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Sample records for mechanics poisson-boltzmann surface

  1. A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

    International Nuclear Information System (INIS)

    Fisicaro, G.; Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.

    2016-01-01

    The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes

  2. A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.

    Science.gov (United States)

    Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S

    2016-01-07

    The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

  3. A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

    Energy Technology Data Exchange (ETDEWEB)

    Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)

    2016-01-07

    The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

  4. 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.

  5. 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)], 10.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.

  6. A modified Poisson-Boltzmann equation applied to protein adsorption.

    Science.gov (United States)

    Gama, Marlon de Souza; Santos, Mirella Simões; Lima, Eduardo Rocha de Almeida; Tavares, Frederico Wanderley; Barreto, Amaro Gomes Barreto

    2018-01-05

    Ion-exchange chromatography has been widely used as a standard process in purification and analysis of protein, based on the electrostatic interaction between the protein and the stationary phase. Through the years, several approaches are used to improve the thermodynamic description of colloidal particle-surface interaction systems, however there are still a lot of gaps specifically when describing the behavior of protein adsorption. Here, we present an improved methodology for predicting the adsorption equilibrium constant by solving the modified Poisson-Boltzmann (PB) equation in bispherical coordinates. By including dispersion interactions between ions and protein, and between ions and surface, the modified PB equation used can describe the Hofmeister effects. We solve the modified Poisson-Boltzmann equation to calculate the protein-surface potential of mean force, treated as spherical colloid-plate system, as a function of process variables. From the potential of mean force, the Henry constants of adsorption, for different proteins and surfaces, are calculated as a function of pH, salt concentration, salt type, and temperature. The obtained Henry constants are compared with experimental data for several isotherms showing excellent agreement. We have also performed a sensitivity analysis to verify the behavior of different kind of salts and the Hofmeister effects. Copyright © 2017 Elsevier B.V. All rights reserved.

  7. Comparison of density functional and modified Poisson-Boltzmann structural properties for a spherical double layer

    Directory of Open Access Journals (Sweden)

    L.B.Bhuiyan

    2005-01-01

    Full Text Available The density functional and modified Poisson-Boltzmann descriptions of a spherical (electric double layer are compared and contrasted vis-a-vis existing Monte Carlo simulation data (for small ion diameter 4.25·10-10 m from the literature for a range of physical parameters such as macroion surface charge, macroion radius, valencies of the small ions, and electrolyte concentration. Overall, the theoretical predictions are seen to be remarkably consistent between themselves, being also in very good agreement with the simulations. Some modified Poisson-Boltzmann results for the zeta potential at small ion diameters of 3 and 2·10-10 m are also reported.

  8. Large Time Behavior of the Vlasov-Poisson-Boltzmann System

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    Li Li

    2013-01-01

    Full Text Available The motion of dilute charged particles can be modeled by Vlasov-Poisson-Boltzmann system. We study the large time stability of the VPB system. To be precise, we prove that when time goes to infinity, the solution of VPB system tends to global Maxwellian state in a rate Ot−∞, by using a method developed for Boltzmann equation without force in the work of Desvillettes and Villani (2005. The improvement of the present paper is the removal of condition on parameter λ as in the work of Li (2008.

  9. SMPBS: Web server for computing biomolecular electrostatics using finite element solvers of size modified Poisson-Boltzmann equation.

    Science.gov (United States)

    Xie, Yang; Ying, Jinyong; Xie, Dexuan

    2017-03-30

    SMPBS (Size Modified Poisson-Boltzmann Solvers) is a web server for computing biomolecular electrostatics using finite element solvers of the size modified Poisson-Boltzmann equation (SMPBE). SMPBE not only reflects ionic size effects but also includes the classic Poisson-Boltzmann equation (PBE) as a special case. Thus, its web server is expected to have a broader range of applications than a PBE web server. SMPBS is designed with a dynamic, mobile-friendly user interface, and features easily accessible help text, asynchronous data submission, and an interactive, hardware-accelerated molecular visualization viewer based on the 3Dmol.js library. In particular, the viewer allows computed electrostatics to be directly mapped onto an irregular triangular mesh of a molecular surface. Due to this functionality and the fast SMPBE finite element solvers, the web server is very efficient in the calculation and visualization of electrostatics. In addition, SMPBE is reconstructed using a new objective electrostatic free energy, clearly showing that the electrostatics and ionic concentrations predicted by SMPBE are optimal in the sense of minimizing the objective electrostatic free energy. SMPBS is available at the URL: smpbs.math.uwm.edu © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  10. Poisson-Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes.

    Science.gov (United States)

    Ubbink, Job; Khokhlov, Alexei R

    2004-03-15

    A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson-Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Angstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson-Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)]. (c) 2004 American Institute of Physics.

  11. PB-AM: An open-source, fully analytical linear poisson-boltzmann solver.

    Science.gov (United States)

    Felberg, Lisa E; Brookes, David H; Yap, Eng-Hui; Jurrus, Elizabeth; Baker, Nathan A; Head-Gordon, Teresa

    2017-06-05

    We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized PB equation, for molecules represented as non-overlapping spherical cavities. The PB-AM software package includes the generation of outputs files appropriate for visualization using visual molecular dynamics, 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. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

  12. Poisson-Boltzmann-Nernst-Planck model

    International Nuclear Information System (INIS)

    Zheng Qiong; Wei Guowei

    2011-01-01

    The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external

  13. DL_MG: A Parallel Multigrid Poisson and Poisson-Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution.

    Science.gov (United States)

    Womack, James C; Anton, Lucian; Dziedzic, Jacek; Hasnip, Phil J; Probert, Matt I J; Skylaris, Chris-Kriton

    2018-03-13

    The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential-a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson-Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10 9 unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein-ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

  14. Poisson-Boltzmann-Nernst-Planck model.

    Science.gov (United States)

    Zheng, Qiong; Wei, Guo-Wei

    2011-05-21

    The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external

  15. The solution of the Poisson-Boltzmann's equation for self-consistent potential of infinite, random, nonlinear and non-uniform system

    International Nuclear Information System (INIS)

    Rasulova, M.Yu

    1998-01-01

    A study has been made of a system of charged particles and inhomogeneities randomly distributed in accordance with the same law in the neighborhoods of corresponding sites of a planar crystal lattice. The existence and uniqueness of the solution of the generalized Poisson-Boltzmann's equation for the average self-consistent potential and average density of surface charges are proved. (author)

  16. Ludwig Boltzmann, mechanics and vitalism

    International Nuclear Information System (INIS)

    Broda, E.

    1990-01-01

    During most of his life Boltzmann considered classical mechanics, based on the ideas of material points and central forces, as the fundament of physics. On this basis he became one of the founders of Statistical Mechanics, through which thermodynamics was interpreted on an atomistic basis. In this work, Boltzmann was opposed by his colleague, Ernst Mach. Boltzmann also devoted much work to attempts to interpret Maxwell's theory of the electromagnetic field, of which he was a main protagonist in Central Europe, through mechanics. However, as a supporter of mechanics Boltzmann was by no means dogmatic. While he was adamant in his rejection of Wilhelm Ostwald's energism, he was openminded in respect to the relationship of mechanics, electromagnetism and atomistics. Personally, Boltzmann wanted to conserve and transmit the enormous achievements of mechanics, especially in connection with the mechanical theory of heat, so that these results should not be lost to future generations, but he encouraged attempts to proceed in new directions. While within the framework of statistical mechanics the atoms were treated like the material points of classical mechanics, Boltzmann resisted the initial, unwarranted, ideas about the structure and the properties of the atoms. When later valid ideas were evolved, Boltzmann warmly welcomed this progress, without however personally taking part in the new developments. In his later years, Boltzmann took an intense interest in biology. He supported Darwin's theories, and he contributed to them. He may be called an 'absolute Darwinist'. In his search for a natural explanation of the phenomena of life, he used the term 'mechanical', without meaning to limit them to the realm of classical mechanics. This terminological laxity is considered as unfortunate. Extending his application of Darwinian principles to advanced species, including man, Boltzmann put forward 'mechanical' explanations of thought, of morality, of the sense of beauty, and of

  17. Advanced diffusion model in compacted bentonite based on modified Poisson-Boltzmann equations

    International Nuclear Information System (INIS)

    Yotsuji, K.; Tachi, Y.; Nishimaki, Y.

    2012-01-01

    Document available in extended abstract form only. Diffusion and sorption of radionuclides in compacted bentonite are the key processes in the safe geological disposal of radioactive waste. JAEA has developed the integrated sorption and diffusion (ISD) model for compacted bentonite by coupling the pore water chemistry, sorption and diffusion processes in consistent way. The diffusion model accounts consistently for cation excess and anion exclusion in narrow pores in compacted bentonite by the electric double layer (EDL) theory. The firstly developed ISD model could predict the diffusivity of the monovalent cation/anion in compacted bentonite as a function of dry density. This ISD model was modified by considering the visco-electric effect, and applied for diffusion data for various radionuclides measured under wide range of conditions (salinity, density, etc.). This modified ISD model can give better quantitative agreement with diffusion data for monovalent cation/anion, however, the model predictions still disagree with experimental data for multivalent cation and complex species. In this study we extract the additional key factors influencing diffusion model in narrow charged pores, and the effects of these factors were investigated to reach a better understanding of diffusion processes in compacted bentonite. We investigated here the dielectric saturation effect and the excluded volume effect into the present ISD model and numerically solved these modified Poisson-Boltzmann equations. In the vicinity of the negatively charged clay surfaces, it is necessary to evaluate concentration distribution of electrolytes considering the dielectric saturation effects. The Poisson-Boltzmann (P-B) equation coupled with the dielectric saturation effects was solved numerically by using Runge-Kutta and Shooting methods. Figure 1(a) shows the concentration distributions of Na + as numerical solutions of the modified and original P-B equations for 0.01 M pore water, 800 kg m -3

  18. A Combined MPI-CUDA Parallel Solution of Linear and Nonlinear Poisson-Boltzmann Equation

    Directory of Open Access Journals (Sweden)

    José Colmenares

    2014-01-01

    Full Text Available The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs.

  19. A discontinuous Poisson-Boltzmann equation with interfacial jump: homogenisation and residual error estimate.

    Science.gov (United States)

    Fellner, Klemens; Kovtunenko, Victor A

    2016-01-01

    A nonlinear Poisson-Boltzmann equation with inhomogeneous Robin type boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic multiphase medium with dilute solid particles. The key issue stems from interfacial jumps, which necessitate discontinuous solutions to the problem. Based on variational techniques, we derive the homogenisation of the discontinuous problem and establish a rigorous residual error estimate up to the first-order correction.

  20. Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System

    Science.gov (United States)

    Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying

    2018-04-01

    The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

  1. Aplicação da equação de Poisson-Boltzmann ao cálculo de propriedades dependentes do pH em proteínas Aplications of the Poisson-Boltzmann equation to the calculation of pH-dependent properties in proteins

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    Thereza A. Soares

    2004-08-01

    Full Text Available The ability of biomolecules to catalyze chemical reactions is due chiefly to their sensitivity to variations of the pH in the surrounding environment. The reason for this is that they are made up of chemical groups whose ionization states are modulated by pH changes that are of the order of 0.4 units. The determination of the protonation states of such chemical groups as a function of conformation of the biomolecule and the pH of the environment can be useful in the elucidation of important biological processes from enzymatic catalysis to protein folding and molecular recognition. In the past 15 years, the theory of Poisson-Boltzmann has been successfully used to estimate the pKa of ionizable sites in proteins yielding results, which may differ by 0.1 unit from the experimental values. In this study, we review the theory of Poisson-Boltzmann under the perspective of its application to the calculation of pKa in proteins.

  2. Charge reversal and surface charge amplification in asymmetric valence restricted primitive model planar electric double layers in the modified Poisson-Boltzmann theory

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    L.B. Bhuiyan

    2017-12-01

    Full Text Available The modified Poisson-Boltzmann theory of the restricted primitive model double layer is revisited and recast in a fresh, slightly broader perspective. Derivation of relevant equations follow the techniques utilized in the earlier MPB4 and MPB5 formulations and clarifies the relationship between these. The MPB4, MPB5, and a new formulation of the theory are employed in an analysis of the structure and charge reversal phenomenon in asymmetric 2:1/1:2 valence electrolytes. Furthermore, polarization induced surface charge amplification is studied in 3:1/1:3 systems. The results are compared to the corresponding Monte Carlo simulations. The theories are seen to predict the "exact" simulation data to varying degrees of accuracy ranging from qualitative to almost quantitative. The results from a new version of the theory are found to be of comparable accuracy as the MPB5 results in many situations. However, in some cases involving low electrolyte concentrations, theoretical artifacts in the form of un-physical "shoulders" in the singlet ionic distribution functions are observed.

  3. Structure of cylindrical electric double layers: Comparison of density functional and modified Poisson-Boltzmann theories with Monte Carlo simulations

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    V.Dorvilien

    2013-01-01

    Full Text Available The structure of cylindrical double layers is studied using a modified Poisson Boltzmann theory and the density functional approach. In the model double layer the electrode is a cylindrical polyion that is infinitely long, impenetrable, and uniformly charged. The polyion is immersed in a sea of equi-sized rigid ions embedded in a dielectric continuum. An in-depth comparison of the theoretically predicted zeta potentials, the mean electrostatic potentials, and the electrode-ion singlet density distributions is made with the corresponding Monte Carlo simulation data. The theories are seen to be consistent in their predictions that include variations in ionic diameters, electrolyte concentrations, and electrode surface charge densities, and are also able to reproduce well some new and existing Monte Carlo results.

  4. AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.

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    Koehl, Patrice; Delarue, Marc

    2010-02-14

    The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE

  5. Analytical estimation of effective charges at saturation in Poisson-Boltzmann cell models

    International Nuclear Information System (INIS)

    Trizac, Emmanuel; Aubouy, Miguel; Bocquet, Lyderic

    2003-01-01

    We propose a simple approximation scheme for computing the effective charges of highly charged colloids (spherical or cylindrical with infinite length). Within non-linear Poisson-Boltzmann theory, we start from an expression for the effective charge in the infinite-dilution limit which is asymptotically valid for large salt concentrations; this result is then extended to finite colloidal concentration, approximating the salt partitioning effect which relates the salt content in the suspension to that of a dialysing reservoir. This leads to an analytical expression for the effective charge as a function of colloid volume fraction and salt concentration. These results compare favourably with the effective charges at saturation (i.e. in the limit of large bare charge) computed numerically following the standard prescription proposed by Alexander et al within the cell model

  6. THE EFFECT OF CHEMICAL-STRUCTURE UPON THE THERMODYNAMICS OF MICELLIZATION OF MODEL ALKYLARENESULPHONATES - PREDICTION OF MICELLAR PROPERTIES WITH THE POISSON-BOLTZMANN MODEL

    NARCIS (Netherlands)

    Bijma, K; Engberts, J B F N

    This paper describes how the theory of the ''dressed micelle'', which is based on the nonlinear Poisson-Boltzmann equation, can be used to calculate a number of thermodynamic quantities for micellization of sodium p-alkylbenzenesulphonates. From the Gibbs energy of micellization, the enthalpy of

  7. Accuracy assessment of the linear Poisson-Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid-protein complexes.

    Science.gov (United States)

    Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

    2015-04-05

    The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson-Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev-Bashford-Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson-Boltzmann model. © 2015 Wiley Periodicals, Inc.

  8. Galerkin methods for Boltzmann-Poisson transport with reflection conditions on rough boundaries

    Science.gov (United States)

    Morales Escalante, José A.; Gamba, Irene M.

    2018-06-01

    We consider in this paper the mathematical and numerical modeling of reflective boundary conditions (BC) associated to Boltzmann-Poisson systems, including diffusive reflection in addition to specularity, in the context of electron transport in semiconductor device modeling at nano scales, and their implementation in Discontinuous Galerkin (DG) schemes. We study these BC on the physical boundaries of the device and develop a numerical approximation to model an insulating boundary condition, or equivalently, a pointwise zero flux mathematical condition for the electron transport equation. Such condition balances the incident and reflective momentum flux at the microscopic level, pointwise at the boundary, in the case of a more general mixed reflection with momentum dependant specularity probability p (k →). We compare the computational prediction of physical observables given by the numerical implementation of these different reflection conditions in our DG scheme for BP models, and observe that the diffusive condition influences the kinetic moments over the whole domain in position space.

  9. Transient finite element analysis of electric double layer using Nernst-Planck-Poisson equations with a modified Stern layer.

    Science.gov (United States)

    Lim, Jongil; Whitcomb, John; Boyd, James; Varghese, Julian

    2007-01-01

    A finite element implementation of the transient nonlinear Nernst-Planck-Poisson (NPP) and Nernst-Planck-Poisson-modified Stern (NPPMS) models is presented. The NPPMS model uses multipoint constraints to account for finite ion size, resulting in realistic ion concentrations even at high surface potential. The Poisson-Boltzmann equation is used to provide a limited check of the transient models for low surface potential and dilute bulk solutions. The effects of the surface potential and bulk molarity on the electric potential and ion concentrations as functions of space and time are studied. The ability of the models to predict realistic energy storage capacity is investigated. The predicted energy is much more sensitive to surface potential than to bulk solution molarity.

