Projective metrics and mixing properties on towers

We study the decay of correlations for towers. Using Birkhoff's projective metrics, we obtain a rate of mixing of the form:

where goes to zero in a way related to the asymptotic mass of upper floors, is some Lipschitz norm and is some norm. The fact that the dependence on is given by an norm is useful to study asymptotic laws of successive entrance times.

     

Quantum n-Vector Anharmonic Crystal II: Displacement Fluctuations

Based on the 1/n-expansion derived in a previous paper, the displacement fluctuations are analyzed in a quantum n-vector model of anharmonic crystal in the large n regime. It is shown that in the ferroelectric phase the n limit of the local fluctuation field has faster large-distance correlation decay than its Hartree–Fock approximation. Also, the critical exponent of the global displacement fluctuation is strictly smaller there than the Hartree–Fock exponent. In particular, the displacement fluctuations may be normal in the ferroelectric phase in spite of the Hartree–Fock prediction.     

Transfer Matrix Spectrum and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We obtain new properties of general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high-temperature region (1). Each model is characterized by a single-site a priori spin distribution, taken to be even. We state our results in terms of the parameter =s ⁴–3s ²², where s ^k denotes the kth moment of the a priori distribution. Associated with the model is a lattice quantum field theory which is known to contain particles. We show that for >0, small, there exists a bound state with mass below the two-particle threshold. The existence of the bound state has implications for the decay of correlations, i.e., the 4-point functions decay at a slower rate than twice that of the 2-point function. These results are obtained using a lattice version of the Bethe–Salpeter equation. The existence results generalize to N-component models with rotationally invariant a priori spin distributions.     

北京谱仪Ⅲ飞行时间计数器系统刻度中的关联分析

利用电子对事例对北京谱仪Ⅲ飞行时间的测量误差, 以及不同测量之间的关联因子随击中位置的变化进行了仔细的研究. 加权的飞行时间由不同的测量值及其相关的误差矩阵计算而得. 蒙特卡罗研究表明. 为北京谱仪Ⅲ开发的关联分析算法 可以正确地处理包含公有误差项的多个实验测量结果的合并, 并且能够为粒子鉴别提供可靠的飞行时间信息.     

Phase and velocity distributions in vertically upward high-viscosity two-phase flow

The two-phase pressure drop in vertical industrial pipes is mainly determined by gravitation and acceleration of the fluid, which means that the void fraction is key an important parameter in any model to predict pressure drops. Typically, these models are applied in industry to size pumps and, e.g., emergency relief systems. There is a shortage of void fraction data in the literature for liquids with a dynamic viscosity above 1000 mPa s. Adiabatic experiments have been performed of mixtures of nitrogen and solutions of polyvinylpyrrolidone (Luviskol^®) in water with dynamic viscosities in the range 900–7000 mPa s. Inner tube diameter was 54.5 mm. Mass flux and quality were varied in a wide range: 8–3500 kg/m²/s and 0–82%, respectively. The corresponding superficial velocities were 0.005–3.4 m/s for the liquid and 0–30 m/s for the nitrogen. For comparison, reference measurements were taken of mixtures of nitrogen with water (1 mPa s). Care has been taken to measure only well-developed flows.     

Selective lighting up of segments around Gly,Ala and Ser/Thr in proteins

Direct detection of ¹³C nucleus can be used as a valuable alternative where ¹H detection poses a challenge due to relaxation effects, chemical exchange and poor chemical shift dispersion. In this context, we have designed a suite of 2D ¹³C^α‐detected hNCA experiments that provide sequential correlations of ¹³C^α with ¹⁵N on one hand and efficient spectroscopic labeling of certain groups of residues, namely, Gly, Ala, Ser and Thr, on the other. These residues act as checkpoints in the sequential walk, which in turn offer new possibilities of backbone assignment of small proteins from a set of 2D experiments, thereby providing great economy in terms of spectrometer time. The direct identification of peptide segments around Gly, Ala, Ser and Thr residues along a protein chain will be highly valuable for deriving important information on sites of ligand binding, phosphorylation, inhibitor/substrate binding, understanding protein folding pathways, comprehending local conformational dynamics etc. without having to obtain complete sequence‐specific assignments, which can be time consuming and at times formidable, especially in large proteins. We have illustratively demonstrated the multifaceted applications of these variants of 2D experiments on ubiquitin and M‐crystallin. We foresee that these 2D hNCA experiments will provide economic and efficient strategies for studying the structure and function of proteins. Copyright © 2012 John Wiley & Sons, Ltd.     

Decay of Correlations and Dispersing Billiards

We give a rigorous proof of exponential decay of correlations for all major classes of planar dispersing billiards: periodic Lorentz gases with and without horizon and dispersing billiard tables with corner points     

Linear quantum Enskog equation. I. Homogeneous quantum fluids

The quantum-statistical generalization of the well-known classical, linear revised Enskog equation is derived for spatially uniform systems. This new quantum kinetic equation allows the study of equilibrium time correlation functions and their associated transport coefficients of normal quantum fluids where static correlations and degeneracy effects due to particle statistics (both are treated exactly) are important. Furthermore, we derive the quantum-statistical analog of the classical ring operator. These microscopic and systematic derivations are based on a recently developed superoperator formalism (including cluster expansion techniques) that, as a main feature, allows a clear distinction between static and dynamic correlations, which is crucial in the discussion of the Enskog approximation.     

Fluids with highly directional attractive forces. IV. Equilibrium polymerization

We investigate approximation methods for systems of molecules interacting by core repulsion and highly directional attraction due to several attraction sites. The force model chosen imitates a chemical bond by providing for bond saturation when binding occurs. The dense fluid is an equilibrium mixture ofs-mers with mutual repulsion. We use a previously derived reformulation of statistical thermodynamics, in which the particle species are monomeric units with a specified set of attraction sites bonded. Thermodynamic perturbation theory (TPT) and integral equations of two types are derived. The use of TPT is illustrated by explicit calculation for a molecular model with two attraction sites, capable of forming chain and ring polymers. Successes and defects of TPT are discussed. The integral equations for pair correlations between particles of specified bonding include calculation of self-consistent densities of species. Methods of calculating thermodynamic properties from the solutions of integral equations are given.Supported by the NSF under grant No. CHE-82-11236.     

Geometry of random sequential adsorption

By sequentially adding line segments to a line or disks to a surface at random positions without overlaps, we obtain configurations of the one- and two-dimensional random sequential adsorption (RSA) problem. We have simulated the one- and two-dimensional problem with periodic boundary condition. The one-dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation. In two dimensions the geometrical properties of the RSA configuration are discussed and in addition known results of the RSA process are reproduced. Various statistical distributions of the Voronoi-Dirichlet (VD) network corresponding to the RSA disk configuration are analyzed. In order to characterize pores in the RSA configuration, we introduce circular holes. There is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and these holes. The hole size distribution is found to be a parabola. We also find general relations that connect the asymptotic behavior of the surface coverage, the correlation function, and the hole size distribution.