Universal reduced potential function for diatomic systems

The potential energy functions of 200 diatomic systems, with dissociation energies De ranging from few eV to hundreds of mueV, are well described by a new three-parameter potential energy function. Identification of the evaluated values of a dimensionless quantity, xin=L2/Ln [Ln=(n!De/fn)1/n, a scaled length parameter, and fn, the nth force constant evaluated at the equilibrium internuclear distance Re], is proposed as a reliable criterion to search for the universal scaling features of potentials and spectroscopic constants for bound diatomic systems. Our study suggests a useful approach to predicting future molecular spectroscopic constants.     

Large deviation function of the partially asymmetric exclusion process

The large deviation function obtained recently by Derrida and Lebowitz [Phys. Rev. Lett. 80, 209 (1998)] for the totally asymmetric exclusion process is generalized to the partially asymmetric case in the scaling limit. The asymmetry parameter rescales the scaling variable in a simple way. The finite-size corrections to the universal scaling function and the universal cumulant ratio are also obtained to the leading order.     

Order parameter statistics in the critical quantum Ising chain

The probability distribution of the order parameter is expected to take a universal scaling form at a phase transition. In a spin system at a quantum critical point, this corresponds to universal statistics in the distribution of the total magnetization in the low-lying states. We obtain this scaling function exactly for the ground state and first excited state of the critical quantum Ising spin chain. This is achieved through a remarkable relation to the partition function of the anisotropic Kondo problem, which can be computed by exploiting the integrability of the system.     

Universal Scaling Behavior of Directed Percolation Around the Upper Critical Dimension

In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function of the control parameter and the conjugated field. Additionally to the universal scaling functions, several universal amplitude combinations are considered. We compare our results with those of a renormalization group approach.     

Absence of hyperscaling violations for phase transitions with positive specific heat exponent

Finite size scaling theory and hyperscaling are analyzed in the ensemble limit which differs from the finite size scaling limit. Different scaling limits are discussed. Hyperscaling relations are related to the identification of thermodynamics as the infinite volume limit of statistical mechanics. This identification combined with finite ensemble scaling leads to the conclusion that hyperscaling relations cannot be violated for phase transitions with strictly positive specific heat exponent. The ensemble limit allows to derive analytical expressions for the universal part of the finite size scaling functions at the critical point. The analytical expressions are given in terms of generalH-functions, scaling dimensions and a new universal shape parameter. The universal shape parameter is found to characterize the type of boundary conditions, symmetry and other universal influences on critical behaviour. The critical finite size scaling functions for the order parameter distribution are evaluated numerically for the cases =3, =5 and =15 where is the equation of state exponent. Using a tentative assignment of periodic boundary conditions to the universal shape parameter yields good agreement between the analytical prediction and Monte-Carlo simulations for the two dimensional Ising model. Analytical expressions for critical amplitude ratios are derived in terms of critical exponents and the universal shape parameters. The paper offers an explanation for the numerical discrepancies and the pathological behaviour of the renormalized coupling constant in mean field theory. Low order moment ratios of difference variables are proposed and calculated which are independent of boundary conditions, and allow to extract estimates for a critical exponent.     

The renormalization group in the problem of turbulent convection of a passive scalar impurity with nonlinear diffusion

The problem of turbulent mixing of a passive scalar impurity is studied within the renormalization-group approach to the stochastic theory of developed turbulence for the case where the diffusion coefficient is an arbitrary function of the impurity concentration. Such a problem incorporates an infinite number of coupling constants (“charges”). A one-loop calculation shows that in the infinite-dimensional space of the charges there is a two-dimensional surface of fixed points of the renormalization-group equations. When the surface has an IR-stability region, the problem has scaling with universal critical dimensionalities, corresponding to the phenomenological laws of Kolmogorov and Richardson, but with nonuniversal (i.e., depending on the Prandtl number and the explicit form of the nonlinearity in the diffusion equation) scaling functions, amplitude factors in the power laws, and value of the “effective Prandtl turbulence number.” Zh. éksp. Teor. Fiz. 112, 1649–1663 (November 1997)     

A simple model for the surface energy of ionic crystals

The surface energy of ionic materials is empirically related to bulk properties (elastic constants, electronic dielectric constant and optical band gap) through an analysis of the cleavage force. This is evaluated at small and large separations of the two crystal halves from phonon dispersion curves and from van der Waals interactions, respectively, and these two limiting behaviours are connected by a scaling hypothesis introduced for metals by Kohn and Yaniv. The experimental data that are available for a few ionic crystals seem to satisfy the suggested relation, with an empirical universal parameter which has roughly the same value as determined for metals.     

