A testbench for the nested dipole hypothesis of Kosterlitz and Thouless

We consider the two-dimensional one-component plasma without a background and confined to a half-plane near a metal wall. The particles are also subjected to an external potential acting perpendicular to the wall with an inverse-power-law Boltzmann factor. The model has a known solvable isotherm which exhibits a Kosterlitz-Thouless-type transition from a conductive to an insulator phase as the power law is varied. This allows predictions of theoretical methods of analyzing the Kosterlitz-Thouless transition to be compared with the exact solution. In particular, we calculate the asymptotic density profile by resumming its low-fugacity expansion near the zero-density critical coupling in the insulator phase, and solving a mean-field equation deduced from the first BGY equation. Agreement with the exact solution is obtained. As the former calculation makes essential use of the nested dipole hypothesis of Kosterlitz and Thouless, the validity of this hypothesis is explicitly verified.     

Superdegenerate point in FCC phase diagram: CVM and Monte Carlo investigations

We investigate the topology of the phase diagram of binary alloys on the fee lattice with first-neighbor antiferromagnetic interactions around the superdegenerate point, where the L1₀ and L1₂ phases meet. We treat the system as a hard-constraint lattice gas, following a procedure previously described by Lebowitzet al. We perform cluster variation method calculations in theT0 limit and Monte Carlo simulations directly atT=0 K on the ground states of the superdegenerate point. We find that: (i) there is no disordered phase in the neighborhood of this point; (ii) a phase L for which two of the four cubic sublattices have the same average occupancy and each of the two others are different appears between L1₀ and L1₂; (iii) the transition L/L1₂ is of first order.     

Turbulence without strange attractor

It is shown that pipe-flow turbulence consists of transients. The fractal dimensions of the dynamical process are thus all zero. Nevertheless, this is compatible with Grassberger-Procaccia analyses suggesting the existence of a high-dimensional strange attractor. The usefulness of the Grassberger-Procaccia method to detect the aging of transients is demonstrated.     

Spin interaction with an ideal Fermi gas

We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them.     

化学键合吸附剂的合成及吸附行为

在无定型硅胶上化学键合十八烷基三氯硅烷，键合率17%-20％，粒度5μm-10μm，以此键合的吸附剂可有效地吸附香烟烟气中的焦油、亚硝胺，吸附率分别为15%-18％和37%-43％，研究了化学键合吸附剂的粒度和加入量对吸附性能的影响。     

Flow injection-spectrophotometric determination of cresol compounds in water by reaction withp-aminophenol

A spectrophotometric method has been developed for the simultaneous determination ofo-cresol andm-cresol in water by reaction withp-aminophenol (PAP). Three different methodologies have been assayed; (i) batch analysis, after reaction in an alkaline medium in the presence of dissolved molecular oxygen as oxidizing agent, (ii) a stopped-flow procedure, carried out in the presence of KIO₄ and (iii) a flow injection method based on the same approach. The batch procedure requires 22 min for the full development of colour witho-cresol and 12 min form-cresol. In the stopped-flow mode, using KIO₄ and a reaction time of 12 min, better sensitivity can be obtained for both compounds and limits of detection of 10 g 1^–1 foro-cresol and 30 g 1^–1 form-cresol were found. The flow injection method has a lower sensitivity but permits more than 80 injections per hour. Based on the different maximum absorbance wavelengths obtained for the reaction products of PAP witho-cresol (614 nm) andm-cresol (632 nm), both compounds can be simultaneously determined in water samples and recoveries of 90 to 115% were found in spiked water samples of different types.     

Algebraic spatial correlations in lattice gas automata violating detailed balance

In this paper we discuss the existence of generic long-range correlations in spatially homogeneous and stable equilibrium states of closed lattice gas automata whose stochastic collision rules violate the symmetry conditions of detailed balance and in addition satisfy local conservation laws. Such correlations occur even though the collision rules are strictly local and invariant under all symmetries of the lattice. First a phenomenological (Langevin equation) approach is discussed. Next we present a theoretical analysis on the basis of an approximate microscopic (ring kinetic) theory. This theory is used to calculate the amplitude ofr ^– tails in the spatial correlations, and the result is compared with computer simulations.     

New results for diffusion in Lorentz lattice gas cellular automata

New calculations to over ten million time steps have revealed a more complex diffusive behavior than previously reported of a point particle on a square and triangular lattice randomly occupied by mirror or rotator scatterers. For the square lattice fully occupied by mirrors where extended closed particle orbits occur, anomalous diffusion was still found. However, for a not fully occupied lattice the superdiffusion, first noticed by Owczarek and Prellberg for a particular concentration, obtains for all concentrations. For the square lattice occupied by rotators and the triangular lattice occupied by mirrors or rotators, an absence of diffusion (trapping) was found for all concentrations, except on critical lines, where anomalous diffusion (extended closed orbits) occurs and hyperscaling holds for all closed orbits withuniversal exponentsd _f =7/4 and =15/7. Only one point on these critical lines can be related to a corresponding percolation problem. The questions arise therefore whether the other critical points can be mapped onto a new percolation-like problem and of the dynamical significance of hyperscaling.     

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two-dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plane Poiseuille flow and the plane Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time , and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Using the analytical solution, it is shown that in Poiseuille flow the bounce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoffet al. in lattice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing.     

Minimum cost multiflows in undirected networks

LetN = (G, T, c, a) be a network, whereG is an undirected graph,T is a distinguished subset of its vertices (calledterminals), and each edgee ofG has nonnegative integer-valuedcapacity c(e) andcost a(e). Theminimum cost maximum multi(commodity)flow problem (*) studied in this paper is to find ac-admissible multiflowf inG such that: (i)f is allowed to contain partial flows connecting any pairs of terminals, (ii) the total value off is as large as possible, and (iii) the total cost off is as small as possible, subject to (ii). This generalizes, on one hand, the undirected version of the classical minimum cost maximum flow problem (when |T| = 2), and, on the other hand, the problem of finding a maximum fractional packing ofT-paths (whena 0). Lovász and Cherkassky independently proved that the latter has a half-integral optimal solution.A pseudo-polynomial algorithm for solving (*) has been developed earlier and, as its consequence, the theorem on the existence of a half-integral optimal solution for (*) was obtained. In the present paper we give a direct, shorter, proof of this theorem. Then we prove the existence of a half-integral optimal solution for the dual problem. Finally, we show that half-integral optimal primal and dual solutions can be designed by a combinatorial strongly polynomial algorithm, provided that some optimal dual solution is known (the latter can be found, in strongly polynomial time, by use of a version of the ellipsoid method).This work was partially supported by Chaire municipale, Mairie de Grenoble, France.