  10. Ca/Na selectivity coefficients from the Poisson-Boltzmann theory

    International Nuclear Information System (INIS)

    Hedstroem, Magnus; Karnland, Ola

    2010-01-01

    Document available in extended abstract form only. A possible scenario in the post-glacial evolution of the bentonite buffer used in a KBS-3 repository for spent nuclear fuel is that parts of the buffer may erode due to sol formation caused by the extensive swelling of, in particular, Na-montmorillonite in water of low ionic strength. Presence of calcium in the interlayer has been shown to promote gel formation even in electrolytes with ionic strengths in the vicinity of those in glacial melt waters. In order to estimate the amount of calcium in the clay at the onset of glaciation one needs information of the selectivity coefficient for Ca/Na exchange. Hitherto, most experimental data for evaluating the Gaines-Thomas selectivity coefficient, K GT have been obtained in batch experiments, i.e. at high water-to-solid ratios. The conditions in highly compacted bentonite are, however, radically different in many respects, e.g. the interlayer space is on the nanometre scale and the concentration of counterions is in molar range. Therefore we would like to theoretically investigate the transferability of the selectivity coefficients, determined in batch experiments, to compacted conditions. We solve the Poisson-Boltzmann (PB) equation for two parallel charged surfaces in equilibrium with an external NaCl/CaCl 2 mixed solution. Integration of the ion concentration profiles obtained from the PB equation gives the occupancy of Na + and Ca 2+ in the clay. That information together with the composition of the external electrolyte is all that is needed for the calculation of K GT . With a surface layer-charge density of one charge per 145 A 2 , which is close to the value for Wyoming montmorillonite, we find a variation of the selectivity coefficient from about 4 M in batch to 8 M for compacted montmorillonite with dry density 1700 kg/m 3 . The significance as well as the physics behind these results will be presented in detail. The predictions, based on the PB theory, will

  11. Exact Analytic Result of Contact Value for the Density in a Modified Poisson-Boltzmann Theory of an Electrical Double Layer.

    Science.gov (United States)

    Lou, Ping; Lee, Jin Yong

    2009-04-14

    For a simple modified Poisson-Boltzmann (SMPB) theory, taking into account the finite ionic size, we have derived the exact analytic expression for the contact values of the difference profile of the counterion and co-ion, as well as of the sum (density) and product profiles, near a charged planar electrode that is immersed in a binary symmetric electrolyte. In the zero ionic size or dilute limit, these contact values reduce to the contact values of the Poisson-Boltzmann (PB) theory. The analytic results of the SMPB theory, for the difference, sum, and product profiles were compared with the results of the Monte-Carlo (MC) simulations [ Bhuiyan, L. B.; Outhwaite, C. W.; Henderson, D. J. Electroanal. Chem. 2007, 607, 54 ; Bhuiyan, L. B.; Henderson, D. J. Chem. Phys. 2008, 128, 117101 ], as well as of the PB theory. In general, the analytic expression of the SMPB theory gives better agreement with the MC data than the PB theory does. For the difference profile, as the electrode charge increases, the result of the PB theory departs from the MC data, but the SMPB theory still reproduces the MC data quite well, which indicates the importance of including steric effects in modeling diffuse layer properties. As for the product profile, (i) it drops to zero as the electrode charge approaches infinity; (ii) the speed of the drop increases with the ionic size, and these behaviors are in contrast with the predictions of the PB theory, where the product is identically 1.

  12. Adaptive maximal poisson-disk sampling on surfaces

    KAUST Repository

    Yan, Dongming

    2012-01-01

    In this paper, we study the generation of maximal Poisson-disk sets with varying radii on surfaces. Based on the concepts of power diagram and regular triangulation, we present a geometric analysis of gaps in such disk sets on surfaces, which is the key ingredient of the adaptive maximal Poisson-disk sampling framework. Moreover, we adapt the presented sampling framework for remeshing applications. Several novel and efficient operators are developed for improving the sampling/meshing quality over the state-of-theart. © 2012 ACM.

  13. Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

    Science.gov (United States)

    Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

    2017-07-11

    Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

  14. Electro-osmosis of non-Newtonian fluids in porous media using lattice Poisson-Boltzmann method.

    Science.gov (United States)

    Chen, Simeng; He, Xinting; Bertola, Volfango; Wang, Moran

    2014-12-15

    Electro-osmosis in porous media has many important applications in various areas such as oil and gas exploitation and biomedical detection. Very often, fluids relevant to these applications are non-Newtonian because of the shear-rate dependent viscosity. The purpose of this study was to investigate the behaviors and physical mechanism of electro-osmosis of non-Newtonian fluids in porous media. Model porous microstructures (granular, fibrous, and network) were created by a random generation-growth method. The nonlinear governing equations of electro-kinetic transport for a power-law fluid were solved by the lattice Poisson-Boltzmann method (LPBM). The model results indicate that: (i) the electro-osmosis of non-Newtonian fluids exhibits distinct nonlinear behaviors compared to that of Newtonian fluids; (ii) when the bulk ion concentration or zeta potential is high enough, shear-thinning fluids exhibit higher electro-osmotic permeability, while shear-thickening fluids lead to the higher electro-osmotic permeability for very low bulk ion concentration or zeta potential; (iii) the effect of the porous medium structure depends significantly on the constitutive parameters: for fluids with large constitutive coefficients strongly dependent on the power-law index, the network structure shows the highest electro-osmotic permeability while the granular structure exhibits the lowest permeability on the entire range of power law indices considered; when the dependence of the constitutive coefficient on the power law index is weaker, different behaviors can be observed especially in case of strong shear thinning. Copyright © 2014 Elsevier Inc. All rights reserved.

  15. Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions

    Directory of Open Access Journals (Sweden)

    Liu Jinn-Liang

    2017-10-01

    Full Text Available We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation effects important in a variety of chemical and biological systems, especially in high field or large concentration conditions found in and near binding sites, ion channels, and electrodes. Steric effects and correlations are apparent when we compare nonlocal Poisson-Fermi results to Poisson-Boltzmann calculations in electric double layer and to experimental measurements on the selectivity of potassium channels for K+ over Na+.

  16. The Poisson equation on Klein surfaces

    Directory of Open Access Journals (Sweden)

    Monica Rosiu

    2016-04-01

    Full Text Available We obtain a formula for the solution of the Poisson equation with Dirichlet boundary condition on a region of a Klein surface. This formula reveals the symmetric character of the solution.

  17. Adaptive maximal poisson-disk sampling on surfaces

    KAUST Repository

    Yan, Dongming; Wonka, Peter

    2012-01-01

    In this paper, we study the generation of maximal Poisson-disk sets with varying radii on surfaces. Based on the concepts of power diagram and regular triangulation, we present a geometric analysis of gaps in such disk sets on surfaces, which

  18. An intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces.

    Science.gov (United States)

    Ying, Xiang; Xin, Shi-Qing; Sun, Qian; He, Ying

    2013-09-01

    Poisson disk sampling has excellent spatial and spectral properties, and plays an important role in a variety of visual computing. Although many promising algorithms have been proposed for multidimensional sampling in euclidean space, very few studies have been reported with regard to the problem of generating Poisson disks on surfaces due to the complicated nature of the surface. This paper presents an intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. In sharp contrast to the conventional parallel approaches, our method neither partitions the given surface into small patches nor uses any spatial data structure to maintain the voids in the sampling domain. Instead, our approach assigns each sample candidate a random and unique priority that is unbiased with regard to the distribution. Hence, multiple threads can process the candidates simultaneously and resolve conflicts by checking the given priority values. Our algorithm guarantees that the generated Poisson disks are uniformly and randomly distributed without bias. It is worth noting that our method is intrinsic and independent of the embedding space. This intrinsic feature allows us to generate Poisson disk patterns on arbitrary surfaces in IR(n). To our knowledge, this is the first intrinsic, parallel, and accurate algorithm for surface Poisson disk sampling. Furthermore, by manipulating the spatially varying density function, we can obtain adaptive sampling easily.

  19. Atoms, mechanics, and probability Ludwig Boltzmann's statistico-mechanical writings : an exegesis

    CERN Document Server

    Darrigol, Olivier

    2018-01-01

    One of the pillars of modern science, statistical mechanics, owes much to one man, the Austrian physicist Ludwig Boltzmann (1844-1906). As a result of his unusual working and writing styles, his enormous contribution remains little read and poorly understood. The purpose of this book is to make the Boltzmann corpus more accessible to physicists, philosophers, and historians, and so give it new life. The means are introductory biographical and historical materials, detailed and lucid summaries of every relevant publication, and a final chapter of critical synthesis. Special attention is given to Boltzmann's theoretical tool-box and to his patient construction of lofty formal systems even before their full conceptual import could be known. This constructive tendency largely accounts for his lengthy style, for the abundance of new constructions, for the relative vagueness of their object--and for the puzzlement of commentators. This book will help the reader cross the stylistic barrier and see how ingeniously B...

  20. Free surface entropic lattice Boltzmann simulations of film condensation on vertical hydrophilic plates

    DEFF Research Database (Denmark)

    Hygum, Morten Arnfeldt; Karlin, Iliya; Popok, Vladimir

    2015-01-01

    A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall. It is sh......A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall...

  1. Nonextensive statistical mechanics of ionic solutions

    International Nuclear Information System (INIS)

    Varela, L.M.; Carrete, J.; Munoz-Sola, R.; Rodriguez, J.R.; Gallego, J.

    2007-01-01

    Classical mean-field Poisson-Boltzmann theory of ionic solutions is revisited in the theoretical framework of nonextensive Tsallis statistics. The nonextensive equivalent of Poisson-Boltzmann equation is formulated revisiting the statistical mechanics of liquids and the Debye-Hueckel framework is shown to be valid for highly diluted solutions even under circumstances where nonextensive thermostatistics must be applied. The lowest order corrections associated to nonadditive effects are identified for both symmetric and asymmetric electrolytes and the behavior of the average electrostatic potential in a homogeneous system is analytically and numerically analyzed for various values of the complexity measurement nonextensive parameter q

  2. Analysis of the gravitational coupled collisionless Boltzmann-poisson equations and numerical simulations of the formation of self-gravitating systems

    International Nuclear Information System (INIS)

    Roy, Fabrice

    2004-01-01

    We study the formation of self-gravitating systems and their properties by means of N-body simulations of gravitational collapse. First, we summarize the major analytical results concerning the collisionless Boltzmann equation and the Poisson's equation which describe the dynamics of collisionless gravitational systems. We present a study of some analytical solutions of this coupled system of equations. We then present the software used to perform the simulations. Some of this has been parallelized and implemented with the aid of MPI. For this reason we give a brief overview of it. Finally, we present the results of the numerical simulations. Analysis of these results allows us to explain some features of self-gravitating systems and the initial conditions needed to trigger the Antonov instability and the radial orbit instability. (author) [fr

  3. Efficient maximal Poisson-disk sampling and remeshing on surfaces

    KAUST Repository

    Guo, Jianwei; Yan, Dongming; Jia, Xiaohong; Zhang, Xiaopeng

    2015-01-01

    Poisson-disk sampling is one of the fundamental research problems in computer graphics that has many applications. In this paper, we study the problem of maximal Poisson-disk sampling on mesh surfaces. We present a simple approach that generalizes the 2D maximal sampling framework to surfaces. The key observation is to use a subdivided mesh as the sampling domain for conflict checking and void detection. Our approach improves the state-of-the-art approach in efficiency, quality and the memory consumption.

  4. Efficient maximal Poisson-disk sampling and remeshing on surfaces

    KAUST Repository

    Guo, Jianwei

    2015-02-01

    Poisson-disk sampling is one of the fundamental research problems in computer graphics that has many applications. In this paper, we study the problem of maximal Poisson-disk sampling on mesh surfaces. We present a simple approach that generalizes the 2D maximal sampling framework to surfaces. The key observation is to use a subdivided mesh as the sampling domain for conflict checking and void detection. Our approach improves the state-of-the-art approach in efficiency, quality and the memory consumption.

  5. An Intrinsic Algorithm for Parallel Poisson Disk Sampling on Arbitrary Surfaces.

    Science.gov (United States)

    Ying, Xiang; Xin, Shi-Qing; Sun, Qian; He, Ying

    2013-03-08

    Poisson disk sampling plays an important role in a variety of visual computing, due to its useful statistical property in distribution and the absence of aliasing artifacts. While many effective techniques have been proposed to generate Poisson disk distribution in Euclidean space, relatively few work has been reported to the surface counterpart. This paper presents an intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. We propose a new technique for parallelizing the dart throwing. Rather than the conventional approaches that explicitly partition the spatial domain to generate the samples in parallel, our approach assigns each sample candidate a random and unique priority that is unbiased with regard to the distribution. Hence, multiple threads can process the candidates simultaneously and resolve conflicts by checking the given priority values. It is worth noting that our algorithm is accurate as the generated Poisson disks are uniformly and randomly distributed without bias. Our method is intrinsic in that all the computations are based on the intrinsic metric and are independent of the embedding space. This intrinsic feature allows us to generate Poisson disk distributions on arbitrary surfaces. Furthermore, by manipulating the spatially varying density function, we can obtain adaptive sampling easily.

  6. Poisson sigma model with branes and hyperelliptic Riemann surfaces

    International Nuclear Information System (INIS)

    Ferrario, Andrea

    2008-01-01

    We derive the explicit form of the superpropagators in the presence of general boundary conditions (coisotropic branes) for the Poisson sigma model. This generalizes the results presented by Cattaneo and Felder [''A path integral approach to the Kontsevich quantization formula,'' Commun. Math. Phys. 212, 591 (2000)] and Cattaneo and Felder ['Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model', Lett. Math. Phys. 69, 157 (2004)] for Kontsevich's angle function [Kontsevich, M., 'Deformation quantization of Poisson manifolds I', e-print arXiv:hep.th/0101170] used in the deformation quantization program of Poisson manifolds. The relevant superpropagators for n branes are defined as gauge fixed homotopy operators of a complex of differential forms on n sided polygons P n with particular ''alternating'' boundary conditions. In the presence of more than three branes we use first order Riemann theta functions with odd singular characteristics on the Jacobian variety of a hyperelliptic Riemann surface (canonical setting). In genus g the superpropagators present g zero mode contributions

  7. Simulating condensation on microstructured surfaces using Lattice Boltzmann Method

    Science.gov (United States)

    Alexeev, Alexander; Vasyliv, Yaroslav

    2017-11-01

    We simulate a single component fluid condensing on 2D structured surfaces with different wettability. To simulate the two phase fluid, we use the athermal Lattice Boltzmann Method (LBM) driven by a pseudopotential force. The pseudopotential force results in a non-ideal equation of state (EOS) which permits liquid-vapor phase change. To account for thermal effects, the athermal LBM is coupled to a finite volume discretization of the temperature evolution equation obtained using a thermal energy rate balance for the specific internal energy. We use the developed model to probe the effect of surface structure and surface wettability on the condensation rate in order to identify microstructure topographies promoting condensation. Financial support is acknowledged from Kimberly-Clark.

  8. Nonlocal surface plasmons by Poisson Green's function matching

    International Nuclear Information System (INIS)

    Morgenstern Horing, Norman J

    2006-01-01

    The Poisson Green's function for all space is derived for the case in which an interface divides space into two separate semi-infinite media, using the Green's function matching method. Each of the separate semi-infinite constituent parts has its own dynamic, nonlocal polarizability, which is taken to be unaffected by the presence of the interface and is represented by the corresponding bulk response property. While this eliminates Friedel oscillatory phenomenology near the interface with p ∼ 2p F , it is nevertheless quite reasonable and useful for a broad range of lower (nonvanishing) wavenumbers, p F . The resulting full-space Poisson Green's function is dynamic, nonlocal and spatially inhomogeneous, and its frequency pole yields the surface plasmon dispersion relation, replete with dynamic and nonlocal features. It also accommodates an ambient magnetic field

  9. A one-level FETI method for the drift–diffusion-Poisson system with discontinuities at an interface

    KAUST Repository

    Baumgartner, Stefan

    2013-06-01

    A 3d feti method for the drift-diffusion-Poisson system including discontinuities at a 2d interface is developed. The motivation for this work is to provide a parallel numerical algorithm for a system of PDEs that are the basic model equations for the simulation of semiconductor devices such as transistors and sensors. Moreover, discontinuities or jumps in the potential and its normal derivative at a 2d surface are included for the simulation of nanowire sensors based on a homogenized model. Using the feti method, these jump conditions can be included with the usual numerical properties and the original Farhat-Roux feti method is extended to the drift-diffusion-Poisson equations including discontinuities. We show two numerical examples. The first example verifies the correct implementation including the discontinuities on a 2d grid divided into eight subdomains. The second example is 3d and shows the application of the algorithm to the simulation of nanowire sensors with high aspect ratios. The Poisson-Boltzmann equation and the drift-diffusion-Poisson system with jump conditions are solved on a 3d grid with real-world boundary conditions. © 2013 Elsevier Inc..

