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

The Use of PRS in Introductory Microeconomics: Some Evidence on Performance and Attendance

This paper uses a sample of 425 students from 4 large sections of Introductory Microeconomics during the period 2005 – 2007 to examine the impact of using the Personal Response System (PRS or Clickers) on class attendance and exam performance. The evidence suggests that the use of PRS has led to improved attendance. The exam scores are similar to classes that used online quizzes instead of the PRS. A survey of student attitudes towards the PRS indicates that the use of PRS helps with student learning and reinforcing important concepts. Based on the results of this study the authors believe that the PRS is a useful tool for all instructors, particularly those faced with large sections.

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

Large-wavelength instabilities in free-surface Hartmann flow at low magnetic Prandtl numbers

We study the linear stability of the flow of a viscous electrically conducting capillary fluid on a planar fixed plate in the presence of gravity and a uniform magnetic field. We first confirm that the Squire transformation for MHD is compatible with the stress and insulating boundary conditions at the free surface, but argue that unless the flow is driven at fixed Galilei and capillary numbers, the critical mode is not necessarily two-dimensional. We then investigate numerically how a flow-normal magnetic field, and the associated Hartmann steady state, affect the soft and hard instability modes of free surface flow, working in the low magnetic Prandtl number regime of laboratory fluids. Because it is a critical layer instability, the hard mode is found to exhibit similar behaviour to the even unstable mode in channel Hartmann flow, in terms of both the weak influence of Pm on its neutral stability curve, and the dependence of its critical Reynolds number Re_c on the Hartmann number Ha. In contrast, the structure of the soft mode's growth rate contours in the (Re, alpha) plane, where alpha is the wavenumber, differs markedly between problems with small, but nonzero, Pm, and their counterparts in the inductionless limit. As derived from large wavelength approximations, and confirmed numerically, the soft mode's critical Reynolds number grows exponentially with Ha in inductionless problems. However, when Pm is nonzero the Lorentz force originating from the steady state current leads to a modification of Re_c(Ha) to either a sublinearly increasing, or decreasing function of Ha, respectively for problems with insulating and conducting walls. In the former, we also observe pairs of Alfven waves, the upstream propagating wave undergoing an instability at large Alfven numbers.Comment: 58 pages, 16 figure

Statistical correlation of structural mode shapes from test measurements and NASTRAN analytical values

The software and procedures of a system of programs used to generate a report of the statistical correlation between NASTRAN modal analysis results and physical tests results from modal surveys are described. Topics discussed include: a mathematical description of statistical correlation, a user's guide for generating a statistical correlation report, a programmer's guide describing the organization and functions of individual programs leading to a statistical correlation report, and a set of examples including complete listings of programs, and input and output data

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.

Mirror formation control in the vicinity of an asteroid

Two strategies are presented for the positioning and control of a spacecraft formation designed to focus sunlight onto a point on the surface of asteroid, thereby sublimating the material and ejecting debris creating thrust. In the first approach, the formation is located at artficial equilibrium points around the asteroid and controlled using the force from the solar radiation pressure. The second approach determines the optimal periodic formation orbits, subject to the gravitational perturbations from the asteroid, the solar radiation pressure and the control acceleration derived from a control law

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

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

Bounds on Quantum Correlations in Bell Inequality Experiments

Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description. However, despite the importance of Bell inequalities, it is not known in general how to determine whether a given entangled state will violate a Bell inequality. This is because one can choose to make many different measurements on a quantum system to test any given Bell inequality and the optimization over measurements is a high-dimensional variational problem. In order to better understand this problem we present algorithms that provide, for a given quantum state, both a lower bound and an upper bound on the maximal expectation value of a Bell operator. Both bounds apply techniques from convex optimization and the methodology for creating upper bounds allows them to be systematically improved. In many cases these bounds determine measurements that would demonstrate violation of the Bell inequality or provide a bound that rules out the possibility of a violation. Examples are given to illustrate how these algorithms can be used to conclude definitively if some quantum states violate a given Bell inequality.Comment: 13 pages, 1 table, 2 figures. Updated version as published in PR