Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models

A ``persistence'' exponent theta has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice, the fraction p(t) of spins not flipped by time t decays to zero like t^[-theta(d)] for low d; for high d, p(t) may decay to p(infinity)>0, because of ``blocking'' (but perhaps still like a power). What are the effects of disorder or changes of lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low d, and then present two examples --- one disordered and one homogeneous --- where p(t) decays exponentially to p(infinity).Comment: 8 pages (LaTeX); to appear in Physical Review Letter

Marketing images and consumers' experiences in selling environments

In a well-functioning market, consumers exert choices not just in purchases of products but also in selections of locations to enjoy shopping. Scholarly research has demonstrated that retail atmospheres impact on shoppers’ pleasurable shopping experiences. Demonstrating the marketing concept in action, shoppers consistently respond to this empowerment by for example, spending more time shopping and spending more money in retail facilities that are perceived to offer a pleasanter atmosphere and experience. This research pivots round an in-depth qualitative study that evaluated the impact of a plasma screens and specific informational content on shopping centre user behaviour. A phenomenological study of the effects of the medium, and the way in which these systems influence behaviour, permitted a far deeper investigation of our sample group vis-àvis increased browsing time and the propensity to spend. A series of eight focus discussions were conducted with local user groups of varying age and gender. Key themes drawn from the group discussions using axial coding indicated that the influence created by the images varied with subjects and settings. The general consensus was that such ‘screens’ created a certain ambience that influenced the way our subjects felt about the selling environment under study. Moreover, for our sample groups, there was clearly a link between the screened images and modern expectations of a selling environment. The plasma screens provided added enjoyment to shoppers’ experiences, providing them with more information enabling more informed shopping choices. The research concludes with implications for strategic marketing, theory and practice

The Real Meaning of Complex Minkowski-Space World-Lines

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.Comment: 16 page

Interfaces (and Regional Congruence?) in Spin Glasses

We present a general theorem restricting properties of interfaces between thermodynamic states and apply it to the spin glass excitations observed numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3 and 4. We show that such excitations, with interface dimension smaller than d, cannot yield regionally congruent thermodynamic states. More generally, zero density interfaces of translation-covariant excitations cannot be pinned (by the disorder) in any d but rather must deflect to infinity in the thermodynamic limit. Additional consequences concerning regional congruence in spin glasses and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter

Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

We consider the Edwards-Anderson Ising spin glass model on the half-plane $Z \times Z^+$ with zero external field and a wide range of choices, including mean zero Gaussian, for the common distribution of the collection J of i.i.d. nearest neighbor couplings. The infinite-volume joint distribution $K(J,\alpha)$ of couplings J and ground state pairs $\alpha$ with periodic (respectively, free) boundary conditions in the horizontal (respectively, vertical) coordinate is shown to exist without need for subsequence limits. Our main result is that for almost every J, the conditional distribution $K(\alpha|J)$ is supported on a single ground state pair.Comment: 20 pages, 3 figure

Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads

Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included

Three dimensional finite-element analysis of finite-thickness fracture specimens

The stress-intensity factors for most of the commonly used fracture specimens (center-crack tension, single and double edge-crack tension, and compact), those that have a through-the-thickness crack, were calculated using a three dimensional finite-element elastic stress analysis. Three-dimensional singularity elements were used around the crack front. The stress intensity factors along the crack front were evaluated by using a force method, developed herein, that requires no prior assumption of either plane stress or plane strain. The calculated stress-intensity factors from the present analysis were compared with those from the literature whenever possible and were generally found to be in good agreement. The stress-intensity factors at the midplane for all specimens analyzed were within 3 percent of the two dimensional plane strain values. The stress intensity factors at the specimen surfaces were considerably lower than at the midplanes. For the center-crack tension specimens with large thickness to crack-length ratios, the stress-intensity factor reached a maximum near the surface of the specimen. In all other specimens considered the maximum stress intensity occurred at the midplane

Improved stress-intensity factors for semi-elliptical surface cracks in finite-thickness plates

Stress-intensity factors for shallow and deep semi-elliptical surface cracks in plates subjected to tension are presented. To verify the accuracy of the three-dimensional finite-element models employed, convergence was studied by varying the number of degrees of freedom in the models from 1500 to 6900. The 6900 degrees of freedom used here were more than twice the number used in previously reported solutions

The Effect of Pure State Structure on Nonequilibrium Dynamics

Motivated by short-range Ising spin glasses, we review some rigorous results and their consequences for the relation between the number/nature of equilibrium pure states and nonequilibrium dynamics. Two of the consequences for spin glass dynamics following a deep quench to a temperature with broken spin flip symmetry are: (1) Almost all initial configurations lie on the boundary between the basins of attraction of multiple pure states. (2) Unless there are uncountably many pure states with almost all pairs having zero overlap, there can be no equilibration to a pure state as time goes to infinity. We discuss the relevance of these results to the difficulty of equilibration of spin glasses. We also review some results concerning the ``nature vs. nurture'' problem of whether the large-time behavior of both ferromagnets and spin glasses following a deep quench is determined more by the initial configuration or by the dynamics realization.Comment: 20 page

Realistic spin glasses below eight dimensions: a highly disordered view

By connecting realistic spin glass models at low temperature to the highly disordered model at zero temperature, we argue that ordinary Edwards-Anderson spin glasses below eight dimensions have at most a single pair of physically relevant pure states at nonzero low temperature. Less likely scenarios that evade this conclusion are also discussed.Comment: 18 pages (RevTeX; 1 figure; to appear in Physical Review E