  10. Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics

    International Nuclear Information System (INIS)

    Czachor, M.

    1996-01-01

    Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)

  11. Lattice Boltzmann simulations of the contact angle in a liquid-gas system

    International Nuclear Information System (INIS)

    Ryu, Seung Yeob; Park, Cheon Tae; Kim, Keung Koo

    2008-01-01

    Recently, the lattice Boltzmann method (LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with multiphase flows, complex geometries and interfacial dynamics may be treated. The shape of a moving droplet is difficult to investigate analytically because the classical continuum hydrodynamic equations of motion with the usual no-slip condition at the surface predict a singularity in the stress at the contact line. Briant et al. have proposed a wetting boundary condition by using the wetting potential. In this study, we introduce the wetting boundary condition into the LBM proposed by Zheng et al. The static contact angle of a droplet onto a wall in order to validate the method is calculated. By adopting a finite difference gradient operator of a sufficient isotropy, the spurious currents can be made small in the wall surface. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows

  12. Poisson-Boltzmann theory of charged colloids: limits of the cell model for salty suspensions

    International Nuclear Information System (INIS)

    Denton, A R

    2010-01-01

    Thermodynamic properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions are commonly modelled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together with counterions and salt ions, confined to a symmetrically shaped, electroneutral cell. While easing numerical solution of the nonlinear PB equation, the cell model neglects microion-induced interactions and correlations between macroions, precluding modelling of macroion ordering phenomena. An alternative approach, which avoids the artificial constraints of cell geometry, exploits the mapping of a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interparticle interactions. In practice, effective-interaction models are usually based on linear-screening approximations, which can accurately describe strong nonlinear screening only by incorporating an effective (renormalized) macroion charge. Combining charge renormalization and linearized PB theories, in both the cell model and an effective-interaction (cell-free) model, we compute osmotic pressures of highly charged colloids and monovalent microions, in Donnan equilibrium with a salt reservoir, over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions from nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modelling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate for predicting osmotic pressures of deionized (counterion-dominated) suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions to the osmotic pressure grows, leading predictions from the cell and effective-interaction models to deviate. No evidence is found for a liquid

  13. Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics

    Science.gov (United States)

    He, Ping

    2012-01-01

    The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically symmetric collisionless self-gravitating systems. We use an approach that is very different from that of the conventional statistical mechanics of short-range interaction systems. We demonstrate that the equilibrium states of self-gravitating systems consist of both mechanical and statistical equilibria, with the former characterized by a series of velocity-moment equations and the latter by statistical equilibrium equations, which should be derived from the entropy principle. The velocity-moment equations of all orders are derived from the steady-state collisionless Boltzmann equation. We point out that the ergodicity is invalid for the whole self-gravitating system, but it can be re-established locally. Based on the local ergodicity, using Fermi-Dirac-like statistics, with the non-degenerate condition and the spatial independence of the local microstates, we rederive the Boltzmann-Gibbs entropy. This is consistent with the validity of the collisionless Boltzmann equation, and should be the correct entropy form for collisionless self-gravitating systems. Apart from the usual constraints of mass and energy conservation, we demonstrate that the series of moment or virialization equations must be included as additional constraints on the entropy functional when performing the variational calculus; this is an extension to the original prescription by White & Narayan. Any possible velocity distribution can be produced by the statistical-mechanical approach that we have developed with the extended Boltzmann-Gibbs/White-Narayan statistics. Finally, we discuss the questions of negative specific heat and ensemble inequivalence for self-gravitating systems.

  14. Experimental investigation of the Boltzmann relation for a bi-Maxwellian distribution in inductively coupled plasmas

    International Nuclear Information System (INIS)

    Bang, Jin Young; Chung, Chin Wook

    2009-01-01

    In plasma, the Boltzmann relation is often used to connect the electron density to the plasma potential because it is not easy to calculate electric potentials on the basis of the Poisson equation due to the quasineutrality. From the Boltzmann relation, the electric potential can be simply obtained from the electron density or vice versa. However, the Boltzmann relation assumes that electrons are in thermal equilibrium and have a Maxwellian distribution, so it cannot be applied to non-Maxwellian distributions. In this paper, the Boltzmann relation for bi-Maxwellian distributions was newly derived from fluid equations and the comparison with the experimental results was given by measuring electron energy probability functions in an inductively coupled plasma. It was found that the spatial distribution of the electron density in bulk plasma is governed by the effective electron temperature, while that of the cold and hot electrons are governed by each electron temperature.

  15. Extending the Solvation-Layer Interface Condition Continum Electrostatic Model to a Linearized Poisson-Boltzmann Solvent.

    Science.gov (United States)

    Molavi Tabrizi, Amirhossein; Goossens, Spencer; Mehdizadeh Rahimi, Ali; Cooper, Christopher D; Knepley, Matthew G; Bardhan, Jaydeep P

    2017-06-13

    We extend the linearized Poisson-Boltzmann (LPB) continuum electrostatic model for molecular solvation to address charge-hydration asymmetry. Our new solvation-layer interface condition (SLIC)/LPB corrects for first-shell response by perturbing the traditional continuum-theory interface conditions at the protein-solvent and the Stern-layer interfaces. We also present a GPU-accelerated treecode implementation capable of simulating large proteins, and our results demonstrate that the new model exhibits significant accuracy improvements over traditional LPB models, while reducing the number of fitting parameters from dozens (atomic radii) to just five parameters, which have physical meanings related to first-shell water behavior at an uncharged interface. In particular, atom radii in the SLIC model are not optimized but uniformly scaled from their Lennard-Jones radii. Compared to explicit-solvent free-energy calculations of individual atoms in small molecules, SLIC/LPB is significantly more accurate than standard parametrizations (RMS error 0.55 kcal/mol for SLIC, compared to RMS error of 3.05 kcal/mol for standard LPB). On parametrizing the electrostatic model with a simple nonpolar component for total molecular solvation free energies, our model predicts octanol/water transfer free energies with an RMS error 1.07 kcal/mol. A more detailed assessment illustrates that standard continuum electrostatic models reproduce total charging free energies via a compensation of significant errors in atomic self-energies; this finding offers a window into improving the accuracy of Generalized-Born theories and other coarse-grained models. Most remarkably, the SLIC model also reproduces positive charging free energies for atoms in hydrophobic groups, whereas standard PB models are unable to generate positive charging free energies regardless of the parametrized radii. The GPU-accelerated solver is freely available online, as is a MATLAB implementation.

  16. Mean electrostatic and Poisson-Boltzmann models for multicomponent transport through compacted clay

    International Nuclear Information System (INIS)

    Steefel, C.I.; Galindez, J.M.

    2012-01-01

    Document available in extended abstract form only. Electrical double layer effects in the pore space of clays become increasingly important as the level of compaction increases and intergrain and interlayer spacings shift towards the range of nano-meters. At such scales, solute transport can no longer be explained by concentration gradients alone and it becomes necessary to include the electrostatic effects on chemical potentials. In fact, the electrical double layer (EDL) that develops in the neighborhood of the negatively charged clay surfaces can extend well into the aqueous phase, effectively constraining the space available to anions (known as anion exclusion), thus distorting the spatial distribution of ionic species in solution. In this study, we make use of two approaches for addressing the accumulation and transport of charged ionic species in the electrical double layers of compacted bentonite: 1) a mean electrostatic approach based on the assumption of Donnan equilibrium, and 2) a 2D numerical approach based on the multicomponent Poisson-Nernst-Planck (NPP) set of equations. For the mean electrostatic or Donnan approach to the electrical double layer [1], two options are considered: 1) a model in which surface complexation in the Stern layer may partly balance the fixed charge of the montmorillonite making up the bentonite buffer, and 2) a model in which the fixed mineral charge is balanced completely by the diffuse layer. In the mean electrostatic approach, one additional equation that balances the charge between the Stern layer and the diffuse layer is added to the multicomponent reactive transport code CrunchFlow. The only additional unknown that is required is the mean electrostatic potential, although it may be necessary in certain cases to consider the volume (or width) of the electrical double layer as an additional implicit unknown. Both ions and neutral species may diffuse within the diffuse layer according to their gradients and species

  17. A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics.

    Science.gov (United States)

    Sun, Hui; Wen, Jiayi; Zhao, Yanxiang; Li, Bo; McCammon, J Andrew

    2015-12-28

    Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods.

  18. Generalized Poisson processes in quantum mechanics and field theory

    International Nuclear Information System (INIS)

    Combe, P.; Rodriguez, R.; Centre National de la Recherche Scientifique, 13 - Marseille; Hoegh-Krohn, R.; Centre National de la Recherche Scientifique, 13 - Marseille; Sirugue, M.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille

    1981-01-01

    In section 2 we describe more carefully the generalized Poisson processes, giving a realization of the underlying probability space, and we characterize these processes by their characteristic functionals. Section 3 is devoted to the proof of the previous formula for quantum mechanical systems, with possibly velocity dependent potentials and in section 4 we give an application of the previous theory to some relativistic Bose field models. (orig.)

  19. Lattice-Boltzmann Simulation of Tablet Disintegration

    Science.gov (United States)

    Jiang, Jiaolong; Sun, Ning; Gersappe, Dilip

    Using the lattice-Boltzmann method, we developed a 2D model to study the tablet disintegration involving the swelling and wicking mechanisms. The surface area and disintegration profile of each component were obtained by tracking the tablet structure in the simulation. Compared to pure wicking, the total surface area is larger for swelling and wicking, which indicates that the swelling force breaks the neighboring bonds. The disintegration profiles show that the tablet disintegrates faster than pure wicking, and there are more wetted active pharmaceutical ingredient particles distributed on smaller clusters. Our results indicate how the porosity would affect the disintegration process by changing the wetting area of the tablet as well as by changing the swelling force propagation.

  20. Self-Consistent Approach to Global Charge Neutrality in Electrokinetics: A Surface Potential Trap Model

    Directory of Open Access Journals (Sweden)

    Li Wan

    2014-03-01

    Full Text Available In this work, we treat the Poisson-Nernst-Planck (PNP equations as the basis for a consistent framework of the electrokinetic effects. The static limit of the PNP equations is shown to be the charge-conserving Poisson-Boltzmann (CCPB equation, with guaranteed charge neutrality within the computational domain. We propose a surface potential trap model that attributes an energy cost to the interfacial charge dissociation. In conjunction with the CCPB, the surface potential trap can cause a surface-specific adsorbed charge layer σ. By defining a chemical potential μ that arises from the charge neutrality constraint, a reformulated CCPB can be reduced to the form of the Poisson-Boltzmann equation, whose prediction of the Debye screening layer profile is in excellent agreement with that of the Poisson-Boltzmann equation when the channel width is much larger than the Debye length. However, important differences emerge when the channel width is small, so the Debye screening layers from the opposite sides of the channel overlap with each other. In particular, the theory automatically yields a variation of σ that is generally known as the “charge regulation” behavior, attendant with predictions of force variation as a function of nanoscale separation between two charged surfaces that are in good agreement with the experiments, with no adjustable or additional parameters. We give a generalized definition of the ζ potential that reflects the strength of the electrokinetic effect; its variations with the concentration of surface-specific and surface-nonspecific salt ions are shown to be in good agreement with the experiments. To delineate the behavior of the electro-osmotic (EO effect, the coupled PNP and Navier-Stokes equations are solved numerically under an applied electric field tangential to the fluid-solid interface. The EO effect is shown to exhibit an intrinsic time dependence that is noninertial in its origin. Under a step-function applied

  1. Dataset for acrylate/silica nanoparticles formulations and photocured composites: Viscosity, filler dispersion and bulk Poisson׳s ratio

    Directory of Open Access Journals (Sweden)

    Hubert Gojzewski

    2017-06-01

    Full Text Available UV-curable polymer composites are of importance in industry, biomedical applications, scientific fields, and daily life. Outstanding physical properties of polymer composites were achieved with nanoparticles as filler, primarily in enhancing mechanical strength or barrier properties. Structure-property relationships of the resulting nanocomposites are dictated by the polymer-filler molecular architecture, i.e. interactions between polymer matrix and filler, and high surface area to volume ratio of the filler particles. Among monomers, acrylates and methacrylates attracted wide attention due to their ease of polymerization and excellent physicochemical and mechanical properties of the derived polymers. We prepared and photopolymerized two series of formulations containing hydrophobized silica nanofiller (Aerosil R7200 dispersed in 2-hydroxyethyl acrylate (HEA or polyethylene glycol diacrylate (PEGDA monomers. We compared selected physical properties of the formulations, both before and after photocuring; specifically the viscosity of formulations and dispersion of the filler in the polymer matrices. Additionally, we estimated the bulk Poisson׳s ratio of the investigated nanocomposites. This article contains data related to the research article entitled “Nanoscale Young׳s modulus and surface morphology in photocurable polyacrylate/nanosilica composites” (Gojzewski et al., 2017 [1].

  2. Analysis of a bubble coalescence in the multiphase lattice Boltzmann method

    International Nuclear Information System (INIS)

    Ryu, Seung Yeob; Park, Cheon Tae; Lee, Chung Chan; Kim, Keung Koo

    2008-01-01

    Recently, the lattice Boltzmann method (LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with multiphase flows, complex geometries and interfacial dynamics may be treated. To study the effect of the mobility coefficient Γ and the width of the interface layer, two stationary bubbles without a collision are considered. The gap of the two bubbles is taken as 4, while the width of the interface (w) and the mobility coefficient Γ are varied. In the present work, the lattice Boltzmann model for multiphase flows proposed by Zheng et al. is used for simulating two stationary bubbles without a collision. By adopting a finite difference gradient operator of a sufficient isotropy, the spurious currents can be made smaller. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows

  3. Direct measurement of sub-Debye-length attraction between oppositely charged surfaces.

    Science.gov (United States)

    Kampf, Nir; Ben-Yaakov, Dan; Andelman, David; Safran, S A; Klein, Jacob

    2009-09-11

    Using a surface force balance with fast video analysis, we have measured directly the attractive forces between oppositely charged solid surfaces (charge densities sigma(+), sigma(-)) across water over the entire range of interaction, in particular, at surface separations D below the Debye screening length lambda(S). At very low salt concentration we find a long-ranged attraction between the surfaces (onset ca. 100 nm), whose variation at DPoisson-Boltzmann theory, when due account is taken of the independently-determined surface charge asymmetry (sigma(+) not equal to |sigma(-)|).

  4. Constructions and classifications of projective Poisson varieties.

    Science.gov (United States)

    Pym, Brent

    2018-01-01

    This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including adjunction, ruled surfaces and blowups, and leading to a statement of the full birational classification. We then describe several constructions of Poisson threefolds, outlining the classification in the regular case, and the case of rank-one Fano threefolds (such as projective space). Following a brief introduction to the notion of Poisson subspaces, we discuss Bondal's conjecture on the dimensions of degeneracy loci on Poisson Fano manifolds. We close with a discussion of log symplectic manifolds with simple normal crossings degeneracy divisor, including a new proof of the classification in the case of rank-one Fano manifolds.

  5. Constructions and classifications of projective Poisson varieties

    Science.gov (United States)

    Pym, Brent

    2018-03-01

    This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including adjunction, ruled surfaces and blowups, and leading to a statement of the full birational classification. We then describe several constructions of Poisson threefolds, outlining the classification in the regular case, and the case of rank-one Fano threefolds (such as projective space). Following a brief introduction to the notion of Poisson subspaces, we discuss Bondal's conjecture on the dimensions of degeneracy loci on Poisson Fano manifolds. We close with a discussion of log symplectic manifolds with simple normal crossings degeneracy divisor, including a new proof of the classification in the case of rank-one Fano manifolds.

  6. Lattice Boltzmann model for thermal free surface flows with liquid-solid phase transition

    International Nuclear Information System (INIS)

    Attar, Elham; Koerner, Carolin

    2011-01-01

    Purpose: The main objective of this work is to develop an algorithm to use the Lattice Boltzmann method for solving free surface thermal flow problems with solid/liquid phase changes. Approach: A multi-distribution function model is applied to simulate hydrodynamic flow and the coupled thermal diffusion-convection problem. Findings: The free surface problem, i.e. the reconstruction of the missing distribution functions at the interface, can be solved by applying a physical transparent momentum and heat flux based methodology. The developed method is subsequently applied to some test cases in order to assess its computational potentials. Practical implications: Many industrial processes involve problems where non-isothermal motion and simultaneous solidification of fluids with free surface is important. Examples are all castings processes and especially foaming processes which are characterized by a huge and strongly changing surface. Value: A reconstruction algorithm to treat a thermal hydrodynamic problem with free surfaces is presented which is physically transparent and easy to implement.

