变分累积展开方法中确定相变点的新方法

在计算有限温度SU(2)格点规范模型Polyakov线的过程中,考虑到变分累积展开法中有限距离相互作用效应与Monte Carlo中的有限体积效应的相似性,采用了新的方法来确定相变点.与已有的方法以及Monte Carlo模拟给出的结果比较,新方法给出的结果更接近Monte Carlo结果.     

An Analytical Study of the d-Dimensional q-State Potts Models on Lattice

We investigate the phase structure of the d-dimensional q-state Potts models on lattice by the variational cumulant expansion (VCE) approach, we calculate the internal energy and specific heat for this model. Specially, we give the results for 2-dimensional q = 4,5,6 states Potts models. A comparison with Monte Carlo (MC) data is also presented. Our formalism can give the results for Potts models in any dimensionality d and any states q straightforwardly.     

Analytical study of Lattice U(1) and U(1)-Higgs Models at Finite Temperature With Symanzik Action

The lattice U(1) and U(1) -Higgs models with Symanzik action are analytically studied at finite temperature using variational cumulant expansion (VCE). The Polyakov lines and the critical index β are calculated. The results show that VCE of system with Symanzik action converges more rapidly than that of Wilson action.     

Variat ional-Cumulant Expansion on the Five-State Clock Model

The phase transition of the 5-state dock model has been studied by standard variationalcumulant expansion (VCE) method. We calculated the fiee energy (F) and the internal energy (E) to the fourth order approximation and the specific heat (C) to the third order approximation with the trial action of one variational parameter. The position of the phase transition point given above is in agreement with the results of the Monte Carlo (MC). We also calculated the model to the third order approximation with the trial action of two variational parameters. The comparison of the results for one variational parameter with that for two is given. From this, we can see how the choice of the trial action affects the result and the trial action must be equivalent to the action of the system. All above has shown that the VCE is convergent in the calculation of the 5-state clock model.     

Improving the sampling efficiency of Monte Carlo molecular simulations: an evolutionary approach

We present a new approach in order to improve the convergence of Monte Carlo (MC) simulations of molecular systems belonging to complex energetic landscapes: the problem is redefined in terms of the dynamic allocation of MC move frequencies depending on their past efficiency, measured with respect to a relevant sampling criterion. We introduce various empirical criteria with the aim of accounting for the proper convergence in phase space sampling. The dynamic allocation is performed over parallel simulations by means of a new evolutionary algorithm involving ‘immortal’ individuals. The method is bench marked with respect to conventional procedures on a model for melt linear polyethylene. We record significant improvement in sampling efficiencies, thus in computational load, while the optimal sets of move frequencies are liable to allow interesting physical insights into the particular systems simulated. This last aspect should provide a new tool for designing more efficient new MC moves.     

Critical behavior of magnetic thin films

We study the critical behavior of magnetic thin films as a function of the film thickness. We use the ferromagnetic Ising model with the high-resolution multiple histogram Monte Carlo (MC) simulation. We show that though the 2D behavior remains dominant at small thicknesses, there is a systematic continuous deviation of the critical exponents from their 2D values. We explain these deviations using the concept of “effective” exponents suggested by Capehart and Fisher in a finite size analysis. The shift of the critical temperature with the film thickness obtained here by MC simulation is in an excellent agreement with their prediction.     

Simulation of polarization-sensitive optical coherence tomography images by a Monte Carlo method

We introduce a new Monte Carlo (MC) method for simulating optical coherence tomography (OCT) images of complex multilayered turbid scattering media. We demonstrate, for the first time of our knowledge, the use of a MC technique to imitate two-dimensional polarization-sensitive OCT images with nonplanar boundaries of layers in the medium like a human skin. The simulation of polarized low-coherent optical radiation is based on the vector approach generalized from the iterative procedure of the solution of Bethe-Saltpeter equation. The performances of the developed method are demonstrated both for conventional and polarization-sensitive OCT modalities.     

Shape fluctuation phase transition of elastic membranes with fluidity

It is confirmed by Monte Carlo (MC) simulation that the elastic membrane corresponding to discrete Polyakov–Kleinert string undergoes a second-order phase transition at finite bending rigidity. This phase transition is considered to be associated with a non-trivial fixed point of the β-function for the inverse bending rigidity.     

