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Sample records for multigroup time-independent boltzmann

  1. New multigroup Monte Carlo scattering algorithm suitable for neutral- and charged-particle Boltzmann and Fokker-Planck calculations

    Energy Technology Data Exchange (ETDEWEB)

    Sloan, D.P.

    1983-05-01

    Morel (1981) has developed multigroup Legendre cross sections suitable for input to standard discrete ordinates transport codes for performing charged-particle Fokker-Planck calculations in one-dimensional slab and spherical geometries. Since the Monte Carlo neutron transport code, MORSE, uses the same multigroup cross section data that discrete ordinates codes use, it was natural to consider whether Fokker-Planck calculations could be performed with MORSE. In order to extend the unique three-dimensional forward or adjoint capability of MORSE to Fokker-Planck calculations, the MORSE code was modified to correctly treat the delta-function scattering of the energy operator, and a new set of physically acceptable cross sections was derived to model the angular operator. Morel (1979) has also developed multigroup Legendre cross sections suitable for input to standard discrete ordinates codes for performing electron Boltzmann calculations. These electron cross sections may be treated in MORSE with the same methods developed to treat the Fokker-Planck cross sections. The large magnitude of the elastic scattering cross section, however, severely increases the computation or run time. It is well-known that approximate elastic cross sections are easily obtained by applying the extended transport (or delta function) correction to the Legendre coefficients of the exact cross section. An exact method for performing the extended transport cross section correction produces cross sections which are physically acceptable. Sample calculations using electron cross sections have demonstrated this new technique to be very effective in decreasing the large magnitude of the cross sections.

  2. CHARTB multigroup transport package

    Energy Technology Data Exchange (ETDEWEB)

    Baker, L.

    1979-03-01

    The physics and numerical implementation of the radiation transport routine used in the CHARTB MHD code are discussed. It is a one-dimensional (Cartesian, cylindrical, and spherical symmetry), multigroup,, diffusion approximation. Tests and applications will be discussed as well.

  3. MCNP: Multigroup/adjoint capabilities

    Energy Technology Data Exchange (ETDEWEB)

    Wagner, J.C.; Redmond, E.L. II; Palmtag, S.P.; Hendricks, J.S.

    1994-04-01

    This report discusses various aspects related to the use and validity of the general purpose Monte Carlo code MCNP for multigroup/adjoint calculations. The increased desire to perform comparisons between Monte Carlo and deterministic codes, along with the ever-present desire to increase the efficiency of large MCNP calculations has produced a greater user demand for the multigroup/adjoint capabilities. To more fully utilize these capabilities, we review the applications of the Monte Carlo multigroup/adjoint method, describe how to generate multigroup cross sections for MCNP with the auxiliary CRSRD code, describe how to use the multigroup/adjoint capability in MCNP, and provide examples and results indicating the effectiveness and validity of the MCNP multigroup/adjoint treatment. This information should assist users in taking advantage of the MCNP multigroup/adjoint capabilities.

  4. Lattice Boltzmann Stokesian dynamics.

    Science.gov (United States)

    Ding, E J

    2015-11-01

    Lattice Boltzmann Stokesian dynamics (LBSD) is presented for simulation of particle suspension in Stokes flows. This method is developed from Stokesian dynamics (SD) with resistance and mobility matrices calculated using the time-independent lattice Boltzmann algorithm (TILBA). TILBA is distinguished from the traditional lattice Boltzmann method (LBM) in that a background matrix is generated prior to the calculation. The background matrix, once generated, can be reused for calculations for different scenarios, thus the computational cost for each such subsequent calculation is significantly reduced. The LBSD inherits the merits of the SD where both near- and far-field interactions are considered. It also inherits the merits of the LBM that the computational cost is almost independent of the particle shape.

  5. Uniqueness of time-independent electromagnetic fields

    DEFF Research Database (Denmark)

    Karlsson, Per W.

    1974-01-01

    As a comment on a recent paper by Steele, a more general uniqueness theorem for time-independent fields is mentioned. ©1974 American Institute of Physics......As a comment on a recent paper by Steele, a more general uniqueness theorem for time-independent fields is mentioned. ©1974 American Institute of Physics...

  6. Procedure to Generate the MPACT Multigroup Library

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Kang Seog [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

    2015-12-17

    The CASL neutronics simulator MPACT is under development for the neutronics and T-H coupled simulation for the light water reactor. The objective of this document is focused on reviewing the current procedure to generate the MPACT multigroup library. Detailed methodologies and procedures are included in this document for further discussion to improve the MPACT multigroup library.

  7. Conception and development of an adaptive energy mesher for multigroup library generation of the transport codes; Conception et developpement d'un mailleur energetique adaptatif pour la generation des bibliotheques multigroupes des codes de transport

    Energy Technology Data Exchange (ETDEWEB)

    Mosca, P.

    2009-12-15

    The deterministic transport codes solve the stationary Boltzmann equation in a discretized energy formalism called multigroup. The transformation of continuous data in a multigroup form is obtained by averaging the highly variable cross sections of the resonant isotopes with the solution of the self-shielding models and the remaining ones with the coarse energy spectrum of the reactor type. So far the error of such an approach could only be evaluated retrospectively. To remedy this, we studied in this thesis a set of methods to control a priori the accuracy and the cost of the multigroup transport computation. The energy mesh optimisation is achieved using a two step process: the creation of a reference mesh and its optimized condensation. In the first stage, by refining locally and globally the energy mesh, we seek, on a fine energy mesh with subgroup self-shielding, a solution equivalent to a reference solver (Monte Carlo or pointwise deterministic solver). In the second step, once fixed the number of groups, depending on the acceptable computational cost, and chosen the most appropriate self-shielding models to the reactor type, we look for the best bounds of the reference mesh minimizing reaction rate errors by the particle swarm optimization algorithm. This new approach allows us to define new meshes for fast reactors as accurate as the currently used ones, but with fewer groups. (author)

  8. Chaotic Boltzmann machines.

    Science.gov (United States)

    Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki

    2013-01-01

    The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented.

  9. Finite Boltzmann schemes

    NARCIS (Netherlands)

    Sman, van der R.G.M.

    2006-01-01

    In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the

  10. Time-independent compaction behavior of quartz sands

    NARCIS (Netherlands)

    Brzesowsky, R. H.; Spiers, C. J.; Peach, C. J.; Hangx, Suzanne

    2014-01-01

    Mechanisms such as grain rearrangement, coupled with elastic deformation and grain breakage, are believed to play an important role in the time-independent compaction of sands, controlling porosity and permeability reduction during burial of clastic sediments and during depletion of highly porous re

  11. Multigroup Free-atom Doppler-broadening Approximation. Theory

    Energy Technology Data Exchange (ETDEWEB)

    Gray, Mark Girard [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-11-06

    Multigroup cross sections at a one target temperature can be Doppler-broadened to multigroup cross sections at a higher target temperature by matrix multiplication if the group structure suf- ficiently resolves the original temperature continuous energy cross section. Matrix elements are the higher temperature group weighted averages of the integral over the lower temperature group boundaries of the free-atom Doppler-broadening kernel. The results match theory for constant and 1/v multigroup cross sections at 618 lanl group structure resolution.

  12. Modelling and simulations of macroscopic multi-group pedestrian flow

    CERN Document Server

    Mahato, Naveen K; Tiwari, Sudarshan

    2016-01-01

    We consider a multi-group microscopic model for pedestrian flow describing the behaviour of large groups. It is based on an interacting particle system coupled to an eikonal equation. Hydrodynamic multi-group models are derived from the underlying particle system as well as scalar multi-group models. The eikonal equation is used to compute optimal paths for the pedestrians. Particle methods are used to solve the macroscopic equations. Numerical test cases are investigated and the models and, in particular, the resulting evacuation times are compared for a wide range of different parameters.

  13. Deriving the time-independent Schrödinger equation

    Science.gov (United States)

    Gorard, Jonathan

    2016-11-01

    A discussion of the physical meaning of the Schrödinger wave equation can not only constitute an exciting introduction to some of the more abstract ideas of quantum mechanics, but serves more generally as a useful demonstration of the application of mathematics to modern physics. This frontline uses physical concepts and mathematical techniques that would be accessible to a sufficiently interested secondary school student, in order to derive the simplest, one-dimensional case of the time-independent Schrödinger equation: the derivation relies only upon aspects of Newtonian/wave mechanics, quantum theory, complex numbers and calculus that would be covered in an advanced secondary school syllabus.

  14. Ludwig Boltzmann: Atomic genius

    Energy Technology Data Exchange (ETDEWEB)

    Cercignani, C. [Department of Mathematics, Politecnico di Milano (Italy)]. E-mail: carcer@mate.polimi.it

    2006-09-15

    On the centenary of the death of Ludwig Boltzmann, Carlo Cercignani examines the immense contributions of the man who pioneered our understanding of the atomic nature of matter. The man who first gave a convincing explanation of the irreversibility of the macroscopic world and the symmetry of the laws of physics was the Austrian physicist Ludwig Boltzmann, who tragically committed suicide 100 years ago this month. One of the key figures in the development of the atomic theory of matter, Boltzmann's fame will be forever linked to two fundamental contributions to science. The first was his interpretation of 'entropy' as a mathematically well-defined measure of the disorder of atoms. The second was his derivation of what is now known as the Boltzmann equation, which describes the statistical properties of a gas as made up of molecules. The equation, which described for the first time how a probability can evolve with time, allowed Boltzmann to explain why macroscopic phenomena are irreversible. The key point is that while microscopic objects like atoms can behave reversibly, we never see broken coffee cups reforming because it would involve a long series of highly improbable interactions - and not because it is forbidden by the laws of physics. (U.K.)

  15. Gli atomi di Boltzmann

    CERN Document Server

    Lindley, David

    2002-01-01

    Ludwig Boltzmann (1844-1906) è il fisico e matematico austriaco che negli ultimi decenni dell'Ottocento e ancora ai primi del Novecento lottò contro l'opinione dominante tra gli scienziati dell'epoca per affermare la teoria atomica della materia. È noto come con Albert Einstein e fino a oggi la fisica si sia sviluppata e abbia celebrato i propri trionfi lungo le linee anticipate da Boltzmann. La controversia con Mach non riguardava soltanto l'esistenza degli atomi, ma l'intero modo di fare fisica che Boltzmann non riteneva di dover limitare allo studio di quantità misurabili, introducendo invece spiegazioni più elaborate basate su ipotesi più ampie.

  16. General time-independent theory of ionization and breakup reactions

    Energy Technology Data Exchange (ETDEWEB)

    Rosenberg, Leonard [Department of Physics, New York University, New York, NY 10003 (United States)], E-mail: lr1@nyu.edu

    2008-08-14

    A rigorous formulation of non-relativistic time-dependent multiparticle collision theory was developed some time ago, in which the effect of long-range Coulomb forces was accounted for by a modification of the standard wave operator that appears in treatments of neutral-particle scattering. This theory is here converted to a time-independent form, with the wave-operator modification replaced by the use of Coulomb-modified plane waves in the construction of the wave packets that appear in the theory. This provides a convenient basis for the development of approximation techniques in configuration space, including the use of variational methods of calculation, based on integral identities for the transition amplitudes. In many cases oscillatory divergences appear in the integrals representing the ionization or breakup amplitudes. A method for removing such divergences by an averaging of the integrand at great distances is defined.

  17. A new time-independent formulation of fractional release

    Science.gov (United States)

    Ostermöller, Jennifer; Bönisch, Harald; Jöckel, Patrick; Engel, Andreas

    2017-03-01

    The fractional release factor (FRF) gives information on the amount of a halocarbon that is released at some point into the stratosphere from its source form to the inorganic form, which can harm the ozone layer through catalytic reactions. The quantity is of major importance because it directly affects the calculation of the ozone depletion potential (ODP). In this context time-independent values are needed which, in particular, should be independent of the trends in the tropospheric mixing ratios (tropospheric trends) of the respective halogenated trace gases. For a given atmospheric situation, such FRF values would represent a molecular property.We analysed the temporal evolution of FRF from ECHAM/MESSy Atmospheric Chemistry (EMAC) model simulations for several halocarbons and nitrous oxide between 1965 and 2011 on different mean age levels and found that the widely used formulation of FRF yields highly time-dependent values. We show that this is caused by the way that the tropospheric trend is handled in the widely used calculation method of FRF.Taking into account chemical loss in the calculation of stratospheric mixing ratios reduces the time dependence in FRFs. Therefore we implemented a loss term in the formulation of the FRF and applied the parameterization of a mean arrival time to our data set.We find that the time dependence in the FRF can almost be compensated for by applying a new trend correction in the calculation of the FRF. We suggest that this new method should be used to calculate time-independent FRFs, which can then be used e.g. for the calculation of ODP.

  18. The Suppression of Energy Discretization Errors in Multigroup Transport Calculations

    Energy Technology Data Exchange (ETDEWEB)

    Larsen, Edward [Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Nuclear Engineering and Radiological Sciences

    2013-06-17

    The Objective of this project is to develop, implement, and test new deterministric methods to solve, as efficiently as possible, multigroup neutron transport problems having an extremely large number of groups. Our approach was to (i) use the standard CMFD method to "coarsen" the space-angle grid, yielding a multigroup diffusion equation, and (ii) use a new multigrid-in-space-and-energy technique to efficiently solve the multigroup diffusion problem. The overall strategy of (i) how to coarsen the spatial an energy grids, and (ii) how to navigate through the various grids, has the goal of minimizing the overall computational effort. This approach yields not only the fine-grid solution, but also coarse-group flux-weighted cross sections that can be used for other related problems.

  19. Multigroup Moderation Test in Generalized Structured Component Analysis

    Directory of Open Access Journals (Sweden)

    Angga Dwi Mulyanto

    2016-05-01

    Full Text Available Generalized Structured Component Analysis (GSCA is an alternative method in structural modeling using alternating least squares. GSCA can be used for the complex analysis including multigroup. GSCA can be run with a free software called GeSCA, but in GeSCA there is no multigroup moderation test to compare the effect between groups. In this research we propose to use the T test in PLS for testing moderation Multigroup on GSCA. T test only requires sample size, estimate path coefficient, and standard error of each group that are already available on the output of GeSCA and the formula is simple so the user does not need a long time for analysis.

  20. Review of multigroup nuclear cross-section processing

    Energy Technology Data Exchange (ETDEWEB)

    Trubey, D.K.; Hendrickson, H.R. (comps.)

    1978-10-01

    These proceedings consist of 18 papers given at a seminar--workshop on ''Multigroup Nuclear Cross-Section Processing'' held at Oak Ridge, Tennessee, March 14--16, 1978. The papers describe various computer code systems and computing algorithms for producing multigroup neutron and gamma-ray cross sections from evaluated data, and experience with several reference data libraries. Separate abstracts were prepared for 13 of the papers. The remaining five have already been cited in ERA, and may be located by referring to the entry CONF-780334-- in the Report Number Index. (RWR)

  1. Training Restricted Boltzmann Machines

    DEFF Research Database (Denmark)

    Fischer, Asja

    Restricted Boltzmann machines (RBMs) are probabilistic graphical models that can also be interpreted as stochastic neural networks. Training RBMs is known to be challenging. Computing the likelihood of the model parameters or its gradient is in general computationally intensive. Thus, training...

  2. A new multigroup method for cross-sections that vary rapidly in energy

    Science.gov (United States)

    Haut, T. S.; Ahrens, C.; Jonko, A.; Lowrie, R.; Till, A.

    2017-01-01

    We present a numerical method for solving the time-independent thermal radiative transfer (TRT) equation or the neutron transport (NT) equation when the opacity (cross-section) varies rapidly in frequency (energy) on the microscale ε; ε corresponds to the characteristic spacing between absorption lines or resonances, and is much smaller than the macroscopic frequency (energy) variation of interest. The approach is based on a rigorous homogenization of the TRT/NT equation in the frequency (energy) variable. Discretization of the homogenized TRT/NT equation results in a multigroup-type system, and can therefore be solved by standard methods. We demonstrate the accuracy and efficiency of the approach on three model problems. First we consider the Elsasser band model with constant temperature and a line spacing ε =10-4 . Second, we consider a neutron transport application for fast neutrons incident on iron, where the characteristic resonance spacing ε necessitates ≈ 16 , 000 energy discretization parameters if Planck-weighted cross sections are used. Third, we consider an atmospheric TRT problem for an opacity corresponding to water vapor over a frequency range 1000-2000 cm-1, where we take 12 homogeneous layers between 1-15 km, and temperature/pressure values in each layer from the standard US atmosphere. For all three problems, we demonstrate that we can achieve between 0.1 and 1 percent relative error in the solution, and with several orders of magnitude fewer parameters than a standard multigroup formulation using Planck-weighted (source-weighted) opacities for a comparable accuracy.

  3. Multigroup Confirmatory Factor Analysis: Locating the Invariant Referent Sets

    Science.gov (United States)

    French, Brian F.; Finch, W. Holmes

    2008-01-01

    Multigroup confirmatory factor analysis (MCFA) is a popular method for the examination of measurement invariance and specifically, factor invariance. Recent research has begun to focus on using MCFA to detect invariance for test items. MCFA requires certain parameters (e.g., factor loadings) to be constrained for model identification, which are…

  4. Parametric lattice Boltzmann method

    Science.gov (United States)

    Shim, Jae Wan

    2017-06-01

    The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the Maxwell-Boltzmann distribution. The ranges of flow velocity and temperature providing positive valued distributions vary with regulating discrete velocities as parameters. New isothermal and thermal compressible models are proposed for flows of the level of the isothermal and thermal compressible Navier-Stokes equations. Thermal compressible shock tube flows are simulated by only five on-lattice discrete velocities. Two-dimensional isothermal and thermal vortices provoked by the Kelvin-Helmholtz instability are simulated by the parametric models.

  5. SIMULATE-4 multigroup nodal code with microscopic depletion model

    Energy Technology Data Exchange (ETDEWEB)

    Bahadir, T. [Studsvik Scandpower, Inc., Newton, MA (United States); Lindahl, St.O. [Studsvik Scandpower AB, Vasteras (Sweden); Palmtag, S.P. [Studsvik Scandpower, Inc., Idaho Falls, ID (United States)

    2005-07-01

    SIMULATE-4 is a three-dimensional multigroup analytical nodal code with microscopic depletion capability. It has been developed employing 'first principal models' thus avoiding ad hoc approximations. The multigroup diffusion equations or, optionally, the simplified P{sub 3} equations are solved. Cross sections are described by a hybrid microscopic-macroscopic model that includes approximately 50 heavy nuclides and fission products. Heterogeneities in the axial direction of an assembly are treated systematically. Radially, the assembly is divided into heterogeneous sub-meshes, thereby overcoming the shortcomings of spatially-averaged assembly cross sections and discontinuity factors generated with zero net-current boundary conditions. Numerical tests against higher order transport methods and critical experiments show substantial improvements compared to results of existing nodal models. (authors)

  6. Fluctuating multicomponent lattice Boltzmann model.

    Science.gov (United States)

    Belardinelli, D; Sbragaglia, M; Biferale, L; Gross, M; Varnik, F

    2015-02-01

    Current implementations of fluctuating lattice Boltzmann equations (FLBEs) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the orthonormal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and nonideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.

  7. Learning thermodynamics with Boltzmann machines

    Science.gov (United States)

    Torlai, Giacomo; Melko, Roger G.

    2016-10-01

    A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modeling thermodynamic observables for physical systems in thermal equilibrium. Through unsupervised learning, we train the Boltzmann machine on data sets constructed with spin configurations importance sampled from the partition function of an Ising Hamiltonian at different temperatures using Monte Carlo (MC) methods. The trained Boltzmann machine is then used to generate spin states, for which we compare thermodynamic observables to those computed by direct MC sampling. We demonstrate that the Boltzmann machine can faithfully reproduce the observables of the physical system. Further, we observe that the number of neurons required to obtain accurate results increases as the system is brought close to criticality.

  8. Training Restricted Boltzmann Machines

    DEFF Research Database (Denmark)

    Fischer, Asja

    Restricted Boltzmann machines (RBMs) are probabilistic graphical models that can also be interpreted as stochastic neural networks. Training RBMs is known to be challenging. Computing the likelihood of the model parameters or its gradient is in general computationally intensive. Thus, training...... relies on sampling based approximations of the log-likelihood gradient. I will present an empirical and theoretical analysis of the bias of these approximations and show that the approximation error can lead to a distortion of the learning process. The bias decreases with increasing mixing rate...... of the applied sampling procedure and I will introduce a transition operator that leads to faster mixing. Finally, a different parametrisation of RBMs will be discussed that leads to better learning results and more robustness against changes in the data representation....

  9. Lattice Boltzmann model for nanofluids

    Energy Technology Data Exchange (ETDEWEB)

    Xuan Yimin; Yao Zhengping [Nanjing University of Science and Technology, School of Power Engineering, Nanjing (China)

    2005-01-01

    A nanofluid is a particle suspension that consists of base liquids and nanoparticles and has great potential for heat transfer enhancement. By accounting for the external and internal forces acting on the suspended nanoparticles and interactions among the nanoparticles and fluid particles, a lattice Boltzmann model is proposed for simulating flow and energy transport processes inside the nanofluids. First, we briefly introduce the conventional lattice Boltzmann model for multicomponent systems. Then, we discuss the irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids and describe a lattice Boltzmann model for simulating nanofluids. Finally, we conduct some calculations for the distribution of the suspended nanoparticles. (orig.)

  10. MUXS: a code to generate multigroup cross sections for sputtering calculations

    Energy Technology Data Exchange (ETDEWEB)

    Hoffman, T.J.; Robinson, M.T.; Dodds, H.L. Jr.

    1982-10-01

    This report documents MUXS, a computer code to generate multigroup cross sections for charged particle transport problems. Cross sections generated by MUXS can be used in many multigroup transport codes, with minor modifications to these codes, to calculate sputtering yields, reflection coefficients, penetration distances, etc.

  11. An improved and fully implicit multi-group non-local electron transport model and its validations

    Science.gov (United States)

    Sijoy, C. D.; Mishra, V.; Chaurasia, S.

    2017-09-01

    The combined effect of thermal flux inhibition and non-local electron heat flux in the radiation hydrodynamics (RHD) simulation of laser-driven systems can be accurately predicted by using non-local electron transport (NLET) models. These models can avoid commonly used space and time-independent ad-hoc flux-limiting procedures. However, the use of classical electron collision frequency in these models is rigorously valid for high temperature non-degenerate plasmas. In laser-driven systems, the electron thermal energy transport is important in regions between the critical density and ablation surface where the plasma is partially degenerate. Therefore, an improved model for electron collision frequency in this regime is required to accurately predict the thermal energy transport. Previously, we have reported an improved single group non-local electron transport model by using a wide-range electron collision frequency model valid from warm-dense matter (WDM) to fully ionized plasmas. In this work, we have extended this idea into a two-dimensional multi-group non-local electron transport (MG-NLET) model. Moreover, we have used a fully implicit numerical integration scheme in which the models for multi-group thermal radiation transport, laser absorption, electron-ion thermal energy relaxation and ion heat conduction are included in a single step. The performance of this improved MG-NLET model has been assessed by comparing the simulated foil trajectories with the reported experimental data for laser-driven plastic foils. The results indicate that the improved model yields results that are in better agreement with the experimental data.

  12. Crystallographic Lattice Boltzmann Method

    Science.gov (United States)

    Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh

    2016-01-01

    Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098

  13. Einstein and Boltzmann

    Science.gov (United States)

    Nauenberg, Michael

    2005-03-01

    In 1916 Einstein published a remarkable paper entitled ``On the Quantum Theory of Radiation''ootnotetextA. Einstein ``On the Quantum theory of Radiation,'' Phys. Zeitschrift 18 (1917) 121. First printed in Mitteilungender Physikalischen Gesellschaft Zurich. No 18, 1916. Translated into English in Van der Waerden ``Sources of Quantum Mechanics'' (North Holland 1967) pp. 63-77. in which he obtained Planck's formula for black-body radiation by introducing a new statistical hypothesis for the emmision and absorption of electromagneic radiation based on discrete bundles of energy and momentum which are now called photons. Einstein radiation theory replaced Maxwell's classical theory by a stochastic process which, when properly interpreted, also gives well known statistics of massless particles with even spin.^2 This quantum distribution, however, was not discovered by Einstein but was communicated to him by Bose in 1924. Like Boltzmann's classical counterpart, Einstein's statistical theory leads to an irreversible approach to thermal equilibrium, but because this violates time reversal, Einstein theory can not be regarded as a fundamental theory of physical process.ootnotetextM. Nauenberg ``The evolution of radiation towards thermal equilibrium: A soluble model which illustrates the foundations of statistical mechanics,'' American Journal of Physics 72 (2004) 313 Apparently Einstein and his contemporaries were unaware of this problem, and even today this problem is ignored in contemporary discussions of Einstein's treatment of the black-body spectrum.

  14. Multigroup Equivalence Analysis for High-Dimensional Expression Data

    Science.gov (United States)

    Yang, Celeste; Bartolucci, Alfred A.; Cui, Xiangqin

    2015-01-01

    Hypothesis tests of equivalence are typically known for their application in bioequivalence studies and acceptance sampling. Their application to gene expression data, in particular high-dimensional gene expression data, has only recently been studied. In this paper, we examine how two multigroup equivalence tests, the F-test and the range test, perform when applied to microarray expression data. We adapted these tests to a well-known equivalence criterion, the difference ratio. Our simulation results showed that both tests can achieve moderate power while controlling the type I error at nominal level for typical expression microarray studies with the benefit of easy-to-interpret equivalence limits. For the range of parameters simulated in this paper, the F-test is more powerful than the range test. However, for comparing three groups, their powers are similar. Finally, the two multigroup tests were applied to a prostate cancer microarray dataset to identify genes whose expression follows a prespecified trajectory across five prostate cancer stages. PMID:26628859

  15. Multigroup Equivalence Analysis for High-Dimensional Expression Data.

    Science.gov (United States)

    Yang, Celeste; Bartolucci, Alfred A; Cui, Xiangqin

    2015-01-01

    Hypothesis tests of equivalence are typically known for their application in bioequivalence studies and acceptance sampling. Their application to gene expression data, in particular high-dimensional gene expression data, has only recently been studied. In this paper, we examine how two multigroup equivalence tests, the F-test and the range test, perform when applied to microarray expression data. We adapted these tests to a well-known equivalence criterion, the difference ratio. Our simulation results showed that both tests can achieve moderate power while controlling the type I error at nominal level for typical expression microarray studies with the benefit of easy-to-interpret equivalence limits. For the range of parameters simulated in this paper, the F-test is more powerful than the range test. However, for comparing three groups, their powers are similar. Finally, the two multigroup tests were applied to a prostate cancer microarray dataset to identify genes whose expression follows a prespecified trajectory across five prostate cancer stages.

  16. Temperature based Restricted Boltzmann Machines.

    Science.gov (United States)

    Li, Guoqi; Deng, Lei; Xu, Yi; Wen, Changyun; Wang, Wei; Pei, Jing; Shi, Luping

    2016-01-13

    Restricted Boltzmann machines (RBMs), which apply graphical models to learning probability distribution over a set of inputs, have attracted much attention recently since being proposed as building blocks of multi-layer learning systems called deep belief networks (DBNs). Note that temperature is a key factor of the Boltzmann distribution that RBMs originate from. However, none of existing schemes have considered the impact of temperature in the graphical model of DBNs. In this work, we propose temperature based restricted Boltzmann machines (TRBMs) which reveals that temperature is an essential parameter controlling the selectivity of the firing neurons in the hidden layers. We theoretically prove that the effect of temperature can be adjusted by setting the parameter of the sharpness of the logistic function in the proposed TRBMs. The performance of RBMs can be improved by adjusting the temperature parameter of TRBMs. This work provides a comprehensive insights into the deep belief networks and deep learning architectures from a physical point of view.

  17. A Note on Boltzmann Brains

    CERN Document Server

    Nomura, Yasunori

    2015-01-01

    Understanding the observed arrow of time is equivalent, under general assumptions, to explaining why Boltzmann brains do not overwhelm ordinary observers. It is usually thought that this provides a condition on the decay rate of every cosmologically accessible de Sitter vacuum, and that this condition is determined by the production rate of Boltzmann brains calculated using semiclassical theory built on each such vacuum. We argue, based on a recently developed picture of microscopic quantum gravitational degrees of freedom, that this thinking needs to be modified. In particular, depending on the structure of the fundamental theory, the decay rate of a de Sitter vacuum may not have to satisfy any condition except possibly the one imposed by the Poincare recurrence. The framework discussed here also addresses the question of whether a Minkowski vacuum may produce Boltzmann brains.

  18. Multigroup covariance matrices for fast-reactor studies

    Energy Technology Data Exchange (ETDEWEB)

    Smith, J.D. III; Broadhead, B.L.

    1981-04-01

    This report presents the multigroup covariance matrices based on the ENDF/B-V nuclear data evaluations. The materials and reactions have been chosen according to the specifications of ORNL-5517. Several cross section covariances, other than those specified by that report, are included due to the derived nature of the uncertainty files in ENDF/B-V. The materials represented are Ni, Cr, /sup 16/O, /sup 12/C, Fe, Na, /sup 235/U, /sup 238/U, /sup 239/Pu, /sup 240/Pu, /sup 241/Pu, and /sup 10/B (present due to its correlation to /sup 238/U). The data have been originally processed into a 52-group energy structure by PUFF-II and subsequently collapsed to smaller subgroup strutures. The results are illustrated in 52-group correlation matrix plots and tabulated into thirteen groups for convenience.

  19. A multi-group firefly algorithm for numerical optimization

    Science.gov (United States)

    Tong, Nan; Fu, Qiang; Zhong, Caiming; Wang, Pengjun

    2017-08-01

    To solve the problem of premature convergence of firefly algorithm (FA), this paper analyzes the evolution mechanism of the algorithm, and proposes an improved Firefly algorithm based on modified evolution model and multi-group learning mechanism (IMGFA). A Firefly colony is divided into several subgroups with different model parameters. Within each subgroup, the optimal firefly is responsible for leading the others fireflies to implement the early global evolution, and establish the information mutual system among the fireflies. And then, each firefly achieves local search by following the brighter firefly in its neighbors. At the same time, learning mechanism among the best fireflies in various subgroups to exchange information can help the population to obtain global optimization goals more effectively. Experimental results verify the effectiveness of the proposed algorithm.

  20. Multi-group dynamic quantum secret sharing with single photons

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Hongwei [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Ma, Haiqiang, E-mail: hqma@bupt.edu.cn [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Wei, Kejin [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Yang, Xiuqing [School of Science, Beijing Jiaotong University, Beijing 100044 (China); Qu, Wenxiu; Dou, Tianqi; Chen, Yitian; Li, Ruixue; Zhu, Wu [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China)

    2016-07-15

    In this letter, we propose a novel scheme for the realization of single-photon dynamic quantum secret sharing between a boss and three dynamic agent groups. In our system, the boss can not only choose one of these three groups to share the secret with, but also can share two sets of independent keys with two groups without redistribution. Furthermore, the security of communication is enhanced by using a control mode. Compared with previous schemes, our scheme is more flexible and will contribute to a practical application. - Highlights: • A multi-group dynamic quantum secret sharing with single photons scheme is proposed. • Any one of the groups can be chosen to share secret through controlling the polarization of photons. • Two sets of keys can be shared simultaneously without redistribution.

  1. Non-Boltzmann behavior from the Boltzmann equation

    NARCIS (Netherlands)

    Hagen, M.H.J.; Lowe, C.P.; Frenkel, D.

    1995-01-01

    We compute the stress autocorrelation function in a two- and three-dimensional system by using the lattice-Boltzmann method. The algebraic long-time behavior ∼t-d/2 in the stress correlation function is clearly observed. The amplitude of this tail is compared with the mode-coupling expression for

  2. Lattice Boltzmann solver of Rossler equation

    Institute of Scientific and Technical Information of China (English)

    GuangwuYAN; LiRUAN

    2000-01-01

    We proposed a lattice Boltzmann model for the Rossler equation. Using a method of multiscales in the lattice Boltzmann model, we get the diffusion reaction as a special case. If the diffusion effect disappeared, we can obtain the lattice Boltzmann solution of the Rossler equation on the mesescopic scale. The numerical results show the method can be used to simulate Rossler equation.

  3. Self-shielding phenomenon modelling in multigroup transport code Apollo-2; Modelisation du phenomene d'autoprotection dans le code de transport multigroupe Apollo 2

    Energy Technology Data Exchange (ETDEWEB)

    Coste-Delclaux, M

    2006-03-15

    This document describes the improvements carried out for modelling the self-shielding phenomenon in the multigroup transport code APOLLO2. They concern the space and energy treatment of the slowing-down equation, the setting up of quadrature formulas to calculate reaction rates, the setting-up of a method that treats directly a resonant mixture and the development of a sub-group method. We validate these improvements either in an elementary or in a global way. Now, we obtain, more accurate multigroup reaction rates and we are able to carry out a reference self-shielding calculation on a very fine multigroup mesh. To end, we draw a conclusion and give some prospects on the remaining work. (author)

  4. Quantum corrections for Boltzmann equation

    Institute of Scientific and Technical Information of China (English)

    M.; Levy; PETER

    2008-01-01

    We present the lowest order quantum correction to the semiclassical Boltzmann distribution function,and the equation satisfied by this correction is given. Our equation for the quantum correction is obtained from the conventional quantum Boltzmann equation by explicitly expressing the Planck constant in the gradient approximation,and the quantum Wigner distribution function is expanded in pow-ers of Planck constant,too. The negative quantum correlation in the Wigner dis-tribution function which is just the quantum correction terms is naturally singled out,thus obviating the need for the Husimi’s coarse grain averaging that is usually done to remove the negative quantum part of the Wigner distribution function. We also discuss the classical limit of quantum thermodynamic entropy in the above framework.

  5. Student understanding of the Boltzmann factor

    CERN Document Server

    Smith, Trevor I; Thompson, John R

    2015-01-01

    We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable, nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations on student discussions about the Boltzmann f...

  6. Are there Boltzmann brains in the vacuum

    CERN Document Server

    Davenport, Matthew

    2010-01-01

    "Boltzmann brains" are human brains that arise as thermal or quantum fluctuations and last at least long enough to think a few thoughts. In many scenarios involving universes of infinite size or duration, Boltzmann brains are infinitely more common than human beings who arise in the ordinary way. Thus we should expect to be Boltzmann brains, in contradiction to observation. We discuss here the question of whether Boltzmann brains can arise as quantum fluctuations in the vacuum. Such Boltzmann brains pose an even worse problem than those arising as fluctuations in the thermal state of an exponentially expanding universe. We give several arguments for and against inclusion of vacuum Boltzmann brains in the anthropic reference class, but find neither choice entirely satisfactory.

  7. Boltzmann Transport in Hybrid PIC HET Modeling

    Science.gov (United States)

    2015-07-01

    Paper 3. DATES COVERED (From - To) July 2015-July 2015 4. TITLE AND SUBTITLE Boltzmann transport in hybrid PIC HET modeling 5a. CONTRACT NUMBER In...produced a variety of self-consistent electron swarm codes, such as the Magboltz code, focused on directly solving the steady Boltzmann trans-port...Std. 239.18 Boltzmann transport in hybrid PIC HET modeling IEPC-2015- /ISTS-2015-b- Presented at Joint Conference of 30th International

  8. Creep-recovery constitutive equation and its time-independent limit

    Energy Technology Data Exchange (ETDEWEB)

    Chang, S J

    1978-01-01

    The effect of strain recovery is taken into consideration in establishing a constitutive equation for metals at elevated temperatures. Internal state variables and Rice's flow potential are used in the representation. Growth law for the state variables is discussed and interpreted to be a more general form of the kinematic hardening condition. Yield condition is obtained from the flow law. Accordingly, the flow rule is established with the effect of the recovery mechanism, as a slightly general version of the time-independent theory with the kinematic hardening rule. In the discussion of the time-independent limit, the duration of time required for the inelastic strain to reach its saturated value is defined.

  9. Simulations of protostellar collapse using multigroup radiation hydrodynamics. I. The first collapse

    CERN Document Server

    Vaytet, Neil; Chabrier, Gilles; Commercon, Benoit; Masson, Jacques

    2012-01-01

    Radiative transfer plays a major role in the process of star formation. Many simulations of gravitational collapse of a cold gas cloud followed by the formation of a protostellar core use a grey treatment of radiative transfer coupled to the hydrodynamics. However, dust opacities which dominate extinction show large variations as a function of frequency. In this paper, we used frequency-dependent radiative transfer to investigate the influence of the opacity variations on the properties of Larson's first core. We used a multigroup M1 moment model in a 1D radiation hydrodynamics code to simulate the spherically symmetric collapse of a 1 solar mass cloud core. Monochromatic dust opacities for five different temperature ranges were used to compute Planck and Rosseland means inside each frequency group. The results are very consistent with previous studies and only small differences were observed between the grey and multigroup simulations. For a same central density, the multigroup simulations tend to produce fi...

  10. Development of a Multi-Group Neutron Cross Section Library Generation System for PWR

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Kang Seog; Hong, Ser Gi; Song, Jae Seung; Lee, Kyung Hoon; Cho, Jin Young; Kim, Ha Yong; Koo, Bon Seung; Shim, Hyung Jin; Park, Sang Yoon

    2008-10-15

    This report describes a generation system of multi-group cross section library which is used in the KARMA lattice calculation code. In particular, the theoretical methodologies, program structures, and input preparations for the constituent programs of the system are described in detail. The library generation system consists of the following five programs : ANJOY, GREDIT, MERIT, SUBDATA, and LIBGEN. ANJOY generates automatically the NJOY input files and two batch files for automatic NJOY run for all the nuclides considered. The automatic NJOY run gives TAPE 23 (PENDF output file of BROADR module of NJOY) and TAPE24 (GENDF output file of GROUPR module of NJOY) files for each nuclide. GREDIT prepares a formatted multi-group cross section file in which the cross sections are tabulated versus temperature and background cross section after reading the TAPE24 file. MERIT generates the hydrogen equivalence factors and the resonance integral tables by solving the slowing down equation with ultra-fine group cross sections which are prepared with the TAPE 23 file. SUBDATA generates the subgroup data including subgroup levels and weights after reading the MERIT output file. Finally, LIBGEN generates the final multi-group library file by assembling the data prepared in the previous steps and by reading the other data such as fission product yield data and decay data.The multi-group cross section library includes general multi-group cross sections, resonance data, subgroup data, fission product yield data, kappa-values (energy release per fission), and all the data which are required in the depletion calculation. The addition or elimination of the cross sections for some nuclides can be easily done by changing the LIBGEN input file if the general multi-group cross section and the subgroup data files are prepared.

  11. Student Understanding of the Boltzmann Factor

    Science.gov (United States)

    Smith, Trevor I.; Mountcastle, Donald B.; Thompson, John R.

    2015-01-01

    We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data…

  12. Lattice Boltzmann equation for relativistic quantum mechanics.

    Science.gov (United States)

    Succi, Sauro

    2002-03-15

    Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation.

  13. SIMPLE LATTICE BOLTZMANN MODEL FOR TRAFFIC FLOWS

    Institute of Scientific and Technical Information of China (English)

    Yan Guangwu; Hu Shouxin

    2000-01-01

    A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed.Using the Chapman-Enskog expansion and multi-scale technique,we obtain the higher-order moments of equilibrium distribution function.A simple traffic light problem is simulated by using the present lattice Boltzmann model,and the result agrees well with analytical solution.

  14. Why Boltzmann Brains Don't Fluctuate Into Existence From the De Sitter Vacuum

    CERN Document Server

    Boddy, Kimberly K; Pollack, Jason

    2015-01-01

    Many modern cosmological scenarios feature large volumes of spacetime in a de Sitter vacuum phase. Such models are said to be faced with a "Boltzmann Brain problem" - the overwhelming majority of observers with fixed local conditions are random fluctuations in the de Sitter vacuum, rather than arising via thermodynamically sensible evolution from a low-entropy past. We argue that this worry can be straightforwardly avoided in the Many-Worlds (Everett) approach to quantum mechanics, as long as the underlying Hilbert space is infinite-dimensional. In that case, de Sitter settles into a truly stationary quantum vacuum state. While there would be a nonzero probability for observing Boltzmann-Brain-like fluctuations in such a state, "observation" refers to a specific kind of dynamical process that does not occur in the vacuum (which is, after all, time-independent). Observers are necessarily out-of-equilibrium physical systems, which are absent in the vacuum. Hence, the fact that projection operators corresponding...

  15. The Einstein-Boltzmann system and positivity

    CERN Document Server

    Lee, Ho

    2012-01-01

    The Einstein-Boltzmann system is studied, with particular attention to the non-negativity of the solution of the Boltzmann equation. A new parametrization of post-collisional momenta in general relativity is introduced and then used to simplify the conditions on the collision cross-section given by Bancel and Choquet-Bruhat. The non-negativity of solutions of the Boltzmann equation on a given curved spacetime has been studied by Bichteler and by Tadmon. By examining to what extent the results of these authors apply in the framework of Bancel and Choquet-Bruhat, the non-negativity problem for the Einstein-Boltzmann system is resolved for a certain class of scattering kernels. It is emphasized that it is a challenge to extend the existing theory of the Cauchy problem for the Einstein-Boltzmann system so as to include scattering kernels which are physically well-motivated.

  16. A sum-over-paths approach to one-dimensional time-independent quantum systems

    Science.gov (United States)

    Malgieri, Massimiliano; Onorato, Pasquale; De Ambrosis, Anna

    2016-09-01

    We present an alternative treatment for simple time-independent quantum systems in one dimension, which can be used in the context of an elementary introduction to quantum physics using the Feynman approach. The method is based on representation of the energy-dependent propagator (or Green function) as a sum of complex amplitudes over all possible paths, classical and non-classical, at fixed energy. We treat both confined and open systems with piecewise-constant potentials, obtaining exact results. We introduce an approximation scheme to extend the method to smooth potentials, recovering the Van Vleck-Gutzwiller propagator. Finally, we discuss the educational application of the method.

  17. Convergence acceleration for time-independent first-order PDE using optimal PNB-approximations

    Energy Technology Data Exchange (ETDEWEB)

    Holmgren, S.; Branden, H. [Uppsala Univ. (Sweden)

    1996-12-31

    We consider solving time-independent (steady-state) flow problems in 2D or 3D governed by hyperbolic or {open_quotes}almost hyperbolic{close_quotes} systems of partial differential equations (PDE). Examples of such PDE are the Euler and the Navier-Stokes equations. The PDE is discretized using a finite difference or finite volume scheme with arbitrary order of accuracy. If the matrix B describes the discretized differential operator and u denotes the approximate solution, the discrete problem is given by a large system of equations.

  18. Thermal cascaded lattice Boltzmann method

    CERN Document Server

    Fei, Linlin

    2016-01-01

    In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is developed in combination with the double-distribution-function (DDF) approach. A density distribution function relaxed by the cascaded scheme is employed to solve the flow field, and a total energy distribution function relaxed by the BGK scheme is used to solve temperature field, where two distribution functions are coupled naturally. The forcing terms are incorporated by means of central moments, which is consistent with the previous force scheme [Premnath \\emph{et al.}, Phys. Rev. E \\textbf{80}, 036702 (2009)] but the derivation is more intelligible and the evolution process is simpler. In the method, the viscous heat dissipation and compression work are taken into account, the Prandtl number and specific-heat ratio are adjustable, the external force is considered directly without the Boussinesq assumption, and the low-Mach number compressible flows can also be simulated. The forcing scheme is tested by simulating a steady Taylor-Green f...

  19. An Infinite Restricted Boltzmann Machine.

    Science.gov (United States)

    Côté, Marc-Alexandre; Larochelle, Hugo

    2016-07-01

    We present a mathematical construction for the restricted Boltzmann machine (RBM) that does not require specifying the number of hidden units. In fact, the hidden layer size is adaptive and can grow during training. This is obtained by first extending the RBM to be sensitive to the ordering of its hidden units. Then, with a carefully chosen definition of the energy function, we show that the limit of infinitely many hidden units is well defined. As with RBM, approximate maximum likelihood training can be performed, resulting in an algorithm that naturally and adaptively adds trained hidden units during learning. We empirically study the behavior of this infinite RBM, showing that its performance is competitive to that of the RBM, while not requiring the tuning of a hidden layer size.

  20. Evaluation of the HTTR criticality and burnup calculations with continuous-energy and multigroup cross sections

    Energy Technology Data Exchange (ETDEWEB)

    Chiang, Min-Han; Wang, Jui-Yu [Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Section 2, Kung-Fu Road, Hsinchu 30013, Taiwan (China); Sheu, Rong-Jiun, E-mail: rjsheu@mx.nthu.edu.tw [Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Section 2, Kung-Fu Road, Hsinchu 30013, Taiwan (China); Department of Engineering System and Science, National Tsing Hua University, 101, Section 2, Kung-Fu Road, Hsinchu 30013, Taiwan (China); Liu, Yen-Wan Hsueh [Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Section 2, Kung-Fu Road, Hsinchu 30013, Taiwan (China); Department of Engineering System and Science, National Tsing Hua University, 101, Section 2, Kung-Fu Road, Hsinchu 30013, Taiwan (China)

    2014-05-01

    The High Temperature Engineering Test Reactor (HTTR) in Japan is a helium-cooled graphite-moderated reactor designed and operated for the future development of high-temperature gas-cooled reactors. Two detailed full-core models of HTTR have been established by using SCALE6 and MCNP5/X, respectively, to study its neutronic properties. Several benchmark problems were repeated first to validate the calculation models. Careful code-to-code comparisons were made to ensure that two calculation models are both correct and equivalent. Compared with experimental data, the two models show a consistent bias of approximately 20–30 mk overestimation in effective multiplication factor for a wide range of core states. Most of the bias could be related to the ENDF/B-VII.0 cross-section library or incomplete modeling of impurities in graphite. After that, a series of systematic analyses was performed to investigate the effects of cross sections on the HTTR criticality and burnup calculations, with special interest in the comparison between continuous-energy and multigroup results. Multigroup calculations in this study were carried out in 238-group structure and adopted the SCALE double-heterogeneity treatment for resonance self-shielding. The results show that multigroup calculations tend to underestimate the system eigenvalue by a constant amount of ∼5 mk compared to their continuous-energy counterparts. Further sensitivity studies suggest the differences between multigroup and continuous-energy results appear to be temperature independent and also insensitive to burnup effects.

  1. Multigroup Analysis in Partial Least Squares (PLS) Path Modeling: Alternative Methods and Empirical Results

    NARCIS (Netherlands)

    Sarstedt, Marko; Henseler, Jörg; Ringle, Christian M.

    2011-01-01

    Purpose – Partial least squares (PLS) path modeling has become a pivotal empirical research method in international marketing. Owing to group comparisons' important role in research on international marketing, we provide researchers with recommendations on how to conduct multigroup analyses in PLS p

  2. A discrete geometric approach to solving time independent Schrödinger equation

    Science.gov (United States)

    Specogna, Ruben; Trevisan, Francesco

    2011-02-01

    The time independent Schrödinger equation stems from quantum theory axioms as a partial differential equation. This work aims at providing a novel discrete geometric formulation of this equation in terms of integral variables associated with precise geometric elements of a pair of three-dimensional interlocked grids, one of them based on tetrahedra. We will deduce, in a purely geometric way, a computationally efficient discrete counterpart of the time independent Schrödinger equation in terms of a standard symmetric eigenvalue problem. Moreover boundary and interface conditions together with non homogeneity and anisotropy of the media involved are accounted for in a straightforward manner. This approach yields to a sensible computational advantage with respect to the finite element method, where a generalized eigenvalue problem has to be solved instead. Such a modeling tool can be used for analyzing a number of quantum phenomena in modern nano-structured devices, where the accounting of the real 3D geometry is a crucial issue.

  3. Pruning Boltzmann networks and hidden Markov models

    DEFF Research Database (Denmark)

    Pedersen, Morten With; Stork, D.

    1996-01-01

    We present sensitivity-based pruning algorithms for general Boltzmann networks. Central to our methods is the efficient calculation of a second-order approximation to the true weight saliencies in a cross-entropy error. Building upon previous work which shows a formal correspondence between linear...... Boltzmann chains and hidden Markov models (HMMs), we argue that our method can be applied to HMMs as well. We illustrate pruning on Boltzmann zippers, which are equivalent to two HMMs with cross-connection links. We verify that our second-order approximation preserves the rank ordering of weight saliencies...

  4. Multiphase lattice Boltzmann methods theory and application

    CERN Document Server

    Huang, Haibo; Lu, Xiyun

    2015-01-01

    Theory and Application of Multiphase Lattice Boltzmann Methods presents a comprehensive review of all popular multiphase Lattice Boltzmann Methods developed thus far and is aimed at researchers and practitioners within relevant Earth Science disciplines as well as Petroleum, Chemical, Mechanical and Geological Engineering. Clearly structured throughout, this book will be an invaluable reference  on the current state of all popular multiphase Lattice Boltzmann Methods (LBMs). The advantages and disadvantages of each model are presented in an accessible manner to enable the reader to choose the

  5. An introduction to the theory of the Boltzmann equation

    CERN Document Server

    Harris, Stewart

    2011-01-01

    Boltzmann's equation (or Boltzmann-like equations) appears extensively in such disparate fields as laser scattering, solid-state physics, nuclear transport, and beyond the conventional boundaries of physics and engineering, in the fields of cellular proliferation and automobile traffic flow. This introductory graduate-level course for students of physics and engineering offers detailed presentations of the basic modern theory of Boltzmann's equation, including representative applications using both Boltzmann's equation and the model Boltzmann equations developed within the text. It emphasizes

  6. Student understanding of the Boltzmann factor

    Science.gov (United States)

    Smith, Trevor I.; Mountcastle, Donald B.; Thompson, John R.