  7. A modified Poisson-Boltmann model including charge regulation for the adsorption of ionizable polyelectrolytes to charged interfaces, applied to lysozyme adsorption on silica

    NARCIS (Netherlands)

    Biesheuvel, P.M.; Veen, van der M.; Norde, W.

    2005-01-01

    The equilibrium adsorption of polyelectrolytes with multiple types of ionizable groups is described using a modified Poisson-Boltzmann equation including charge regulation of both the polymer and the interface. A one-dimensional mean-field model is used in which the electrostatic potential is

  8. Axisymmetric Lattice Boltzmann Model of Droplet Impact on Solid Surfaces

    Science.gov (United States)

    Dalgamoni, Hussein; Yong, Xin

    2017-11-01

    Droplet impact is a ubiquitous fluid phenomena encountered in scientific and engineering applications such as ink-jet printing, coating, electronics manufacturing, and many others. It is of great technological importance to understand the detailed dynamics of drop impact on various surfaces. The lattice Boltzmann method (LBM) emerges as an efficient method for modeling complex fluid systems involving rapidly evolving fluid-fluid and fluid-solid interfaces with complex geometries. In this work, we model droplet impact on flat solid substrates with well-defined wetting behavior using a two-phase axisymmetric LBM with high density and viscosity contrasts. We extend the two-dimensional Lee and Liu model to capture axisymmetric effect in the normal impact. First we compare the 2D axisymmetric results with the 2D and 3D results reported by Lee and Liu to probe the effect of axisymmetric terms. Then, we explore the effects of Weber number, Ohnesorge number, and droplet-surface equilibrium contact angle on the impact. The dynamic contact angle and spreading factor of the droplet during impact are investigated to qualitatively characterize the impact dynamics.

  9. A lattice Boltzmann model for substrates with regularly structured surface roughness

    Science.gov (United States)

    Yagub, A.; Farhat, H.; Kondaraju, S.; Singh, T.

    2015-11-01

    Superhydrophobic surface characteristics are important in many industrial applications, ranging from the textile to the military. It was observed that surfaces fabricated with nano/micro roughness can manipulate the droplet contact angle, thus providing an opportunity to control the droplet wetting characteristics. The Shan and Chen (SC) lattice Boltzmann model (LBM) is a good numerical tool, which holds strong potentials to qualify for simulating droplets wettability. This is due to its realistic nature of droplet contact angle (CA) prediction on flat smooth surfaces. But SC-LBM was not able to replicate the CA on rough surfaces because it lacks a real representation of the physics at work under these conditions. By using a correction factor to influence the interfacial tension within the asperities, the physical forces acting on the droplet at its contact lines were mimicked. This approach allowed the model to replicate some experimentally confirmed Wenzel and Cassie wetting cases. Regular roughness structures with different spacing were used to validate the study using the classical Wenzel and Cassie equations. The present work highlights the strength and weakness of the SC model and attempts to qualitatively conform it to the fundamental physics, which causes a change in the droplet apparent contact angle, when placed on nano/micro structured surfaces.

  10. Lattice-Boltzmann simulations of droplet evaporation

    KAUST Repository

    Ledesma-Aguilar, Rodrigo; Vella, Dominic; Yeomans, Julia M.

    2014-01-01

    © 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

  11. 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

  12. Electrostatic attraction between overall neutral surfaces.

    Science.gov (United States)

    Adar, Ram M; Andelman, David; Diamant, Haim

    2016-08-01

    Two overall neutral surfaces with positively and negatively charged domains ("patches") have been shown in recent experiments to exhibit long-range attraction when immersed in an ionic solution. Motivated by the experiments, we calculate analytically the osmotic pressure between such surfaces within the Poisson-Boltzmann framework, using a variational principle for the surface-averaged free energy. The electrostatic potential, calculated beyond the linear Debye-Hückel theory, yields an overall attraction at large intersurface separations, over a wide range of the system's controlled length scales. In particular, the attraction is stronger and occurs at smaller separations for surface patches of larger size and charge density. In this large patch limit, we find that the attraction-repulsion crossover separation is inversely proportional to the square of the patch-charge density and to the Debye screening length.

  13. The intellectual quadrangle: Mach-Boltzmann-Planck-Einstein

    International Nuclear Information System (INIS)

    Broda, E.

    1981-01-01

    These four men were influential in the transition from classical to modern physics. They interacted as scientists, often antagonistically. Thus Boltzmann was the greatest champion of the atom, while Mach remained unconvinced all his life. As a aphysicist, Einstein was greatly influenced by both Mach and Boltzmann, although Mach in the end rejected relativity as well. Because of his work on statistical mechanics, fluctuations, and quantum theory, Einstein has been called the natural successor to Boltzmann. Planck also was influenced by Mach at first. Hence he and Boltzmann were adversaries antil Planck converted to atomistics in 1900 and used the statistical interpretation of entropy to establish his radiation law. Planck accepted relativity early, but in quantum theory he was for a long time partly opposed to Einstein, and vice versa - Einstein considered Planck's derivation of his radiation law as unsound, while Planck could not accept the light quantum. In the case of all four physicists, science was interwoven with philosophy. Boltzmann consistently fought Mach's positivism, while Planck and Einstein moved from positivism to realism. All were also, though in very different ways, actively interested in public affairs. (orig.)

  14. Ion distributions at charged aqueous surfaces: Synchrotron X-ray scattering studies

    Energy Technology Data Exchange (ETDEWEB)

    Bu, Wei [Iowa State Univ., Ames, IA (United States)

    2009-01-01

    Surface sensitive synchrotron X-ray scattering studies were performed to obtain the distribution of monovalent ions next to a highly charged interface at room temperature. To control surface charge density, lipids, dihexadecyl hydrogen-phosphate (DHDP) and dimysteroyl phosphatidic acid (DMPA), were spread as monolayer materials at the air/water interface, containing CsI at various concentrations. Five decades in bulk concentrations (CsI) are investigated, demonstrating that the interfacial distribution is strongly dependent on bulk concentration. We show that this is due to the strong binding constant of hydronium H3O+ to the phosphate group, leading to proton-transfer back to the phosphate group and to a reduced surface charge. Using anomalous reflectivity off and at the L3 Cs+ resonance, we provide spatial counterion (Cs+) distributions next to the negatively charged interfaces. The experimental ion distributions are in excellent agreement with a renormalized surface charge Poisson-Boltzmann theory for monovalent ions without fitting parameters or additional assumptions. Energy Scans at four fixed momentum transfers under specular reflectivity conditions near the Cs+ L3 resonance were conducted on 10-3 M CsI with DHDP monolayer materials on the surface. The energy scans exhibit a periodic dependence on photon momentum transfer. The ion distributions obtained from the analysis are in excellent agreement with those obtained from anomalous reflectivity measurements, providing further confirmation to the validity of the renormalized surface charge Poisson-Boltzmann theory for monovalent ions. Moreover, the dispersion corrections f0 and f00 for Cs+ around L3 resonance, revealing the local environment of a Cs+ ion in the solution at the interface, were extracted simultaneously with output of ion distributions.

  15. Non-holonomic dynamics and Poisson geometry

    International Nuclear Information System (INIS)

    Borisov, A V; Mamaev, I S; Tsiganov, A V

    2014-01-01

    This is a survey of basic facts presently known about non-linear Poisson structures in the analysis of integrable systems in non-holonomic mechanics. It is shown that by using the theory of Poisson deformations it is possible to reduce various non-holonomic systems to dynamical systems on well-understood phase spaces equipped with linear Lie-Poisson brackets. As a result, not only can different non-holonomic systems be compared, but also fairly advanced methods of Poisson geometry and topology can be used for investigating them. Bibliography: 95 titles

  16. 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. PMID:23558425

  17. Surface effects on the mechanical properties of nanoporous materials

    International Nuclear Information System (INIS)

    Lu Zixing; Zhang Cungang; Liu Qiang; Yang Zhenyu

    2011-01-01

    In this paper, surface effects on the mechanical behaviour of nanoporous materials are investigated using the theory of surface elasticity and Timoshenko beam theory based on the tetrakaidecahedron (or Kelvin) open-cell foam model. Meanwhile, the influence of surface elasticity and residual surface stress on the mechanical properties of nanoporous materials is discussed. In addition, the results derived from the theory of Euler-Bernoulli beam model are also provided for comparison. Theoretical results show that the effective Young's modulus of the nanoporous materials increases as the diameter of the strut decreases, but in contrast Poisson's ratio and the brittle collapse strength decrease with the diameter of the strut. The contribution of shear deformation to surface effects on elastic properties is more significant, while the surface effects on brittle collapse strength are not sensitive to shear deformation, and it can even be neglected. As the strut size increases, the present results can be reduced to the cases without considering surface effects, which verifies the efficiency of the present model to a certain extent.

  18. POISSON SUPERFISH, Poisson Equation Solver for Radio Frequency Cavity

    International Nuclear Information System (INIS)

    Colman, J.

    2001-01-01

    field specification defined by the user. PAN-T calculates the temperature distribution in the walls of a RF-cavity given the electric field at the walls, the thermal conductivity of the wall materials, and the temperature at the outer surface of the wall. TEKPLOT plots the physical boundaries and mesh resulting from a LATTICE run and equipotential or field lines generated as a result of POISSON, PANDIRA, MIRT, or SUPERFISH runs. SF01 and SHY process results from SUPERFISH runs. SF01 calculates quantities useful for a drift-tube linac. SHY calculates the value of the electric field in the TM mode over an area in the XY-plane. 2 - Method of solution: The POISSON group of codes solves Maxwell's static equations (MSE's) in integral form and in two dimensions. When the MSE's are taken together with the boundary conditions, they are equivalent to a generalized form of Poisson's equations in two dimensions. POISSON uses a successive point over-relaxation (SPOR) method to solve the equations, while PANDIRA directly solves the block tridiagonal system of difference equations, and iteration is required only for nonlinear problems. After solving the equations, both compute the derivatives of the potential, namely the fields and their gradients, and calculate the stored energy. SUPERFISH uses the same direct solution method as PANDIRA for the Helmholtz eigenvalue problem. 3 - Restrictions on the complexity of the problem: POISSON: 16000 mesh points, 30 regions; SUPERFISH: 32000 mesh points; 125 max value for k max and/or l max , 60 segments and 3 regions

  19. On poisson-stopped-sums that are mixed poisson

    OpenAIRE

    Valero Baya, Jordi; Pérez Casany, Marta; Ginebra Molins, Josep

    2013-01-01

    Maceda (1948) characterized the mixed Poisson distributions that are Poisson-stopped-sum distributions based on the mixing distribution. In an alternative characterization of the same set of distributions here the Poisson-stopped-sum distributions that are mixed Poisson distributions is proved to be the set of Poisson-stopped-sums of either a mixture of zero-truncated Poisson distributions or a zero-modification of it. Peer Reviewed

  20. Boltzmann statistical consideration on the excitation mechanism of iron atomic lines emitted from glow discharge plasmas

    International Nuclear Information System (INIS)

    Zhang Lei; Kashiwakura, Shunsuke; Wagatsuma, Kazuaki

    2011-01-01

    A Boltzmann plot for many iron atomic lines having excitation energies of 3.3–6.9 eV was investigated in glow discharge plasmas when argon or neon was employed as the plasma gas. The plot did not show a linear relationship over a wide range of the excitation energy, but showed that the emission lines having higher excitation energies largely deviated from a normal Boltzmann distribution whereas those having low excitation energies (3.3–4.3 eV) well followed it. This result would be derived from an overpopulation among the corresponding energy levels. A probable reason for this is that excitations for the high-lying excited levels would be caused predominantly through a Penning-type collision with the metastable atom of argon or neon, followed by recombination with an electron and then stepwise de-excitations which can populate the excited energy levels just below the ionization limit of iron atom. The non-thermal excitation occurred more actively in the argon plasma rather than the neon plasma, because of a difference in the number density between the argon and the neon metastables. The Boltzmann plots yields important information on the reason why lots of Fe I lines assigned to high-lying excited levels can be emitted from glow discharge plasmas. - Highlights: ► This paper shows the excitation mechanism of Fe I lines from a glow discharge plasma. ► A Boltzmann distribution is studied among iron lines of various excitation levels. ► We find an overpopulation of the high-lying energy levels from the normal distribution. ► It is caused through Penning-type collision of iron atom with argon metastable atom.

  1. Effective Wettability of Heterogenous Fracture Surfaces Using the Lattice-Boltzmann Method

    Science.gov (United States)

    E Santos, J.; Prodanovic, M.; Landry, C. J.

    2017-12-01

    Fracture walls in the subsurface are often structured by minerals of different composition (potentially further altered in contact with fluids during hydrocarbon extraction or CO2 sequestration), this yields in a heterogeneous wettability of the surface in contact with the fluids. The focus of our work is to study how surfaces presenting different mineralogy and roughness affect multiphase flow in fractures. Using the Shan-Chen model of the lattice-Boltzmann method (LBM) we define fluid interaction and surface attraction parameters to simulate a system of a wetting and a non-wetting fluid. In this work, we use synthetically created fractures presenting different arrangements of wetting and non-wetting patches, and with or without roughness; representative of different mineralogy, similar workflow can be applied to fractures extracted from X-ray microtomography images of fractures porous media. The results from the LBM simulations provide an insight on how the distribution of mineralogy and surface roughness are related with the observed macroscopic contact angle. We present a comparison between the published analytical models, and our results based on surface areas, spatial distribution and local fracture aperture. The understanding of the variables that affect the contact angle is useful for the comprehension of multiphase processes in naturally fractured reservoirs like primary oil production, enhanced oil recovery and CO2 sequestration. The macroscopic contact angle analytical equations for heterogeneous surfaces with variable roughness are no longer valid in highly heterogeneous systems; we quantify the difference thus offering an alternative to analytical models.

  2. Formulation of Hamiltonian mechanics with even and odd Poisson brackets

    International Nuclear Information System (INIS)

    Khudaverdyan, O.M.; Nersesyan, A.P.

    1987-01-01

    A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs

  3. Entropic lattice Boltzmann representations required to recover Navier-Stokes flows.

    Science.gov (United States)

    Keating, Brian; Vahala, George; Yepez, Jeffrey; Soe, Min; Vahala, Linda

    2007-03-01

    There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional simulations are performed which illustrate some of the differences between standard lattice Boltzmann and entropic lattice Boltzmann schemes, as well as the role played by the number of phase-space velocities used in the discretization.

  4. Lattice Boltzmann Study of Bubbles on a Patterned Superhydrophobic Surface under Shear Flow

    Science.gov (United States)

    Chen, Wei; Wang, Kai; Hou, Guoxiang; Leng, Wenjun

    2018-01-01

    This paper studies shear flow over a 2D patterned superhydrophobic surface using lattice Boltzmann method (LBM). Single component Shan-Chen multiphase model and Carnahan-Starling EOS are adopted to handle the liquid-gas flow on superhydrophobic surface with entrapped micro-bubbles. The shape of bubble interface and its influence on slip length under different shear rates are investigated. With increasing shear rate, the bubble interface deforms. Then the contact lines are depinned from the slot edges and move downstream. When the shear rate is high enough, a continuous gas layer forms. If the protrusion angle is small, the gas layer forms and collapse periodically, and accordingly the slip length changes periodically. While if the protrusion angle is large, the gas layer is steady and separates the solid wall from liquid, resulting in a very large slip length.

  5. Metastable states of plasma particles close to a charged surface

    Energy Technology Data Exchange (ETDEWEB)

    Shavlov, A. V., E-mail: shavlov@ikz.ru [The Institute of the Earth Cryosphere, RAS Siberian branch, 625000, P.O. 1230, Tyumen (Russian Federation); Tyumen State Oil and Gas University, 38, Volodarskogo St., 625000, Tyumen (Russian Federation); Dzhumandzhi, V. A. [The Institute of the Earth Cryosphere, RAS Siberian branch, 625000, P.O. 1230, Tyumen (Russian Federation)

    2015-09-15

    The free energy of the plasma particles and the charged surface that form an electroneutral system is calculated on the basis of the Poisson-Boltzmann equation. It is shown that, owing to correlation of light plasma particles near the charged surface and close to heavy particles of high charge, there can be metastable states in plasma. The corresponding phase charts of metastable states of the separate components of plasma, and plasma as a whole, are constructed. These charts depend on temperature, the charge magnitude, the size of the particles, and the share of the charge of the light carriers out of the total charge of the plasma particles.

  6. A modified Poisson-Boltzmann surface excess calculation with a field dependent dielectric constant

    International Nuclear Information System (INIS)

    Gordillo, G.J.; Molina, F.V.; Posadas, D.

