Effect of band structure discretization on the performance of full-band Monte Carlo simulation

Full-band Monte Carlo simulation offers a very accurate simulation technique, but is often limited by its high demand on computation time. The advantage of a numerical representation of the band structure over an analytical approximation is the accurate representation of the energy bands in the high energy regime. This allows accurate treatment of hot carrier effects in semiconductors. In this work we outline an efficient full-band Monte Carlo (FBMC) simulator and investigate the accuracy of simulation results for different meshing approaches for the Brillouin zone.     

A time saving algorithm for the Monte Carlo method of Metropolis

A time saving algorithm for the Monte Carlo method of Metropolis is presented. The technique is tested with different potential models and number of particles. The coupling of the method with neighbor lists, linked lists, Ewald sum and reaction field techniques is also analyzed. It is shown that the proposed algorithm is particularly suitable for computationally heavy intermolecular potentials.     

Computer simulation of two continuous spin models using Wang-Landau-Transition-Matrix Monte Carlo algorithm

Monte Carlo simulation using a combination of Wang-Landau (WL) and Transition Matrix (TM) Monte Carlo algorithms to simulate two lattice spin models with continuous energy is described. One of the models, the one-dimensional Lebwohl-Lasher model has an exact solution and we have used this to test the performance of the mixed algorithm (WLTM). The other system we have worked on is the two-dimensional XY-model. The purpose of the present work is to test the performance of the WLTM algorithm in continuous models and to suggest methods for obtaining best results in such systems using this algorithm.     

Fast recall of state-history in kinetic Monte Carlo simulations utilizing the Zobrist key

We present a novel application of the Zobrist hashing method, known in the computer chess literature, to simulation of diffusional phase transformations in metal alloys. A history of previously visited states can be easily maintained, allowing very fast lookup of energies and transition rates calculated earlier in the simulation. The method has been applied to the simulation of a Fe-1at.%Cu system, with simple potentials and a transition rate for diffusional events approximated from the difference in internal energy between trial states. In this simple model at temperatures of 1073 K we find that 61.2% of the states considered during the simulation have been seen previously, and that this proportion rises to 85.1% at 773 K and even to 99.9% at 373 K. Rapid recall of these states reduces the computational time taken for the same sequence of atom-vacancy exchange moves by a factor of 6.3 at 773 K rising to over 100 at 373 K. We suggest that a similar speedup factor will be found using more sophisticated models of diffusion and that the method can, with small modifications, be applied to a wide range of kinetic Monte Carlo simulations of atomistic diffusion processes.     

Reduction of the self-forces in Monte Carlo simulations of semiconductor devices on unstructured meshes

When using an unstructured mesh for device geometry, the ensemble Monte Carlo simulations of semiconductor devices may be affected by unwanted self-forces resulting from the particle-mesh coupling. We report on the progress in minimisation of the self-forces on arbitrary meshes by showing that they can be greatly reduced on a finite element mesh with proper interpolation functions. The developed methodology is included into a self-consistent finite element 3D Monte Carlo device simulator. Minimising of the self-forces using the proper interpolation functions is tested by simulating the electron transport in a 10 nm gate length, 6.1 nm body thick, double gate metal-oxide-semiconductor field-effect transistor (MOSFET). We demonstrate the reduction in the self-force and illustrate the practical distinction by showing I-V characteristics for the device.     

Solving constrained Markovian evolution in QCD with the help of the non-Markovian Monte Carlo

