SEARCH · Search NASA
Results for “Constant Number Monte Carlo”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Nanoparticle dynamics in the spatial afterglows of nonthermal plasma synthesis reactors
Nonthermal plasma flow tube reactors are industrially scalable systems for the production of nanocrystal (NC) based materials and coatings. One key advantage of nonthermal plasma synthesis is the ability to both synthesize NCs and deposit films in a single reactor, as at the reactor outlet, NCs can be inertially deposited onto a target substrate. The size and morphology of deposited particles can substantially influence the film structure and function. Though NCs are typically near-spherical and monodispersed as-produced in plasma synthesis reactors, NC charge and growth dynamics can be altered substantially when NCs are sampled out of the plasma and through the spatial afterglow region, affecting deposition. Experiments have demonstrated changes of NC size and charge in the spatial afterglow; however, these dynamics remain unexplored and unexplained via theory and simulation. To address this, we developed a constant number Monte Carlo (CNMC) simulation model to examine the mechanisms of NC decharging and growth in the spatial afterglow of plasma flow tube reactors. Collisions between NC and plasma species, diffusive deposition, and electron desorption from NCs are incorporated in the CNMC simulation. The simulation results are specifically compared with previous experiments on Si NCs synthesized from a low pressure Ar-SiH 4 nonthermal plasma reactor. Furthermore, the experiment-model comparison shows that CNMC models can be implemented which accurately model NC size distribution evolution in a spatial afterglow. Simultaneously, results show that improved collision models, energetic species diffusion models, and electron desorption models will be necessary to accurately depict NC dynamics in spatial afterglows.
Particle charge distributions in the effluent of a flow-through atmospheric pressure low temperature plasma
Atmospheric pressure low-temperature plasmas are often utilized to perform particle synthesis, treatment, and removal. It is well-known that dust particles are highly negatively charged in these plasmas; however, little is known about dust particle charging behavior as particles leave the plasma volume and pass through the spatial afterglow region. In this work, monodisperse particles of various sizes and work functions were introduced into an atmospheric pressure radiofrequency capacitively coupled flow-through plasma. Dust particle electrical mobility distributions downstream of the flow-through plasma were measured utilizing a differential mobility analyzer in conjunction with a condensation particle counter at various gas flow velocities. Charge distributions were determined from the measured electrical mobility distributions. Experiments confirm that particles become less negatively charged, and even net-positively charged after leaving the plasma volume, with a distribution that follows a shifted Boltzmann charge distribution. Additionally, particle charge in the effluent of the flow-through plasma is negligibly dependent on work function but highly size and flow velocity dependent. Larger particles were shown to have a higher magnitude of charge under all studied conditions; however, particle polarity was switchable by varying gas flow velocity. The charging dynamics were simulated utilizing a constant number Monte Carlo model that accounts for electron temperature decay and the transition from ambipolar to free diffusion of electrons and ions in the spatial afterglow. Simulation results also suggest that, at the same flow velocity, larger particles obtain a greater magnitude of charge, negative or positive. Furthermore, the decrease in electron mobility and the difference between ion and electron convective loss rates create an ion-rich region in the plasma effluent that promotes ion–particle collisions and drives particle charge removal and even reversal of polarity. Larger particles more favorably collide with energetic species in these environments, which results in higher charge states.
Understanding the depletion of electrons in dusty plasmas at atmospheric pressure
The nucleation and growth of NPs in the gas phase using atmospheric-pressure plasma systems is an important approach to synthesizing novel dimensionally-controlled materials. In this paper, we investigated the effect of the NPs on a typical type of continuous-flow, substrate-free plasma at atmospheric pressure to understand their potential contribution to electron density changes. A tandem plasma system was set up consisting of one plasma reactor that produced carbonaceous NPs from mixtures of argon and hexane, and another identical plasma reactor where the as-grown particles were injected and non-intrusive electrical and optical measurements were performed. The electron densities obtained from conductivity measurements and a plasma fluid model were found to decrease in the presence of NPs. However, control experiments revealed that the main source of the electron depletion was residual vapor or reaction byproducts in the form of molecular species or nanoclusters and not the particles themselves. These results were validated by constant number Monte Carlo simulations which showed that at the experimentally-measured conditions, the NPs were not of sufficiently high enough concentration to reduce the electron density; however, if molecules or clusters are ionizable, they remain in sufficient concentration to deplete electron densities. Our study shows that at atmospheric pressure, because of their typically larger electron density values, particle-producing plasmas are distinct from those at low pressure, and nanoparticle formation does not have the same impact while molecular-scale species may be a more important consideration.