    1990-01-01

    The Unequal Radius Modified Gouy-Chapman (URMGC) was applied to mixtures of electrolytes. It was considered that the two anions, (1) and (2), have different radius, r 1 and r 2 , being r 2 smaller than r 1 . The dielectric constant was taken as a function of the electric field, using the theoretical Booth equation, or as a linear dependence varying between 6 and 78 when r 2 1 . The results show that the surface excess of anion 2 is much greater than the one predicted by Gouy-Chapman theory when the proportion of 2 increases in the mixture, while both the other anion and the cation show negative deviation. This effect is more evident in mixtures than in the case of single electrolytes, and has a maximum for a composition that depends on the chosen parameters for the model. (Author) [es

  7. Boltzmann statistical consideration on the excitation mechanism of iron atomic lines emitted from glow discharge plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Lei; Kashiwakura, Shunsuke; Wagatsuma, Kazuaki, E-mail: wagatuma@imr.tohoku.ac.jp

    2011-11-15

    A Boltzmann plot for many iron atomic lines having excitation energies of 3.3-6.9 eV was investigated in glow discharge plasmas when argon or neon was employed as the plasma gas. The plot did not show a linear relationship over a wide range of the excitation energy, but showed that the emission lines having higher excitation energies largely deviated from a normal Boltzmann distribution whereas those having low excitation energies (3.3-4.3 eV) well followed it. This result would be derived from an overpopulation among the corresponding energy levels. A probable reason for this is that excitations for the high-lying excited levels would be caused predominantly through a Penning-type collision with the metastable atom of argon or neon, followed by recombination with an electron and then stepwise de-excitations which can populate the excited energy levels just below the ionization limit of iron atom. The non-thermal excitation occurred more actively in the argon plasma rather than the neon plasma, because of a difference in the number density between the argon and the neon metastables. The Boltzmann plots yields important information on the reason why lots of Fe I lines assigned to high-lying excited levels can be emitted from glow discharge plasmas. - Highlights: Black-Right-Pointing-Pointer This paper shows the excitation mechanism of Fe I lines from a glow discharge plasma. Black-Right-Pointing-Pointer A Boltzmann distribution is studied among iron lines of various excitation levels. Black-Right-Pointing-Pointer We find an overpopulation of the high-lying energy levels from the normal distribution. Black-Right-Pointing-Pointer It is caused through Penning-type collision of iron atom with argon metastable atom.

  8. On the theoretical description of weakly charged surfaces.

    Science.gov (United States)

    Wang, Rui; Wang, Zhen-Gang

    2015-03-14

    It is widely accepted that the Poisson-Boltzmann (PB) theory provides a valid description for charged surfaces in the so-called weak coupling limit. Here, we show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. In the presence of dielectric discontinuity, there is no limiting condition for which the PB theory is valid.

  9. Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

    Science.gov (United States)

    Martínez-Torres, David; Miranda, Eva

    2018-01-01

    We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.

  10. Polynomial Poisson algebras: Gel'fand-Kirillov problem and Poisson spectra

    OpenAIRE

    Lecoutre, César

    2014-01-01

    We study the fields of fractions and the Poisson spectra of polynomial Poisson algebras.\\ud \\ud First we investigate a Poisson birational equivalence problem for polynomial Poisson algebras over a field of arbitrary characteristic. Namely, the quadratic Poisson Gel'fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is isomorphic to the field of fractions of a Poisson affine space, i.e. a polynomial algebra such that the Poisson bracket of two generators is equal to...

  11. Effects of surface roughness and electrokinetic heterogeneity on electroosmotic flow in microchannel

    Energy Technology Data Exchange (ETDEWEB)

    Masilamani, Kannan; Ganguly, Suvankar; Feichtinger, Christian; Bartuschat, Dominik; Rüde, Ulrich, E-mail: suva_112@yahoo.co.in [Department of Computer Science 10 University of Erlangen-Nuremberg, Cauerstr.11 91058 Erlangen (Germany)

    2015-06-15

    In this paper, a hybrid lattice-Boltzmann and finite-difference (LB-FD) model is applied to simulate the effects of three-dimensional surface roughness and electrokinetic heterogeneity on electroosmotic flow (EOF) in a microchannel. The lattice-Boltzmann (LB) method has been employed to obtain the flow field and a finite-difference (FD) method is used to solve the Poisson-Boltzmann (PB) equation for the electrostatic potential distribution. Numerical simulation of flow through a square cross-section microchannel with designed roughness is conducted and the results are critically analysed. The effects of surface heterogeneity on the electroosmotic transport are investigated for different roughness height, width, roughness interval spacing, and roughness surface potential. Numerical simulations reveal that the presence of surface roughness changes the nature of electroosmotic transport through the microchannel. It is found that the electroosmotic velocity decreases with the increase in roughness height and the velocity profile becomes asymmetric. For the same height of the roughness elements, the EOF velocity rises with the increase in roughness width. For the heterogeneously charged rough channel, the velocity profile shows a distinct deviation from the conventional plug-like flow pattern. The simulation results also indicate locally induced flow vortices which can be utilized to enhance the flow and mixing within the microchannel. The present study has important implications towards electrokinetic flow control in the microchannel, and can provide an efficient way to design a microfluidic system of practical interest. (paper)

  12. Boltzmann

    International Nuclear Information System (INIS)

    Lin, X.

    1991-01-01

    This paper reports the development of an object-oriented programming methodology for particle simulations. It is established on the [m reductionist] view that many physical phenomena cana be reduced to many-body problems. By doing the reduction, many seemly unrelated physical phenomena can be simulated in a systematic way and a high-level programming system can be constructed to facilitate the programming and the solution of the simulations. In the object-oriented particle simulation methodology, a hierarchy of abstract particles is defined to represent a variety of characteristics in physical system simulations. A simulation program is constructed from particles derived from the abstract particles. The object- oriented particle simulation methodology provides a unifying modeling and simulation framework for a variety of simulation applications with the use of particle methods. It allows easy composition of simulation programs from predefined software modules and facilitates software reusability. It greatly increase the productivity of simulation program constructions. Boltzmann (after Ludwig Boltzmann, 1844-1906) is a prototype programming system in the object-oriented particle simulation methodology. Boltzmann is implemented in C++ and the X Window System. It contains a library of data types and functions that support simulations in particle methods. Moreover, it provides a visualization window to support friendly user-computer interaction. Examples of the application of the Boltzmann programming system are presented. The effectiveness of the object-oriented particle simulation methodology is demonstrated. A user's manual is included in the appendix

  13. Does the Boltzmann Principle Need a Dynamical Correction?

    Science.gov (United States)

    Adib, Artur B.

    2004-11-01

    In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived (M. Bianucci, R. Mannella, B. J. West and P. Grigolini, Phys. Rev. E 51: 3002 (1995)) which differs from the one that follows from the Boltzmann principle S = kln Ω( E) via the thermodynamic relation 1/ T=∂ S / ∂ E by additional terms of "dynamical" character, which are argued to correct and generalize the Boltzmann principle for small systems (here Ω( E) is the area of the constant-energy surface). In the present work, the underlying definition of temperature in the Fokker-Planck formalism of Bianucci et al., is investigated and shown to coincide with an approximate form of the equipartition temperature. Its exact form, however, is strictly related to the "volume" entropy S = k ln Ф( E) via the thermodynamic relation above for systems of any number of degrees of freedom ( Ф( E) is the phase space volume enclosed by the constant-energy surface). This observation explains and clarifies the numerical results of Bianucci et al., and shows that a dynamical correction for either the temperature or the entropy is unnecessary, at least within the class of systems considered by those authors. Explicit analytical and numerical results for a particle coupled to a small chain ( N~10) of quartic oscillators are also provided to further illustrate these facts.

  14. New Directions in Mathematical Fluid Mechanics

    CERN Document Server

    Fursikov, Andrei V

    2010-01-01

    The scientific interests of Professor A.V. Kazhikhov were fundamentally devoted to Mathematical Fluid Mechanics, where he achieved outstanding results that had, and still have, a significant influence on this field. This volume, dedicated to the memory of A.V. Kazhikhov, presents the latest contributions from renowned world specialists in a number of new important directions of Mathematical Physics, mostly of Mathematical Fluid Mechanics, and, more generally, in the field of nonlinear partial differential equations. These results are mostly related to boundary value problems and to control problems for the Navier-Stokes equations, and for equations of heat convection. Other important topics include non-equilibrium processes, Poisson-Boltzmann equations, dynamics of elastic body, and related problems of function theory and nonlinear analysis.

  15. Modelling and investigation of partial wetting surfaces for drop dynamics using lattice Boltzmann method

    Science.gov (United States)

    Pravinraj, T.; Patrikar, Rajendra

    2017-07-01

    Partial wetting surfaces and its influence on the droplet movement of micro and nano scale being contemplated for many useful applications. The dynamics of the droplet usually analyzed with a multiphase lattice Boltzmann method (LBM). In this paper, the influence of partial wetting surface on the dynamics of droplet is systematically analyzed for various cases. Splitting of droplets due to chemical gradient of the surface is studied and analyses of splitting time for various widths of the strips for different Weber numbers are computed. With the proposed model one can tune the splitting volume and time by carefully choosing a strip width and droplet position. The droplet spreading on chemically heterogeneous surfaces shows that the spreading can be controlled not only by parameters of Weber number but also by tuning strip width ratio. The transportation of the droplet from hydrophobic surface to hydrophilic surface due to chemical gradient is simulated and analyzed using our hybrid thermodynamic-image processing technique. The results prove that with the progress of time the surface free energy decreases with increase in spreading area. Finally, the transportation of a droplet on microstructure gradient is demonstrated. The model explains the temporal behaviour of droplet during the spreading, recoiling and translation along with tracking of contact angle hysteresis phenomenon.

  16. Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics

    International Nuclear Information System (INIS)

    Niven, Robert K.

    2005-01-01

    The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a 'binary decision', exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems

  17. 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

  18. GEPOIS: a two dimensional nonuniform mesh Poisson solver

    International Nuclear Information System (INIS)

    Quintenz, J.P.; Freeman, J.R.

    1979-06-01

    A computer code is described which solves Poisson's equation for the electric potential over a two dimensional cylindrical (r,z) nonuniform mesh which can contain internal electrodes. Poisson's equation is solved over a given region subject to a specified charge distribution with either Neumann or Dirichlet perimeter boundary conditions and with Dirichlet boundary conditions on internal surfaces. The static electric field is also computed over the region with special care given to normal electric field components at boundary surfaces

  19. Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.

    Science.gov (United States)

    Frejlich, Pedro; Mărcuț, Ioan

    2018-01-01

    Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Our second result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all structure maps in normal form. We conclude by illustrating our results with examples arising from Lie algebras.

  20. Comparison of Poisson structures and Poisson-Lie dynamical r-matrices

    OpenAIRE

    Enriquez, B.; Etingof, P.; Marshall, I.

    2004-01-01

    We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices of Balog-Feher-Palla.

  1. On Poisson functions

    OpenAIRE

    Terashima, Yuji

    2008-01-01

    In this paper, defining Poisson functions on super manifolds, we show that the graphs of Poisson functions are Dirac structures, and find Poisson functions which include as special cases both quasi-Poisson structures and twisted Poisson structures.

  2. On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems

    Science.gov (United States)

    Tessarotto, Massimo; Cremaschini, Claudio; Mond, Michael; Asci, Claudio; Soranzo, Alessandro; Tironi, Gino

    2018-03-01

    The problem is posed of the prescription of the so-called Boltzmann-Grad limit operator (L_{BG}) for the N-body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. It is proved, that, despite the non-commutative property of the operator L_{BG}, the Boltzmann equation can nevertheless be uniquely determined. In particular, consistent with the claim of Uffink and Valente (Found Phys 45:404, 2015) that there is "no time-asymmetric ingredient" in its derivation, the Boltzmann equation is shown to be time-reversal symmetric. The proof is couched on the "ab initio" axiomatic approach to the classical statistical mechanics recently developed (Tessarotto et al. in Eur Phys J Plus 128:32, 2013). Implications relevant for the physical interpretation of the Boltzmann H-theorem and the phenomenon of decay to kinetic equilibrium are pointed out.

  3. Immiscible multicomponent lattice Boltzmann model for fluids with ...

    Indian Academy of Sciences (India)

    College of Mechanical Engineering, Tongji University, 4800# Cao'an Road, ... was developed from a discretized fluid model known as the lattice gas automata ... of two immiscible fluids, several lattice Boltzmann (LB) models have been ...

  4. Ludwig Boltzmann - pioneer of atomistics and evolution

    International Nuclear Information System (INIS)

    Stiller, W.

    1986-01-01

    At first a short introduction to Ludwig Boltzmann's life (1844 - 1906) and work is given. Some theoretical results of his work (H-theorem, classical Boltzmann statistics, Boltzmann's kinetic equation) are treated in detail. His experimental work is briefly discussed. In addition Boltzmann's philosophical work is characterized. Finally, the influence of Boltzmann's ideas on our time is investigated. (author)

  5. A lattice Boltzmann simulation of coalescence-induced droplet jumping on superhydrophobic surfaces with randomly distributed structures

    Science.gov (United States)

    Zhang, Li-Zhi; Yuan, Wu-Zhi

    2018-04-01

    The motion of coalescence-induced condensate droplets on superhydrophobic surface (SHS) has attracted increasing attention in energy-related applications. Previous researches were focused on regularly rough surfaces. Here a new approach, a mesoscale lattice Boltzmann method (LBM), is proposed and used to model the dynamic behavior of coalescence-induced droplet jumping on SHS with randomly distributed rough structures. A Fast Fourier Transformation (FFT) method is used to generate non-Gaussian randomly distributed rough surfaces with the skewness (Sk), kurtosis (K) and root mean square (Rq) obtained from real surfaces. Three typical spreading states of coalesced droplets are observed through LBM modeling on various rough surfaces, which are found to significantly influence the jumping ability of coalesced droplet. The coalesced droplets spreading in Cassie state or in composite state will jump off the rough surfaces, while the ones spreading in Wenzel state would eventually remain on the rough surfaces. It is demonstrated that the rough surfaces with smaller Sks, larger Rqs and a K at 3.0 are beneficial to coalescence-induced droplet jumping. The new approach gives more detailed insights into the design of SHS.

  6. Formal equivalence of Poisson structures around Poisson submanifolds

    NARCIS (Netherlands)

    Marcut, I.T.

    2012-01-01

    Let (M,π) be a Poisson manifold. A Poisson submanifold P ⊂ M gives rise to a Lie algebroid AP → P. Formal deformations of π around P are controlled by certain cohomology groups associated to AP. Assuming that these groups vanish, we prove that π is formally rigid around P; that is, any other Poisson

  7. (Quasi-)Poisson enveloping algebras

    OpenAIRE

    Yang, Yan-Hong; Yao, Yuan; Ye, Yu

    2010-01-01

    We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.

  8. Contact angle determination in multicomponent lattice Boltzmann simultations

    NARCIS (Netherlands)

    Schmieschek, S.M.P.; Harting, J.D.R.

    2011-01-01

    Droplets on hydrophobic surfaces are ubiquitous in microfluidic applications and there exists a number of commonly used multicomponent and multiphase lattice Boltzmann schemes to study such systems. In this paper we focus on a popular implementation of a multicomponent model as introduced by Shan

  9. Mechanical properties investigation on single-wall ZrO2 nanotubes: A finite element method with equivalent Poisson's ratio for chemical bonds

    Science.gov (United States)

    Yang, Xiao; Li, Huijian; Hu, Minzheng; Liu, Zeliang; Wärnå, John; Cao, Yuying; Ahuja, Rajeev; Luo, Wei

    2018-04-01

    A method to obtain the equivalent Poisson's ratio in chemical bonds as classical beams with finite element method was proposed from experimental data. The UFF (Universal Force Field) method was employed to calculate the elastic force constants of Zrsbnd O bonds. By applying the equivalent Poisson's ratio, the mechanical properties of single-wall ZrNTs (ZrO2 nanotubes) were investigated by finite element analysis. The nanotubes' Young's modulus (Y), Poisson's ratio (ν) of ZrNTs as function of diameters, length and chirality have been discussed, respectively. We found that the Young's modulus of single-wall ZrNTs is calculated to be between 350 and 420 GPa.

  10. Boltzmann, Einstein, Natural Law and Evolution

    International Nuclear Information System (INIS)

    Broda, E.