We present the constrained Monte Carlo (CMC) algorithm for the QCD evolution. The constraint resides in that the total longitudinal energy of the emissions in the MC and in the underlying QCD evolution is predefined (constrained). This CMC implements exactly the full DGLAP evolution of the parton distributions in the hadron with respect to the logarithm of the energy scale. The algorithm of the CMC is referred to as the non-Markovian type. The non-Markovian MC algorithm is defined as the one in which the multiplicity of emissions is chosen randomly as the first variable and not the last one, as in the Markovian MC algorithms. The former case resembles that of the fixed-order matrix element calculations. The CMC algorithm can serve as an alternative to the so-called backward evolution Markovian algorithm of Sjöstrand, which is used for modeling the initial-state parton shower in modern QCD MC event generators. We test practical feasibility and efficiency of our CMC implementation in a series of numerical exercises, comparing its results with those from other MC and non-MC programs, in a wide range of Q and x, down to the 0.1% precision level. In particular, satisfactory numerical agreement is found with the results of the Markovian MC program of our own and the other non-MC program. The efficiency of the new constrained MC is found to be quite good.     

A Beowulf-class computing cluster for the Monte Carlo production of the LHCb experiment

The computing cluster built at Bologna to provide the LHCb Collaboration with a powerful Monte Carlo production tool is presented. It is a performance oriented Beowulf-class cluster, made of rack mounted commodity components, designed to minimize operational support requirements and to provide full and continuous availability of the computing resources. In this paper we describe the architecture of the cluster, and discuss the technical solutions adopted for each specialized sub-system.     

A hardware generator of multi-point distributed random numbers for Monte Carlo simulation

Monte Carlo simulation of weak approximations of stochastic differential equations constitutes an intensive computational task. In applications such as finance, for instance, to achieve “real time” execution, as often required, one needs highly efficient implementations of the multi-point distributed random number generator underlying the simulations. In this paper, a fast and flexible dedicated hardware solution on a field programmable gate array is presented. A comparative performance analysis between a software-only and the proposed hardware solution demonstrates that the hardware solution is bottleneck-free, retains the flexibility of the software solution and significantly increases the computational efficiency. Moreover, simulations in applications such as economics, insurance, physics, population dynamics, epidemiology, structural mechanics, chemistry and biotechnology can benefit from the obtained speedups.     

Monte Carlo simulation of thermodynamic systems with cluster formation under different boundary conditions

Thethermodynamic state function free energy F(T,V,N) as function of the cluster distribution N and the thermodynamic parameters (temperature T and volume V) is calculated in the canonical ensemble. With the help of the Legendre transformation we get all other state functions for different boundary conditions. Monte Carlo simulations with 15000 particles starting from metastable homogeneous initial conditions are made for water and methanol. The Bethe-Weizsäcker ansatz and the Padé approximation are used for the binding energy of clusters. A first-order phase transition is observed under appropriate conditions.     

A Monte Carlo C-code for calculating transmission efficiency of recoil separators and viewing residue trajectories

We present a semimicroscopic Monte Carlo code for calculating absolute transmission efficiency of recoil separators for heavy ion-induced complete fusion reactions. The code generates realistic distributions for energy, charge state and angle of evaporation residues. Residue trajectories are calculated using first order ion optical transfer matrices. Trajectory plots in the dispersive and the non-dispersive planes are generated. Using this code, we have obtained good agreement between calculated and measured transmission efficiencies for the Heavy Ion Reaction Analyzer at IUAC. The code can be adapted easily to any other electromagnetic recoil separator.

Program summary

Program title: TERSCatalogue identifier: AEBD_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBD_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 6818No. of bytes in distributed program, including test data, etc.: 1 216 097Distribution format: tar.gzProgramming language: CComputer: The code has been developed and tested on a PC with Intel Pentium IV processorOperating system: LinuxRAM: About 8 MbytesClassification: 17.7External routines: pgplot graphics subroutine library [1] should be installed in the system for generating residue trajectory plots.Nature of problem: Recoil separators are employed to select and identify nuclei of interest, produced in a nuclear reaction, rejecting unreacted beam and other undesired reaction products. It is important to know what fraction of the selected nuclei, leaving the target, reaches the detection system. This information is crucial for determining absolute cross section of the studied reaction.Solution method:Interaction of projectiles with target nuclei is treated event by event, semimicroscopically. Position and angle (with respect to beam direction), energy and charge state of the reaction products are calculated by Monte Carlo method. Trajectory of each nuclei inside the separator is then calculated by ion optical transfer matrix method. Ratio of the number of trajectories completing their journey up to the detection system to the total number of trajectories is a direct measure of absolute transmission efficiency of the separator.Restrictions: The present version of the code is applicable to complete fusion reactions only. The code can be applied to other types of reactions (e.g., few nucleon transfer) as well, by suitably modifying energy and angular distribution of reaction products. Also, ion optical specifications and acceptance are unique for each recoil separator. Transmission efficiency calculation has been done for a specific recoil separator, viz. the Heavy Ion Reaction Analyzer [2,3] at IUAC. One has to make necessary changes in the code, while performing calculations for other recoil separators. Further, atomic number of the residual nucleus should not exceed 92, as the method used for calculating stopping power of ions [4] is valid for Z?92.Running time: From few seconds to several minutes depending on the reaction, number of events and separator layout.References:

