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Showing papers on "Dynamic Monte Carlo method published in 2002"



Book
26 Aug 2002
TL;DR: A short and systematic theoretical introduction to the Monte Carlo method and a practical guide with plenty of examples and exercises for the student.
Abstract: Introduction - purpose and scope of this volume, and some general comments theoretical foundation of the Monte Carlo method and its application in statistical physics guide to practical work with the Monte Carlo method some important recent developments of the Monte Carlo methodology.

892 citations


Journal ArticleDOI
TL;DR: In this paper, Monte Carlo sampling is used for nonlinear inverse problems where no analytical expression for the forward relation between data and model parameters is available, and where linearization is unsuccessful.
Abstract: Monte Carlo methods have become important in analysis of nonlinear inverse problems where no analytical expression for the forward relation between data and model parameters is available, and where linearization is unsuccessful. In such cases a direct mathematical treatment is impossible, but the forward relation materializes itself as an algorithm allowing data to be calculated for any given model. Monte Carlo methods can be divided into two categories: the sampling methods and the optimization methods. Monte Carlo sampling is useful when the space of feasible solutions is to be explored, and measures of resolution and uncertainty of solution are needed. The Metropolis algorithm and the Gibbs sampler are the most widely used Monte Carlo samplers for this purpose, but these methods can be refined and supplemented in various ways of which the neighbourhood algorithm is a notable example. Monte Carlo optimization methods are powerful tools when searching for globally optimal solutions amongst numerous local optima. Simulated annealing and genetic algorithms have shown their strength in this respect, but they suffer from the same fundamental problem as the Monte Carlo sampling methods: no provably optimal strategy for tuning these methods to a given problem has been found, only a number of approximate methods.

311 citations


Journal ArticleDOI
TL;DR: A variety of high-level algorithms are devised that serve as an interface between the user and a traditional MC code and enable the direct determination of composition-temperature phase boundaries without requiring the calculation of the whole free energy surface of the alloy system.
Abstract: Monte Carlo (MC) simulations of lattice models are a widely used way to compute thermodynamic properties of substitutional alloys. A limitation to their more widespread use is the difficulty of driving a MC simulation in order to obtain the desired quantities. To address this problem, we have devised a variety of high-level algorithms that serve as an interface between the user and a traditional MC code. The user specifies the goals sought in a high-level form that our algorithms convert into elementary tasks to be performed by a standard MC code. For instance, our algorithms permit the determination of the free energy of an alloy phase over its entire region of stability within a specified accuracy, without requiring any user intervention during the calculations. Our algorithms also enable the direct determination of composition-temperature phase boundaries without requiring the calculation of the whole free energy surface of the alloy system.

298 citations


Journal ArticleDOI
TL;DR: Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities are presented, as models of biological membranes, and show that the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase.

231 citations


Journal ArticleDOI
TL;DR: Results concerning the structural, conformational, and volumetric properties of linear, monodisperse polyethylene melts, simulated with a new united-atom molecular model, are in excellent agreement with experimental data.
Abstract: Two novel connectivity-altering atomistic Monte Carlo moves are presented for the fast equilibration of condensed phases of long-chain systems with a variety of chain architectures. With the new moves, isotropic or oriented melts of linear or long-chain branched polymers, dense brushes of terminally grafted macromolecules, and cyclic peptides can be simulated. Results concerning the structural, conformational, and volumetric properties of linear, monodisperse polyethylene melts, simulated with a new united-atom molecular model, are in excellent agreement with experimental data.

228 citations


Journal ArticleDOI
TL;DR: A rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau is presented and a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case is established.
Abstract: We present a rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau [Phys. Rev. Lett. 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples configurations according to their inverse density of states using Monte Carlo moves; the estimate for the density of states is refined at each simulation step and is ultimately used to calculate thermodynamic properties. We present an implementation for atomic systems based on a rigorous separation of kinetic and configurational contributions to the density of states. By constructing a "uniform" ensemble for configurational degrees of freedom-in which all potential energies, volumes, and numbers of particles are equally probable-we establish a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case. To demonstrate the generality of our approach, we perform sample calculations for the Lennard-Jones fluid using two implementation variants and in both cases find good agreement with established literature values for the vapor-liquid coexistence locus.

