Kinetic limit of a conservative lattice gas dynamics showing long-range correlations

An anisotropic lattice gas dynamics is investigated for which particles on ^d jump to empty nearest neighbor sites with (fast) rate ^–2 in a specified direction and some particular configuration-dependent rates in the other directions. The model is translation and reflection invariant and is particle conserving. The space coordinate in the fast-rate direction is rescaled by ^–1. It follows that the density field converges in probability, as 0, to the corresponding solution of a nonlinear diffusion-type equation. The microscopic fluctuations about the deterministic macroscopic evolution are determined explicitly and it is found that the stationary fluctuations decay via a power law (1/r ^d ) with the direction dependence of a quadrupole field.     

Size distribution of fractured areas in one-dimensional systems

We study a one-dimensional model for fracture, identifying fractured areas with intervals on which a stress field exceeds a threshold value. When is a diffusion process, the cumulative numberN(l) of fractured areas whose length is greater thanl obeys a power lawCl ^–p asl0 with probability one. The exponentp and the constantC are determined. The exponentp agrees with the Hausdorff dimension of the end points of fractured areas, i.e., ^–1(). Even if is self-similar with parameterH>0, i.e.,(cx)– is equivalent toc ^H {(x)–} for anyc>0, the exponentp does not depend solely onH;p=H, where(0, 1/H) is another parameter characterizing. Non-diffusion processes are given whereN(l) does not follow a power law.     

Defect of the five-thirds law using the Wiener-Hermite expansion

Application of the refined Wiener-Hermite expansion with moderate to high Reynolds numbers Re to homogeneous, isotropic turbulence is presented. The results show a defect to Kolmogorov's five-thirds law, increase in the absolute value of the exponent comparable with many theoretical predictions. Midrange spectra up to fluctuation Reynolds numbers of 10⁸ show little, if any, dependence of the defect on Re, as long as the initial spectra do not deviate too far from their equilibrium states. The renormalization scheme has also been proven to have no effect on the final shape of the spectrum.     

Intrinsic field theory of chemical reactions

An intrinsic principle of least action is presented for the intrinsic dynamism of chemical reactions. Then, as the stationary trajectory, a meta-IRC (intrinsic reaction coordinate) draws a geodesic curve in a rigged Riemannian space. This establishes a geodesic law for the intrinsic dynamism. Moreover, a diagrammatic perturbation theory is formulated for the intrinsic dynamism, and a dynamical interaction between a chemically reacting system and a background system is investigated. Then, the structural stability of the system is discussed using a new concept of the dynamical potential field. An example is given in order to elucidate the present theory.Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday.     

高聚物亚浓溶液区标度律的蒙特卡洛模拟

利用蒙特卡洛模拟方法对线形链和星形键在亚浓溶液区的标度律作了验证与讨论。我们的计算结果证明线形链渗透压Π与体积分数Φ在亚浓溶液区的标度规律是与德热纳的理论结果相一致的。同时还证明了星形链在亚浓溶液区具有与线形链相同的标度行为。     

Importance of the Debye interaction in organic solutions: Henry's law constants for polar liquids in nonpolar solvents and vice versa

Henry's law constants have been determined for -butyrolactone (BL), ethyl acetate (EA), and 2-methyl-3-pentanol (MEP) in mixtures of iso-octane (ISO) and toluene (TOL), for BL, EA, TOL, and ISO in cinnamaldehyde (CIN) and for TOL and ISO in each other and in BL. From these data and published vapor pressures, the activity coefficients at infinite dilution and the standard molar Gibbs free energy of transfer, G ₂ ⁰ of the solutes from dilute solution in ISO to dilute solution in each solvent medium have been calculated. The different behavior patterns of BL and EA are attributed to differences in their abilities to exist in different conformations possessing different dipole moments. For polar solutes, G ₂ ⁰ decreases with increasing polarizability of the solvent and with increasing dipole moment of the solute, suggesting increased contributions from dipole-induced dipole (Debye) interactions. The sigmoidal plot of G ₂ ⁰ against the change in pair potential energy calculated from the classical expressions suggests that G ₂ ⁰ seriously underestimates the strength of the Debye interactions in comparison with the London interactions.     

Hydrodynamic equations for attractive particle systems on ℤ

Hydrodynamic properties for a class of nondiffusive particle systems are investigated. The method allows one to study local equilibria for a class of asymmetric zero-range processes, and applies as well to other models, such as asymmetric simple exclusion and misanthropes. Attractiveness is an essential ingredient. The hydrodynamic equations present shock wave phenomena. Preservation of local equilibrium is proven to hold away from the shocks. The problem of breakdown of local ergodicity at the shocks, which was investigated by D. Wick in a particular model, remains open in this more general setup.     

Resistance distance and Laplacian spectrum

The resistance distance r _ij between two vertices v _i and v _j of a (connected, molecular) graph G is equal to the resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any two adjacent points is unity. We show how the matrix elements r _ij can be expressed in terms of the Laplacian eigenvalues and eigenvectors of G. In addition, we determine certain properties of the resistance matrix R=||r _ij ||. AcknowledgementsThis research was supported by the Natural Science Foundation of China and Fujian Province, and by the Ministry of Sciences, Technologies and Development of Serbia, within Project no. 1389. The authors thank Douglas J. Klein (Galveston) for useful comments.     

Hygrometric Determination of Water Activities and Osmotic and Activity Coefficients of NH4Cl–LiCl–H2O at 25°C

The mixed aqueous electrolyte system of ammonium and lithium chlorides has been studied by the hygrometric method at 25°C. The relative humidities of this system are measured at total molalities from 0.3 to 6 mol-kg^{– 1} for different ionic-strength fractions y of NH₄Cl with y = 0.33, 0.50, and 0.67. The data obtained allow the deduction of new water activities and osmotic coefficients. The experimental results are compared with the predictions of the ECA (extended composed additivity) law proposed in our previous work. The Zdanovskii–Stokes–Robinson (ZSR), the Robinson–Stokes (RS), Reilly–Wood–Robinson (RWR), the Pitzer, and the Lietzke–Stoughton (LS II) models are also compared with our results. Predictions made using these models are, in general, consistent with our results. From these measurements, new Pitzer mixing ionic parameters are determined and used to predict the solute activity coefficients in the mixture for different ionic-strength fractions.     

Mechanism and control of molecular energy flow: a modeling perspective

 Vibrational energy flow in organic molecules occurs by a multiple-time-scale mechanism that can be modeled by a single exponential only in its initial stages. The mechanism is a consequence of the hierarchical structure of the vibrational Hamiltonian, which leads to diffusion of vibrational wavepackets on a manifold with far fewer than the 3N−6 dimensions of the full vibrational state space. The dynamics are controlled by a local density of states, which does not keep increasing with molecular size. In addition, the number of vibrational coordinates severely perturbed during chemical reaction is small, leading to preservation of the hierarchical structure at chemically interesting energies. This regularity opens up the possibility of controlling chemical reactions by controlling the vibrational energy flow. Computationally, laser control of intramolecular vibrational energy redistribution can be modeled by quantum-classical, or by purely quantum-mechanical models of the molecule and control field. Received: 26 July 2002 / Accepted: 30 September 2002 / Published online: 2 December 2002 Electronic Supplementary Material to this paper can be obtained by using the Springer Link server located at http://dx.doi.org/10.1007/s00214-002-0394-2. Acknowledgements. This work was supported by NSF grant CHE 9986670. Correspondence to: M. Gruebele e-mail: gruebele@scs.uiuc.edu