    2015-12-01

    [This paper is part of the Focused Collection on Upper Division Physics Courses.] We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations of student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions.

  7. Boltzmann and the art of flying

    CERN Document Server

    Dahmen, Silvio R

    2007-01-01

    One of the less known facets of Ludwig Boltzmann was that of an advocate of Aviation, one of the most challenging technological problems of his times. Boltzmann followed closely the studies of pioneers like Otto Lilienthal in Berlin, and during a lecture on a prestigious conference he vehemently defended further investments in the area. In this article I discuss his involvement with Aviation, his role in its development and his correspondence with two flight pioneers, Otto Lilienthal e Wilhelm Kress.

  8. Lattice Boltzmann approach for complex nonequilibrium flows.

    Science.gov (United States)

    Montessori, A; Prestininzi, P; La Rocca, M; Succi, S

    2015-10-01

    We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion.

  9. Matrix-valued Quantum Lattice Boltzmann Method

    CERN Document Server

    Mendl, Christian B

    2013-01-01

    We develop a numerical framework for the quantum analogue of the "classical" lattice Boltzmann method (LBM), with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac function. To accommodate the spin density matrix, the distribution functions become 2x2-matrix valued. We show that the efficient, commonly used BGK approximation of the collision operator is valid in the present setting. The framework could leverage the principles of LBM for simulating complex spin systems, with applications to spintronics.

  10. Acoustical Klein-Gordon equation: a time-independent perturbation analysis.

    Science.gov (United States)

    Forbes, Barbara J; Pike, E Roy

    2004-07-30

    The perturbation analysis of an ideal acoustical duct was first made by Rayleigh in 1878 and the result has since stood in the literature. However, the analysis is based on the assumption of potential and kinetic energy densities that remain constant as a change in cross section occurs, whereas, in fact, they may fluctuate significantly in comparison to the slowly varying "wave function," Psi(x,t), of the acoustical Klein-Gordon equation. The square of the time-independent eigenfunction, psi(2)(x), is directly proportional to the potential energy per unit length of fluid, and it is shown that it is precisely the perturbation in potential energy that defines correctly the eigenvalue shifts.

  11. Gray and multigroup radiation transport through 3D binary stochastic media with different sphere radii distributions

    Science.gov (United States)

    Olson, Gordon L.

    2017-03-01

    Gray and multigroup radiation is transported through 3D media consisting of spheres randomly placed in a uniform background. Comparisons are made between using constant radii spheres and three different distributions of sphere radii. Because of the computational cost of 3D calculations, only the lowest angle order, n=1, is tested. If the mean chord length is held constant, using different radii distributions makes little difference. This is true for both gray and multigroup solutions. 3D transport solutions are compared to 2D and 1D solutions with the same mean chord lengths. 2D disk and 3D sphere media give solutions that are nearly identical while 1D slab solutions are fundamentally different.

  12. Exploiting time-independent Hamiltonian structure as controls for manipulating quantum dynamics.

    Science.gov (United States)

    Beltrani, Vincent; Rabitz, Herschel

    2012-09-07

    The opportunities offered by utilizing time-independent Hamiltonian structure as controls are explored for manipulating quantum dynamics. Two scenarios are investigated using different manifestations of Hamiltonian structure to illustrate the generality of the concept. In scenario I, optimally shaped electrostatic potentials are generated to flexibly control electron scattering in a two-dimensional subsurface plane of a semiconductor. A simulation is performed showing the utility of optimally setting the individual voltages applied to a multi-pixel surface gate array in order to produce a spatially inhomogeneous potential within the subsurface scattering plane. The coherent constructive and destructive electron wave interferences are manipulated by optimally adjusting the potential shapes to alter the scattering patterns. In scenario II, molecular vibrational wave packets are controlled by means of optimally selecting the Hamiltonian structure in cooperation with an applied field. As an illustration of the concept, a collection (i.e., a level set) of dipole functions is identified where each member serves with the same applied electric field to produce the desired final transition probability. The level set algorithm additionally found Hamiltonian structure controls exhibiting desirable physical properties. The prospects of utilizing the applied field and Hamiltonian structure simultaneously as controls is also explored. The control scenarios I and II indicate the gains offered by algorithmically guided molecular or material discovery for manipulating quantum dynamics phenomenon.

  13. Two-parameter Failure Model Improves Time-independent and Time-dependent Failure Predictions

    Energy Technology Data Exchange (ETDEWEB)

    Huddleston, R L

    2004-01-27

    A new analytical model for predicting failure under a generalized, triaxial stress state was developed by the author and initially reported in 1984. The model was validated for predicting failure under elevated-temperature creep-rupture conditions. Biaxial data for three alloy steels, Types 304 and 316 stainless steels and Inconel 600, demonstrated two to three orders of magnitude reduction in the scatter of predicted versus observed creep-rupture times as compared to the classical failure models of Mises, Tresca, and Rankine. In 1990, the new model was incorporated into American Society of Mechanical Engineers (ASME) Code Case N47-29 for design of components operating under creep-rupture conditions. The current report provides additional validation of the model for predicting failure under time-independent conditions and also outlines a methodology for predicting failure under cyclic, time-dependent, creep-fatigue conditions. The later extension of the methodology may have the potential to improve failure predictions there as well. These results are relevant to most design applications, but they have special relevance to high-performance design applications such as components for high-pressure equipment, nuclear reactors, and jet engines.

  14. Two-parameter Failure Model Improves Time-independent and Time-dependent Failure Predictions

    Energy Technology Data Exchange (ETDEWEB)

    Huddleston, R L

    2004-01-27

    A new analytical model for predicting failure under a generalized, triaxial stress state was developed by the author and initially reported in 1984. The model was validated for predicting failure under elevated-temperature creep-rupture conditions. Biaxial data for three alloy steels, Types 304 and 316 stainless steels and Inconel 600, demonstrated two to three orders of magnitude reduction in the scatter of predicted versus observed creep-rupture times as compared to the classical failure models of Mises, Tresca, and Rankine. In 1990, the new model was incorporated into American Society of Mechanical Engineers (ASME) Code Case N47-29 for design of components operating under creep-rupture conditions. The current report provides additional validation of the model for predicting failure under time-independent conditions and also outlines a methodology for predicting failure under cyclic, time-dependent, creep-fatigue conditions. The later extension of the methodology may have the potential to improve failure predictions there as well. These results are relevant to most design applications, but they have special relevance to high-performance design applications such as components for high-pressure equipment, nuclear reactors, and jet engines.

  15. Time-independent and time-dependent contributions to the unavailability of standby safety system components

    Energy Technology Data Exchange (ETDEWEB)

    Lofgren, E.V. [Science Applications International Corp., Fairfax Station, VA (United States); Uryasev, S.; Samanta, P. [Brookhaven National Lab., Upton, NY (United States)

    1997-03-01

    The unavailability of standby safety system components due to failures in nuclear power plants is considered to involve a time independent and a time dependent part. The former relates to the component`s unavailability from demand stresses due to usage, and the latter represents the component`s unavailability due to standby time stresses related to the environment. In this paper, data from the nuclear plant reliability data system (NPRDS) were used to partition the component`s unavailability into the contributions from standby time stress (i.e., due to environmental factors) and demand stress (i.e., due to usage). Analyses are presented of motor operated valves (MOVs), motor driven pumps (MDPs), and turbine driven pumps (FDPs). MOVs fail predominantly (approx. 78%) from environmental factors (standby time stress failures). MDPs fail slightly more frequently from demand stresses (approx. 63%) than standby time stresses, while TDPs fail predominantly from standby time stresses (approx. 78%). Such partitions of component unavailability have many uses in risk informed and performance based regulation relating to modifications to Technical Specification, in-service testing, precise determination of dominant accident sequences, and implementation of maintenance rules.

  16. Search for time-independent Lorentz violation using muon neutrino to muon antineutrino transitions in MINOS

    CERN Document Server

    Adamson, P; Aurisano, A; Barr, G; Bishai, M; Blake, A; Bock, G J; Bogert, D; Cao, S V; Carroll, T J; Castromonte, C M; Chen, R; Childress, S; Coelho, J A B; Corwin, L; Cronin-Hennessy, D; de Jong, J K; de Rijck, S; Devan, A V; Devenish, N E; Diwan, M V; Escobar, C O; Evans, J J; Falk, E; Feldman, G J; Flanagan, W; Frohne, M V; Gabrielyan, M; Gallagher, H R; Germani, S; Gomes, R A; Goodman, M C; Gouffon, P; Graf, N; Gran, R; Grzelak, K; Habig, A; Hahn, S R; Hartnell, J; Hatcher, R; Holin, A; Huang, J; Hylen, J; Irwin, G M; Isvan, Z; James, C; Jensen, D; Kafka, T; Kasahara, S M S; Koizumi, G; Kordosky, M; Kreymer, A; Lang, K; Ling, J; Litchfield, P J; Lucas, P; Mann, W A; Marshak, M L; Mayer, N; McGivern, C; Medeiros, M M; Mehdiyev, R; Meier, J R; Messier, M D; Miller, W H; Mishra, S R; Sher, S Moed; Moore, C D; Mualem, L; Musser, J; Naples, D; Nelson, J K; Newman, H B; Nichol, R J; Nowak, J A; O'Connor, J; Orchanian, M; Pahlka, R B; Paley, J; Patterson, R B; Pawloski, G; Perch, A; Pfützner, M M; Phan, D D; Phan-Budd, S; Plunkett, R K; Poonthottathil, N; Qiu, X; Radovic, A; Rebel, B; Rosenfeld, C; Rubin, H A; Sail, P; Sanchez, M C; Schneps, J; Schreckenberger, A; Schreiner, P; Sharma, R; Sousa, A; Tagg, N; Talaga, R L; Thomas, J; Thomson, M A; Tian, X; Timmons, A; Todd, J; Tognini, S C; Toner, R; Torretta, D; Tzanakos, G; Urheim, J; Vahle, P; Viren, B; Weber, A; Webb, R C; White, C; Whitehead, L; Whitehead, L H; Wojcicki, S G; Zwaska, R

    2016-01-01

    Data from the MINOS experiment has been used to search for mixing between muon neutrinos and muon antineutrinos using a time-independent Lorentz-violating formalism derived from the Standard-Model Extension (SME). MINOS is uniquely capable of searching for muon neutrino-antineutrino mixing given its long baseline and ability to distinguish between neutrinos and antineutrinos on an event-by-event basis. Neutrino and antineutrino interactions were observed in the MINOS Near and Far Detectors from an exposure of 10.56$\\times10^{20}$ protons-on-target from the NuMI neutrino-optimized beam. No evidence was found for such transitions and new, highly stringent limits were placed on the SME coefficients governing them. We place the first limits on the SME parameters $(c_{L})^{TT}_{\\mu\\mu} $ and $(c_{L})^{TT}_{\\tau\\tau}$ at $-8.4\\times10^{-23} < (c_{L})^{TT}_{\\mu\\mu} < 8.0\\times10^{-23}$ and $-8.0\\times10^{-23} < (c_{L})^{TT}_{\\tau\\tau} < 8.4\\times10^{-23}$, and the world's best limits on the $\\tilde{g}^{Z...

  17. Time-independent and time-dependent contributions to the unavailability of standby safety system components

    Energy Technology Data Exchange (ETDEWEB)

    Lofgren, E.V. [Science Applications International Corp., Fairfax Station, VA (United States); Uryasev, S.; Samanta, P. [Brookhaven National Lab., Upton, NY (United States)

    1997-02-01

    The unavailability of standby safety system components due to failures in nuclear power plants is considered to involve a time-independent and a time-dependent part. The former relates to the component`s unavailability from demand stresses due to usage, and the latter represents the component`s unavailability due to standby-time stresses related to the environment. In this paper, data from the nuclear plant reliability data system (NPRDS) were used to partition the component`s unavailability into the contributions from standby-time stress (i.e., due to environmental factors) and demand stress (i.e., due to usage). Analyses are presented of motor-operated valves (MOVs), motor-driven pumps (MDPs), and turbine-driven pumps (TDPs). MOVs fail predominantly (approx. 78 %) from environmental factors (standby-time stress failures). MDPs fail slightly more frequently from demand stresses (approx. 63 %) than standby-time stresses, while TDPs fail predominantly from standby-time stresses (approx. 78 %). Such partitions of component unavailability have many uses in risk-informed and performance-based regulation relating to modifications to Technical Specification, in-service testing, precise determination of dominant accident sequences, and implementation of maintenance rules.

  18. The hydrogen tunneling splitting in malonaldehyde: A full-dimensional time-independent quantum mechanical method

    Science.gov (United States)

    Wu, Feng; Ren, Yinghui; Bian, Wensheng

    2016-08-01

    The accurate time-independent quantum dynamics calculations on the ground-state tunneling splitting of malonaldehyde in full dimensionality are reported for the first time. This is achieved with an efficient method developed by us. In our method, the basis functions are customized for the hydrogen transfer process which has the effect of greatly reducing the size of the final Hamiltonian matrix, and the Lanczos method and parallel strategy are used to further overcome the memory and central processing unit time bottlenecks. The obtained ground-state tunneling splitting of 24.5 cm-1 is in excellent agreement with the benchmark value of 23.8 cm-1 computed with the full-dimensional, multi-configurational time-dependent Hartree approach on the same potential energy surface, and we estimate that our reported value has an uncertainty of less than 0.5 cm-1. Moreover, the role of various vibrational modes strongly coupled to the hydrogen transfer process is revealed.

  19. Riccati and Ermakov Equations in Time-Dependent and Time-Independent Quantum Systems

    Directory of Open Access Journals (Sweden)

    Dieter Schuch

    2008-05-01

    Full Text Available The time-evolution of the maximum and the width of exact analytic wave packet (WP solutions of the time-dependent Schrödinger equation (SE represents the particle and wave aspects, respectively, of the quantum system. The dynamics of the maximum, located at the mean value of position, is governed by the Newtonian equation of the corresponding classical problem. The width, which is directly proportional to the position uncertainty, obeys a complex nonlinear Riccati equation which can be transformed into a real nonlinear Ermakov equation. The coupled pair of these equations yields a dynamical invariant which plays a key role in our investigation. It can be expressed in terms of a complex variable that linearizes the Riccati equation. This variable also provides the time-dependent parameters that characterize the Green's function, or Feynman kernel, of the corresponding problem. From there, also the relation between the classical and quantum dynamics of the systems can be obtained. Furthermore, the close connection between the Ermakov invariant and the Wigner function will be shown. Factorization of the dynamical invariant allows for comparison with creation/annihilation operators and supersymmetry where the partner potentials fulfil (real Riccati equations. This provides the link to a nonlinear formulation of time-independent quantum mechanics in terms of an Ermakov equation for the amplitude of the stationary state wave functions combined with a conservation law. Comparison with SUSY and the time-dependent problems concludes our analysis.

  20. Retraining of interjoint arm coordination after stroke using robot-assisted time-independent functional training

    Directory of Open Access Journals (Sweden)

    Elizabeth B. Brokaw, MS

    2011-05-01

    Full Text Available We have developed a haptic-based approach for retraining of interjoint coordination following stroke called time-independent functional training (TIFT and implemented this mode in the ARMin III robotic exoskeleton. The ARMin III robot was developed by Drs. Robert Riener and Tobias Nef at the Swiss Federal Institute of Technology Zurich (Eidgenossische Technische Hochschule Zurich, or ETH Zurich, in Zurich, Switzerland. In the TIFT mode, the robot maintains arm movements within the proper kinematic trajectory via haptic walls at each joint. These arm movements focus training of interjoint coordination with highly intuitive real-time feedback of perform-ance; arm movements advance within the trajectory only if their movement coordination is correct. In initial testing, 37 nondisabled subjects received a single session of learning of a complex pattern. Subjects were randomized to TIFT or visual demonstration or moved along with the robot as it moved though the pattern (time-dependent [TD] training. We examined visual demonstration to separate the effects of action observation on motor learning from the effects of the two haptic guidance methods. During these training trials, TIFT subjects reduced error and interaction forces between the robot and arm, while TD subject performance did not change. All groups showed significant learning of the trajectory during unassisted recall trials, but we observed no difference in learning between groups, possibly because this learning task is dominated by vision. Further testing in stroke populations is warranted.

  1. Search for Time-Independent Lorentz Violation using Muon Neutrino to Muon Antineutrino Transitions in MINOS

    Energy Technology Data Exchange (ETDEWEB)

    Adamson, P.; et al.

    2016-05-10

    Data from the MINOS experiment has been used to search for mixing between muon neutrinos and muon antineutrinos using a time-independent Lorentz-violating formalism derived from the Standard-Model Extension (SME). MINOS is uniquely capable of searching for muon neutrino-antineutrino mixing given its long baseline and ability to distinguish between neutrinos and antineutrinos on an event-by-event basis. Neutrino and antineutrino interactions were observed in the MINOS Near and Far Detectors from an exposure of 10.56$\\times10^{20}$ protons-on-target from the NuMI neutrino-optimized beam. No evidence was found for such transitions and new, highly stringent limits were placed on the SME coefficients governing them. We place the first limits on the SME parameters $(c_{L})^{TT}_{\\mu\\mu} $ and $(c_{L})^{TT}_{\\tau\\tau}$ at $-8.4\\times10^{-23} < (c_{L})^{TT}_{\\mu\\mu} < 8.0\\times10^{-23}$ and $-8.0\\times10^{-23} < (c_{L})^{TT}_{\\tau\\tau} < 8.4\\times10^{-23}$, and the world's best limits on the $\\tilde{g}^{ZT}_{\\mu\\overline{\\mu}}$ and $\\tilde{g}^{ZT}_{\\tau\\overline{\\tau}}$ parameters at $|\\tilde{g}^{ZT}_{\\mu\\overline{\\mu}}| < 3.3\\times 10^{-23}$ and $|\\tilde{g}^{ZT}_{\\tau\\overline{\\tau}}| < 3.3\\times 10^{-23}$, all limits quoted at $3\\sigma$.

  2. A multigroup radiation diffusion test problem: Comparison of code results with analytic solution

    Energy Technology Data Exchange (ETDEWEB)

    Shestakov, A I; Harte, J A; Bolstad, J H; Offner, S R

    2006-12-21

    We consider a 1D, slab-symmetric test problem for the multigroup radiation diffusion and matter energy balance equations. The test simulates diffusion of energy from a hot central region. Opacities vary with the cube of the frequency and radiation emission is given by a Wien spectrum. We compare results from two LLNL codes, Raptor and Lasnex, with tabular data that define the analytic solution.

  3. EXTENSION OF THE 1D FOUR-GROUP ANALYTIC NODAL METHOD TO FULL MULTIGROUP

    Energy Technology Data Exchange (ETDEWEB)

    B. D. Ganapol; D. W. Nigg

    2008-09-01

    In the mid 80’s, a four-group/two-region, entirely analytical 1D nodal benchmark appeared. It was readily acknowledged that this special case was as far as one could go in terms of group number and still achieve an analytical solution. In this work, we show that by decomposing the solution to the multigroup diffusion equation into homogeneous and particular solutions, extension to any number of groups is a relatively straightforward exercise using the mathematics of linear algebra.

  4. Phantom cosmology and Boltzmann brains problem

    CERN Document Server

    Astashenok, Artyom V; Yurov, Valerian V

    2013-01-01

    We consider the well-known Boltzmann brains problem in frames of simple phantom energy models with little rip, big rip and big freeze singularity. It is showed that these models (i) satisfy to observational data and (ii) may be free from Boltzmann brains problem. The human observers in phantom models can exist only in during for a certain period $tBoltzmann brains problem doesn't appear. The bounds on model parameters derived from such requirement don't contradict to allowable range from observational data.

  5. Boltzmann-Electron Model in Aleph.

    Energy Technology Data Exchange (ETDEWEB)

    Hughes, Thomas Patrick; Hooper, Russell

    2014-11-01

    We apply the Boltzmann-electron model in the electrostatic, particle-in-cell, finite- element code Aleph to a plasma sheath. By assuming a Boltzmann energy distribution for the electrons, the model eliminates the need to resolve the electron plasma fre- quency, and avoids the numerical "grid instability" that can cause unphysical heating of electrons. This allows much larger timesteps to be used than with kinetic electrons. Ions are treated with the standard PIC algorithm. The Boltzmann-electron model re- quires solution of a nonlinear Poisson equation, for which we use an iterative Newton solver (NOX) from the Trilinos Project. Results for the spatial variation of density and voltage in the plasma sheath agree well with an analytic model

  6. How good is the Lattice Boltzmann method?

    Science.gov (United States)

    Kocheemoolayil, Joseph; Barad, Michael; Kiris, Cetin

    2016-11-01

    Conflicting opinions exist in literature regarding how efficient the lattice Boltzmann method is relative to high-order finite difference approximations of the Navier-Stokes equations on Cartesian meshes, especially at high Mach numbers. We address the question from the pragmatic viewpoint of a practitioner. Dispersion, dissipation and aliasing errors of various lattice Boltzmann models are systematically quantified. The number of floating point operations and memory required for a desired accuracy level are carefully compared for the two numerical methods. Turbulent kinetic energy budgets for several standard test cases such as the decaying Taylor-Green vortex problem are used to evaluate how effective the stabilization mechanisms necessary for lattice Boltzmann method at high Reynolds numbers are. Detailed comments regarding the cyclomatic complexity of the underlying software, scalability of the underlying algorithm on state-of-the-art high-performance computing platforms and wall clock times and relative accuracy for selected simulations conducted using the two approaches are also made.

  7. Hierarchical Boltzmann simulations and model error estimation

    Science.gov (United States)

    Torrilhon, Manuel; Sarna, Neeraj

    2017-08-01

    A hierarchical simulation approach for Boltzmann's equation should provide a single numerical framework in which a coarse representation can be used to compute gas flows as accurately and efficiently as in computational fluid dynamics, but a subsequent refinement allows to successively improve the result to the complete Boltzmann result. We use Hermite discretization, or moment equations, for the steady linearized Boltzmann equation for a proof-of-concept of such a framework. All representations of the hierarchy are rotationally invariant and the numerical method is formulated on fully unstructured triangular and quadrilateral meshes using a implicit discontinuous Galerkin formulation. We demonstrate the performance of the numerical method on model problems which in particular highlights the relevance of stability of boundary conditions on curved domains. The hierarchical nature of the method allows also to provide model error estimates by comparing subsequent representations. We present various model errors for a flow through a curved channel with obstacles.

  8. Adaptive Lattice Boltzmann Model for Compressible Flows

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    A new lattice Boltzmann model for compressible flows is presented. The main difference from the standard lattice Boltzmann model is that the particle velocities are no longer constant, but vary with the mean velocity and internal energy. The adaptive nature of the particle velocities permits the mean flow to have a high Mach number. The introduction of a particle potential energy makes the model suitable for a perfect gas with arbitrary specific heat ratio. The Navier-Stokes (N-S) equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation. Two kinds of simulations have been carried out on the hexagonal lattice to test the proposed model. One is the Sod shock-tube simulation. The other is a strong shock of Mach number 5.09 diffracting around a corner.

  9. Overview of the Uniform California Earthquake Rupture Forecast Version 3 (UCERF3) Time-Independent Model

    Science.gov (United States)

    Field, E. H.; Arrowsmith, R.; Biasi, G. P.; Bird, P.; Dawson, T. E.; Felzer, K. R.; Jackson, D. D.; Johnson, K. M.; Jordan, T. H.; Madugo, C. M.; Michael, A. J.; Milner, K. R.; Page, M. T.; Parsons, T.; Powers, P.; Shaw, B. E.; Thatcher, W. R.; Weldon, R. J.; Zeng, Y.

    2013-12-01

    We present the time-independent component of the Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3), where the primary achievements have been to relax fault segmentation and include multi-fault ruptures, both limitations of UCERF2. The rates of all earthquakes are solved for simultaneously, and from a broader range of data, using a system-level 'grand inversion' that is both conceptually simple and extensible. The inverse problem is large and underdetermined, so a range of models is sampled using an efficient simulated annealing algorithm. The approach is more derivative than prescriptive (e.g., magnitude-frequency distributions are no longer assumed), so new analysis tools were developed for exploring solutions. Epistemic uncertainties were also accounted for using 1440 alternative logic tree branches, necessitating access to supercomputers. The most influential uncertainties include alternative deformation models (fault slip rates), a new smoothed seismicity algorithm, alternative values for the total rate of M≥5 events, and different scaling relationships, virtually all of which are new. As a notable first, three deformation models are based on kinematically consistent inversions of geodetic and geologic data, also providing slip-rate constraints on faults previously excluded due to lack of geologic data. The grand inversion constitutes a system-level framework for testing hypotheses and balancing the influence of different experts. For example, we demonstrate serious challenges with the Gutenberg-Richter hypothesis for individual faults. UCERF3 is still an approximation of the system, however, and the range of models is limited (e.g., constrained to stay close to UCERF2). Nevertheless, UCERF3 removes the apparent UCERF2 over-prediction of M6.5-7 earthquake rates, and also includes types of multi-fault ruptures seen in nature. While UCERF3 fits the data better than UCERF2 overall, there may be areas that warrant further site

  10. Incipient cytotoxicity: A time-independent measure of cytotoxic potency in vitro.

    Science.gov (United States)

    Gülden, Michael; Kähler, Daria; Seibert, Hasso

    2015-09-01

    Time is an important determinant of toxicity but largely ignored in in vitro toxicity assays where exposure times chosen are rather arbitrary. To investigate the impact of time on the cytotoxic potency of chemicals in vitro, the concentration dependent cytotoxic action of selected chemicals (surfactants, metals, oxidative stressors, a mitochondrial poison) was determined after various exposure times (1-72 h) in cultures of Balb/c 3T3 cells. Time affected the cytotoxic potency as well as the cytotoxic efficacy. The median cytotoxic concentrations, EC50, decreased and in most cases approached an "incipient" value, EC50,∞, within 72 h. Cytotoxicity due to mitochondrial insult occurred after a threshold time which was dependent on the medium glucose concentration. Within the chemicals studied the extent of potency change with time ranged from 3- to >1000-fold and the "time to incipient cytotoxicity", tic, from 4 to >72 h. Hence, also the relative cytotoxic potencies depend on exposure time. Ignoring this may lead to severe bias in toxicological hazard and risk assessment. Therefore it is recommended to determine the incipient cytotoxic potency of chemical compounds, represented by, e.g., the incipient median effect (EC50,∞), no effect (NEC∞) or lowest effect concentrations (LEC∞) instead of measures obtained after arbitrary exposure times. If this is not possible, the 72 h-potency measurements appear to be useful surrogates. These time-independent incipient potency values can be reasonably compared between substances, endpoints, cells and biological test systems and may serve to define points of departure for quantitative in vitro-in vivo extrapolations.

  11. Sample problems for the novice user of the AMPX-II system. [For generating coupled multigroup neutron--gamma libraries, in FORTRAN IV for IBM 360/91

    Energy Technology Data Exchange (ETDEWEB)

    Ford, W.E. III; Roussin, R.W.; Petrie, L.M.; Diggs, B.R.; Comolander, H.E.

    1979-01-01

    Contents of the IBM version of the APMX system distributed by the Radiation Shielding Information Center (APMX-II) are described. Sample problems which demonstrate the procedure for implementing AMPX-II modules to generate point cross sections; generate multigroup neutron, photon production, and photon interaction cross sections for various transport codes; collapse multigroup cross sections; check, edit, and punch multigroup cross sections; and execute a one-dimensional discrete ordinates transport calculation are detailed. 25 figures, 9 tables.

  12. Kinetic Boltzmann, Vlasov and Related Equations

    CERN Document Server

    Sinitsyn, Alexander; Vedenyapin, Victor

    2011-01-01

    Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in

  13. Grid refinement for entropic lattice Boltzmann models.

    Science.gov (United States)

    Dorschner, B; Frapolli, N; Chikatamarla, S S; Karlin, I V

    2016-11-01

    We propose a multidomain grid refinement technique with extensions to entropic incompressible, thermal, and compressible lattice Boltzmann models. Its validity and accuracy are assessed by comparison to available direct numerical simulation and experiment for the simulation of isothermal, thermal, and viscous supersonic flow. In particular, we investigate the advantages of grid refinement for the setups of turbulent channel flow, flow past a sphere, Rayleigh-Bénard convection, as well as the supersonic flow around an airfoil. Special attention is paid to analyzing the adaptive features of entropic lattice Boltzmann models for multigrid simulations.

  14. Grid refinement for entropic lattice Boltzmann models

    CERN Document Server

    Dorschner, B; Chikatamarla, S S; Karlin, I V

    2016-01-01

    We propose a novel multi-domain grid refinement technique with extensions to entropic incompressible, thermal and compressible lattice Boltzmann models. Its validity and accuracy are accessed by comparison to available direct numerical simulation and experiment for the simulation of isothermal, thermal and viscous supersonic flow. In particular, we investigate the advantages of grid refinement for the set-ups of turbulent channel flow, flow past a sphere, Rayleigh-Benard convection as well as the supersonic flow around an airfoil. Special attention is payed to analyzing the adaptive features of entropic lattice Boltzmann models for multi-grid simulations.

  15. Fast lattice Boltzmann solver for relativistic hydrodynamics.

    Science.gov (United States)

    Mendoza, M; Boghosian, B M; Herrmann, H J; Succi, S

    2010-07-01

    A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud. This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativistic outflows.

  16. Celebrating Cercignani's conjecture for the Boltzmann equation

    KAUST Repository

    Villani, Cédric

    2011-01-01

    Cercignani\\'s conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann\\'s nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s. © American Institute of Mathematical Sciences.

  17. Fluctuating lattice Boltzmann method for the diffusion equation.

    Science.gov (United States)

    Wagner, Alexander J; Strand, Kyle

    2016-09-01

    We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

  18. Multispeed models in off-lattice Boltzmann simulations

    NARCIS (Netherlands)

    Bardow, A.; Karlin, I.V.; Gusev, A.A.

    2008-01-01

    The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models [S. Chikatamarla et al., Phys. Rev. Lett. 97 190601 (2006)] by exploiting the flexibility offered by off-lattice Boltzmann methods.

  19. A Fluctuating Lattice Boltzmann Method for the Diffusion Equation

    CERN Document Server

    Wagner, Alexander J

    2016-01-01

    We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

  20. A Capacity-Restraint Transit Assignment Model When a Predetermination Method Indicates the Invalidity of Time Independence

    Directory of Open Access Journals (Sweden)

    Haoyang Ding

    2015-01-01

    Full Text Available The statistical independence of time of every two adjacent bus links plays a crucial role in deciding the feasibility of using many mathematical models to analyze urban transit networks. Traditional research generally ignores the time independence that acts as the ground of their models. Assumption is usually made that time independence of every two adjacent links is sound. This is, however, actually groundless and probably causes problematic conclusions reached by corresponding models. Many transit assignment models such as multinomial probit-based models lose their effects when the time independence is not valid. In this paper, a simple method to predetermine the time independence is proposed. Based on the predetermination method, a modified capacity-restraint transit assignment method aimed at engineering practice is put forward and tested through a small contrived network and a case study in Nanjing city, China, respectively. It is found that the slope of regression equation between the mean and standard deviation of normal distribution acts as the indicator of time independence at the same time. Besides, our modified assignment method performs better than the traditional one with more reasonable results while keeping the property of simplicity well.

  1. The Bloch wave operator: generalizations and applications: Part I. The time-independent case

    Energy Technology Data Exchange (ETDEWEB)

    Killingbeck, John P [Mathematics Department, University of Hull, Hull HU6 7RX (United Kingdom); Jolicard, Georges [Observatoire de Besancon (UMR-CNRS 6091), Universite de Franche-Comte, 41 bis, Avenue de l' Observatoire, 25000 Besancon (France)

    2003-05-23

    This is part 1 of a two-part review on wave operator theory and methods. The basic theory of the time-independent wave operator is presented in terms of partitioned matrix theory for the benefit of general readers, with a discussion of the links between the matrix and projection operator approaches. The matrix approach is shown to lead to simple derivations of the wave operators and effective Hamiltonians of Loewdin, Bloch, Des Cloizeaux and Kato as well as to some associated variational forms. The principal approach used throughout stresses the solution of the nonlinear equation for the reduced wave operator, leading to the construction of the effective Hamiltonians of Bloch and of Des Cloizeaux. Several mathematical techniques which are useful in implementing this approach are explained, some of them being relatively little known in the area of wave operator calculations. The theoretical discussion is accompanied by several specimen numerical calculations which apply the described techniques to a selection of test matrices taken from the previous literature on wave operator methods. The main emphasis throughout is on the use of numerical methods which use iterative or perturbation algorithms, with simple Pade approximant methods being found sufficient to deal with most of the cases of divergence which are encountered. The use of damping factors and relaxation parameters is found to be effective in stabilizing calculations which use the energy-dependent effective Hamiltonian of Loewdin. In general the computations suggest that the numerical applications of the nonlinear equation for the reduced wave operator are best carried out with the equation split into a pair of equations in which the Bloch effective Hamiltonian appears as a separate entity. The presentation of the theoretical and computational details throughout is accompanied by references to and discussion of many works which have used wave operator methods in physics, chemistry and engineering. Some of

  2. Uniform California earthquake rupture forecast, version 3 (UCERF3): the time-independent model

    Science.gov (United States)

    Field, Edward H.; Biasi, Glenn P.; Bird, Peter; Dawson, Timothy E.; Felzer, Karen R.; Jackson, David D.; Johnson, Kaj M.; Jordan, Thomas H.; Madden, Christopher; Michael, Andrew J.; Milner, Kevin R.; Page, Morgan T.; Parsons, Thomas; Powers, Peter M.; Shaw, Bruce E.; Thatcher, Wayne R.; Weldon, Ray J.; Zeng, Yuehua; ,

    2013-01-01

    In this report we present the time-independent component of the Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3), which provides authoritative estimates of the magnitude, location, and time-averaged frequency of potentially damaging earthquakes in California. The primary achievements have been to relax fault segmentation assumptions and to include multifault ruptures, both limitations of the previous model (UCERF2). The rates of all earthquakes are solved for simultaneously, and from a broader range of data, using a system-level "grand inversion" that is both conceptually simple and extensible. The inverse problem is large and underdetermined, so a range of models is sampled using an efficient simulated annealing algorithm. The approach is more derivative than prescriptive (for example, magnitude-frequency distributions are no longer assumed), so new analysis tools were developed for exploring solutions. Epistemic uncertainties were also accounted for using 1,440 alternative logic tree branches, necessitating access to supercomputers. The most influential uncertainties include alternative deformation models (fault slip rates), a new smoothed seismicity algorithm, alternative values for the total rate of M≥5 events, and different scaling relationships, virtually all of which are new. As a notable first, three deformation models are based on kinematically consistent inversions of geodetic and geologic data, also providing slip-rate constraints on faults previously excluded because of lack of geologic data. The grand inversion constitutes a system-level framework for testing hypotheses and balancing the influence of different experts. For example, we demonstrate serious challenges with the Gutenberg-Richter hypothesis for individual faults. UCERF3 is still an approximation of the system, however, and the range of models is limited (for example, constrained to stay close to UCERF2). Nevertheless, UCERF3 removes the apparent UCERF2 overprediction of

  3. The Non-Classical Boltzmann Equation, and Diffusion-Based Approximations to the Boltzmann Equation

    CERN Document Server

    Frank, Martin; Larsen, Edward W; Vasques, Richard

    2014-01-01

    We show that several diffusion-based approximations (classical diffusion or SP1, SP2, SP3) to the linear Boltzmann equation can (for an infinite, homogeneous medium) be represented exactly by a non-classical transport equation. As a consequence, we indicate a method to solve diffusion-based approximations to the Boltzmann equation via Monte Carlo, with only statistical errors - no truncation errors.

  4. Full Boltzmann equations for leptogenesis including scattering

    CERN Document Server

    Hahn-Woernle, F; Wong, Y Y Y

    2009-01-01

    We study the evolution of a cosmological baryon asymmetry produced via leptogenesis by means of the full classical Boltzmann equations, without the assumption of kinetic equilibrium and including all quantum statistical factors. Beginning with the full mode equations we derive the usual equations of motion for the right-handed neutrino number density and integrated lepton asymmetry, and show explicitly the impact of each assumption on these quantities. For the first time, we investigate also the effects of scattering of the right-handed neutrino with the top quark to leading order in the Yukawa couplings by means of the full Boltzmann equations. We find that in our full Boltzmann treatment the final lepton asymmetry can be suppressed by as much as a factor of 1.5 in the weak wash-out regime (K1), the full Boltzmann treatment and the integrated approach give nearly identical final lepton asymmetries (within 10 % of each other at K>3). Finally, we show that the opposing effects of quantum statistics on decays/i...

  5. Stefan-Boltzmann law for massive photons

    CERN Document Server

    Moreira, E S

    2015-01-01

    Thirty years ago a paper appeared in the literature generalizing the Stefan-Boltzmann law to include massive photons. The paper suffers from a flaw though: it assumes that a massive photon travels at the speed of (massless) light. The present work fixes the mistake and presents the correct formula for the radiance.

  6. Stefan-Boltzmann Law for Massive Photons

    Science.gov (United States)

    Moreira, E. S.; Ribeiro, T. G.

    2016-08-01

    This paper generalizes the Stefan-Boltzmann law to include massive photons. A crucial ingredient to obtain the correct formula for the radiance is to realize that a massive photon does not travel at the speed of (massless) light. It follows that, contrary to what could be expected, the radiance is not proportional to the energy density times the speed of light.

  7. Boltzmann und das Ende des mechanistischen Weltbildes

    CERN Document Server

    Renn, Jürgen

    2007-01-01

    Der Wissenschaftshistoriker und Physiker Jürgen Renn untersucht die Rolle des österreichischen Physikers und Philosophen Ludwig Boltzmann (18441906) bei der Entwicklung der modernen Physik. Boltzmann war einer der letzen Vertreter des mechanistischen Weltbildes und stand somit am Ende eines Zeitalters. Renn porträtiert den Wissenschaftler aber als einen Pionier der modernen Physik, dessen Beschäftigung mit den inneren Spannungen der klassischen Physik ihn visionär zukünftige Fragestellungen aufgreifen ließ. So befasste sich Boltzmann etwa mit den Grenzproblemen zwischen Mechanik und Thermodynamik, die ihn zur Entwicklung immer raffinierterer Instrumente der statistischen Physik antrieb, die schließlich zu Schlüsselinstrumenten der modernen Physik wurden. Boltzmanns Werk steht somit am Übergang vom mechanistischen Weltbild zur Relativitäts- und Quantentheorie. Der Aussage des viel bekannteren Physikers Albert Einstein, dass Fantasie wichtiger sei als Wissen, hält Jürgen Renn im Hinblick auf Leben ...

  8. Entropic lattice Boltzmann model for Burgers's equation.

    Science.gov (United States)

    Boghosian, Bruce M; Love, Peter; Yepez, Jeffrey

    2004-08-15

    Entropic lattice Boltzmann models are discrete-velocity models of hydrodynamics that possess a Lyapunov function. This feature makes them useful as nonlinearly stable numerical methods for integrating hydrodynamic equations. Over the last few years, such models have been successfully developed for the Navier-Stokes equations in two and three dimensions, and have been proposed as a new category of subgrid model of turbulence. In the present work we develop an entropic lattice Boltzmann model for Burgers's equation in one spatial dimension. In addition to its pedagogical value as a simple example of such a model, our result is actually a very effective way to simulate Burgers's equation in one dimension. At moderate to high values of viscosity, we confirm that it exhibits no trace of instability. At very small values of viscosity, however, we report the existence of oscillations of bounded amplitude in the vicinity of the shock, where gradient scale lengths become comparable with the grid size. As the viscosity decreases, the amplitude at which these oscillations saturate tends to increase. This indicates that, in spite of their nonlinear stability, entropic lattice Boltzmann models may become inaccurate when the ratio of gradient scale length to grid spacing becomes too small. Similar inaccuracies may limit the utility of the entropic lattice Boltzmann paradigm as a subgrid model of Navier-Stokes turbulence.

  9. General relativistic Boltzmann equation, I: Covariant treatment

    NARCIS (Netherlands)

    Debbasch, F.; van Leeuwen, W.A.

    2009-01-01

    This series of two articles aims at dissipating the rather dense haze existing in the present literature around the General Relativistic Boltzmann equation. In this first article, the general relativistic one-particle distribution function in phase space is defined as an average of delta functions.

  10. Geometric variations of the Boltzmann entropy

    OpenAIRE

    Kalogeropoulos, Nikos

    2008-01-01

    We perform a calculation of the first and second order infinitesimal variations, with respect to energy, of the Boltzmann entropy of constant energy hypersurfaces of a system with a finite number of degrees of freedom. We comment on the stability interpretation of the second variation in this framework.

  11. THREE WAY DECOMPOSITION FOR THE BOLTZMANN EQUATION

    Institute of Scientific and Technical Information of China (English)

    Ilgis Ibragimov; Sergej Rjasanow

    2009-01-01

    The initial value problem for the spatially homogeneous Boltzmann equation is considered. A deterministic numerical scheme for this problem is developed by the use of the three way decomposition of the unknown function as well as of the collision integral. On this way, almost linear complexity of the algorithm is achieved. Some numerical examples are presented.

  12. Boltzmann Samplers for Colored Combinatorial Objects

    CERN Document Server

    Bodini, Olivier

    2009-01-01

    In this paper, we give a general framework for the Boltzmann generation of colored objects belonging to combinatorial constructible classes. We propose an intuitive notion called profiled objects which allows the sampling of size-colored objects (and also of k-colored objects) although the corresponding class cannot be described by an analytic ordinary generating function.

  13. Measurement invariance via multigroup SEM: Issues and solutions with chi-square-difference tests.

    Science.gov (United States)

    Yuan, Ke-Hai; Chan, Wai

    2016-09-01

    Multigroup structural equation modeling (SEM) plays a key role in studying measurement invariance and in group comparison. When population covariance matrices are deemed not equal across groups, the next step to substantiate measurement invariance is to see whether the sample covariance matrices in all the groups can be adequately fitted by the same factor model, called configural invariance. After configural invariance is established, cross-group equalities of factor loadings, error variances, and factor variances-covariances are then examined in sequence. With mean structures, cross-group equalities of intercepts and factor means are also examined. The established rule is that if the statistic at the current model is not significant at the level of .05, one then moves on to testing the next more restricted model using a chi-square-difference statistic. This article argues that such an established rule is unable to control either Type I or Type II errors. Analysis, an example, and Monte Carlo results show why and how chi-square-difference tests are easily misused. The fundamental issue is that chi-square-difference tests are developed under the assumption that the base model is sufficiently close to the population, and a nonsignificant chi-square statistic tells little about how good the model is. To overcome this issue, this article further proposes that null hypothesis testing in multigroup SEM be replaced by equivalence testing, which allows researchers to effectively control the size of misspecification before moving on to testing a more restricted model. R code is also provided to facilitate the applications of equivalence testing for multigroup SEM. (PsycINFO Database Record

  14. Simulate-HEX - The multi-group diffusion equation in hexagonal-z geometry

    Energy Technology Data Exchange (ETDEWEB)

    Lindahl, S. O. [Studsvik Scandpower, Stensborgsg. 4, SE-72132 Vaesteraes (Sweden)

    2013-07-01

    The multigroup diffusion equation is solved for the hexagonal-z geometry by dividing each hexagon into 6 triangles. In each triangle, the Fourier solution of the wave equation is approximated by 8 plane waves to describe the intra-nodal flux accurately. In the end an efficient Finite Difference like equation is obtained. The coefficients of this equation depend on the flux solution itself and they are updated once per power/void iteration. A numerical example demonstrates the high accuracy of the method. (authors)

  15. Asymptotic behavior of stochastic multi-group epidemic models with distributed delays

    Science.gov (United States)

    Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

    2017-02-01

    In this paper, we introduce stochasticity into multi-group epidemic models with distributed delays and general kernel functions. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by using the method of stochastic Lyapunov functions, we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the stochastic system oscillates around the disease-free equilibrium E0, while if R0 > 1, the solution of the stochastic model fluctuates around the endemic equilibrium E∗. Moreover, we also establish sufficient conditions of these results.

  16. Multigroup radiation transport in one-dimensional Lagrangian radiation-hydrodynamics codes

    Energy Technology Data Exchange (ETDEWEB)

    Rottler, J.S.

    1987-01-01

    A new treatment of radiation transport has been added to the Lagrangian radiation-hydrodynamics code CHARTD. The new energy flow model was derived based on the assumption that the directional dependence of the radiation energy density can be represented by the first two terms of a spherical harmonic expansion, and that the photon energy spectrum can be partitioned into energy groups. The time derivative in the second moment equation, which is usually neglected, is retained in this implementation of the multigroup P-1 approximation. An accelerated iterative scheme is used to solve the difference equations. The new energy flow model and the iterative scheme will be described.

  17. Geospatial Data Fusion and Multigroup Decision Support for Surface Water Quality Management

    Science.gov (United States)

    Sun, A. Y.; Osidele, O.; Green, R. T.; Xie, H.

    2010-12-01

    Social networking and social media have gained significant popularity and brought fundamental changes to many facets of our everyday life. With the ever-increasing adoption of GPS-enabled gadgets and technology, location-based content is likely to play a central role in social networking sites. While location-based content is not new to the geoscience community, where geographic information systems (GIS) are extensively used, the delivery of useful geospatial data to targeted user groups for decision support is new. Decision makers and modelers ought to make more effective use of the new web-based tools to expand the scope of environmental awareness education, public outreach, and stakeholder interaction. Environmental decision processes are often rife with uncertainty and controversy, requiring integration of multiple sources of information and compromises between diverse interests. Fusing of multisource, multiscale environmental data for multigroup decision support is a challenging task. Toward this goal, a multigroup decision support platform should strive to achieve transparency, impartiality, and timely synthesis of information. The latter criterion often constitutes a major technical bottleneck to traditional GIS-based media, featuring large file or image sizes and requiring special processing before web deployment. Many tools and design patterns have appeared in recent years to ease the situation somewhat. In this project, we explore the use of Web 2.0 technologies for “pushing” location-based content to multigroups involved in surface water quality management and decision making. In particular, our granular bottom-up approach facilitates effective delivery of information to most relevant user groups. Our location-based content includes in-situ and remotely sensed data disseminated by NASA and other national and local agencies. Our project is demonstrated for managing the total maximum daily load (TMDL) program in the Arroyo Colorado coastal river basin

  18. Multi-group pin power reconstruction method based on colorset form functions

    Institute of Scientific and Technical Information of China (English)

    HUANG Hao

    2009-01-01

    A multi-group pin power reconstruction method that fully exploits nodal information obtained from global coarse mesh solution has been developed.It expands the intra-nodal flux distributions into nonseparable semi-analytic basis functions,and a colorset based form function generating method is proposed,which can accurately model the spectral interaction occurring at assembly interface.To demonstrate its accuracy and applicability to realistic problems,the new method is tested against two benchmark problems,including a mixed-oxide fuel problem.The results show that the new method is comparable in accuracy to fine-mesh methods.

  19. Global Stability of Multigroup SIRS Epidemic Model with Varying Population Sizes and Stochastic Perturbation around Equilibrium

    Directory of Open Access Journals (Sweden)

    Xiaoming Fan

    2014-01-01

    Full Text Available We discuss multigroup SIRS (susceptible, infectious, and recovered epidemic models with random perturbations. We carry out a detailed analysis on the asymptotic behavior of the stochastic model; when reproduction number ℛ0>1, we deduce the globally asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time average. Numerical methods are employed to illustrate the dynamic behavior of the model and simulate the system of equations developed. The effect of the rate of immunity loss on susceptible and recovered individuals is also analyzed in the deterministic model.

  20. Uncertainty in reactor lattice physics calculations. The effect of dilution on the covariance of multigroup cross sections

    Energy Technology Data Exchange (ETDEWEB)

    McEwan, C.; Ball, M.; Novog, D., E-mail: mcewac2@mcmaster.ca [McMaster Univ., Hamilton, Ontario (Canada)

    2013-07-01

    Simulation results are of little use if nothing is known about the uncertainty in the results. In order to assess the uncertainty in a set of output parameters due to uncertainty in a set of input parameters, knowledge of the covariance between input parameters is required. Current practice is to apply the covariance between multigroup cross sections at infinite dilution to all cross sections including those at non-infinite dilutions. In this work, the effect of dilution on multigroup cross section covariance is investigated as well as the effect on the covariance between the few group homogenized cross sections produced by lattice code DRAGON. (author)

  1. Nonequilibrium thermodynamics of restricted Boltzmann machines

    Science.gov (United States)

    Salazar, Domingos S. P.

    2017-08-01

    In this work, we analyze the nonequilibrium thermodynamics of a class of neural networks known as restricted Boltzmann machines (RBMs) in the context of unsupervised learning. We show how the network is described as a discrete Markov process and how the detailed balance condition and the Maxwell-Boltzmann equilibrium distribution are sufficient conditions for a complete thermodynamics description, including nonequilibrium fluctuation theorems. Numerical simulations in a fully trained RBM are performed and the heat exchange fluctuation theorem is verified with excellent agreement to the theory. We observe how the contrastive divergence functional, mostly used in unsupervised learning of RBMs, is closely related to nonequilibrium thermodynamic quantities. We also use the framework to interpret the estimation of the partition function of RBMs with the annealed importance sampling method from a thermodynamics standpoint. Finally, we argue that unsupervised learning of RBMs is equivalent to a work protocol in a system driven by the laws of thermodynamics in the absence of labeled data.

