Monte Carlo method for evaluating the quantum real time propagator

A new exact representation of the quantum propagator is derived in terms of semiclassical initial value representations. The resulting expression may be expanded in a series, of which the leading order term is the semiclassical one. Motion of a Gaussian wave packet on a symmetric double well potential is used to demonstrate numerical convergence of the series and the ability to compute each element in the series using Monte Carlo methods.     

Thermodynamically guided nonequilibrium Monte Carlo method for generating realistic shear flows in polymeric systems

A thermodynamically guided atomistic Monte Carlo methodology is presented for simulating systems beyond equilibrium by expanding the statistical ensemble to include a tensorial variable accounting for the overall structure of the system subjected to flow. For a given shear rate, the corresponding tensorial conjugate field is determined iteratively through independent nonequilibrium molecular dynamics simulations. Test simulations for the effect of flow on the conformation of a C50H102 polyethylene liquid show that the two methods (expanded Monte Carlo and nonequilibrium molecular dynamics) provide identical results.     

Monte Carlo simulations for the slow relaxation of crumpled surfaces

In this paper we study crumpled surfaces through Monte Carlo Simulations. A crumpled surface is represented by a cluster of spins pointing up; spins pointing down represent the air both inside and around the surface. We follow the time dynamics of this fractal structure and we show that it presents a stretched exponential behaviour.     

The time scale of Monte Carlo experiments

The time required to reach equilibrium in a standard Monte Carlo experiment is estimated on the basis of exact bounds on the longest time scale in one-dimensional models. The result implies the empirical law of Arrhenius at low temperatures if there are energy barriers.     

水下光场的蒙特卡罗法求解

水下光场分布对水下光电成像质量具有决定性的影响,通过水下光场分布可以得到水下图像的传输退化模型。在给定水体光学参数的前提下,建立光子水下传输概率模型,利用Monte Carlo法模拟光子在水下的运动,可以获得水下光子散射点体积密度分布,求解出水下光场;在水体体散射函数为球形对称的条件下,利用Monte Carlo法得到的水下光场分布与理论公式的计算结果具有很好的一致性,验证了该方法的有效性;最后给出了水下理想点光源形成的水下光场分布。基于此结论,可以将Monte Carlo法求解水下光场的应用范围推广至水体体散射函数为一般表达式的情形。     

Monte Carlo method for the many-body scattering problem

The non-relativistic many-body scattering problem is cast in a form suitable for treatment by Monte Carlo methods. The formulation is based on resonant standing waves of the compound system, similar to those used in the R-matrix theory of nuclear reactions. Integral expressions are derived from which the scattering matrix elements at low energies can be evaluated. The method is demonstrated by application to simple one- and two-channel one-dimensional scattering problems.     

A Monte Carlo method for simulating fractal surfaces

A Monte Carlo method is presented for simulating rough surfaces with the fractal behavior. The simulation is based on power-law size distribution of asperity diameter and self-affine property of roughness on surfaces. A probability model based on random number for asperity sizes is developed to generate the surfaces. By iteration, this method can be used to simulate surfaces that exhibit the aforementioned properties. The results indicate that the variation of the surface topography is related to the effects of scaling constant G and the fractal dimension D of the profile of rough surface. The larger value of D or smaller value of G signifies the smoother surface topography. This method may have the potential in prediction of the transport properties (such as friction, wear, lubrication, permeability and thermal or electrical conductivity, etc.) on rough surfaces.     

New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.     

A quantum Monte Carlo method for nucleon systems

We describe a quantum Monte Carlo method for Hamiltonians which include tensor and other spin interactions such as those that are commonly encountered in nuclear structure calculations. The main ingredients are a Hubbard-Stratonovich transformation to uncouple the spin degrees of freedom along with a fixed node approximation to maintain stability. We apply the method to neutron matter interacting with a central, spin-exchange, and tensor forces. The addition of isospin degrees of freedom is straightforward.     

A Monte Carlo model for seeded atomic flows in the transition regime

A simple model for the numerical determination of separation effects in seeded atomic gas flows is presented. The model is based on the known possibility to provide a statistically convergent estimate of the exact solution for a linear transport equation using the test particle Monte Carlo method. Accordingly, the flow field of the main gas is preliminary calculated and as a second step the linear transport equations obtained by fixing the target distribution in the collision term of the Boltzmann equation for both main and minority components are solved. Both solutions are based on appropriately devised test particle Monte Carlo methods. The second step, the critical one in evaluating the separation effects, is exact and thereby completely free of numerical diffusion. The model is described in details and illustrated by 2D test cases of atomic separation in shock fronts.     

Monte Carlo method and sensitivity estimations

It is shown that, starting from any existing Monte Carlo algorithm for estimation of a physical quantity A, it is possible to implement a simple additional procedure that simultaneously estimates the sensitivity of A to any problem parameter. The corresponding supplementary cost is very low as no additional random sampling is required. The principle is presented on a formal basis and simple radiative transfer examples are used for illustration.