    1980-01-01

    Like Boltzmann, Einstein was a protagonist of atomistics. As a physicist, he has been called Boltzmann's true successor. Also in epistemology, after overcoming the positivist influence of Mach, Einstein approached Boltzmann. Any difference between Boltzmann's realism, or even materialism, and Einstein's pantheism may be merely a matter of emphasis. Yet a real difference exists in another respect. Boltzmann explained man's power of thinking and feeling, his morality and his esthetic sense, on an evolutionary, Darwinian, basis. In contrast, evolution had no role in Einstein's thought, though Darwin was accepted by him. This lack of appreciation of the importance of evolution is now attributed to socio-political factors. (author)

  11. Poisson Autoregression

    DEFF Research Database (Denmark)

    Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag

    This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time...

  12. Poisson Autoregression

    DEFF Research Database (Denmark)

    Fokianos, Konstantinos; Rahbæk, Anders; Tjøstheim, Dag

    This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, making an interpretation as an integer valued GARCH process possible. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model...

  13. Poisson Coordinates.

    Science.gov (United States)

    Li, Xian-Ying; Hu, Shi-Min

    2013-02-01

    Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

  14. Limitations of Boltzmann's principle

    International Nuclear Information System (INIS)

    Lavenda, B.H.

    1995-01-01

    The usual form of Boltzmann's principle assures that maximum entropy, or entropy reduction, occurs with maximum probability, implying a unimodal distribution. Boltzmann's principle cannot be applied to nonunimodal distributions, like the arcsine law, because the entropy may be concave only over a limited portion of the interval. The method of subordination shows that the arcsine distribution corresponds to a process with a single degree of freedom, thereby confirming the invalidation of Boltzmann's principle. The fractalization of time leads to a new distribution in which arcsine and Cauchy distributions can coexist simultaneously for nonintegral degrees of freedom between √2 and 2

  15. 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.)

  16. Constructing irregular surfaces to enclose macromolecular complexes for mesoscale modeling using the discrete surface charge optimization (DISCO) algorithm.

    Science.gov (United States)

    Zhang, Qing; Beard, Daniel A; Schlick, Tamar

    2003-12-01

    Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK

  17. Fragment-based quantum mechanical calculation of protein-protein binding affinities.

    Science.gov (United States)

    Wang, Yaqian; Liu, Jinfeng; Li, Jinjin; He, Xiao

    2018-04-29

    The electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method has been successfully utilized for efficient linear-scaling quantum mechanical (QM) calculation of protein energies. In this work, we applied the EE-GMFCC method for calculation of binding affinity of Endonuclease colicin-immunity protein complex. The binding free energy changes between the wild-type and mutants of the complex calculated by EE-GMFCC are in good agreement with experimental results. The correlation coefficient (R) between the predicted binding energy changes and experimental values is 0.906 at the B3LYP/6-31G*-D level, based on the snapshot whose binding affinity is closest to the average result from the molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) calculation. The inclusion of the QM effects is important for accurate prediction of protein-protein binding affinities. Moreover, the self-consistent calculation of PB solvation energy is required for accurate calculations of protein-protein binding free energies. This study demonstrates that the EE-GMFCC method is capable of providing reliable prediction of relative binding affinities for protein-protein complexes. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

  18. Topological Poisson Sigma models on Poisson-Lie groups

    International Nuclear Information System (INIS)

    Calvo, Ivan; Falceto, Fernando; Garcia-Alvarez, David

    2003-01-01

    We solve the topological Poisson Sigma model for a Poisson-Lie group G and its dual G*. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of both models in the open geometry reveals that there exists a map from the reduced phase of each model (P and P*) to the main symplectic leaf of the Heisenberg double (D 0 ) such that the symplectic forms on P, P* are obtained as the pull-back by those maps of the symplectic structure on D 0 . This uncovers a duality between P and P* under the exchange of bulk degrees of freedom of one model with boundary degrees of freedom of the other one. We finally solve the Poisson Sigma model for the Poisson structure on G given by a pair of r-matrices that generalizes the Poisson-Lie case. The Hamiltonian analysis of the theory requires the introduction of a deformation of the Heisenberg double. (author)

  19. 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.

  20. Poisson distribution

    NARCIS (Netherlands)

    Hallin, M.; Piegorsch, W.; El Shaarawi, A.

    2012-01-01

    The random variable X taking values 0,1,2,…,x,… with probabilities pλ(x) = e−λλx/x!, where λ∈R0+ is called a Poisson variable, and its distribution a Poisson distribution, with parameter λ. The Poisson distribution with parameter λ can be obtained as the limit, as n → ∞ and p → 0 in such a way that

  1. Poisson traces, D-modules, and symplectic resolutions.

    Science.gov (United States)

    Etingof, Pavel; Schedler, Travis

    2018-01-01

    We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

  2. Poisson traces, D-modules, and symplectic resolutions

    Science.gov (United States)

    Etingof, Pavel; Schedler, Travis

    2018-03-01

    We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

  3. A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects

    NARCIS (Netherlands)

    Kamali, M.R.

    2013-01-01

    The aim of the present research was to explore the promises and shift the limits of the numerical framework of lattice Boltzmann (LB) for studying the physics behind multi-component two-phase heterogeneous non-isothermal reactive flows under industrial conditions. An example of such an industrially

  4. Boltzmann electron PIC simulation of the E-sail effect

    Directory of Open Access Journals (Sweden)

    P. Janhunen

    2015-12-01

    Full Text Available 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 hybrid 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 of trapped electrons which still behaves in a physically meaningful way in the sense of producing not more than one solar wind ion deflection shock upstream of the tether. By this prescription we obtain thrust per tether length values that are in line with earlier estimates, although somewhat smaller. We conclude that the Boltzmann PIC simulation is a new tool for simulating the E-sail thrust. This tool enables us to calculate solutions rapidly and allows to easily study different scenarios for trapped electrons.

  5. Almost Poisson integration of rigid body systems

    International Nuclear Information System (INIS)

    Austin, M.A.; Krishnaprasad, P.S.; Li-Sheng Wang

    1993-01-01

    In this paper we discuss the numerical integration of Lie-Poisson systems using the mid-point rule. Since such systems result from the reduction of hamiltonian systems with symmetry by lie group actions, we also present examples of reconstruction rules for the full dynamics. A primary motivation is to preserve in the integration process, various conserved quantities of the original dynamics. A main result of this paper is an O(h 3 ) error estimate for the Lie-Poisson structure, where h is the integration step-size. We note that Lie-Poisson systems appear naturally in many areas of physical science and engineering, including theoretical mechanics of fluids and plasmas, satellite dynamics, and polarization dynamics. In the present paper we consider a series of progressively complicated examples related to rigid body systems. We also consider a dissipative example associated to a Lie-Poisson system. The behavior of the mid-point rule and an associated reconstruction rule is numerically explored. 24 refs., 9 figs

  6. The Boltzmann project

    Science.gov (United States)

    Fischer, J.; Fellmuth, B.; Gaiser, C.; Zandt, T.; Pitre, L.; Sparasci, F.; Plimmer, M. D.; de Podesta, M.; Underwood, R.; Sutton, G.; Machin, G.; Gavioso, R. M.; Madonna Ripa, D.; Steur, P. P. M.; Qu, J.; Feng, X. J.; Zhang, J.; Moldover, M. R.; Benz, S. P.; White, D. R.; Gianfrani, L.; Castrillo, A.; Moretti, L.; Darquié, B.; Moufarej, E.; Daussy, C.; Briaudeau, S.; Kozlova, O.; Risegari, L.; Segovia, J. J.; Martín, M. C.; del Campo, D.

    2018-04-01

    The International Committee for Weights and Measures (CIPM), at its meeting in October 2017, followed the recommendation of the Consultative Committee for Units (CCU) on the redefinition of the kilogram, ampere, kelvin and mole. For the redefinition of the kelvin, the Boltzmann constant will be fixed with the numerical value 1.380 649  ×  10-23 J K-1. The relative standard uncertainty to be transferred to the thermodynamic temperature value of the triple point of water will be 3.7  ×  10-7, corresponding to an uncertainty in temperature of 0.10 mK, sufficiently low for all practical purposes. With the redefinition of the kelvin, the broad research activities of the temperature community on the determination of the Boltzmann constant have been very successfully completed. In the following, a review of the determinations of the Boltzmann constant k, important for the new definition of the kelvin and performed in the last decade, is given.

  7. Poisson Autoregression

    DEFF Research Database (Denmark)

    Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag

    2009-01-01

    In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies...... to the conditional variance, making possible interpretation as an integer-valued generalized autoregressive conditional heteroscedasticity process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and past observations. As a particular example, we consider...... an exponential autoregressive Poisson model for time series. Under geometric ergodicity, the maximum likelihood estimators are shown to be asymptotically Gaussian in the linear model. In addition, we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric...

  8. 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.

  9. Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods

    International Nuclear Information System (INIS)

    Klassen, Alexander; Scharowsky, Thorsten; Körner, Carolin

    2014-01-01

    Evaporation plays an important role in many technical applications including beam-based additive manufacturing processes, such as selective electron beam or selective laser melting (SEBM/SLM). In this paper, we describe an evaporation model which we employ within the framework of a two-dimensional free surface lattice Boltzmann method. With this method, we solve the hydrodynamics as well as thermodynamics of the molten material taking into account the mass and energy losses due to evaporation and the recoil pressure acting on the melt pool. Validation of the numerical model is performed by measuring maximum melt depths and evaporative losses in samples of pure titanium and Ti–6Al–4V molten by an electron beam. Finally, the model is applied to create processing maps for an SEBM process. The results predict that the penetration depth of the electron beam, which is a function of the acceleration voltage, has a significant influence on evaporation effects. (paper)

  10. Poisson-Like Spiking in Circuits with Probabilistic Synapses

    Science.gov (United States)

    Moreno-Bote, Rubén

    2014-01-01

    Neuronal activity in cortex is variable both spontaneously and during stimulation, and it has the remarkable property that it is Poisson-like over broad ranges of firing rates covering from virtually zero to hundreds of spikes per second. The mechanisms underlying cortical-like spiking variability over such a broad continuum of rates are currently unknown. We show that neuronal networks endowed with probabilistic synaptic transmission, a well-documented source of variability in cortex, robustly generate Poisson-like variability over several orders of magnitude in their firing rate without fine-tuning of the network parameters. Other sources of variability, such as random synaptic delays or spike generation jittering, do not lead to Poisson-like variability at high rates because they cannot be sufficiently amplified by recurrent neuronal networks. We also show that probabilistic synapses predict Fano factor constancy of synaptic conductances. Our results suggest that synaptic noise is a robust and sufficient mechanism for the type of variability found in cortex. PMID:25032705

  11. A high order solver for the unbounded Poisson equation

    DEFF Research Database (Denmark)

    Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe

    2013-01-01

    . The method is extended to directly solve the derivatives of the solution to Poissonʼs equation. In this way differential operators such as the divergence or curl of the solution field can be solved to the same high order convergence without additional computational effort. The method, is applied......A high order converging Poisson solver is presented, based on the Greenʼs function solution to Poissonʼs equation subject to free-space boundary conditions. The high order convergence is achieved by formulating regularised integration kernels, analogous to a smoothing of the solution field...... and validated, however not restricted, to the equations of fluid mechanics, and can be used in many applications to solve Poissonʼs equation on a rectangular unbounded domain....

  12. Poisson structures for reduced non-holonomic systems

    International Nuclear Information System (INIS)

    Ramos, Arturo

    2004-01-01

    Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the Hamiltonian function being the reduced energy. We study further the algebraic origin of these Poisson structures, showing that they are of rank 2 and therefore the mentioned rescaling is not necessary. We show that they are determined, up to a non-vanishing factor function, by the existence of a system of first-order differential equations providing two integrals of motion. We generalize the form of the Poisson structures and extend their domain of definition. We apply the theory to the rolling disc, the Routh's sphere, the ball rolling on a surface of revolution, and its special case of a ball rolling inside a cylinder

  13. Boltzmann factor and Hawking radiation

    International Nuclear Information System (INIS)

    Ryskin, Gregory

    2014-01-01

    Hawking radiation has thermal spectrum corresponding to the temperature T H =(8πM) −1 , where M is the mass (energy) of the black hole. Corrections to the Hawking radiation spectrum were discovered by Kraus and Wilczek (1995) and Parikh and Wilczek (2000). Here I show that these corrections follow directly from the basic principles of thermodynamics and statistical mechanics. In essence, it is the Boltzmann factor that ought to be corrected; corrections to the Hawking (or any other) radiation spectrum then follow necessarily

  14. Influence of surface charge on the transport characteristics of nanowire-field effect transistors in liquid environments

    Energy Technology Data Exchange (ETDEWEB)

    Nozaki, Daijiro, E-mail: daijiro.nozaki@gmail.com, E-mail: research@nano.tu-dresden.de [Institute for Materials Science and Max Bergmann Center of Biomaterials, TU Dresden, 01062 Dresden (Germany); Kunstmann, Jens [Institute for Materials Science and Max Bergmann Center of Biomaterials, TU Dresden, 01062 Dresden (Germany); Theoretical Chemistry, Department of Chemistry and Food Chemistry, TU Dresden, 01062 Dresden (Germany); Zörgiebel, Felix [Institute for Materials Science and Max Bergmann Center of Biomaterials, TU Dresden, 01062 Dresden (Germany); Center for Advancing Electronics Dresden (cfAED), TU Dresden, 01062 Dresden (Germany); Cuniberti, Gianaurelio [Institute for Materials Science and Max Bergmann Center of Biomaterials, TU Dresden, 01062 Dresden (Germany); Center for Advancing Electronics Dresden (cfAED), TU Dresden, 01062 Dresden (Germany); Dresden Center for Computational Materials Science (DCCMS), TU Dresden, 01062 Dresden (Germany)

    2015-05-18

    One dimensional nanowire field effect transistors (NW-FETs) are a promising platform for sensor applications. The transport characteristics of NW-FETs are strongly modified in liquid environment due to the charging of surface functional groups accompanied with protonation or deprotonation. In order to investigate the influence of surface charges and ionic concentrations on the transport characteristics of Schottky-barrier NW-FETs, we have combined the modified Poisson-Boltzmann theory with the Landauer-Büttiker transport formalism. For a typical device, the model is able to capture the reduction of the sensitivity of NW-FETs in ionic solutions due to the screening from counter ions as well as a local gating from surface functional groups. Our approach allows to model, to investigate, and to optimize realistic Schottky-barrier NW-FET devices in liquid environment.

  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. Numerical simulation of electroosmotic flow in rough microchannels using the lattice Poisson-Nernst-Planck methods

    Science.gov (United States)

    Kamali, Reza; Soloklou, Mohsen Nasiri; Hadidi, Hooman

    2018-05-01

    In this study, coupled Lattice Boltzmann method is applied to solve the dynamic model for an electroosmotic flow and investigate the effects of roughness in a 2-D flat microchannel. In the present model, the Poisson equation is solved for the electrical potential, the Nernst- Planck equation is solved for the ion concentration. In the analysis of electroosmotic flows, when the electric double layers fully overlap or the convective effects are not negligible, the Nernst-Planck equation must be used to find the ionic distribution throughout the microchannel. The effects of surface roughness height, roughness interval spacing and roughness surface potential on flow conditions are investigated for two different configurations of the roughness, when the EDL layers fully overlap through the microchannel. The results show that in both arrangements of roughness in homogeneously charged rough channels, the flow rate decreases by increasing the roughness height. A discrepancy in the mass flow rate is observed when the roughness height is about 0.15 of the channel width, which its average is higher for the asymmetric configuration and this difference grows by increasing the roughness height. In the symmetric roughness arrangement, the mass flow rate increases until the roughness interval space is almost 1.5 times the roughness width and it decreases for higher values of the roughness interval space. For the heterogeneously charged rough channel, when the roughness surface potential ψr is less than channel surface potential ψs , the net charge density increases by getting far from the roughness surface, while in the opposite situation, when ψs is more than ψr , the net charge density decreases from roughness surface to the microchannel middle center. Increasing the roughness surface potential induces stronger electric driving force on the fluid which results in larger velocities in the flow.

  17. Lattice gas cellular automata and lattice Boltzmann models an introduction

    CERN Document Server

    Wolf-Gladrow, Dieter A

    2000-01-01

    Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

  18. Observation of distorted Maxwell-Boltzmann distribution of epithermal ions in LHD

    Science.gov (United States)

    Ida, K.; Kobayashi, T.; Yoshinuma, M.; Akiyama, T.; Tokuzawa, T.; Tsuchiya, H.; Itoh, K.; LHD Experiment Group

    2017-12-01

    A distorted Maxwell-Boltzmann distribution of epithermal ions is observed associated with the collapse of energetic ions triggered by the tongue shaped deformation. The tongue shaped deformation is characterized by the plasma displacement localized in the toroidal, poloidal, and radial directions at the non-rational magnetic flux surface in toroidal plasma. Moment analysis of the ion velocity distribution measured with charge exchange spectroscopy is studied in order to investigate the impact of tongue event on ion distribution. A clear non-zero skewness (3rd moment) and kurtosis (4th moment -3) of ion velocity distribution in the epithermal region (within three times of thermal velocity) is observed after the tongue event. This observation indicates the clear evidence of the distortion of ion velocity distribution from Maxwell-Boltzmann distribution. This distortion from Maxwell-Boltzmann distribution is observed in one-third of plasma minor radius region near the plasma edge and disappears in the ion-ion collision time scale.