[1]

http://www.astro.caltech.edu/~tjp/pgplot/.

[2]

A.K. Sinha, N. Madhavan, J.J. Das, P. Sugathan, D.O. Kataria, A.P. Patro, G.K. Mehta, Nucl. Instr. Methods A 339 (1994) 543.

[3]

S. Nath, Nucl. Instr. Methods A 576 (2007) 403.

[4]

J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, vol. I, Pergamon Press, Oxford, 1984.

     

DRAGON: Monte Carlo generator of particle production from a fragmented fireball in ultrarelativistic nuclear collisions

A Monte Carlo generator of the final state of hadrons emitted from an ultrarelativistic nuclear collision is introduced. An important feature of the generator is a possible fragmentation of the fireball and emission of the hadrons from fragments. Phase space distribution of the fragments is based on the blast wave model extended to azimuthally non-symmetric fireballs. Parameters of the model can be tuned and this allows to generate final states from various kinds of fireballs. A facultative output in the OSCAR1999A format allows for a comprehensive analysis of phase-space distributions and/or use as an input for an afterburner.

Program summary

Program title: DRAGONCatalogue identifier: AEDK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 6383No. of bytes in distributed program, including test data, etc.: 32 756Distribution format: tar.gzProgramming language: C++Computer: PC Pentium 4, though no particular tuning for this machine was performedOperating system: Linux; the program has been successfully run on Gentoo Linux 2.6, RedHat Linux 9, Debian Linux 4.0, all with g++ compiler. It also ran successfully on MS Windows under Microsoft Visual C++ 2008 Express Edition as well as under cygwin/g++RAM: 100 MbytesSupplementary material: Sample output files from the test run, provided in the distribution, are available.Classification: 11.2Nature of problem: Deconfined matter produced in ultrarelativistic nuclear collisions expands and cools down and eventually returns into the confined phase. If the expansion is fast, the fireball could fragment either due to spinodal decomposition or due to suddenly arising bulk viscous force. Particle abundances are reasonably well described with just a few parameters within the statistical approach. Momentum spectra integrated over many events can be interpreted as produced from an expanding and locally thermalised fireball. The present Monte Carlo model unifies these approaches: fireball decays into fragments of some characteristic size. The fragments recede from each other as given by the pre-existing expansion of the fireball. They subsequently emit stable and unstable hadrons with momenta generated according to thermal distribution. Resonances then decay and their daughters acquire momenta as dictated by decay kinematics.Solution method: The Monte Carlo generator repeats a loop in which it generates individual events. First, sizes of fragments are generated. Then the fragments are placed within the decaying fireball and their velocities are determined from the one-to-one correspondence between the position and the expansion velocity in the blast wave model. Since hadrons may be emitted from fragments as well as from the remaining bulk fireball, first those from the bulk are generated according to the blast wave model. Then, hadron production from the fragments is treated. Each hadron is generated in the rest frame of the fragment and then boosted to the global frame. Finally, after all directly produced hadrons are generated, resonance decay channels are chosen and the momenta and positions of final state hadrons are determined.Running time: Generation of 100 events can take anything between 2 hours to a couple of days. This depends mainly on the size and density of fragments. Simulations with small fragments may be very slow. At the beginning of a run there is a period of up to 1 hour in which the program calculates thermal weights due to statistical model. This period is long if many species are included in the simulation.     