Analytic Representation of Critical Equations of State

A new form is proposed for equations of state (EOS) of thermodynamic systems in the 3-dimensional Ising universality class. The new EOS guarantees the correct universality and scaling behavior close to critical points and is formulated in terms of the scaling fields only—unlike the traditional Schofield representation, which uses a parametric form. Close to a critical point, the new EOS expresses the square of the strong scaling field $\Sigma $ as an explicit function $\Sigma ^2=D^{2e_{-1}}W(D^{-e_0}\Theta )$ of the thermal scaling field $\Theta $ and the dependent scaling field $D>0$ , with a smooth, universal function $W$ and the universal exponents $e_{-1}=\delta /(\delta +1)$ , $e_0=1/(2-\alpha )$ . A numerical expression for $W$ is derived, valid close to critical points. As a consequence of the construction it is shown that the dependent scaling field can be written as an explicit function of the relevant scaling fields without causing strongly singular behavior of the thermodynamic potential in the one-phase region. Augmented by additional scaling correction fields, the new EOS also describes the state space further away from critical points. It is indicated how to use the new EOS to model multiphase fluid mixtures, in particular for vapor–liquid–liquid equilibrium where the traditional revised scaling approach fails.     

随机多孔介质逾渗模型渗透率的临界标度性质

研究了一类非零键渗透率满足均匀分布的随机多孔介质逾渗模型-数值计算了该模型系统渗透率在临界点处的标度指数-结果表明该指数并不能看作是普适常数,而与均匀分布的参数有关-这意味着即使非零键渗透率值的概率密度函数满足负一阶矩存在条件,系统渗透率在逾渗临界点处的标度指数仍然依赖于分布函数的具体参数,并不是常数-这一数值结果与Sahimi对此问题的结论不同- 关键词： 逾渗 随机多孔介质 标度指数 渗透率     

Closure approach to high-order structure functions of turbulence

Let T(p) be the structure function of order p of turbulence. First T2 is determined, then T3 is derived from T2, and finally T(p) (p>3) are derived from T2 and T3. This closure scheme is realized by a non-Gaussian statistical model. We use it to study the scaling law of T(p), and we find that the available data on scaling exponents favor Kolmogorov's 1941 theory rather than his 1962 theory. We also predict the high-order universal constants of inertial-range scaling.     

Scaling analysis of high temperature superconductors under pressure

The scaling relation of single parameter scaling hypothesis is applied to the study of the scaling behavior of high temperature superconductors under pressure. The data of resistance and specific heat coefficient under various pressures are scaled onto a universal curve according to this scaling relation. The scaling parameters are pressure dependent while temperature independent. It is found that the controlling parameter Bi equals to the relative critical temperature tcP, which indicates that the superconducting energy gap at the zero temperature 2Δs0 is the controlling parameter in this scaling.     

Evidence of emergent scaling in mechanical systems

In previous work, electrical networks of randomly distributed resistors and capacitors driven with a periodic voltage have shown emergent scaling behaviour: a logarithmic scaling rule is found to dictate the conductance of the bulk network as a function of frequency. This feature has also been shown in other bi-materials and is thought to be independent of the materials involved and, hence, “universal” in nature. The present article examines the potential universality of these scaling laws by considering a mechanically loaded random network. In particular, the mechanical network under consideration is a statically loaded truss. The mechanical system shows an emergent region and percolation paths, much like its electrical counterpart, further suggesting that random, networked systems may have a universal character.     

A JUSTIFICATION FOR THE SCALING OF THE THOM-SYSTEM

In the present paper we discuss the critical behavior of Thornsystem using Catastrophe Theory. The universal critical asymptotic form of the family of free energy functions for Thomsystem with one order parameter and two field parameters is obtained. The expressions of critical exponents, the scaling laws, and the scaling hypotheses are all derived from this universal asymptotic form.     