  19. Poisson processes

    NARCIS (Netherlands)

    Boxma, O.J.; Yechiali, U.; Ruggeri, F.; Kenett, R.S.; Faltin, F.W.

    2007-01-01

    The Poisson process is a stochastic counting process that arises naturally in a large variety of daily life situations. We present a few definitions of the Poisson process and discuss several properties as well as relations to some well-known probability distributions. We further briefly discuss the

  20. Relativistic Boltzmann theory for a plasma

    International Nuclear Information System (INIS)

    Erkelens, H. van.

    1984-01-01

    This thesis gives a self-contained treatment of the relativistic Boltzmann theory for a plasma. Here plasma means any mixture containing electrically charged particles. The relativistic Boltzmann equation is linearized for the case of a plasma. The Chapman-Enskog method is elaborated further for transport phenomena. Linear laws for viscous phenomena are derived. Then the collision term in the Boltzmann theory is dealt with. Using the transport equation, a kinetic theory of wave phenomena is developed and the dissipation of hydromagnetic waves in a relativistic plasma is investigated. In the final chapter, it is demonstrated how the relativistic Boltzmann theory can be applied in cosmology. In doing so, expressions are derived for the electric conductivity of the cosmological plasma in the lepton era, the plasma era and the annihilation era. (Auth.)

  1. Singular Poisson tensors

    International Nuclear Information System (INIS)

    Littlejohn, R.G.

    1982-01-01

    The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular

  2. Poisson Processes in Free Probability

    OpenAIRE

    An, Guimei; Gao, Mingchu

    2015-01-01

    We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of (compound) Poisson processes in classical probability. We proved that the sum of finitely many freely independent compound free Poisson processes is a compound free Poisson processes. We give a step by step procedure for constructing a (compound) free Poisso...

  3. Surface reconstruction through poisson disk sampling.

    Directory of Open Access Journals (Sweden)

    Wenguang Hou

    Full Text Available This paper intends to generate the approximate Voronoi diagram in the geodesic metric for some unbiased samples selected from original points. The mesh model of seeds is then constructed on basis of the Voronoi diagram. Rather than constructing the Voronoi diagram for all original points, the proposed strategy is to run around the obstacle that the geodesic distances among neighboring points are sensitive to nearest neighbor definition. It is obvious that the reconstructed model is the level of detail of original points. Hence, our main motivation is to deal with the redundant scattered points. In implementation, Poisson disk sampling is taken to select seeds and helps to produce the Voronoi diagram. Adaptive reconstructions can be achieved by slightly changing the uniform strategy in selecting seeds. Behaviors of this method are investigated and accuracy evaluations are done. Experimental results show the proposed method is reliable and effective.

  4. Nambu–Poisson gauge theory

    Energy Technology Data Exchange (ETDEWEB)

    Jurčo, Branislav, E-mail: jurco@karlin.mff.cuni.cz [Charles University in Prague, Faculty of Mathematics and Physics, Mathematical Institute, Prague 186 75 (Czech Republic); Schupp, Peter, E-mail: p.schupp@jacobs-university.de [Jacobs University Bremen, 28759 Bremen (Germany); Vysoký, Jan, E-mail: vysokjan@fjfi.cvut.cz [Jacobs University Bremen, 28759 Bremen (Germany); Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Prague 115 19 (Czech Republic)

    2014-06-02

    We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.

  5. Nambu–Poisson gauge theory

    International Nuclear Information System (INIS)

    Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

    2014-01-01

    We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.

  6. 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

  7. The electric double layer at high surface potentials: The influence of excess ion polarizability

    NARCIS (Netherlands)

    Hatlo, M. M.; van Roij, R.H.H.G.; Lue, L.

    2012-01-01

    By including the excess ion polarizability into the Poisson-Boltzmann theory, we show that the decrease in differential capacitance with voltage, observed for metal electrodes above a threshold potential, can be understood in terms of thickening of the double layer due to ion-induced polarizability

  8. High order Poisson Solver for unbounded flows

    DEFF Research Database (Denmark)

    Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe

    2015-01-01

    This paper presents a high order method for solving the unbounded Poisson equation on a regular mesh using a Green’s function solution. The high order convergence was achieved by formulating mollified integration kernels, that were derived from a filter regularisation of the solution field....... The method was implemented on a rectangular domain using fast Fourier transforms (FFT) to increase computational efficiency. The Poisson solver was extended to directly solve the derivatives of the solution. This is achieved either by including the differential operator in the integration kernel...... the equations of fluid mechanics as an example, but can be used in many physical problems to solve the Poisson equation on a rectangular unbounded domain. For the two-dimensional case we propose an infinitely smooth test function which allows for arbitrary high order convergence. Using Gaussian smoothing...

  9. Numerical solution of Boltzmann's equation

    International Nuclear Information System (INIS)

    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. Perbandingan Regresi Binomial Negatif dan Regresi Conway-Maxwell-Poisson dalam Mengatasi Overdispersi pada Regresi Poisson

    Directory of Open Access Journals (Sweden)

    Lusi Eka Afri

    2017-03-01

    Full Text Available Regresi Binomial Negatif dan regresi Conway-Maxwell-Poisson merupakan solusi untuk mengatasi overdispersi pada regresi Poisson. Kedua model tersebut merupakan perluasan dari model regresi Poisson. Menurut Hinde dan Demetrio (2007, terdapat beberapa kemungkinan terjadi overdispersi pada regresi Poisson yaitu keragaman hasil pengamatan keragaman individu sebagai komponen yang tidak dijelaskan oleh model, korelasi antar respon individu, terjadinya pengelompokan dalam populasi dan peubah teramati yang dihilangkan. Akibatnya dapat menyebabkan pendugaan galat baku yang terlalu rendah dan akan menghasilkan pendugaan parameter yang bias ke bawah (underestimate. Penelitian ini bertujuan untuk membandingan model Regresi Binomial Negatif dan model regresi Conway-Maxwell-Poisson (COM-Poisson dalam mengatasi overdispersi pada data distribusi Poisson berdasarkan statistik uji devians. Data yang digunakan dalam penelitian ini terdiri dari dua sumber data yaitu data simulasi dan data kasus terapan. Data simulasi yang digunakan diperoleh dengan membangkitkan data berdistribusi Poisson yang mengandung overdispersi dengan menggunakan bahasa pemrograman R berdasarkan karakteristik data berupa , peluang munculnya nilai nol (p serta ukuran sampel (n. Data dibangkitkan berguna untuk mendapatkan estimasi koefisien parameter pada regresi binomial negatif dan COM-Poisson.   Kata Kunci: overdispersi, regresi binomial negatif, regresi Conway-Maxwell-Poisson Negative binomial regression and Conway-Maxwell-Poisson regression could be used to overcome over dispersion on Poisson regression. Both models are the extension of Poisson regression model. According to Hinde and Demetrio (2007, there will be some over dispersion on Poisson regression: observed variance in individual variance cannot be described by a model, correlation among individual response, and the population group and the observed variables are eliminated. Consequently, this can lead to low standard error

  11. Soft-Deep Boltzmann Machines

    OpenAIRE

    Kiwaki, Taichi

    2015-01-01

    We present a layered Boltzmann machine (BM) that can better exploit the advantages of a distributed representation. It is widely believed that deep BMs (DBMs) have far greater representational power than its shallow counterpart, restricted Boltzmann machines (RBMs). However, this expectation on the supremacy of DBMs over RBMs has not ever been validated in a theoretical fashion. In this paper, we provide both theoretical and empirical evidences that the representational power of DBMs can be a...

  12. Lattice Boltzmann model for simulating immiscible two-phase flows

    International Nuclear Information System (INIS)

    Reis, T; Phillips, T N

    2007-01-01

    The lattice Boltzmann equation is often promoted as a numerical simulation tool that is particularly suitable for predicting the flow of complex fluids. This paper develops a two-dimensional 9-velocity (D2Q9) lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio using a single relaxation time for each fluid. In the macroscopic limit, this model is shown to recover the Navier-Stokes equations for two-phase flows. This is achieved by constructing a two-phase component of the collision operator that induces the appropriate surface tension term in the macroscopic equations. A theoretical expression for surface tension is determined. The validity of this analysis is confirmed by comparing numerical and theoretical predictions of surface tension as a function of density. The model is also shown to predict Laplace's law for surface tension and Poiseuille flow of layered immiscible binary fluids. The spinodal decomposition of two fluids of equal density but different viscosity is then studied. At equilibrium, the system comprises one large low viscosity bubble enclosed by the more viscous fluid in agreement with theoretical arguments of Renardy and Joseph (1993 Fundamentals of Two-Fluid Dynamics (New York: Springer)). Two other simulations, namely the non-equilibrium rod rest and the coalescence of two bubbles, are performed to show that this model can be used to simulate two fluids with a large density ratio

  13. Topology optimization and lattice Boltzmann methods

    DEFF Research Database (Denmark)

    Nørgaard, Sebastian Arlund

    This thesis demonstrates the application of the lattice Boltzmann method for topology optimization problems. Specifically, the focus is on problems in which time-dependent flow dynamics have significant impact on the performance of the devices to be optimized. The thesis introduces new topology...... a discrete adjoint approach. To handle the complexity of the discrete adjoint approach more easily, a method for computing it based on automatic differentiation is introduced, which can be adapted to any lattice Boltzmann type method. For example, while it is derived in the context of an isothermal lattice...... Boltzmann model, it is shown that the method can be easily extended to a thermal model as well. Finally, the predicted behavior of an optimized design is compared to the equiva-lent prediction from a commercial finite element solver. It is found that the weakly compressible nature of the lattice Boltzmann...

  14. Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow

    International Nuclear Information System (INIS)

    Zheng, Lin; Zheng, Song; Zhai, Qinglan

    2016-01-01

    In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.

  15. Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow

    Energy Technology Data Exchange (ETDEWEB)

    Zheng, Lin, E-mail: lz@njust.edu.cn [School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094 (China); Zheng, Song [School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018 (China); Zhai, Qinglan [School of Economics Management and Law, Chaohu University, Chaohu 238000 (China)

    2016-02-05

    In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.

  16. Modelling and investigation of partial wetting surfaces for drop dynamics using lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Pravinraj, T., E-mail: pravinraj1711@gmail.com; Patrikar, Rajendra

    2017-07-01

    Highlights: • A LBM model on partial wetting surface for droplet dynamics is presented by introducing a simple initial partial wetting boundary condition in SC model. • With our approach one can tune the splitting volume and time by carefully choosing strip width and position. • It is shown that the droplet spreading on chemically heterogeneous surfaces can be controlled not only by Weber number but also by tuning strip width ratio. • The directional transportation of a droplet due to chemical wetting gradient is simulated and analyzed using hybrid thermodynamic-image processing technique. • Microstructure surface and its influence on the directional wetting based transportation of droplet are demonstrated. - Abstract: Partial wetting surfaces and its influence on the droplet movement of micro and nano scale being contemplated for many useful applications. The dynamics of the droplet usually analyzed with a multiphase lattice Boltzmann method (LBM). In this paper, the influence of partial wetting surface on the dynamics of droplet is systematically analyzed for various cases. Splitting of droplets due to chemical gradient of the surface is studied and analyses of splitting time for various widths of the strips for different Weber numbers are computed. With the proposed model one can tune the splitting volume and time by carefully choosing a strip width and droplet position. The droplet spreading on chemically heterogeneous surfaces shows that the spreading can be controlled not only by parameters of Weber number but also by tuning strip width ratio. The transportation of the droplet from hydrophobic surface to hydrophilic surface due to chemical gradient is simulated and analyzed using our hybrid thermodynamic-image processing technique. The results prove that with the progress of time the surface free energy decreases with increase in spreading area. Finally, the transportation of a droplet on microstructure gradient is demonstrated. The model explains

  17. Joint Training of Deep Boltzmann Machines

    OpenAIRE

    Goodfellow, Ian; Courville, Aaron; Bengio, Yoshua

    2012-01-01

    We introduce a new method for training deep Boltzmann machines jointly. Prior methods require an initial learning pass that trains the deep Boltzmann machine greedily, one layer at a time, or do not perform well on classifi- cation tasks.

  18. Enhanced charging kinetics of porous electrodes: surface conduction as a short-circuit mechanism.

    Science.gov (United States)

    Mirzadeh, Mohammad; Gibou, Frederic; Squires, Todd M

    2014-08-29

    We use direct numerical simulations of the Poisson-Nernst-Planck equations to study the charging kinetics of porous electrodes and to evaluate the predictive capabilities of effective circuit models, both linear and nonlinear. The classic transmission line theory of de Levie holds for general electrode morphologies, but only at low applied potentials. Charging dynamics are slowed appreciably at high potentials, yet not as significantly as predicted by the nonlinear transmission line model of Biesheuvel and Bazant. We identify surface conduction as a mechanism which can effectively "short circuit" the high-resistance electrolyte in the bulk of the pores, thus accelerating the charging dynamics and boosting power densities. Notably, the boost in power density holds only for electrode morphologies with continuous conducting surfaces in the charging direction.

  19. Combinatorial optimization on a Boltzmann machine

    NARCIS (Netherlands)

    Korst, J.H.M.; Aarts, E.H.L.

    1989-01-01

    We discuss the problem of solving (approximately) combinatorial optimization problems on a Boltzmann machine. It is shown for a number of combinatorial optimization problems how they can be mapped directly onto a Boltzmann machine by choosing appropriate connection patterns and connection strengths.

  20. Quantum linear Boltzmann equation

    International Nuclear Information System (INIS)

    Vacchini, Bassano; Hornberger, Klaus

    2009-01-01

    We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

  1. The convergence of parallel Boltzmann machines

    NARCIS (Netherlands)

    Zwietering, P.J.; Aarts, E.H.L.; Eckmiller, R.; Hartmann, G.; Hauske, G.

    1990-01-01

    We discuss the main results obtained in a study of a mathematical model of synchronously parallel Boltzmann machines. We present supporting evidence for the conjecture that a synchronously parallel Boltzmann machine maximizes a consensus function that consists of a weighted sum of the regular

  2. Transport in semiconductor nanowire superlattices described by coupled quantum mechanical and kinetic models.

    Science.gov (United States)

    Alvaro, M; Bonilla, L L; Carretero, M; Melnik, R V N; Prabhakar, S

    2013-08-21

    In this paper we develop a kinetic model for the analysis of semiconductor superlattices, accounting for quantum effects. The model consists of a Boltzmann-Poisson type system of equations with simplified Bhatnagar-Gross-Krook collisions, obtained from the general time-dependent Schrödinger-Poisson model using Wigner functions. This system for superlattice transport is supplemented by the quantum mechanical part of the model based on the Ben-Daniel-Duke form of the Schrödinger equation for a cylindrical superlattice of finite radius. The resulting energy spectrum is used to characterize the Fermi-Dirac distribution that appears in the Bhatnagar-Gross-Krook collision, thereby coupling the quantum mechanical and kinetic parts of the model. The kinetic model uses the dispersion relation obtained by the generalized Kronig-Penney method, and allows us to estimate radii of quantum wire superlattices that have the same miniband widths as in experiments. It also allows us to determine more accurately the time-dependent characteristics of superlattices, in particular their current density. Results, for several experimentally grown superlattices, are discussed in the context of self-sustained coherent oscillations of the current density which are important in an increasing range of current and potential applications.

  3. Parallel Boltzmann machines : a mathematical model

    NARCIS (Netherlands)

    Zwietering, P.J.; Aarts, E.H.L.

    1991-01-01

    A mathematical model is presented for the description of parallel Boltzmann machines. The framework is based on the theory of Markov chains and combines a number of previously known results into one generic model. It is argued that parallel Boltzmann machines maximize a function consisting of a

  4. A free-surface lattice Boltzmann method for modelling the filling of expanding cavities by Bingham fluids.

    Science.gov (United States)

    Ginzburg, Irina; Steiner, Konrad

    2002-03-15

    The filling process of viscoplastic metal alloys and plastics in expanding cavities is modelled using the lattice Boltzmann method in two and three dimensions. These models combine the regularized Bingham model for viscoplastic fluids with a free-interface algorithm. The latter is based on a modified immiscible lattice Boltzmann model in which one species is the fluid and the other one is considered to be a vacuum. The boundary conditions at the curved liquid-vacuum interface are met without any geometrical front reconstruction from a first-order Chapman-Enskog expansion. The numerical results obtained with these models are found in good agreement with available theoretical and numerical analysis.

