Dynamics and scaling of noise-induced domain growth

The domain growth processes originating from noise-induced nonequilibrium phase transitions are analyzed, both for non-conserved and conserved dynamics. The existence of a dynamical scaling regime is established in the two cases, and the corresponding growth laws are determined. The resulting universal dynamical scaling scenarios are those of Allen-Cahn and Lifshitz-Slyozov, respectively. Additionally, the effect of noise sources on the behaviour of the pair correlation function at short distances is studied. Received 28 June 2000 and Received in final form 29 September 2000     

One-dimensional Ising-like systems: an analytical investigation of the static and dynamic properties, applied to spin-crossover relaxation

We investigate the dynamical properties of the 1-D Ising-like Hamiltonian taking into account short and long range interactions, in order to predict the static and dynamic behavior of spin crossover systems. The stochastic treatment is carried out within the frame of the local equilibrium method [1]. The calculations yield, at thermodynamic equilibrium, the exact analytic expression previously obtained by the transfer matrix technique [2]. We mainly discuss the shape of the relaxation curves: (i) for large (positive) values of the short range interaction parameter, a saturation of the relaxation curves is observed, reminiscent of the behavior of the width of the static hysteresis loop [3]; (ii) a sigmoidal (self-accelerated) behavior is obtained for large enough interactions of any type; (iii) the relaxation curves exhibit a sizeable tail (with respect to the mean-field curves) which is clearly associated with the transient onset of first-neighbor correlations in the system, due to the effect of short-range interactions. The case of negative short-range interaction is briefly discussed in terms of two-step properties. Received 29 October 1999 and Received in final form 30 December 1999     

A new universality for random sequential deposition of needles

Percolation and jamming phenomena are investigated for random sequential deposition of rectangular needles on d=2 square lattices. Associated thresholds and are determined for various needle sizes. Their ratios are found to be a constant for all sizes. In addition the ratio of jamming thresholds for respectively square blocks and needles is also found to be a constant . These constants exhibit some universal connexion in the geometry of jamming and percolation for both anisotropic shapes (needles versus square lattices) and isotropic shapes (square blocks on square lattices). A universal empirical law is proposed for all three thresholds as a function of a. Received 27 January 2000 and Received in final form 2 February 2000     

Phase transitions in “small” systems

Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and classified for small systems. “Small” systems are systems where the linear dimension is of the characteristic range of the interaction between the particles; i.e. also astrophysical systems are “small” in this sense. Boltzmann defines the entropy as the logarithm of the area of the surface in the mechanical N-body phase space at total energy E. The topology of S(E,N) or more precisely, of the curvature determinant allows the classification of phase transitions without taking the thermodynamic limit. Micro-canonical thermo-statistics and phase transitions will be discussed here for a system coupled by short range forces in another situation where entropy is not extensive. The first calculation of the entire entropy surface S(E,N) for the diluted Potts model (ordinary (q=3)-Potts model plus vacancies) on a square lattice is shown. The regions in {E,N} where D>0 correspond to pure phases, ordered resp. disordered, and D<0 represent transitions of first order with phase separation and “surface tension”. These regions are bordered by a line with D=0. A line of continuous transitions starts at the critical point of the ordinary (q=3)-Potts model and runs down to a branching point P_m. Along this line vanishes in the direction of the eigenvector of D with the largest eigen-value . It characterizes a maximum of the largest eigenvalue . This corresponds to a critical line where the transition is continuous and the surface tension disappears. Here the neighboring phases are indistinguishable. The region where two or more lines with D=0 cross is the region of the (multi)-critical point. The micro-canonical ensemble allows to put these phenomena entirely on the level of mechanics. Received 18 October 1999 and received in final form 17 November 1999     

配体交换反应速差动力学法同时测定稀土混合物的数学模型

提出了用可逆模型进行曲线拟合处理数据,并以稀土偶氮肿Ⅲ络合物与CyDTA交换反应为例作验证,结果理论曲线与实验曲线能很好地吻合,提高了用动力学法测定混合稀土的准确度。     