Parallel computing for lattice Monte Carlo simulation of large-scale thin film growth

This paper proposes two viable computing strategies for distributed parallel systems: domain division with sub-domain overlapping and asynchronous communication. We have implemented a parallel computing procedure for simulation of Ti thin film growing process of a system with 1000 x 1000 atoms by means of the Monte Carlo (MC) method. This approach greatly reduces the computation time for simulation of large-scale thin film growth under realistic deposition rates. The multi-lattice MC model of deposition comprises two basic events: deposition, and surface diffusion. Since diffusion constitutes more than 90% of the total simulation time of the whole deposition process at high temperature, we concentrated on implementing a new parallel diffusion simulation that reduces communication time during simulation. Asynchronous communication and domain overlapping techniques are used to reduce the waiting time and communication time among parallel processors. The parallel algorithms we propose can simulate the thin     

Accelerated event-by-event Monte Carlo microdosimetric calculations of electrons and protons tracks on a multi-core CPU and a CUDA-enabled GPU

For microdosimetric calculations event-by-event Monte Carlo (MC) methods are considered the most accurate. The main shortcoming of those methods is the extensive requirement for computational time. In this work we present an event-by-event MC code of low projectile energy electron and proton tracks for accelerated microdosimetric MC simulations on a graphic processing unit (GPU). Additionally, a hybrid implementation scheme was realized by employing OpenMP and CUDA in such a way that both GPU and multi-core CPU were utilized simultaneously. The two implementation schemes have been tested and compared with the sequential single threaded MC code on the CPU. Performance comparison was established on the speed-up for a set of benchmarking cases of electron and proton tracks. A maximum speedup of 67.2 was achieved for the GPU-based MC code, while a further improvement of the speedup up to 20% was achieved for the hybrid approach. The results indicate the capability of our CPU–GPU implementation for accelerated MC microdosimetric calculations of both electron and proton tracks without loss of accuracy.     

Differential negative resistance effect of output characteristics in deep sub-micrometer wurtzite AlGaN/GaN MODFETs

We obtained the output characteristics in wurtzite Al0.15Ga0.85N/GaN MODFETs with the full band Monte Carlo method. The gate length Lg and the channel length Los in the device are 0.2 μm and 0.4 urn, respectively. In the output characteristics we found a differential negative resistance effect. That is, as VDS is a constant, initially, VDS increases with increasing VDS. When VDS exceeds a certain critical value, IDS decreases with increasing VDS. The analysis for velocity-field characteristics in wurtzite CaN, the distributions of the electric field and the electron velocity in the two dimensional electron gas channel indicates that the differential negative resistance effect of the electron average velocity results in the differential negative resistance effect of the output characteristics. The transient transport also is related to the differential negative resistance effect of the output characteristics. This effect only can be observed in the devices with very short channel.     

MCFTLE: Monte Carlo Rendering of Finite‐Time Lyapunov Exponent Fields

Traditionally, Lagrangian fields such as finite‐time Lyapunov exponents (FTLE) are precomputed on a discrete grid and are ray casted afterwards. This, however, introduces both grid discretization errors and sampling errors during ray marching. In this work, we apply a progressive, view‐dependent Monte Carlo‐based approach for the visualization of such Lagrangian fields in time‐dependent flows. Our approach avoids grid discretization and ray marching errors completely, is consistent, and has a low memory consumption. The system provides noisy previews that converge over time to an accurate high‐quality visualization. Compared to traditional approaches, the proposed system avoids explicitly predefined fieldline seeding structures, and uses a Monte Carlo sampling strategy named Woodcock tracking to distribute samples along the view ray. An acceleration of this sampling strategy requires local upper bounds for the FTLE values, which we progressively acquire during the rendering. Our approach is tailored for high‐quality visualizations of complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface structures as indicators for Lagrangian coherent structures (LCS). We demonstrate the effectiveness of our approach by using a set of analytic test cases and real‐world numerical simulations.     