  2. Lattice-Boltzmann simulations of droplet evaporation

    KAUST Repository

    Ledesma-Aguilar, Rodrigo

    2014-09-04

    © the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is

  3. The group-level consequences of sexual conflict in multigroup populations.

    Directory of Open Access Journals (Sweden)

    Omar Tonsi Eldakar

    Full Text Available In typical sexual conflict scenarios, males best equipped to exploit females are favored locally over more prudent males, despite reducing female fitness. However, local advantage is not the only relevant form of selection. In multigroup populations, groups with less sexual conflict will contribute more offspring to the next generation than higher conflict groups, countering the local advantage of harmful males. Here, we varied male aggression within- and between-groups in a laboratory population of water striders and measured resulting differences in local population growth over a period of three weeks. The overall pool fitness (i.e., adults produced of less aggressive pools exceeded that of high aggression pools by a factor of three, with the high aggression pools essentially experiencing no population growth over the course of the study. When comparing the fitness of individuals across groups, aggression appeared to be under stabilizing selection in the multigroup population. The use of contextual analysis revealed that overall stabilizing selection was a product of selection favoring aggression within groups, but selected against it at the group-level. Therefore, this report provides further evidence to show that what evolves in the total population is not merely an extension of within-group dynamics.

  4. Consistent Multigroup Theory Enabling Accurate Course-Group Simulation of Gen IV Reactors

    Energy Technology Data Exchange (ETDEWEB)

    Rahnema, Farzad; Haghighat, Alireza; Ougouag, Abderrafi

    2013-11-29

    The objective of this proposal is the development of a consistent multi-group theory that accurately accounts for the energy-angle coupling associated with collapsed-group cross sections. This will allow for coarse-group transport and diffusion theory calculations that exhibit continuous energy accuracy and implicitly treat cross- section resonances. This is of particular importance when considering the highly heterogeneous and optically thin reactor designs within the Next Generation Nuclear Plant (NGNP) framework. In such reactors, ignoring the influence of anisotropy in the angular flux on the collapsed cross section, especially at the interface between core and reflector near which control rods are located, results in inaccurate estimates of the rod worth, a serious safety concern. The scope of this project will include the development and verification of a new multi-group theory enabling high-fidelity transport and diffusion calculations in coarse groups, as well as a methodology for the implementation of this method in existing codes. This will allow for a higher accuracy solution of reactor problems while using fewer groups and will reduce the computational expense. The proposed research represents a fundamental advancement in the understanding and improvement of multi- group theory for reactor analysis.

  5. Longitudinal multigroup invariance analysis of the satisfaction with food-related life scale in university students.

    Science.gov (United States)

    Schnettler, Berta; Miranda, Horacio; Miranda-Zapata, Edgardo; Salinas-Oñate, Natalia; Grunert, Klaus G; Lobos, Germán; Sepúlveda, José; Orellana, Ligia; Hueche, Clementina; Bonilla, Héctor

    2017-06-01

    This study examined longitudinal measurement invariance in the Satisfaction with Food-related Life (SWFL) scale using follow-up data from university students. We examined this measure of the SWFL in different groups of students, separated by various characteristics. Through non-probabilistic longitudinal sampling, 114 university students (65.8% female, mean age: 22.5) completed the SWFL questionnaire three times, over intervals of approximately one year. Confirmatory factor analysis was used to examine longitudinal measurement invariance. Two types of analysis were conducted: first, a longitudinal invariance by time, and second, a multigroup longitudinal invariance by sex, age, socio-economic status and place of residence during the study period. Results showed that the 3-item version of the SWFL exhibited strong longitudinal invariance (equal factor loadings and equal indicator intercepts). Longitudinal multigroup invariance analysis also showed that the 3-item version of the SWFL displays strong invariance by socio-economic status and place of residence during the study period over time. Nevertheless, it was only possible to demonstrate equivalence of the longitudinal factor structure among students of both sexes, and among those older and younger than 22 years. Generally, these findings suggest that the SWFL scale has satisfactory psychometric properties for longitudinal measurement invariance in university students with similar characteristics as the students that participated in this research. It is also possible to suggest that satisfaction with food-related life is associated with sex and age.

  6. The Boltzmann equation in the difference formulation

    Energy Technology Data Exchange (ETDEWEB)

    Szoke, Abraham [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Brooks III, Eugene D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2015-05-06

    First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.

  7. Boltzmann equations for neutrinos with flavor mixings

    OpenAIRE

    Yamada, Shoichi

    2000-01-01

    With a view of applications to the simulations of supernova explosion and proto neutron star cooling, we derive the Boltzmann equations for the neutrino transport with the flavor mixing based on the real time formalism of the nonequilibrium field theory and the gradient expansion of the Green function. The relativistic kinematics is properly taken into account. The advection terms are derived in the mean field approximation for the neutrino self-energy whiles the collision terms are obtained ...

  8. Application de la methode des sous-groupes au calcul Monte-Carlo multigroupe

    Science.gov (United States)

    Martin, Nicolas

    This thesis is dedicated to the development of a Monte Carlo neutron transport solver based on the subgroup (or multiband) method. In this formalism, cross sections for resonant isotopes are represented in the form of probability tables on the whole energy spectrum. This study is intended in order to test and validate this approach in lattice physics and criticality-safety applications. The probability table method seems promising since it introduces an alternative computational way between the legacy continuous-energy representation and the multigroup method. In the first case, the amount of data invoked in continuous-energy Monte Carlo calculations can be very important and tend to slow down the overall computational time. In addition, this model preserves the quality of the physical laws present in the ENDF format. Due to its cheap computational cost, the multigroup Monte Carlo way is usually at the basis of production codes in criticality-safety studies. However, the use of a multigroup representation of the cross sections implies a preliminary calculation to take into account self-shielding effects for resonant isotopes. This is generally performed by deterministic lattice codes relying on the collision probability method. Using cross-section probability tables on the whole energy range permits to directly take into account self-shielding effects and can be employed in both lattice physics and criticality-safety calculations. Several aspects have been thoroughly studied: (1) The consistent computation of probability tables with a energy grid comprising only 295 or 361 groups. The CALENDF moment approach conducted to probability tables suitable for a Monte Carlo code. (2) The combination of the probability table sampling for the energy variable with the delta-tracking rejection technique for the space variable, and its impact on the overall efficiency of the proposed Monte Carlo algorithm. (3) The derivation of a model for taking into account anisotropic

  9. Hybrid lattice Boltzmann method on overlapping grids.

    Science.gov (United States)

    Di Ilio, G; Chiappini, D; Ubertini, S; Bella, G; Succi, S

    2017-01-01

    In this work, a hybrid lattice Boltzmann method (HLBM) is proposed, where the standard lattice Boltzmann implementation based on the Bhatnagar-Gross-Krook (LBGK) approximation is combined together with an unstructured finite-volume lattice Boltzmann model. The method is constructed on an overlapping grid system, which allows the coexistence of a uniform lattice nodes spacing and a coordinate-free lattice structure. The natural adaptivity of the hybrid grid system makes the method particularly suitable to handle problems involving complex geometries. Moreover, the provided scheme ensures a high-accuracy solution near walls, given the capability of the unstructured submodel of achieving the desired level of refinement in a very flexible way. For these reasons, the HLBM represents a prospective tool for solving multiscale problems. The proposed method is here applied to the benchmark problem of a two-dimensional flow past a circular cylinder for a wide range of Reynolds numbers and its numerical performances are measured and compared with the standard LBGK ones.

  10. Consistent lattice Boltzmann equations for phase transitions.

    Science.gov (United States)

    Siebert, D N; Philippi, P C; Mattila, K K

    2014-11-01

    Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling.

  11. On the full Boltzmann equations for Leptogenesis

    CERN Document Server

    Garayoa, J; Pinto, T; Rius, N; Vives, O

    2009-01-01

    We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T=0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ~< 1) the final lepton asymmetry can change up to a factor four with respect to previous...

  12. On the full Boltzmann equations for leptogenesis

    Energy Technology Data Exchange (ETDEWEB)

    Garayoa, J.; Pastor, S.; Pinto, T.; Rius, N.; Vives, O., E-mail: garayoa@ific.uv.es, E-mail: pastor@ific.uv.es, E-mail: teguayco@gmail.com, E-mail: nuria@ific.uv.es, E-mail: vives@ific.uv.es [Depto. de Física Teórica and IFIC, Universidad de Valencia-CSIC, Edificio de Institutos de Paterna, Apt. 22085, 46071 Valencia (Spain)

    2009-09-01

    We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T = 0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ∼< 1) the final lepton asymmetry can change up to a factor four with respect to previous estimates.

  13. Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms.

    Science.gov (United States)

    Bouchard, Hugo; Bielajew, Alex

    2015-07-07

    To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano's theorem. Additionally, Lewis' approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano's and Lewis' approaches are stated in this new equation. Fano's theorem is found not to apply in the presence of electromagnetic fields. Lewis' theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms.

  14. Lattice Boltzmann solution of the transient Boltzmann transport equation in radiative and neutron transport.

    Science.gov (United States)

    Wang, Yahui; Yan, Liming; Ma, Yu

    2017-06-01

    Applications of the transient Boltzmann transport equation (BTE) have undergone much investigation, such as radiative heat transfer and neutron transport. This paper provides a lattice Boltzmann model to efficiently resolve the multidimensional transient BTE. For a higher angular resolution, enough transport directions are considered while the transient BTE in each direction is treated as a conservation law equation and solved independently. Both macroscopic equations recovered from a Chapman-Enskog expansion and simulated results of typical benchmark problems show not only the second-order accuracy but also the flexibility and applicability of the proposed lattice Boltzmann model. This approach may contribute a powerful technique for the parallel simulation of large-scale engineering and some alternative perspectives for solving the nonlinear transport problem further.

  15. The projection Galerkin method for solving the time-independent differential diffusion equation in a semi-infinite domain

    Science.gov (United States)

    Makarenkov, A. M.; Seregina, E. V.; Stepovich, M. A.

    2017-05-01

    Using the diffusion equation as an example, results of applying the projection Galerkin method for solving time-independent heat and mass transfer equations in a semi-infinite domain are presented. The convergence of the residual corresponding to the approximate solution of the timeindependent diffusion equation obtained by the projection method using the modified Laguerre functions is proved. Computational results for a two-dimensional toy problem are presented.

  16. GLOBAL STABILITY OF EXTENDED MULTI-GROUP SIR EPIDEMIC MODELS WITH PATCHES THROUGH MIGRATION AND CROSS PATCH INFECTION

    Institute of Scientific and Technical Information of China (English)

    Yoshiaki MUROYA; Yoichi ENATSU; Toshikazu KUNIYA

    2013-01-01

    In this article,we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models,which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups.As a result,we partially generalize the recent result in the article [16].

  17. Boltzmann equation integration in thermionic converter conditions. Part II. Terms in Boltzmann equation

    Energy Technology Data Exchange (ETDEWEB)

    Stoenescu, M.L.

    1977-06-01

    The terms in Boltzmann kinetic equation corresponding to elastic short range collisions, inelastic excitational collisions, coulomb interactions and electric field acceleration are evaluated numerically for a standard distribution function minimizing the computational volume by expressing the terms as linear combinations with recalculable coefficients, of the distribution function and its derivatives. The present forms are suitable for spatial distribution calculations.

  18. SIRIUS - A one-dimensional multigroup analytic nodal diffusion theory code

    Energy Technology Data Exchange (ETDEWEB)

    Forslund, P. [Westinghouse Atom AB, Vaesteraas (Sweden)

    2000-09-01

    In order to evaluate relative merits of some proposed intranodal cross sections models, a computer code called Sirius has been developed. Sirius is a one-dimensional, multigroup analytic nodal diffusion theory code with microscopic depletion capability. Sirius provides the possibility of performing a spatial homogenization and energy collapsing of cross sections. In addition a so called pin power reconstruction method is available for the purpose of reconstructing 'heterogeneous' pin qualities. consequently, Sirius has the capability of performing all the calculations (incl. depletion calculations) which are an integral part of the nodal calculation procedure. In this way, an unambiguous numerical analysis of intranodal cross section models is made possible. In this report, the theory of the nodal models implemented in sirius as well as the verification of the most important features of these models are addressed.

  19. Ethnic Residential Segregation: A Multilevel, Multigroup, Multiscale Approach Exemplified by London in 2011.

    Science.gov (United States)

    Jones, Kelvyn; Johnston, Ron; Manley, David; Owen, Dewi; Charlton, Chris

    2015-12-01

    We develop and apply a multilevel modeling approach that is simultaneously capable of assessing multigroup and multiscale segregation in the presence of substantial stochastic variation that accompanies ethnicity rates based on small absolute counts. Bayesian MCMC estimation of a log-normal Poisson model allows the calculation of the variance estimates of the degree of segregation in a single overall model, and credible intervals are obtained to provide a measure of uncertainty around those estimates. The procedure partitions the variance at different levels and implicitly models the dependency (or autocorrelation) at each spatial scale below the topmost one. Substantively, we apply the model to 2011 census data for London, one of the world's most ethnically diverse cities. We find that the degree of segregation depends both on scale and group.

  20. Radiation Transport for Explosive Outflows: A Multigroup Hybrid Monte Carlo Method

    CERN Document Server

    Wollaeger, Ryan T; Graziani, Carlo; Couch, Sean M; Jordan, George C; Lamb, Donald Q; Moses, Gregory A

    2013-01-01

    We explore the application of Implicit Monte Carlo (IMC) and Discrete Diffusion Monte Carlo (DDMC) to radiation transport in strong fluid outflows with structured opacity. The IMC method of Fleck & Cummings is a stochastic computational technique for nonlinear radiation transport. IMC is partially implicit in time and may suffer in efficiency when tracking Monte Carlo particles through optically thick materials. The DDMC method of Densmore accelerates an IMC computation where the domain is diffusive. Recently, Abdikamalov extended IMC and DDMC to multigroup, velocity-dependent neutrino transport with the intent of modeling neutrino dynamics in core-collapse supernovae. Densmore has also formulated a multifrequency extension to the originally grey DDMC method. In this article we rigorously formulate IMC and DDMC over a high-velocity Lagrangian grid for possible application to photon transport in the post-explosion phase of Type Ia supernovae. The method described is suitable for a large variety of non-mono...

  1. Global dynamics of a novel multi-group model for computer worms

    Institute of Scientific and Technical Information of China (English)

    Gong Yong-Wang; Song Yu-Rong; Jiang Guo-Ping

    2013-01-01

    In this paper,we study worm dynamics in computer networks composed of many autonomous systems.A novel multigroup SIQR (susceptible-infected-quarantined-removed) model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure.Then,the basic reproduction number of worm R0 is derived and the global dynamics of the model are established.It is shown that if R0 is less than or equal to 1,the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually,whereas,if R0 is greater than 1,one unique endemic equilibrium exists and it is globally asymptotically stable,thus the worm persists in the network.Finally,numerical simulations are given to illustrate the theoretical results.

  2. Validation of the Resilience Scale for Adolescents (READ) in Ireland: a multi-group analysis.

    Science.gov (United States)

    Kelly, Yvonne; Fitzgerald, Amanda; Dooley, Barbara

    2016-04-29

    Resilience is a process reflecting positive adaptation in the face of adversity. The Resilience Scale for Adolescence (READ) incorporates intrapersonal and interpersonal protective factors mapping onto the three salient domains of resilience, including individual, family and external environment. This study investigated the validity and reliability of the READ by means of factor analysis, multi-group analysis, inter-correlations and internal consistency measures. Participants were 6085 young people in Ireland aged 12-18 years. Participants completed the My World Survey - Second Level (MWS-SL), assessing risk and protective factors of mental health. Confirmatory factor analysis validated the original five-factor structure of the READ including Personal Competence, Social Competence, Structured Style, Family Cohesion, and Social Resources, χ(2) (340) = 6146.02, p resilience factors among adolescents in Ireland, demonstrating its applicability in a different cultural context and with a wider age range of adolescents. Copyright © 2016 John Wiley & Sons, Ltd.

  3. MINX: a multigroup interpretation of nuclear X-sections from ENDF/B

    Energy Technology Data Exchange (ETDEWEB)

    Weisbin, C.R.; Soran, P.D.; MacFarlane, R.E.; Harris, D.R.; LaBauve, R.J.; Hendricks, J.S.; White, J.E.; Kidman, R.B.

    1976-09-01

    MINX calculates fine-group averaged infinitely dilute cross sections, self-shielding factors, and group-to-group transfer matrices from ENDF/B-IV data. Its primary purpose is to generate pseudo-composition independent multigroup libraries in the standard CCCC-III interface formats for use in the design and analysis of nuclear systems. MINX incorporates and improves upon the resonance capabilities of existing codes such as ETOX and ENDRUN and the high-Legendre-order transfer matrices of ETOG and SUPERTOG. Group structure, Legendre order, weight function, temperature, dilutions, and processing tolerances are all under user control. Paging and variable dimensioning allow very large problems to be run. Both CDC and IBM versions of MINX are available.

  4. Global dynamics of a novel multi-group model for computer worms

    Science.gov (United States)

    Gong, Yong-Wang; Song, Yu-Rong; Jiang, Guo-Ping

    2013-04-01

    In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multi-group SIQR (susceptible-infected-quarantined-removed) model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.

  5. Solution of the multilayer multigroup neutron diffusion equation in cartesian geometry by fictitious borders power method

    Energy Technology Data Exchange (ETDEWEB)

    Zanette, Rodrigo; Petersen, Caudio Zen [Univ. Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcello [Univ. Federal de Pelotas (Brazil). Centro de Engenharias; Zabadal, Jorge Rodolfo [Univ. Federal do Rio Grande do Sul, Tramandai (Brazil)

    2017-05-15

    In this paper a solution for the one-dimensional steady state Multilayer Multigroup Neutron Diffusion Equation in cartesian geometry by Fictitious Borders Power Method and a perturbative analysis of this solution is presented. For each new iteration of the power method, the neutron flux is reconstructed by polynomial interpolation, so that it always remains in a standard form. However when the domain is long, an almost singular matrix arises in the interpolation process. To eliminate this singularity the domain segmented in R regions, called fictitious regions. The last step is to solve the neutron diffusion equation for each fictitious region in analytical form locally. The results are compared with results present in the literature. In order to analyze the sensitivity of the solution, a perturbation in the nuclear parameters is inserted to determine how a perturbation interferes in numerical results of the solution.

  6. Compilation of multigroup cross-section covariance matrices for several important reactor materials

    Energy Technology Data Exchange (ETDEWEB)

    Drischler, J.D.; Weisbin, C.R.

    1977-10-01

    Multigroup cross-section covariance matrices are presented for fission in /sup 235/U, /sup 238/U, /sup 239/Pu, and /sup 241/Pu; capture in /sup 235/U, /sup 238/U, /sup 239/Pu, /sup 240/Pu, and /sup 241/Pu; fission neutron yield (anti nu) for /sup 235/U, /sup 238/U, /sup 239/Pu, and /sup 240/Pu; elastic scattering for Na and Fe; non-elastic reactions for Na and Fe; first-level inelastic scattering for /sup 238/U; and all reactions provided in the ENDF/B-IV covariance description of N, O, and C. Other data files generated are included for reference but have not yet been tested. The report presents the nultigroup data in six, ten, and fifteen energy group forms corresponding to weighting of the covariance data with fission (GODIVA), LMFBR (ZPR-6/7) and 1/E spectra, respectively.

  7. Testing a new multigroup inference approach to reconstructing past environmental conditions

    Directory of Open Access Journals (Sweden)

    Maria RIERADEVALL

    2008-08-01

    Full Text Available A new, quantitative, inference model for environmental reconstruction (transfer function, based for the first time on the simultaneous analysis of multigroup species, has been developed. Quantitative reconstructions based on palaeoecological transfer functions provide a powerful tool for addressing questions of environmental change in a wide range of environments, from oceans to mountain lakes, and over a range of timescales, from decades to millions of years. Much progress has been made in the development of inferences based on multiple proxies but usually these have been considered separately, and the different numeric reconstructions compared and reconciled post-hoc. This paper presents a new method to combine information from multiple biological groups at the reconstruction stage. The aim of the multigroup work was to test the potential of the new approach to making improved inferences of past environmental change by improving upon current reconstruction methodologies. The taxonomic groups analysed include diatoms, chironomids and chrysophyte cysts. We test the new methodology using two cold-environment training-sets, namely mountain lakes from the Pyrenees and the Alps. The use of multiple groups, as opposed to single groupings, was only found to increase the reconstruction skill slightly, as measured by the root mean square error of prediction (leave-one-out cross-validation, in the case of alkalinity, dissolved inorganic carbon and altitude (a surrogate for air-temperature, but not for pH or dissolved CO2. Reasons why the improvement was less than might have been anticipated are discussed. These can include the different life-forms, environmental responses and reaction times of the groups under study.

  8. Privacy-Preserving Restricted Boltzmann Machine

    Science.gov (United States)

    Li, Yu

    2014-01-01

    With the arrival of the big data era, it is predicted that distributed data mining will lead to an information technology revolution. To motivate different institutes to collaborate with each other, the crucial issue is to eliminate their concerns regarding data privacy. In this paper, we propose a privacy-preserving method for training a restricted boltzmann machine (RBM). The RBM can be got without revealing their private data to each other when using our privacy-preserving method. We provide a correctness and efficiency analysis of our algorithms. The comparative experiment shows that the accuracy is very close to the original RBM model. PMID:25101139

  9. Application of lattice Boltzmann scheme to nanofluids

    Institute of Scientific and Technical Information of China (English)

    XUAN Yimin; LI Qiang; YAO Zhengping

    2004-01-01

    A nanofluid is a particle suspension that consists of base liquids and nanoparticles. Nanofluid has greater potential for heat transfer enhancement than traditional solid-liquid mixture. By accounting for the external and internal forces acting on the suspended nanoparticles and interactions among the nanoparticles and fluid particles,a lattice Boltzmann model for simulating flow and energy transport processes inside the nanofluids is proposed. The irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids are discussed. The distributions of suspended nanoparticles inside nanofluids are calculated.

  10. Lattice-Boltzmann-based Simulations of Diffusiophoresis

    Science.gov (United States)

    Castigliego, Joshua; Kreft Pearce, Jennifer

    We present results from a lattice-Boltzmann-base Brownian Dynamics simulation on diffusiophoresis and the separation of particles within the system. A gradient in viscosity that simulates a concentration gradient in a dissolved polymer allows us to separate various types of particles by their deformability. As seen in previous experiments, simulated particles that have a higher deformability react differently to the polymer matrix than those with a lower deformability. Therefore, the particles can be separated from each other. This simulation, in particular, was intended to model an oceanic system where the particles of interest were zooplankton, phytoplankton and microplastics. The separation of plankton from the microplastics was achieved.

  11. Celebrating Cercignani's conjecture for the Boltzmann equation

    CERN Document Server

    Desvillettes, Laurent; Villani, Cédric

    2010-01-01

    Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.

  12. General relativistic Boltzmann equation, II: Manifestly covariant treatment

    NARCIS (Netherlands)

    Debbasch, F.; van Leeuwen, W.A.

    2009-01-01

    In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann equati

  13. Soluble Boltzmann equations for internal state and Maxwell models

    NARCIS (Netherlands)

    Futcher, E.; Hoare, M.R.; Hendriks, E.M.; Ernst, M.H.

    1980-01-01

    We consider a class of scalar nonlinear Boltzmann equations describing the evolution of a microcanonical ensemble in which sub-systems exchange internal energy ‘randomly’ in binary interactions. In the continuous variable version these models can equally be interpreted as Boltzmann equations for Ma

  14. Reciprocal Symmetric Boltzmann Function and Unified Boson-Fermion Statistics

    OpenAIRE

    2007-01-01

    The differential equation for Boltzmann's function is replaced by the corresponding discrete finite difference equation. The difference equation is, then, symmetrized so that the equation remains invariant when step d is replaced by -d. The solutions of this equation come in Boson-Fermion pairs. Reciprocal symmetric Boltzmann's function, thus, unifies both Bosonic and Fermionic distributions.

  15. Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos

    Science.gov (United States)

    Boozer, A. D.

    2011-01-01

    We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…

  16. General relativistic Boltzmann equation, II: Manifestly covariant treatment

    NARCIS (Netherlands)

    Debbasch, F.; van Leeuwen, W.A.

    2009-01-01

    In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann

  17. Axisymmetric multiphase lattice Boltzmann method for generic equations of state

    NARCIS (Netherlands)

    Reijers, Sten Arjen; Gelderblom, Hanneke; Toschi, F.

    2016-01-01

    We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation

  18. Distributional Monte Carlo Methods for the Boltzmann Equation

    Science.gov (United States)

    2013-03-01

    become the first to possess non - Maxwellian distributions, and therefore become the only location where 112 collisions are required to be calculated... Maxwellian . . . . . . . . . . . . . . . . . 16 fMB Maxwell-Boltzmann Density . . . . . . . . . . . . . . . . . . . . . . . . 16 nMB Maxwell-Boltzmann...is equivalent to assuming that millions of actual particles all share the exact velocity vector. This assumption is non -physical in the sense that

  19. Thermal equation of state for lattice Boltzmann gases

    Institute of Scientific and Technical Information of China (English)

    Ran Zheng

    2009-01-01

    The Galilean invaxiance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar-Gross-Krook model axe proposed together with their rigorous theoretical background. From the viewpoint of group invariance,recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar-Gross-Krook equation (LBGKE) induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics.

  20. Hot electrons in superlattices: quantum transport versus Boltzmann equation

    DEFF Research Database (Denmark)

    Wacker, Andreas; Jauho, Antti-Pekka; Rott, S.;

    1999-01-01

    A self-consistent solution of the transport equation is presented for semiconductor superlattices within different approaches: (i) a full quantum transport model based on nonequilibrium Green functions, (ii) the semiclassical Boltzmann equation for electrons in a miniband, and (iii) Boltzmann...

  1. Axisymmetric multiphase lattice Boltzmann method for generic equations of state

    NARCIS (Netherlands)

    Reijers, S.A.; Gelderblom, H.; Toschi, F.

    2016-01-01

    We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation

  2. Time-independent wormholes

    Science.gov (United States)

    Fu, Zicao; Marolf, Donald; Mefford, Eric

    2016-12-01

    We study two-sided static wormholes with an exact Killing symmetry that translates both mouths of the wormhole toward the future. This differs from the familiar Kruskal wormhole whose time translation is future-directed only in one asymptotic region and is instead past-directed in the other. Our spacetimes are solutions to Einstein-Hilbert gravity sourced by scalar domain walls. Explicit examples are found in the thin wall approimation. More generally, we show that such spacetimes can arise in the presence of scalar fields with potentials that are C 1 but not C 2 and find examples numerically. However, solutions with an exact such Killing symmetry are forbidden when the scalar potential is smooth. Finally, we consider the mutual information of boundary regions associated with such wormholes in AdS/CFT. Although the interior of our solutions are unstable, we find that even mutual informations between opposite boundaries are already thermalized at any finite t in the sense that they agree with the t → ∞ limit of results from the familiar AdS-Kruskal solution.

  3. Time-independent wormholes

    CERN Document Server

    Fu, Zicao; Mefford, Eric

    2016-01-01

    We study two-sided static wormholes with an exact Killing symmetry that translates both mouths of the wormhole toward the future. This differs from the familiar Kruskal wormhole whose time translation is future-directed only in one asymptotic region and is instead past-directed in the other. Our spacetimes are solutions to Einstein-Hilbert gravity sourced by scalar domain walls. Explicit examples are found in the thin wall approximation. More generally, we show that such spacetimes can arise in the presence of scalar fields with potentials that are $C^1$ but not $C^2$ and find examples numerically. However, solutions with an exact such Killing symmetry are forbidden when the scalar potential is smooth. Finally, we consider the mutual information of boundary regions associated with such wormholes in AdS/CFT. Although the interior of our solutions are unstable, we find that even mutual informations between opposite boundaries are already thermalized at any finite $t$ in the sense that they agree with the $t\\rig...

  4. Time-independent wormholes

    Energy Technology Data Exchange (ETDEWEB)

    Fu, Zicao; Marolf, Donald; Mefford, Eric [Department of Physics, University of California,Santa Barbara, CA 93106 (United States)

    2016-12-06

    We study two-sided static wormholes with an exact Killing symmetry that translates both mouths of the wormhole toward the future. This differs from the familiar Kruskal wormhole whose time translation is future-directed only in one asymptotic region and is instead past-directed in the other. Our spacetimes are solutions to Einstein-Hilbert gravity sourced by scalar domain walls. Explicit examples are found in the thin wall approimation. More generally, we show that such spacetimes can arise in the presence of scalar fields with potentials that are C{sup 1} but not C{sup 2} and find examples numerically. However, solutions with an exact such Killing symmetry are forbidden when the scalar potential is smooth. Finally, we consider the mutual information of boundary regions associated with such wormholes in AdS/CFT. Although the interior of our solutions are unstable, we find that even mutual informations between opposite boundaries are already thermalized at any finite t in the sense that they agree with the t→∞ limit of results from the familiar AdS-Kruskal solution.

  5. Multireflection boundary conditions for lattice Boltzmann models.

    Science.gov (United States)

    Ginzburg, Irina; d'Humières, Dominique

    2003-12-01

    We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder.

  6. Entropic Lattice Boltzmann Methods for Fluid Mechanics

    Science.gov (United States)

    Chikatamarla, Shyam; Boesch, Fabian; Sichau, David; Karlin, Ilya

    2013-11-01

    With its roots in statistical mechanics and kinetic theory, the lattice Boltzmann method (LBM) is a paradigm-changing innovation, offering for the first time an intrinsically parallel CFD algorithm. Over the past two decades, LBM has achieved numerous results in the field of CFD and is now in a position to challenge state-of-the art CFD techniques. Our major restyling of LBM resulted in an unconditionally stable entropic LBM which restored Second Law (Boltzmann H theorem) in the LBM kinetics and thus enabled affordable direct simulations of fluid turbulence. We review here recent advances in ELBM as a practical, modeling-free tool for simulation of turbulent flows in complex geometries. We shall present recent simulations including turbulent channel flow, flow past a circular cylinder, knotted vortex tubes, and flow past a surface mounted cube. ELBM listed all admissible lattices supporting a discrete entropy function and has classified them in hierarchically increasing order of accuracy. Applications of these higher-order lattices to simulations of turbulence and thermal flows shall also be presented. This work was supported CSCS grant s437.

  7. Immersed boundary lattice Boltzmann model based on multiple relaxation times.

    Science.gov (United States)

    Lu, Jianhua; Han, Haifeng; Shi, Baochang; Guo, Zhaoli

    2012-01-01

    As an alterative version of the lattice Boltzmann models, the multiple relaxation time (MRT) lattice Boltzmann model introduces much less numerical boundary slip than the single relaxation time (SRT) lattice Boltzmann model if some special relationship between the relaxation time parameters is chosen. On the other hand, most current versions of the immersed boundary lattice Boltzmann method, which was first introduced by Feng and improved by many other authors, suffer from numerical boundary slip as has been investigated by Le and Zhang. To reduce such a numerical boundary slip, an immerse boundary lattice Boltzmann model based on multiple relaxation times is proposed in this paper. A special formula is given between two relaxation time parameters in the model. A rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single-relaxation-time-based model.

  8. Boltzmann equations for a binary one-dimensional ideal gas.

    Science.gov (United States)

    Boozer, A D

    2011-09-01

    We consider a time-reversal invariant dynamical model of a binary ideal gas of N molecules in one spatial dimension. By making time-asymmetric assumptions about the behavior of the gas, we derive Boltzmann and anti-Boltzmann equations that describe the evolution of the single-molecule velocity distribution functions for an ensemble of such systems. We show that for a special class of initial states of the ensemble one can obtain an exact expression for the N-molecule velocity distribution function, and we use this expression to rigorously prove that the time-asymmetric assumptions needed to derive the Boltzmann and anti-Boltzmann equations hold in the limit of large N. Our results clarify some subtle issues regarding the origin of the time asymmetry of Boltzmann's H theorem.

  9. Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers.

    Science.gov (United States)

    Wang, Nuo; Zhou, Shenggao; Kekenes-Huskey, Peter M; Li, Bo; McCammon, J Andrew

    2014-12-26

    Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.

  10. Poisson–Boltzmann versus Size-Modified Poisson–Boltzmann Electrostatics Applied to Lipid Bilayers

    Science.gov (United States)

    2015-01-01

    Mean-field methods, such as the Poisson–Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson–Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation. PMID:25426875

  11. A multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR

    CERN Document Server

    Shestakov, A I

    2007-01-01

    We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate level-solve packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation (PTC). We analyze the magnitude of the PTC parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary dat...

  12. An analytical representation for the solution of neutron kinetic transport equation in slab-geometry multigroup discrete ordinates formulation

    Energy Technology Data Exchange (ETDEWEB)

    Tomaschewski, Fernanda K.; Segatto, Cynthia F., E-mail: fernandasls_89@hotmail.com, E-mail: cynthia.segatto@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada; Barros, Ricardo C., E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Departamento de Modelagem Computacional

    2015-07-01

    Presented here is a decomposition method based on series representation of the group angular fluxes and delayed neutron precursors in smoothly continuous functions for energy multigroups, slab-geometry discrete ordinates kinetics equations supplemented with a prescribed number of delayed neutron precursors. Numerical results to a non-reflected sub-critical slab stabilized by steady-state sources are given to illustrate the accuracy and efficiency of the o offered method. (author)

  13. Validation of multigroup neutron cross sections and calculational methods for the advanced neutron source against the FOEHN critical experiments measurements

    Energy Technology Data Exchange (ETDEWEB)

    Smith, L.A.; Gallmeier, F.X. [Oak Ridge Institute for Science and Energy, TN (United States); Gehin, J.C. [Oak Ridge National Lab., TN (United States)] [and others

    1995-05-01

    The FOEHN critical experiment was analyzed to validate the use of multigroup cross sections and Oak Ridge National Laboratory neutronics computer codes in the design of the Advanced Neutron Source. The ANSL-V 99-group master cross section library was used for all the calculations. Three different critical configurations were evaluated using the multigroup KENO Monte Carlo transport code, the multigroup DORT discrete ordinates transport code, and the multigroup diffusion theory code VENTURE. The simple configuration consists of only the fuel and control elements with the heavy water reflector. The intermediate configuration includes boron endplates at the upper and lower edges of the fuel element. The complex configuration includes both the boron endplates and components in the reflector. Cross sections were processed using modules from the AMPX system. Both 99-group and 20-group cross sections were created and used in two-dimensional models of the FOEHN experiment. KENO calculations were performed using both 99-group and 20-group cross sections. The DORT and VENTURE calculations were performed using 20-group cross sections. Because the simple and intermediate configurations are azimuthally symmetric, these configurations can be explicitly modeled in R-Z geometry. Since the reflector components cannot be modeled explicitly using the current versions of these codes, three reflector component homogenization schemes were developed and evaluated for the complex configuration. Power density distributions were calculated with KENO using 99-group cross sections and with DORT and VENTURE using 20-group cross sections. The average differences between the measured values and the values calculated with the different computer codes range from 2.45 to 5.74%. The maximum differences between the measured and calculated thermal flux values for the simple and intermediate configurations are {approx} 13%, while the average differences are < 8%.

  14. Boltzmann babies in the proper time measure

    Energy Technology Data Exchange (ETDEWEB)

    Bousso, Raphael; Bousso, Raphael; Freivogel, Ben; Yang, I-Sheng

    2007-12-20

    After commenting briefly on the role of the typicality assumption in science, we advocate a phenomenological approach to the cosmological measure problem. Like any other theory, a measure should be simple, general, well defined, and consistent with observation. This allows us to proceed by elimination. As an example, we consider the proper time cutoff on a geodesic congruence. It predicts that typical observers are quantum fluctuations in the early universe, or Boltzmann babies. We sharpen this well-known youngness problem by taking into account the expansion and open spatial geometry of pocket universes. Moreover, we relate the youngness problem directly to the probability distribution for observables, such as the temperature of the cosmic background radiation. We consider a number of modifications of the proper time measure, but find none that would make it compatible with observation.

  15. Lattice Boltzmann Model for Numerical Relativity

    CERN Document Server

    Ilseven, E

    2015-01-01

    In the Bona-Masso formulation, Einstein equations are written as a set of flux conservative first order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for Numerical Relativity. Our model is validated with well-established tests, showing good agreement with analytical solutions. Furthermore, we show that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improves. Finally, in order to show the potential of our approach a linear scaling law for parallelisation with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

  16. Lattice Boltzmann model with nearly constant density.

    Science.gov (United States)

    Fang, Hai-ping; Wan, Rong-zheng; Lin, Zhi-fang

    2002-09-01

    An improved lattice Boltzmann model is developed to simulate fluid flow with nearly constant fluid density. The ingredient is to incorporate an extra relaxation for fluid density, which is realized by introducing a feedback equation in the equilibrium distribution functions. The pressure is dominated by the moving particles at a node, while the fluid density is kept nearly constant and explicit mass conservation is retained as well. Numerical simulation based on the present model for the (steady) plane Poiseuille flow and the (unsteady) two-dimensional Womersley flow shows a great improvement in simulation results over the previous models. In particular, the density fluctuation has been reduced effectively while achieving a relatively large pressure gradient.

  17. Lattice Boltzmann modelling of intrinsic permeability

    CERN Document Server

    Li, Jun; Wu, Lei; Zhang, Yonghao

    2016-01-01

    Lattice Boltzmann method (LBM) has been applied to predict flow properties of porous media including intrinsic permeability, where it is implicitly assumed that the LBM is equivalent to the incompressible (or near incompressible) Navier-Stokes equation. However, in LBM simulations, high-order moments, which are completely neglected in the Navier-Stokes equation, are still available through particle distribution functions. To ensure that the LBM simulation is correctly working at the Navier-Stokes hydrodynamic level, the high-order moments have to be negligible. This requires that the Knudsen number (Kn) is small so that rarefaction effect can be ignored. In this technical note, we elaborate this issue in LBM modelling of porous media flows, which is particularly important for gas flows in ultra-tight media.

  18. The Lattice Boltzmann method principles and practice

    CERN Document Server

    Krüger, Timm; Kuzmin, Alexandr; Shardt, Orest; Silva, Goncalo; Viggen, Erlend Magnus

    2017-01-01

    This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a va...

  19. A lattice Boltzmann model for adsorption breakthrough

    Energy Technology Data Exchange (ETDEWEB)

    Agarwal, Saurabh; Verma, Nishith [Indian Institute of Technology Kanpur, Department of Chemical Engineering, Kanpur (India); Mewes, Dieter [Universitat Hannover, Institut fur Verfahrenstechnik, Hannover (Germany)

    2005-07-01

    A lattice Boltzmann model is developed to simulate the one-dimensional (1D) unsteady state concentration profiles, including breakthrough curves, in a fixed tubular bed of non-porous adsorbent particles. The lattice model solves the 1D time dependent convection-diffusion-reaction equation for an ideal binary gaseous mixture, with solute concentrations at parts per million levels. The model developed in this study is also able to explain the experimental adsorption/desorption data of organic vapours (toluene) on silica gel under varying conditions of temperature, concentrations and flowrates. Additionally, the programming code written for simulating the adsorption breakthrough is modified with minimum changes to successfully simulate a few flow problems, such as Poiseuille flow, Couette flow, and axial dispersion in a tube. The present study provides an alternative numerical approach to solving such types of mass transfer related problems. (orig.)

  20. Ordinal Boltzmann Machines for Collaborative Filtering

    CERN Document Server

    Truyen, Tran The; Venkatesh, Svetha

    2012-01-01

    Collaborative filtering is an effective recommendation technique wherein the preference of an individual can potentially be predicted based on preferences of other members. Early algorithms often relied on the strong locality in the preference data, that is, it is enough to predict preference of a user on a particular item based on a small subset of other users with similar tastes or of other items with similar properties. More recently, dimensionality reduction techniques have proved to be equally competitive, and these are based on the co-occurrence patterns rather than locality. This paper explores and extends a probabilistic model known as Boltzmann Machine for collaborative filtering tasks. It seamlessly integrates both the similarity and co-occurrence in a principled manner. In particular, we study parameterisation options to deal with the ordinal nature of the preferences, and propose a joint modelling of both the user-based and item-based processes. Experiments on moderate and large-scale movie recomm...

  1. Lattice Boltzmann model for numerical relativity.

    Science.gov (United States)

    Ilseven, E; Mendoza, M

    2016-02-01

    In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

  2. Lattice Boltzmann model for resistive relativistic magnetohydrodynamics

    CERN Document Server

    Mohseni, F; Succi, S; Herrmann, H J

    2015-01-01

    In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfv\\'en waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to $\\sigma^{-\\frac{1}{2}}$, $\\sigma$ being the conductivity, w...

  3. Training Restricted Boltzmann Machines on Word Observations

    CERN Document Server

    Dahl, George E; Larochelle, Hugo

    2012-01-01

    The restricted Boltzmann machine (RBM) is a flexible tool for modeling complex data, however there have been significant computational difficulties in using RBMs to model high-dimensional multinomial observations. In natural language processing applications, words are naturally modeled by K-ary discrete distributions, where K is determined by the vocabulary size and can easily be in the hundred thousands. The conventional approach to training RBMs on word observations is limited because it requires sampling the states of K-way softmax visible units during block Gibbs updates, an operation that takes time linear in K. In this work, we address this issue by employing a more general class of Markov chain Monte Carlo operators on the visible units, yielding updates with computational complexity independent of K. We demonstrate the success of our approach by training RBMs on hundreds of millions of word n-grams using larger vocabularies than previously feasible with RBMs and using the learned features to improve p...

  4. Lattice Boltzmann modeling of water entry problems

    Science.gov (United States)

    Zarghami, A.; Falcucci, G.; Jannelli, E.; Succi, S.; Porfiri, M.; Ubertini, S.

    2014-12-01

    This paper deals with the simulation of water entry problems using the lattice Boltzmann method (LBM). The dynamics of the free surface is treated through the mass and momentum fluxes across the interface cells. A bounce-back boundary condition is utilized to model the contact between the fluid and the moving object. The method is implemented for the analysis of a two-dimensional flow physics produced by a symmetric wedge entering vertically a weakly-compressible fluid at a constant velocity. The method is used to predict the wetted length, the height of water pile-up, the pressure distribution and the overall force on the wedge. The accuracy of the numerical results is demonstrated through comparisons with data reported in the literature.

  5. Classification of Sets using Restricted Boltzmann Machines

    CERN Document Server

    Louradour, Jérôme

    2011-01-01

    We consider the problem of classification when inputs correspond to sets of vectors. This setting occurs in many problems such as the classification of pieces of mail containing several pages, of web sites with several sections or of images that have been pre-segmented into smaller regions. We propose generalizations of the restricted Boltzmann machine (RBM) that are appropriate in this context and explore how to incorporate different assumptions about the relationship between the input sets and the target class within the RBM. In experiments on standard multiple-instance learning datasets, we demonstrate the competitiveness of approaches based on RBMs and apply the proposed variants to the problem of incoming mail classification.

  6. Flux Limiter Lattice Boltzmann for Compressible Flows

    Institute of Scientific and Technical Information of China (English)

    陈峰; 许爱国; 张广财; 李英骏

    2011-01-01

    In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann (LB) model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations.

  7. Migrating songbirds tested in computer-controlled Emlen funnels use stellar cuesfor a time-independent compass

    DEFF Research Database (Denmark)

    Mouritsen, Henrik Østergaard; Larsen, Ole Næsbye

    2001-01-01

    detailed temporal analyses. First, we showed that the birds use a star compass. Then, we tested the birds under a stationary planetarium sky, which simulated the star pattern of the local sky at 02:35 h for 11 consecutive hours of the night, and compared the birds' directional choices as a function of time...... with the predictions from five alternative stellar orientation hypotheses. The results supported the hypothesis suggesting that birds use a time-independent star compass based on learned geometrical star configurations to pinpoint the rotational point of the starry sky (north). In contrast, neither hypotheses...... suggesting that birds use the stars for establishing their global position and then perform true star navigation nor those suggesting the use of a time-compensated star compass were supported....

  8. Effective time-independent studies on resonance Raman spectroscopy of trans-stilbene including the Duschinsky effect

    Science.gov (United States)

    Lin, Na; Barone, Vincenzo; Cappelli, Chiara; Zhao, Xian; Ruud, Kenneth; Santoro, Fabrizio

    2013-07-01

    We simulate the resonance Raman spectra of trans-stilbene using a recently developed time-independent method that allows computations of the full two-dimensional spectrum as a function of the incident and scattered frequencies, including both the Franck-Condon and the Herzberg-Teller contributions. The potential energy surfaces (PESs) of the ground and resonant states are described in the harmonic approximation using density functional theory PBE0/6-31+G(d,p) calculations in gas phase and in cyclohexane. The simulated spectra are in good agreement with the experimental data [J. Chem. Phys. 83, 5000 (1985)] measured at four different excitation wavelengths, and allow us to unambiguously assign the main experimental bands. We perform an extensive comparison of the performance of four different vertical or adiabatic models for the PES of the resonant state, dissecting the effects of nuclear displacements and Duschinsky mixings on the spectra.

  9. Accurate deterministic solutions for the classic Boltzmann shock profile

    Science.gov (United States)

    Yue, Yubei

    The Boltzmann equation or Boltzmann transport equation is a classical kinetic equation devised by Ludwig Boltzmann in 1872. It is regarded as a fundamental law in rarefied gas dynamics. Rather than using macroscopic quantities such as density, temperature, and pressure to describe the underlying physics, the Boltzmann equation uses a distribution function in phase space to describe the physical system, and all the macroscopic quantities are weighted averages of the distribution function. The information contained in the Boltzmann equation is surprisingly rich, and the Euler and Navier-Stokes equations of fluid dynamics can be derived from it using series expansions. Moreover, the Boltzmann equation can reach regimes far from the capabilities of fluid dynamical equations, such as the realm of rarefied gases---the topic of this thesis. Although the Boltzmann equation is very powerful, it is extremely difficult to solve in most situations. Thus the only hope is to solve it numerically. But soon one finds that even a numerical simulation of the equation is extremely difficult, due to both the complex and high-dimensional integral in the collision operator, and the hyperbolic phase-space advection terms. For this reason, until few years ago most numerical simulations had to rely on Monte Carlo techniques. In this thesis I will present a new and robust numerical scheme to compute direct deterministic solutions of the Boltzmann equation, and I will use it to explore some classical gas-dynamical problems. In particular, I will study in detail one of the most famous and intrinsically nonlinear problems in rarefied gas dynamics, namely the accurate determination of the Boltzmann shock profile for a gas of hard spheres.

  10. Cluster Analysis of Time-Dependent Crystallographic Data: Direct Identification of Time-Independent Structural Intermediates

    Science.gov (United States)

    Kostov, Konstantin S.; Moffat, Keith

    2011-01-01

    The initial output of a time-resolved macromolecular crystallography experiment is a time-dependent series of difference electron density maps that displays the time-dependent changes in underlying structure as a reaction progresses. The goal is to interpret such data in terms of a small number of crystallographically refinable, time-independent structures, each associated with a reaction intermediate; to establish the pathways and rate coefficients by which these intermediates interconvert; and thereby to elucidate a chemical kinetic mechanism. One strategy toward achieving this goal is to use cluster analysis, a statistical method that groups objects based on their similarity. If the difference electron density at a particular voxel in the time-dependent difference electron density (TDED) maps is sensitive to the presence of one and only one intermediate, then its temporal evolution will exactly parallel the concentration profile of that intermediate with time. The rationale is therefore to cluster voxels with respect to the shapes of their TDEDs, so that each group or cluster of voxels corresponds to one structural intermediate. Clusters of voxels whose TDEDs reflect the presence of two or more specific intermediates can also be identified. From such groupings one can then infer the number of intermediates, obtain their time-independent difference density characteristics, and refine the structure of each intermediate. We review the principles of cluster analysis and clustering algorithms in a crystallographic context, and describe the application of the method to simulated and experimental time-resolved crystallographic data for the photocycle of photoactive yellow protein. PMID:21244840

  11. Multi-Group Reductions of LTE Air Plasma Radiative Transfer in Cylindrical Geometries

    Science.gov (United States)

    Scoggins, James; Magin, Thierry Edouard Bertran; Wray, Alan; Mansour, Nagi N.

    2013-01-01

    Air plasma radiation in Local Thermodynamic Equilibrium (LTE) within cylindrical geometries is studied with an application towards modeling the radiative transfer inside arc-constrictors, a central component of constricted-arc arc jets. A detailed database of spectral absorption coefficients for LTE air is formulated using the NEQAIR code developed at NASA Ames Research Center. The database stores calculated absorption coefficients for 1,051,755 wavelengths between 0.04 µm and 200 µm over a wide temperature (500K to 15 000K) and pressure (0.1 atm to 10.0 atm) range. The multi-group method for spectral reduction is studied by generating a range of reductions including pure binning and banding reductions from the detailed absorption coefficient database. The accuracy of each reduction is compared to line-by-line calculations for cylindrical temperature profiles resembling typical profiles found in arc-constrictors. It is found that a reduction of only 1000 groups is sufficient to accurately model the LTE air radiation over a large temperature and pressure range. In addition to the reduction comparison, the cylindrical-slab formulation is compared with the finite-volume method for the numerical integration of the radiative flux inside cylinders with varying length. It is determined that cylindrical-slabs can be used to accurately model most arc-constrictors due to their high length to radius ratios.