Modeling of Ethylene Polymerization Kinetics over Supported Chromium Oxide Catalysts

Summary: Silica supported chromium oxide catalysts have been used for many years to manufacture polyethylene and they still account for more than 50% of world production of high‐density polyethylene. Along with its commercial success, the catalytic mechanism and polymerization kinetics of silica supported chromium oxide catalysts have been the subject of intense research. However, there is a lack of modeling effort for the quantitative prediction of polymerization rate and polymer molecular weight properties. The chromium oxide catalyzed ethylene polymerization is often characterized by the presence of an induction period followed by a steady increase in polymerization rate. The molecular weight distribution is also quite broad. In this paper, a two‐site kinetic model is developed for the modeling of ethylene polymerization over supported chromium oxide catalyst. To model the induction period, it is proposed that divalent chromium sites are deactivated by catalyst poison and the reactivation of the deactivated chromium sites is slow and rate controlling. To model the molecular weight distribution broadening, each active chromium site is assumed to have different monomer chain transfer ability. The experimental data of semibatch liquid slurry polymerization of ethylene is compared with the model simulations and a quite satisfactory agreement has been obtained for the polymerization conditions employed.

Polymerization rates at different reaction temperatures: symbols – data, lines – model simulations.     

Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems

We show that the numerical method based on the off-equilibrium fluctuation-dissipation relation does work and is very useful and powerful in the study of disordered systems which show a very slow dynamics. We have verified that it gives the right information in the known cases (diluted ferromagnets and random field Ising model far from the critical point) and we used it to obtain more convincing results on the frozen phase of four-dimensional spin glasses. Moreover we used it to study the Griffiths phase of the diluted and the random field Ising models. Received 1 December 1998 and Received in final form 17 February 1999     

Collapse of the magnetic ordering and structural anomalies in the U La S system: neutron diffraction and specific heat measurements

We report specific heat and neutron diffraction measurements of seven samples in the solid solution system U_xLa_1-xS. All samples have the simple fcc NaCl crystal structure. Both specific heat and neutron diffraction confirm the suggestion from the earlier magnetic measurements that the ferromagnetism disappears abruptly at 0.57. Near there is a doubling of the electronic contribution to the specific heat, as compared to the value of 23 mJ mol^-1K^-2 in pure US. Around the widths of the nuclear Bragg peaks show a considerable broadening, as well as anomalies in the mean lattice parameter, as compared to those expected from Vegard's law. A preliminary analysis suggests this broadening may be due to a loss of long range lattice order near . However, these changes are independent of temperature, so that further experiments are necessary before they can be associated with the changes in magnetic behavior at . Received 18 September 1998     

Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects

The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reveals that the Luttinger liquid spin susceptibility approaches zero temperature with an infinite slope in striking contrast with the Fermi liquid result and with the behavior of the compressibility in the absence of umklapp scattering. This effect comes from the leading marginally irrelevant operator, in analogy with the Heisenberg spin 1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher temperature reveal that non-logarithmic terms are important in that regime. These contributions are evaluated from an effective interaction that includes the same set of diagrams as those that give the leading logarithmic terms in the renormalization group approach. Comments on the third law of thermodynamics as well as reasons for the failure of approaches that work in higher dimensions are given. Received 2 March 1999     

Lévy-flight spreading of epidemic processes leading to percolating clusters

We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical point, to directed and isotropic percolation respectively, we consider long-range infections with a probability distribution decaying in d dimensions with the distance as . By means of Wilson's momentum shell renormalization-group recursion relations, the critical exponents characterizing the growing fractal clusters are calculated to first order in an -expansion. It is shown that the long-range critical behavior changes continuously to its short-range counterpart for a decay exponent of the infection . Received: 17 July 1998 / Revised: 20 July 1998 / Accepted: 28 July 1998