditions are satisfied. The effect of mode-coupling is also briefly considered. The relation to previous results on atomic chains, and also to experimental results on strongly-coupled dust layers in gas discharge plasmas, is briefly discussed.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Intrinsic localized modes in dust lattices

Intrinsic Localized Modes (ILM) (or Discrete Breathers, DB) are localized oscillatory modes known to occur in atomic or molecular chains characterized by coupling and/or on-site potential nonlinearity. Quasi-crystals of charged mesoscopic dust grains (dust lattices), which have been observed since hardly a decade ago, are an exciting paradigm of such a nonlinear chain. In gas-discharge experiments, these crystals are subject to forces due to an externally imposed electric and/or magnetic field(s), which balance(s) gravity at the levitated equilibrium position, as well as to electrostatic inter-grain interaction forces. Despite the profound role of nonlinearity, which may be due to inter-grain coupling, mode- coupling and to the sheath environment, the elucidation of the nonlinear mechanisms governing dust crystals is still in a preliminary stage. This study is devoted to an investigation, from very first principles, of the existence of discrete localized modes in dust layers. Relying on a set of evolution equation for transverse charged grain displacements, we examine the conditions for the existence and sustainance of discrete localized modes and discuss the dependence of their characteristics on intrinsic plasma parameters. In addition, the possibility of DB stabilisation via an external force is discussed.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

On a semiclassical model for ion-acoustic solitons in ultrarelativistic pair plasmas and its classical counterpart

Large ion-acoustic solitary waves are investigated in a multispecies plasma model consisting of warm positive ions in the presence of ultrarelativistic electrons and positrons, in a Sagdeev pseudopotential formalism. A parametric investigation determines existence regions in terms of fractional densities, temperature ratios, and soliton speeds. Various examples of pseudopotential functional forms, as well as those of the resulting soliton and electric field profiles, can then be generated numerically, and some typical illustrations have been included. Rather than adiabatic pressure-density relations for the hot species, the classical nonrelativistic counterpart involves Boltzmann distributions, which differ qualitatively from the literature. Surprisingly, the soliton and electric field profiles show scant differences at the same compositional parameters between the two extremes even though the physical description of the hot species is radically different. A brief comparison has also been included between the fully nonlinear Sagdeev pseudopotential descriptions and their respective associated weak-amplitude limits (treated via a reductive perturbation technique) in which nonlinearities have been truncated to low powers of the electrostatic potential. Again, the soliton profiles are not radically different at comparable amplitudes, leaving the underlying physical reasons for such a similarity an open problem

Structural systems and tuned mass dampers of super-tall buildings : case study of Taipei 101

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2007.Includes bibliographical references (leaves 68-69).The design of the first generation of skyscrapers was based on strength. Heavy masonry cladding and wall curtains used at that period added a considerable amount of stiffness and damping to the structure. Inter-storey drifts and peak accelerations were relatively small. Advances in the material science technology enabled the use of high-performance concrete, steel and composite sections. The former combined with the use of sophisticated 3-D structural design software packages resulted in the evolution of a new generation of more economical and structurally efficient skyscrapers. However, the increased flexibility and lower damping makes these structures more vulnerable to wind induced vibrations, causing severe human discomfort due to excessive accelerations. Several solutions have been engineered to mitigate the motions of Super-Tall buildings including structural, aerodynamic and auxiliary changes with the goal of increasing the inherent damping of the building.(cont.) The current thesis is comprised of three parts: a review of past and current trends in structural systems of tall buildings, including a comparison of the twenty tallest buildings globally; an investigation of passive control-Tuned Mass Dampers-with also several examples of structures which have such a system; and a demonstration of the effectiveness of Tuned Mass Dampers through a case study of the current tallest building to the structural top in the world, a 508m tremendous architectural, engineering and construction achievement - Taipei 101. The change in the response of the tower due to a wind-induced vibration is illustrated by performing a time-history analysis with and without the TMD in a SAP2000 model. Finally, recommendations for future research in the field of distributed TMDs are offered.by Ioannis Kourakis.M.Eng

Ion-beam/plasma modes in ultradense relativistic quantum plasmas: Dispersion characteristics and beam-driven instability

A relativistic quantum-hydrodynamic plasma model is proposed, to model the propagation of electrostatic waves in an ultradense quantum electron-ion plasma in the presence of an ion beam. A dispersion relation is derived for harmonic waves, and the stability of electrostatic wavepackets is investigated. Three types of waves are shown to exist, representing a modified electron plasma (Langmuir-type) mode, a low-frequency ion acoustic mode, and an ion-beam driven mode, respectively. Stability analysis reveals the occurrence of an imaginary frequency part in three regions. The dependence of the instability growth rate on the ion beam parameters (concentration and speed) has been investigate