  12. Concepts of Confidence in Tendency Survey Research: An Assessment with Multi-group Confirmatory Factor Analysis.

    Science.gov (United States)

    Białowolski, Piotr

    In this paper, we investigate the link between the formal definition of confidence in tendency surveys and its measurement. We advocate for the use of reflective measures in an assessment of the confidence level in both consumer and industrial indicators. Based on the data from Poland's tendency survey research, we use a multi-group confirmatory factor analytical approach to demonstrate that the set of indicators proposed by the European Commission methodology that is currently used might be not appropriate to measure the concept of confidence consistently, both within and between periods. The conclusion is true for the confidence indicator in the area of consumer tendency surveys and for the tendency survey in the manufacturing industry. We search for possible amendments that help either to find the sources of instability for the indicators proposed by the guidelines of the European Commission or to select a different set of indicators for the concept of confidence. However, we determine that the differences between the newly proposed indicator that describe industrial confidence and the indicators based on the European Commission methodology are small in terms of correlations and predictive validity.

  13. Sample-size calculations for multi-group comparison in population pharmacokinetic experiments.

    Science.gov (United States)

    Ogungbenro, Kayode; Aarons, Leon

    2010-01-01

    This paper describes an approach for calculating sample size for population pharmacokinetic experiments that involve hypothesis testing based on multi-group comparison detecting the difference in parameters between groups under mixed-effects modelling. This approach extends what has been described for generalized linear models and nonlinear population pharmacokinetic models that involve only binary covariates to more complex nonlinear population pharmacokinetic models. The structural nonlinear model is linearized around the random effects to obtain the marginal model and the hypothesis testing involving model parameters is based on Wald's test. This approach provides an efficient and fast method for calculating sample size for hypothesis testing in population pharmacokinetic models. The approach can also handle different design problems such as unequal allocation of subjects to groups and unbalanced sampling times between and within groups. The results obtained following application to a one compartment intravenous bolus dose model that involved three different hypotheses under different scenarios showed good agreement between the power obtained from NONMEM simulations and nominal power.

  14. Multigroup radiation hydrodynamics with flux-limited diffusion and adaptive mesh refinement

    CERN Document Server

    González, Matthias; Commerçon, Benoît; Masson, Jacques

    2015-01-01

    Radiative transfer plays a key role in the star formation process. Due to a high computational cost, radiation-hydrodynamics simulations performed up to now have mainly been carried out in the grey approximation. In recent years, multi-frequency radiation-hydrodynamics models have started to emerge, in an attempt to better account for the large variations of opacities as a function of frequency. We wish to develop an efficient multigroup algorithm for the adaptive mesh refinement code RAMSES which is suited to heavy proto-stellar collapse calculations. Due to prohibitive timestep constraints of an explicit radiative transfer method, we constructed a time-implicit solver based on a stabilised bi-conjugate gradient algorithm, and implemented it in RAMSES under the flux-limited diffusion approximation. We present a series of tests which demonstrate the high performance of our scheme in dealing with frequency-dependent radiation-hydrodynamic flows. We also present a preliminary simulation of a three-dimensional p...

  15. Modelling diseases with relapse and nonlinear incidence of infection: a multi-group epidemic model

    Science.gov (United States)

    Wang, Jinliang; Pang, Jingmei; Liu, Xianning

    2014-01-01

    In this paper, we introduce a basic reproduction number for a multi-group SIR model with general relapse distribution and nonlinear incidence rate. We find that basic reproduction number plays the role of a key threshold in establishing the global dynamics of the model. By means of appropriate Lyapunov functionals, a subtle grouping technique in estimating the derivatives of Lyapunov functionals guided by graph-theoretical approach and LaSalle invariance principle, it is proven that if it is less than or equal to one, the disease-free equilibrium is globally stable and the disease dies out; whereas if it is larger than one, some sufficient condition is obtained in ensuring that there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. Furthermore, our results suggest that general relapse distribution are not the reason of sustained oscillations. Biologically, our model might be realistic for sexually transmitted diseases, such as Herpes, Condyloma acuminatum, etc. PMID:24963980

  16. Modelling diseases with relapse and nonlinear incidence of infection: a multi-group epidemic model.

    Science.gov (United States)

    Wang, Jinliang; Pang, Jingmei; Liu, Xianning

    2014-01-01

    In this paper, we introduce a basic reproduction number for a multi-group SIR model with general relapse distribution and nonlinear incidence rate. We find that basic reproduction number plays the role of a key threshold in establishing the global dynamics of the model. By means of appropriate Lyapunov functionals, a subtle grouping technique in estimating the derivatives of Lyapunov functionals guided by graph-theoretical approach and LaSalle invariance principle, it is proven that if it is less than or equal to one, the disease-free equilibrium is globally stable and the disease dies out; whereas if it is larger than one, some sufficient condition is obtained in ensuring that there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. Furthermore, our results suggest that general relapse distribution are not the reason of sustained oscillations. Biologically, our model might be realistic for sexually transmitted diseases, such as Herpes, Condyloma acuminatum, etc.

  17. Young Adults’ Attitude Towards Advertising: a multi-group analysis by ethnicity

    Directory of Open Access Journals (Sweden)

    Hiram Ting

    2015-08-01

    Full Text Available Objective – This study aims to investigate the attitude of Malaysian young adults towards advertising. How this segment responds to advertising, and how ethnic/cultural differences moderate are assessed. Design/methodology/approach – A quantitative questionnaire is used to collect data at two universities. Purposive sampling technique is adopted to ensure the sample represents the actual population. Structural equation modelling (SEM and multi-group analysis (MGA are utilized in analysis. Findings - The findings show that product information, hedonism, and good for economy are significant predictors of attitude towards advertising among young adults. Additionally, falsity is found to be significant among the Chinese, while social role and materialism among the Dayaks. No difference is observed in the effect of attitude on intention towards advertising by ethnicity. While homogeneity in advertising beliefs is assumed across ethnic groups, the Chinese and Dayak young adults are different in some of their advertising beliefs. Practical implications – Despite cultural effect being well-documented, young adults today seem to have similar beliefs and attitude towards advertising. Knowing what is shared and what is not for this segment is essential. Hence, it is imperative to keep track of their values in diversified communities to ensure effective communication process in advertising. Originality/value – In addition to the theory of reasoned action, MGA is utilized to assess the moderating effect of ethnic/culture on the whole model. This affords a more comprehensive understanding on the subject matter in multi-ethnic and cultural countries.

  18. Three-dimensional h-adaptivity for the multigroup neutron diffusion equations

    KAUST Repository

    Wang, Yaqi

    2009-04-01

    Adaptive mesh refinement (AMR) has been shown to allow solving partial differential equations to significantly higher accuracy at reduced numerical cost. This paper presents a state-of-the-art AMR algorithm applied to the multigroup neutron diffusion equation for reactor applications. In order to follow the physics closely, energy group-dependent meshes are employed. We present a novel algorithm for assembling the terms coupling shape functions from different meshes and show how it can be made efficient by deriving all meshes from a common coarse mesh by hierarchic refinement. Our methods are formulated using conforming finite elements of any order, for any number of energy groups. The spatial error distribution is assessed with a generalization of an error estimator originally derived for the Poisson equation. Our implementation of this algorithm is based on the widely used Open Source adaptive finite element library deal.II and is made available as part of this library\\'s extensively documented tutorial. We illustrate our methods with results for 2-D and 3-D reactor simulations using 2 and 7 energy groups, and using conforming finite elements of polynomial degree up to 6. © 2008 Elsevier Ltd. All rights reserved.

  19. Non-Regenerative Multi-Antenna Multi-Group Multi-Way Relaying

    Directory of Open Access Journals (Sweden)

    Klein Anja

    2011-01-01

    Full Text Available Abstract We consider non-regenerative multi-group multi-way (MGMW relaying. A half-duplex non-regenerative multi-antenna relay station (RS assists multiple communication groups. In each group, multiple half-duplex nodes exchange messages. In our proposal, the required number of communication phases is equal to the maximum number of nodes among the groups. In the first phase, all nodes transmit simultaneously to the RS. Assuming perfect channel state information is available at the RS, in the following broadcast (BC phases the RS applies transceive beamforming to its received signal and transmits simultaneously to all nodes. We propose three BC strategies for the BC phases: unicasting, multicasting and hybrid uni/multicasting. For the multicasting strategy, network coding is applied to maintain the same number of communication phases as for the other strategies. We address transceive beamforming maximising the sum rate of non-regenerative MGMW relaying. Due to the high complexity of finding the optimum transceive beamforming maximising the sum rate, we design generalised low complexity transceive beamforming algorithms for all BC strategies: matched filter, zero forcing, minimisation of mean square error and BC-strategy-aware transceive beamforming. It is shown that the sum rate performance of non-regenerative MGMW relaying depends both on the chosen BC strategies and the applied transceive beamforming at the RS.

  20. Simulations of protostellar collapse using multigroup radiation hydrodynamics. II. The second collapse

    CERN Document Server

    Vaytet, N; Audit, E; Commercon, B; Masson, J; Ferguson, J; Delahaye, F

    2013-01-01

    Star formation begins with the gravitational collapse of a dense core inside a molecular cloud. As the collapse progresses, the centre of the core begins to heat up as it becomes optically thick. The temperature and density in the centre eventually reach high enough values where fusion reactions can ignite; the protostar is born. This sequence of events entail many physical processes, of which radiative transfer is of paramount importance. Many simulations of protostellar collapse make use of a grey treatment of radiative transfer coupled to the hydrodynamics. However, interstellar gas and dust opacities present large variations as a function of frequency. In this paper, we follow-up on a previous paper on the collapse and formation of Larson's first core using multigroup radiation hydrodynamics (Paper I) by extending the calculations to the second phase of the collapse and the formation of Larson's second core. We have made the use of a non-ideal gas equation of state as well as an extensive set of spectral ...

  1. MENDF71x. Multigroup Neutron Cross Section Data Tables Based upon ENDF/B-VII.1

    Energy Technology Data Exchange (ETDEWEB)

    Conlin, Jeremy Lloyd [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Parsons, Donald Kent [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gardiner, Steven J. [Univ. of California, Davis, CA (United States); Gray, Mark Girard [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Lee, Mary Beth [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); White, Morgan Curtis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-12-17

    A new multi-group neutron cross section library has been released along with the release of NDI version 2.0.20. The library is named MENDF71x and is based upon the evaluations released in ENDF/B-VII.1 which was made publicly available in December 2011. ENDF/B-VII.1 consists of 423 evaluations of which ten are excited states evaluations and 413 are ground state evaluations. MENDF71x was created by processing the 423 evaluations into 618-group, downscatter only NDI data tables. The ENDF/B evaluation files were processed using NJOY version 99.393 with the exception of 35Cl and 233U. Those two isotopes had unique properties that required that we process the evaluation using NJOY version 2012. The MENDF71x library was only processed to room temperature, i.e., 293.6 K. In the future, we plan on producing a multi-temperature library based on ENDF/B-VII.1 and compatible with MENDF71x.

  2. Offensive Strategy in the 2D Soccer Simulation League Using Multi-Group Ant Colony Optimization

    Directory of Open Access Journals (Sweden)

    Shengbing Chen

    2016-02-01

    Full Text Available The 2D soccer simulation league is one of the best test beds for the research of artificial intelligence (AI. It has achieved great successes in the domain of multi-agent cooperation and machine learning. However, the problem of integral offensive strategy has not been solved because of the dynamic and unpredictable nature of the environment. In this paper, we present a novel offensive strategy based on multi-group ant colony optimization (MACO-OS. The strategy uses the pheromone evaporation mechanism to count the preference value of each attack action in different environments, and saves the values of success rate and preference in an attack information tree in the background. The decision module of the attacker then selects the best attack action according to the preference value. The MACO-OS approach has been successfully implemented in our 2D soccer simulation team in RoboCup competitions. The experimental results have indicated that the agents developed with this strategy, along with related techniques, delivered outstanding performances.

  3. Longitudinal multigroup invariance analysis of the satisfaction with food-related life scale in university students

    DEFF Research Database (Denmark)

    Schnettler, Berta; Miranda, Horacio; Miranda-Zapata, Edgardo

    2017-01-01

    This study examined longitudinal measurement invariance in the Satisfaction with Food-related Life (SWFL) scale using follow-up data from university students. We examined this measure of the SWFL in different groups of students, separated by various characteristics. Through non-probabilistic long......This study examined longitudinal measurement invariance in the Satisfaction with Food-related Life (SWFL) scale using follow-up data from university students. We examined this measure of the SWFL in different groups of students, separated by various characteristics. Through non......-probabilistic longitudinal sampling, 114 university students (65.8% female, mean age: 22.5) completed the SWFL questionnaire three times, over intervals of approximately one year. Confirmatory factor analysis was used to examine longitudinal measurement invariance. Two types of analysis were conducted: first, a longitudinal...... invariance by time, and second, a multigroup longitudinal invariance by sex, age, socio-economic status and place of residence during the study period. Results showed that the 3-item version of the SWFL exhibited strong longitudinal invariance (equal factor loadings and equal indicator intercepts...

  4. Testing the Nursing Worklife Model in Canada and Australia: a multi-group comparison study.

    Science.gov (United States)

    Roche, Michael A; Spence Laschinger, Heather K; Duffield, Christine

    2015-02-01

    To test a model derived from the Nursing Worklife Model linking elements of supportive practice environments to nurses' turnover intentions and behaviours in Canada and Australia. With the worldwide shortage of nurses, retaining nurses within fiscally challenged health care systems is critical to sustaining the future of the nursing workforce and ultimately safe patient care. The Nursing Worklife Model describes a pattern of relationships amongst environmental factors that support nursing practice and link to nurse turnover. This model has been tested in north American settings but not in other countries. A secondary analysis of data collected in two cross-sectional studies in Canadian and Australian hospitals (N=4816) was conducted to test our theoretical model. Multigroup structural equation modelling techniques were used to determine the validity of our model in both countries and to identify differences between countries. The hypothesized model relationships were supported in both countries with few differences between groups. Components of supportive professional practice work environments, particularly resources, were significantly linked to nurses' turnover intentions and active search for new jobs. Leadership played a critical role in shaping the pattern of relationships to other components of supportive practice environments and ultimately turnover behaviours. The Nursing Worklife Model was shown to be valid in both countries, suggesting that management efforts to ensure that features of supportive practice environments are in place to promote the retention of valuable nursing resources. Copyright © 2014 Elsevier Ltd. All rights reserved.

  5. Testing of the ABBN-RF multigroup data library in photon transport calculations

    Directory of Open Access Journals (Sweden)

    Koscheev Vladimir

    2017-01-01

    Full Text Available Gamma radiation is produced via both of nuclear fuel and shield materials. Photon interaction is known with appropriate accuracy, but secondary gamma ray production known much less. The purpose of this work is studying secondary gamma ray production data from neutron induced reactions in iron and lead by using MCNP code and modern nuclear data as ROSFOND, ENDF/B-7.1, JEFF-3.2 and JENDL-4.0. Results of calculations show that all of these nuclear data have different photon production data from neutron induced reactions and have poor agreement with evaluated benchmark experiment. The ABBN-RF multigroup cross-section library is based on the ROSFOND data. It presented in two forms of micro cross sections: ABBN and MATXS formats. Comparison of group-wise calculations using both ABBN and MATXS data to point-wise calculations with the ROSFOND library shows a good agreement. The discrepancies between calculation and experimental C/E results in neutron spectra are in the limit of experimental errors. For the photon spectrum they are out of experimental errors. Results of calculations using group-wise and point-wise representation of cross sections show a good agreement both for photon and neutron spectra.

  6. Testing of the ABBN-RF multigroup data library in photon transport calculations

    Science.gov (United States)

    Koscheev, Vladimir; Lomakov, Gleb; Manturov, Gennady; Tsiboulia, Anatoly

    2017-09-01

    Gamma radiation is produced via both of nuclear fuel and shield materials. Photon interaction is known with appropriate accuracy, but secondary gamma ray production known much less. The purpose of this work is studying secondary gamma ray production data from neutron induced reactions in iron and lead by using MCNP code and modern nuclear data as ROSFOND, ENDF/B-7.1, JEFF-3.2 and JENDL-4.0. Results of calculations show that all of these nuclear data have different photon production data from neutron induced reactions and have poor agreement with evaluated benchmark experiment. The ABBN-RF multigroup cross-section library is based on the ROSFOND data. It presented in two forms of micro cross sections: ABBN and MATXS formats. Comparison of group-wise calculations using both ABBN and MATXS data to point-wise calculations with the ROSFOND library shows a good agreement. The discrepancies between calculation and experimental C/E results in neutron spectra are in the limit of experimental errors. For the photon spectrum they are out of experimental errors. Results of calculations using group-wise and point-wise representation of cross sections show a good agreement both for photon and neutron spectra.

  7. VENTURE/PC manual: A multidimensional multigroup neutron diffusion code system

    Energy Technology Data Exchange (ETDEWEB)

    Shapiro, A.; Huria, H.C.; Cho, K.W. (Cincinnati Univ., OH (United States))

    1991-12-01

    VENTURE/PC is a recompilation of part of the Oak Ridge BOLD VENTURE code system, which will operate on an IBM PC or compatible computer. Neutron diffusion theory solutions are obtained for multidimensional, multigroup problems. This manual contains information associated with operating the code system. The purpose of the various modules used in the code system, and the input for these modules are discussed. The PC code structure is also given. Version 2 included several enhancements not given in the original version of the code. In particular, flux iterations can be done in core rather than by reading and writing to disk, for problems which allow sufficient memory for such in-core iterations. This speeds up the iteration process. Version 3 does not include any of the special processors used in the previous versions. These special processors utilized formatted input for various elements of the code system. All such input data is now entered through the Input Processor, which produces standard interface files for the various modules in the code system. In addition, a Standard Interface File Handbook is included in the documentation which is distributed with the code, to assist in developing the input for the Input Processor.

  8. VENTURE/PC manual: A multidimensional multigroup neutron diffusion code system. Version 3

    Energy Technology Data Exchange (ETDEWEB)

    Shapiro, A.; Huria, H.C.; Cho, K.W. [Cincinnati Univ., OH (United States)

    1991-12-01

    VENTURE/PC is a recompilation of part of the Oak Ridge BOLD VENTURE code system, which will operate on an IBM PC or compatible computer. Neutron diffusion theory solutions are obtained for multidimensional, multigroup problems. This manual contains information associated with operating the code system. The purpose of the various modules used in the code system, and the input for these modules are discussed. The PC code structure is also given. Version 2 included several enhancements not given in the original version of the code. In particular, flux iterations can be done in core rather than by reading and writing to disk, for problems which allow sufficient memory for such in-core iterations. This speeds up the iteration process. Version 3 does not include any of the special processors used in the previous versions. These special processors utilized formatted input for various elements of the code system. All such input data is now entered through the Input Processor, which produces standard interface files for the various modules in the code system. In addition, a Standard Interface File Handbook is included in the documentation which is distributed with the code, to assist in developing the input for the Input Processor.

  9. Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

    Science.gov (United States)

    Wang, Zhi-Gang; Gao, Rui-Mei; Fan, Xiao-Ming; Han, Qi-Xing

    2014-09-01

    We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ0, when the stochastic system obeys some conditions and ℛ0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.

  10. Noise source identification with the lattice Boltzmann method.

    Science.gov (United States)

    Vergnault, Etienne; Malaspinas, Orestis; Sagaut, Pierre

    2013-03-01

    In this paper the sound source identification problem is addressed with the use of the lattice Boltzmann method. To this aim, a time-reversed problem coupled to a complex differentiation method is used. In order to circumvent the inherent instability of the time-reversed lattice Boltzmann scheme, a method based on a split of the lattice Boltzmann equation into a mean and a perturbation component is used. Lattice Boltzmann method formulation around an arbitrary base flow is recalled and specific applications to acoustics are presented. The implementation of the noise source detection method for two-dimensional weakly compressible (low Mach number) flows is discussed, and the applicability of the method is demonstrated.

  11. Explicit finite-difference lattice Boltzmann method for curvilinear coordinates.

    Science.gov (United States)

    Guo, Zhaoli; Zhao, T S

    2003-06-01

    In this paper a finite-difference-based lattice Boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method [R. Mei and W. Shyy, J. Comput. Phys. 143, 426 (1998)] in which the collision term of the Boltzmann Bhatnagar-Gross-Krook equation for discrete velocities is treated implicitly. In the present method, the implicitness of the numerical scheme is removed by introducing a distribution function different from that being used currently. As a result, an explicit finite-difference lattice Boltzmann method for curvilinear coordinates is obtained. The scheme is applied to a two-dimensional Poiseuille flow, an unsteady Couette flow, a lid-driven cavity flow, and a steady flow around a circular cylinder. The numerical results are in good agreement with the results of previous studies. Extensions to other lattice Boltzmann models based on nonuniform meshes are also discussed.

  12. Lattice Boltzmann method fundamentals and engineering applications with computer codes

    CERN Document Server

    Mohamad, A A

    2014-01-01

    Introducing the Lattice Boltzmann Method in a readable manner, this book provides detailed examples with complete computer codes. It avoids the most complicated mathematics and physics without scarifying the basic fundamentals of the method.

  13. Analysis of spectral methods for the homogeneous Boltzmann equation

    KAUST Repository

    Filbet, Francis

    2011-04-01

    The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.

  14. Lattice Boltzmann modeling of directional wetting: Comparing simulations to experiments

    NARCIS (Netherlands)

    Jansen, H.P.; Sotthewes, K.; Swigchem, van J.; Zandvliet, H.J.W.; Kooij, E.S.

    2013-01-01

    Lattice Boltzmann Modeling (LBM) simulations were performed on the dynamic behavior of liquid droplets on chemically striped patterned surfaces, ultimately with the aim to develop a predictive tool enabling reliable design of future experiments. The simulations accurately mimic experimental results,

  15. Comparison of Boltzmann Equations with Quantum Dynamics for Scalar Fields

    CERN Document Server

    Lindner, Manfred; Lindner, Manfred; Muller, Markus Michael

    2006-01-01

    Boltzmann equations are often used to study the thermal evolution of particle reaction networks. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after relativistic heavy ion collisions. However, Boltzmann equations are only a classical approximation of the quantum thermalization process which is described by the so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the full Kadanoff-Baym equations. Therefore, we present in this paper a detailed comparison between the Kadanoff-Baym and Boltzmann equations in the framework of a scalar Phi^4 quantum field theory in 3+1 space-time dimensions. The obtained numerical solutions reveal significant discrepancies in the results predicted by both types of equations. Most notably, apart from quantitative discrepancies, on a qualitative level the universality observed for the Kadanoff-Baym equations is severely restricted in the case o...

  16. Permit Allocation in Emissions Trading using the Boltzmann Distribution

    CERN Document Server

    Park, Ji-Won; Isard, Walter

    2011-01-01

    In emissions trading, the initial permit allocation is an intractable issue because it needs to be essentially fair to the participating countries. There are many ways to distribute a given total amount of emissions permits among countries, but the existing distribution methods such as auctioning and grandfathering have been debated. Here we describe a new model for permit allocation in emissions trading using the Boltzmann distribution. The Boltzmann distribution is introduced to permit allocation by combining it with concepts in emissions trading. A price determination mechanism for emission permits is then developed in relation to the {\\beta} value in the Boltzmann distribution. Finally, it is demonstrated how emissions permits can be practically allocated among participating countries in empirical results. The new allocation model using the Boltzmann distribution describes a most probable, natural, and unbiased distribution of emissions permits among multiple countries. Based on its simplicity and versati...

  17. Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The overall objective of the proposed project is to develop a generalized lattice Boltzmann (GLB) approach as a potential computational aeroacoustics (CAA) tool for...

  18. Maxwell iteration for the lattice Boltzmann method with diffusive scaling.

    Science.gov (United States)

    Zhao, Weifeng; Yong, Wen-An

    2017-03-01

    In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.

  19. Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation

    OpenAIRE

    Gamba, I. M.; Panferov, V.; Villani, C.

    2007-01-01

    For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique to propagation of upper Maxwellian bounds in the spatially-inhomogeneous case are discussed.

  20. A new lattice Boltzmann model for incompressible magnetohydrodynamics

    Institute of Scientific and Technical Information of China (English)

    Chen Xing-Wang; Shi Bao-Chang

    2005-01-01

    Most of the existing lattice Boltzmann magnetohydrodynamics (MHD) models can be viewed as compressible schemes to simulate incompressible MHD flows. The compressible effect might lead to some undesired errors in numerical simulations. In this paper a new incompressible lattice Boltzmann MHD model without compressible effect is presented for simulating incompressible MHD flows. Numerical simulations of the Hartmann flow are performed. We do numerous tests and make comparison with Dellar's model in detail. The numerical results are in good agreement with the analytical error.

  1. [Welding arc temperature field measurements based on Boltzmann spectrometry].

    Science.gov (United States)

    Si, Hong; Hua, Xue-Ming; Zhang, Wang; Li, Fang; Xiao, Xiao

    2012-09-01

    Arc plasma, as non-uniform plasma, has complicated energy and mass transport processes in its internal, so plasma temperature measurement is of great significance. Compared with absolute spectral line intensity method and standard temperature method, Boltzmann plot measuring is more accurate and convenient. Based on the Boltzmann theory, the present paper calculates the temperature distribution of the plasma and analyzes the principle of lines selection by real time scanning the space of the TIG are measurements.

  2. Boltzmann Samplers for v-balanced Colored Necklaces

    CERN Document Server

    Bodini, Olivier

    2009-01-01

    This paper is devoted to the random generation of particular colored necklaces for which the number of beads of a given color is constrained (these necklaces are called v-balanced). We propose an efficient sampler (its expected time complexity is linear) which satisfies the Boltzmann model principle introduced by Duchon, Flajolet, Louchard and Schaeffer. Our main motivation is to show that the absence of a decomposable specification can be circumvented by mixing the Boltzmann samplers with other types of samplers.

  3. Meshless lattice Boltzmann method for the simulation of fluid flows.

    Science.gov (United States)

    Musavi, S Hossein; Ashrafizaadeh, Mahmud

    2015-02-01

    A meshless lattice Boltzmann numerical method is proposed. The collision and streaming operators of the lattice Boltzmann equation are separated, as in the usual lattice Boltzmann models. While the purely local collision equation remains the same, we rewrite the streaming equation as a pure advection equation and discretize the resulting partial differential equation using the Lax-Wendroff scheme in time and the meshless local Petrov-Galerkin scheme based on augmented radial basis functions in space. The meshless feature of the proposed method makes it a more powerful lattice Boltzmann solver, especially for cases in which using meshes introduces significant numerical errors into the solution, or when improving the mesh quality is a complex and time-consuming process. Three well-known benchmark fluid flow problems, namely the plane Couette flow, the circular Couette flow, and the impulsively started cylinder flow, are simulated for the validation of the proposed method. Excellent agreement with analytical solutions or with previous experimental and numerical results in the literature is observed in all the simulations. Although the computational resources required for the meshless method per node are higher compared to that of the standard lattice Boltzmann method, it is shown that for cases in which the total number of nodes is significantly reduced, the present method actually outperforms the standard lattice Boltzmann method.

  4. KOMPUTASI DISTRIBUSI NEUTRON DALAM STATISTIK MAXWELL BOLTZMANN

    Directory of Open Access Journals (Sweden)

    Tuti Purwoningsih

    2013-03-01

    Full Text Available The migration of neutron is arranged by some probability distributions such as probability of spread distribution, probability of distance distribution, probability of energy distribution and probability of flux distribution. One application of these pattern distributions is modelling the reaction between neutron and elements which compose the tissue related to the absorption of neutron in brain cancer tissues. This article explores computation analysis of pattern of distribution of neutron flux in a reactor system. Variables were the amount of neutron simulated and the depth of cylindrical reactor system. Simulations showed that 20-120 minutes was needed in executing 100,000 neutrons to build the distribution pattern of neutrons flux. This pattern was also depended on the depth of the system. In all depths, the peak of neutron flux distribution pattern was in the 3rd bin. Comparison between this simulations and experiment results in literatures showed that by analyzing the simulation of the distribution of neutron flux, a Poisson distribution which follows the Maxwell-Boltzmann was resulted. Perpindahan neutron diatur dengan beberapa peluang distribusi, seperti peluang distribusi sudut hamburan, peluang distribusi jarak perpindahan, peluang distribusi energi transfer, serta peluang distribusi fluks neutron. Salah satu aplikasi dari pola distribusi ini adalah pemodelan reaksi antara neutron dengan elemen-elemen penyusun jaringan yang terkait dengan serapan neutron dan dosis yang terserap oleh jaringan tumor otak pada terapi BNCT (Boron Neutron Capture Therapy. Dalam penelitian ini dibahas analisis komputasi tentang pola distribusi fluks neutron dalam suatu sistem reaktor. Variabel dalam penelitian ini adalah banyaknya neutron yang disimulasikan, serta kedalaman sistem reaktor yang dalam penelitian ini menggunakan sistem reaktor berbentuk silinder. Hasil simulasi menunjukkan bahwa dengan neutron sebanyak 100.000 diperlukan waktu eksekusi sekitar

  5. Steady shear flow behavior of sage seed gum affected by various salts and sugars: Time-independent properties.

    Science.gov (United States)

    Yousefi, Ali R; Eivazlou, Razieh; Razavi, Seyed M A

    2016-10-01

    The rheological properties of food hydrocolloids are remarkably influenced by the quality of solvent/cosolutes in a food system. In this work, the steady shear flow behavior of sage seed gum (SSG, 0.5% w/w) at the presence of different levels of salts (KCl & MgCl2, 0-100mM) and sugars (sucrose, lactose & glucose, 0-6% w/w) was studied. It was found that the rheological properties of SSG were affected by the type of sugars and salts and their concentrations as well. Synergistic interaction was observed between SSG and sugars which enhanced the viscosity of gum solutions, while salts addition diminished the viscosity. SSG solutions exhibited a shear thinning behavior at all conditions tested. Various time-independent rheological models were used to fit the shear stress-shear rate data, although the Herschel-Bulkley (R(2)=0.994-0.999) and Sisko (R(2)=0.995-0.999) models showed the best results to describe the flow behavior of SSG. In the presence of salts, the yield stress (τ0), consistency coefficient (k), and flow behavior index (n) values decreased. The k and τ0 values enhanced and the n value lowered in the presence of sugars. Divalent cations of Mg(2+) and sucrose roughly showed more effect on rheological parameters than others.

  6. Accurate lineshape spectroscopy and the Boltzmann constant.

    Science.gov (United States)

    Truong, G-W; Anstie, J D; May, E F; Stace, T M; Luiten, A N

    2015-10-14

    Spectroscopy has an illustrious history delivering serendipitous discoveries and providing a stringent testbed for new physical predictions, including applications from trace materials detection, to understanding the atmospheres of stars and planets, and even constraining cosmological models. Reaching fundamental-noise limits permits optimal extraction of spectroscopic information from an absorption measurement. Here, we demonstrate a quantum-limited spectrometer that delivers high-precision measurements of the absorption lineshape. These measurements yield a very accurate measurement of the excited-state (6P1/2) hyperfine splitting in Cs, and reveals a breakdown in the well-known Voigt spectral profile. We develop a theoretical model that accounts for this breakdown, explaining the observations to within the shot-noise limit. Our model enables us to infer the thermal velocity dispersion of the Cs vapour with an uncertainty of 35 p.p.m. within an hour. This allows us to determine a value for Boltzmann's constant with a precision of 6 p.p.m., and an uncertainty of 71 p.p.m.

  7. Extended lattice Boltzmann scheme for droplet combustion

    Science.gov (United States)

    Ashna, Mostafa; Rahimian, Mohammad Hassan; Fakhari, Abbas

    2017-05-01

    The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n -butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.

  8. Analysis of Jeans instability from Boltzmann equation

    CERN Document Server

    Kremer, Gilberto M

    2015-01-01

    The dynamics of self-gravitating fluids is analyzed within the framework of a collisionless Boltzmann equation in the presence of gravitational fields and Poisson equation. The equilibrium distribution function takes into account the expansion of the Universe and a pressureless fluid in the matter dominated Universe. Without invoking Jeans "swindle" a dispersion relation is obtained by considering small perturbations of the equilibrium values of the distribution function and gravitational potential. The collapse criterion -- which happens in an unstable region where the solution grows exponentially with time -- is determined from the dispersion relation. The collapse criterion in a static Universe occurs when the wavenumber $k$ is smaller than the Jeans wavenumber $k_J$, which was the solution found by Jeans. For an expanding Universe it is shown that this criterion is $k\\leq\\sqrt{7/6}\\,k_J$. As a consequence the ratio of the mass contained in a sphere of diameter equal to the wavelength $\\lambda=2\\pi/k$ to t...

  9. Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.

    Science.gov (United States)

    Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J

    2015-08-01

    In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.

  10. Extended lattice Boltzmann scheme for droplet combustion.

    Science.gov (United States)

    Ashna, Mostafa; Rahimian, Mohammad Hassan; Fakhari, Abbas

    2017-05-01

    The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n-butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.

  11. Symmetry breaking in the opinion dynamics of a multi-group project organization

    Science.gov (United States)

    Zhu, Zhen-Tao; Zhou, Jing; Li, Ping; Chen, Xing-Guang

    2012-10-01

    A bounded confidence model of opinion dynamics in multi-group projects is presented in which each group's opinion evolution is driven by two types of forces: (i) the group's cohesive force which tends to restore the opinion back towards the initial status because of its company culture; and (ii) nonlinear coupling forces with other groups which attempt to bring opinions closer due to collaboration willingness. Bifurcation analysis for the case of a two-group project shows a cusp catastrophe phenomenon and three distinctive evolutionary regimes, i.e., a deadlock regime, a convergence regime, and a bifurcation regime in opinion dynamics. The critical value of initial discord between the two groups is derived to discriminate which regime the opinion evolution belongs to. In the case of a three-group project with a symmetric social network, both bifurcation analysis and simulation results demonstrate that if each pair has a high initial discord, instead of symmetrically converging to consensus with the increase of coupling scale as expected by Gabbay's result (Physica A 378 (2007) p. 125 Fig. 5), project organization (PO) may be split into two distinct clusters because of the symmetry breaking phenomenon caused by pitchfork bifurcations, which urges that apart from divergence in participants' interests, nonlinear interaction can also make conflict inevitable in the PO. The effects of two asymmetric level parameters are tested in order to explore the ways of inducing dominant opinion in the whole PO. It is found that the strong influence imposed by a leader group with firm faith on the flexible and open minded follower groups can promote the formation of a positive dominant opinion in the PO.

  12. Symmetry breaking in the opinion dynamics of a multi-group project organization

    Institute of Scientific and Technical Information of China (English)

    Zhu Zhen-Tao; Zhou Jing; Li Ping; Chen Xing-Guang

    2012-01-01

    A bounded confidence model of opinion dynamics in multi-group projects is presented in which each group's opinion evolution is driven by two types of forces:(i) the group's cohesive force which tends to restore the opinion back towards the initial status because of its company culture; and (ii) nonlinear coupling forces with other groups which attempt to bring opinions closer due to collaboration willingness.Bifurcation analysis for the case of a two-group project shows a cusp catastrophe phenomenon and three distinctive evolutionary regimes,i.e.,a deadlock regime,a convergence regime,and a bifurcation regime in opinion dynamics.The critical value of initial discord between the two groups is derived to discriminate which regime the opinion evolution belongs to.In the case of a three-group project with a symmetric social network,both bifurcation analysis and simulation results demonstrate that if each pair has a high initial discord,instead of symmetrically converging to consensus with the increase of coupling scale as expected by Gabbay's result (Physica A 378 (2007) p.125 Fig.5),project organization (PO) may be split into two distinct clusters because of the symmetry breaking phenomenon caused by pitchfork bifurcations,which urges that apart from divergence in participants' interests,nonlinear interaction can also make conflict inevitable in the PO.The effects of two asymmetric level parameters are tested in order to explore the ways of inducing dominant opinion in the whole PO.It is found that the strong influence imposed by a leader group with firm faith on the flexible and open minded follower groups can promote the formation of a positive dominant opinion in the PO.

  13. Questionnaires for Students with Special Educational Needs in the Area of Learning: Results from Multi-Group Analysis

    Directory of Open Access Journals (Sweden)

    Lena Nusser

    2015-05-01

    Full Text Available This article focuses on measurement invariance of the assessment of educationally relevant constructs via written questionnaires for students at special schools and at low track schools attending 5th grade. To examine optimal conditions of administration for students with special educational needs in the area of learning an experimental design was implemented. If accommodated questionnaires, different school enrollments as well as competence differences allow equivalent assessment of reading motivation and academic self-concepts will be investigated with multi-group comparison of confirmatory factor analysis. The results indicate that comparisons between groups of students at special schools and low track schools are meaningful for certain constructs.

  14. Lattice Boltzmann method and its applications in engineering thermophysics

    Institute of Scientific and Technical Information of China (English)

    HE YaLing; LI Qing; WANG Yong; TANG GuiHua

    2009-01-01

    The lattice Boltzmann method (LBM),a mesoscopic method between the molecular dynamics method and the conventional numerical methods,has been developed into a very efficient numerical alternative in the past two decades.Unlike conventional numerical methods,the kinetic theory based LBM simulates fluid flows by tracking the evolution of the particle distribution function,and then accumulates the distribution to obtain macroscopic averaged properties.In this article we review some work on LBM applications in engineering thermophysics:(1) brief introduction to the development of the LBM; (2)fundamental theory of LBM including the Boltzmann equation,Maxwell distribution function,Boltzmann-BGK equation,and the lattice Boltzmann-BGK equation; (3) lattice Boltzmann models for compressible flows and non-equilibrium gas flows,bounce back-specular-reflection boundary scheme for microscale gaseous flows,the mass modified outlet boundary scheme for fully developed flows,and an implicit-explicit finite-difference-based LBM; and (4) applications of the LBM to oscillating flow,compressible flow,porous media flow,non-equilibrium flow,and gas resonant oscillating flow.

  15. Lattice Boltzmann Model for Compressible Fluid on a Square Lattice

    Institute of Scientific and Technical Information of China (English)

    SUN Cheng-Hai

    2000-01-01

    A two-level four-direction lattice Boltzmann model is formulated on a square lattice to simulate compressible flows with a high Mach number. The particle velocities are adaptive to the mean velocity and internal energy. Therefore, the mean flow can have a high Mach number. Due to the simple form of the equilibrium distribution, the 4th order velocity tensors are not involved in the calculations. Unlike the standard lattice Boltzmann model, o special treatment is need for the homogeneity of 4th order velocity tensors on square lattices. The Navier-Stokes equations were derived by the Chapman-Enskog method from the BGK Boltzmann equation. The model can be easily extended to three-dimensional cubic lattices. Two-dimensional shock-wave propagation was simulated

  16. Navier-Stokes Dynamics by a Discrete Boltzmann Model

    Science.gov (United States)

    Rubinstein, Robet

    2010-01-01

    This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

  17. Caveat on the Boltzmann distribution function use in biology.

    Science.gov (United States)

    Sevcik, Carlos

    2017-08-01

    Sigmoid semilogarithmic functions with shape of Boltzmann equations, have become extremely popular to describe diverse biological situations. Part of the popularity is due to the easy availability of software which fits Boltzmann functions to data, without much knowledge of the fitting procedure or the statistical properties of the parameters derived from the procedure. The purpose of this paper is to explore the plasticity of the Boltzmann function to fit data, some aspects of the optimization procedure to fit the function to data and how to use this plastic function to differentiate the effect of treatment on data and to attest the statistical significance of treatment effect on the data. Copyright © 2017. Published by Elsevier Ltd.

  18. Physical scales in the Wigner-Boltzmann equation.

    Science.gov (United States)

    Nedjalkov, M; Selberherr, S; Ferry, D K; Vasileska, D; Dollfus, P; Querlioz, D; Dimov, I; Schwaha, P

    2013-01-01

    The Wigner-Boltzmann equation provides the Wigner single particle theory with interactions with bosonic degrees of freedom associated with harmonic oscillators, such as phonons in solids. Quantum evolution is an interplay of two transport modes, corresponding to the common coherent particle-potential processes, or to the decoherence causing scattering due to the oscillators. Which evolution mode will dominate depends on the scales of the involved physical quantities. A dimensionless formulation of the Wigner-Boltzmann equation is obtained, where these scales appear as dimensionless strength parameters. A notion called scaling theorem is derived, linking the strength parameters to the coupling with the oscillators. It is shown that an increase of this coupling is equivalent to a reduction of both the strength of the electric potential, and the coherence length. Secondly, the existence of classes of physically different, but mathematically equivalent setups of the Wigner-Boltzmann evolution is demonstrated.

  19. Stabilizing the thermal lattice Boltzmann method by spatial filtering.

    Science.gov (United States)

    Gillissen, J J J

    2016-10-01

    We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.

  20. Electrostatic forces in the Poisson-Boltzmann systems.

    Science.gov (United States)

    Xiao, Li; Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

    2013-09-07

    Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.

  1. Lattice Boltzmann Large Eddy Simulation Model of MHD

    CERN Document Server

    Flint, Christopher

    2016-01-01

    The work of Ansumali \\textit{et al.}\\cite{Ansumali} is extended to Two Dimensional Magnetohydrodynamic (MHD) turbulence in which energy is cascaded to small spatial scales and thus requires subgrid modeling. Applying large eddy simulation (LES) modeling of the macroscopic fluid equations results in the need to apply ad-hoc closure schemes. LES is applied to a suitable mesoscopic lattice Boltzmann representation from which one can recover the MHD equations in the long wavelength, long time scale Chapman-Enskog limit (i.e., the Knudsen limit). Thus on first performing filter width expansions on the lattice Boltzmann equations followed by the standard small Knudsen expansion on the filtered lattice Boltzmann system results in a closed set of MHD turbulence equations provided we enforce the physical constraint that the subgrid effects first enter the dynamics at the transport time scales. In particular, a multi-time relaxation collision operator is considered for the density distribution function and a single rel...

  2. An integrable 3D lattice model with positive Boltzmann weights

    CERN Document Server

    Mangazeev, Vladimir V; Sergeev, Sergey M

    2013-01-01

    In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D generalisation of the Yang-Baxter equation. The weights depend on a free parameter 0Boltzmann weights.

  3. Multi-group acculturation orientations in a changing context: Palestinian Christian Arab adolescents in Israel after the lost decade.

    Science.gov (United States)

    Munayer, Salim J; Horenczyk, Gabriel

    2014-10-01

    Grounded in a contextual approach to acculturation of minorities, this study examines changes in acculturation orientations among Palestinian Christian Arab adolescents in Israel following the "lost decade of Arab-Jewish coexistence." Multi-group acculturation orientations among 237 respondents were assessed vis-à-vis two majorities--Muslim Arabs and Israeli Jews--and compared to 1998 data. Separation was the strongest endorsed orientation towards both majority groups. Comparisons with the 1998 data also show a weakening of the Integration attitude towards Israeli Jews, and also distancing from Muslim Arabs. For the examination of the "Westernisation" hypothesis, multi-dimensional scaling (MDS) analyses of perceptions of Self and group values clearly showed that, after 10 years, Palestinian Christian Arabs perceive Israeli Jewish culture as less close to Western culture, and that Self and the Christian Arab group have become much closer, suggesting an increasing identification of Palestinian Christian Arab adolescents with their ethnoreligious culture. We discuss the value of a multi-group, multi-method, and multi-wave approach to the examination of the role of the political context in acculturation processes.

  4. 2D Multi-Angle, Multi-Group Neutrino Radiation-Hydrodynamic Simulations of Postbounce Supernova Cores

    CERN Document Server

    Ott, Christian D; Dessart, Luc; Livne, Eli

    2008-01-01

    We perform axisymmetric (2D) multi-angle, multi-group neutrino radiation-hydrodynamics calculations of the postbounce phase of core-collapse supernovae using a genuinely 2D discrete-ordinate (S_n) method. We follow the long-term postbounce evolution of the cores of one nonrotating and one rapidly-rotating 20-solar-mass stellar model for ~400 milliseconds from 160 ms to ~550 ms after bounce. We present a multi-D analysis of the multi-angle neutrino radiation fields and compare in detail with counterpart simulations carried out in the 2D multi-group flux-limited diffusion (MGFLD) approximation to neutrino transport. We find that 2D multi-angle transport is superior in capturing the global and local radiation-field variations associated with rotation-induced and SASI-induced aspherical hydrodynamic configurations. In the rotating model, multi-angle transport predicts much larger asymptotic neutrino flux asymmetries with pole to equator ratios of up to ~2.5, while MGFLD tends to sphericize the radiation fields al...

  5. On a Boltzmann-type price formation model

    KAUST Repository

    Burger, Martin

    2013-06-26

    In this paper, we present a Boltzmann-type price formation model, which is motivated by a parabolic free boundary model for the evolution of price presented by Lasry and Lions in 2007. We discuss the mathematical analysis of the Boltzmann-type model and show that its solutions converge to solutions of the model by Lasry and Lions as the transaction rate tends to infinity. Furthermore, we analyse the behaviour of the initial layer on the fast time scale and illustrate the price dynamics with various numerical experiments. © 2013 The Author(s) Published by the Royal Society. All rights reserved.

  6. Revisiting Boltzmann learning: parameter estimation in Markov random fields

    DEFF Research Database (Denmark)

    Hansen, Lars Kai; Andersen, Lars Nonboe; Kjems, Ulrik

    1996-01-01

    This article presents a generalization of the Boltzmann machine that allows us to use the learning rule for a much wider class of maximum likelihood and maximum a posteriori problems, including both supervised and unsupervised learning. Furthermore, the approach allows us to discuss regularization...... and generalization in the context of Boltzmann machines. We provide an illustrative example concerning parameter estimation in an inhomogeneous Markov field. The regularized adaptation produces a parameter set that closely resembles the “teacher” parameters, hence, will produce segmentations that closely reproduce...

  7. Boundary Conditions for Free Interfaces with the Lattice Boltzmann Method

    CERN Document Server

    Bogner, Simon; Rüde, Ulrich

    2014-01-01

    In this paper we analyze the boundary treatment of the Lattice Boltzmann method for simulating 3D flows with free surfaces. The widely used free surface boundary condition of K\\"orner et al. (2005) is shown to be first order accurate. The article presents new free surface boundary schemes that are suitable for the lattice Boltzmann method and that have second order spatial accuracy. The new method takes the free boundary position and orientation with respect to the computational lattice into account. Numerical experiments confirm the theoretical findings and illustrate the the difference between the old and the new method.

  8. Spinor Boltzmann Equation with Two Momenta at the Fermi Level

    Institute of Scientific and Technical Information of China (English)

    王正川

    2012-01-01

    Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. The lon- gitudinal charge currents, transverse spin currents and the continuity equations satisfied by them are then studied, it indicates that both the charge currents and spin currents decay oscillately along with position, which is due to the momenta integral over the Fermi surface. We also compare our charge currents and spin currents with the corresponding results of one momentum spinor Boltzmann equation, the differences are obvious.

  9. The Boltzmann equation near a rotational local Maxwellian

    CERN Document Server

    Kim, Chanwoo

    2011-01-01

    In rotationally symmetric domains, the Boltzmann equation with specular reflection boundary condition has a special type of equilibrium states called the rotational local Maxwellian which, unlike the uniform Maxwellian, has an additional term related to the angular momentum of the gas. In this paper, we consider the initial boundary value problem of the Boltzmann equation near the rotational local Maxwellian. Based on the L2-L1 framework of [12], we establish the global well-posedness and the convergence toward such equilibrium states.

  10. Acoustic limit of the Boltzmann equation: classical solutions

    OpenAIRE

    Jang, Juhi; Jiang, Ning

    2009-01-01

    We study the acoustic limit from the Boltzmann equation in the framework of classical solutions. For a solution $F_\\varepsilon=\\mu +\\varepsilon \\sqrt{\\mu}f_\\varepsilon$ to the rescaled Boltzmann equation in the acoustic time scaling \\partial_t F_\\varepsilon +\\vgrad F_\\varepsilon =\\frac{1}{\\varepsilon} \\Q(F_\\varepsilon,F_\\varepsilon), inside a periodic box $\\mathbb{T}^3$, we establish the global-in-time uniform energy estimates of $f_\\varepsilon$ in $\\varepsilon$ and prove that $f_\\varepsilon$...

  11. Contact line dynamics in binary lattice Boltzmann simulations

    CERN Document Server

    Pooley, C M; Yeomans, J M; 10.1103/PhysRevE.78.056709

    2008-01-01

    We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state lead to incorrect results for the equilibrium contact angle. We identify the origins of these spurious currents, and demonstrate how the results can be greatly improved by using a lattice Boltzmann method based on a multiple-relaxation-time algorithm. By considering capillary filling we describe the dependence of the advancing contact angle on the interface velocity.

  12. Axisymmetric multiphase Lattice Boltzmann method for generic equations of state

    CERN Document Server

    Reijers, Sten A; Toschi, Federico

    2015-01-01

    We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid-gas density ratios up to $10^3$. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation equations. We validate the model by showing that a stationary droplet obeys the Young-Laplace law, comparing the second oscillation mode of a droplet with respect to an analytical solution and showing correct mass conservation of a propagating density wave.