Collaborative Research: Understanding Nanoparticle-Plasma Interactions in Dusty Non-Thermal Plasmas by Nanoparticle Probes and Online Aerosol Characterization (Final Technical Report)
This report describes results from the University of Minnesota’s contribution to studies performed under the award DE-SC0018202 (principal Investigator: Christopher J. Hogan Jr.. This award is a collaborative research grant with support equally provided to Case Western Reserve University and to the University of Illinois (with principal investigator R. Mohan Sankaran). To date ten peer-reviewed published papers have resulted from the studies performed with University of Minnesota personnel contributing; this report describes the results of these studies as well as several unpublished studies, grouped into seven separate study types. The overarching goal of the carried out studies was to understand nanoparticle behavior and dynamics in non-thermal plasma synthesis reactors, specifically adapting aerosol measurement technology to provide online measurements of particle size, charge, and structure in plasma reactor systems.
A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging
Monte Carlo simulations based on weighted simulation particles can solve a variety of population balance problems and allow thus to formulate a solution-framework for many chemical engineering processes. This study presents a novel concept for the calculation of coagulation rates of weighted Monte Carlo particles by introducing a family of transformations to non-weighted Monte Carlo particles. The tuning of the accuracy (named ‘stochastic resolution’ in this paper) of those transformations allows the construction of a constant-number coagulation scheme. Furthermore, a parallel algorithm for the inclusion of newly formed Monte Carlo particles due to nucleation is presented in the scope of a constant-number scheme: the low-weight merging. This technique is found to create significantly less statistical simulation noise than the conventional technique (named ‘random removal’ in this paper). Both concepts are combined into a single GPU-based simulation method which is validated by comparison with the discrete-sectional simulation technique. Two test models describing a constant-rate nucleation coupled to a simultaneous coagulation in 1) the free-molecular regime or 2) the continuum regime are simulated for this purpose.
MC3, Version 1
The MC3 code is used to perform Monte Carlo simulations in the isothermal-isobaric ensemble (constant number of particles, temperature, and pressure) on molecular crystals. The molecules within the periodic simulation cell are treated as rigid bodies, alleviating the requirement for a complex interatomic potential. Intermolecular interactions are described using generic, atom-centered pair potentials whose parameterization is taken from the literature [D. E. Williams, J. Comput. Chem., 22, 1154 (2001)] and electrostatic interactions arising from atom-centered, fixed, point partial charges. The primary uses of the MC3 code are the computation of i) the temperature and pressure dependence of lattice parameters and thermal expansion coefficients, ii) tensors of elastic constants and compliances via the Parrinello and Rahman’s fluctuation formula [M. Parrinello and A. Rahman, J. Chem. Phys., 76, 2662 (1982)], and iii) the investigation of polymorphic phase transformations. The MC3 code is written in Fortran90 and requires LAPACK and BLAS linear algebra libraries to be linked during compilation. Computationally expensive loops are accelerated using OpenMP.
MC3, Version 1
The MC3 code is used to perform Monte Carlo simulations in the isothermal-isobaric ensemble (constant number of particles, temperature, and pressure) on molecular crystals. The molecules within the periodic simulation cell are treated as rigid bodies, alleviating the requirement for a complex interatomic potential. Intermolecular interactions are described using generic, atom-centered pair potentials whose parameterization is taken from the literature [D. E. Williams, J. Comput. Chem., 22, 1154 (2001)] and electrostatic interactions arising from atom-centered, fixed, point partial charges. The primary uses of the MC3 code are the computation of i) the temperature and pressure dependence of lattice parameters and thermal expansion coefficients, ii) tensors of elastic constants and compliances via the Parrinello and Rahman’s fluctuation formula [M. Parrinello and A. Rahman, J. Chem. Phys., 76, 2662 (1982)], and iii) the investigation of polymorphic phase transformations. The MC3 code is written in Fortran90 and requires LAPACK and BLAS linear algebra libraries to be linked during compilation. Computationally expensive loops are accelerated using OpenMP.
