A dynamical test of phase transition order: New things in old places or old wine in new bottles

We first discuss nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to take place discontinuously (theory of Halperin, Lubensky, and Ma)-but the discontinuity may be immeasurably small. Then, we describe a new dynamical test of phase transition order, developed by Cladiset al., that turns out to be more sensitive than x-ray diffraction and adiabatic calorimetry. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of HLM.This is the text of an after-banquet talk given at the CNLS Workshop on the Dynamics of Concentrated Systems.     

Weak convergence of the U-statistic and weak invariance of the one-sample rank order statistic for Markov processes and ARMA models

Harel and Puri (1989, J. Multivariate Anal. 29) studied the asymptotic behavior of the U-statistic and the one-sample rank order statistic for nonstationary absolutely regular processes. In this note, we present some applications of these results for Markov processes as well as ARMA processes.     

两类方程亚纯解(n,1)级的上界估计

本文给出Riccati方程及另外一类具有代表性微分方程的亚纯解（n,1)级的上界估计，在一定条件下确立了文[2]中的猜测的正确性。     

Cosmic dust and our origins

The small solid particles in the space between the stars provide the surfaces for the production of many simple and complex molecules. Processes involving the effects of ultraviolet irradiation of the thin (hundredth micron) mantles are shown to produce a wide range of molecules and ions also seen in comets. Some of the more complex ones inferred from laboratory experiments are expected to play an important role in the origin of life. An outline of the chemical evolution of interstellar dust as observed and as studied in the laboratory is presented. Observations of comets are shown to provide substantial evidence for their being fluffy aggregates of interstellar dust as it was in the protosolar nebula, i.e. the interstellar cloud which collapsed to form the solar system. The theory that comets may have brought the progenitors of life to the earth is summarized.     

Non-universal critical behaviour of heteronuclear dimers on a square lattice––A Monte Carlo study

Monte Carlo simulation within the grand canonical ensemble, the histogram reweighting technique, and finite size scaling analysis are used to explore the phase behaviour of heteronuclear dimers, composed of A and B type atoms, on a square lattice. We have found that for the models with attractive BB and AB nearest-neighbour energy, u_BB=u_AB=−1, and for non-repulsive energy between AA nearest-neighbour sites, u_AA<0, the system belongs to the universality class of the two-dimensional Ising model. However, when u_AA>0, the system exhibits a non-universal critical behaviour. We have evaluated the dependences of the critical point characteristics on the value of u_AA.     

ON HYPERBOLIC TIME DISCOUNTING IN EXHAUSTIBLE RESOURCE MODELS: AN APPLICATION TO WORLD OIL RESOURCES

ABSTRACT. Recent research on discounting in long term economic models involves hyperbolic discounting, in which the marginal discount rate shrinks as time passes. To investigate hyperbolic discounting and exhaustible resource allocation, this work develops a discrete‐time world oil model and model solution procedure, then uses the model to examine the consequences of adopting conventional (constant annual) discounting when hyperbolic discounting is appropriate, of adopting one hyperbolic discount rate path when a different hyperbolic path is appropriate, and of adopting hyperbolic discounting when conventional discounting is appropriate. Five conventional and two hyperbolic discount rate paths are considered. One hyperbolic path is that used by Nordhaus and Boyer [2000]; the other is that recommended by Weitzman [2001]. The generality of the findings is also assessed.     

Lower Bounds from State Space Relaxations for Concave Cost Network Flow Problems

In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications. Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can be obtained for concave cost network flow problems, particularly for fixed-charge problems.     

Approximation of photonuclear interaction cross-sections

Photonuclear interaction cross-sections from the GEANT4 database are approximated for all nuclei and all energies (from the hadron production threshold to about 40 TeV). The approximation methods in the giant-dipole resonance region, nucleon resonance region, and high-energy region are improved with respect to existing approximations. As an application of the approximation for photonuclear cross-sections, an improved method of calculating electronuclear cross-sections is developed. The interaction cross-section of virtual photons with nuclei at high Q² are approximated and a simple algorithm for describing the electronuclear reactions, including high-Q² scattering, is proposed. Received: 22 February 2002 / Accepted: 6 May 2002     

双折射滤光片的色散特性研究

研究了由理想线偏振片和单轴双折射晶体波片组成的双折射滤光片倾斜放置时的二阶色散和 三阶色散特性，包括波片厚度、光线入射角和光轴旋转角的变化对二阶和三阶色散的影响. 还给出了双折射滤光片的群延迟表达式，并就色散特性与GT干涉仪进行了详细比较. 关键词： 双折射滤光片 群延迟 二阶色散 三阶色散     

Generalized lattice model of liquid state and its relation to Ginzburg–Landau theory

Basic principles of the generalized lattice model of multicomponent condensed systems are formulated. Short-range parts of interatomic interactions are taken into account by means of the geometric constraints method. Long-range parts of the interactions are taken into account in mean field approximation. The expression for Helmholtz free energy is obtained. A system of integral equations for the equilibrium distributions of components is derived. The asymptotic properties of its solutions are investigated. Moment expansion of interatomic interactions and localization of integral terms in free energy is obtained. A Ginzburg–Landau-like functional of free energy is derived.