  13. Two-dimensional lattice Boltzmann model for magnetohydrodynamics.

    Science.gov (United States)

    Schaffenberger, Werner; Hanslmeier, Arnold

    2002-10-01

    We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.

  14. CORRECTIONS TO THE COLLISION TERM IN THE BGK BOLTZMANN EQUATION

    Institute of Scientific and Technical Information of China (English)

    FENG SHI-DE; REN RONG-CAI; CUI XIAO-PENG; JI ZHONG-ZHEN

    2001-01-01

    With the discrete method of the hexagonal cell and three different velocities of particle population in each cell,a two-dimensional lattice Boltzmann model is developed in this paper.[1,2] The collision operator in the Boltzmann equation is expanded to fourth order using the Taylor expansion.[3,4] With this model, good results have been obtained from the numerical simulation of the reflection phenomenon of the shock wave on the surface of an obstacle, and the numerical stability is also good. Thus the applicability of the D2Q19 model is verified.

  15. Application of an excited state LDA exchange energy functional for the calculation of transition energy of atoms within time-independent density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Shamim, Md; Harbola, Manoj K, E-mail: sami@iitk.ac.i, E-mail: mkh@iitk.ac.i [Department of Physics, Indian Institute of Technology, Kanpur 208 016 (India)

    2010-11-14

    Transition energies of a new class of excited states (two-gap systems) of various atoms are calculated in time-independent density functional formalism by using a recently proposed local density approximation exchange energy functional for excited states. It is shown that the excitation energies calculated with this functional compare well with those calculated with exact exchange theories.

  16. Multi-Population Invariance with Dichotomous Measures: Combining Multi-Group and MIMIC Methodologies in Evaluating the General Aptitude Test in the Arabic Language

    Science.gov (United States)

    Sideridis, Georgios D.; Tsaousis, Ioannis; Al-harbi, Khaleel A.

    2015-01-01

    The purpose of the present study was to extend the model of measurement invariance by simultaneously estimating invariance across multiple populations in the dichotomous instrument case using multi-group confirmatory factor analytic and multiple indicator multiple causes (MIMIC) methodologies. Using the Arabic version of the General Aptitude Test…

  17. Determining Planetary Temperatures with the Stefan-Boltzmann Law

    Science.gov (United States)

    LoPresto, Michael C.; Hagoort, Nichole

    2011-01-01

    What follows is a description of several activities involving the Stefan-Boltzmann radiation law that can provide laboratory experience beyond what is normally found in traditional introductory thermodynamics experiments on thermal expansion, specific heat, and heats of transformation. The activities also provide more extensive coverage of and…

  18. Determining Planetary Temperatures with the Stefan-Boltzmann Law

    Science.gov (United States)

    LoPresto, Michael C.; Hagoort, Nichole

    2011-01-01

    What follows is a description of several activities involving the Stefan-Boltzmann radiation law that can provide laboratory experience beyond what is normally found in traditional introductory thermodynamics experiments on thermal expansion, specific heat, and heats of transformation. The activities also provide more extensive coverage of and…

  19. An efficient learning procedure for deep Boltzmann machines.

    Science.gov (United States)

    Salakhutdinov, Ruslan; Hinton, Geoffrey

    2012-08-01

    We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent statistics are estimated using a variational approximation that tends to focus on a single mode, and data-independent statistics are estimated using persistent Markov chains. The use of two quite different techniques for estimating the two types of statistic that enter into the gradient of the log likelihood makes it practical to learn Boltzmann machines with multiple hidden layers and millions of parameters. The learning can be made more efficient by using a layer-by-layer pretraining phase that initializes the weights sensibly. The pretraining also allows the variational inference to be initialized sensibly with a single bottom-up pass. We present results on the MNIST and NORB data sets showing that deep Boltzmann machines learn very good generative models of handwritten digits and 3D objects. We also show that the features discovered by deep Boltzmann machines are a very effective way to initialize the hidden layers of feedforward neural nets, which are then discriminatively fine-tuned.

  20. Boltzmann-type control of opinion consensus through leaders.

    Science.gov (United States)

    Albi, G; Pareschi, L; Zanella, M

    2014-11-13

    The study of formations and dynamics of opinions leading to the so-called opinion consensus is one of the most important areas in mathematical modelling of social sciences. Following the Boltzmann-type control approach recently introduced by the first two authors, we consider a group of opinion leaders who modify their strategy accordingly to an objective functional with the aim of achieving opinion consensus. The main feature of the Boltzmann-type control is that, owing to an instantaneous binary control formulation, it permits the minimization of the cost functional to be embedded into the microscopic leaders' interactions of the corresponding Boltzmann equation. The related Fokker-Planck asymptotic limits are also derived, which allow one to give explicit expressions of stationary solutions. The results demonstrate the validity of the Boltzmann-type control approach and the capability of the leaders' control to strategically lead the followers' opinion. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

  1. The peeling process of infinite Boltzmann planar maps

    DEFF Research Database (Denmark)

    Budd, Timothy George

    2016-01-01

    criterion has a very simple interpretation. The finite random planar maps under consideration were recently proved to possess a well-defined local limit known as the infinite Boltzmann planar map (IBPM). Inspired by recent work of Curien and Le Gall, we show that the peeling process on the IBPM can...

  2. Lattice Boltzmann method for linear oscillatory noncontinuum flows.

    Science.gov (United States)

    Shi, Yong; Yap, Ying Wan; Sader, John E

    2014-03-01

    Oscillatory gas flows are commonly generated by micro- and nanoelectromechanical systems. Due to their small size and high operating frequencies, these devices often produce noncontinuum gas flows. Theoretical analysis of such flows requires solution of the unsteady Boltzmann equation, which can present a formidable challenge. In this article, we explore the applicability of the lattice Boltzmann (LB) method to such linear oscillatory noncontinuum flows; this method is derived from the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation. We formulate four linearized LB models in the frequency domain, based on Gaussian-Hermite quadratures of different algebraic precision (AP). The performance of each model is assessed by comparison to high-accuracy numerical solutions to the linearized Boltzmann-BGK equation for oscillatory Couette flow. The numerical results demonstrate that high even-order LB models provide superior performance over the greatest noncontinuum range. Our results also highlight intrinsic deficiencies in the current LB framework, which is incapable of capturing noncontinuum behavior at high oscillation frequencies, regardless of quadrature AP and the Knudsen number.

  3. Lattice Boltzmann method for linear oscillatory noncontinuum flows

    Science.gov (United States)

    Shi, Yong; Yap, Ying Wan; Sader, John E.

    2014-03-01

    Oscillatory gas flows are commonly generated by micro- and nanoelectromechanical systems. Due to their small size and high operating frequencies, these devices often produce noncontinuum gas flows. Theoretical analysis of such flows requires solution of the unsteady Boltzmann equation, which can present a formidable challenge. In this article, we explore the applicability of the lattice Boltzmann (LB) method to such linear oscillatory noncontinuum flows; this method is derived from the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation. We formulate four linearized LB models in the frequency domain, based on Gaussian-Hermite quadratures of different algebraic precision (AP). The performance of each model is assessed by comparison to high-accuracy numerical solutions to the linearized Boltzmann-BGK equation for oscillatory Couette flow. The numerical results demonstrate that high even-order LB models provide superior performance over the greatest noncontinuum range. Our results also highlight intrinsic deficiencies in the current LB framework, which is incapable of capturing noncontinuum behavior at high oscillation frequencies, regardless of quadrature AP and the Knudsen number.

  4. A Parallel Lattice Boltzmann Model of a Carotid Artery

    Science.gov (United States)

    Boyd, J.; Ryan, S. J.; Buick, J. M.

    2008-11-01

    A parallel implementation of the lattice Boltzmann model is considered for a three dimensional model of the carotid artery. The computational method and its parallel implementation are described. The performance of the parallel implementation on a Beowulf cluster is presented, as are preliminary hemodynamic results.

  5. Analytical solutions of the lattice Boltzmann BGK model

    CERN Document Server

    Zou, Q; Doolen, G D; Zou, Qisu; Hou, Shuling; Doolen, Gary D.

    1995-01-01

    Abstract: Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time representation of these two flows without any approximation.

  6. Generalized Relativistic Chapman-Enskog Solution of the Boltzmann Equation

    CERN Document Server

    García-Perciante, A L; García-Colin, L S

    2007-01-01

    The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to the thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are proved based on the standard theory of integral equations. The mathematical implications of the generalization here introduced are briefly explored.

  7. Nonequilibrium phenomena in QCD and BEC. Boltzmann and beyond

    Energy Technology Data Exchange (ETDEWEB)

    Stockamp, T.

    2006-12-22

    In chapter 2 we chose the real time formalism to discuss some basic principles in quantum field theory at finite temperature. This enables us to derive the quantum Boltzmann equation from the Schwinger-Dyson series. We then shortly introduce the basic concepts of QCD which are needed to understand the physics of QGP formation. After a detailed account on the bottom-up scenario we show the consistency of this approach by a diagramatical analysis of the relevant Boltzmann collision integrals. Chapter 3 deals with BEC dynamics out of equilibrium. After an introduction to the fundamental theoretical tool - namely the Gross-Pitaevskii equation - we focus on a generalization to finite temperature developed by Zaremba, Nikuni and Griffin (ZNG). These authors use a Boltzmann equation to describe the interactions between condensed and excited atoms and manage in this way to describe condensate growth. We then turn to a discussion on the 2PI effective action and derive equations of motion for a relativistic scalar field theory. In the nonrelativistic limit these equations are shown to coincide with the ZNG theory when a quasiparticle approximation is applied. Finally, we perform a numerical analysis of the full 2PI equations. These remain valid even at strong coupling and far from equilibrium, and thus go far beyond Boltzmann's approach. For simplicity, we limit ourselves to a homogeneous system and present the first 3+1 dimensional study of condensate melting. (orig.)

  8. Metamaterial characterization using Boltzmann's kinetic equation for electrons

    DEFF Research Database (Denmark)

    Novitsky, Andrey; Zhukovsky, Sergei; Novitsky, D.

    2013-01-01

    Statistical properties of electrons in metals are taken into consideration to describe the microscopic motion of electrons. Assuming degenerate electron gas in metal, we introduce the Boltzmann kinetic equation to supplement Maxwell's equations. The solution of these equations clearly shows the r...

  9. Numerical solution of Boltzmann's equation

    Energy Technology Data Exchange (ETDEWEB)

    Sod, G.A.

    1976-04-01

    The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig.

  10. The lattice Boltzmann method and the problem of turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Djenidi, L. [School of Engineering The University of Newcastle, Callaghan NSW 2308 (Australia)

    2015-03-10

    This paper reports a brief review of numerical simulations of homogeneous isotopic turbulence (HIT) using the lattice Boltzmann method (LBM). The LBM results shows that the details of HIT are well captured and in agreement with existing data. This clearly indicates that the LBM is as good as current Navier-Stokes solvers and is very much adequate for investigating the problem of turbulence.

  11. Measuring Boltzmann's Constant with Carbon Dioxide

    Science.gov (United States)

    Ivanov, Dragia; Nikolov, Stefan

    2013-01-01

    In this paper we present two experiments to measure Boltzmann's constant--one of the fundamental constants of modern-day physics, which lies at the base of statistical mechanics and thermodynamics. The experiments use very basic theory, simple equipment and cheap and safe materials yet provide very precise results. They are very easy and…

  12. EXTERNAL BODY FORCE IN FINITE DIFFERENCE LATTICE BOLTZMANN METHOD

    Institute of Scientific and Technical Information of China (English)

    CHEN Sheng; LIU Zhao-hui; SHI Bao-chang; ZHENG Chu-guang

    2005-01-01

    A new finite difference lattice Boltzmann scheme is developed. Because of analyzing the influence of external body force roundly, the correct Navier-Stokes equations with the external body force are recovered, without any additional unphysical terms. And some numerical results are presented. The result which close agreement with analytical data shows the good performance of the model.

  13. Lattice Boltzmann simulations of droplet formation during microchannel emulsification

    NARCIS (Netherlands)

    Zwan, van der E.A.; Sman, van der R.G.M.; Schroën, C.G.P.H.; Boom, R.M.

    2009-01-01

    In this study, we compared microchannel droplet formation in a microfluidics device with a two phase lattice Boltzmann simulation. The droplet formation was found to be qualitatively described, with a slightly smaller droplet in the simulation. This was due to the finite thickness of the interface i

  14. Performance evaluation of a parallel sparse lattice Boltzmann solver

    NARCIS (Netherlands)

    Axner, L.; Bernsdorf, J.; Zeiser, T.; Lammers, P.; Linxweiler, J.; Hoekstra, A.G.

    2008-01-01

    We develop a performance prediction model for a parallelized sparse lattice Boltzmann solver and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and

  15. Measuring Boltzmann's Constant with Carbon Dioxide

    Science.gov (United States)

    Ivanov, Dragia; Nikolov, Stefan

    2013-01-01

    In this paper we present two experiments to measure Boltzmann's constant--one of the fundamental constants of modern-day physics, which lies at the base of statistical mechanics and thermodynamics. The experiments use very basic theory, simple equipment and cheap and safe materials yet provide very precise results. They are very easy and…

  16. Distribution Learning in Evolutionary Strategies and Restricted Boltzmann Machines

    DEFF Research Database (Denmark)

    Krause, Oswin

    The thesis is concerned with learning distributions in the two settings of Evolutionary Strategies (ESs) and Restricted Boltzmann Machines (RBMs). In both cases, the distributions are learned from samples, albeit with different goals. Evolutionary Strategies are concerned with finding an optimum ...

  17. Thermal creep problems by the discrete Boltzmann equation

    Directory of Open Access Journals (Sweden)

    L. Preziosi

    1991-05-01

    Full Text Available This paper deals with an initial-boundary value problem for the discrete Boltzmann equation confined between two moving walls at different temperature. A model suitable for the quantitative analysis of the initial boundary value problem and the relative existence theorem are given.

  18. A Multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR

    Energy Technology Data Exchange (ETDEWEB)

    Shestakov, A I; Offner, S R

    2006-09-21

    We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate 'level-solve' packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation ({Psi}tc). We analyze the magnitude of the {Psi}tc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the 'partial temperature' scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of {Psi}tc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory

  19. A Multigroup diffusion Solver Using Pseudo Transient Continuation for a Radiaiton-Hydrodynamic Code with Patch-Based AMR

    Energy Technology Data Exchange (ETDEWEB)

    Shestakov, A I; Offner, S R

    2007-03-02

    We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate 'level-solve' packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation ({Psi}tc). We analyze the magnitude of the {Psi}tc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the 'partial temperature' scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of {Psi}tc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory

  20. A fast iterative scheme for the linearized Boltzmann equation

    Science.gov (United States)

    Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

    2017-06-01

    Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference

  1. Nuclear Data Uncertainty Propagation in Depletion Calculations Using Cross Section Uncertainties in One-group or Multi-group

    Science.gov (United States)

    Díez, C. J.; Cabellos, O.; Martínez, J. S.

    2015-01-01

    Several approaches have been developed in last decades to tackle nuclear data uncertainty propagation problems of burn-up calculations. One approach proposed was the Hybrid Method, where uncertainties in nuclear data are propagated only on the depletion part of a burn-up problem. Because only depletion is addressed, only one-group cross sections are necessary, and hence, their collapsed one-group uncertainties. This approach has been applied successfully in several advanced reactor systems like EFIT (ADS-like reactor) or ESFR (Sodium fast reactor) to assess uncertainties on the isotopic composition. However, a comparison with using multi-group energy structures was not carried out, and has to be performed in order to analyse the limitations of using one-group uncertainties.

  2. Time-dependent Multi-group Multidimensional Relativistic Radiative Transfer Code Based On Spherical Harmonic Discrete Ordinate Method

    CERN Document Server

    Tominaga, Nozomu; Blinnikov, Sergei I

    2015-01-01

    We develop a time-dependent multi-group multidimensional relativistic radiative transfer code, which is required to numerically investigate radiation from relativistic fluids involved in, e.g., gamma-ray bursts and active galactic nuclei. The code is based on the spherical harmonic discrete ordinate method (SHDOM) that evaluates a source function including anisotropic scattering in spherical harmonics and implicitly solves the static radiative transfer equation with a ray tracing in discrete ordinates. We implement treatments of time dependence, multi-frequency bins, Lorentz transformation, and elastic Thomson and inelastic Compton scattering to the publicly available SHDOM code. Our code adopts a mixed frame approach; the source function is evaluated in the comoving frame whereas the radiative transfer equation is solved in the laboratory frame. This implementation is validated with various test problems and comparisons with results of a relativistic Monte Carlo code. These validations confirm that the code ...

  3. Conjugate heat transfer with the entropic lattice Boltzmann method.

    Science.gov (United States)

    Pareschi, G; Frapolli, N; Chikatamarla, S S; Karlin, I V

    2016-07-01

    A conjugate heat-transfer model is presented based on the two-population entropic lattice Boltzmann method. The present approach relies on the extension of Grad's boundary conditions to the two-population model for thermal flows, as well as on the appropriate exact conjugate heat-transfer condition imposed at the fluid-solid interface. The simplicity and efficiency of the lattice Boltzmann method (LBM), and in particular of the entropic multirelaxation LBM, are retained in the present approach, thus enabling simulations of turbulent high Reynolds number flows and complex wall boundaries. The model is validated by means of two-dimensional parametric studies of various setups, including pure solid conduction, conjugate heat transfer with a backward-facing step flow, and conjugate heat transfer with the flow past a circular heated cylinder. Further validations are performed in three dimensions for the case of a turbulent flow around a heated mounted cube.

  4. Analysis of Jeans instability from the Boltzmann equation

    Science.gov (United States)

    Kremer, Gilberto M.

    2016-11-01

    The dynamics of self-gravitating fluids is analyzed within the framework of a collisionless Boltzmann equation in the presence of gravitational fields and Poisson equation. Two cases are analyzed: a system with baryonic and dark matter in a static universe and a single system in an expanding universe. The amplitudes of the perturbed distribution functions are considered as a linear combination of the collision invariants of the Boltzmann equation. For the system of baryonic and dark matter, the Jeans mass of the combined system is smaller than the one of the single system indicating that a smaller mass is needed to initiate the collapse. For the single system in an expanding universe it is not necessary to make use of Jeans "swindle"and it shown that for small wavelengths the density contrast oscillates while for large wavelengths it grows with time and the Jeans instability emerges.

  5. Lattice Boltzmann model for incompressible flows through porous media.

    Science.gov (United States)

    Guo, Zhaoli; Zhao, T S

    2002-09-01

    In this paper a lattice Boltzmann model is proposed for isothermal incompressible flow in porous media. The key point is to include the porosity into the equilibrium distribution, and add a force term to the evolution equation to account for the linear and nonlinear drag forces of the medium (the Darcy's term and the Forcheimer's term). Through the Chapman-Enskog procedure, the generalized Navier-Stokes equations for incompressible flow in porous media are derived from the present lattice Boltzmann model. The generalized two-dimensional Poiseuille flow, Couette flow, and lid-driven cavity flow are simulated using the present model. It is found the numerical results agree well with the analytical and/or the finite-difference solutions.

  6. Quadrature-based Lattice Boltzmann Model for Relativistic Flows

    CERN Document Server

    Blaga, Robert

    2016-01-01

    A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.

  7. Big-Bang Nucleosynthesis verifies classical Maxwell-Boltzmann distribution

    CERN Document Server

    Hou, S Q; Parikh, A; Daid, K; Bertulani, C

    2014-01-01

    We provide the most stringent constraint to date on possible deviations from the usually-assumed Maxwell-Boltzmann (MB) velocity distribution for nuclei in the Big-Bang plasma. The impact of non-extensive Tsallis statistics on thermonuclear reaction rates involved in standard models of Big-Bang Nucleosynthesis (BBN) has been investigated. We find that the non-extensive parameter $q$ may deviate by, at most, $|\\delta q|$=6$\\times$10$^{-4}$ from unity for BBN predictions to be consistent with observed primordial abundances; $q$=1 represents the classical Boltzmann-Gibbs statistics. This constraint arises primarily from the {\\em super}sensitivity of endothermic rates on the value of $q$, which is found for the first time. As such, the implications of non-extensive statistics in other astrophysical environments should be explored. This may offer new insight into the nucleosynthesis of heavy elements.

  8. Boltzmann transport calculation of collinear spin transport on short timescales

    Science.gov (United States)

    Nenno, Dennis M.; Kaltenborn, Steffen; Schneider, Hans Christian

    2016-09-01

    A spin-dependent Boltzmann transport equation is used to describe charge and spin dynamics resulting from the excitation of hot electrons in a ferromagnet/normal metal heterostructure. As the microscopic Boltzmann equation works with k -dependent distribution functions, it can describe far-from-equilibrium excitations, which are outside the scope of drift-diffusion theories. We study different scenarios for spin-dependent carrier injection into a nonmagnetic metal using an effectively two-dimensional phase space. While the charge signal is robust for various excitation schemes, the shape of the resulting spin current/density depends critically on the interplay between transport and scattering, and on the energetic distribution of the injected carriers. Our results imply that the energy dependence of the injected hot electrons has a decisive effect on the spin dynamics.

  9. CMB spectral distortions as solutions to the Boltzmann equations

    CERN Document Server

    Ota, Atsuhisa

    2016-01-01

    We newly re-interpret cosmic microwave background spectral distortions as solutions to the Boltzmann equation at second order. This approach makes it possible to solve the equation of the momentum dependent temperature perturbations explicitly. In addition, we define higher order spectral distortions systematically, assuming that the collision term is linear in the photon distribution functions. For example, we find the linear Sunyaev-Zel'dovich effect whose momentum shape is different from the usual $y$ distortion, and show that the higher order spectral distortions are also generated as a result of the diffusion process in a language of higher order Boltzmann equations. The method may be applicable to a wider class of problems and has potential to give a general prescription to non-equilibrium physics.

  10. Viscous QCD matter in a hybrid hydrodynamic+Boltzmann approach

    CERN Document Server

    Song, Huichao; Heinz, Ulrich W

    2010-01-01

    A hybrid transport approach for the bulk evolution of viscous QCD matter produced in ultra-relativistic heavy-ion collisions is presented. The expansion of the dense deconfined phase of the reaction is modeled with viscous hydrodynamics while the dilute late hadron gas stage is described microscopically by the Boltzmann equation. The advantages of such a hybrid approach lie in the improved capability of handling large dissipative corrections in the late dilute phase of the reaction, including a realistic treatment of the non-equilibrium hadronic chemistry and kinetic freeze-out. By varying the switching temperature at which the hydrodynamic output is converted to particles for further propagation with the Boltzmann cascade we test the ability of the macroscopic hydrodynamic approach to emulate the microscopic evolution during the hadronic stage and extract the temperature dependence of the effective shear viscosity of the hadron resonance gas produced in the collision. We find that the extracted values depend...

  11. Lattice Boltzmann method with the cell-population equilibrium

    Institute of Scientific and Technical Information of China (English)

    Zhou Xiao-Yang; Cheng Bing; Shi Bao-Chang

    2008-01-01

    The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium.In this paper,a multi-speed 1D cell-model of Boltzmann equation is proposed,in which the cell-population equilibrium,a direct nonnegative approximation to the continuous Maxwellian distribution,plays an important part.By applying the explicit one-order Chapman-Enskog distribution,the model reduces the transportation and collision,two basic evolution steps in LBM,to the transportation of the non-equilibrium distribution.Furthermore,1D dam-break problem is performed and the numerical results agree well with the analytic solutions.

  12. LATTICE-BOLTZMANN MODEL FOR COMPRESSIBLE PERFECT GASES

    Institute of Scientific and Technical Information of China (English)

    Sun Chenghai

    2000-01-01

    We present an adaptive lattice Boltzmann model to simulate super sonic flows. The particle velocities are determined by the mean velocity and internal energy. The adaptive nature of particle velocities permits the mean flow to have high Mach number. A particle potential energy is introduced so that the model is suitable for the perfect gas with arbitrary specific heat ratio. The Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation.As preliminary tests, two kinds of simulations have been performed on hexagonal lattices. One is the one-dimensional simulation for sinusoidal velocity distributions.The velocity distributions are compared with the analytical solution and the mea sured viscosity is compared with the theoretical values. The agreements are basically good. However, the discretion error may cause some non-isotropic effects. The other simulation is the 29 degree shock reflection.

  13. Contact angles in the pseudopotential lattice Boltzmann modeling of wetting

    CERN Document Server

    Li, Q; Kang, Q J; Chen, Q

    2014-01-01

    In this paper, we aim to investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio. The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994)] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model, the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions: the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper, are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles, however, is unable to reproduce static contact angles close to 180 degrees. Meanwhile, it is found that the proposed modif...

  14. Dynamics of annihilation. I. Linearized Boltzmann equation and hydrodynamics.

    Science.gov (United States)

    García de Soria, María Isabel; Maynar, Pablo; Schehr, Grégory; Barrat, Alain; Trizac, Emmanuel

    2008-05-01

    We study the nonequilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of ballistic annihilation therefore constantly loses particles. The dynamics of perturbations around the free decay regime is investigated using the spectral properties of the linearized Boltzmann operator, which characterize linear excitations on all time scales. The linearized Boltzmann equation is solved in the hydrodynamic limit by a projection technique, which yields the evolution equations for the relevant coarse-grained fields and expressions for the transport coefficients. We finally present the results of molecular dynamics simulations that validate the theoretical predictions.

  15. Boltzmann Samplers, P\\'olya Theory, and Cycle Pointing

    CERN Document Server

    Bodirsky, Manuel; Kang, Mihyun; Vigerske, Stefan

    2010-01-01

    We introduce a general method to count unlabeled combinatorial structures and to efficiently generate them at random. The approach is based on pointing unlabeled structures in an "unbiased" way that a structure of size n gives rise to n pointed structures. We extend Polya theory to the corresponding pointing operator, and present a random sampling framework based on both the principles of Boltzmann sampling and on P\\'olya operators. All previously known unlabeled construction principles for Boltzmann samplers are special cases of our new results. Our method is illustrated on several examples: in each case, we provide enumerative results and efficient random samplers. The approach applies to unlabeled families of plane and nonplane unrooted trees, and tree-like structures in general, but also to families of graphs (such as cacti graphs and outerplanar graphs) and families of planar maps.

  16. Lattice Boltzmann Numerical Simulation of a Circular Cylinder

    Institute of Scientific and Technical Information of China (English)

    冯士德; 赵颖; 郜宪林; 季仲贞

    2002-01-01

    The lattice Boltzmann equation (LBE) model based on the Boltzmann equation is suitable for the numerical simulation of various flow fields. The fluid dynamics equation can be recovered from the LBE model. However,compared to the Navier-Stokes transport equation, the fluid dynamics equation derived from the LBE model is somewhat different in the viscosity transport term, which contains not only the Navier-Stokes transport equation but also nonsteady pressure and momentum flux terms. The two nonsteady terms can produce the same function as the random stirring force term introduced in the direct numerical or large-eddy vortex simulation of turbulence.Through computation of a circular cylinder, it is verified that the influence of the two nonsteady terms on flow field stability cannot be ignored, which is helpful for the study of turbulence.

  17. Accelerated Monte Carlo simulations with restricted Boltzmann machines

    Science.gov (United States)

    Huang, Li; Wang, Lei

    2017-01-01

    Despite their exceptional flexibility and popularity, Monte Carlo methods often suffer from slow mixing times for challenging statistical physics problems. We present a general strategy to overcome this difficulty by adopting ideas and techniques from the machine learning community. We fit the unnormalized probability of the physical model to a feed-forward neural network and reinterpret the architecture as a restricted Boltzmann machine. Then, exploiting its feature detection ability, we utilize the restricted Boltzmann machine to propose efficient Monte Carlo updates to speed up the simulation of the original physical system. We implement these ideas for the Falicov-Kimball model and demonstrate an improved acceptance ratio and autocorrelation time near the phase transition point.

  18. Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines

    CERN Document Server

    Huang, Li

    2016-01-01

    Despite their exceptional flexibility and popularity, the Monte Carlo methods often suffer from slow mixing times for challenging statistical physics problems. We present a general strategy to overcome this difficulty by adopting ideas and techniques from the machine learning community. We fit the unnormalized probability of the physical model to a feedforward neural network and reinterpret the architecture as a restricted Boltzmann machine. Then, exploiting its feature detection ability, we utilize the restricted Boltzmann machine for efficient Monte Carlo updates and to speed up the simulation of the original physical system. We implement these ideas for the Falicov-Kimball model and demonstrate improved acceptance ratio and autocorrelation time near the phase transition point.

  19. A Lattice Boltzmann Model of Binary Fluid Mixture

    CERN Document Server

    Orlandini, E; Yeomans, J M; Orlandini, Enzo; Swift, Michael R.

    1995-01-01

    We introduce a lattice Boltzmann for simulating an immiscible binary fluid mixture. Our collision rules are derived from a macroscopic thermodynamic description of the fluid in a way motivated by the Cahn-Hilliard approach to non-equilibrium dynamics. This ensures that a thermodynamically consistent state is reached in equilibrium. The non-equilibrium dynamics is investigated numerically and found to agree with simple analytic predictions in both the one-phase and the two-phase region of the phase diagram.

  20. Filter-matrix lattice Boltzmann model for microchannel gas flows.

    Science.gov (United States)

    Zhuo, Congshan; Zhong, Chengwen

    2013-11-01

    The lattice Boltzmann method has been shown to be successful for microscale gas flows, and it has attracted significant research interest. In this paper, the recently proposed filter-matrix lattice Boltzmann (FMLB) model is first applied to study the microchannel gas flows, in which a Bosanquet-type effective viscosity is used to capture the flow behaviors in the transition regime. A kinetic boundary condition, the combined bounce-back and specular-reflection scheme with the second-order slip scheme, is also designed for the FMLB model. By analyzing a unidirectional flow, the slip velocity and the discrete effects related to the boundary condition are derived within the FMLB model, and a revised scheme is presented to overcome such effects, which have also been validated through numerical simulations. To gain an accurate simulation in a wide range of Knudsen numbers, covering the slip and the entire transition flow regimes, a set of slip coefficients with an introduced fitting function is adopted in the revised second-order slip boundary condition. The periodic and pressure-driven microchannel flows have been investigated by the present model in this study. The numerical results, including the velocity profile and the mass flow rate, as well as the nonlinear pressure distribution along the channel, agree fairly well with the solutions of the linearized Boltzmann equation, the direct simulation Monte Carlo results, the experimental data, and the previous results of the multiple effective relaxation lattice Boltzmann model. Also, the present results of the velocity profile and the mass flow rate show that the present model with the fitting function can yield improved predictions for the microchannel gas flow with higher Knudsen numbers in the transition flow regime.

  1. Discrete Boltzmann model of shallow water equations with polynomial equilibria

    CERN Document Server

    Meng, Jianping; Emerson, David R; Peng, Yong; Zhang, Jianmin

    2016-01-01

    A hierarchy of discrete Boltzmann model is proposed for simulating shallow water flows. By using the Hermite expansion and Gauss-Hermite quadrature, the conservation laws are automatically satisfied without extra effort. Moreover, the expansion order and quadrature can be chosen flexibly according to the problem for striking the balance of accuracy and efficiency. The models are then tested using the classical one-dimensional dam-breaking problem, and successes are found for both supercritical and subcritical flows.

  2. A non-slip boundary condition for lattice Boltzmann simulations

    CERN Document Server

    Inamuro, T; Ogino, F; Inamuro, Takaji; Yoshino, Masato; Ogino, Fumimaru

    1995-01-01

    A non-slip boundary condition at a wall for the lattice Boltzmann method is presented. In the present method unknown distribution functions at the wall are assumed to be an equilibrium distribution function with a counter slip velocity which is determined so that fluid velocity at the wall is equal to the wall velocity. Poiseuille flow and Couette flow are calculated with the nine-velocity model to demonstrate the accuracy of the present boundary condition.

  3. Efficient Asymptotic Preserving Deterministic methods for the Boltzmann Equation

    Science.gov (United States)

    2011-04-01

    important role in modelling granular gases (Bobylev et al., 2000), charged particles in semiconductors (Markowich et al., 1989), neutron transport (Jin...1.6 The splitting approach 1 THE BOLTZMANN EQUATION • Granular gas models : particles undergo inelastic collisions . Energy is dissipated by the model ...A model for collision processes in gases i. small amplitute processes in charged and neutral one component systems. Phys. Rev., 94:511–525. 8

  4. Metamaterial characterization using Boltzmann's kinetic equation for electrons

    DEFF Research Database (Denmark)

    Novitsky, Andrey; Zhukovsky, Sergei; Novitsky, D.;

    2013-01-01

    Statistical properties of electrons in metals are taken into consideration to describe the microscopic motion of electrons. Assuming degenerate electron gas in metal, we introduce the Boltzmann kinetic equation to supplement Maxwell's equations. The solution of these equations clearly shows the r...... the resonant behavior of electronic response to an external electromagnetic field. We demonstrate the approach for planar and circular geometries of the metamolecules....

  5. The Nonclassical Diffusion Approximation to the Nonclassical Linear Boltzmann Equation

    CERN Document Server

    Vasques, Richard

    2015-01-01

    We show that, by correctly selecting the probability distribution function $p(s)$ for a particle's distance-to-collision, the nonclassical diffusion equation can be represented exactly by the nonclassical linear Boltzmann equation for an infinite homogeneous medium. This choice of $p(s)$ preserves the $true$ mean-squared free path of the system, which sheds new light on the results obtained in previous work.

  6. Boltzmann learning of parameters in cellular neural networks

    DEFF Research Database (Denmark)

    Hansen, Lars Kai

    1992-01-01

    The use of Bayesian methods to design cellular neural networks for signal processing tasks and the Boltzmann machine learning rule for parameter estimation is discussed. The learning rule can be used for models with hidden units, or for completely unsupervised learning. The latter is exemplified...... by unsupervised adaptation of an image segmentation cellular network. The learning rule is applied to adaptive segmentation of satellite imagery...

  7. Classical Boltzmann equation and high-temperature QED

    OpenAIRE

    Brandt, F. T.; Ferreira, R. B.; Thuorst, J. F.

    2015-01-01

    The equivalence between thermal field theory and the Boltzmann transport equation is investigated at higher orders in the context of quantum electrodynamics. We compare the contributions obtained from the collisionless transport equation with the high temperature limit of the one-loop thermal Green's function. Our approach employs the representation of the thermal Green's functions in terms of forward scattering amplitudes. The general structure of these amplitudes clearly indicates that the ...

  8. On the Spectral Problems for the Discrete Boltzmann Models

    Institute of Scientific and Technical Information of China (English)

    Aq Kwang-Hua Chu; J. FANG Jing

    2000-01-01

    The discrete Boltzmann models are used to study the spectral problems related to the one-dimensional plane wave propaogation in monatomic gases which are fundamental in the nonequilibrium tatistical thermodynamics. The results show that the 8-velocity model can only describe the propagation of the diffusion mode (entropy wave) in the intermediate Knudsen number regime. The 4- and 6-velocity models, instead, can describe the propagation of sound modes quite well, after comparison with the continuum-mechanical results.

  9. Boltzmann-Langevin one-body dynamics for fermionic systems

    Directory of Open Access Journals (Sweden)

    Napolitani P.

    2012-07-01

    Full Text Available A full implementation of the Boltzmann-Langevin equation for fermionic systems is introduced in a transport model for dissipative collisions among heavy nuclei. Fluctuations are injected in phase space and not, like in more conventional approaches, as a projection on suitable subspaces. The advantage of this model is to be specifically adapted to describe processes characterised by instabilities, like the formation of fragments from a hot nuclear system, and by dissipation, like the transparency in nucleus-nucleus collisions.

  10. Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions

    Science.gov (United States)

    Briant, Marc; Guo, Yan

    2016-12-01

    In a general C1 domain, we study the perturbative Cauchy theory for the Boltzmann equation with Maxwell boundary conditions with an accommodation coefficient α in (√{ 2 / 3 } , 1 ], and discuss this threshold. We consider polynomial or stretched exponential weights m (v) and prove existence, uniqueness and exponential trend to equilibrium around a global Maxwellian in Lx,v∞ (m). Of important note is the fact that the methods do not involve contradiction arguments.

  11. A lattice Boltzmann method based on generalized polynomials

    CERN Document Server

    Coelho, Rodrigo C V; Doria, Mauro M

    2015-01-01

    We propose a lattice Boltzmann method based on the expansion of the equilibrium distribution function in powers of generalized orthonormal polynomials which are weighted by the equilibrium distribution function itself. The D-dimensional Euclidean space Hermite polynomials correspond to the particular weight of a gaussian function. The proposed polynomials give a general method to obtain an expansion of the equilibrium distribution function in powers of the ratio between the displacement velocity and the local scale velocity of the fluid.

  12. Deviations from Boltzmann-Gibbs Statistics in Confined Optical Lattices.

    Science.gov (United States)

    Dechant, Andreas; Kessler, David A; Barkai, Eli

    2015-10-23

    We investigate the semiclassical phase-space probability distribution P(x,p) of cold atoms in a Sisyphus cooling lattice with an additional harmonic confinement. We pose the question of whether this nonequilibrium steady state satisfies the equivalence of energy and probability. This equivalence is the foundation of Boltzmann-Gibbs and generalized thermostatic statistics, and a prerequisite for the description in terms of a temperature. At large energies, P(x,p) depends only on the Hamiltonian H(x,p) and the answer to the question is yes. In distinction to the Boltzmann-Gibbs state, the large-energy tails are power laws P(x,p)∝H(x,p)(-1/D), where D is related to the depth of the optical lattice. At intermediate energies, however, P(x,p) cannot be expressed as a function of the Hamiltonian and the equivalence between energy and probability breaks down. As a consequence the average potential and kinetic energy differ and no well-defined temperature can be assigned. The Boltzmann-Gibbs state is regained only in the limit of deep optical lattices. For strong confinement relative to the damping, we derive an explicit expression for the stationary phase-space distribution.

  13. Low uncertainty Boltzmann constant determinations and the kelvin redefinition.

    Science.gov (United States)

    Fischer, J

    2016-03-28

    At its 25th meeting, the General Conference on Weights and Measures (CGPM) approved Resolution 1 'On the future revision of the International System of Units, the SI', which sets the path towards redefinition of four base units at the next CGPM in 2018. This constitutes a decisive advance towards the formal adoption of the new SI and its implementation. Kilogram, ampere, kelvin and mole will be defined in terms of fixed numerical values of the Planck constant, elementary charge, Boltzmann constant and Avogadro constant, respectively. The effect of the new definition of the kelvin referenced to the value of the Boltzmann constant k is that the kelvin is equal to the change of thermodynamic temperature T that results in a change of thermal energy kT by 1.380 65×10(-23) J. A value of the Boltzmann constant suitable for defining the kelvin is determined by fundamentally different primary thermometers such as acoustic gas thermometers, dielectric constant gas thermometers, noise thermometers and the Doppler broadening technique. Progress to date of the measurements and further perspectives are reported. Necessary conditions to be met before proceeding with changing the definition are given. The consequences of the new definition of the kelvin on temperature measurement are briefly outlined. © 2016 The Author(s).

  14. High-order hydrodynamics via lattice Boltzmann methods.

    Science.gov (United States)

    Colosqui, Carlos E

    2010-02-01

    In this work, closure of the Boltzmann-Bhatnagar-Gross-Krook (Boltzmann-BGK) moment hierarchy is accomplished via projection of the distribution function f onto a space H(N) spanned by N-order Hermite polynomials. While successive order approximations retain an increasing number of leading-order moments of f , the presented procedure produces a hierarchy of (single) N-order partial-differential equations providing exact analytical description of the hydrodynamics rendered by ( N-order) lattice Boltzmann-BGK (LBBGK) simulation. Numerical analysis is performed with LBBGK models and direct simulation Monte Carlo for the case of a sinusoidal shear wave (Kolmogorov flow) in a wide range of Weissenberg number Wi=taunuk(2) (i.e., Knudsen number Kn=lambdak=square root Wi); k is the wave number, [corrected] tau is the relaxation time of the system, and lambda approximately tauc(s) is the mean-free path, where c(s) is the speed of sound. The present results elucidate the applicability of LBBGK simulation under general nonequilibrium conditions.

  15. Multigroup and few-group cross sections for ENDF/B-IV fission products; the TOAFEW collapsing code and data file of 154-group fission-product cross sections. [In FORTRAN

    Energy Technology Data Exchange (ETDEWEB)

    Wilson, W.B.; England, T.R.; LaBauve, R.J.

    1978-02-01

    The ENDF/B-IV fission-product data file includes data describing 824 nuclides. Cross sections, given for 181 of these nuclides, were processed into 154 neutron energy groups. The production of the data file is described. The TOAFEW code, useful in collapsing the multigroup values to few-group cross sections, is presented with instructions and examples of its use. The file of multigroup cross sections is available on request. 3 figures, 11 tables.

  16. Non-Boltzmann Ensembles and Monte Carlo Simulations

    Science.gov (United States)

    Murthy, K. P. N.

    2016-10-01

    Boltzmann sampling based on Metropolis algorithm has been extensively used for simulating a canonical ensemble and for calculating macroscopic properties of a closed system at desired temperatures. An estimate of a mechanical property, like energy, of an equilibrium system, is made by averaging over a large number microstates generated by Boltzmann Monte Carlo methods. This is possible because we can assign a numerical value for energy to each microstate. However, a thermal property like entropy, is not easily accessible to these methods. The reason is simple. We can not assign a numerical value for entropy, to a microstate. Entropy is not a property associated with any single microstate. It is a collective property of all the microstates. Toward calculating entropy and other thermal properties, a non-Boltzmann Monte Carlo technique called Umbrella sampling was proposed some forty years ago. Umbrella sampling has since undergone several metamorphoses and we have now, multi-canonical Monte Carlo, entropic sampling, flat histogram methods, Wang-Landau algorithm etc. This class of methods generates non-Boltzmann ensembles which are un-physical. However, physical quantities can be calculated as follows. First un-weight a microstates of the entropic ensemble; then re-weight it to the desired physical ensemble. Carry out weighted average over the entropic ensemble to estimate physical quantities. In this talk I shall tell you of the most recent non- Boltzmann Monte Carlo method and show how to calculate free energy for a few systems. We first consider estimation of free energy as a function of energy at different temperatures to characterize phase transition in an hairpin DNA in the presence of an unzipping force. Next we consider free energy as a function of order parameter and to this end we estimate density of states g(E, M), as a function of both energy E, and order parameter M. This is carried out in two stages. We estimate g(E) in the first stage. Employing g

  17. The high-energy multi-group HEST1.0 library based on ENDF/B-VII.0: development, verification and preliminary application

    Science.gov (United States)

    Wu, Jun; Chen, Yi-Xue; Wang, Wei-Jin; Yin, Wen; Liang, Tian-Jiao; Jia, Xue-Jun

    2012-03-01

    ENDF/B-VII.0, which was released by the USA Cross Section Evaluation Working Group (CSEWG) in December 2006, was demonstrated to perform much better than previous ENDF evaluations over a broad range of benchmark experiments. A high-energy (up to 150 MeV) multi-group library set named HEST1.0 with 253-neutron and 48-photon groups has been developed based on ENDF/B-VII.0 using the NJOY code. This paper provides a summary of the procedure to produce the library set and a detailed description of the verification of the multi-group library set by several shielding benchmark devices, in particular for high-energy neutron data. In addition, the first application of HEST1.0 to the shielding design of the China Spallation Neutron Source (CSNS) is demonstrated.

  18. The high-energy multi-group HEST1.0 library based on ENDF/B-Ⅶ.0: development, verification and preliminary application

    Institute of Scientific and Technical Information of China (English)

    WU Jun; CHEN Yi-Xue; WANG Wei-Jin; YIN Wen; LIANG Tian-Jiao; JIA Xue-Jun

    2012-01-01

    ENDF/B-Ⅶ.0,which was released by the USA Cross Section Evaluation Working Group (CSEWG)in December 2006,was demonstrated to perform much better than previous ENDF evaluations over a broad range of benchmark experiments.A high-energy (up to 150 MeV) multi-group library set named HEST1.0with 253-neutron and 48-photon groups has been developed based on ENDF/B-Ⅶ.0 using the N JOY code.This paper provides a summary of the procedure to produce the library set and a detailed description of the verification of the multi-group library set by several shielding benchmark devices,in particular for high-energy neutron data.In addition,the first application of HEST1.0 to the shielding design of the China Spallation Neutron Source (CSNS) is demonstrated.

  19. Status report on multigroup cross section generation code development for high-fidelity deterministic neutronics simulation system.

    Energy Technology Data Exchange (ETDEWEB)

    Yang, W. S.; Lee, C. H. (Nuclear Engineering Division)

    2008-05-16

    Under the fast reactor simulation program launched in April 2007, development of an advanced multigroup cross section generation code was initiated in July 2007, in conjunction with the development of the high-fidelity deterministic neutron transport code UNIC. The general objectives are to simplify the existing multi-step schemes and to improve the resolved and unresolved resonance treatments. Based on the review results of current methods and the fact that they have been applied successfully to fast critical experiment analyses and fast reactor designs for last three decades, the methodologies of the ETOE-2/MC{sup 2}-2/SDX code system were selected as the starting set of methodologies for multigroup cross section generation for fast reactor analysis. As the first step for coupling with the UNIC code and use in a parallel computing environment, the MC{sup 2}-2 code was updated by modernizing the memory structure and replacing old data management package subroutines and functions with FORTRAN 90 based routines. Various modifications were also made in the ETOE-2 and MC{sup 2}-2 codes to process the ENDF/B-VII.0 data properly. Using the updated ETOE-2/MC{sup 2}-2 code system, the ENDF/B-VII.0 data was successfully processed for major heavy and intermediate nuclides employed in sodium-cooled fast reactors. Initial verification tests of the MC{sup 2}-2 libraries generated from ENDF/B-VII.0 data were performed by inter-comparison of twenty-one group infinite dilute total cross sections obtained from MC{sup 2}-2, VIM, and NJOY. For almost all nuclides considered, MC{sup 2}-2 cross sections agreed very well with those from VIM and NJOY. Preliminary validation tests of the ENDF/B-VII.0 libraries of MC{sup 2}-2 were also performed using a set of sixteen fast critical benchmark problems. The deterministic results based on MC{sup 2}-2/TWODANT calculations were in good agreement with MCNP solutions within {approx}0.25% {Delta}{rho}, except a few small LANL fast assemblies

  20. Time-Independent and Time-Dependent Rheological Characterization of Dispersions with Varying Contents of Chickpea Flour and Gum Arabic Employing the Multiple Loop Experiments.

    Science.gov (United States)

    J, Shanthilal; Bhattacharya, Suvendu

    2016-08-01

    The chickpea (Cicer arietinum) flour dispersions as the model system with different contents of flour (37% to 43%) and gum arabic (0% to 5%) were subjected to multiple loop experiments for simultaneous determination of the time-independent and time-dependent rheological characteristics. The Herschel-Bulkley model was suitable (0.993 ≤ r ≤ 0.999) to relate the time-independent characteristics linking shear stress and shear rate data for the individual upward and downward curves. The yield stress, consistency index, and apparent viscosity increased with the increasing flour and/or gum contents while flow behavior index (n) decreased. The yield stress generally decreased with the number of loops but n increased. In the individual loop tests, the n values for the decreasing shear stress/shear rate curves were always higher than corresponding increasing curves meaning a shift toward Newtonian characteristics. The time-independent properties (yield stress, apparent viscosity, consistency index, and n), the time-dependent characteristics like the area of the loop, and liquid characteristics like pourability and the nonoral sensory attributes (viscosity, spreadability, and tackiness) were individually predicted by artificial neural networks wherein the root mean square errors were between 3.6% and 17.2%. The sensory assessment indicated that the desirable parameters for a free-flowing and easily pourable spherical chickpea batter droplets occurred when the average pourability and spreadability values were 6.9 and 5.9, respectively. The normalized indices for these 2 parameters indicated that the batter having 40% flour and 2% gum contents was most suitable exhibiting a deviation of only 10% from the ideal sensory scores; these values were 40% and 0% to 3%, and 43% and 0%, respectively exhibiting up to 20% deviation.

  1. A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

    Science.gov (United States)

    Luo, Li-Shi

    1998-01-01

    A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.

  2. Global Solutions of the Boltzmann Equation Over {{R}^D} Near Global Maxwellians with Small Mass

    Science.gov (United States)

    Bardos, Claude; Gamba, Irene M.; Golse, François; Levermore, C. David

    2016-09-01

    We study the dynamics defined by the Boltzmann equation set in the Euclidean space {{R}^D} in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the collision integral vanishes identically. In this setting, the dispersion due to the advection operator quenches the dissipative effect of the Boltzmann collision integral. As a result, the large time limit of solutions of the Boltzmann equation in this regime is given by noninteracting, freely transported states and can be described with the tools of scattering theory.

  3. Pathways among exposure to violence, maternal depression, family structure, and child outcomes through parenting: a multigroup analysis.

