Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.     

Basis Set Orbital Relaxation in Atomic and Molecular Hydrogen Systems

Orbital relaxation (OR) amounts to variation of the orbital exponents in hydrogen molecules and ions relative to the exponents of the isolated atom; it is represented as the sum of the one- and two-center contributions depending on the effective atomic charge and on the presence of other atoms in the molecule. The procedure for isolating the contributions of the exponent includes treatment of the OR of hydrogen in a special set of neutral and charged atoms and molecules with certain multiplicities of their electronic states. Within the framework of the spin-unrestricted Hartree-Fock method, we found and discussed the optimal values of the exponents of the basis orbitals of hydrogen atoms and molecules using the minimal split valence-shell basis set, the basis set that includes the polarization function, and the expanded set of grouped natural orbitals. A simple energy model is suggested for OR. Expressions are derived for evaluating the exponents of the relaxed orbitals in hydrogen-containing systems.Original Russian Text Copyright © 2004 by A. I. Ermakov, A. E. Merkulov, A. A. Svechnikova, and V. V. Belousov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 973–978, November–December, 2004.     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.     

SEC–MALLS analysis of cellulose using LiCl/1,3-dimethyl-2-imidazolidinone as an eluent

The lithium chloride/1,3-dimethyl-2-imidazolidinone (LiCl/DMI) solvent system for cellulose was adopted as a mobile phase of size-exclusion chromatographic (SEC) analysis of cellulose, and the applicability of this system was examined using multi-angle laser light scattering and ¹³C-NMR analysis. The results indicate that 8% (w/v) LiCl/DMI ID a true solvent for cellulose, and that cellulose molecules dissolving ID 1% (w/v) LiCl/DMI are separated orderly depending on their molecular mass (MM) or root-mean-square (RMS) radius by the SEC system. Practically, no aggregates were detected ID the dilute cellulose/LiCl/DMI solutions. Furthermore, high stability of cellulose/LiCl/DMI solutions has been demonstrated; only a few percent of decline ID average MM was observed even after storage for 6 months at room temperature. Relationships between RMS radius and MM for hardwood bleached kraft pulp ID 1% LiCl/DMI was estimated as the following equation: _g^0.59, corresponding to a Mark–Houwink–Sakurada exponent of 0.77.     

Comparative analysis of affine scaling algorithms based on simplifying assumptions

We analyze several affine potential reduction algorithms for linear programming based on simplifying assumptions. We show that, under a strong probabilistic assumption regarding the distribution of the data in an iteration, the decrease in the primal potential function will be with high probability, compared to the guaranteed(1). ( 2n is a parameter in the potential function andn is the number of variables.) Under the same assumption, we further show that the objective reduction rate of Dikin's affine scaling algorithm is with high probability, compared to no guaranteed convergence rate.Research supported in part by NSF Grant DDM-8922636.     

Finite-size scaling for Potts models

Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by _m (L)=(Inq/E)L ^–d +O(L ^–2d ) with respect to the infinite-volume transition point _t . We also propose an alternative definition of the finite-volume transition temperature _t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from _t .     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

On the Scaling Study for the A_f-A_g Type Free Radical Polymerization

根据Ａｆ－Ａｇ自由基加聚反应的数量分布函数，导出凝胶点附近的渐进分布函数和高分子矩的表示式．进一步应用标度变换，得到了描述溶胶－凝胶相变的广义标度律，从而揭示了Ａｆ－Ａｇ自由基加聚的固化反应是一个相变过程．     

On the ν-dimensional one-component classical plasma: The thermodynamic limit problem revisited

We prove theH-stability property and the existence of the thermodynamic limit of the free energy density of the two-dimensional, one-component classical plasma. We give lower and upper bounds on the free energy density in any dimensionv and draw some consequences.