Asymptotic modal analysis and statistical energy analysis

Asymptotic Modal Analysis (AMA) is a method which is used to model linear dynamical systems with many participating modes. The AMA method was originally developed to show the relationship between statistical energy analysis (SEA) and classical modal analysis (CMA). In the limit of a large number of modes of a vibrating system, the classical modal analysis result can be shown to be equivalent to the statistical energy analysis result. As the CMA result evolves into the SEA result, a number of systematic assumptions are made. Most of these assumptions are based upon the supposition that the number of modes approaches infinity. It is for this reason that the term 'asymptotic' is used. AMA is the asymptotic result of taking the limit of CMA as the number of modes approaches infinity. AMA refers to any of the intermediate results between CMA and SEA, as well as the SEA result which is derived from CMA. The main advantage of the AMA method is that individual modal characteristics are not required in the model or computations. By contrast, CMA requires that each modal parameter be evaluated at each frequency. In the latter, contributions from each mode are computed and the final answer is obtained by summing over all the modes in the particular band of interest. AMA evaluates modal parameters only at their center frequency and does not sum the individual contributions from each mode in order to obtain a final result. The method is similar to SEA in this respect. However, SEA is only capable of obtaining spatial averages or means, as it is a statistical method. Since AMA is systematically derived from CMA, it can obtain local spatial information as well

Mean Flow Effects in Model Equations for Faraday Waves

We review model equations for parametric surface waves (Faraday waves) in the limit of small viscous dissipation. The equations account for two effects of viscosity, namely damping of the waves and slowly varying streaming and large scale flows (mean flow). Equations for the mean flow can be derived by a multiple scale analysis and are coupled to an order parameter equation describing the evolution of the surface waves. In addition, the equations incorporate a phenomenological damping term due to viscous dissipation. The nonlinear terms, which are undetermined by the derivation of the equation for the surface waves, are chosen so that the primary bifurcation is to a set of standing waves in the form of stripes. Results for the secondary instabilities of the primary waves are presented, including a weak amplification of both Eckhaus and Transverse Amplitude Modulation instabilities due to the mean flow, and a new longitudinal oscillatory instability which is absent without mean flow. Generation of mean flow due to dislocation defects in regular patterns is studied by numerical simulations

Quantized vortices in superfluid helium and atomic Bose-Einstein condensates

This article reviews recent developments in the physics of quantized vortices in superfluid helium and atomic Bose-Einstein condensates. Quantized vortices appear in low-temperature quantum condensed systems as the direct product of Bose-Einstein condensation. Quantized vortices were first discovered in superfluid 4He in the 1950s, and have since been studied with a primary focus on the quantum hydrodynamics of this system. Since the discovery of superfluid 3He in 1972, quantized vortices characteristic of the anisotropic superfluid have been studied theoretically and observed experimentally using rotating cryostats. The realization of atomic Bose-Einstein condensation in 1995 has opened new possibilities, because it became possible to control and directly visualize condensates and quantized vortices. Historically, many ideas developed in superfluid 4He and 3He have been imported to the field of cold atoms and utilized effectively. Here, we review and summarize our current understanding of quantized vortices, bridging superfluid helium and atomic Bose-Einstein condensates. This review article begins with a basic introduction, which is followed by discussion of modern topics such as quantum turbulence and vortices in unusual cold atom condensates.Comment: 99 pages, 20 figures, Review articl

Deformation and Depinning of Superconducting Vortices from Artificial Defects: A Ginzburg-Landau Study

Using Ginzburg-Landau theory, we have performed detailed studies of vortices in the presence of artificial defect arrays, for a thin film geometry. We show that when a vortex approaches the vicinity of a defect, an abrupt transition occurs in which the vortex core develops a ``string'' extending to the defect boundary, while simultaneously the supercurrents and associated magnetic flux spread out and engulf the defect. Current induced depinning of vortices is shown to be dominated by the core string distortion in typical experimental situations. Experimental consequences of this unusual depinning behavior are discussed.Comment: 10 pages,9 figure

Patterns and Collective Behavior in Granular Media: Theoretical Concepts

Granular materials are ubiquitous in our daily lives. While they have been a subject of intensive engineering research for centuries, in the last decade granular matter attracted significant attention of physicists. Yet despite a major efforts by many groups, the theoretical description of granular systems remains largely a plethora of different, often contradicting concepts and approaches. Authors give an overview of various theoretical models emerged in the physics of granular matter, with the focus on the onset of collective behavior and pattern formation. Their aim is two-fold: to identify general principles common for granular systems and other complex non-equilibrium systems, and to elucidate important distinctions between collective behavior in granular and continuum pattern-forming systems.Comment: Submitted to Reviews of Modern Physics. Full text with figures (2Mb pdf) avaliable at http://mti.msd.anl.gov/AransonTsimringReview/aranson_tsimring.pdf Community responce is appreciated. Comments/suggestions send to [email protected]

Orientational correlations and the effect of spatial gradients in the equilibrium steady state of hard rods in 2D : A study using deposition-evaporation kinetics

Deposition and evaporation of infinitely thin hard rods (needles) is studied in two dimensions using Monte Carlo simulations. The ratio of deposition to evaporation rates controls the equilibrium density of rods, and increasing it leads to an entropy-driven transition to a nematic phase in which both static and dynamical orientational correlation functions decay as power laws, with exponents varying continuously with deposition-evaporation rate ratio. Our results for the onset of the power-law phase agree with those for a conserved number of rods. At a coarse-grained level, the dynamics of the non-conserved angle field is described by the Edwards-Wilkinson equation. Predicted relations between the exponents of the quadrupolar and octupolar correlation functions are borne out by our numerical results. We explore the effects of spatial inhomogeneity in the deposition-evaporation ratio by simulations, entropy-based arguments and a study of the new terms introduced in the free energy. The primary effect is that needles tend to align along the local spatial gradient of the ratio. A uniform gradient thus induces a uniformly aligned state, as does a gradient which varies randomly in magnitude and sign, but acts only in one direction. Random variations of deposition-evaporation rates in both directions induce frustration, resulting in a state with glassy characteristics.Comment: modified version, Accepted for publication in Physical Review