    Science.gov (United States)

    Westbrook, T'pring R; Harden, Brenda Jones

    2010-07-01

    The present study examined the impact of proximal (maternal depression, family structure) and distal (exposure to violence) risk factors on parenting characteristics (warmth, control), which were in turn hypothesized to affect child social-emotional functioning. Using the Family and Child Experiences Study (FACES) 2000 cohort, findings revealed that study variables were significant predictors of child social-emotional functioning. Despite limited significant pathways in the structural equation models, the cumulative effect of the variables resulted in models accounting for 21%-37% of the outcome. Multigroup analysis revealed that although the amount of variance explained varied, the model held across subgroups. Findings support theories such as the family stress model that suggest that family risk factors negatively influencing children's development through influencing parenting behaviors. Findings also support considering both warmth and control as key parenting dimensions. It may be impractical for practitioners to address the myriad of potential risks encountered by low-income families, but parents can be equipped with mental health services, parent education, and other assistance to help them maintain positive parenting practices in the face of challenges.

  4. Multi-Group Formulation of the Temperature-Dependent Resonance Scattering Model and its Impact on Reactor Core Parameters

    Energy Technology Data Exchange (ETDEWEB)

    Ghrayeb, Shadi Z. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mechanical and Nuclear Engineering; Ougouag, Abderrafi M. [Idaho National Laboratory (INL), Idaho Falls, ID (United States); Ouisloumen, Mohamed [Westinghouse Electric Company, Cranberry Township, PA (United States); Ivanov, Kostadin N. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mechanical and Nuclear Engineering

    2014-01-01

    A multi-group formulation for the exact neutron elastic scattering kernel is developed. It incorporates the neutron up-scattering effects, stemming from lattice atoms thermal motion and accounts for it within the resulting effective nuclear cross-section data. The effects pertain essentially to resonant scattering off of heavy nuclei. The formulation, implemented into a standalone code, produces effective nuclear scattering data that are then supplied directly into the DRAGON lattice physics code where the effects on Doppler Reactivity and neutron flux are demonstrated. The correct accounting for the crystal lattice effects influences the estimated values for the probability of neutron absorption and scattering, which in turn affect the estimation of core reactivity and burnup characteristics. The results show an increase in values of Doppler temperature feedback coefficients up to -10% for UOX and MOX LWR fuels compared to the corresponding values derived using the traditional asymptotic elastic scattering kernel. This paper also summarizes the results done on this topic to date.

  5. An Investigation of Neutrino-Driven Convection and the Core Collapse Supernova Mechanism Using Multigroup Neutrino Transport

    CERN Document Server

    Mezzacappa, A; Bruenn, S W; Blondin, J M; Guidry, M W; Strayer, M R; Umar, A S

    1996-01-01

    We investigate neutrino-driven convection in core collapse supernovae and its ramifications for the explosion mechanism. We begin with an ``optimistic'' 15 solar mass precollapse model, which is representative of the class of stars with compact iron cores. This model is evolved through core collapse and bounce in one dimension using multigroup (neutrino-energy--dependent) flux-limited diffusion (MGFLD) neutrino transport and Lagrangian hydrodynamics, providing realistic initial conditions for the postbounce convection and evolution. Our two-dimensional simulation begins at 106 ms after bounce at a time when there is a well-developed gain region, and proceeds for 400 ms. We couple two-dimensional (PPM) hydrodynamics to one-dimensional MGFLD neutrino transport. At 225 ms after bounce we see large-scale convection behind the shock, characterized by high-entropy, mushroom-like, expanding upflows and dense, low-entropy, finger-like downflows. The upflows reach the shock and distort it from sphericity. The radial c...

  6. A Multigroup Confirmatory Factor Analysis of the Patient Health Questionnaire-9 among English- and Spanish-speaking Latinas

    Science.gov (United States)

    Merz, Erin L.; Malcarne, Vanessa L.; Roesch, Scott C.; Riley, Natasha; Sadler, Georgia Robins

    2014-01-01

    Depression is a significant problem for ethnic minorities that remains understudied partly due to a lack of strong measures with established psychometric properties. One screening tool, the Patient Health Questionnaire-9 (PHQ-9), which was developed for use in primary care has also gained popularity in research settings. The reliability and validity of the PHQ-9 has been well established among predominantly Caucasian samples, in addition to many minority groups. However, there is little evidence regarding its utility among Hispanic Americans, a large and growing cultural group in the United States. In this study, we investigated the reliability and structural validity of the PHQ-9 in Hispanic American women. A community sample of 479 Latina women from southern California completed the PHQ-9 in their preferred language of English or Spanish. Cronbach’s alphas suggested that there was good internal consistency for both the English- and Spanish-language versions. Structural validity was investigated using multigroup confirmatory factor analysis (CFA). Results support a similar one-factor structure with equivalent response patterns and variances among English- and Spanish-speaking Latinas. These results suggest that the PHQ-9 can be used with confidence in both English and Spanish versions to screen Latinas for depression. PMID:21787063

  7. Knowledge extraction algorithm for variances handling of CP using integrated hybrid genetic double multi-group cooperative PSO and DPSO.

    Science.gov (United States)

    Du, Gang; Jiang, Zhibin; Diao, Xiaodi; Yao, Yang

    2012-04-01

    Although the clinical pathway (CP) predefines predictable standardized care process for a particular diagnosis or procedure, many variances may still unavoidably occur. Some key index parameters have strong relationship with variances handling measures of CP. In real world, these problems are highly nonlinear in nature so that it's hard to develop a comprehensive mathematic model. In this paper, a rule extraction approach based on combing hybrid genetic double multi-group cooperative particle swarm optimization algorithm (PSO) and discrete PSO algorithm (named HGDMCPSO/DPSO) is developed to discovery the previously unknown and potentially complicated nonlinear relationship between key parameters and variances handling measures of CP. Then these extracted rules can provide abnormal variances handling warning for medical professionals. Three numerical experiments on Iris of UCI data sets, Wisconsin breast cancer data sets and CP variances data sets of osteosarcoma preoperative chemotherapy are used to validate the proposed method. When compared with the previous researches, the proposed rule extraction algorithm can obtain the high prediction accuracy, less computing time, more stability and easily comprehended by users, thus it is an effective knowledge extraction tool for CP variances handling.

  8. Lattice Boltzmann method for the fractional advection-diffusion equation.

    Science.gov (United States)

    Zhou, J G; Haygarth, P M; Withers, P J A; Macleod, C J A; Falloon, P D; Beven, K J; Ockenden, M C; Forber, K J; Hollaway, M J; Evans, R; Collins, A L; Hiscock, K M; Wearing, C; Kahana, R; Villamizar Velez, M L

    2016-04-01

    Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β, the fractional order α, and the single relaxation time τ, the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.

  9. Lattice Boltzmann method for the fractional advection-diffusion equation

    Science.gov (United States)

    Zhou, J. G.; Haygarth, P. M.; Withers, P. J. A.; Macleod, C. J. A.; Falloon, P. D.; Beven, K. J.; Ockenden, M. C.; Forber, K. J.; Hollaway, M. J.; Evans, R.; Collins, A. L.; Hiscock, K. M.; Wearing, C.; Kahana, R.; Villamizar Velez, M. L.

    2016-04-01

    Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.

  10. Relativistic rotating Boltzmann gas using the tetrad formalism

    CERN Document Server

    Ambrus, Victor E

    2015-01-01

    We consider an application of the tetrad formalism introduced by Cardall et al. [Phys. Rev. D 88 (2013) 023011] to the problem of a rigidly rotating relativistic gas in thermal equilibrium and discuss the possible applications of this formalism to relativistic lattice Boltzmann simulations. We present in detail the transformation to the comoving frame, the choice of tetrad, as well as the explicit calculation and analysis of the components of the equilibrium particle flow four-vector and of the equilibrium stress-energy tensor.

  11. Direct determination of the Boltzmann constant by an optical method.

    Science.gov (United States)

    Daussy, C; Guinet, M; Amy-Klein, A; Djerroud, K; Hermier, Y; Briaudeau, S; Bordé, Ch J; Chardonnet, C

    2007-06-22

    We have recorded the Doppler profile of a well-isolated rovibrational line in the nu(2) band of (14)NH(3). Ammonia gas was placed in an absorption cell thermalized by a water-ice bath. By extrapolating to zero pressure, we have deduced the Doppler width which gives a first measurement of the Boltzmann constant k(B) by laser spectroscopy. A relative uncertainty of 2 x 10(-4) has been obtained. The present determination should be significantly improved in the near future and contribute to a new definition of the kelvin.

  12. Jet propagation within a Linearized Boltzmann Transport model

    Energy Technology Data Exchange (ETDEWEB)

    Luo, Tan; He, Yayun [Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079 (China); Wang, Xin-Nian [Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079 (China); Nuclear Science Division, Mailstop 70R0319, Lawrence Berkeley National Laboratory, Berkeley, CA 94740 (United States); Zhu, Yan [Departamento de Física de Partículas and IGFAE, Universidade de Santiago de Compostela, E-15706 Santiago de Compostela, Galicia (Spain)

    2014-12-15

    A Linearized Boltzmann Transport (LBT) model has been developed for the study of parton propagation inside quark–gluon plasma. Both leading and thermal recoiled partons are tracked in order to include the effect of jet-induced medium excitation. In this talk, we present a study within the LBT model in which we implement the complete set of elastic parton scattering processes. We investigate elastic parton energy loss and their energy and length dependence. We further investigate energy loss and transverse shape of reconstructed jets. Contributions from the recoiled thermal partons and jet-induced medium excitations are found to have significant influences on the jet energy loss and transverse profile.

  13. Least-squares finite-element lattice Boltzmann method.

    Science.gov (United States)

    Li, Yusong; LeBoeuf, Eugene J; Basu, P K

    2004-06-01

    A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method's geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimization. For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow and Couette flow.

  14. Coupling lattice Boltzmann and molecular dynamics models for dense fluids

    Science.gov (United States)

    Dupuis, A.; Kotsalis, E. M.; Koumoutsakos, P.

    2007-04-01

    We propose a hybrid model, coupling lattice Boltzmann (LB) and molecular dynamics (MD) models, for the simulation of dense fluids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The MD and LB formulations communicate via the exchange of velocities and velocity gradients at the interface. We validate the present LB-MD model in simulations of two- and three-dimensional flows of liquid argon past and through a carbon nanotube. Comparisons with existing hybrid algorithms and with reference MD solutions demonstrate the validity of the present approach.

  15. Lattice Boltzmann model for nonlinear convection-diffusion equations.

    Science.gov (United States)

    Shi, Baochang; Guo, Zhaoli

    2009-01-01

    A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.

  16. Hydrodynamic behaviour of Lattice Boltzmann and Lattice BGK models

    CERN Document Server

    Behrend, O; Warren, P

    1993-01-01

    Abstract: We present a numerical analysis of the validity of classical and generalized hydrodynamics for Lattice Boltzmann Equation (LBE) and Lattice BGK methods in two and three dimensions, as a function of the collision parameters of these models. Our analysis is based on the wave-number dependence of the evolution operator. Good ranges of validity are found for BGK models as long as the relaxation time is chosen smaller than or equal to unity. The additional freedom in the choice of collision parameters for LBE models does not seem to give significant improvement.

  17. Classical Boltzmann equation and high-temperature QED

    Science.gov (United States)

    Brandt, F. T.; Ferreira, R. B.; Thuorst, J. F.

    2015-02-01

    The equivalence between thermal field theory and the Boltzmann transport equation is investigated at higher orders in the context of quantum electrodynamics. We compare the contributions obtained from the collisionless transport equation with the high temperature limit of the one-loop thermal Green's function. Our approach employs the representation of the thermal Green's functions in terms of forward scattering amplitudes. The general structure of these amplitudes clearly indicates that the physics described by the leading high temperature limit of quantum electrodynamics can be obtained from the Boltzman transport equation. We also present some explicit examples of this interesting equivalence.

  18. Classical Boltzmann equation and high-temperature QED

    CERN Document Server

    Brandt, F T; Thuorst, J F

    2015-01-01

    The equivalence between thermal field theory and the Boltzmann transport equation is investigated at higher orders in the context of Quantum Electrodynamics. We compare the contributions obtained from the collisionless transport equation with the high temperature limit of the one-loop thermal Green's function. Our approach employs the representation of the thermal Green's functions in terms of forward scattering amplitudes. The general structure of these amplitudes clearly indicates that the physics described by the leading high temperature limit of Quantum Electrodynamics can be obtained from the Boltzman transport equation. We also present some explicit examples of this interesting equivalence.

  19. Lattice-Boltzmann Method for Geophysical Plastic Flows

    CERN Document Server

    Leonardi, Alessandro; Mendoza, Miller; Herrmann, Hans J

    2015-01-01

    We explore possible applications of the Lattice-Boltzmann Method for the simulation of geophysical flows. This fluid solver, while successful in other fields, is still rarely used for geotechnical applications. We show how the standard method can be modified to represent free-surface realization of mudflows, debris flows, and in general any plastic flow, through the implementation of a Bingham constitutive model. The chapter is completed by an example of a full-scale simulation of a plastic fluid flowing down an inclined channel and depositing on a flat surface. An application is given, where the fluid interacts with a vertical obstacle in the channel.

  20. Diffusion dominated evaporation in multicomponent lattice Boltzmann simulations

    Science.gov (United States)

    Hessling, Dennis; Xie, Qingguang; Harting, Jens

    2017-02-01

    We present a diffusion dominated evaporation model using the popular pseudopotential multicomponent lattice Boltzmann method introduced by Shan and Chen. With an analytical computation of the diffusion coefficients, we demonstrate that Fick's law is obeyed. We then validate the applicability of our model by demonstrating the agreement of the time evolution of the interface position of an evaporating planar film to the analytical prediction. Furthermore, we study the evaporation of a freely floating droplet and confirm that the effect of Laplace pressure is significant for predicting the time evolution of small droplet radii.

  1. Diffusive limit for a quantum linear Boltzmann dynamics

    CERN Document Server

    Clark, Jeremy

    2010-01-01

    We study the diffusive behavior for a quantum test particle interacting with a dilute background gas. The model we begin with is a reduced picture for the test particle dynamics given by a quantum linear Boltzmann equation in which the scattering with the gas particles is assumed to occur through a hard-sphere interaction. The state of the particle is represented by a density matrix evolving according to a translation-covariant Lindblad equation. Our main result is a proof that the particle diffuses for large times.

  2. Thrombosis modeling in intracranial aneurysms: a lattice Boltzmann numerical algorithm

    Science.gov (United States)

    Ouared, R.; Chopard, B.; Stahl, B.; Rüfenacht, D. A.; Yilmaz, H.; Courbebaisse, G.

    2008-07-01

    The lattice Boltzmann numerical method is applied to model blood flow (plasma and platelets) and clotting in intracranial aneurysms at a mesoscopic level. The dynamics of blood clotting (thrombosis) is governed by mechanical variations of shear stress near wall that influence platelets-wall interactions. Thrombosis starts and grows below a shear rate threshold, and stops above it. Within this assumption, it is possible to account qualitatively well for partial, full or no occlusion of the aneurysm, and to explain why spontaneous thrombosis is more likely to occur in giant aneurysms than in small or medium sized aneurysms.

  3. Topological Interactions in a Boltzmann-Type Framework

    Science.gov (United States)

    Blanchet, Adrien; Degond, Pierre

    2016-04-01

    We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another particle, the leader. The follower chooses its leader according to the proximity rank of the latter with respect to the former. We study the limit of a system size going to infinity and, under the assumption of propagation of chaos, show that the limit equation is akin to the Boltzmann equation. However, it exhibits a spatial non-locality instead of the classical non-locality in velocity space. This result relies on the approximation properties of Bernstein polynomials. We illustrate the dynamics with numerical simulations.

  4. A lattice Boltzmann method for dilute polymer solutions.

    Science.gov (United States)

    Singh, Shiwani; Subramanian, Ganesh; Ansumali, Santosh

    2011-06-13

    We present a lattice Boltzmann approach for the simulation of non-Newtonian fluids. The method is illustrated for the specific case of dilute polymer solutions. With the appropriate local equilibrium distribution, phase-space dynamics on a lattice, driven by a Bhatnagar-Gross-Krook (BGK) relaxation term, leads to a solution of the Fokker-Planck equation governing the probability density of polymer configurations. Results for the bulk rheological characteristics for steady and start-up shear flow are presented, and compare favourably with those obtained using Brownian dynamics simulations. The new method is less expensive than stochastic simulation techniques, particularly in the range of small to moderate Weissenberg numbers (Wi).

  5. Static contact angle in lattice Boltzmann models of immiscible fluids.

    Science.gov (United States)

    Latva-Kokko, M; Rothman, Daniel H

    2005-10-01

    We study numerically the capillary rise between two horizontal plates and in a rectangular tube, using a lattice Boltzmann (LB) method. We derive an equation for the static fluid-solid contact angle as a function of the wetting tendency of the walls and test its validity. We show that the generalized Laplace law with two independent radii of curvature is followed in capillary rise in rectangular tubes. Our method removes the history dependence of the fluid-solid contact angle that had been present in earlier LB schemes.

  6. LATTICE BOLTZMANN EQUATION MODEL IN THE CORIOLIS FIELD

    Institute of Scientific and Technical Information of China (English)

    FENG SHI-DE; MAO JIANG-YU; ZHANG QIONG

    2001-01-01

    In a large-scale field of rotational fluid, various unintelligible and surprising dynamic phenomena are produced due to the effect of the Coriolis force. The lattice Boltzmann equation (LBE) model in the Coriolis field is developed based on previous works.[1-4] Geophysical fluid dynamics equations are derived from the model. Numerical simulations have been made on an ideal atmospheric circulation of the Northern Hemisphere by using the model and they reproduce the Rossby wave motion well. Hence the applicability of the model is verified in both theory and experiment.

  7. On space enrichment estimator for nonlinear Poisson-Boltzmann

    Science.gov (United States)

    Randrianarivony, Maharavo

    2013-10-01

    We consider the mathematical aspect of the nonlinear Poisson-Boltzmann equation which physically governs the ionic interaction between solute and solvent media. The presented a-posteriori estimates can be computed locally in a very efficient manner. The a-posteriori error is based upon hierarchical space enrichment which ensures its efficiency and reliability. A brief survey of the solving of the nonlinear system resulting from the FEM discretization is reported. To corroborate the analysis, we report on a few numerical results for illustrations. We numerically examine some values of the constants encountered in the theoretical study.

  8. Numerical Poisson-Boltzmann Model for Continuum Membrane Systems.

    Science.gov (United States)

    Botello-Smith, Wesley M; Liu, Xingping; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

    2013-01-01

    Membrane protein systems are important computational research topics due to their roles in rational drug design. In this study, we developed a continuum membrane model utilizing a level set formulation under the numerical Poisson-Boltzmann framework within the AMBER molecular mechanics suite for applications such as protein-ligand binding affinity and docking pose predictions. Two numerical solvers were adapted for periodic systems to alleviate possible edge effects. Validation on systems ranging from organic molecules to membrane proteins up to 200 residues, demonstrated good numerical properties. This lays foundations for sophisticated models with variable dielectric treatments and second-order accurate modeling of solvation interactions.

  9. Adjoint Parameter Sensitivity Analysis for the Hydrodynamic Lattice Boltzmann Method with Applications to Design Optimization

    DEFF Research Database (Denmark)

    Pingen, Georg; Evgrafov, Anton; Maute, Kurt

    2009-01-01

    We present an adjoint parameter sensitivity analysis formulation and solution strategy for the lattice Boltzmann method (LBM). The focus is on design optimization applications, in particular topology optimization. The lattice Boltzmann method is briefly described with an in-depth discussion...

  10. Numerical simulation for the Gross-Pitaevskii equation based on the lattice Boltzmann method

    Science.gov (United States)

    Wang, Huimin

    2017-09-01

    A lattice Boltzmann model for the Gross-Pitaevskii equation is proposed in this paper. Some numerical tests for one- and two-dimensional Gross-Pitaevskii equation have been conducted. The waves of the Gross-Pitaevskii equation are simulated. Numerical results show that the lattice Boltzmann method is an effective method for the wave of the Gross-Pitaevskii equation.

  11. An Exact Solution to the Two-Particle Boltzmann Equation System for Maxwell Gases

    Institute of Scientific and Technical Information of China (English)

    布仁满都拉; 赵迎春

    2012-01-01

    An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equation is also given.

  12. Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

    Energy Technology Data Exchange (ETDEWEB)

    Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte

    2015-07-01

    This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

  13. Boltzmann-Gibbs Entropy Versus Tsallis Entropy: Recent Contributions to Resolving the Argument of Einstein Concerning "Neither Herr Boltzmann nor Herr Planck has given a definition of W"?

    OpenAIRE

    Haubold, H. J.; Mathai, A. M.; Saxena, R. K.

    2004-01-01

    Classical statistical mechanics of macroscopic systems in equilibrium is based on Boltzmann's principle. Tsallis has proposed a generalization of Boltzmann-Gibbs statistics. Its relation to dynamics and nonextensivity of statistical systems are matters of intense investigation and debate. This essay review has been prepared at the occasion of awarding the 'Mexico Prize for Science and Technology 2003'to Professor Constantino Tsallis from the Brazilian Center for Research in Physics.

  14. Contact angles in the pseudopotential lattice Boltzmann modeling of wetting

    Science.gov (United States)

    Li, Qing; Luo, K. H.; Kang, Q. J.; Chen, Q.

    2014-11-01

    In this paper we investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio ρL/ρV=500 . The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994), 10.1103/PhysRevE.49.2941] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions, the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles θ static contact angles close to 180∘. Meanwhile, it is found that the proposed modified pseudopotential-based interaction performs better in light of the maximum and the minimum densities and is overall more suitable for simulating large contact angles θ >90∘ as compared with the two other types of fluid-solid interactions. Furthermore, the spurious currents are found to be enlarged when the fluid-solid interaction force is introduced. Increasing the kinematic viscosity ratio between the vapor and liquid phases is shown to be capable of reducing the spurious currents caused by the fluid-solid interactions.

  15. Polyelectrolyte Microcapsules: Ion Distributions from a Poisson-Boltzmann Model

    Science.gov (United States)

    Tang, Qiyun; Denton, Alan R.; Rozairo, Damith; Croll, Andrew B.

    2014-03-01

    Recent experiments have shown that polystyrene-polyacrylic-acid-polystyrene (PS-PAA-PS) triblock copolymers in a solvent mixture of water and toluene can self-assemble into spherical microcapsules. Suspended in water, the microcapsules have a toluene core surrounded by an elastomer triblock shell. The longer, hydrophilic PAA blocks remain near the outer surface of the shell, becoming charged through dissociation of OH functional groups in water, while the shorter, hydrophobic PS blocks form a networked (glass or gel) structure. Within a mean-field Poisson-Boltzmann theory, we model these polyelectrolyte microcapsules as spherical charged shells, assuming different dielectric constants inside and outside the capsule. By numerically solving the nonlinear Poisson-Boltzmann equation, we calculate the radial distribution of anions and cations and the osmotic pressure within the shell as a function of salt concentration. Our predictions, which can be tested by comparison with experiments, may guide the design of microcapsules for practical applications, such as drug delivery. This work was supported by the National Science Foundation under Grant No. DMR-1106331.

  16. Moving charged particles in lattice Boltzmann-based electrokinetics.

    Science.gov (United States)

    Kuron, Michael; Rempfer, Georg; Schornbaum, Florian; Bauer, Martin; Godenschwager, Christian; Holm, Christian; de Graaf, Joost

    2016-12-07

    The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions into the Capuani scheme has been lacking. Moving boundary conditions are needed to simulate multiple arbitrarily moving colloids. In this paper, we detail how to introduce such a particle coupling scheme, based on an analogue to the moving boundary method for the pure lattice Boltzmann solver. The key ingredients in our method are mass and charge conservation for the solute species and a partial-volume smoothing of the solute fluxes to minimize discretization artifacts. We demonstrate our algorithm's effectiveness by simulating the electrophoresis of charged spheres in an external field; for a single sphere we compare to the equivalent electro-osmotic (co-moving) problem. Our method's efficiency and ease of implementation should prove beneficial to future simulations of the dynamics in a wide range of complex nanoscopic and colloidal systems that were previously inaccessible to lattice-based continuum algorithms.

  17. High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

    Science.gov (United States)

    Li, Weidong

    2017-09-01

    This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

  18. Lattice Boltzmann model for a steady radiative transfer equation.

    Science.gov (United States)

    Yi, Hong-Liang; Yao, Feng-Ju; Tan, He-Ping

    2016-08-01

    A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed.

  19. Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation

    Directory of Open Access Journals (Sweden)

    Bertrand Lods

    2015-06-01

    Full Text Available Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a suitable set Ɛ of mutually absolutely continuous densities. We study in particular the fine properties of the Kullback-Liebler divergence in this context. We also show that this setting is well-suited for the study of the spatially homogeneous Boltzmann equation if Ɛ is a set of positive densities with finite relative entropy with respect to the Maxwell density. More precisely, we analyze the Boltzmann operator in the geometric setting from the point of its Maxwell’s weak form as a composition of elementary operations in the exponential manifold, namely tensor product, conditioning, marginalization and we prove in a geometric way the basic facts, i.e., the H-theorem. We also illustrate the robustness of our method by discussing, besides the Kullback-Leibler divergence, also the property of Hyvärinen divergence. This requires us to generalize our approach to Orlicz–Sobolev spaces to include derivatives.

  20. Avoiding Boltzmann Brain domination in holographic dark energy models

    Science.gov (United States)

    Horvat, R.

    2015-11-01

    In a spatially infinite and eternal universe approaching ultimately a de Sitter (or quasi-de Sitter) regime, structure can form by thermal fluctuations as such a space is thermal. The models of Dark Energy invoking holographic principle fit naturally into such a category, and spontaneous formation of isolated brains in otherwise empty space seems the most perplexing, creating the paradox of Boltzmann Brains (BB). It is thus appropriate to ask if such models can be made free from domination by Boltzmann Brains. Here we consider only the simplest model, but adopt both the local and the global viewpoint in the description of the Universe. In the former case, we find that if a dimensionless model parameter c, which modulates the Dark Energy density, lies outside the exponentially narrow strip around the most natural c = 1 line, the theory is rendered BB-safe. In the latter case, the bound on c is exponentially stronger, and seemingly at odds with those bounds on c obtained from various observational tests.

  1. Detection of Hypertension Retinopathy Using Deep Learning and Boltzmann Machines

    Science.gov (United States)

    Triwijoyo, B. K.; Pradipto, Y. D.

    2017-01-01

    hypertensive retinopathy (HR) in the retina of the eye is disturbance caused by high blood pressure disease, where there is a systemic change of arterial in the blood vessels of the retina. Most heart attacks occur in patients caused by high blood pressure symptoms of undiagnosed. Hypertensive retinopathy Symptoms such as arteriolar narrowing, retinal haemorrhage and cotton wool spots. Based on this reasons, the early diagnosis of the symptoms of hypertensive retinopathy is very urgent to aim the prevention and treatment more accurate. This research aims to develop a system for early detection of hypertension retinopathy stage. The proposed method is to determine the combined features artery and vein diameter ratio (AVR) as well as changes position with Optic Disk (OD) in retinal images to review the classification of hypertensive retinopathy using Deep Neural Networks (DNN) and Boltzmann Machines approach. We choose this approach of because based on previous research DNN models were more accurate in the image pattern recognition, whereas Boltzmann machines selected because It requires speedy iteration in the process of learning neural network. The expected results from this research are designed a prototype system early detection of hypertensive retinopathy stage and analysed the effectiveness and accuracy of the proposed methods.

  2. SIMULATION OF MIXED CONVECTIVE HEAT TRANSFER USING LATTICE BOLTZMANN METHOD

    Directory of Open Access Journals (Sweden)

    A. R. M. Rosdzimin

    2010-12-01

    Full Text Available In this paper, mixed (forced–natural convective heat transfer around a heated square cylinder located inside a lid driven cavity has been studied numerically using the lattice Boltzmann method in the range of 100≤ Re ≤ 1000 with the corresponding Richardson number 0.01≤Ri≤10. The double-population lattice Boltzmann formulation is used as the governing equation. Two dimensional nine-velocity models are used for the computation of the velocity field while a four-velocity model is used for the computation of the temperature field. We found that the combination of nine- and four-velocity models can be applied to the calculation without losing its accuracy. The results are presented in the form of streamline and isotherm plots as well as the variation of local Nusselt number at the top surface of the heated square. The computational results demonstrate that the flow pattern, formation of vortex and also the Nusselt number are influence by the Reynolds number and Richardson number.

  3. Avoiding Boltzmann Brain domination in holographic dark energy models

    Directory of Open Access Journals (Sweden)

    R. Horvat

    2015-11-01

    Full Text Available In a spatially infinite and eternal universe approaching ultimately a de Sitter (or quasi-de Sitter regime, structure can form by thermal fluctuations as such a space is thermal. The models of Dark Energy invoking holographic principle fit naturally into such a category, and spontaneous formation of isolated brains in otherwise empty space seems the most perplexing, creating the paradox of Boltzmann Brains (BB. It is thus appropriate to ask if such models can be made free from domination by Boltzmann Brains. Here we consider only the simplest model, but adopt both the local and the global viewpoint in the description of the Universe. In the former case, we find that if a dimensionless model parameter c, which modulates the Dark Energy density, lies outside the exponentially narrow strip around the most natural c=1 line, the theory is rendered BB-safe. In the latter case, the bound on c is exponentially stronger, and seemingly at odds with those bounds on c obtained from various observational tests.

  4. Wall Orientation and Shear Stress in the Lattice Boltzmann Model

    CERN Document Server

    Matyka, Maciej; Mirosław, Łukasz

    2013-01-01

    The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near ...

  5. Avoiding Boltzmann Brain domination in holographic dark energy models

    CERN Document Server

    Horvat, R

    2015-01-01

    In a spatially infinite and eternal universe approaching ultimately a de Sitter (or quasi-de Sitter) regime, structure can form by thermal fluctuations as such a space is thermal. The models of Dark Energy invoking holographic principle fit naturally into such a category, and spontaneous formation of isolated brains in otherwise empty space seems the most perplexing, creating the paradox of Boltzmann Brains (BB). It is thus appropriate to ask if such models can be made free from domination by Boltzmann Brains. Here we consider only the simplest model, but adopt both the local and the global viewpoint in the description of the Universe. In the former case, we find that if a parameter $c$, which modulates the Dark Energy density, lies outside the exponentially narrow strip around the most natural $c = 1$ line, the theory is rendered BB-safe. In the later case, the bound on $c$ is exponentially stronger, and seemingly at odds with those bounds on $c$ obtained from various observational tests.

  6. A Boltzmann Transport Simulation Using Open Source Physics

    Science.gov (United States)

    Hasbun, Javier

    2004-03-01

    The speed of a charged particle, under an applied electric field, in a conducting media, is, usually, simply modelled by writing Newton's 2nd law in the form mfrac ddtv=qE-mfrac vτ ; (1), where v is the speed, E is the applied electric field, q is the charge, m is the mass, and τ is the scattering time between collisions. Here, we simulate a numerical solution of the Boltzmann transport equation,frac partial partial tf+ vot nabla _rf+Fot nabla _pf=frac partial partial tf|_coll (2), where in general the Boltzmann distribution function f=f(r,p,t) depends on position, momentum, and time. Our numerical solution is made possible by neglecting the 2nd term on the LHS, and by modelling the RHS collision term as fracpartial partial tf|_coll=-frac 1τ . With these approximations, in addition to considering only one dimension, we find, our numerical solution of (2). The average velocity numerically obtained through the resulting distribution is compared to that obtained by the analytic solution of (1). An efficient method of carrying out the numerical solution of (2) due to P. Drallos and M. Wadehra [Journal of Applied Physics 63, 5601(1988)] is incorporated here. A final version of an applet that performs the full Java simulation will be located at http://www.westga.edu/ jhasbun/osp/osp.htm.

  7. Three-dimensional lattice Boltzmann model for electrodynamics.

    Science.gov (United States)

    Mendoza, M; Muñoz, J D

    2010-11-01

    In this paper we introduce a three-dimensional Lattice-Boltzmann model that recovers in the continuous limit the Maxwell equations in materials. In order to build conservation equations with antisymmetric tensors, like the Faraday law, the model assigns four auxiliary vectors to each velocity vector. These auxiliary vectors, when combined with the distribution functions, give the electromagnetic fields. The evolution is driven by the usual Bhatnager-Gross-Krook (BGK) collision rule, but with a different form for the equilibrium distribution functions. This lattice Bhatnager-Gross-Krook (LBGK) model allows us to consider for both dielectrics and conductors with realistic parameters, and therefore it is adequate to simulate the most diverse electromagnetic problems, like the propagation of electromagnetic waves (both in dielectric media and in waveguides), the skin effect, the radiation pattern of a small dipole antenna and the natural frequencies of a resonant cavity, all with 2% accuracy. Actually, it shows to be one order of magnitude faster than the original Finite-difference time-domain (FDTD) formulation by Yee to reach the same accuracy. It is, therefore, a valuable alternative to simulate electromagnetic fields and opens lattice Boltzmann for a broad spectrum of new applications in electrodynamics.

  8. Element Free Lattice Boltzmann Method for Fluid-Flow Problems

    Energy Technology Data Exchange (ETDEWEB)

    Jo, Jong Chull; Roh, Kyung Wan; Yune, Young Gill; Kim, Hho Jhung [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of); Kwon, Young Kwon [US Naval Postgraduate School, New York (United States)

    2007-10-15

    The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Most of the those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. Some techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the iso-parametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, the element free technique is also quite useful to analyze a complex shape of domain because there is no need to divide a domain by a compatible finite element mesh. This paper presents a new finite element and element free formulations for the lattice Boltzmann equation using the general weighted residual technique. Then, a series of validation examples are presented.

  9. Lattice Boltzmann Simulation for Complex Flow in a Solar Wall

    Institute of Scientific and Technical Information of China (English)

    CHEN Rou; Shao Jiu-Gu; ZHENG You-Qu; YU Hui-Dan; XU You-Sheng

    2013-01-01

    In this letter,we present a lattice Boltzmann simulation for complex flow in a solar wall system which includes porous media flow and heat transfer,specifically for solar energy utilization through an unglazed transpired solar air collector (UTC).Besides the lattice Boltzmann equation (LBE) for time evolution of particle distribution function for fluid field,we introduce an analogy,LBE for time evolution of distribution function for temperature.Both temperature fields of fluid (air) and solid (porous media) are modeled.We study the effects of fan velocity,solar radiation intensity,porosity,etc.on the thermal performance of the UTC.In general,our simulation results are in good agreement with what in literature.With the current system setting,both fan velocity and solar radiation intensity have significant effect on the thermal performance of the UTC.However,it is shown that the porosity has negligible effect on the heat collector indicating the current system setting might not be realistic.Further examinations of thermal performance in different UTC systems are ongoing.The results are expected to present in near future.

  10. Lattice Boltzmann methods for global linear instability analysis

    Science.gov (United States)

    Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis

    2016-11-01

    Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.

  11. Proposal for a New Test of the Time Independence Of The Fine Structure Constant, alpha, Using Orthogonally Polarised Whispering Gallery Modes in a Single Sapphire Resonator

    CERN Document Server

    Tobar, M E; Tobar, Michael Edmund; Hartnett, John Gideon

    2003-01-01

    A new experiment to test for the time independence of the fine structure constant, alpha, is proposed. The experiment utilizes orthogonally polarized Transverse Electric and Transverse Magnetic Whispering Gallery Modes in a single sapphire resonator tuned to similar frequencies. When configured as a dual mode sapphire clock, we show that the anisotropy of sapphire makes it is possible to undertake a sensitive measurement from the beat frequency between the two modes. At infrared frequencies this is possible due to the different effect of the lowest phonon frequency on the two orthogonally polarized modes. At microwave frequencies we show that the phonon effect is too small. We show that the Electron Spin Resonance of paramagnetic impurities (such as Cr3+) in the lattice effects only one polarization with an alpha^6 dependence. This enables an enhancement of the sensitivity to temporal changes in a at microwave frequencies.

  12. Boltzmann and Einstein: Statistics and dynamics –An unsolved problem

    Indian Academy of Sciences (India)

    E G D Cohen

    2005-05-01

    The struggle of Boltzmann with the proper description of the behavior of classical macroscopic bodies in equilibrium in terms of the properties of the particles out of which they consist will be sketched. He used both a dynamical and a statistical method. However, Einstein strongly disagreed with Boltzmann's statistical method, arguing that a statistical description of a system should be based on the dynamics of the system. This opened the way, especially for complex systems, for other than Boltzmann statistics. The first non-Boltzmann statistics, not based on dynamics though, was proposed by Tsallis. A generalization of Tsallis' statistics as a special case of a new class of superstatistics, based on Einstein's criticism of Boltzmann, is discussed. It seems that perhaps a combination of dynamics and statistics is necessary to describe systems with complicated dynamics.

  13. Discretization of the velocity space in solution of the Boltzmann equation

    CERN Document Server

    Shan, X; Shan, Xiaowen; He, Xiaoyi

    1998-01-01

    We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite polynomial expansion. Discretizing the Boltzmann equation with a BGK collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers. Higher order approximations to the Boltzmann equation can be achieved by using more velocities in the quadrature.

  14. Dynamical localization in chaotic systems: spectral statistics and localization measure in the kicked rotator as a paradigm for time-dependent and time-independent systems.

    Science.gov (United States)

    Manos, Thanos; Robnik, Marko

    2013-06-01

    We study the kicked rotator in the classically fully chaotic regime using Izrailev's N-dimensional model for various N≤4000, which in the limit N→∞ tends to the quantized kicked rotator. We do treat not only the case K=5, as studied previously, but also many different values of the classical kick parameter 5≤K≤35 and many different values of the quantum parameter kε[5,60]. We describe the features of dynamical localization of chaotic eigenstates as a paradigm for other both time-periodic and time-independent (autonomous) fully chaotic or/and mixed-type Hamilton systems. We generalize the scaling variable Λ=l(∞)/N to the case of anomalous diffusion in the classical phase space by deriving the localization length l(∞) for the case of generalized classical diffusion. We greatly improve the accuracy and statistical significance of the numerical calculations, giving rise to the following conclusions: (1) The level-spacing distribution of the eigenphases (or quasienergies) is very well described by the Brody distribution, systematically better than by other proposed models, for various Brody exponents β(BR). (2) We study the eigenfunctions of the Floquet operator and characterize their localization properties using the information entropy measure, which after normalization is given by β(loc) in the interval [0,1]. The level repulsion parameters β(BR) and β(loc) are almost linearly related, close to the identity line. (3) We show the existence of a scaling law between β(loc) and the relative localization length Λ, now including the regimes of anomalous diffusion. The above findings are important also for chaotic eigenstates in time-independent systems [Batistić and Robnik, J. Phys. A: Math. Gen. 43, 215101 (2010); arXiv:1302.7174 (2013)], where the Brody distribution is confirmed to a very high degree of precision for dynamically localized chaotic eigenstates, even in the mixed-type systems (after separation of regular and chaotic eigenstates).

  15. Simulating High Reynolds Number Flow by Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    KANG Xiu-Ying; LIU Da-He; ZHOU Jing; JIN Yong-Juan

    2005-01-01

    @@ A two-dimensional channel flow with different Reynolds numbers is tested by using the lattice Boltzmann method under different pressure and velocity boundary conditions. The results show that the simulation error increases,and the pressure and the flow rate become unstable under a high Reynolds number. To improve the simulation precision under a high Reynolds number, the number of fluid nodes should be enlarged. For a higher Reynoldsnumber flow, the velocity boundary with an approximately parabolic velocity profile is found to be more adaptive.Blood flow in an artery with cosine shape symmetrical narrowing is then simulated under a velocity boundary condition. Its velocity, pressure and wall shear stress distributions are consistent with previous studies.

  16. Moving Charged Particles in Lattice Boltzmann-Based Electrokinetics

    CERN Document Server

    Kuron, Michael; Schornbaum, Florian; Bauer, Martin; Godenschwager, Christian; Holm, Christian; de Graaf, Joost

    2016-01-01

    The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann (LB) algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions, which are needed to simulate moving colloids, into the Capuani scheme has been lacking. In this paper, we detail how to introduce such moving boundaries, based on an analogue to the moving boundary method for the pure LB solver. The key ingredients in our method are mass and charge conservation for the solute spec...

  17. Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

    Science.gov (United States)

    Orr, Jeb S.; Powers, Joseph F.; Yang, Hong Q

    2015-01-01

    A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments is based upon a novel approach that relies on the global momentum conservation of the closed fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. A numerical example illustrates the method's application to prediction of bulk fluid behavior during a spacecraft ullage settling maneuver.

  18. Boltzmann equation for the electron gas of a nondegenerate plasma

    Science.gov (United States)

    Gould, R. J.

    1974-01-01

    The collision terms in the Boltzmann equation associated with various processes are derived. For processes having a Fokker-Planck (F-P) limit, the associated F-P operator is derived by means of physical arguments to determine the form of the operator; its multiplying constant is fixed by calculating the total energy exchange rate and comparing with the rate computed by other means. In this manner, the F-P operator is derived for electron-ion scattering, electron-electron scattering in the high-velocity limit, electron-atom elastic scattering, Compton scattering, and the high-velocity limit for inelastic scattering. Other processes considered are bremsstrahlung, radiative-recombination, photoionization, collisional ionization of atoms, and suprathermal-particle ionization of atoms.

  19. Lattice Boltzmann Simulation of Multiple Bubbles Motion under Gravity

    Directory of Open Access Journals (Sweden)

    Deming Nie

    2015-01-01

    Full Text Available The motion of multiple bubbles under gravity in two dimensions is numerically studied through the lattice Boltzmann method for the Eotvos number ranging from 1 to 12. Two kinds of initial arrangement are taken into account: vertical and horizontal arrangement. In both cases the effects of Eotvos number on the bubble coalescence and rising velocity are investigated. For the vertical arrangement, it has been found that the coalescence pattern is similar. The first coalescence always takes place between the two uppermost bubbles. And the last coalescence always takes place between the coalesced bubble and the bottommost bubble. For four bubbles in a horizontal arrangement, the outermost bubbles travel into the wake of the middle bubbles in all cases, which allows the bubbles to coalesce. The coalescence pattern is more complex for the case of eight bubbles, which strongly depends on the Eotvos number.

  20. Poisson-Boltzmann Calculations: van der Waals or Molecular Surface?

    Science.gov (United States)

    Pang, Xiaodong; Zhou, Huan-Xiang

    2013-01-01

    The Poisson-Boltzmann equation is widely used for modeling the electrostatics of biomolecules, but the calculation results are sensitive to the choice of the boundary between the low solute dielectric and the high solvent dielectric. The default choice for the dielectric boundary has been the molecular surface, but the use of the van der Waals surface has also been advocated. Here we review recent studies in which the two choices are tested against experimental results and explicit-solvent calculations. The assignment of the solvent high dielectric constant to interstitial voids in the solute is often used as a criticism against the van der Waals surface. However, this assignment may not be as unrealistic as previously thought, since hydrogen exchange and other NMR experiments have firmly established that all interior parts of proteins are transiently accessible to the solvent.

  1. Lattice Boltzmann based discrete simulation for gas-solid fluidization

    CERN Document Server

    Wang, Limin; Wang, Xiaowei; Ge, Wei

    2013-01-01

    Discrete particle simulation, a combined approach of computational fluid dynamics and discrete methods such as DEM (Discrete Element Method), SPH (Smoothed Particle Hydrodynamics), PIC (Particle-In-Cell), etc., is becoming a practical tool for exploring lab-scale gas-solid systems owing to the fast development of its parallel computation. However, the gas-solid coupling and the corresponding fluid flow solver remain immature. In this work, we presented a modified lattice Boltzmann approach to consider the effect of both the local solid volume fraction and the local relative velocity between the particles and the fluid, which was different from the traditional volume-averaged Navier-Stokes equations. This approach is combined with a time-driven hard sphere algorithm to simulate the motion of individual particles in which particles interact with each other via hard-sphere collisions but the collision detection and motion of the particle are performed at constant time intervals, and the EMMS (energy minimization...

  2. Interpolated lattice Boltzmann boundary conditions for surface reaction kinetics.

    Science.gov (United States)

    Walsh, S D C; Saar, M O

    2010-12-01

    This paper describes a method for implementing surface reaction kinetics in lattice Boltzmann simulations. The interpolated boundary conditions are capable of simulating surface reactions and dissolution at both stationary and moving solid-fluid and fluid-fluid interfaces. Results obtained with the boundary conditions are compared to analytical solutions for first-order and constant-flux kinetic surface reactions in a one-dimensional half space, as well as to the analytical solution for evaporation from the surface of a cylinder. Excellent agreement between analytical and simulated results is obtained for a wide range of diffusivities, lattice velocities, and surface reaction rates. The boundary model's ability to represent dissolution in binary fluid mixtures is demonstrated by modeling diffusion from a rising bubble and dissolution of a droplet near a flat plate.

  3. Determination of the Boltzmann Constant Using the Differential - Cylindrical Procedure

    CERN Document Server

    Feng, X J; Lin, H; Gillis, K A; Moldover, M R

    2015-01-01

    We report in this paper the progresses on the determination of the Boltzmann constant using the acoustic gas thermometer (AGT) of fixed-length cylindrical cavities. First, we present the comparison of the molar masses of pure argon gases through comparing speeds of sound of gases. The procedure is independent from the methodology by Gas Chromatography-Mass Spectrometry (GC-MS). The experimental results show good agreement between both methods. The comparison offers an independent inspection of the analytical results by GC-MS. Second, we present the principle of the novel differential-cylindrical procedure based on the AGT of two fixed-length cavities. The deletion mechanism for some major perturbations is analyzed for the new procedure. The experimental results of the differential-cylindrical procedure demonstrate some major improvements on the first, second acoustic and third virial coefficients, and the excess half-widths. The three acoustic virial coefficients agree well with the stated-of-the-art experime...

  4. Lattice Boltzmann method for shape optimization of fluid distributor

    CERN Document Server

    Wang, Limin; Luo, Lingai

    2013-01-01

    This paper presents the shape optimization of a flat-type arborescent fluid distributor for the purpose of process intensification. A shape optimization algorithm based on the lattice Boltzmann method (LBM) is proposed with the objective of decreasing the flow resistance of such distributor at the constraint of constant fluid volume. Prototypes of the initial distributor as well as the optimized one are designed. Fluid distribution and hydraulic characteristics of these distributors are investigated numerically. Results show that the pressure drop of the optimized distributor is between 15.9% and 25.1% lower than that of the initial reference while keeping a uniform flow distribution, demonstrating the process intensification in fluid distributor, and suggesting the interests of the proposed optimization algorithm in engineering optimal design.

  5. Thermal Correction to the Molar Polarizability of a Boltzmann Gas

    CERN Document Server

    Jentschura, U D; Mohr, P J

    2013-01-01

    Metrology in atomic physics has been crucial for a number of advanced determinations of fundamental constants. In addition to very precise frequency measurements, the molar polarizability of an atomic gas has recently also been measured very accurately. Part of the motivation for the measurements is due to ongoing efforts to redefine the International System of Units (SI) for which an accurate value of the Boltzmann constant is needed. Here, we calculate the dominant shift of the molar polarizability in an atomic gas due to thermal effects. It is given by the relativistic correction to the dipole interaction, which emerges when the probing electric field is Lorenz transformed into the rest frame of the atoms that undergo thermal motion. While this effect is small when compared to currently available experimental accuracy, the relativistic correction to the dipole interaction is much larger than the thermal shift of the polarizability induced by blackbody radiation.

  6. Lattice Boltzmann modeling of water-like fluids

    Directory of Open Access Journals (Sweden)

    Sauro eSucci

    2014-04-01

    Full Text Available We review recent advances on the mesoscopic modeling of water-like fluids,based on the lattice Boltzmann (LB methodology.The main idea is to enrich the basic LB (hydro-dynamics with angular degrees of freedom responding to suitable directional potentials between water-like molecules.The model is shown to reproduce some microscopic features of liquid water, such as an average number of hydrogen bonds per molecules (HBs between $3$ and $4$, as well as a qualitatively correctstatistics of the hydrogen bond angle as a function of the temperature.Future developments, based on the coupling the present water-like LB model with the dynamics of suspended bodies,such as biopolymers, may open new angles of attack to the simulation of complex biofluidic problems, such as protein folding and aggregation, and the motion of large biomolecules in complex cellular environments.

  7. The peeling process of infinite Boltzmann planar maps

    CERN Document Server

    Budd, Timothy

    2015-01-01

    We start by studying a peeling process on finite random planar maps with faces of arbitrary degrees determined by a general weight sequence, which satisfies an admissibility criterion. The corresponding perimeter process is identified as a biased random walk, in terms of which the admissibility criterion has a very simple interpretation. The finite random planar maps under consideration were recently proved to possess a well-defined local limit known as the infinite Boltzmann planar map (IBPM). Inspired by recent work of Curien and Le Gall, we show that the peeling process on the IBPM can be obtained from the peeling process of finite random maps by conditioning the perimeter process to stay positive. The simplicity of the resulting description of the peeling process allows us to obtain the scaling limit of the associated perimeter and volume process for arbitrary regular critical weight sequences.

  8. A Lattice Boltzmann Model for Oscillating Reaction-Diffusion

    Science.gov (United States)

    Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio

    2016-07-01

    A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.

