Statistics of Pressure Fluctuations in Decaying, Isotropic Turbulence

We present results from a systematic direct-numerical simulation study of pressure fluctuations in an unforced, incompressible, homogeneous, and isotropic, three-dimensional turbulent fluid. At cascade completion, isosurfaces of low pressure are found to be organised as slender filaments, whereas the predominant isostructures appear sheet-like. We exhibit several new results, including plots of probability distributions of the spatial pressure-difference, the pressure-gradient norm, and the eigenvalues of the pressure-hessian tensor. Plots of the temporal evolution of the mean pressure-gradient norm, and the mean eigenvalues of the pressure-hessian tensor are also exhibited. We find the statistically preferred orientations between the eigenvectors of the pressure-hessian tensor, the pressure-gradient, the eigenvectors of the strain-rate tensor, the vorticity, and the velocity. Statistical properties of the non-local part of the pressure-hessian tensor are also exhibited, for the first time. We present numerical tests (in the viscous case) of some conjectures of Ohkitani [Phys. Fluids A {\bf 5}, 2570 (1993)] and Ohkitani and Kishiba [Phys. Fluids {\bf 7}, 411 (1995)] concerning the pressure-hessian and the strain-rate tensors, for the unforced, incompressible, three-dimensional Euler equations.Comment: 10 pages, 29 figures, Accepted for publication in Physical Review

Seismic Analysis Capability in NASTRAN

Seismic analysis is a technique which pertains to loading described in terms of boundary accelerations. Earthquake shocks to buildings is the type of excitation which usually comes to mind when one hears the word seismic, but this technique also applied to a broad class of acceleration excitations which are applied at the base of a structure such as vibration shaker testing or shocks to machinery foundations. Four different solution paths are available in NASTRAN for seismic analysis. They are: Direct Seismic Frequency Response, Direct Seismic Transient Response, Modal Seismic Frequency Response, and Modal Seismic Transient Response. This capability, at present, is invoked not as separate rigid formats, but as pre-packaged ALTER packets to existing RIGID Formats 8, 9, 11, and 12. These ALTER packets are included with the delivery of the NASTRAN program and are stored on the computer as a library of callable utilities. The user calls one of these utilities and merges it into the Executive Control Section of the data deck to perform any of the four options are invoked by setting parameter values in the bulk data

A reconfigurable real-time morphological system for augmented vision

There is a significant number of visually impaired individuals who suffer sensitivity loss to high spatial frequencies, for whom current optical devices are limited in degree of visual aid and practical application. Digital image and video processing offers a variety of effective visual enhancement methods that can be utilised to obtain a practical augmented vision head-mounted display device. The high spatial frequencies of an image can be extracted by edge detection techniques and overlaid on top of the original image to improve visual perception among the visually impaired. Augmented visual aid devices require highly user-customisable algorithm designs for subjective configuration per task, where current digital image processing visual aids offer very little user-configurable options. This paper presents a highly user-reconfigurable morphological edge enhancement system on field-programmable gate array, where the morphological, internal and external edge gradients can be selected from the presented architecture with specified edge thickness and magnitude. In addition, the morphology architecture supports reconfigurable shape structuring elements and configurable morphological operations. The proposed morphology-based visual enhancement system introduces a high degree of user flexibility in addition to meeting real-time constraints capable of obtaining 93 fps for high-definition image resolution

Statistical correlation analysis for comparing vibration data from test and analysis

A theory was developed to compare vibration modes obtained by NASTRAN analysis with those obtained experimentally. Because many more analytical modes can be obtained than experimental modes, the analytical set was treated as expansion functions for putting both sources in comparative form. The dimensional symmetry was developed for three general cases: nonsymmetric whole model compared with a nonsymmetric whole structural test, symmetric analytical portion compared with a symmetric experimental portion, and analytical symmetric portion with a whole experimental test. The theory was coded and a statistical correlation program was installed as a utility. The theory is established with small classical structures

