Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Dynamic domain formation in membranes: Thickness-modulation-induced phase separation

A simple model investigates the amplification of fluctuations on membranes constituted of two lipids having different lengths. Van der Waals and electrostatic interactions across the lipid bilayer result in a destabilization favoring thickness variations of the membrane. Close to spontaneous demixing of the two components, the additional gain in free energy due to thickness undulations shifts the stability boundary which promotes phase separation into domains. Interestingly, this effect can be induced by an applied electric field or membrane potential. In biological systems, the dynamic model presented here indicates that electric fields might be important for controlling phase separation and the formation of domains called rafts.Received: 26 March 2004, Published online: 15 July 2004PACS: 87.16.Dg Membranes, bilayers, and vesicles - 68.35.Rh Phase transitions and critical phenomena - 82.70.Uv Surfactants, micellar solutions, vesicles, lamellae, amphiphilic systems, (hydrophilic and hydrophobic interactions)     

Computer simulation study of phase separation in a binary mixture with a glass-forming component

We present a computer simulation study of spinodal decomposition with one of the two phases freezing in a glassy state during phase separation. As a model we used the Cahn-Hilliard equation with a concentration-dependent mobility coefficient which decreases rapidly with increasing concentration of the glass-forming component. We solved the Cahn-Hilliard equation numerically for two dimensions. The domain growth depends crucially on the volume fraction of the glassy phase. For high volume fractions, when the glassy phase forms a percolating matrix, a novel coarsening mechanism is discovered, which arises from the migration and coalescence of liquid droplets within the glassy matrix. Various quantities characterizing the time-dependent domain pattern, like droplet size distribution, one- and two-point distribution function and structure factor of the concentration field, are computed. We checked the validity of the dynamic scaling hypothesis.     

Vapour-liquid equilibria of the two- and three-dimensional monoatomic classical fluids interacting via double Yukawa potential

We have carried out Monte Carlo simulations in Gibbs ensemble for two-and three-dimensional double Yukawa fluid. We have compared liquid-vapour equilibrium curve with that of Lennard-Jones, when parameters occurring in double Yukawa potential are chosen to fit Lennard-Jones potential. The results are in good agreement. The role of repulsive and attractive contributions for the potential on the liquid-vapour coexistence region as well as on critical temperature and critical density has been studied. The critical temperature is found to be more sensitive than the critical density to the variation in repulsive and attractive parts of the potential. Also, the range of the attractive interaction directly influences range of the liquid vapour coexistence region. It has been found that smaller the values of the attractive parameter, larger is the coexistence region.     

Computer simulations of critical phenomena and phase behaviour of fluids

Computer simulation techniques such as Monte Carlo (MC) and Molecular Dynamics (MD) methods yield numerically exact information (apart from statistical errors) on model systems of classical statistical mechanics. However, a systematic limitation is the restriction to a finite (and often rather small) particle number N (or box linear dimension L, respectively). This limitation is particularly restrictive near critical points (due to the divergence of the correlation length of the order parameter) and for the study of phase equilibria (possibly involving interfaces, droplets, etc.). Starting out with simple lattice gas (Ising) models, finite size scaling analyses have been developed to overcome this limitation. These techniques work for both simple Lennard-Jones fluids and their mixtures, including generalizations to approximate models for quadrupolar fluids such as carbon dioxide, benzene etc. and various mixtures, whose phase behaviour can be predicted. A combination of MC and MD allows the study of dynamic critical phenomena, and specialised techniques (umbrella sampling plus thermodynamic integration) yield the surface free energy of droplets as function of droplet size. Thus, computer simulation has become a versatile and widely applicable tool for the study of fluids.     

The Local Front Reconstruction Method for direct simulation of two- and three-dimensional multiphase flows

We present a new interface reconstruction technique, the Local Front Reconstruction Method (LFRM), for incompressible multiphase flows. This new method falls in the category of Front Tracking methods but it shares automatic topology handling characteristics of the previously proposed Level Contour Reconstruction Method (LCRM). The LFRM tracks the phase interface explicitly as in Front Tracking but there is no logical connectivity between interface elements thus greatly easing the algorithmic complexity. Topological changes such as interfacial merging or pinch off are dealt with automatically and naturally as in the Level Contour Reconstruction Method. Here the method is described for both two- and three-dimensional flow geometries. The interfacial reconstruction technique in the LFRM differs from that in the LCRM formulation by foregoing using an Eulerian distance field function. Instead, the LFRM uses information from the original interface elements directly to generate the new interface in a mass conservative way thus showing significantly improved local mass conservation. Because the reconstruction procedure is independently carried out in each individual reconstruction cell after an initial localization process, an adaptive reconstruction procedure can be easily implemented to increase the accuracy while at the same time significantly decreasing the computational time required to perform the reconstruction. Several benchmarking tests are performed to validate the improved accuracy and computational efficiency as compared to the LCRM. The results demonstrate superior performance of the LFRM in maintaining detailed interfacial shapes and good local mass conservation especially when using low-resolution Eulerian grids.     