  9. From bijels to Pickering emulsions: A lattice Boltzmann study

    Science.gov (United States)

    Jansen, Fabian; Harting, Jens

    2011-04-01

    Particle stabilized emulsions are ubiquitous in the food and cosmetics industry, but our understanding of the influence of microscopic fluid-particle and particle-particle interactions on the macroscopic rheology is still limited. In this paper we present a simulation algorithm based on a multicomponent lattice Boltzmann model to describe the solvents combined with a molecular dynamics solver for the description of the solved particles. It is shown that the model allows a wide variation of fluid properties and arbitrary contact angles on the particle surfaces. We demonstrate its applicability by studying the transition from a “bicontinuous interfacially jammed emulsion gel” (bijel) to a “Pickering emulsion” in dependence on the contact angle, the particle concentration, and the ratio of the solvents.

  10. Full Eulerian lattice Boltzmann model for conjugate heat transfer.

    Science.gov (United States)

    Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

    2015-12-01

    In this paper a full Eulerian lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results.

  11. Modeling of metal foaming with lattice Boltzmann automata

    Energy Technology Data Exchange (ETDEWEB)

    Koerner, C.; Thies, M.; Singer, R.F. [WTM Institute, Department of Materials Science, University of Erlangen, Martensstrasse 5, D-91058 Erlangen (Germany)

    2002-10-01

    The formation and decay of foams produced by gas bubble expansion in a molten metal is numerically simulated with the Lattice Boltzmann Method (LBM) which belongs to the cellular automaton techniques. The present state of the two dimensional model allows the investigation of the foam evolution process comprising bubble expansion, bubble coalescence, drainage, and eventually foam collapse. Examples demonstrate the influence of the surface tension, viscosity and gravity on the foaming process and the resulting cell structure. In addition, the potential of the LBM to solve problems with complex boundary conditions is illustrated by means of a foam developing within the constraints of a mould as well as a foaming droplet exposed to gravity. (Abstract Copyright [2002], Wiley Periodicals, Inc.)

  12. Spreading Dynamics of Nanodrops: A Lattice Boltzmann Study

    CERN Document Server

    Gross, Markus

    2014-01-01

    Spreading of nano-droplets is an interesting and technologically relevant phenomenon where thermal fluctuations lead to unexpected deviations from well-known deterministic laws. Here, we apply the newly developed fluctuating non-ideal lattice Boltzmann method [Gross et al., J. Stat. Mech., P03030 (2011)] for the study of this issue. Confirming the predictions of Davidovich and coworkers [PRL 95, 244905 (2005)], we provide the first independent evidence for the existence of an asymptotic, self-similar noise-driven spreading regime in both two- and three-dimensional geometry. The cross over from the deterministic Tanner's law, where the drop's base radius $b$ grows (in 3D) with time as $b \\sim t^{1/10}$ and the noise dominated regime where $b \\sim t^{1/6}$ is also observed by tuning the strength of thermal noise.

  13. Two Dimensional Lattice Boltzmann Method for Cavity Flow Simulation

    Directory of Open Access Journals (Sweden)

    Panjit MUSIK

    2004-01-01

    Full Text Available This paper presents a simulation of incompressible viscous flow within a two-dimensional square cavity. The objective is to develop a method originated from Lattice Gas (cellular Automata (LGA, which utilises discrete lattice as well as discrete time and can be parallelised easily. Lattice Boltzmann Method (LBM, known as discrete Lattice kinetics which provide an alternative for solving the Navier–Stokes equations and are generally used for fluid simulation, is chosen for the study. A specific two-dimensional nine-velocity square Lattice model (D2Q9 Model is used in the simulation with the velocity at the top of the cavity kept fixed. LBM is an efficient method for reproducing the dynamics of cavity flow and the results which are comparable to those of previous work.

  14. Chemical-potential-based Lattice Boltzmann Method for Nonideal Fluids

    CERN Document Server

    Wen, Binghai; He, Bing; Zhang, Chaoying; Fang, Haiping

    2016-01-01

    Chemical potential is an effective way to drive phase transition or express wettability. In this letter, we present a chemical-potential-based lattice Boltzmann model to simulate multiphase flows. The nonideal force is directly evaluated by a chemical potential. The model theoretically satisfies thermodynamics and Galilean invariance. The computational efficiency is improved owing to avoiding the calculation of pressure tensor. We have derived several chemical potentials of the popular equations of state from the free-energy density function. An effective chemical-potential boundary condition is implemented to investigate the wettability of a solid surface. Remarkably, the numerical results show that the contact angle can be linearly tuned by the surface chemical potential.

  15. Free Surface Lattice Boltzmann with Enhanced Bubble Model

    CERN Document Server

    Anderl, Daniela; Rauh, Cornelia; Rüde, Ulrich; Delgado, Antonio

    2016-01-01

    This paper presents an enhancement to the free surface lattice Boltzmann method (FSLBM) for the simulation of bubbly flows including rupture and breakup of bubbles. The FSLBM uses a volume of fluid approach to reduce the problem of a liquid-gas two-phase flow to a single-phase free surface simulation. In bubbly flows compression effects leading to an increase or decrease of pressure in the suspended bubbles cannot be neglected. Therefore, the free surface simulation is augmented by a bubble model that supplies the missing information by tracking the topological changes of the free surface in the flow. The new model presented here is capable of handling the effects of bubble breakup and coalesce without causing a significant computational overhead. Thus, the enhanced bubble model extends the applicability of the FSLBM to a new range of practically relevant problems, like bubble formation and development in chemical reactors or foaming processes.

  16. Lattice Boltzmann implementation for Fluids Flow Simulation in Porous Media

    Directory of Open Access Journals (Sweden)

    Xinming Zhang

    2011-06-01

    Full Text Available In this paper, the lattice-Boltzmann method is developed to investigate the behavior of isothermal two-phase fluid flow in porous media. The method is based on the Shan–Chen multiphase model of nonideal fluids that allow coexistence of two phases of a single substance. We reproduce some different idealized situations (phase separation, surface tension, contact angle, pipe flow, and fluid droplet motion, et al in which the results are already known from theory or laboratory measurements and show the validity of the implementation for the physical two-phase flow in porous media. Application of the method to fluid intrusion in porous media is discussed and shows the effect of wettability on the fluid flow. The capability of reproducing critical flooding phenomena under strong wettability conditions is also proved.

  17. Double MRT thermal lattice Boltzmann method for simulating convective flows

    Energy Technology Data Exchange (ETDEWEB)

    Mezrhab, Ahmed, E-mail: mezrhab@fso.ump.m [Laboratoire de Mecanique and Energetique, Departement de Physique, Faculte des Sciences, Universite Mohammed 1er, 60000 Oujda (Morocco); Amine Moussaoui, Mohammed; Jami, Mohammed [Laboratoire de Mecanique and Energetique, Departement de Physique, Faculte des Sciences, Universite Mohammed 1er, 60000 Oujda (Morocco); Naji, Hassan [Universite Lille Nord de France, F-59000 Lille, and LML UMR CNRS 8107, F-59655 Villeneuve d' Ascq cedex (France); Bouzidi, M' hamed [Universite Clermont 2, LaMI EA 3867, IUT de Montlucon, Av. A. Briand, BP 2235, F-03101 Montlucon cedex (France)

    2010-07-26

    A two-dimensional double Multiple Relaxation Time-Thermal Lattice Boltzmann Equation (2-MRT-TLBE) method is developed for predicting convective flows in a square differentially heated cavity filled with air (Pr=0.71). In this Letter, we propose a numerical scheme to solve the flow and the temperature fields using the MRT-D2Q9 model and the MRT-D2Q5 model, respectively. Thus, the main objective of this study is to show the effectiveness of such model to predict thermodynamics for heat transfer. This model is validated by the numerical simulations of the 2-D convective square cavity flow. Excellent agreements are obtained between numerical predictions. These results demonstrate the accuracy and the effectiveness of the proposed methodology.

  18. Electric Conductivity from the solution of the Relativistic Boltzmann Equation

    CERN Document Server

    Puglisi, A; Greco, V

    2014-01-01

    We present numerical results of electric conductivity $\\sigma_{el}$ of a fluid obtained solving the Relativistic Transport Boltzmann equation in a box with periodic boundary conditions. We compute $\\sigma_{el}$ using two methods: the definition itself, i.e. applying an external electric field, and the evaluation of the Green-Kubo relation based on the time evolution of the current-current correlator. We find a very good agreement between the two methods. We also compare numerical results with analytic formulas in Relaxation Time Approximation (RTA) where the relaxation time for $\\sigma_{el}$ is determined by the transport cross section $\\sigma_{tr}$, i.e. the differential cross section weighted with the collisional momentum transfer. We investigate the electric conductivity dependence on the microscopic details of the 2-body scatterings: isotropic and anisotropic cross-section, and massless and massive particles. We find that the RTA underestimates considerably $\\sigma_{el}$; for example at screening masses $...

  19. Emergence of Compositional Representations in Restricted Boltzmann Machines

    CERN Document Server

    Tubiana, Jérôme

    2016-01-01

    Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for this purpose, and to be able to generate distributed and graded representations of the data. We characterize the structural conditions (sparsity of the weights, low effective temperature, nonlinearities in the activation functions of hidden units, and adaptation of fields maintaining the activity in the visible layer) allowing RBM to operate in such a compositional phase. Evidence is provided by the replica analysis of an adequate statistical ensemble of random RBMs and by RBM trained on the handwritten digits dataset MNIST.

  20. Boundary Slip and Surface Interaction: A Lattice Boltzmann Simulation

    Institute of Scientific and Technical Information of China (English)

    CHEN Yan-Yan; YI Hou-Hui; LI Hua-Bing

    2008-01-01

    The factors affecting slip length in Couette geometry flows are analysed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactions.The main factors influencing the boundary slip are the strength of interactions between fluid-fluid and fluid-wall particles.Other factors,such as fluid viscosity,bulk pressure may also change the slip length.We find that boundary slip only occurs under a certain density(bulk pressure).If the density is large enough,the slip length will tend to zero.In our simulations,a low density layer near the wall does not need to be postulated a priori but emerges naturally from the underlying non-ideal mesoscopic dynamics.It is the low density layer that induces the boundary slip.The results may be helpful to understand recent experimental observations on the slippage of micro flows.

  1. Convection in multiphase flows using Lattice Boltzmann methods

    CERN Document Server

    Biferale, L; Sbragaglia, M; Toschi, F

    2011-01-01

    We present high resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a Lattice Boltzmann method. We first validate the thermodynamical and kinematical properties of the algorithm. Then, we perform a series of 3d numerical simulations at changing the mean properties in the phase diagram and compare convection with and without phase coexistence at $Ra \\sim 10^7$. We show that in presence of nucleating bubbles non-Oberbeck Boussinesq effects develops, mean temperature profile becomes asymmetric, heat-transfer and heat-transfer fluctuations are enhanced. We also show that small-scale properties of velocity and temperature fields are strongly affected by the presence of buoyant bubble leading to high non-Gaussian profiles in the bulk.

  2. Flavoured quantum Boltzmann equations from cQPA

    CERN Document Server

    Fidler, Christian; Kainulainen, Kimmo; Rahkila, Pyry Matti

    2011-01-01

    We develop a Boltzmann-type quantum transport theory for interacting fermion and scalar fields including both flavour and particle-antiparticle mixing. Our formalism is based on the coherent quasiparticle approximation (cQPA) for the 2-point correlation functions, whose extended phase-space structure contains new spectral shells for flavour- and particle-antiparticle coherence. We derive explicit cQPA propagators and Feynman rules for the transport theory. In particular the nontrivial Wightman functions can be written as composite operators $\\sim {\\cal A} F {\\cal A}$, which generalize the usual Kadanoff-Baym ansatz. Our numerical results show that particle-antiparticle coherence can strongly influence CP-violating flavour mixing even for relatively slowly-varying backgrounds. Thus, unlike recently suggested, these correlations cannot be neglected when studying asymmetry generation due to time-varying mass transition, for example in electroweak-type baryogenesis models. Finally, we show that the cQPA coherence...

  3. Modeling Image Structure with Factorized Phase-Coupled Boltzmann Machines

    CERN Document Server

    Cadieu, Charles F

    2010-01-01

    We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squared filter outputs (Ranzato and Hinton, 2010). Here, we extend this model to $L_p$-spherically symmetric subspaces. In order to model local amplitude and phase structure in images, we focus on the case of two dimensional subspaces, and the $L_2$-norm. When trained on natural images the model learns subspaces resembling quadrature-pair Gabor filters. We then introduce an additional set of hidden units that model the dependencies among subspace phases. These hidden units form a combinatorial mixture of phase coupling distributions, concentrated in the sum and difference of phase pairs. When adapted to natural images, these distributions capture local spatial phase structure in natural images.

  4. Boltzmann-Shannon entropy and the double-slit experiment

    Science.gov (United States)

    Norwich, Kenneth H.

    2016-11-01

    We study the Boltzmann-Shannon entropy lost (information gained) by the observer in a double-slit experiment when the slit taken by a photon is known, and when the corresponding entropy gained by the photon at the level of the screen can be calculated. Using a Gedanken experiment involving infinitesimal slits and a distant cylindrical screen, entropy values assume a very simple form. The entropy changes (at the slit and screen) are found to be equal in magnitude and opposite in sign, and correspond to the minimum change permitted by Heisenberg's Uncertainty Principle. Moreover, when welcher Weg information is knowable a priori, we see that the "cost" of this information (knowing which slit is taken) is reversion to a single slit pattern.

  5. Lattice Boltzmann simulations of convection heat transfer in porous media

    Science.gov (United States)

    Liu, Qing; He, Ya-Ling

    2017-01-01

    A non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed to study convection heat transfer in porous media at the representative elementary volume scale based on the generalized non-Darcy model. In the method, two different LB models are constructed: one is constructed in the framework of the double-distribution-function approach, and the other is constructed in the framework of the hybrid approach. In particular, the transformation matrices used in the MRT-LB models are non-orthogonal matrices. The present method is applied to study mixed convection flow in a porous channel and natural convection flow in a porous cavity. It is found that the numerical results are in good agreement with the analytical solutions and/or other results reported in previous studies. Furthermore, the non-orthogonal MRT-LB method shows better numerical stability in comparison with the BGK-LB method.

  6. Approximate message passing with restricted Boltzmann machine priors

    Science.gov (United States)

    Tramel, Eric W.; Drémeau, Angélique; Krzakala, Florent

    2016-07-01

    Approximate message passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problems. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernoulli prior which utilizes a restricted Boltzmann machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple i.i.d. priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance.

  7. Lattice Boltzmann modeling an introduction for geoscientists and engineers

    CERN Document Server

    Sukop, Michael C

    2005-01-01

    Lattice Boltzmann models have a remarkable ability to simulate single- and multi-phase fluids and transport processes within them. A rich variety of behaviors, including higher Reynolds numbers flows, phase separation, evaporation, condensation, cavitation, buoyancy, and interactions with surfaces can readily be simulated. This book provides a basic introduction that emphasizes intuition and simplistic conceptualization of processes. It avoids the more difficult mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those with more interest in model application than detailed mathematical foundations will find this a powerful "quick start" guide. Example simulations, exercises, and computer codes are included. Working code is provided on the Internet.

  8. Approximate Message Passing with Restricted Boltzmann Machine Priors

    CERN Document Server

    Tramel, Eric W; Krzakala, Florent

    2015-01-01

    Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple iid priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance.

  9. Distribution Learning in Evolutionary Strategies and Restricted Boltzmann Machines

    DEFF Research Database (Denmark)

    Krause, Oswin

    of the thesis is concerned with RBMs that are fitted to a dataset using maximum log-likelihood. As the computation of the distribution's normalization constant is intractable, Markov Chain Monte Carlo methods are required to estimate and follow the log-likelihood gradient. The thesis investigates...... the approximation properties of stacked RBMs used to model the distribution of real valued data. Further, estimation algorithms of the normalization constant of an RBM are compared and a theoretical framework is introduced from which a number of well known algorithms can be derived. Lastly, a method based......The thesis is concerned with learning distributions in the two settings of Evolutionary Strategies (ESs) and Restricted Boltzmann Machines (RBMs). In both cases, the distributions are learned from samples, albeit with different goals. Evolutionary Strategies are concerned with finding an optimum...

  10. Simulation of a Microfluidic Gradient Generator using Lattice Boltzmann Methods

    CERN Document Server

    Simon, Tanaka

    2013-01-01

    Microfluidics provides a powerful and versatile technology to accurately control spatial and temporal conditions for cell culturing and can therefore be used to study cellular responses to gradients. Here we use Lattice Boltzmann methods (LBM) to solve both the Navier-Stokes equation (NSE) for the fluid and the coupled convection-diffusion equation (CDE) for the compounds that form the diffusion-based gradient. The design of a microfluidic chamber for diffusion-based gradients must avoid flow through the cell chamber. This can be achieved by alternately opening the source and the sink channels. The fast toggling of microfluidic valves requires switching between different boundary conditions. We demonstrate that the LBM is a powerful method for handling complex geometries, high Peclet number conditions, discontinuities in the boundary conditions, and multiphysics coupling.

  11. Nonaligned shocks for discrete velocity models of the Boltzmann equation

    Directory of Open Access Journals (Sweden)

    J. M. Greenberg

    1991-05-01

    Full Text Available At the conclusion of I. Bonzani's presentation on the existence of structured shock solutions to the six-velocity, planar, discrete Boltzmann equation (with binary and triple collisions, Greenberg asked whether such solutions were possible in directions e(α=(cosα ,sinα when α was not one of the particle flow directions. This question generated a spirited discussion but the question was still open at the conclusion of the conference. In this note the author will provide a partial resolution to the question raised above. Using formal perturbation arguments he will produce approximate solutions to the equation considered by Bonzani which represent traveling waves propagating in any direction e(α=(cosα ,sinα.

  12. Using an Interactive Lattice Boltzmann Solver in Fluid Mechanics Instruction

    Directory of Open Access Journals (Sweden)

    Mirjam S. Glessmer

    2017-07-01

    Full Text Available This article gives an overview of the diverse range of teaching applications that can be realized using an interactive lattice Boltzmann simulation tool in fluid mechanics instruction and outreach. In an inquiry-based learning framework, examples are given of learning scenarios that address instruction on scientific results, scientific methods or the scientific process at varying levels of student activity, from consuming to applying to researching. Interactive live demonstrations on portable hardware enable new and innovative teaching concepts for fluid mechanics, also for large audiences and in the early stages of the university education. Moreover, selected examples successfully demonstrate that the integration of high-fidelity CFD methods into fluid mechanics teaching facilitates high-quality student research work within reach of the current state of the art in the respective field of research.

  13. A Boltzmann machine for the organization of intelligent machines

    Science.gov (United States)

    Moed, Michael C.; Saridis, George N.

    1989-01-01

    In the present technological society, there is a major need to build machines that would execute intelligent tasks operating in uncertain environments with minimum interaction with a human operator. Although some designers have built smart robots, utilizing heuristic ideas, there is no systematic approach to design such machines in an engineering manner. Recently, cross-disciplinary research from the fields of computers, systems AI and information theory has served to set the foundations of the emerging area of the design of intelligent machines. Since 1977 Saridis has been developing an approach, defined as Hierarchical Intelligent Control, designed to organize, coordinate and execute anthropomorphic tasks by a machine with minimum interaction with a human operator. This approach utilizes analytical (probabilistic) models to describe and control the various functions of the intelligent machine structured by the intuitively defined principle of Increasing Precision with Decreasing Intelligence (IPDI) (Saridis 1979). This principle, even though resembles the managerial structure of organizational systems (Levis 1988), has been derived on an analytic basis by Saridis (1988). The purpose is to derive analytically a Boltzmann machine suitable for optimal connection of nodes in a neural net (Fahlman, Hinton, Sejnowski, 1985). Then this machine will serve to search for the optimal design of the organization level of an intelligent machine. In order to accomplish this, some mathematical theory of the intelligent machines will be first outlined. Then some definitions of the variables associated with the principle, like machine intelligence, machine knowledge, and precision will be made (Saridis, Valavanis 1988). Then a procedure to establish the Boltzmann machine on an analytic basis will be presented and illustrated by an example in designing the organization level of an Intelligent Machine. A new search technique, the Modified Genetic Algorithm, is presented and proved

  14. Generalizing the Boltzmann equation in complex phase space.

    Science.gov (United States)

    Zadehgol, Abed

    2016-08-01

    In this work, a generalized form of the BGK-Boltzmann equation is proposed, where the velocity, position, and time can be represented by real or complex variables. The real representation leads to the conventional BGK-Boltzmann equation, which can recover the continuity and Navier-Stokes equations. We show that the complex representation yields a different set of equations, and it can also recover the conservation and Navier-Stokes equations, at low Mach numbers, provided that the imaginary component of the macroscopic mass can be neglected. We briefly review the Constant Speed Kinetic Model (CSKM), which was introduced in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014)JCTPAH0021-999110.1016/j.jcp.2014.06.053] and Zadehgol [Phys. Rev. E 91, 063311 (2015)PLEEE81539-375510.1103/PhysRevE.91.063311]. The CSKM is then used as a basis to show that the complex-valued equilibrium distribution function of the present model can be identified with a simple singularity in the complex phase space. The virtual particles, in the present work, are concentrated on virtual "branes" which surround the computational nodes. Employing the Cauchy integral formula, it is shown that certain variations of the "branes," in the complex phase space, do not affect the local kinetic states. This property of the new model, which is referred to as the "apparent jumps" in the present work, is used to construct new models. The theoretical findings have been tested by simulating three benchmark flows. The results of the present simulations are in excellent agreement with the previous results reported by others.

  15. Towards Full Aircraft Airframe Noise Prediction: Lattice Boltzmann Simulations

    Science.gov (United States)

    Khorrami, Mehdi R.; Fares, Ehab; Casalino, Damiano

    2014-01-01

    Computational results for an 18%-scale, semi-span Gulfstream aircraft model are presented. Exa Corporation's lattice Boltzmann PowerFLOW(trademark) solver was used to perform time-dependent simulations of the flow field associated with this high-fidelity aircraft model. The simulations were obtained for free-air at a Mach number of 0.2 with the flap deflected at 39 deg (landing configuration). We focused on accurately predicting the prominent noise sources at the flap tips and main landing gear for the two baseline configurations, namely, landing flap setting without and with gear deployed. Capitalizing on the inherently transient nature of the lattice Boltzmann formulation, the complex time-dependent flow features associated with the flap were resolved very accurately and efficiently. To properly simulate the noise sources over a broad frequency range, the tailored grid was very dense near the flap inboard and outboard tips. Extensive comparison of the computed time-averaged and unsteady surface pressures with wind tunnel measurements showed excellent agreement for the global aerodynamic characteristics and the local flow field at the flap inboard and outboard tips and the main landing gear. In particular, the computed fluctuating surface pressure field for the flap agreed well with the measurements in both amplitude and frequency content, indicating that the prominent airframe noise sources at the tips were captured successfully. Gear-flap interaction effects were remarkably well predicted and were shown to affect only the inboard flap tip, altering the steady and unsteady pressure fields in that region. The simulated farfield noise spectra for both baseline configurations, obtained using a Ffowcs-Williams and Hawkings acoustic analogy approach, were shown to be in close agreement with measured values.

  16. Generalizing the Boltzmann equation in complex phase space

    Science.gov (United States)

    Zadehgol, Abed

    2016-08-01

    In this work, a generalized form of the BGK-Boltzmann equation is proposed, where the velocity, position, and time can be represented by real or complex variables. The real representation leads to the conventional BGK-Boltzmann equation, which can recover the continuity and Navier-Stokes equations. We show that the complex representation yields a different set of equations, and it can also recover the conservation and Navier-Stokes equations, at low Mach numbers, provided that the imaginary component of the macroscopic mass can be neglected. We briefly review the Constant Speed Kinetic Model (CSKM), which was introduced in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014), 10.1016/j.jcp.2014.06.053] and Zadehgol [Phys. Rev. E 91, 063311 (2015), 10.1103/PhysRevE.91.063311]. The CSKM is then used as a basis to show that the complex-valued equilibrium distribution function of the present model can be identified with a simple singularity in the complex phase space. The virtual particles, in the present work, are concentrated on virtual "branes" which surround the computational nodes. Employing the Cauchy integral formula, it is shown that certain variations of the "branes," in the complex phase space, do not affect the local kinetic states. This property of the new model, which is referred to as the "apparent jumps" in the present work, is used to construct new models. The theoretical findings have been tested by simulating three benchmark flows. The results of the present simulations are in excellent agreement with the previous results reported by others.

  17. Lattice Boltzmann formulation for conjugate heat transfer in heterogeneous media.

    Science.gov (United States)

    Karani, Hamid; Huber, Christian

    2015-02-01

    In this paper, we propose an approach for studying conjugate heat transfer using the lattice Boltzmann method (LBM). The approach is based on reformulating the lattice Boltzmann equation for solving the conservative form of the energy equation. This leads to the appearance of a source term, which introduces the jump conditions at the interface between two phases or components with different thermal properties. The proposed source term formulation conserves conductive and advective heat flux simultaneously, which makes it suitable for modeling conjugate heat transfer in general multiphase or multicomponent systems. The simple implementation of the source term approach avoids any correction of distribution functions neighboring the interface and provides an algorithm that is independent from the topology of the interface. Moreover, our approach is independent of the choice of lattice discretization and can be easily applied to different advection-diffusion LBM solvers. The model is tested against several benchmark problems including steady-state convection-diffusion within two fluid layers with parallel and normal interfaces with respect to the flow direction, unsteady conduction in a three-layer stratified domain, and steady conduction in a two-layer annulus. The LBM results are in excellent agreement with analytical solution. Error analysis shows that our model is first-order accurate in space, but an extension to a second-order scheme is straightforward. We apply our LBM model to heat transfer in a two-component heterogeneous medium with a random microstructure. This example highlights that the method we propose is independent of the topology of interfaces between the different phases and, as such, is ideally suited for complex natural heterogeneous media. We further validate the present LBM formulation with a study of natural convection in a porous enclosure. The results confirm the reliability of the model in simulating complex coupled fluid and thermal dynamics

  18. Contact angles in the pseudopotential lattice Boltzmann modeling of wetting.

    Science.gov (United States)

    Li, Qing; Luo, K H; Kang, Q J; Chen, Q

    2014-11-01

    In this paper we investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio ρ_{L}/ρ_{V}=500. The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994)10.1103/PhysRevE.49.2941] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions, the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles θstatic contact angles close to 180^{∘}. Meanwhile, it is found that the proposed modified pseudopotential-based interaction performs better in light of the maximum and the minimum densities and is overall more suitable for simulating large contact angles θ>90^{∘} as compared with the two other types of fluid-solid interactions. Furthermore, the spurious currents are found to be enlarged when the fluid-solid interaction force is introduced. Increasing the kinematic viscosity ratio between the vapor and liquid phases is shown to be capable of reducing the spurious currents caused by the fluid-solid interactions.

  19. Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times

    Directory of Open Access Journals (Sweden)

    Kosuke Hayashi

    2012-06-01

    Full Text Available An immersed boundary-lattice Boltzmann method (IB-LBM using a two-relaxation time model (TRT is proposed. The collision operator in the lattice Boltzmann equation is modeled using two relaxation times. One of them is used to set the fluid viscosity and the other is for numerical stability and accuracy. A direct-forcing method is utilized for treatment of immersed boundary. A multi-direct forcing method is also implemented to precisely satisfy the boundary conditions at the immersed boundary. Circular Couette flows between a stationary cylinder and a rotating cylinder are simulated for validation of the proposed method. The method is also validated through simulations of circular and spherical falling particles. Effects of the functional forms of the direct-forcing term and the smoothed-delta function, which interpolates the fluid velocity to the immersed boundary and distributes the forcing term to fixed Eulerian grid points, are also examined. As a result, the following conclusions are obtained: (1 the proposed method does not cause non-physical velocity distribution in circular Couette flows even at high relaxation times, whereas the single-relaxation time (SRT model causes a large non-physical velocity distortion at a high relaxation time, (2 the multi-direct forcing reduces the errors in the velocity profile of a circular Couette flow at a high relaxation time, (3 the two-point delta function is better than the four-point delta function at low relaxation times, but worse at high relaxation times, (4 the functional form of the direct-forcing term does not affect predictions, and (5 circular and spherical particles falling in liquids are well predicted by using the proposed method both for two-dimensional and three-dimensional cases.

  20. Polarizable Atomic Multipole Solutes in a Poisson-Boltzmann Continuum

    Science.gov (United States)

    Schnieders, Michael J.; Baker, Nathan A.; Ren, Pengyu; Ponder, Jay W.

    2008-01-01

    Modeling the change in the electrostatics of organic molecules upon moving from vacuum into solvent, due to polarization, has long been an interesting problem. In vacuum, experimental values for the dipole moments and polarizabilities of small, rigid molecules are known to high accuracy; however, it has generally been difficult to determine these quantities for a polar molecule in water. A theoretical approach introduced by Onsager used vacuum properties of small molecules, including polarizability, dipole moment and size, to predict experimentally known permittivities of neat liquids via the Poisson equation. Since this important advance in understanding the condensed phase, a large number of computational methods have been developed to study solutes embedded in a continuum via numerical solutions to the Poisson-Boltzmann equation (PBE). Only recently have the classical force fields used for studying biomolecules begun to include explicit polarization in their functional forms. Here we describe the theory underlying a newly developed Polarizable Multipole Poisson-Boltzmann (PMPB) continuum electrostatics model, which builds on the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. As an application of the PMPB methodology, results are presented for several small folded proteins studied by molecular dynamics in explicit water as well as embedded in the PMPB continuum. The dipole moment of each protein increased on average by a factor of 1.27 in explicit water and 1.26 in continuum solvent. The essentially identical electrostatic response in both models suggests that PMPB electrostatics offers an efficient alternative to sampling explicit solvent molecules for a variety of interesting applications, including binding energies, conformational analysis, and pKa prediction. Introduction of 150 mM salt lowered the electrostatic solvation energy between 2–13 kcal/mole, depending on the formal charge of the protein, but had only a

  1. An introduction to the Boltzmann equation and transport processes in gases

    Energy Technology Data Exchange (ETDEWEB)

    Kremer, Gilberto Medeiros [Universidade Federal do Parana, Curitiba (Brazil). Dept. de Fisica

    2010-07-01

    This book deals with the classical kinetic theory of gases. Its aim is to present the basic principles of this theory within an elementary framework and from a more rigorous approach based on the Boltzmann equation. The subjects are presented in a self-contained manner such that the readers can understand and learn some methods used in the kinetic theory of gases in order to investigate the Boltzmann equation. It is expected that this book could be useful as a textbook for students and researchers who are interested in the principles of the Boltzmann equation and in the methods used in the kinetic theory of gases. (orig.)

  2. A precise Boltzmann distribution law for the fluorescence intensity ratio of two thermally coupled levels

    Science.gov (United States)

    Qin, Feng; Zhao, Hua; Cai, Wei; Zhang, Zhiguo; Cao, Wenwu

    2016-06-01

    Noncontact monitoring temperature is very important in modern medicine, science, and technologies. The fluorescence intensity ratio (FIR) technique based on the Boltzmann distribution law exhibits excellent application potential, but the observed FIR deviates from the Boltzmann distribution law in the low temperature range. We propose a fluorescence intensity ratio relation FIR* = ηFIR by introducing a quantity η representing thermal population degree, which can be obtained from measured fluorescence decay curves of the upper emitting level. Using Eu3+ as an example, the method is confirmed that the deviated FIR is able to be corrected and return to follow the Boltzmann law.

  3. The effect of surface roughness on rarefied gas flows by lattice Boltzmann method

    Institute of Scientific and Technical Information of China (English)

    Liu Chao-Feng; Ni Yu-Shan

    2008-01-01

    This paper studies the roughness effect combining with effects of rarefaction and compressibility by a lattice Boltzmann model for rarefied gas flows at high Knudsen numbers. By discussing the effect of the tangential momentum accommodation coefficient on the rough boundary condition, the lattice Boltzmann simulations of nitrogen and helium flows are performed in a two-dimensional microchannel with rough boundaries. The surface roughness effects in the microchannel on the velocity field, the mass flow rate and the friction coefficient are studied and analysed. Numerical results for the two gases in micro scale show different characteristics from macroscopic flows and demonstrate the feasibility of the lattice Boltzmann model in rarefied gas dynamics.

  4. THE NON-CUTOFF BOLTZMANN EQUATION WITH POTENTIAL FORCE IN THE WHOLE SPACE

    Institute of Scientific and Technical Information of China (English)

    Yuanjie LEI

    2014-01-01

    This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1-3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].

  5. An analytical solution of the time-independent Schrödinger equation for the Woods-Saxon potential for arbitrary angular momentum l states

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, P. Rajesh [Open University Malaysia, Lot G (7-06-01), Blok 7 Presint Alami, Pusat Perniagaan Worldwide 2, Jalan Tinju, Seksyen 13, 40100 Shah Alam, Selangor (Malaysia); Wong, B. R. [International University of Malaya-Wales, Block A, City Campus, Jalan Tun Ismail, 50480 Kuala Lumpur (Malaysia); Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur (Malaysia)

    2015-04-24

    The Woods-Saxon potential is probably the most studied and widely used short range potential in all of nuclear physics. For the angular momentum l= 0 case, Flügge had devised a method to obtain an analytical expression for the bound state energies of the radial time-independent Schrödinger equation for a neutron confined in a Woods-Saxon potential well. In this study, we extend Flügge's method to solve the radial Schrödinger equation for a neutron within the Woods-Saxon potential and the centrifugal potential for arbitrary values of l. Here, the Pekeris method is used to deal with the centrifugal term. We obtain an analytical expression for the bound states, valid for arbitrary angular momentum, and show that our expression reduces to that of Flügge, which applies to the l= 0 case. The numerical computations performed also show very good agreement with our analytical expression.

  6. Employee critical psychological states as determinants of employee brand equity in banking: a multi-group analysis

    Directory of Open Access Journals (Sweden)

    Mohsin Altaf

    2017-09-01

    Full Text Available The objective of the study is to investigate the moderating role of affective sentiments of brand psychological ownership of an employee in the relationship among the cognitive sentiments of employee brand understanding and employee brand equity of conventional and Islamic banks. Survey method was adopted to collect data from respondents from conventional and Islamic banks. Data were collected from 279 employees from the banking sector using two-stage probability sampling. Disproportionate stratified random sampling and simple random sampling were employed to collect responses. To analyze the data, multi-group analysis was applied using PLS-SEM technique through SmartPLS 3.0. Results demonstrated that congruence between brand image and individuals has a moderating effect on the relationship between brand confidence and employee brand equity in conventional banking. Responsibility to maintain brand image has a moderating effect on the relationship between brand knowledge and employee brand equity in conventional banking. In case of Islamic banking, only congruence between brand image and individuals exhibited a moderating role on the relationship between brand knowledge and employee brand equity. The importance of brand understanding of employees and psychological ownership of a brand has been widely discussed in branding literature. However, only a few studies investigated the relationship between dimensions of employee brand understanding and the employee brand psychological ownership with employee brand equity. The cognitive and affective sentiments of both exogenous latent constructs, their relationships, and the interaction effect of cognitive and affective sentiments were seldom discussed in branding literature. This study covers the in-depth view and investigation of brand understanding of employ¬ees and the affective and cognitive sentiments of brand psychological ownership with em¬ployee behavior toward a brand. This study also

  7. Anisotropies in the Neutrino Fluxes and Heating Profiles in Two-dimensional, Time-dependent, Multi-group Radiation Hydrodynamics Simulations of Rotating Core-Collapse Supernovae

    CERN Document Server

    Walder, R; Ott, C D; Livne, E; Jarrah, M

    2004-01-01

    Using the 2D multi-group, flux-limited diffusion version of the code VULCAN/2D, that also incorporates rotation, we have calculated the collapse, bounce, shock formation, and early post-bounce evolutionary phases of a core-collapse supernova for a variety of initial rotation rates. This is the first series of such multi-group calculations undertaken in supernova theory with fully multi-D tools. We find that though rotation generates pole-to-equator angular anisotropies in the neutrino radiation fields, the magnitude of the asymmetries is not as large as previously estimated. Moreover, we find that the radiation field is always more spherically symmetric than the matter distribution, with its plumes and convective eddies. We present the dependence of the angular anisotropy of the neutrino fields on neutrino species, neutrino energy, and initial rotation rate. Only for our most rapidly rotating model do we start to see qualitatively different hydrodynamics, but for the lower rates consistent with the pre-collap...

  8. Advanced Neutron Source Cross Section Libraries (ANSL-V): ENDF/B-V based multigroup cross-section libraries for advanced neutron source (ANS) reactor studies

    Energy Technology Data Exchange (ETDEWEB)

    Ford, W.E. III; Arwood, J.W.; Greene, N.M.; Moses, D.L.; Petrie, L.M.; Primm, R.T. III; Slater, C.O.; Westfall, R.M.; Wright, R.Q.

    1990-09-01

    Pseudo-problem-independent, multigroup cross-section libraries were generated to support Advanced Neutron Source (ANS) Reactor design studies. The ANS is a proposed reactor which would be fueled with highly enriched uranium and cooled with heavy water. The libraries, designated ANSL-V (Advanced Neutron Source Cross Section Libraries based on ENDF/B-V), are data bases in AMPX master format for subsequent generation of problem-dependent cross-sections for use with codes such as KENO, ANISN, XSDRNPM, VENTURE, DOT, DORT, TORT, and MORSE. Included in ANSL-V are 99-group and 39-group neutron, 39-neutron-group 44-gamma-ray-group secondary gamma-ray production (SGRP), 44-group gamma-ray interaction (GRI), and coupled, 39-neutron group 44-gamma-ray group (CNG) cross-section libraries. The neutron and SGRP libraries were generated primarily from ENDF/B-V data; the GRI library was generated from DLC-99/HUGO data, which is recognized as the ENDF/B-V photon interaction data. Modules from the AMPX and NJOY systems were used to process the multigroup data. Validity of selected data from the fine- and broad-group neutron libraries was satisfactorily tested in performance parameter calculations.

  9. Immiscible multicomponent lattice Boltzmann model for fluids with high relaxation time ratio

    Indian Academy of Sciences (India)

    Tao Jiang; Qiwei Gong; Ruofan Qiu; Anlin Wang

    2014-10-01

    An immiscible multicomponent lattice Boltzmann model is developed for fluids with high relaxation time ratios, which is based on the model proposed by Shan and Chen (SC). In the SC model, an interaction potential between particles is incorporated into the discrete lattice Boltzmann equation through the equilibrium velocity. Compared to the SC model, external forces in our model are discretized directly into the discrete lattice Boltzmann equation, as proposed by Guo et al. We develop it into a new multicomponent lattice Boltzmann (LB) model which has the ability to simulate immiscible multicomponent fluids with relaxation time ratio as large as 29.0 and to reduce `spurious velocity’. In this work, the improved model is validated and studied using the central bubble case and the rising bubble case. It finds good applications in both static and dynamic cases for multicomponent simulations with different relaxation time ratios.

  10. Global classical solutions of the Boltzmann equation with long-range interactions

    National Research Council Canada - National Science Library

    Philip T. Gressman; Robert M. Strain; Richard V. Kadison

    2010-01-01

    This is a brief announcement of our recent proof of global existence and rapid decay to equilibrium of classical solutions to the Boltzmann equation without any angular cutoff, that is, for long-range interactions...

  11. Progress towards an accurate determination of the Boltzmann constant by Doppler spectroscopy

    National Research Council Canada - National Science Library

    Lemarchand, Cyril; Triki, Meriam; Darquié, Benoît; J. Bordé, Christian; Chardonnet, Christian; Daussy, Christophe

    2011-01-01

    In this paper, we present significant progress performed on an experiment dedicated to the determination of the Boltzmann constant, k, by accurately measuring the Doppler absorption profile of a line...

  12. Gevrey Regularity for the Noncutoff Nonlinear Homogeneous Boltzmann Equation with Strong Singularity

    Directory of Open Access Journals (Sweden)

    Shi-you Lin

    2014-01-01

    Full Text Available The Cauchy problem of the nonlinear spatially homogeneous Boltzmann equation without angular cutoff is studied. By using analytic techniques, one proves the Gevrey regularity of the C∞ solutions in non-Maxwellian and strong singularity cases.

  13. Lattice Boltzmann simulation of transverse wave travelling in Maxwell viscoelastic fluid

    Institute of Scientific and Technical Information of China (English)

    Li Hua-Bing; Fang Hai-Ping

    2004-01-01

    A nine-velocity lattice Boltzmann method for Maxwell viscoelastic fluid is proposed. Travelling of transverse wave in Maxwell viscoelastic fluid is simulated. The instantaneous oscillating velocity, transverse shear speed and decay rate agree with theoretical results very well.

  14. A Stability Notion for the viscous Shallow Water Lattice Boltzmann Equations

    CERN Document Server

    Banda, Mapundi K

    2015-01-01

    The stability of Lattice Boltzmann Equations modelling Shallow Water Equations in the special case of reduced gravity is investigated theoretically. A stability notion is defined as applied in incompressible Navier-Stokes equations in Banda, M. K., Yong, W.- A. and Klar, A: A stability notion for lattice Boltzmann equations. SIAM J. Sci. Comput. {\\bf 27(6)}, 2098-2111 (2006). It is found that to maintain stability a careful choice of the value of the reduced gravity must be made. The stability notion is employed to investigate different shallow water lattice Boltzmann Equations. The effect of the reduced gravity on the mechanism of instability is investigated. Results are tested using the Lattice Boltzmann Method for various values of the governing parameters of the flow. It is observed that even for the discrete model the reduced gravity has a significant effect on the stability.

  15. A Novel Lattice Boltzmann Model For Reactive Flows with Fast Chemistry

    Institute of Scientific and Technical Information of China (English)

    CHEN Sheng; LIU Zhao-Hui; HE Zhu; ZHANG Chao; TIAN Zhi-Wei; SHI Bao-Chang; ZHENG Chu-Guang

    2006-01-01

    @@ A novel lattice Boltzmann model, in which we take the ratio of temperature difference in the temperature field to the environment one to be more than one order of magnitude than before, is developed to simulate two dimensional reactive flows with fast chemistry. Different from the hybrid scheme for reactive flows [Comput.Phys. Commun. 129 (2000)267], this scheme is strictly in a pure lattice Boltzmann style (i.e., we solve the flow, temperature, and concentration fields using the lattice Boltzmann method only). Different from the recent non-coupled lattice Boltzmann scheme [Int. J. Mod. Phys. B 17(2003) 197], the fluid density in our model is coupled directly with the temperature. Excellent agreement between the present results and other numerical data shows that this scheme is an efficient numerical method for practical reactive flows with fast chemistry.

  16. Equivalence Between Forward and Backward Boltzmann Equations in Multi-Component Medium

    Institute of Scientific and Technical Information of China (English)

    张竹林

    2002-01-01

    The author generalized the propagator function theory introduced first by Sigmund, and gave a explicitly proof of a equivalence between forward and backward Boltzmann equations in a multi-component medium by using the generalized propagator function theory.

  17. An introduction to the Boltzmann equation and transport processes in gases

    CERN Document Server

    Kremer, Gilberto M; Colton, David

    2010-01-01

    This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.

  18. Comparison of Boltzmann Kinetics with Quantum Dynamics for a Chiral Yukawa Model Far From Equilibrium

    CERN Document Server

    Lindner, Manfred

    2007-01-01

    Boltzmann equations are often used to describe the non-equilibrium time-evolution of many-body systems in particle physics. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after a relativistic heavy ion collision. However, Boltzmann equations are only a classical approximation of the quantum thermalization process, which is described by so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the complete Kadanoff-Baym equations. Therefore, we present in this article a detailed comparison of Boltzmann and Kadanoff-Baym equations in the framework of a chirally invariant Yukawa-type quantum field theory including fermions and scalars. The obtained numerical results reveal significant differences between both types of equations. Apart from quantitative differences, on a qualitative level the late-time universality respected by Kadanoff-Baym equations is severely restricted in th...

  19. The Simulation of High Reynolds Number Cavity Flow Based on Fractional Volumetric Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    HAN Shan-ling; ZHU Ping; LIN Zhong-qin

    2005-01-01

    The fractional volumetric lattice Boltzmann method with much better stability was used to simulate two dimensional cavity flows. Because the effective viscosity was reduced by the fraction factor, it is very effective forsimulating high Reynolds number flows. Simulations were carried out on a uniform grids system. The stream lines and the velocity profiles obtained from the simulations agree well with the standard lattice Boltzmann method simulations. Comparisons of detailed flow patterns with other studies via location of vortex centers are also satisfactory.

  20. Note on Invariance of One-Dimensional Lattice-Boltzmann Equation

    Institute of Scientific and Technical Information of China (English)

    RAN Zheng

    2007-01-01

    Invariance of the one-dimensional lattice Boltzmann model is proposed together with its rigorous theoretical background.It is demonstrated that the symmetry inherent in Navier-Stokes equations is not really recovered in the one-dimensional lattice Boltzmann equation (LBE),especially for shock calculation.Symmetry breaking may be the inherent cause for the non-physical oscillations in the vicinity of the shock for LBE calculation.

  1. On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

    Directory of Open Access Journals (Sweden)

    Nikolai N. Bogoliubov (Jr.

    2007-01-01

    Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

  2. Lattice Boltzmann model for the perfect gas flows with near-vacuum region

    Institute of Scientific and Technical Information of China (English)

    GuangwuYAN; LiYUAN

    2000-01-01

    It is known that the standard lattice Boltzmann method has near-vacuum limit,i. e., when the density is near zero, this method is invalid. In this letter, we propose a simple lattice Boltzmann model for one-dimensional flows. It possesses the ability of simulating nearvacuum area by setting a limitation of the relaxation factor. Thus, the model overcomes the disadvantage of non-physical pressure and the density. The numerical examples show these results are satisfactory.

  3. A Lattice Boltzmann Model and Simulation of KdV-Burgers Equation

    Institute of Scientific and Technical Information of China (English)

    ZHANGChao-Ying; TANHui-Li; LIUMu-Ren; KONGLing-Jiang

    2004-01-01

    A lattice Boltzmann model of KdV-Burgers equation is derived by using the single-relaxation form of the lattice Boltzmann equation. With the present model, we simulate the traveling-wave solutions, the solitary-wave solutions, and the sock-wave solutions of KdV-Burgers equation, and calculate the decay factor and the wavelength of the sock-wave solution, which has exponential decay. The numerical results agree with the analytical solutions quite well.

  4. A New Lattice Boltzmann Model for KdV-Burgers Equation

    Institute of Scientific and Technical Information of China (English)

    MA Chang-Feng

    2005-01-01

    @@ A new lattice Boltzmann model with amending-function for KdV-Burgers equation, ut +uux - αuxx +βuxxx = 0,is presented by using the single-relaxation form of the lattice Boltzmann equation. Applying the proposed model,we simulate the solutions ofa kind of KdV-Burgers equations, and the numerical results agree with the analytical solutions quite well.

  5. Head and neck (192)Ir HDR-brachytherapy dosimetry using a grid-based Boltzmann solver.

    Science.gov (United States)

    Siebert, Frank-André; Wolf, Sabine; Kóvacs, George

    2013-12-01

    To compare dosimetry for head and neck cancer patients, calculated with TG-43 formalism and a commercially available grid-based Boltzmann solver. This study included 3D-dosimetry of 49 consecutive brachytherapy head and neck cancer patients, computed by a grid-based Boltzmann solver that takes into account tissue inhomogeneities as well as TG-43 formalism. 3D-treatment planning was carried out by using computed tomography. Dosimetric indices D90 and V100 for target volume were about 3% lower (median value) for the grid-based Boltzmann solver relative to TG-43-based computation (p Boltzmann solver to TG-43 (p Boltzmann solver and TG-43 formalism for high-dose-rate head and neck brachytherapy patients to the target volume were found. Distinctions in D90 of CTV were low (2.63 Gy for grid-based Boltzmann solver vs. 2.71 Gy TG-43 in mean). In our clinical practice, prescription doses remain unchanged for high-dose-rate head and neck brachytherapy for the time being.

  6. Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)

    Science.gov (United States)

    Badino, M.

    2011-11-01

    An intricate, long, and occasionally heated debate surrounds Boltzmann's H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt's 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first part, I discuss the development of Boltzmann's research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt's challenge and Boltzmann's response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject.

  7. Lattice Boltzmann modeling of three-phase incompressible flows

    Science.gov (United States)

    Liang, H.; Shi, B. C.; Chai, Z. H.

    2016-01-01

    In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.

  8. Evaluation of a lattice Boltzmann method in a complex nanoflow.

    Science.gov (United States)

    Suga, K; Takenaka, S; Ito, T; Kaneda, M; Kinjo, T; Hyodo, S

    2010-07-01

    In order to establish a cost-effective strategy to simulate complex flows in continuum to slip and transitional regimes, the present study assesses the performance of a lattice Boltzmann method (LBM) formerly discussed by the present authors' group [Niu, Phys. Rev. E 76, 036711 (2007)]. This LBM is based on a diffuse scattering wall boundary condition, a regularization procedure, and an effective relaxation time associated with the Knudsen number. The present assessment is on its regularization procedure and third-order truncated system based on the two-dimensional twenty-one discrete velocity (D2Q21) model for the Cartesian lattices. The test flow cases are force-driven Poiseuille flows, the Couette flows and a flow around a square cylinder situated in a nanochannel. For producing the reference data of the square cylinder flow, the molecular dynamics simulation using Lennard-Jones potential is also performed. Although the flow profiles and the slip velocities of the Poiseuille flows and the Couette flows are more accurately predicted by the third-order truncated system, the general velocity profiles around the square cylinder are also well predicted by the second-order truncated system based on the two-dimensional nine discrete velocity (D2Q9) model. It is also confirmed that without the regularization process, the entire flow field prediction suffers unphysical momentum oscillations around the square cylinder.