216 citations


Journal ArticleDOI
TL;DR: This work determines the depletion-induced phase-behavior of hard-sphere colloids and interacting polymers by large-scale Monte Carlo simulations using very accurate coarse-graining techniques and shows that including excluded-volume interactions between polymers leads to qualitative differences in the phase diagrams.
Abstract: We determine the depletion-induced phase-behavior of hard-sphere colloids and interacting polymers by large-scale Monte Carlo simulations using very accurate coarse-graining techniques. A comparison with standard Asakura-Oosawa model theories and simulations shows that including excluded-volume interactions between polymers leads to qualitative differences in the phase diagrams. These effects become increasingly important for larger relative polymer size. Our simulation results agree quantitatively with recent experiments.

195 citations


Journal ArticleDOI
TL;DR: In this paper, Monte Carlo simulations of swelling clays are studied by computer simulations (Monte Carlo and molecular dynamics) for comparison of structural and dynamic properties of two montmorillonites with different kinds of counterions.
Abstract: Models of swelling clays are studied by computer simulations (Monte Carlo and molecular dynamics). We focus on the comparison of structural and dynamic properties of two montmorillonites with different kinds of counterions Na+ and Cs+. The calculated values are compared with available experimental quantities such as interlayer spacing as a function of water content and diffusion coefficients of both water molecules and counterions in the monohydrated state. The results are consistent with experimental values and previous simulations. For the dynamics, the short time behavior of water as observed with quasielastic neutron scattering is in agreement with simulated one. For the ions, the experimental values are related to macroscopic long time motions and are much smaller than the short time values calculated from MD. Thus, the present study provides a detailed insight in the microscopic dynamics of ions related to the structure of the clay: it is shown that Cs+ diffuse faster than Na+ and that the arrangeme...

169 citations


Journal ArticleDOI
TL;DR: Taking expression of Escherichia coli beta-galactosidase as an example, it is shown that the program is able to simulate systems composed of reactions varying in several orders of magnitude by means of reaction rates and the numbers of molecules involved.
Abstract: Motivation: The availability of a huge amount of molecular data concerning various biochemical reactions provoked numerous attempts to study the dynamics of cellular processes by means of kinetic models and computer simulations. Biochemical processes frequently involve small numbers of molecules (e.g. a few molecules of a transcriptional regulator binding to one ‘molecule’ of a DNA regulatory region). Such reactions are subject to significant stochastic fluctuations. Monte Carlo methods must be employed to study the functional consequences of the fluctuations and simulate processes that cannot be modelled by continuous fluxes of matter. This provides the motivation to develop software dedicated to Monte Carlo simulations of cellular processes with the rigorously proven Gillespie algorithm. Results: STOCKS, software for the stochastic kinetic simulation of biochemical processes is presented. The program uses a rigorously derived Gillespie algorithm that has been shown to be applicable to the study of prokaryotic gene expression. Features dedicated to the study of cellular processes are implemented, such as the possibility to study a process in the range of several cell generations with the application of a simple cell division model. Taking expression of Escherichia coli betagalactosidase as an example, it is shown that the program is able to simulate systems composed of reactions varying in several orders of magnitude by means of reaction rates and the numbers of molecules involved. Availability: The software is available at ftp://ibbrain.ibb. waw.pl/stocks and http://www.ibb.waw.pl/stocks. Supplementary information: Parameters of the model of prokaryotic gene expression are available in example files of software distribution.

162 citations


Journal ArticleDOI
TL;DR: In this article, a Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum, where a random walk in the two-dimensional space of particle number and energy is used to estimate the density of states of the system; this density is continuously updated as the random walk visits individual states.
Abstract: A Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum A random walk in the two-dimensional space of particle number and energy is used to estimate the density of states of the system; this density of states is continuously updated as the random walk visits individual states The validity and usefulness of the method are demonstrated by applying it to the simulation of a Lennard-Jones fluid Results for its thermodynamic properties, including the vapor–liquid phase coexistence curve, are shown to be in good agreement with high-accuracy literature data

Book
Neal Madras1
01 Jan 2002
TL;DR: Introduction Generating random numbers Variance reduction techniques Markov chain Monte Carlo statistical analysis of simulation output and the Ising model.
Abstract: Introduction Generating random numbers Variance reduction techniques Markov chain Monte Carlo Statistical analysis of simulation output The Ising model and related examples Bibliography.

