We study the iteration of block spin transformations in the O(3) symmetric non-linear σ-model on a two-dimensional square lattice with help of the Monte Carlo method. In contrast to the classical Monte Carlo Renormalization Group approach, we do attempt to explicitly compute the block spin effective actions. Using two different methods for the determination of effective couplings, we study the ...

We investigate the inclusion of 10-dimensional string loop corrections to the entropy function of twocharge extremal small black holes of the heterotic string theory compactified on S1 × T 5 and show that the entropy is given by π √ a q1q2 + b q1 where q1 and q2 are the charges with q1 ≫ q2 ≫ 1 and a and b are constants. Incorporating certain multi-string states into the microstate counting, we...

A scaling hypothesis for the n-particle spectral densities of the O(3) nonlinear sigma-model is described. It states that for large particle numbers the n-particle spectral densities are “self-similar” in being basically rescaled copies of a universal shape function. This can be viewed as a 2-dimensional, but non-perturbative analogue of the KNO scaling in QCD. Promoted to a working hypothesis,...

We examine the long time behaviour of A + B → 0 reaction diffusion systems with initially segregated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constants DA, DB, and initial concentrations a0 and b0 of A’s and B’s. We divide the domain of the partial differential equations describing the problem into several regions in which they can be ...

The dynamics of randomly crosslinked liquids is addressed via a Rouseand a Zimm-type model with crosslink statistics taken either from bond percolation or Erdős–Rényi random graphs. While the Rouse-type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoheren...

a spectrophotometric method is used to determine the acidity constants of some derivatives of 9,10-anthraquinone in binary methanol-water mixtures at 25 °c. there is a linear inverse relationship between pka of all acids and the mole fraction of methanol in the mixed solvent. the influence of substituents in the molecular structure on the ionization constants is discussed.

We introduce new discretizations of the action for static quarks. They achieve an exponential improvement (compared to the Eichten-Hill regularization) on the signal to noise ratio in static–light correlation functions. This is explicitly checked in a quenched simulation and it is understood quantitatively in terms of the self energy of a static quark and the lattice heavy quark potential at ze...

We introduce new discretizations of the action for static quarks. They achieve an exponential improvement (compared to the Eichten-Hill regularization) on the signal to noise ratio in static–light correlation functions. This is explicitly checked in a quenched simulation and it is understood quantitatively in terms of the self energy of a static quark and the lattice heavy quark potential at ze...

The closing of the nuclear fuel cycle is an unsolved problem of great importance. Separating radionuclides produced in a nuclear reactor is useful both for the storage of nuclear waste and for recycling of nuclear fuel. These separations can be performed by designing appropriate chelation chemistries and liquid-liquid extraction schemes, such as in the TALSPEAK process (Trivalent Actinide-Lanth...

Let A be a p-variate real Wishart matrix on n degrees of freedom with identity covariance. The distribution of the largest eigenvalue in A has important applications in multivariate statistics. Consider the asymptotics when p grows in proportion to n, it is known from Johnstone (2001) that after centering and scaling, these distributions approach the orthogonal Tracy-Widom law for real-valued d...