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A nonlinear realisation of the nonstandard (super-Jordanian) deformed ${\cal U}_{\sf h}(sl(N|1))$ algebra is given for arbitrary $N$.

Using a contraction procedure developed earlier, we construct, in the first part of the present paper, the Jordanian quantum Hopf algebra h(sl(3)) which has a remarkably simple coalgebraic structure and contains the Jordanian algebra h(sl(2)), obtained by Ohn, as a Hopf subalgebra. A nonlinear map between the quantum h(sl(3)) and the classical (sl(3)) algebras is then established; and the universal h-matrix of the h(sl(3)) algebra is given. In the second part, we give the higher dimensional Jordanian algebras h(sl(N)) for all N. The universal h-matrix of the h(sl(N)) algebra is also given.

In the classification of Hietarinta, three triangular $4\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find the bialgebras which are in duality with these three exotic matrix bialgebras. We note that the $L-T$ duality of FRT is not sufficient for the construction of the bialgebras in duality. We find also the quantum planes corresponding to these bialgebras both by the Wess-Zumino R-matrix method and by Manin's method., Comment: 25 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeqn

We propose a new structure ${\cal U}^{r}_{\displaystyle{q}}(sl(2)) $. This is realized by multiplying $\delta$ ($q=e^{\delta}$, $\delta\in \CC$) by $\theta$, where $\theta$ is a real nilpotent -paragrassmannian- variable of order $r$ ($\theta^{r+1}=0$) that we call the order of deformation, the limit $r\rightarrow \infty$ giving back the standard ${\cal U}_{\displaystyle {q}}(sl(2))$. In particular we show that, for $r=1$, there exists a new ${\cal R}$-matrix associated with $sl(2)$. We also proof that the restriction of the values of the parameters of deformation give nonlinear algebras as particular cases.

A microscopic lattice model for nematic liquid crystals in the presence of random fields is studied by Monte Carlo simulations. The order parameter autocorrelation function shows a standard dynamical scaling for weak random fields, and an activated dynamical scaling for strong random fields. These results are consistent with recent experiments. Evidence is also found that local correlations in the orientation of the liquid crystals along the pore surface should be taken into account for some details of the scaling functions observed in recent experiments.

We report results of a large-scale Monte Carlo study of a grafted-polymer "brush" composed of two types of chains of length N = 100 segments under near-melt conditions, with respulsive interactions of strength χ acting between segments of the two species. Following a quench from χ = 0 to χ = 1, we observe the formation of a strongly segregated structure which is laterally microphase-separated, or "rippled" with a modulation wavelength comparable to the distance that chains fluctuate from side to side.

The author presents the first direct numerical study of a model for stochastically growing interfaces with a conserved height-field, proposed by Sun, Guo and Grant (1989). The scaling exponent calculated in the simulation is in excellent agreement with the dynamic renormalization group calculations by the above authors.

The authors present a simple model that simulates the dynamics of the long flexible self-associating polymer chains immersed in water and develop a dynamical scaling description for the cluster size distribution function for irreversible aggregation. Each chain may have one or several functional groups at each end that can associate with one another. They find that the chain length is a new scaling variable that appears explicitly in the scaling function. The validity of their scaling predictions is confirmed by extensive computer simulations.

We review some recent results concerning numerical studies of the Cahn-Hilliard equation in three dimensions to describe the phase separation process in a mixture after a quench within the coexistence curve. We focus on the late time behavior for two experimentally relevant systems: binary alloys and binary polymer blends. We find that, in both systems, dynamical scaling with a time dependent characteristic length R(t) holds at sufficiently late times and that the late-time behavior for R(t) can be described by a modified Lifschitz-Slyozov law: R(t) = c + dtn, where n = 1/3. For polymer mixtures, the independence of the growth law exponent n of the quench temperature is in contradiction with some recent experiments on polymer systems.

We construct exotic bialgebras that arise from multiparameter 9 × 9 R-matrices, some of which are new. We also construct the dual bialgebras of two of these exotic bialgebras.

The bond-diluted O(n) model for 1

The author presents results obtained from a Monte Carlo simulation of the torque relaxation in a classical Ruderman-Kittel-Kasuya-Yosida spin glass in the presence of weak anisotropic Dzyaloshinskii-Moriya interactions. The simulations are carried out at zero temperature and correspond to the short-time results observed in experiments. For weak anisotropy, the results are consistent with those seen in experiments on CuMn in the short-time limit. For strong anisotropy the qualitative features seen in the simulation are interesting and should be checked in experiments.