Aggregation kinetics and the nature of phase separation in two-dimensional dipolar fluids

The kinetics of aggregation in a monolayer of dipolar particles are studied using stochastic dynamics computer simulations. Transient concentrations of end defects (at low density) and Y-shaped defects (at high density) clearly exceed those at equilibrium. Although very large dipole moments are expected to disfavor such defects at equilibrium, it is found that the transient defect concentrations increase with increasing dipole moment. The results suggest that the conditions for defect-driven condensation--as proposed by Tlusty and Safran [T. Tlusty and S. A. Safran, Science 290, 1328 (2000)]--could be met by kinetic trapping, giving rise to a metastable phase transition between isotropic fluid phases.     

Synthesis of three-dimensional phase images of nanoobjects: Numerical simulation

A way to synthesize three-dimensional phase-diffraction images of nanoobjects is proposed based on the numerical method of backward propagation of a field from the best focusing plane. The obtained phase images are used for solving the applied problem of object defect finding by methods of pattern recognition. The probability of defect detection by phase images is shown to be higher than for amplitude images.     

The autowave modes of solid phase polymerization of metal-containing monomers in two- and three-dimensional fiberglass-filled matrices

The phenomenon of autowave (frontal) solid phase polymerization of metal-containing monomers based on metal-acrylamide complexes is considered. The comparison of the features of autowave processes realized in both the single-component matrices of the monomer and the matrices filled by the fiberglass materials is performed. The unstable regimes of the polymerization wave as well as the conditions for the stabilization of the flat front in the filled matrices are described. The peculiarities of the frontal regimes in the three- and two-dimensional media are studied. Some possibilities for using of autowave polymerization in the fabrication of the polymer-fiberglass composites and composition prepregs are discussed. (c) 1999 American Institute of Physics.     

空间静电场的计算机模拟--轴测投影法

采用轴测投影法,通过三维坐标的二维投影变换,实现空间静电场的计算机模拟。     

Numerical simulation for separation of multi-phase immiscible fluids in porous media

Based on a lattice Boltzmann method and general principles of porous flow, a numerical technique is presented for analysing the separation of multi-phase immiscible fluids in porous media. The total body force acting on fluid particles is modified by axiding relative permeability in Nithiarasu＇s expression with an axiditional surface tension term. As a test of this model, we simulate the phase separation for the case of two immiscible fluids. The numerical results show that the two coupling relative permeability coefficients K12 and K21 have the same magnitude, so the linear flux-forcing relationships satisfy Onsager reciprocity. Phase separation phenomenon is shown with the time evolution of density distribution and bears a strong similarity to the results obtained from other numerical models and the flows in sands. At the same time, the dynamical rules in this model are local, therefore it can be run on massively parallel computers with well computational efficiency.     

T型正弦微通道内气液两相流动的数值研究

在T型微通道的基础上,对其结构进行改造,提出了一种T型正弦波节微通道,并构建了微型气液反应装置。运用CFD方法,数值研究了微通道内的气泡形成过程及气液分布情况,拟合出了计算T型微通道内气泡液柱尺寸的关联式。结果表明:T型正弦波节微通道内的气泡形成机制与常规T型微通道相同,为挤压机制,颈部断裂过程经历的时间较常规T型微通道稍长。该结构类型的正弦波节微通道与常规平直圆管相比,当量直径增大了50%,气液接触面积相应增大了25%,有效地提高了传质效率。     

Molecular phase separation and cluster size in GeSe2 glass

The local vibrational modes and the microscopic nature of Te sites in GeSe₂-_xTe_x alloy glasses have been examined using Raman and¹²⁹I Mossbauer emission spectroscopy. Two distinct types (A, B) of chalcogen (Te) sites are observed. The Mossbauer site intensities I_B/I_A(x) reveal a power-law variation which on statistical grounds requires that these sites be formed in a cluster. The characteristic size of the cluster is found to be 60–75 A.     

Metal-insulator transition in two- and three-dimensional logarithmic plasmas

We consider the scaling of the mean square dipole moment in a plasma with logarithmic interactions in a two- and three-dimensional systems. In both cases, we establish the existence of a low-temperature regime where the mean square dipole moment does not scale with system size and a high-temperature regime where it does scale with system size. Thus, there is a nonanalytic change in the polarizability of the system as a function of temperature and hence a metal-insulator transition in both cases. The relevance of this transition in three dimensions to quantum phase transitions in (2+1)-dimensional systems is briefly discussed.     

Reorientation phase transition in temperature in a two- and three-dimensional ferromagnet with the account of magnetoelastic coupling

In the paper, we have investigated reorientation phase transitions in a two-dimensional ferromagnet. It is shown that the account of magnetoelastic coupling results in the appearance of an angular phase, and the phase transitions are of the first order. The temperature interval of the angular phase existence is determined mainly by elastic and magnetoelastic parameters of the system. For a three-dimensional system the observable effect disappears. The obtained results are consistent with experimental data.     

Computer simulation studies of magnetic phase transitions

The advancements which have been made in the use of computer simulations to study magnetic-phase transitions and critical phenomena are reviewed. We describe how the use of a combination of sophisticated Monte Carlo simulation algorithms and reweighting (histogram) techniques have allowed the determination of the static critical behavior with unprecedented precision. The study of “dynamic” critical behavior in simple spin models by both Monte Carlo and spin dynamics methods is also reviewed. Recent estimates for dynamic critical exponents are given including those for true dynamics.