Improving the sampling efficiency of the Grand Canonical Simulated Quenching approach
Most common atomistic simulation techniques, like molecular dynamics or Metropolis Monte Carlo, operate under a constant interatomic Hamiltonian with a fixed number of atoms. Internal (atom positions or velocities) or external (simulation cell size or geometry) variables are then evolved dynamically or stochastically to yield sampling in different ensembles, such as microcanonical (NVE), canonical (NVT), isothermal-isobaric (NPT), etc. Averages are then taken to compute relevant physical properties. At least two limitations of these standard approaches can seriously hamper their application to many important systems: (1) they do not allow for the exchange of particles with a reservoir, and (2) the sampling efficiency is insufficient to allow the obtention of converged results because of the very long intrinsic timescales associated with these quantities. To fix ideas, one might want to identify low (free) energy configurations of grain boundaries (GB). In reality, grain boundaries are in contact the grains which act as reservoirs of defects (e.g., vacancies and interstitials). Since the GB can exchange particles with its environment, the most stable configuration cannot provably be found by sampling from NVE or NVT ensembles alone: one needs to allow the number of atoms in the sample to fluctuate. The first limitation can be circumvented by working in the grand canonical ensemble (TV ) or its derivatives (such as the semi-grand-canonical ensemble useful for the study of substitutional alloys). Monte Carlo methods have been the first to adapt to this kind of system where the number of atoms is allowed to fluctuate. Many of these methods are based on the Widom insertion method [Widom63] where the chemical potential of a given chemical species can be inferred from the potential energy changes upon random insertion of a new particle within the simulation cell. Other techniques, such as the Gibbs ensemble Monte Carlo [Panagiotopoulos87] where exchanges of particles are attempted to equilibrate the chemical potential between two cells and hence allow for the calculation of coexistence curves, exploit the same idea: particle insertion (or exchange) is attempted and accepted with a Metropolis-like rule that depends exponentially on the energy change upon insertion. A well known limitation of this kind of approach is that the probability of accepting such a move decreases extremely rapidly with increasing density, due to the extremely large short-range repulsion between atoms. In response to these difficulties it became apparent that a solution to the problem might be to avoid abrupt insertions but instead to proceed gradually, so as to allow the system to react and make way for the incoming particle. In this view of things, the 'occupation' of a certain atomic site can be viewed as a continuous variable, ranging between 0 and 1, representing 'how much' of the particle is present at any given time. These ideas proved ideal in Molecular Dynamics (MD) settings because equations of motions for these occupation variables can sometimes be obtained. For example, in the case of Grand Canonical Molecular Dynamics [Cagin91], one special particle is allowed to have a fractional occupation. This can lead to either its destruction (occupation = 0) or its complex creation (occupation = 1) so as to enforce a given chemical potential. These approaches proved useful, but mostly in the liquid state where the probability of successfully inserting a new particle is sufficiently high. At higher densities, convergence proved to be hampered by very inefficient sampling. In this work, we explore the use of a related MD-based grand canonical technique, the Grand Canonical Simulated Quenching (GCSQ) of Phillpot and Rickman [Phillpot92,Phillpot94], and explore its application to the grand canonical sampling of solid state systems. We show that, in conjunction with advanced sampling techniques, GCSQ can be a useful tool to sample conformations of complex systems, such as GBs, and assist in the identification of their most stable states and/or most likely defective states.
Direct Monte Carlo Simulations of Chemical Equilibrium Composition of Molecular Fluid Mixtures Under Shock Conditions
A new Monte Carlo simulation method is implemented which holds the number and kind of atoms constant rather than the number and kind of molecules for a molecular fluid mixture. Chemical reactions are allowed as a correlated move of atoms such as an interchange of atoms between molecules. Equilibrium chemical composition is determined as an average over the simulation along with equation of state quantities. Results are presented for N 2 + O 2 → 2NO at 30GPa and 3000K. The equilibrium composition is shown to be sensitive to the potentials between unlike species.
Defect energetics of cubic hafnia from quantum Monte Carlo simulations
Cubic hafnia (HfO 2 ) is of great interest for a number of applications in electronics because of its high dielectric constant. However, common defects in such applications degrade the properties of hafina. We have investigated the electronic properties of oxygen vacancies and nitrogen substitution in cubic HfO 2 using first-principles calculations based on density functional theory (DFT) and many-body diffusion Monte Carlo (DMC) methods. We investigate five different charge defect states of oxygen vacancies, as well as substitutional N defects which can lead to local magnetic moments. Both DMC and DFT calculations shows that an oxygen vacancy induces strong lattice relaxations around the defect. Finally, we compare defect formation energies, charge and spin densities obtained from DMC with results obtained using DFT. While the obtained formation energies from DMC are 0.6–1.5 eV larger than those from GGA+ U , the agreement for the most important defects, neutral and positively charged oxygen vacancies, and nitrogen substitutional defect, under oxygen-poor conditions are in reasonably good agreement. Lastly, our work confirms that nitrogen can act to passivate cubic hafnia for applications in electronics.
