Reaction-Convection in Incompressible 3D-Fluid: A Homogenization Problem

We consider reaction-convection in a stationary incompressible flow which is close to a planar motion. Under certain conditions, we introduce the notion of relative entropy for such a deterministic flow to describe the motion of the spot occupied by an ingredient. The work was supported in part by an NSF grant DMS0503950.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

Space-Time Directional Lyapunov Exponents for Cellular Automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved.     

Direct measurement of the magnetocaloric effect in La0.67Ca0.33MnO3

Polycrystalline perovskite La_0.67Ca_0.33MnO₃ was synthesized by a sol–gel method. Its adiabatic temperature change ΔT_ad induced by a magnetic field change was measured directly. At 268 K, near its Curie temperature T_C, ΔT_ad of La_0.67Ca_0.33MnO₃ induced by a magnetic field change of 2.02 T reaches 2.4 K. The latent heat Q and magnetic entropy change −ΔS_M induced by a magnetic field change were calculated from the temperature dependence of ΔT_ad and zero-field heat capacity C_p. The maximum values of Q and −ΔS_M in La_0.67Ca_0.33MnO₃ induced by a magnetic field change of 2.02 T are 1.85 J g⁻¹ and 6.9 J kg⁻¹ K⁻¹, respectively. The former is larger than the phase transition latent heat of heating or cooling, which is about 1.70 J g⁻¹.     

Entropic criterion for model selection

Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback–Leibler distance or relative entropy as a selection criterion. Yet that will raise two questions, why use this criterion and are there any other criteria. Besides, conventional approaches require a reference prior, which is usually difficult to get. Following the logic of inductive inference proposed by Caticha [Relative entropy and inductive inference, in: G. Erickson, Y. Zhai (Eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, vol. 707, 2004 (available from arXiv.org/abs/physics/0311093)], we show relative entropy to be a unique criterion, which requires no prior information and can be applied to different fields. We examine this criterion by considering a physical problem, simple fluids, and results are promising.     

Jamming and crystallization in athermal polymer packings

Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization.     

Room temperature magnetocaloric effect in Pr1.75Sr1.25Mn2O7 double-layered perovskite manganite system

Abstract

In this work, we have studied on double-layered perovskite (Ruddlesden–Popper) manganite structure in Pr_1.75Sr_1.25Mn₂O₇ synthesised by sol–gel method. The crystal structure of the double-layered perovskite is found as tetragonal from the X-ray diffraction analysis with I4/mmm space group. A high Curie temperature, T_C = 305 K is observed from the temperature dependence of magnetisation measurement. The isothermal magnetisation curves showed that magnetic phase transition is second order due to the positive slope of the Arrott plots. Maximum magnetic entropy change (ΔS_M) and adiabatic temperature change (ΔT_ad) values are calculated as 3.99 J kg^?1 K^?1 and 2.1 K under external magnetic field of 70 kOe, respectively. Since our double-layered perovskite manganite sample has desired T_C value and relatively high ΔS_M, it can be a potential candidate as a magnetocaloric material for room temperature magnetic cooling systems.     

Measuring causality by taking the directional symbolic mutual information approach

We propose a novel measure to assess causality through the comparison of symbolic mutual information between the future of one random quantity and the past of the other.This provides a new perspective that is different from the conventional conceptions.Based on this point of view,a new causality index is derived that uses the definition of directional symbolic mutual information.This measure presents properties that are different from the time delayed mutual information since the symbolization captures the dynamic features of the analyzed time series.In addition to characterizing the direction and the amplitude of the information flow,it can also detect coupling delays.This method has the property of robustness,conceptual simplicity,and fast computational speed.     

太赫兹逆合成孔径雷达相位误差分析和补偿方法

通过对太赫兹逆合成孔径雷达(THz-ISAR)成像原理进行分析,构造目标回波距离维相位误差的多项式表示形式,提出了基于启发式最小熵搜索的二次相位误差校正方法和基于距离维自聚焦的三次及三次以上相位误差校正方法,校正了THz-ISAR回波信号距离维的相位误差,进而消除THz-ISAR一维距离像和二维成像结果中的散焦和展宽现象。理论分析和仿真实验结果都表明该方法能够有效补偿目标回波距离维相位误差,提高一维距离像和二维成像的聚焦效果。