Journal ArticleDOI
TL;DR: In this paper, Monte Carlo (MC) and density functional theory (DFT) results are reported for an electrolyte, consisting of charged hard spheres of diameter 3 A with the solvent modeled as a dielectric continuum, near a charged flat uniformly charged electrode.
Abstract: Monte Carlo (MC) and density functional theory (DFT) results are reported for an electrolyte, consisting of charged hard spheres of diameter 3 A with the solvent modeled as a dielectric continuum, near a charged flat uniformly charged electrode. These results are more interesting than the earlier MC results of Torrie and Valleau [J. Chem. Phys. 73, 5807 (1980); J. Phys. Chem. 86, 3251 (1982)] for 4.25 A spheres because the popular Gouy–Chapman (GC) theory is less successful for this system. The DFT results are in good agreement with the MC results. Both the MC and DFT results show particularly interesting features when the counterions are divalent. For such divalent counterions, the diffuse layer potential passes through a maximum magnitude, then declines, and ultimately has a sign that is opposite to that of the electrode charge. The consequences of this behavior are discussed. In contrast, the well-known GC theory consistently overestimates the magnitude of the diffuse layer potential, does not have any unusual behavior, and is in poor agreement with the simulation results.

Journal ArticleDOI
01 Aug 2002-Proteins
TL;DR: A novel Monte Carlo algorithm called parallel hyperbolic sampling (PHS) is developed that logarithmically flattens local high‐energy barriers and, therefore, allows the simulation to tunnel more efficiently through energetically inaccessible regions to low‐energy valleys.
Abstract: Among the major difficulties in protein structure prediction is the roughness of the energy landscape that must be searched for the global energy minimum. To address this issue, we have developed a novel Monte Carlo algorithm called parallel hyperbolic sampling (PHS) that logarithmically flattens local high-energy barriers and, therefore, allows the simulation to tunnel more efficiently through energetically inaccessible regions to low-energy valleys. Here, we show the utility of this approach by applying it to the SICHO (SIde-CHain-Only) protein model. For the same CPU time, the parallel hyperbolic sampling method can identify much lower energy states and explore a larger region phase space than the commonly used replica sampling (RS) Monte Carlo method. By clustering the simulated structures obtained in the PHS implementation of the SICHO model, we can successfully predict, among a representative benchmark 65 proteins set, 50 cases in which one of the top 5 clusters have a root-mean-square deviation (RMSD) from the native structure below 6.5 A. Compared with our previous calculations that used RS as the conformational search procedure, the number of successful predictions increased by four and the CPU cost is reduced. By comparing the structure clusters produced by both PHS and RS, we find a strong correlation between the quality of predicted structures and the minimum relative RMSD (mrRMSD) of structures clusters identified by using different search engines. This mrRMSD correlation may be useful in blind prediction as an indicator of the likelihood of successful folds.

Journal ArticleDOI
TL;DR: In this paper, fixed node diffusion Monte Carlo (FN-DMC) atomization energies are calculated for a benchmark set of 55 molecules using single determinant trial wave functions, comparison with experiment yields an average absolute deviation of 2.9 kcal/mol.
Abstract: Fixed node diffusion Monte Carlo (FN-DMC) atomization energies are calculated for a benchmark set of 55 molecules. Using single determinant trial wave functions, comparison with experiment yields an average absolute deviation of 2.9 kcal/mol, placing this simplest form of FN-DMC roughly at the same level of accuracy as the CCSD(T)/aug-cc-pVQZ method. However, unlike perturbative wave function expansion approaches, FN-DMC is applicable to systems containing thousands of valence electrons. For the P2 molecule, a number of possible sources of error are explored in detail. Results show that the main error is due to the fixed-node approximation and that this can be improved significantly with multireference trial wave functions.

Journal ArticleDOI
TL;DR: In this paper, the authors used the random two-dimensional Ising model as a test example and performed on it both classical and quantum (pathintegral) Monte Carlo annealing.
Abstract: Quantum annealing was recently found experimentally in a disordered spin-$\frac{1}{2}$ magnet to be more effective than its classical, thermal counterpart. We use the random two-dimensional Ising model as a test example and perform on it both classical and quantum (path-integral) Monte Carlo annealing. A systematic study of the dependence of the final residual energy on the annealing Monte Carlo time quantitatively demonstrates the superiority of quantum relative to classical annealing in this system. In order to determine the parameter regime for optimal efficiency of the quantum annealing procedure we explore a range of values of Trotter slice number P and temperature T. This identifies two different regimes of freezing with respect to efficiency of the algorithm, and leads to useful guidelines for the optimal choice of quantum annealing parameters.