Diagrammatic theories of anharmonic molecular vibrations
In this review, we summarise recent developments in our laboratory in the field of many-body quantum-mechanical calculations of the anharmonic vibrational structure of molecules. Our size-extensive vibrational self-consistent field (XVSCF) and size-extensive second-order many-body perturbation (XVMP2) methods are, unlike their parent methods (VSCF and VMP2), defined in diagram- matic formulations of the energies and Dyson self-energies, leading to manifestly size-consistent expressions for zero-point energies and anharmonic vibrational frequencies calculable with much greater efficiency. The effective one-mode potentials of XVSCF are quadratic and hence the Schrödinger equation for each mode can be solved analytically, unlike VSCF, where a basis-set expansion of wave functions on more complex one-mode potentials need to be performed; VSCF potentials and their minima (anharmonic geometry) are shown to reduce to the quadratic potentials and their minima (also given analytically) of XVSCF in the thermodynamic limit. By self-consistently solving the Dyson equation with frequency-dependent self-energies, XVMP2 has the ability to calculate anharmonic frequencies of fundamentals as well as combinations and overtones in the presence of strong anharmonic resonance without a multireference or quasi-degenerate formulation, which tends to be non-size-consistent. To eliminate the computational bottleneck of XVSCF and XVMP2, which is the high-rank force-constant evaluation, we have developed alternative algorithms in which the diagrammatic equations are recast as a small number of high-dimensional integrals and then evaluated stochastically using a Metropolis Monte Carlo (MC) method. These MC-XVSCF and MC-XVMP2 methods not only remove the need for force-constant evaluation or storage, but also take into account force constants of up to infinite order according to their importance. Furthermore, they are a new branch of quantum Monte Carlo which can calculate frequencies (excitation energies) directly without fixed-node errors.
SU-G-201-06: Directional Low-Dose Rate Brachytherapy: Determination of the TG-43 Dose-Rate Constant Analog for a New Pd-103 Source
Purpose: The aim of this work is to determine the TG-43 dose-rate constant analog for a new directional low-dose rate brachytherapy source based on experimental methods and comparison to Monte Carlo simulations. The CivaSheet™ is a new commercially available planar source array comprised of a variable number of discrete directional source elements called “CivaDots”. Given the directional nature and non-conventional design of the source, modifications to the AAPM TG-43 protocol for dosimetry are required. As a result, various parameters of the TG-43 dosimetric formalism have to be adapted to accommodate this source. This work focuses on the dose-rate constant analog determination for a CivaDot. Methods: Dose to water measurements of the CivaDot were performed in a polymethyl methacrylate phantom (20×20×12 cm{sup 3}) using thermoluminescent dosimeters (TLDs) and Gafchromic EBT3 film. The source was placed in the center of the phantom, and nine TLD micro-cubes were irradiated along its central axis at a distance of 1 cm. For the film measurements, the TLDs were substituted by a (3×3) cm{sup 2} EBT3 film. Primary air-kerma strength measurements of the source were performed using a variable-aperture free-air chamber. Finally, the source was modeled using the Monte Carlo N-Particle Transport Code 6. Results: Dose-rate constant analog observed for a total of eight CivaDots using TLDs and five CivaDots using EBT3 film was within ±7.0% and ±2.9% of the Monte Carlo predicted value respectively. The average difference observed was −4.8% and −0.1% with a standard deviation of 1.7% and 2.1% for the TLD and the film measurements respectively, which are both within the comparison uncertainty. Conclusion: A preliminary investigation to determine the doserate constant analog for a CivaDot was conducted successfully with good agreement between experimental and Monte Carlo based methods. This work will aid in the eventual realization of a clinically-viable dosimetric framework for the CivaSheet. This work was partially supported by NCI contract (HHSN261201200052C) through CivaTech Oncology Inc.