  9. Application of Lattice Boltzmann Method to Flows in Microgeometries

    Directory of Open Access Journals (Sweden)

    Anoop K. Dass

    2010-07-01

    Full Text Available In the present investigation, Lattice Boltzmann Method (LBM is used to simulate rarefied gaseous microflows in three microgeometries. These are micro-couette, micro lid-driven cavity and micro-poiseuille flows. The Knudsen number is used to measure the degree of rarefaction in the microflows. First, micro-couette flow is computed with the effects of varying Knudsen number in the slip and threshold of the transition regime and the results compare well with existing results. After having thus established the credibility of the code and the method including boundary conditions, LBM is then used to investigate the micro lid-driven cavity flow with various aspect ratios. Simulation of microflow not only requires an appropriate method, it also requires suitable boundary conditions to provide a well-posed problem and unique solution. In this work, LBM and three slip boundary conditions, namely, diffuse scattering boundary condition, specular reflection and a combination of bounce-back and specular reflection is used to predict the micro lid-driven cavity flow fields. Then the LBM simulation is extended to micro-poiseuille flow. The results are substantiated through comparison with existing results and it is felt that the present methodology is reasonable to be employed in analyzing the flow in micro-systems.

  10. Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann

    CERN Document Server

    Das, Santosh K; Greco, Vincenzo

    2013-01-01

    The propagation of heavy quarks through the quark-gluon plasma (QGP) has been often treated within the framework of Langevin equation (LV), i.e. assuming the heavy flavor momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass $m_D$. We address a thorough study of the approximations involved in Langevin dynamics by mean of a direct comparison with the solution of the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked ($m_D\\cong T $) or the mass to temperature ratio is quite large ($M_q/T \\gtrsim 8-10$) there are significant differences in the evolution of the $p-$spectra with time and consequently on the so-called nuclear modification factor $R_{AA}(p_T)$. However for charm quark we find that very similar $R_{AA}(p_T)$ between the LV and BM can be obtained, but the estimate of the underlying diffusion coefficient can differ by about $\\sim 15-50\\%$ depending on t...

  11. Lattice Boltzmann models for the grain growth in polycrystalline systems

    Directory of Open Access Journals (Sweden)

    Yonggang Zheng

    2016-08-01

    Full Text Available In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.

  12. Flow visualisation of downhill skiers using the lattice Boltzmann method

    Science.gov (United States)

    Asai, Takeshi; Hong, Sungchan; Ijuin, Koichi

    2017-03-01

    In downhill alpine skiing, skiers often exceed speeds of 120 km h-1, with air resistance substantially affecting the overall race times. To date, studies on air resistance in alpine skiing have used wind tunnels and actual skiers to examine the relationship between the gliding posture and magnitude of drag and for the design of skiing equipment. However, these studies have not revealed the flow velocity distribution and vortex structure around the skier. In the present study, computational fluid dynamics are employed with the lattice Boltzmann method to derive the relationship between total drag and the flow velocity around a downhill skier in the full-tuck position. Furthermore, the flow around the downhill skier is visualised, and its vortex structure is examined. The results show that the total drag force in the downhill skier model is 27.0 N at a flow velocity of 15 m s-1, increasing to 185.8 N at 40 m s-1. From analysis of the drag distribution and the flow profile, the head, upper arms, lower legs, and thighs (including buttocks) are identified as the major sources of drag on a downhill skier. Based on these results, the design of suits and equipment for reducing the drag from each location should be the focus of research and development in ski equipment. This paper describes a pilot study that introduces undergraduate students of physics or engineering into this research field. The results of this study are easy to understand for undergraduate students.

  13. Lattice Boltzmann Simulations of Evaporating Droplets with Nanoparticles

    Science.gov (United States)

    Zhao, Mingfei; Yong, Xin

    2016-11-01

    Elucidating the nanoparticle dynamics in drying droplets provides fundamental hydrodynamic insight into the evaporation-induced self-assembly, which is of great importance to materials printing and thin film processing. We develop a free-energy-based multiphase lattice Boltzmann model coupled with Lagrangian particle tracking to simulate evaporating particle-laden droplets on a solid substrate with specified wetting behavior. This work focuses on the interplay between the evaporation-driven advection and the self-organization of nanoparticles inside the droplet and at the droplet surface. For static droplets, the different parameters, fluid-particle interaction strength and particle number, governing the nanoparticle-droplet dynamics are systematically investigated, such as particle radial and circumferential distribution. We clarify the effect of nanoparticle presence on the droplet surface tension and wetting behavior. For evaporating droplets, we observe how droplet evaporation modulates the self-assembly of nanoparticles when the droplet has different static contact angles and hysteresis windows. We also confirm that the number of nanoparticles at the liquid-vapor interface influences the evaporation flux at the liquid-vapor interface.

  14. Multiple anisotropic collisions for advection-diffusion Lattice Boltzmann schemes

    Science.gov (United States)

    Ginzburg, Irina

    2013-01-01

    This paper develops a symmetrized framework for the analysis of the anisotropic advection-diffusion Lattice Boltzmann schemes. Two main approaches build the anisotropic diffusion coefficients either from the anisotropic anti-symmetric collision matrix or from the anisotropic symmetric equilibrium distribution. We combine and extend existing approaches for all commonly used velocity sets, prescribe most general equilibrium and build the diffusion and numerical-diffusion forms, then derive and compare solvability conditions, examine available anisotropy and stable velocity magnitudes in the presence of advection. Besides the deterioration of accuracy, the numerical diffusion dictates the stable velocity range. Three techniques are proposed for its elimination: (i) velocity-dependent relaxation entries; (ii) their combination with the coordinate-link equilibrium correction; and (iii) equilibrium correction for all links. Two first techniques are also available for the minimal (coordinate) velocity sets. Even then, the two-relaxation-times model with the isotropic rates often gains in effective stability and accuracy. The key point is that the symmetric collision mode does not modify the modeled diffusion tensor but it controls the effective accuracy and stability, via eigenvalue combinations of the opposite parity eigenmodes. We propose to reduce the eigenvalue spectrum by properly combining different anisotropic collision elements. The stability role of the symmetric, multiple-relaxation-times component, is further investigated with the exact von Neumann stability analysis developed in diffusion-dominant limit.

  15. High-order regularization in lattice-Boltzmann equations

    Science.gov (United States)

    Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.

    2017-04-01

    A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.

  16. A Lattice-Boltzmann Method for Partially Saturated Computational Cells

    Science.gov (United States)

    Noble, D. R.; Torczynski, J. R.

    The lattice-Boltzmann (LB) method is applied to complex, moving geometries in which computational cells are partially filled with fluid. The LB algorithm is modified to include a term that depends on the percentage of the cell saturated with fluid. The method is useful for modeling suspended obstacles that do not conform to the grid. Another application is to simulations of flow through reconstructed media that are not easily segmented into solid and liquid regions. A detailed comparison is made with FIDAP simulation results for the flow about a periodic line of cylinders in a channel at a non-zero Reynolds number. Two cases are examined. In the first simulation, the cylinders are given a constant velocity along the axis of the channel, and the steady solution is acquired. The transient behavior of the system is then studied by giving the cylinders an oscillatory velocity. For both steady and oscillatory flows, the method provides excellent agreement with FIDAP simulation results, even at locations close to the surface of a cylinder. In contrast to step-like solutions produced using the "bounce-back" condition, the proposed condition gives close agreement with the smooth FIDAP predictions. Computed drag forces with the proposed condition exhibit apparent quadratic convergence with grid refinement rather than the linear convergence exhibited by other LB boundary conditions.

  17. Treatment of moving boundaries in lattice-Boltzmann simulations.

    Science.gov (United States)

    Indireshkumar, K.; Pal, A.; Brasseur, J. G.

    2000-11-01

    We consider the treatment of moving boundaries with the lattice-Boltzmann (LB) technique, where the treatment of the boundary often does not precisely conserve mass and spurious fluctuations in density/pressure result from boundary motion through fixed grids. First, we applied the extrapolation method proposed by Chen et. al.(S. Y. Chen, D. Martinez, and R Mei, Phys. Fluids) 8, 2527 (1996) to incompressible flow induced by the movement of a piston in a 2D ``cylinder'' with mass flow out of or into the cylinder. In these simulations, the velocity of the boundary nodes is set equal to the (known) velocity of the boundary (piston) in the equilibrium distribution function (Method I). In a second set of simulations, the boundary node velocities are obtained by interpolating between interior nodes and the boundary, thus including the effect of boundary position more precisely (Method II). Comparison of LB predictions with simulations using FIDAP show pressure agreement to witnin 2 %. The total mass is conserved to within 0.1% with Method I and improves to within 0.02 % using method II. Spurious fluctuations in density/pressure due to boundary movement is about 0.9% with Method I, which improves significantly to about 0.3% with Method II. The application of these simple techniques to more complex geometries and wall (and fluid) motions in a stomach during gastric emptying will be presented.

  18. Exploring the Limits of the Iterative Boltzmann Inversion

    Science.gov (United States)

    Faller, Roland; Bayramoglu, Beste

    2014-03-01

    We explore the limits of the purely structure based coarse-graining technique, the iterative Boltzmann inversion (IBI), for confined systems using the example of polystyrene solutions. First some technical considerations and challenges encountered in the course of the optimization process are presented. The choice of the initial potentials and the cross-dependency of the interactions as well as the order of optimization are discussed in detail. Furthermore, the transferability between different degrees of confinement is examined. We investigate if a CG force field developed for a confined polymer solution by IBI is sensitive to changes in the degree of localization or arrangement of polymers near the surfaces although the concentration is kept constant. The differences in the structure and dynamics of the chains are addressed. Results are compared with those of an unconfined (bulk) system at the same concentration. The chain dimensions and orientations as a function of the distance from the surfaces are also reported. We find that the arrangement of monomers and solvent molecules near the surfaces is an important factor that needs to be paid attention to when considering the application of a CG force field developed by IBI to different degrees of confinement.

  19. Macroscopic model and truncation error of discrete Boltzmann method

    Science.gov (United States)

    Hwang, Yao-Hsin

    2016-10-01

    A derivation procedure to secure the macroscopically equivalent equation and its truncation error for discrete Boltzmann method is proffered in this paper. Essential presumptions of two time scales and a small parameter in the Chapman-Enskog expansion are disposed of in the present formulation. Equilibrium particle distribution function instead of its original non-equilibrium form is chosen as key variable in the derivation route. Taylor series expansion encompassing fundamental algebraic manipulations is adequate to realize the macroscopically differential counterpart. A self-contained and comprehensive practice for the linear one-dimensional convection-diffusion equation is illustrated in details. Numerical validations on the incurred truncation error in one- and two-dimensional cases with various distribution functions are conducted to verify present formulation. As shown in the computational results, excellent agreement between numerical result and theoretical prediction are found in the test problems. Straightforward extensions to more complicated systems including convection-diffusion-reaction, multi-relaxation times in collision operator as well as multi-dimensional Navier-Stokes equations are also exposed in the Appendix to point out its expediency in solving complicated flow problems.

  20. Lattice Boltzmann modeling of directional wetting: Comparing simulations to experiments

    Science.gov (United States)

    Jansen, H. Patrick; Sotthewes, Kai; van Swigchem, Jeroen; Zandvliet, Harold J. W.; Kooij, E. Stefan

    2013-07-01

    Lattice Boltzmann Modeling (LBM) simulations were performed on the dynamic behavior of liquid droplets on chemically striped patterned surfaces, ultimately with the aim to develop a predictive tool enabling reliable design of future experiments. The simulations accurately mimic experimental results, which have shown that water droplets on such surfaces adopt an elongated shape due to anisotropic preferential spreading. Details of the contact line motion such as advancing of the contact line in the direction perpendicular to the stripes exhibit pronounced similarities in experiments and simulations. The opposite of spreading, i.e., evaporation of water droplets, leads to a characteristic receding motion first in the direction parallel to the stripes, while the contact line remains pinned perpendicular to the stripes. Only when the aspect ratio is close to unity, the contact line also starts to recede in the perpendicular direction. Very similar behavior was observed in the LBM simulations. Finally, droplet movement can be induced by a gradient in surface wettability. LBM simulations show good semiquantitative agreement with experimental results of decanol droplets on a well-defined striped gradient, which move from high- to low-contact angle surfaces. Similarities and differences for all systems are described and discussed in terms of the predictive capabilities of LBM simulations to model direction wetting.

  1. Lattice Boltzmann models for the grain growth in polycrystalline systems

    Science.gov (United States)

    Zheng, Yonggang; Chen, Cen; Ye, Hongfei; Zhang, Hongwu

    2016-08-01

    In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.

  2. Lattice-Boltzmann Simulations of Microswimmer-Tracer Interactions

    CERN Document Server

    de Graaf, Joost

    2016-01-01

    Hydrodynamic interactions in systems comprised of self-propelled particles, such as swimming microorganisms, and passive tracers have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force/counter-force based lattice-Boltzmann (LB) algorithm [J. de Graaf~\\textit{et al.}, J. Chem. Phys.~\\textbf{144}, 134106 (2016)], in order to validate its applicability to study large-scale microswimmer suspensions. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The LB algorithm has an inherent near-field renormalization of the flow field, due to the force interpolation between the swimmers and the lattice. This strongly pe...

  3. A dynamically adaptive lattice Boltzmann method for thermal convection problems

    Directory of Open Access Journals (Sweden)

    Feldhusen Kai

    2016-12-01

    Full Text Available Utilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103 up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103 up to 105 are compared with benchmark results.

  4. Boltzmann electron PIC simulation of the E-sail effect

    CERN Document Server

    Janhunen, Pekka

    2015-01-01

    The solar wind electric sail (E-sail) is a planned in-space propulsion device that uses the natural solar wind momentum flux for spacecraft propulsion with the help of long, charged, centrifugally stretched tethers. The problem of accurately predicting the E-sail thrust is still somewhat open, however, due to a possible electron population trapped by the tether. Here we develop a new type of particle-in-cell (PIC) simulation for predicting E-sail thrust. In the new simulation, electrons are modelled as a fluid, hence resembling hydrid simulation, but in contrast to normal hybrid simulation, the Poisson equation is used as in normal PIC to calculate the self-consistent electrostatic field. For electron-repulsive parts of the potential, the Boltzmann relation is used. For electron-attractive parts of the potential we employ a power law which contains a parameter that can be used to control the number of trapped electrons. We perform a set of runs varying the parameter and select the one with the smallest number...

  5. Acoustic equations of state for simple lattice Boltzmann velocity sets.

    Science.gov (United States)

    Viggen, Erlend Magnus

    2014-07-01

    The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ξ(iα)∈(-1,0,1) for all i, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics.

  6. Lattice Boltzmann Simulation Optimization on Leading Multicore Platforms

    Energy Technology Data Exchange (ETDEWEB)

    Williams, Samuel; Carter, Jonathan; Oliker, Leonid; Shalf, John; Yelick, Katherine

    2008-02-01

    We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Clovertown, AMD Opteron X2, Sun Niagara2, STI Cell, as well as the single core Intel Itanium2. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned LBMHD application achieves up to a 14x improvement compared with the original code. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.

  7. Energy-Dependent Octagonal Lattice Boltzmann Modeling for Compressible Flows

    Science.gov (United States)

    Pavlo, Pavol; Vahala, Linda; Vahala, George

    2000-10-01

    There has been much interest in thermal lattice Boltzmann modeling (TLBM) for compressible flows because of their inherent parallelizeability. Instead of applying CFD techniques to the nonlinear conservation equations, one instead solves a linear BGK kinetic equation. To reduce storage requirements, the velocity space is discretized and lattice geometries are so chosen to minimize the number of degrees of freedom that must be retained in the Chapman-Enskog recovery of the original macroscopic equations. The simplest (and most efficient) TLBM runs at a CFL=1, so that no numerical diffusion or dissipation is introduced. The algorithm involves Lagrangian streaming (shift operator) and purely local operations. Because of the underlying discrete lattice symmetry, the relaxation distributions cannot be Maxwellian and hence the inherent numerical instability problem in TLBM. We are investigating the use of energy-dependent lattices so as to allow simulation of problems of interest in divertor physics, The appeal of TLBM is that it can provide a unified representation for both strongly collisional (‘fluid’) and weakly collisional (‘Monte Carlo’) regimes. Moreover, our TLBM code is more efficiently solved on mulit-PE platforms than the corresponding CFD codes and is readily extended to 3D. MHD can also be handled by TLBM.

  8. A new scheme based on the Hermite expansion to construct lattice Boltzmann models associated with arbitrary specific heat ratio

    CERN Document Server

    Hu, Kainan; Geng, Shaojuan

    2016-01-01

    A new lattice Boltzmann scheme associated with flexible specific heat ratio is proposed. The new free degree is introduced via the internal energy associated with the internal structure. The evolution equation of the distribution function is reduced to two evolution equations. One is connected to the density and velocity, the other is of the energy. A two-dimensional lattice Boltzmann model and a three-dimensional lattice Boltzmann model are derived via the Hermite expansion. The two lattice Boltzmann models are applied to simulating the shock tube of one dimension. Good agreement between the numerical results and the analytical solutions are obtained.

  9. An Extended Decomposed Theory of Planned Behaviour to Predict the Usage Intention of the Electric Car: A Multi-Group Comparison

    Directory of Open Access Journals (Sweden)

    Ingrid Moons

    2015-05-01

    Full Text Available An Extended Decomposed Theory of Planned Behaviour (DTPB is developed that integrates emotions towards car driving and electric cars as well as car driving habits of the DTPB, and is empirically validated in a Belgian sample (n = 1023. Multi-group comparisons explore how the determinants of usage intention are different between groups of consumers differing in environmentally-friendly behaviour, environmental concern, innovativeness and personal values. Besides attitudes, media, perceived complexity, compatibility and relative advantage, emotions towards the electric car and reflective emotions towards car driving have a strong effect on usage intention. Car driving habits and perceived behavioural control (facilitators and constraints do not substantially affect usage intention. Only people differing in personal values show a different motivational structure for a number of important drivers of usage intention.

  10. Using Multigroup-Multiphase Latent State-Trait Models to Study Treatment-Induced Changes in Intra-Individual State Variability: An Application to Smokers' Affect.

    Science.gov (United States)

    Geiser, Christian; Griffin, Daniel; Shiffman, Saul

    2016-01-01

    Sometimes, researchers are interested in whether an intervention, experimental manipulation, or other treatment causes changes in intra-individual state variability. The authors show how multigroup-multiphase latent state-trait (MG-MP-LST) models can be used to examine treatment effects with regard to both mean differences and differences in state variability. The approach is illustrated based on a randomized controlled trial in which N = 338 smokers were randomly assigned to nicotine replacement therapy (NRT) vs. placebo prior to quitting smoking. We found that post quitting, smokers in both the NRT and placebo group had significantly reduced intra-individual affect state variability with respect to the affect items calm and content relative to the pre-quitting phase. This reduction in state variability did not differ between the NRT and placebo groups, indicating that quitting smoking may lead to a stabilization of individuals' affect states regardless of whether or not individuals receive NRT.

  11. Using Multigroup-Multiphase Latent State-Trait Models to Study Treatment-Induced Changes in Intra-Individual State Variability: An Application to Smokers’ Affect

    Directory of Open Access Journals (Sweden)

    Christian Geiser

    2016-07-01

    Full Text Available Sometimes, researchers are interested in whether an intervention, experimental manipulation, or other treatment causes changes in intra-individual state variability. The authors show how multigroup-multiphase latent state-trait (MG-MP-LST models can be used to examine treatment effects with regard to both mean differences and differences in state variability. The approach is illustrated based on a randomized controlled trial in which N = 338 smokers were randomly assigned to nicotine replacement therapy (NRT versus placebo prior to quitting smoking. We found that post quitting, smokers in both the NRT and placebo group had significantly reduced intra-individual affect variability with respect to the affect items calm and content relative to the pre-quitting phase. This reduction in state variability did not differ between the NRT and placebo groups, indicating that quitting smoking may lead to a stabilization of individuals’ affect states regardless of whether or not individuals receive NRT.

  12. On an evaluation of the continuous flux and dominant Eigenvalue problem for the steady state multi-group multi-layer neutron diffusion equation

    Energy Technology Data Exchange (ETDEWEB)

    Ceolin, C.; Schramm, M.; Vilhena, M.T.; Bodmann, B.E.J., E-mail: celina.ceolin@gmail.com, E-mail: marceloschramm@hotmail.com, E-mail: vilhena@pq.cnpq.br, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica

    2013-07-01

    In this work the authors solved the steady state neutron diffusion equation for a multi-layer slab assuming the multi-group energy model. The method to solve the equation system is based on a expansion in Taylor Series, which was proven to be useful in [1] [2] [3]. The results obtained can be used as initial condition for neutron space kinetics problems. The neutron scalar flux was expanded in a power series, and the coefficients were found by using the ordinary differential equation and the boundary and interface conditions. The effective multiplication factor k was evaluated using the power method [4]. We divided the domain into several slabs to guarantee the convergence with a low truncation order. We present the formalism together with some numerical simulations. (author)

  13. On an analytical evaluation of the flux and dominant eigenvalue problem for the steady state multi-group multi-layer neutron diffusion equation

    Energy Technology Data Exchange (ETDEWEB)

    Ceolin, Celina; Schramm, Marcelo; Bodmann, Bardo Ernst Josef; Vilhena, Marco Tullio Mena Barreto de [Universidade Federal do Rio Grande do Sul, Porto Alegre (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Bogado Leite, Sergio de Queiroz [Comissao Nacional de Energia Nuclear, Rio de Janeiro (Brazil)

    2014-11-15

    In this work the authors solved the steady state neutron diffusion equation for a multi-layer slab assuming the multi-group energy model. The method to solve the equation system is based on an expansion in Taylor Series resulting in an analytical expression. The results obtained can be used as initial condition for neutron space kinetics problems. The neutron scalar flux was expanded in a power series, and the coefficients were found by using the ordinary differential equation and the boundary and interface conditions. The effective multiplication factor k was evaluated using the power method. We divided the domain into several slabs to guarantee the convergence with a low truncation order. We present the formalism together with some numerical simulations.

  14. Comparison of a 3-D multi-group SN particle transport code with Monte Carlo for intracavitary brachytherapy of the cervix uteri.

    Science.gov (United States)

    Gifford, Kent A; Wareing, Todd A; Failla, Gregory; Horton, John L; Eifel, Patricia J; Mourtada, Firas

    2009-12-03

    A patient dose distribution was calculated by a 3D multi-group S N particle transport code for intracavitary brachytherapy of the cervix uteri and compared to previously published Monte Carlo results. A Cs-137 LDR intracavitary brachytherapy CT data set was chosen from our clinical database. MCNPX version 2.5.c, was used to calculate the dose distribution. A 3D multi-group S N particle transport code, Attila version 6.1.1 was used to simulate the same patient. Each patient applicator was built in SolidWorks, a mechanical design package, and then assembled with a coordinate transformation and rotation for the patient. The SolidWorks exported applicator geometry was imported into Attila for calculation. Dose matrices were overlaid on the patient CT data set. Dose volume histograms and point doses were compared. The MCNPX calculation required 14.8 hours, whereas the Attila calculation required 22.2 minutes on a 1.8 GHz AMD Opteron CPU. Agreement between Attila and MCNPX dose calculations at the ICRU 38 points was within +/- 3%. Calculated doses to the 2 cc and 5 cc volumes of highest dose differed by not more than +/- 1.1% between the two codes. Dose and DVH overlays agreed well qualitatively. Attila can calculate dose accurately and efficiently for this Cs-137 CT-based patient geometry. Our data showed that a three-group cross-section set is adequate for Cs-137 computations. Future work is aimed at implementing an optimized version of Attila for radiotherapy calculations.

  15. Lattice Boltzmann simulations of multiple-droplet interaction dynamics

    Science.gov (United States)

    Zhou, Wenchao; Loney, Drew; Fedorov, Andrei G.; Degertekin, F. Levent; Rosen, David W.

    2014-03-01

    A lattice Boltzmann (LB) formulation, which is consistent with the phase-field model for two-phase incompressible fluid, is proposed to model the interface dynamics of droplet impingement. The interparticle force is derived by comparing the macroscopic transport equations recovered from LB equations with the governing equations of the continuous phase-field model. The inconsistency between the existing LB implementations and the phase-field model in calculating the relaxation time at the phase interface is identified and an approximation is proposed to ensure the consistency with the phase-field model. It is also shown that the commonly used equilibrium velocity boundary for the binary fluid LB scheme does not conserve momentum at the wall boundary and a modified scheme is developed to ensure the momentum conservation at the boundary. In addition, a geometric formulation of the wetting boundary condition is proposed to replace the popular surface energy formulation and results show that the geometric approach enforces the prescribed contact angle better than the surface energy formulation in both static and dynamic wetting. The proposed LB formulation is applied to simulating droplet impingement dynamics in three dimensions and results are compared to those obtained with the continuous phase-field model, the LB simulations reported in the literature, and experimental data from the literature. The results show that the proposed LB simulation approach yields not only a significant speed improvement over the phase-field model in simulating droplet impingement dynamics on a submillimeter length scale, but also better accuracy than both the phase-field model and the previously reported LB techniques when compared to experimental data. Upon validation, the proposed LB modeling methodology is applied to the study of multiple-droplet impingement and interactions in three dimensions, which demonstrates its powerful capability of simulating extremely complex interface

  16. Expected energy-based restricted Boltzmann machine for classification.

    Science.gov (United States)

    Elfwing, S; Uchibe, E; Doya, K

    2015-04-01

    In classification tasks, restricted Boltzmann machines (RBMs) have predominantly been used in the first stage, either as feature extractors or to provide initialization of neural networks. In this study, we propose a discriminative learning approach to provide a self-contained RBM method for classification, inspired by free-energy based function approximation (FE-RBM), originally proposed for reinforcement learning. For classification, the FE-RBM method computes the output for an input vector and a class vector by the negative free energy of an RBM. Learning is achieved by stochastic gradient-descent using a mean-squared error training objective. In an earlier study, we demonstrated that the performance and the robustness of FE-RBM function approximation can be improved by scaling the free energy by a constant that is related to the size of network. In this study, we propose that the learning performance of RBM function approximation can be further improved by computing the output by the negative expected energy (EE-RBM), instead of the negative free energy. To create a deep learning architecture, we stack several RBMs on top of each other. We also connect the class nodes to all hidden layers to try to improve the performance even further. We validate the classification performance of EE-RBM using the MNIST data set and the NORB data set, achieving competitive performance compared with other classifiers such as standard neural networks, deep belief networks, classification RBMs, and support vector machines. The purpose of using the NORB data set is to demonstrate that EE-RBM with binary input nodes can achieve high performance in the continuous input domain. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

  17. Podolsky electromagnetism and a modification in Stefan-Boltzmann law

    Energy Technology Data Exchange (ETDEWEB)

    Bonin, Carlos Alberto; Bufalo, Rodrigo Santos; Escobar, Bruto Max Pimentel; Zambrano, German Enrique Ramos [Instituto de Fisica Teorica (IFT/UNESP), Sao Paulo, SP (Brazil)

    2009-07-01

    Full text. As it is well-known, gauge fields that emerge from the gauge principle are massless vector fields. Considering the photon as a Proca particle, experience sets an upper limit on its mass. This limit is m{sub Proca} < 6X10{sup -17}eV (PDG 2006). However, a mass term, regardless how small, breaks the gauge symmetry. Nevertheless, there exists a theory in which is possible to introduce a mass term preserving all symmetries of Maxwell electromagnetism, including the gauge one: such theory is known as Podolsky Electromagnetism. Podolsky theory is a second- order-derivative theory and has some remarkable properties, despite those already mentioned: the theory has two sectors, a massive one and massless one, it depends on a free parameter (which happens to be the mass of the massive sector) that, like all other elementary particles's masses of the Standard Model, must be fixed through experiences, and the fact that the electrostatic potential is finite everywhere, including over a punctual charge. Just like Maxwell electromagnetism, Podolsky's is a constrained theory and, since it is of second order in the derivatives, it consists in a much richer theoretical structure. Therefore, from both, theoretical and experimental points of view, Podolsky electromagnetism is a very attractive theory. In this work we study a gas of Podolsky photons at finite temperature through path integration. We show that the massless sector leads to the famous Planck's law for black-body radiation and, therefore, to the Stefan-Boltzmann law. We also show that the massive sector of the Podolsky theory induces a modification in both these laws. It is possible to set limits on the Podolsky parameter through comparison of our results with data from cosmic microwave background radiation. (author)

  18. Multiple-relaxation-time lattice Boltzmann kinetic model for combustion.

    Science.gov (United States)

    Xu, Aiguo; Lin, Chuandong; Zhang, Guangcai; Li, Yingjun

    2015-04-01

    To probe both the hydrodynamic nonequilibrium (HNE) and thermodynamic nonequilibrium (TNE) in the combustion process, a two-dimensional multiple-relaxation-time (MRT) version of lattice Boltzmann kinetic model (LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Aside from describing the evolutions of the conserved quantities, the density, momentum, and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some nonconserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model, both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various nonequilibrium behaviors, including the complex interplays between various HNEs, between various TNEs, and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses.

  19. Boltzmann analyses of swarm experiments over the years

    Science.gov (United States)

    Pitchford, Leanne

    2013-09-01

    Art Phelps was one of the ``grand old men'' in field of gaseous electronics. He was a graduate student when the GEC got started and he attended almost all of the meetings over the years. During his remarkably long career, he produced a number of the classic papers in our field as a glance at Web of Science will show. Art was my mentor and friend, and I had the privilege of working with him for many years on various topics related mainly to electron scattering and transport in weakly ionized gases. In this talk, I will discuss the originality of some of his early work on these subjects in the context of their times, focusing in particular on his publications from the mid-1960's with his colleagues from Westinghouse Research Laboratories. These report the first numerical solutions of the Boltzmann equation for electrons, to my knowledge, and they inspired much subsequent work related to the extraction of quantitative information about low-energy electron scatting with simple gases from measurements of macroscopic parameters (mobility, diffusion,..). I will outline some of the work he and I did together in this topical area using more sophisticated numerical techniques. This and other work in the field eventually led to the establishment of the ongoing GEC Plasma Data Exchange Project which now involves a number of people (the LXCat team), as discussed in Tuesday's workshop. The LXCat team had completed work on noble gases and had just started working on evaluations of cross sections for simple molecules when Art died. We are fortunate to have had his involvement on these projects. Art had ideas for future work in these areas, and some are included in a long e-mail message from Art a couple of years ago that I will share because it includes some suggestions [to the community] for future work.

  20. Peristaltic particle transport using the Lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Connington, Kevin William [Los Alamos National Laboratory; Kang, Qinjun [Los Alamos National Laboratory; Viswanathan, Hari S [Los Alamos National Laboratory; Abdel-fattah, Amr [Los Alamos National Laboratory; Chen, Shiyi [JOHNS HOPKINS UNIV.

    2009-01-01

    Peristaltic transport refers to a class of internal fluid flows where the periodic deformation of flexible containing walls elicits a non-negligible fluid motion. It is a mechanism used to transport fluid and immersed solid particles in a tube or channel when it is ineffective or impossible to impose a favorable pressure gradient or desirous to avoid contact between the transported mixture and mechanical moving parts. Peristaltic transport occurs in many physiological situations and has myriad industrial applications. We focus our study on the peristaltic transport of a macroscopic particle in a two-dimensional channel using the lattice Boltzmann method. We systematically investigate the effect of variation of the relevant dimensionless parameters of the system on the particle transport. We find, among other results, a case where an increase in Reynolds number can actually lead to a slight increase in particle transport, and a case where, as the wall deformation increases, the motion of the particle becomes non-negative only. We examine the particle behavior when the system exhibits the peculiar phenomenon of fluid trapping. Under these circumstances, the particle may itself become trapped where it is subsequently transported at the wave speed, which is the maximum possible transport in the absence of a favorable pressure gradient. Finally, we analyze how the particle presence affects stress, pressure, and dissipation in the fluid in hopes of determining preferred working conditions for peristaltic transport of shear-sensitive particles. We find that the levels of shear stress are most hazardous near the throat of the channel. We advise that shear-sensitive particles should be transported under conditions where trapping occurs as the particle is typically situated in a region of innocuous shear stress levels.

  1. Poisson-Helmholtz-Boltzmann model of the electric double layer: analysis of monovalent ionic mixtures.

    Science.gov (United States)

    Bohinc, Klemen; Shrestha, Ahis; Brumen, Milan; May, Sylvio

    2012-03-01

    In the classical mean-field description of the electric double layer, known as the Poisson-Boltzmann model, ions interact exclusively through their Coulomb potential. Ion specificity can arise through solvent-mediated, nonelectrostatic interactions between ions. We employ the Yukawa pair potential to model the presence of nonelectrostatic interactions. The combination of Yukawa and Coulomb potential on the mean-field level leads to the Poisson-Helmholtz-Boltzmann model, which employs two auxiliary potentials: one electrostatic and the other nonelectrostatic. In the present work we apply the Poisson-Helmholtz-Boltzmann model to ionic mixtures, consisting of monovalent cations and anions that exhibit different Yukawa interaction strengths. As a specific example we consider a single charged surface in contact with a symmetric monovalent electrolyte. From the minimization of the mean-field free energy we derive the Poisson-Boltzmann and Helmholtz-Boltzmann equations. These nonlinear equations can be solved analytically in the weak perturbation limit. This together with numerical solutions in the nonlinear regime suggests an intricate interplay between electrostatic and nonelectrostatic interactions. The structure and free energy of the electric double layer depends sensitively on the Yukawa interaction strengths between the different ion types and on the nonelectrostatic interactions of the mobile ions with the surface.

  2. A lattice based solution of the collisional Boltzmann equation with applications to microchannel flows

    Science.gov (United States)

    Green, B. I.; Vedula, Prakash

    2013-07-01

    An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework.

  3. Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lema\\^itre-Robertson-Walker spacetime

    CERN Document Server

    Bazow, D; Heinz, U; Martinez, M; Noronha, J

    2016-01-01

    The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lema\\^itre-Robertson-Walker (FLRW) universe is studied. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of non-hydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the non-hydrodynamic modes decouple completely from the hydrodynamic degrees of freedom. This results in the system flowing as an ideal fluid while at the same time producing entropy. The solutions to the nonlinear Boltzmann equation exhibit transient tails of the distribution function with nontrivial momentum dependence. The evolution of this tail is not correctly captured by the relaxation time approximation nor by the linearized Boltzmann equation...

  4. Lattice Boltzmann method for three-dimensional moving particles in a Newtonian fluid

    Institute of Scientific and Technical Information of China (English)

    Fang Hai-Ping; Chen Shi-Yi

    2004-01-01

    @@ A lattice Boltzmann method is developed to simulate three-dimensional solid particle motions in fluids. In the present model, a uniform grid is used and the exact spatial location of the physical boundary of the suspended particles is determined using an interpolation scheme. The numerical accuracy and efficiency of the proposed lattice Boltzmann method is demonstrated by simulating the sedimentation of a single sphere in a square cylinder. Highly accurate simulation results can be achieved with few meshes, compared with the previous lattice Boltzmann methods. The present method is expected to find applications on the flow systems with moving boundaries, such as the blood flow in distensible vessels, the particle-flow interaction and the solidification of alloys.

  5. The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics.

    Science.gov (United States)

    Tirnakli, Ugur; Borges, Ernesto P

    2016-03-23

    As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide class of such systems, it has been shown in recent years that the correct approach is to use Tsallis statistics instead. Here we show how the dynamics of the paradigmatic conservative (area-preserving) stan-dard map exhibits, in an exceptionally clear manner, the crossing from one statistics to the other. Our results unambiguously illustrate the domains of validity of both Boltzmann-Gibbs and Tsallis statistical distributions. Since various important physical systems from particle confinement in magnetic traps to autoionization of molecular Rydberg states, through particle dynamics in accelerators and comet dynamics, can be reduced to the standard map, our results are expected to enlighten and enable an improved interpretation of diverse experimental and observational results.

  6. Comment on ‘A low-uncertainty measurement of the Boltzmann constant’

    Science.gov (United States)

    Macnaughton, Donald B.

    2016-02-01

    The International Committee for Weights and Measures has projected a major revision of the International System of Units in which all the base units will be defined by fixing the values of certain fundamental constants of nature. To assist, de Podesta et al recently experimentally obtained a precise new estimate of the Boltzmann constant. This estimate is proposed as a basis for the redefinition of the unit of temperature, the kelvin. The present paper reports a reanalysis of de Podesta et al’s data that reveals systematic non-random patterns in the residuals of the key fitted model equation. These patterns violate the assumptions underlying the analysis and thus they raise questions about the validity of de Podesta et al’s estimate of the Boltzmann constant. An approach is discussed to address these issues, which should lead to an accurate estimate of the Boltzmann constant with a lower uncertainty.

  7. Flow Simulation Around Cambered Airfoil by Using Conformal Mapping and Intermediate Domain in Lattice Boltzmann Method

    Science.gov (United States)

    Poozesh, Amin; Mirzaei, Masoud

    2017-01-01

    In this paper the developed interpolation lattice Boltzmann method is used for simulation of unsteady fluid flow. It combines the desirable features of the lattice Boltzmann and the Joukowski transformation methods. This approach has capability to simulate flow around curved boundary geometries such as airfoils in a body fitted grid system. Simulation of unsteady flow around a cambered airfoil in a non-uniform grid for the first time is considered to show the capability of this method for modeling of fluid flow around complex geometries and complicated long-term periodic flow phenomena. The developed solver is also coupled with a fast adaptive grid generator. In addition, the new approach retains all the advantages of the standard lattice Boltzmann method. The Strouhal number, the pressure, the drag and the lift coefficients obtained from the simulations agree well with classical computational fluid dynamics simulations. Numerical studies for various test cases illustrate the strength of this new approach.

  8. Combining generative and discriminative representation learning for lung CT analysis with convolutional restricted Boltzmann machines

    DEFF Research Database (Denmark)

    van Tulder, Gijs; de Bruijne, Marleen

    2016-01-01

    unlabeled data, but does not necessarily produce features that are optimal for classification. In this paper we propose the convolutional classification restricted Boltzmann machine, which combines a generative and a discriminative learning objective. This allows it to learn filters that are good both......The choice of features greatly influences the performance of a tissue classification system. Despite this, many systems are built with standard, predefined filter banks that are not optimized for that particular application. Representation learning methods such as restricted Boltzmann machines may...... outperform these standard filter banks because they learn a feature description directly from the training data. Like many other representation learning methods, restricted Boltzmann machines are unsupervised and are trained with a generative learning objective; this allows them to learn representations from...

  9. Solution of time-dependent Boltzmann equation for electrons in non-thermal plasma

    Energy Technology Data Exchange (ETDEWEB)

    Trunec, D; Bonaventura, Z; Necas, D [Department of Physical Electronics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37 Brno (Czech Republic)

    2006-06-21

    The time development of the electron distribution function and electron macroscopic parameters was studied by solving the time-dependent Boltzmann equation for low temperature plasma. A new technique for solving the time-dependent Boltzmann equation was developed. This technique is based on a multi-term approximation of the electron distribution function expansion in Legendre polynomials. The results for electron relaxation in Reid's ramp model and argon plasma are presented. The effect of negative mobility was studied and is discussed for argon plasma. Finally, the time-dependent Boltzmann equation was solved for pulsed microwave discharge in nitrogen. The accuracy of all results was confirmed by the Monte Carlo simulation.

  10. Simulation of Magnetorheological Fluids Based on Lattice Boltzmann Method with Double Meshes

    Directory of Open Access Journals (Sweden)

    Xinhua Liu

    2012-01-01

    Full Text Available In order to study the rheological characteristics of magnetorheological fluids, a novel approach based on the two-component Lattice Boltzmann method with double meshes was proposed, and the micro-scale structures of magnetorheological fluids in different strength magnetic fields were simulated. The framework composed of three steps for the simulation of magnetorheological fluids was addressed, and the double meshes method was elaborated. Moreover, the various internal and external forces acting on the magnetic particles were analyzed and calculated. The two-component Lattice Boltzmann model was set up, and the flowchart for the simulation of magnetorheological fluids based on the two-component Lattice Boltzmann method with double meshes was designed. Finally, a physics experiment was carried out, and the simulation examples were provided. The comparison results indicated that the proposed approach was feasible, efficient, and outperforming others.

  11. PB-AM: An open-source, fully analytical linear poisson-boltzmann solver

    Energy Technology Data Exchange (ETDEWEB)

    Felberg, Lisa E. [Department of Chemical and Biomolecular Engineering, University of California Berkeley, Berkeley California 94720; Brookes, David H. [Department of Chemistry, University of California Berkeley, Berkeley California 94720; Yap, Eng-Hui [Department of Systems and Computational Biology, Albert Einstein College of Medicine, Bronx New York 10461; Jurrus, Elizabeth [Division of Computational and Statistical Analytics, Pacific Northwest National Laboratory, Richland Washington 99352; Scientific Computing and Imaging Institute, University of Utah, Salt Lake City Utah 84112; Baker, Nathan A. [Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland Washington 99352; Division of Applied Mathematics, Brown University, Providence Rhode Island 02912; Head-Gordon, Teresa [Department of Chemical and Biomolecular Engineering, University of California Berkeley, Berkeley California 94720; Department of Chemistry, University of California Berkeley, Berkeley California 94720; Department of Bioengineering, University of California Berkeley, Berkeley California 94720; Chemical Sciences Division, Lawrence Berkeley National Labs, Berkeley California 94720

    2016-11-02

    We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized Poisson Boltzmann equation. The PB-AM software package includes the generation of outputs files appropriate for visualization using VMD, a Brownian dynamics scheme that uses periodic boundary conditions to simulate dynamics, the ability to specify docking criteria, and offers two different kinetics schemes to evaluate biomolecular association rate constants. Given that PB-AM defines mutual polarization completely and accurately, it can be refactored as a many-body expansion to explore 2- and 3-body polarization. Additionally, the software has been integrated into the Adaptive Poisson-Boltzmann Solver (APBS) software package to make it more accessible to a larger group of scientists, educators and students that are more familiar with the APBS framework.

  12. Entropic Lattice Boltzmann Method for Moving and Deforming Geometries in Three Dimensions

    CERN Document Server

    Dorschner, B; Karlin, I V

    2016-01-01

    Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work Dorschner et al. [11] as well as for three dimensional one-way coupled simulations of engine-type geometries in Dorschner et al. [12] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases including two-way coupling between fluid and structure, turbulence and deformable meshes. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil at a Reynolds number of Re = 40000 an...

  13. Measuring the usefulness of hidden units in Boltzmann machines with mutual information.

    Science.gov (United States)

    Berglund, Mathias; Raiko, Tapani; Cho, Kyunghyun

    2015-04-01

    Restricted Boltzmann machines (RBMs) and deep Boltzmann machines (DBMs) are important models in deep learning, but it is often difficult to measure their performance in general, or measure the importance of individual hidden units in specific. We propose to use mutual information to measure the usefulness of individual hidden units in Boltzmann machines. The measure is fast to compute, and serves as an upper bound for the information the neuron can pass on, enabling detection of a particular kind of poor training results. We confirm experimentally that the proposed measure indicates how much the performance of the model drops when some of the units of an RBM are pruned away. We demonstrate the usefulness of the measure for early detection of poor training in DBMs. Copyright © 2014 Elsevier Ltd. All rights reserved.

  14. Development of a coarse-grained water forcefield via multistate iterative Boltzmann inversion

    CERN Document Server

    Moore, Timothy C; McCabe, Clare

    2015-01-01

    A coarse-grained water model is developed using multistate iterative Boltzmann inversion. Following previous work, the k-means algorithm is used to dynamically map multiple water molecules to a single coarse-grained bead, allowing the use of structure-based coarse-graining methods. The model is derived to match the bulk and interfacial properties of liquid water and improves upon previous work that used single state iterative Boltzmann inversion. The model accurately reproduces the density and structural correlations of water at 305 K and 1.0 atm, stability of a liquid droplet at 305 K, and shows little tendency to crystallize at physiological conditions. This work also illustrates several advantages of using multistate iterative Boltzmann inversion for deriving generally applicable coarse-grained forcefields.

  15. Simple Navier’s slip boundary condition for the non-Newtonian Lattice Boltzmann fluid dynamics solver

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skoček, Jan

    2013-01-01

    The ability of the Lattice Boltzmann method, as the fluid dynamics solver, to properly simulate macroscopic Navier’s slip boundary condition is investigated. An approximate equation relating the Lattice Boltzmann variable slip boundary condition with the macroscopic Navier’s slip boundary condition...

  16. An integrated Boltzmann+hydrodynamics approach to heavy ion collisions

    Energy Technology Data Exchange (ETDEWEB)

    Petersen, Hannah

    2009-04-22

    In this thesis the first fully integrated Boltzmann+hydrodynamics approach to relativistic heavy ion reactions has been developed. After a short introduction that motivates the study of heavy ion reactions as the tool to get insights about the QCD phase diagram, the most important theoretical approaches to describe the system are reviewed. The hadron-string transport approach that this work is based on is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. Predictions for the charged particle multiplicities at LHC energies are made. The next step is the development of a new framework to calculate the baryon number density in a transport approach. Time evolutions of the net baryon number and the quark density have been calculated at AGS, SPS and RHIC energies. Studies of phase diagram trajectories using hydrodynamics are performed. The hybrid approach that has been developed as the main part of this thesis is based on the UrQMD transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The full (3+1) dimensional ideal relativistic one fluid dynamics evolution is solved using the SHASTA algorithm. Three different equations of state have been used, namely a hadron gas equation of state without a QGP phase transition, a chiral EoS and a bag model EoS including a strong first order phase transition. For the freeze-out transition from hydrodynamics to the cascade calculation two different set-ups are employed. The parameter dependences of the model are investigated and the time evolution of different quantities is explored. The hybrid model calculation is able to reproduce the experimentally measured integrated as well as transverse momentum dependent v{sub 2} values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from E{sub lab}=2-160 A GeV. The HBT correlation of the negatively charged pion source

  17. Multilevel Methods for the Poisson-Boltzmann Equation

    Science.gov (United States)

    Holst, Michael Jay

    We consider the numerical solution of the Poisson -Boltzmann equation (PBE), a three-dimensional second order nonlinear elliptic partial differential equation arising in biophysics. This problem has several interesting features impacting numerical algorithms, including discontinuous coefficients representing material interfaces, rapid nonlinearities, and three spatial dimensions. Similar equations occur in various applications, including nuclear physics, semiconductor physics, population genetics, astrophysics, and combustion. In this thesis, we study the PBE, discretizations, and develop multilevel-based methods for approximating the solutions of these types of equations. We first outline the physical model and derive the PBE, which describes the electrostatic potential of a large complex biomolecule lying in a solvent. We next study the theoretical properties of the linearized and nonlinear PBE using standard function space methods; since this equation has not been previously studied theoretically, we provide existence and uniqueness proofs in both the linearized and nonlinear cases. We also analyze box-method discretizations of the PBE, establishing several properties of the discrete equations which are produced. In particular, we show that the discrete nonlinear problem is well-posed. We study and develop linear multilevel methods for interface problems, based on algebraic enforcement of Galerkin or variational conditions, and on coefficient averaging procedures. Using a stencil calculus, we show that in certain simplified cases the two approaches are equivalent, with different averaging procedures corresponding to different prolongation operators. We also develop methods for nonlinear problems based on a nonlinear multilevel method, and on linear multilevel methods combined with a globally convergent damped-inexact-Newton method. We derive a necessary and sufficient descent condition for the inexact-Newton direction, enabling the development of extremely

  18. Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations.

    Science.gov (United States)

    Blossey, R; Maggs, A C; Podgornik, R

    2017-06-01

    We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by Bazant et al. [Phys. Rev. Lett. 106, 046102 (2011)]PRLTAO0031-900710.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.

  19. From Pore Scale to Turbulent Flow with the Unstructured Lattice Boltzmann Method

    DEFF Research Database (Denmark)

    Matin, Rastin

    Abstract: The lattice Boltzmann method is a class of methods in computational fluid dynamics for simulating fluid flow. Implementations on unstructured grids are particularly relevant for various engineering applications, where geometric flexibility or high resolution near a body or a wall...... is required. The main topic of this thesis is to further develop unstructured lattice Boltzmann methods for simulations of Newtonian fluid flow in three dimensions, in particular porous flow. Two methods are considered in this thesis based on the finite volume method and finite element method, respectively...

  20. Semi-Lagrangian off-lattice Boltzmann method for weakly compressible flows.

    Science.gov (United States)

    Krämer, Andreas; Küllmer, Knut; Reith, Dirk; Joppich, Wolfgang; Foysi, Holger

    2017-02-01

    The lattice Boltzmann method is a simulation technique in computational fluid dynamics. In its standard formulation, it is restricted to regular computation grids, second-order spatial accuracy, and a unity Courant-Friedrichs-Lewy (CFL) number. This paper advances the standard lattice Boltzmann method by introducing a semi-Lagrangian streaming step. The proposed method allows significantly larger time steps, unstructured grids, and higher-order accurate representations of the solution to be used. The appealing properties of the approach are demonstrated in simulations of a two-dimensional Taylor-Green vortex, doubly periodic shear layers, and a three-dimensional Taylor-Green vortex.