Journal ArticleDOI
TL;DR: Karayiannis et al. as mentioned in this paper used double bridging and intramolecular double rebridging chain connectivity-altering Monte Carlo moves to simulate polyethylene (PE) melts of molecular length ranging from C78 up to C1000.
Abstract: This work is concerned with the atomistic simulation of the volumetric, conformational and structural properties of monodisperse polyethylene (PE) melts of molecular length ranging from C78 up to C1000. In the past, polydisperse models of these melts have been simulated in atomistic detail with the end-bridging Monte Carlo algorithm [Pant and Theodorou, Macromolecules 28, 7224 (1995); Mavrantzas et al., Macromolecules 32, 5072 (1999)]. In the present work, strictly monodisperse as well as polydisperse PE melts are simulated using the recently introduced double bridging and intramolecular double rebridging chain connectivity-altering Monte Carlo moves [Karayiannis et al., Phys. Rev. Lett. 88, 105503 (2002)]. These algorithms constitute generalizations of the EB move, since they entail the construction of two trimer bridges between two properly chosen pairs of dimers along the backbones of two different chains or along the same chain. In the simulations, a new molecular model is employed which is a hybrid o...


Proceedings ArticleDOI
18 Apr 2002
TL;DR: This work introduces Stochustic Roadmap Sirrrcllation (SRS), a new approach for exploring the kinetics of molecular motion by simultaneously examining multiple pathways encoded compactly in a graph, called a roadmap, and shows that, in the limit, SRS converges to the same distribution as Monte Carlo simulation.
Abstract: Classic techniques for simulating molecular motion, such as the Monte Carlo and molecular dynamics methods, generate individual motion pathways one at a time and spend most of their time trying to escape from the local minima of the energy landscape of a molecule. Their high computational cost prevents them from being used to analyze many pathways. We introduce Stochustic Roadmap Sirrrcllation (SRS), a new approach for exploring the kinetics of molecular motion by simultaneously examining multiple pathways encoded compactly in a graph, called a roadmap. A roadmap is computed by sampling a molecule's conformation space at random. The computation does not suffer from the localminima problem encountered with existing methods. Each path in the roadmap represents a potential motion pathway and is associated with a probability indicating the likelihood that the molecule follows this pathway. By viewing the roadmap as a Markov chain, we can efficiently compute kinetic properties of molecular motion over the entire molecular energy landscape. We also prove that, in the limit, SRS converges to the same distribution as Monte Carlo simulation. To test the effectiveness of our approach, we apply it to the computation of the transmission coefficients for protein folding, an important order parameter that measures the "kinetic distance" of a protein's conformation to its native state Our computational studies show that SRS obtains more accurate results and achieves several orders- of- magnitude reduction in computation time, compared with Monte Carlo simulatio.

Journal ArticleDOI
TL;DR: It is found that the new approach greatly improves the structural description, alleviating the common problem in standard reverse Monte Carlo method (RMC) of generating structures with a high proportion of unphysical small rings.
Abstract: An improved method for the modelling of carbon structures based on a hybrid reverse Monte Carlo (HRMC) method is presented. This algorithm incorporates an accurate environment dependent interaction potential (EDIP) in conjunction with the commonly used constraints derived from experimental data. In this work, we compare this new method with other modelling results for a small system of 2.9 g/cc amorphous carbon. We find that the new approach greatly improves the structural description, alleviating the common problem in standard reverse Monte Carlo method (RMC) of generating structures with a high proportion of unphysical small rings. The advantage of our method is that larger systems can now be modelled, allowing the incorporation of mesoscopic scale features.

Journal ArticleDOI
TL;DR: The formula derived in this paper is useful for Monte Carlo simulations of gas discharges and based on the screened Coulomb potential between electrons and neutral atoms, it is possible to construct differential cross sections for electron scattering by Ar, N2, and CH4.
Abstract: The purpose of this Brief Report is to point out the mistake in a formula for anisotropic electron scattering, previously published in Phys. Rev. A 41, 1112 (1990), which is widely used in Monte Carlo models of gas discharges. Anisotropic electron scattering is investigated based on the screened Coulomb potential between electrons and neutral atoms. The approach is also applied for electron scattering by nonpolar neutral molecules. Differential cross sections for electron scattering by Ar, ${\mathrm{N}}_{2},$ and ${\mathrm{CH}}_{4}$ are constructed on the basis of momentum and integrated cross sections. The formula derived in this paper is useful for Monte Carlo simulations of gas discharges.

