High Temperature Expansions and Dynamical Systems

We develop a resummed high-temperature expansion for lattice spin systems with long range interactions, in models where the free energy is not, in general, analytic. We establish uniqueness of the Gibbs state and exponential decay of the correlation functions. Then, we apply this expansion to the Perron-Frobenius operator of weakly coupled map lattices.Comment: 33 pages, Latex; [email protected]; [email protected]

START in a five-dimensional conformal domain

In this paper we give a brief review of the pseudo-Riemannian geometry of the five-dimensional homogeneous space for the conformal group O(4,2). Its topology is described and its relation to the conformally compactified Minkowski space is described. Its metric is calculated using a generalized half-space representation. Compactification via Lie-sphere geometry is outlined. Possible applications to Jaime Keller's START theory may follow by using its predecessor - the 5-optics of Yu. B. Rumer. The point of view of Rumer is given extensively in the last section of the paper. Keywords. Kaluza,Klein, Rumer, conformal symmetry, hyperbolic space, START, fifth dimension, action coordinate, 5-opticsComment: Latex, 13 pages, 3 figures, added sections 3.2. Christoffel symbols and geodesics and 3.3. {\Sigma}- as the space of hyperboloids; accepted for publication in the special volume of AACA in memory of Prof. Jaime Kelle

Design of Three-Dimensional Hypersonic Inlets with Rectangular to Elliptical Shape Transition

A methodology has been devised for the design of three-dimensional hypersonic inlets which include a rectangular to elliptical shape transition. This methodology makes extensive use of inviscid streamtracing techniques to generate a smooth shape transition from a rectangular-like capture to an elliptical throat. Highly swept leading edges and a significantly notched cowl enable use of these inlets in fixed geometry configurations. The design procedure includes a three dimensional displacement thickness calculation and uses established correlations to check for boundary layer separation due to shock wave interactions. Complete details of the design procedure are presented and the characteristics of a modular inlet with rectangular to elliptical shape transition and a design point of Mach 7.1 are examined. Comparison with a classical two-dimensional inlet optimized for maximum total pressure recovery indicates that this three-dimensional inlet demonstrates good performance even well below its design point

Casimir Effects: An Optical Approach I. Foundations and Examples

We present the foundations of a new approach to the Casimir effect based on classical ray optics. We show that a very useful approximation to the Casimir force between arbitrarily shaped smooth conductors can be obtained from knowledge of the paths of light rays that originate at points between these bodies and close on themselves. Although an approximation, the optical method is exact for flat bodies, and is surprisingly accurate and versatile. In this paper we present a self-contained derivation of our approximation, discuss its range of validity and possible improvements, and work out three examples in detail. The results are in excellent agreement with recent precise numerical analysis for the experimentally interesting configuration of a sphere opposite an infinite plane.Comment: Minor corrections. Submitted to Nucl. Phys.

Affection, virtue, pleasure, and profit: Developing an understanding of friendship closeness and intimacy in western and Asian societies

The development of friendship understanding has rarely been explored from a cross-cultural perspective. In this study, children and adolescents from Iceland, China, Russia, and the former East Germany were investigated in one longitudinal and three cross-sectional samples. Children from three different Chinese ecologies were interviewed to account for within-culture variation. Participants were interviewed about friendship closeness and intimacy at ages 7, 9, 12, and 15 years. Their statements were scored according to (a) structural-developmental stages and (b) content aspects of friendship reasoning. Results reveal that the development of friendship reasoning of participants from all societies could be captured by the cognitive-structural stages and content categories developed in western cultures. At the same time, distinct cultural differences emerged, especially between the Russian and Chinese participants, on the one hand, and the Icelandic and East German participants, on the other hand. The within-China analyses reveal little differences for the content aspects of friendship understanding between the three ecologies, but differences in the cognitive-structural aspects of friendship reasoning were found. © 2008 The International Society for the Study of Behavioural Development

Complementarity in classical dynamical systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.Comment: 18 pages, no figure

Analysis of the distribution of the number of bidders in construction contract auctions

The number of bidders, N, involved in a construction procurement auction is known to have an important effect on the value of the lowest bid and the mark-up applied by bidders. In practice, for example, it is important for a bidder to have a good estimate of N when bidding for a current contract. One approach, instigated by Friedman in 1956, is to make such an estimate by statistical analysis and modelling. Since then, however, finding a suitable model for N has been an enduring problem for researchers and, despite intensive research activity in the subsequent 30 years, little progress has been made, due principally to the absence of new ideas and perspectives. The debate is resumed by checking old assumptions, providing new evidence relating to concomitant variables and proposing a new model. In doing this and in order to ensure universality, a novel approach is developed and tested by using a unique set of 12 construction tender databases from four continents. This shows the new model provides a significant advancement on previous versions. Several new research questions are also posed and other approaches identified for future study

Metastable Random Field Ising model with exchange enhancement: a simple model for Exchange Bias

We present a simple model that allows hysteresis loops with exchange bias to be reproduced. The model is a modification of the T=0 random field Ising model driven by an external field and with synchronous local relaxation dynamics. The main novelty of the model is that a certain fraction f of the exchange constants between neighbouring spins is enhanced to a very large value J_E. The model allows the dependence of the exchange bias and other properties of the hysteresis loops to be analyzed as a function of the parameters of the model: the fraction f of enhanced bonds, the amount of the enhancement J_E and the amount of disorder which is controlled by the width sigma of the Gaussian distribution of the random fields.Comment: 8 pages, 11 figure

Random walks in space time mixing environments

We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.Comment: 28 page