Uncertainty quantification of few group diffusion theory constants generated by the B1 theory-augmented Monte Carlo method
The purpose of this paper is to quantify uncertainties of fuel pin cell or fuel assembly (FA) homogenized few group diffusion theory constants generated from the B1 theory-augmented Monte Carlo (MC) method. A mathematical formulation of the first kind is presented to quantify uncertainties of the few group constants in terms of the two major sources of the MC method; statistical and nuclear cross section and nuclide number density input data uncertainties. The formulation is incorporated into the Seoul National Univ. MC code McCARD. It is then used to compute the uncertainties of the burnup-dependent homogenized two group constants of a low-enriched UO{sub 2} fuel pin cell and a PWR FA on the condition that nuclear cross section input data of U-235 and U-238 from JENDL 3.3 library and nuclide number densities from the solution to fuel depletion equations have uncertainties. The contribution of the MC input data uncertainties to the uncertainties of the two group constants of the two fuel systems is separated from that of the statistical uncertainties. The utilities of uncertainty quantifications are then discussed from the standpoints of safety analysis of existing power reactors, development of new fuel or reactor system design, and improvement of covariance files of the evaluated nuclear data libraries. (authors)
Monte Carlo based toy model for fission process
There are many models and calculation techniques to obtain visible image of fission yield process. In particular, fission yield can be calculated by using two calculations approach, namely macroscopic approach and microscopic approach. This work proposes another calculation approach in which the nucleus is treated as a toy model. Hence, the fission process does not represent real fission process in nature completely. The toy model is formed by Gaussian distribution of random number that randomizes distance like the distance between particle and central point. The scission process is started by smashing compound nucleus central point into two parts that are left central and right central points. These three points have different Gaussian distribution parameters such as mean (μ{sub CN}, μ{sub L}, μ{sub R}), and standard deviation (σ{sub CN}, σ{sub L}, σ{sub R}). By overlaying of three distributions, the number of particles (N{sub L}, N{sub R}) that are trapped by central points can be obtained. This process is iterated until (N{sub L}, N{sub R}) become constant numbers. Smashing process is repeated by changing σ{sub L} and σ{sub R}, randomly.
A quasi-static Monte Carlo algorithm for the simulation of sub-prompt critical transients
A pseudo-time-dependent Monte Carlo algorithm suitable for simulating thermal reactor transients with timescales on the order of seconds is presented. An initial experimental implementation has been written into the Monte Carlo Application ToolKit (MCATK) developed at Los Alamos National Laboratory. The algorithm is essentially a combination of the fully time-dependent Monte Carlo algorithm, including the explicit simulation of delayed neutron precursors, and a quasi-static algorithm that does not use the point-kinetics equations. The fully time-dependent calculation is performed for some number of inactive and active micro time steps. The dynamic reactor time constant and delayed neutron precursor production rates are calculated directly from the active cycles, rather than from point-kinetics parameters. These quantities are then used to advance the neutron population and delayed neutron precursors forward in time across a macro time step. As a result, the method is applied to the C5G7-TD benchmark operating in steady state and in transient mode.
Simulations of classical three-body thermalization in one dimension
One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of pointlike particles, typically the dominant process for reaching thermal equilibrium in higher-dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential V ij ∝ 1/|x i –x j | n or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equation to evolve a perturbed thermal state with temperature T toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low-density limit. For the inverse power-law potential, the rate of thermalization is proportional to ρ 2 T$\frac{1}{2}$ – $\frac{1}{n}$, where ρ is the number density. Furthermore, the corresponding proportionality constant decreases with increasing n.
Statistical effects related to low numbers of reacting molecules analyzed for a reversible association reaction A + B = C in ideally dispersed systems: An apparent violation of the law of mass action
Theoretical analysis and computer simulations (Monte Carlo and numerical integration of differential equations) show that the statistical effect of a small number of reacting molecules depends on a way the molecules are distributed among the small volume nano-reactors (droplets in this study). A simple reversible association A + B = C was chosen as a model reaction, enabling to observe both thermodynamic (apparent equilibrium constant) and kinetic effects of a small number of reactant molecules. When substrates are distributed uniformly among droplets, all containing the same equal number of substrate molecules, the apparent equilibrium constant of the association is higher than the chemical one (observed in a macroscopic—large volume system). The average rate of the association, being initially independent of the numbers of molecules, becomes (at higher conversions) higher than that in a macroscopic system: the lower the number of substrate molecules in a droplet, the higher is the rate. This results in the correspondingly higher apparent equilibrium constant. A quite opposite behavior is observed when reactant molecules are distributed randomly among droplets: the apparent association rate and equilibrium constants are lower than those observed in large volume systems, being the lower, the lower is the average number of reacting molecules in a droplet. The random distribution of reactant molecules corresponds to ideal (equal sizes of droplets) dispersing of a reaction mixture. Our simulations have shown that when the equilibrated large volume system is dispersed, the resulting droplet system is already at equilibrium and no changes of proportions of droplets differing in reactant compositions can be observed upon prolongation of the reaction time.