Journal ArticleDOI
TL;DR: There are many kinetic Monte Carlo approaches that can simulate chemical vapor deposition, ranging from coarse-grained model systems with hypothetical input parameters to physically realistic atomic simulations with accurate chemical kinetic input.
Abstract: ▪ Abstract The kinetic Monte Carlo method is a powerful tool for exploring the evolution and properties of a wide range of problems and systems. Kinetic Monte Carlo is ideally suited for modeling the process of chemical vapor deposition, which involves the adsorption, desorption, evolution, and incorporation of vapor species at the surface of a growing film. Deposition occurs on a time scale that is generally not accessible to fully atomistic approaches such as molecular dynamics, whereas an atomically resolved Monte Carlo method parameterized by accurate chemical kinetic data is capable of exploring deposition over long times (min) on large surfaces (mm2). There are many kinetic Monte Carlo approaches that can simulate chemical vapor deposition, ranging from coarse-grained model systems with hypothetical input parameters to physically realistic atomic simulations with accurate chemical kinetic input. This article introduces the kinetic Monte Carlo technique, reviews some of the major approaches, details ...

Journal ArticleDOI
TL;DR: In this article, the equilibrium between vapour and liquid in a square-well system has been determined by a hybrid simulation approach combining chemical potentials calculated via the Gibbs ensemble Monte Carlo technique with pressures calculated by the standard NVT Monte Carlo method.
Abstract: The equilibrium between vapour and liquid in a square-well system has been determined by a hybrid simulation approach combining chemical potentials calculated via the Gibbs ensemble Monte Carlo technique with pressures calculated by the standard NVT Monte Carlo method. The phase equilibrium was determined from the thermodynamic conditions of equality of pressure and chemical potential between the two phases. The results of this hybrid approach were tested by independent NPT and μPT calculations and are shown to be of much higher accuracy than those of conventional GEMC simulations. The coexistence curves, vapour pressures and critical points were determined for SW systems of interaction ranges λ = 1.25, 1.5, 1.75 and 2. The new results show a systematic dependence on the range λ, in agreement with results from perturbation theory where previous work had shown more erratic behaviour.

Journal ArticleDOI
TL;DR: In this paper, a Monte Carlo algorithm is used to estimate the density of states of a protein via a random walk on the energy surface, thereby allowing the system to escape from local free-energy minima with relative ease.
Abstract: A Monte Carlo algorithm that performs a random walk in energy space has been used to study random coil–helix and random coil–beta sheet transitions in model proteins. This method permits estimation of the density of states of a protein via a random walk on the energy surface, thereby allowing the system to escape from local free-energy minima with relative ease. A cubic lattice model and a knowledge based force field are employed for these simulations. It is shown that, for a given amino acid sequence, the method is able to fold long polypeptides reproducibly. Its results compare favorably with those of annealing and parallel tempering simulations, which have been used before in the same context. This method is used to examine the effect of amino acid sequence and chain length on the folding of several designer polypeptides.

Journal ArticleDOI
TL;DR: In this article, an exact relationship between the vibrational relaxation number (ZvDSMC) used in the direct simulation Monte Carlo method and that employed in continuum simulations was developed, where the translational temperature is larger than vibrational temperature.
Abstract: Exact relationship is developed that connects the vibrational relaxation number, ZvDSMC, used in the direct simulation Monte Carlo method and that employed in continuum simulations. An approximate expression for ZvDSMC is also derived that is cost-effective and applicable when translational temperature is larger than vibrational temperature.

Journal ArticleDOI
TL;DR: In this paper, a general strategy for sampling configurations from a given distribution, not based on the standard Metropolis (Markov chain) strategy, is described, which uses the fact that nontrivial problems in statistical physics are high dimensional and often close to Markovian.