Phase Structures of U(l) and SU(2) Lattice Gauge Models at Finite Temperature

With the variational-cumulant expansion (VCE) method, the phase structures of the U(1) and SU(2) lattice gauge models at finite temperature are studied. The order parameter Polyakov line with N_T = 2 is calculated to the fourth order. For the U(1) and SU(2) lattice gauge models in D = 3 + 1 and D = 2 + 1 at finite temperature, the results show the existence of the second order phase transition.     

Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows

With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.     

Hybrid MC/RISM technique for simulation of polymer solutions: Monte Carlo+ RISM integral equations

A new (hybrid) method is reported for modelling complex macromolecular systems. The approach combines the traditional atomistic Monte Carlo (MC) computer simulation of flexible polymer chains with the numerical solution of the site-site Ornstein-Zernike-like (RISM) integral equations. The method is used for calculating properties of a linear polymer in dilute solution. Since the condensed-phase environment of a flexible macromolecule affects the equilibrium configuration probability distribution of the macromolecule, the site-site intramolecular correlation function and the intramolecular potential field are treated in a self-consistent manner. Briefly, the MC method is applied to generate the configurations of a single chain molecule. Using the coordinates of chain beads, the averaged intrapolymer correlation function is obtained. Then, solving the coupled RISM equations for a given density of solvent particles, we find the polymer-solvent correlation functions. This yields the medium-induced intrapolymer potential and the corresponding effective intramolecular energies, which are used in the standard Metropolis MC procedure. The structural properties of the polymer chain are computed by averaging over the statistically representative set of configurations. As a result of many such iterations, the intramolecular structure is determined self-consistently. Using the hybrid MC/RISM method, extensive studies have been made of static properties of flexible polymer chains surrounded by LJ particles with purely repulsive interactions between the particles and chain beads. Also, direct molecular dynamics simulations have been carried out and have demonstrated that the hybrid MC/RISM approach gives a quite accurate prediction for condensed-phase effects.     

Monte-Carlo simulations of rotating clusters

A new scheme for estimating densities of states at non zero angular momentum is proposed, using the Monte-Carlo (MC) and multiple histogram methods. It is based on a rigorous expression of the classical density of states for a rotating system. Two features appear: the centrifugal energy ( angular momentum and I the instantaneous inertia tensor in the center of mass reference frame) is added to the potential energy and the configurational densities of states is weighted by . Comparing the MC results for the 13-atom Lennard-Jones cluster and a calculation based on molecular dynamics (MD) shows that this weight is important if the rotation induces a structural change at a finite temperature. The MC algorithm proves to be much more efficient than MD, even at finite . Received: 27 January 1998 / Received in final form: 15 June 1998 / Accepted: 18 June 1998     

A systematic Monte Carlo simulation and renormalized perturbation theoretical study of the dielectric constant of the polarizable Stockmayer fluid

A systematic Monte Carlo (MC) simulation and perturbation theory (PT) study is reported for the dielectric constant of the polarizable Stockmayer fluid. Our MC simulations apply the ‘pair approximation for polarization interaction’ procedure suggested by P?edota et al. The theoretical approach is based on our newly introduced equation (Valiskó et al., 2002, Molec. Phys., 100, 559) which is a density expansion for the dielectric constant using Wertheim's renormalized PT method. The agreement between our MC and PT results is excellent for low to moderate dipole moments and polarizabilities. At stronger dipolar interactions ergodicity problems and anisotropic behaviour appear where simulation results become uncertain and the theoretical approach becomes invalid.     

多层伊辛膜的磁学性质

用变分累积展开(VCE)方法的一阶近似计算了包括最近邻和次近邻作用的多层伊辛膜的磁学 性质,导出了自发磁化强度、矫顽力、居里点、奈尔点、顺磁磁化率及分子场系数与层数的关系表达式,并做了数值计算和讨论. 关键词： 多层膜 伊辛模型 磁化     

Modified nonlinear morphological correlation using Laplace filtering

A Laplace filtering based morphological correlation (LBMC) is proposed as a modified approach to improve the properties of the classical morphological correlation (MC). For the LBMC, power spectrum of Laplace operator is introduced to filter the joint power spectrum (JPS) of the MC before final inverse Fourier transform. Computer simulation results show that, as compared with the linear correlation (LC) and the conventional MC, LBMC provides better discrimination capability with sharp and unmistakable correlation signal and its performance metrics are more stable when input scene is corrupted by outlier noise (salt-and-pepper noise) and additive white Gaussian noise. Although the LBMC is not illumination invariant when multiplication illumination factor is larger than unity, considerable discrimination capability is still obtained.     