利用蒙特卡洛法对船厂纳期风险进行仿真评估

船厂的材料供应问题直接关系到船舶生产计划的准时执行,通过对船厂材料纳期过程的分析,建立了服从一般随机过程的船厂材料纳期数学模型,对随机过程中的数字特征给出了估算的方法,并用蒙特卡洛法对船厂纳期风险进行仿真估算.在特殊情况下,针对随机过程的一个样本函数, 讨论了数字特征的意义及其风险估算的方法.研究表明,供应商的材料计划运抵时间分布密度函数,并不局限于正态分布,有可能为分布甚至是均匀分布,这取决于不同供应商的自身情况.因此,利用该方法对指导船厂纳期天数的计划具有实用意义.     

The stationary phase auxiliary field Monte Carlo method: a new strategy for reducing the sign problem of auxiliary field methodologies

In this paper we focus on a new computational procedure, which permits an efficient calculation within the classical auxiliary field methodology. As has been previously reported, the method suffers from a sign problem, typically encountered in methodologies based on a field-theoretical approach. To ameliorate its statistical convergence, the efforts have so far exclusively been concentrated on the development of efficient analytical integral transformation techniques, such as the method of Gaussian equivalent representation of Efimov et al. In the present work we reformulate the classical auxiliary field methodology according to the concepts of the stationary phase Monte Carlo method of Doll et al., a numerical strategy originally developed for the simulation with real-time path integrals. The procedure, which is here employed for the first time for auxiliary field computation, utilizes an importance sampling strategy, to identify the regions of configuration space that contribute most strongly to the functional integral averages. Its efficiency is here compared to the method of Gaussian equivalent representation.     

MERADGEN 1.0: Monte Carlo generator for the simulation of radiative events in parity conserving doubly-polarized Møller scattering

The Monte Carlo generator MERADGEN 1.0 for the simulation of radiative events in parity conserving doubly-polarized Møller scattering has been developed. Analytical integration wherever it is possible provides rather fast and accurate generation. Some numerical tests and histograms are presented.

Program summary

Program title: MERADGEN 1.0Catalogue identifier:ADYM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYM_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneProgramming language: FORTRAN 77Computer(s) for which the program has been designed: allOperating system(s) for which the program has been designed: LinuxRAM required to execute with typical data: 1 MBNo. of lines in distributed program, including test data, etc.:2196No. of bytes in distributed program, including test data, etc.:23 501Distribution format:tar.gzHas the code been vectorized or parallelized?: noNumber of processors used: 1Supplementary material: noneExternal routines/libraries used: noneCPC Program Library subprograms used: noneNature of problem: Simulation of radiative events in parity conserving doubly-polarized Møller scattering.Solution method: Monte Carlo method for simulation within QED, analytical integration wherever it is possible that provides rather fast and accurate generation.Restrictions: noneUnusual features: noneAdditional comments: noneRunning time: The simulation of 10⁸ radiative events for itest:=1 takes up to 45 seconds on AMD Athlon 2.80 GHz processor.     

Finite-Sample Adjustments for Homogeneity and Symmetry Tests in Systems of Demand Equations: A Monte Carlo Evaluation

This paper gives simulation results comparing the finite-sample performance of three commonly used homogeneity and symmetry asymptotic tests, and some size-corrected tests that can be used when the sample size is small. The results suggest that such finite-sample corrections can be effective in bringing the empirical sizes of the tests closer to their nominal levels. They also suggest that the likelihood ratio test is, in general, more reliable than the Wald and Lagrange multiplier tests. Finally, it is shown that size-corrections of homogeneity tests tend to introduce reductions in power, which can be very large when bootstrap corrections are used. An application to a well known data set is also presented.