非平衡相变的临界标度理论及普适性

综述了作者近年来在非平衡相变临界（ Ｎ Ｐ Ｃ） 标度理论及普适性研究的进展。主要包括一般 Ｎ Ｐ Ｃ 系统规格化模型,局域序参量的概率分布,广义势的临界渐近形式,空时有关函数及其临界奇异行为。论证了 Ｎ Ｐ Ｃ 系统的临界可标度性,导出了一组普适的 Ｎ Ｐ Ｃ 标度关系,由之计算出的４ 种 Ｎ Ｐ Ｃ 普适类的临界指数与目前已知的实验及理论结果吻合得非常好。此外,还讨论了非平衡相变临界标度理论的普适性,将平衡相变临界标度理论作为一种特殊极限情况含于同一理论体系中。     

非平衡相变的临界标度理论及普适性

综述了作者近年来在非平衡相变临界（ Ｎ Ｐ Ｃ） 标度理论及普适性研究的进展。主要包括一般 Ｎ Ｐ Ｃ 系统规格化模型,局域序参量的概率分布,广义势的临界渐近形式,空时有关函数及其临界奇异行为。论证了 Ｎ Ｐ Ｃ 系统的临界可标度性,导出了一组普适的 Ｎ Ｐ Ｃ 标度关系,由之计算出的４ 种 Ｎ Ｐ Ｃ 普适类的临界指数与目前已知的实验及理论结果吻合得非常好。此外,还讨论了非平衡相变临界标度理论的普适性,将平衡相变临界标度理论作为一种特殊极限情况含于同一理论体系中。     

Thom系统标度性的证明

本文应用突变论(catastrophe theory)证得了Thom系统自由能函数族的普适的临界渐近形式,并从它推导了临界指数公式,标度律和标度假设。 关键词：     

Steady-state scaling function of the (1 + 1)-dimensional single-step model

The steady-state height-height correlation function for the (1 + 1)-dimensional single-step model is calculated in a large-scale Monte Carlo simulation. Analysis of the data yields a universal ratio of scaling amplitudes which differs from the value obtained recently from a mode-coupling calculation. An empirical form for a universal scaling function is also presented.     

The self-consistent pendulum picture of the free electron laser revised

We reconsider the one-particle dynamics of a Free Electron Laser, adopting the so-called universal scaling. By a fully hamiltonian treatment of the electron and radiation field variables, we show that the electron phase-plane is never that of a pendulum. Actually, besides an elliptic and a hyperbolic pendulum-like fixed point, an extra elliptic point is present at the same phase value as the hyperbolic one, for large values of the detuning parameter δ. On decreasing δ, these two points collapse, which implies a dramatic change in the electron orbit topology, at a value of the detuning parameter which coincides with the instability threshold for exponential gain in the many-electron system.     

Superscaling predictions for neutral current quasielastic neutrino-nucleus scattering

The application of superscaling ideas to predict neutral-current (NC) quasielastic (QE) neutrino cross sections is investigated. The relativistic impulse approximation (RIA) using the same relativistic mean field potential (RMF) for both initial and final nucleons - a model that reproduces the experimental (e,e(')) scaling function - is used to illustrate our findings. While NC reactions are apparently not well suited for scaling analyses, to a large extent, the RIA-RMF predictions do exhibit superscaling. Independence of the scaled response on the nuclear species is very well fulfilled. The RIA-RMF NC superscaling function is in good agreement with the experimental (e,e(')) one. The idea that electroweak processes can be described with a universal scaling function, provided that mild restrictions on the kinematics are assumed, is shown to be valid.     

Scaling behavior of semiclassical gravity

Using the idea of metric scaling we examine the scaling behavior of the stress tensor of a scalar quantum field in curved space-time. The renormalization of the stress tensor results in a departure from naive scaling. We view the process of renormalizing the stress tensor as being equivalent to renormalizing the coupling constants in the Lagrangian for gravity (with terms quadratic in the curvature included). Thus the scaling of the stress tensor is interpreted as a nonnaive scaling of these coupling constants. In particular, we find that the cosmological constant and the gravitational constant approach UV fixed points. The constants associated with the terms which are quadratic in the curvature logarithmically diverge. This suggests that quantum gravity is asymptotically scale invariant.