Application of discontinuity layout optimization to plane plasticity problems

A new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described. The procedure is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems. Potential discontinuities, which interlink nodes laid out over the body under consideration, are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient linear programming solvers can be employed when certain popular failure criteria are specified (e. g. Tresca or Mohr Coulomb in plane strain). Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward. The procedure, coined 'discontinuity layout optimization' (DLO), is related to that used to identify the optimum layout of bars in trusses, with discontinuities (e. g. slip-lines) in a translational failure mechanism corresponding to bars in an optimum truss. Hence, a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here. The procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems. Close agreement with the exact analytical solutions is obtained

A New Exponential Gravity

We propose a new exponential f(R) gravity model with f(R)=(R-\lambda c)e^{\lambda(c/R)^n} and n>3, \lambda\geq 1, c>0 to explain late-time acceleration of the universe. At the high curvature region, the model behaves like the \LambdaCDM model. In the asymptotic future, it reaches a stable de-Sitter spacetime. It is a cosmologically viable model and can evade the local gravity constraints easily. This model share many features with other f(R) dark energy models like Hu-Sawicki model and Exponential gravity model. In it the dark energy equation of state is of an oscillating form and can cross phantom divide line \omega_{de}=-1. In particular, in the parameter range 3< n\leq 4, \lambda \sim 1, the model is most distinguishable from other models. For instance, when n=4, \lambda=1, the dark energy equation of state will cross -1 in the earlier future and has a stronger oscillating form than the other models, the dark energy density in asymptotical future is smaller than the one in the high curvature region. This new model can evade the local gravity tests easily when n>3 and \lambda>1.Comment: 12 pages, 8 figure

Multi-Factor Policy Evaluation and Selection in the One-Sample Situation

Firms nowadays need to make decisions with fast information obsolesce. In this paper I deal with one class of decision problems in this situation, called the “one-sample” problems: we have finite options and one sample of the multiple criteria with which we use to evaluate those options. I develop evaluation procedures based on bootstrapping DEA (Data Envelopment Envelopment) and the related decision-making methods. This paper improves the bootstrap procedure proposed by Simar and Wilson (1998) and shows how to exploit information from bootstrap outputs for decision-making

The Computational Complexity of the Game of Set and its Theoretical Applications

The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and establish interesting connections with other classical computational problems. Specifically, we first show that a natural generalization of the problem of finding a single Set, parameterized by the size of the sought Set is W-hard; our reduction applies also to a natural parameterization of Perfect Multi-Dimensional Matching, a result which may be of independent interest. Second, we observe that a version of the game where one seeks to find the largest possible number of disjoint Sets from a given set of cards is a special case of 3-Set Packing; we establish that this restriction remains NP-complete. Similarly, the version where one seeks to find the smallest number of disjoint Sets that overlap all possible Sets is shown to be NP-complete, through a close connection to the Independent Edge Dominating Set problem. Finally, we study a 2-player version of the game, for which we show a close connection to Arc Kayles, as well as fixed-parameter tractability when parameterized by the number of rounds played

Spectral properties of a generalized chGUE

We consider a generalized chiral Gaussian Unitary Ensemble (chGUE) based on a weak confining potential. We study the spectral correlations close to the origin in the thermodynamic limit. We show that for eigenvalues separated up to the mean level spacing the spectral correlations coincide with those of chGUE. Beyond this point, the spectrum is described by an oscillating number variance centered around a constant value. We argue that the origin of such a rigid spectrum is due to the breakdown of the translational invariance of the spectral kernel in the bulk of the spectrum. Finally, we compare our results with the ones obtained from a critical chGUE recently reported in the literature. We conclude that our generalized chGUE does not belong to the same class of universality as the above mentioned model.Comment: 12 pages, 3 figure

L^2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method

We consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L^2 perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show that up to a time-dependent translation of the shock, the L^2 norm of a perturbed solution relative to the shock wave is bounded above by the L^2 norm of the initial perturbation.Comment: 17 page

Intersecting S-Brane Solutions of D=11 Supergravity

We construct all possible orthogonally intersecting S-brane solutions in 11-dimensions corresponding to standard supersymmetric M-brane intersections. It is found that the solutions can be obtained by multiplying the brane and the transverse directions with appropriate powers of two hyperbolic functions of time. This is the S-brane analog of the ``harmonic function rule''. The transverse directions can be hyperbolic, flat or spherical. We also discuss some properties of these solutions.Comment: 12 pages, Latex, a reference adde

Influence of heavy modes on perturbations in multiple field inflation

We investigate linear cosmological perturbations in multiple field inflationary models where some of the directions are light while others are heavy (with respect to the Hubble parameter). By integrating out the massive degrees of freedom, we determine the multi-dimensional effective theory for the light degrees of freedom and give explicitly the propagation matrix that replaces the effective sound speed of the one-dimensional case. We then examine in detail the consequences of a sudden turn along the inflationary trajectory, in particular the possible breakdown of the low energy effective theory in case the heavy modes are excited. Resorting to a new basis in field space, instead of the usual adiabatic/entropic basis, we study the evolution of the perturbations during the turn. In particular, we compute the power spectrum and compare with the result obtained from the low energy effective theory.Comment: 24 pages, 13 figures; v2 substantial changes in sec.V; v3 matching the published version on JCA

Theory of Chiral Modulations and Fluctuations in Smectic-A Liquid Crystals Under an Electric Field

Chiral liquid crystals often exhibit periodic modulations in the molecular director; in particular, thin films of the smectic-C* phase show a chiral striped texture. Here, we investigate whether similar chiral modulations can occur in the induced molecular tilt of the smectic-A phase under an applied electric field. Using both continuum elastic theory and lattice simulations, we find that the state of uniform induced tilt can become unstable when the system approaches the smectic-A--smectic-C* transition, or when a high electric field is applied. Beyond that instability point, the system develops chiral stripes in the tilt, which induce corresponding ripples in the smectic layers. The modulation persists up to an upper critical electric field and then disappears. Furthermore, even in the uniform state, the system shows chiral fluctuations, including both incipient chiral stripes and localized chiral vortices. We compare these predictions with observed chiral modulations and fluctuations in smectic-A liquid crystals.Comment: 11 pages, including 9 postscript figures, uses REVTeX 3.0 and epsf.st

Proteomic analysis of the rat ovary following chronic low-dose exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD)

2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) is a ubiquitously distributed endocrine-disrupting chemical and reproductive toxicant. In order to elucidate low-dose TCDD-mediated effects on reproductive or endocrine functions, female Sprague-Dawley rats were orally administered various concentrations (20, 50, or 125 ng/kg once weekly) TCDD for 29 wk. A proteomic analysis of the ovaries by two-dimensional gel electrophoresis and matrix-assisted laser desorption/ionization (MALDI) tandem mass spectrometry showed distinct changes in the levels of several proteins that are relevant markers of TCDD toxicity. Serum estradiol (E2) levels of TCDD-treated animals were markedly lower than control. There were no significant differences in bone mineral density (BMD) of femurs. The body weight of the 125-ng/kg TCDD group was significantly decreased relative to control and there was also a significant reduction in absolute and relative ovarian weights. Expressions of selenium binding protein 2, glutathione S-transferase mu type 3, Lrpap1 protein, NADPH, and peptidylprolyl isomerase D were upregulated, while prohibitin and N-ethylmaleimide-sensitive factor expression levels were downregulated. Data provide further insight into the mechanisms by which TCDD disrupts ovarian function by indicating which differential protein expressions following low-dose TCDD exposure