Inhomogeneous 2D Lennard-Jones Fluid: Theory and Computer Simulation

In this work, thermodynamical properties of a two-dimensional (2D) Lennard-Jones (LJ) fluid are studied. Here, to increase the accuracy of our theoretical calculations, the correlation functions in three-particle level (triplet) are applied. To obtain the triplet correlation functions, the Attard's source particle method is extended to 2D systems. In the Attard's procedure, the inhomogeneous Ornstein-Zernike (OZ) equation is solved using the Treizenberg-Zwanzwig (TZ) expression and a closure relation like the hypernetted-chain (HNC) approximation. In the present work, we also have performed the Monte Carlo (MC) simulation. The theoretical results are in fairly agreement with the MC simulation. Also, our results show that the approach proposed here is suitable to study the 2D LJ fluid.     

Inhomogeneous 2D Lennard-Jones Fluid: Theory and Computer Simulation

In this work, thermodynamical properties of a two-dimensional (2D) Lennard-Jones (LJ) fluid are studied. Here, to increase the accuracy of our theoretical calculations, the correlation functions in three-particle level (triplet) are applied. To obtain the triplet correlation functions, the Attard's source particle method is extended to 2D systems. In the Attard's procedure, the inhomogeneous Ornstein-Zernike (OZ) equation is solved using the Treizenberg-Zwanzwig (TZ) expression and a closure relation like the hypernetted-chain (HNC) approximation. In the present work, we also have performed the Monte Carlo (MC) simulation. The theoretical results are in fairly agreement with the MC simulation. Also, our results show that the approach proposed here is suitable to study the 2D LJ fluid.     

Analytic simulation of the backscattering of hundreds eV positrons from elemental solids

Backscattering (Bcs) coefficients for low-energy positrons (∼100 eV) from elemental solids have been simulated using an analytic approach. The model is based on the use of the transport cross-sections (TCSs) and the stopping power calculated from partial wave methods and the best-fit stopping power data of Ashley, respectively. The new result is an extension of recent calculations in the medium energy range. Comparisons, when possible, with experimental and Monte-Carlo (MC) simulation data have been made.     

The effective geometry Monte Carlo algorithm: Applications to molecular communication

In this work, we address the systematic biases and random errors stemming from finite step sizes encountered in diffusion simulations. We introduce the Effective Geometry Monte Carlo (EG-MC) simulation algorithm which modifies the geometry of the receiver. We motivate our approach in a 1D toy model and then apply our findings to a spherical absorbing receiver in a 3D unbounded environment. We show that with minimal computational cost the impulse response of this receiver can be precisely simulated using EG-MC. Afterwards, we demonstrate the accuracy of our simulations and give tight constraints on the single free parameter in EG-MC. Finally, we comment on the range of applicability of our results. While we present the EG-MC algorithm for the specific case of molecular diffusion, we believe that analogous methods with effective geometry manipulations can be utilized to approach a variety of problems in other branches of physics such as condensed matter physics and cosmological large scale structure simulations.     

近红外光早期宫颈癌诊断的频域逆蒙特卡洛光学参量重构研究

研究了基于时域蒙特卡洛模拟的频域信息提取方法、光学参量反演方法和提高反演速度的措施.提出了利用离散傅立叶变换（传统法）和改进法两种提取频域信号幅值相位的方法.通过建立一定散射系数范围内的正向MC模拟数据库、采用拟合方法以及利用朗伯 比尔定理,解决了光学参量反演中快速获得MC模拟结果的问题.模拟实验结果表明：改进法无论在反演准确度还是计算时间上均优于传统法,当其中一个参量不变时,散射系数的反演相对误差小于±6%,吸收系数的反演相对误差小于±10%;当吸收和散射系数同时变化时（30<μs<100 cm－1,0.2<μa<0.50 cm－1）,两个参量反演相对误差在±10%以内.采用快速反演技术重构一组光学参量所需要的计算时间小于1分钟.