Journal ArticleDOI
TL;DR: In this paper, the saddle-point binding energies of a many-body embedded-atom method (EAM) potential are modeled by simple pair interactions on rigid lattice, and these microscopic parameters are integrated in a Monte Carlo scheme.
Abstract: The precipitation kinetics in alloys is now widely studied at a microscopic scale, using Monte Carlo simulations and simple energetic and diffusion models. In the present paper, we first test the assumptions of these models, in the case of the copper precipitation in α-iron, using static relaxation of a many-body embedded-atom-method (EAM) potential. In dilute alloys, the EAM configurational energies can be described by simple pair interactions on rigid lattice. The EAM vacancy migration barriers are reproduced by saddle-point binding energies which are very sensitive to both the nature of the jumping atom and that of the first neighbors of the saddle point. Finally, these microscopic parameters are integrated in a Monte Carlo scheme. The dependence of the saddle-point binding energies on the local atomic configurations modifies the relative mobility of small Cu clusters and Cu monomers. At high temperature, it leads to a slowing down of the precipitation by a constant ratio of on the time scale, but at low temperature, the kinetic pathway is dramatically modified.

Journal ArticleDOI
TL;DR: The interaction of a high-intensity laser with a solid target generates a large current of fast electrons flowing into the target, which generates significant electric and magnetic fields in the target and rapidly heat it to high temperatures, causing errors in results obtained by Monte Carlo modeling.
Abstract: The interaction of a high-intensity laser with a solid target generates a large current of fast electrons flowing into the target. Due to the large value of the current, the fast electrons generate significant electric and magnetic fields in the target and rapidly heat it to high temperatures. However, these effects were neglected in interpreting x-ray emission experiments, so the details of the fast electron generation that were inferred could be incorrect. This is considered, theoretically, for layered target, $K\ensuremath{\alpha}$ emission experiments, by using a hybrid Monte Carlo code that includes field generation. The code is used to model such experiments with aluminum and plastic targets, using fast electron parameters taken from experimental results for average intensities of around ${10}^{18}{\mathrm{W}\mathrm{}\mathrm{cm}}^{\ensuremath{-}2}.$ These numerical results are then interpreted in the same manner as previous experiments, using only the Monte Carlo part of the code. The field generation leads to lower total emission and to an apparent two-temperature fast electron distribution. The laser absorption into fast electrons inferred by Monte Carlo modeling is consistently lower than the actual value. The mean fast electron energy inferred could be either higher or lower than the actual value, depending on the experimental setup and the cone angle and energy distribution used in the Monte Carlo modeling. The errors caused by neglecting the fields are, in general, greater for plastic than aluminum targets, leading to inconsistencies in results obtained by Monte Carlo modeling.

Journal ArticleDOI
TL;DR: In this article, the Direct Simulation Monte Carlo (DSMC) method is used to numerically solve the Enskog equation for a granular binary mixture in the homogeneous cooling state (HCS).
Abstract: The Direct Simulation Monte Carlo (DSMC) method is used to numerically solve the Enskog equation for a granular binary mixture in the homogeneous cooling state (HCS). The fourth velocity moments, the temperature ratio, and also the velocity distribution functions are obtained and compared with approximate analytical results derived recently from a Sonine polynomial expansion [V. Garzo and J. W. Dufty, Phys. Rev. E 60, 5706 (1999)]. The comparison shows an excellent agreement between both approaches, even for strong dissipation or disparate values of the mechanical parameters of the mixture. In contrast to previous studies, the partial temperatures of each species are clearly different, so that the total energy is not equally distributed between both species. Finally, in the same way as in the one-component case, the simulation as well as the theory show a high energy tail of the distribution functions.

Journal ArticleDOI
TL;DR: In this paper, the authors presented detailed Monte Carlo-based calculations of the electron dynamics in GaN-AlGaN heterostructures in the presence of strain polarization fields.
Abstract: We present detailed Monte Carlo based calculations of the electron dynamics in GaN–AlGaN heterostructures in the presence of strain polarization fields. The model consists of a fully numerical self-consistent solution of the Schrodinger–Poisson equation with a Monte Carlo transport model. The two-dimensional sub-band energies, wave functions and carrier scattering mechanisms are computed numerically and included within a Monte Carlo simulation. The electron energy, steady-state and transient drift velocity and band occupancy are calculated as a function of electric field for different AlGaN–GaN heterostructure compositions. The effect of piezoelectrically induced strain fields on the transport dynamics is examined. A field dependent mobility model is also developed from the Monte Carlo results.