Thermal fluctuation field for current-induced domain wall motion

Current-induced domain wall motion in magnetic nanowires is affected by thermal fluctuation. In order to account for this effect, the Landau-Lifshitz-Gilbert equation includes a thermal fluctuation field and literature often utilizes the fluctuation-dissipation theorem to characterize statistical properties of the thermal fluctuation field. However, the theorem is not applicable to the system under finite current since it is not in equilibrium. To examine the effect of finite current on the thermal fluctuation, we adopt the influence functional formalism developed by Feynman and Vernon, which is known to be a useful tool to analyze effects of dissipation and thermal fluctuation. For this purpose, we construct a quantum mechanical effective Hamiltonian describing current-induced domain wall motion by generalizing the Caldeira-Leggett description of quantum dissipation. We find that even for the current-induced domain wall motion, the statistical properties of the thermal noise is still described by the fluctuation-dissipation theorem if the current density is sufficiently lower than the intrinsic critical current density and thus the domain wall tilting angle is sufficiently lower than pi/4. The relation between our result and a recent result, which also addresses the thermal fluctuation, is discussed. We also find interesting physical meanings of the Gilbert damping alpha and the nonadiabaticy parameter beta; while alpha characterizes the coupling strength between the magnetization dynamics (the domain wall motion in this paper) and the thermal reservoir (or environment), beta characterizes the coupling strength between the spin current and the thermal reservoir.Comment: 16 page, no figur

Planets opening dust gaps in gas disks

We investigate the interaction of gas and dust in a protoplanetary disk in the presence of a massive planet using a new two-fluid hydrodynamics code. In view of future observations of planet-forming disks we focus on the condition for gap formation in the dust fluid. While only planets more massive than 1 Jupiter mass (MJ) open up a gap in the gas disk, we find that a planet of 0.1 MJ already creates a gap in the dust disk. This makes it easier to find lower-mass planets orbiting in their protoplanetary disk if there is a significant population of mm-sized particles.Comment: 5 pages, 3 figures, accepted for publication in A&A Letter

Positioning systems in Minkowski space-time: Bifurcation problem and observational data

In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, {\em all} of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system.Comment: 10 pages, 7 figures. The version published in PRD contains a misprint in the caption of Figure 3, which is here amende

Any-order propagation of the nonlinear Schroedinger equation

We derive an exact propagation scheme for nonlinear Schroedinger equations. This scheme is entirely analogous to the propagation of linear Schroedinger equations. We accomplish this by defining a special operator whose algebraic properties ensure the correct propagation. As applications, we provide a simple proof of a recent conjecture regarding higher-order integrators for the Gross-Pitaevskii equation, extend it to multi-component equations, and to a new class of integrators.Comment: 10 pages, no figures, submitted to Phys. Rev.

Data-driven pattern identification and outlier detection in time series

We address the problem of data-driven pattern identification and outlier detection in time series. To this end, we use singular value decomposition (SVD) which is a well-known technique to compute a low-rank approximation for an arbitrary matrix. By recasting the time series as a matrix it becomes possible to use SVD to highlight the underlying patterns and periodicities. This is done without the need for specifying user-defined parameters. From a data mining perspective, this opens up new ways of analyzing time series in a data-driven, bottom-up fashion. However, in order to get correct results, it is important to understand how the SVD-spectrum of a time series is influenced by various characteristics of the underlying signal and noise. In this paper, we have extended the work in earlier papers by initiating a more systematic analysis of these effects. We then illustrate our findings on some real-life data

A Parameterized Centrality Metric for Network Analysis

A variety of metrics have been proposed to measure the relative importance of nodes in a network. One of these, alpha-centrality [Bonacich, 2001], measures the number of attenuated paths that exist between nodes. We introduce a normalized version of this metric and use it to study network structure, specifically, to rank nodes and find community structure of the network. Specifically, we extend the modularity-maximization method [Newman and Girvan, 2004] for community detection to use this metric as the measure of node connectivity. Normalized alpha-centrality is a powerful tool for network analysis, since it contains a tunable parameter that sets the length scale of interactions. By studying how rankings and discovered communities change when this parameter is varied allows us to identify locally and globally important nodes and structures. We apply the proposed method to several benchmark networks and show that it leads to better insight into network structure than alternative methods.Comment: 11 pages, submitted to Physical Review