  5. Lattice Boltzmann model for free-surface flow and its application to filling process in casting

    CERN Document Server

    Ginzburg, I

    2003-01-01

    A generalized lattice Boltzmann model to simulate free-surface is constructed in both two and three dimensions. The proposed model satisfies the interfacial boundary conditions accurately. A distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid. To maintain a sharp interfacial front, the method includes an anti-diffusion algorithm. The unknown distribution functions at the interfacial region are constructed according to the first-order Chapman-Enskog analysis. The interfacial boundary conditions are satisfied exactly by the coefficients in the Chapman-Enskog expansion. The distribution functions are naturally expressed in the local interfacial coordinates. The macroscopic quantities at the interface are extracted from the least-square solutions of a locally linearized system obtained from the known distribution functions. The proposed method does not require any geometric front construction and is robust for any interfacial ...

  6. Ethic and Evolution in Boltzmann's and Einstein's Thought

    Energy Technology Data Exchange (ETDEWEB)

    Broda, E.

    1980-07-01

    In physics and to a large extent in epistomology, Einstein was the natural successor to Boltzmann. But while Boltzmann was an ardent evolutionist, Einstein cared little for biology. Boltzmann applied Darwinian principles also to ethics, but remained aloof from politics. In contrast, Einstein's morality, though expressed in magnificent and selfless activity, lacked a firm theoretical basis. (author)

  7. Ethic and Evolution in Boltzmann's and Einstein's Thought

    International Nuclear Information System (INIS)

    Broda, E.

    1980-01-01

    In physics and to a large extent in epistomology, Einstein was the natural successor to Boltzmann. But while Boltzmann was an ardent evolutionist, Einstein cared little for biology. Boltzmann applied Darwinian principles also to ethics, but remained aloof from politics. In contrast, Einstein's morality, though expressed in magnificent and selfless activity, lacked a firm theoretical basis. (author)

  8. Atoms and Ions; Universality, Singularity and Particularity:. on Boltzmann's Vision a Century Later

    Science.gov (United States)

    Fisher, Michael

    2008-12-01

    Ludwig Boltzmann died by his own hand 101 years ago last September. He was a passionate believer in atoms: underlying thermodynamics, he felt, lay a statistical world governed by the mechanics of individual particles. His struggles against critics -- "Have you ever seen an atom?" taunted Ernst Mach -- left him pessimistic. Nevertheless, following Maxwell and clarified by Gibbs, he established the science of Statistical Mechanics. But today, especially granted our understanding of critical singularities and their universality, how much do atomic particles and their charged partners, ions, really matter? The answers we have also met opposition. But Boltzmann would have welcomed the insights gained and approved of applications of statistical dynamics to biology, sociology, and other enterprises. Note from Publisher: This article contains the abstract only.

  9. Exploring cluster Monte Carlo updates with Boltzmann machines.

    Science.gov (United States)

    Wang, Lei

    2017-11-01

    Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.

  10. Exploring cluster Monte Carlo updates with Boltzmann machines

    Science.gov (United States)

    Wang, Lei

    2017-11-01

    Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.

  11. On a Poisson homogeneous space of bilinear forms with a Poisson-Lie action

    Science.gov (United States)

    Chekhov, L. O.; Mazzocco, M.

    2017-12-01

    Let \\mathscr A be the space of bilinear forms on C^N with defining matrices A endowed with a quadratic Poisson structure of reflection equation type. The paper begins with a short description of previous studies of the structure, and then this structure is extended to systems of bilinear forms whose dynamics is governed by the natural action A\\mapsto B ABT} of the {GL}_N Poisson-Lie group on \\mathscr A. A classification is given of all possible quadratic brackets on (B, A)\\in {GL}_N× \\mathscr A preserving the Poisson property of the action, thus endowing \\mathscr A with the structure of a Poisson homogeneous space. Besides the product Poisson structure on {GL}_N× \\mathscr A, there are two other (mutually dual) structures, which (unlike the product Poisson structure) admit reductions by the Dirac procedure to a space of bilinear forms with block upper triangular defining matrices. Further generalisations of this construction are considered, to triples (B,C, A)\\in {GL}_N× {GL}_N× \\mathscr A with the Poisson action A\\mapsto B ACT}, and it is shown that \\mathscr A then acquires the structure of a Poisson symmetric space. Generalisations to chains of transformations and to the quantum and quantum affine algebras are investigated, as well as the relations between constructions of Poisson symmetric spaces and the Poisson groupoid. Bibliography: 30 titles.

  12. Thermal, Microchannel, and Immersed Boundary Extension Validation for the Lattice-Boltzmann Method: Report 2 in Discrete Nano Scale Mechanics and Simulations Series

    Science.gov (United States)

    2017-07-01

    Lattice- Boltzmann Method Report 2 in “Discrete Nano-Scale Mechanics and Simulations” Series In fo rm at io n Te ch no lo gy L ab or at or y...William P. England and Jeffrey B. Allen July 2017 Approved for public release; distribution is unlimited. The U.S. Army Engineer Research and...Development Center (ERDC) solves the nation’s toughest engineering and environmental challenges. ERDC develops innovative solutions in civil and

  13. Homogeneous Poisson structures

    International Nuclear Information System (INIS)

    Shafei Deh Abad, A.; Malek, F.

    1993-09-01

    We provide an algebraic definition for Schouten product and give a decomposition for any homogenenous Poisson structure in any n-dimensional vector space. A large class of n-homogeneous Poisson structures in R k is also characterized. (author). 4 refs

  14. A note on Boltzmann brains

    Energy Technology Data Exchange (ETDEWEB)

    Nomura, Yasunori, E-mail: ynomura@berkeley.edu

    2015-10-07

    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 for the one imposed by the Poincaré recurrence. The framework discussed here also addresses the question of whether a Minkowski vacuum may produce Boltzmann brains.

  15. Particle-wave discrimination in Poisson spot experiments

    International Nuclear Information System (INIS)

    Reisinger, T; Bracco, G; Holst, B

    2011-01-01

    Matter-wave interferometry has been used extensively over the last few years to demonstrate the quantum-mechanical wave nature of increasingly larger and more massive particles. We have recently suggested the use of the historical Poisson spot setup to test the diffraction properties of larger objects. In this paper, we present the results of a classical particle van der Waals (vdW) force model for a Poisson spot experimental setup and compare these to Fresnel diffraction calculations with a vdW phase term. We include the effect of disc-edge roughness in both models. Calculations are performed with D 2 and with C 70 using realistic parameters. We find that the sensitivity of the on-axis interference/focus spot to disc-edge roughness is very different in the two cases. We conclude that by measuring the intensity on the optical axis as a function of disc-edge roughness, it can be determined whether the objects behave as de Broglie waves or classical particles. The scaling of the Poisson spot experiment to larger molecular masses is, however, not as favorable as in the case of near-field light-grating-based interferometers. Instead, we discuss the possibility of studying the Casimir-Polder potential using the Poisson spot setup.

  16. Non-Boltzmann Ensembles and Monte Carlo Simulations

    International Nuclear Information System (INIS)

    Murthy, K. P. N.

    2016-01-01

    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

  17. Lattice Boltzmann study of slip flow over structured surface with transverse slots

    Science.gov (United States)

    Chen, Wei; Wang, Kai; Wang, Lei; Hou, Guoxiang; Leng, Wenjun

    2018-04-01

    Slip flow over structured superhydrophobic surface with transverse slots is investigated by the lattice Boltzmann method. The Shan-Chen multiphase model is employed to simulate the flow over gas bubbles in the slots. The Carnahan-Starling equation of state is applied to obtain large density ratio. The interface thickness of the multiphase model is discussed. We find that the Cahn number Cn should be smaller than 0.02 when the temperature T = 0.5T c to restrict the influence of interface thickness on slip length. Influences of slot fraction on slip length is then studied, and the result is compared with single LB simulation of which the interface is treated as free-slip boundary. The slip length obtained by the multiphase model is a little smaller. After that, the shape of the liquid-gas interface is considered, and simulations with different initial protrusion angles and capillary numbers are performed. Effective slip length as a function of initial protrusion angle is obtained. The result is in qualitative agreement with a previous study and main features are reproduced. Furthermore, the influence of Capillary number Ca is studied. Larger Ca causes larger interface deformation and smaller slip length. But when the interface is concaving into the slot, this influence is less obvious.

  18. High energy ion range and deposited energy calculation using the Boltzmann-Fokker-Planck splitting of the Boltzmann transport equation

    International Nuclear Information System (INIS)

    Mozolevski, I.E.

    2001-01-01

    We consider the splitting of the straight-ahead Boltzmann transport equation in the Boltzmann-Fokker-Planck equation, decomposing the differential cross-section into a singular part, corresponding to small energy transfer events, and in a regular one, which corresponds to large energy transfer. The convergence of implantation profile, nuclear and electronic energy depositions, calculated from the Boltzmann-Fokker-Planck equation, to the respective exact distributions, calculated from Monte-Carlo method, was exanimate in a large-energy interval for various values of splitting parameter and for different ion-target mass relations. It is shown that for the universal potential there exists an optimal value of splitting parameter, for which range and deposited energy distributions, calculated from the Boltzmann-Fokker-Planck equation, accurately approximate the exact distributions and which minimizes the computational expenses

  19. Lattice Boltzmann simulation of endothermal catalytic reaction in catalyst porous media

    International Nuclear Information System (INIS)

    Li Xunfeng; Cai Jun; Xin Fang; Huai Xiulan; Guo Jiangfeng

    2013-01-01

    Gas catalytic reaction in a fixed bed reactor is a general process in chemical industry. The chemical reaction process involves the complex multi-component flow, heat and mass transfer coupling chemical reaction in the catalyst porous structure. The lattice Boltzmann method is developed to simulate the complex process of the surface catalytic reaction in the catalyst porous media. The non-equilibrium extrapolation method is used to treat the boundaries. The porous media is structured by Sierpinski carpet fractal structure. The velocity correction is adopted on the reaction surface. The flow, temperature and concentration fields calculated by the lattice Boltzmann method are compared with those computed by the CFD software. The effects of the inlet velocity, porosity and inlet components ratio on the conversion are also studied. Highlights: ► LBM is developed to simulate the surface catalytic reaction. ► The Sierpinski carpet structure is used to construct the porous media. ► The LBM results are in agreement with the CFD predictions. ► Velocity, temperature and concentration fields are obtained. ► Effects of the velocity, porosity and concentration on conversion are analyzed.

  20. Universal Poisson Statistics of mRNAs with Complex Decay Pathways.

    Science.gov (United States)

    Thattai, Mukund

    2016-01-19

    Messenger RNA (mRNA) dynamics in single cells are often modeled as a memoryless birth-death process with a constant probability per unit time that an mRNA molecule is synthesized or degraded. This predicts a Poisson steady-state distribution of mRNA number, in close agreement with experiments. This is surprising, since mRNA decay is known to be a complex process. The paradox is resolved by realizing that the Poisson steady state generalizes to arbitrary mRNA lifetime distributions. A mapping between mRNA dynamics and queueing theory highlights an identifiability problem: a measured Poisson steady state is consistent with a large variety of microscopic models. Here, I provide a rigorous and intuitive explanation for the universality of the Poisson steady state. I show that the mRNA birth-death process and its complex decay variants all take the form of the familiar Poisson law of rare events, under a nonlinear rescaling of time. As a corollary, not only steady-states but also transients are Poisson distributed. Deviations from the Poisson form occur only under two conditions, promoter fluctuations leading to transcriptional bursts or nonindependent degradation of mRNA molecules. These results place severe limits on the power of single-cell experiments to probe microscopic mechanisms, and they highlight the need for single-molecule measurements. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

  1. Understanding poisson regression.

    Science.gov (United States)

    Hayat, Matthew J; Higgins, Melinda

    2014-04-01

    Nurse investigators often collect study data in the form of counts. Traditional methods of data analysis have historically approached analysis of count data either as if the count data were continuous and normally distributed or with dichotomization of the counts into the categories of occurred or did not occur. These outdated methods for analyzing count data have been replaced with more appropriate statistical methods that make use of the Poisson probability distribution, which is useful for analyzing count data. The purpose of this article is to provide an overview of the Poisson distribution and its use in Poisson regression. Assumption violations for the standard Poisson regression model are addressed with alternative approaches, including addition of an overdispersion parameter or negative binomial regression. An illustrative example is presented with an application from the ENSPIRE study, and regression modeling of comorbidity data is included for illustrative purposes. Copyright 2014, SLACK Incorporated.

  2. Modifications to POISSON

    International Nuclear Information System (INIS)

    Harwood, L.H.

    1981-01-01

    At MSU we have used the POISSON family of programs extensively for magnetic field calculations. In the presently super-saturated computer situation, reducing the run time for the program is imperative. Thus, a series of modifications have been made to POISSON to speed up convergence. Two of the modifications aim at having the first guess solution as close as possible to the final solution. The other two aim at increasing the convergence rate. In this discussion, a working knowledge of POISSON is assumed. The amount of new code and expected time saving for each modification is discussed

  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. Painleve test and discrete Boltzmann equations

    International Nuclear Information System (INIS)

    Euler, N.; Steeb, W.H.

    1989-01-01

    The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs

  5. A numerical model for simulating electroosmotic micro- and nanochannel flows under non-Boltzmann equilibrium

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Kyoungjin; Kwak, Ho Sang [School of Mechanical Engineering, Kumoh National Institute of Technology, 1 Yangho, Gumi, Gyeongbuk 730-701 (Korea, Republic of); Song, Tae-Ho, E-mail: kimkj@kumoh.ac.kr, E-mail: hskwak@kumoh.ac.kr, E-mail: thsong@kaist.ac.kr [Department of Mechanical, Aerospace and Systems Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong, Yuseong, Daejeon 305-701 (Korea, Republic of)

    2011-08-15

    This paper describes a numerical model for simulating electroosmotic flows (EOFs) under non-Boltzmann equilibrium in a micro- and nanochannel. The transport of ionic species is represented by employing the Nernst-Planck equation. Modeling issues related to numerical difficulties are discussed, which include the handling of boundary conditions based on surface charge density, the associated treatment of electric potential and the evasion of nonlinearity due to the electric body force. The EOF in the entrance region of a straight channel is examined. The numerical results show that the present model is useful for the prediction of the EOFs requiring a fine resolution of the electric double layer under either the Boltzmann equilibrium or non-equilibrium. Based on the numerical results, the correlation between the surface charge density and the zeta potential is investigated.

  6. A new method for extracting near-surface mass-density anomalies from land-based gravity data, based on a special case of Poisson's PDE at the Earth's surface: A case study of salt diapirs in the south of Iran

    Science.gov (United States)

    AllahTavakoli, Y.; Safari, A.; Ardalan, A.; Bahroudi, A.

    2015-12-01

    The current research provides a method for tracking near-surface mass-density anomalies via using only land-based gravity data, which is based on a special version of Poisson's Partial Differential Equation (PDE) of the gravitational field at Earth's surface. The research demonstrates how the Poisson's PDE can provide us with a capability to extract the near-surface mass-density anomalies from land-based gravity data. Herein, this version of the Poisson's PDE is mathematically introduced to the Earth's surface and then it is used to develop the new method for approximating the mass-density via derivatives of the Earth's gravitational field (i.e. via the gradient tensor). Herein, the author believes that the PDE can give us new knowledge about the behavior of the Earth's gravitational field at the Earth's surface which can be so useful for developing new methods of Earth's mass-density determination. In a case study, the proposed method is applied to a set of gravity stations located in the south of Iran. The results were numerically validated via certain knowledge about the geological structures in the area of the case study. Also, the method was compared with two standard methods of mass-density determination. All the numerical experiments show that the proposed approach is well-suited for tracking near-surface mass-density anomalies via using only the gravity data. Finally, the approach is also applied to some petroleum exploration studies of salt diapirs in the south of Iran.

  7. Four-dimensional gravity as an almost-Poisson system

    Science.gov (United States)

    Ita, Eyo Eyo

    2015-04-01

    In this paper, we examine the phase space structure of a noncanonical formulation of four-dimensional gravity referred to as the Instanton representation of Plebanski gravity (IRPG). The typical Hamiltonian (symplectic) approach leads to an obstruction to the definition of a symplectic structure on the full phase space of the IRPG. We circumvent this obstruction, using the Lagrange equations of motion, to find the appropriate generalization of the Poisson bracket. It is shown that the IRPG does not support a Poisson bracket except on the vector constraint surface. Yet there exists a fundamental bilinear operation on its phase space which produces the correct equations of motion and induces the correct transformation properties of the basic fields. This bilinear operation is known as the almost-Poisson bracket, which fails to satisfy the Jacobi identity and in this case also the condition of antisymmetry. We place these results into the overall context of nonsymplectic systems.

  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. Monte Carlo variance reduction approaches for non-Boltzmann tallies

    International Nuclear Information System (INIS)

    Booth, T.E.

    1992-12-01

    Quantities that depend on the collective effects of groups of particles cannot be obtained from the standard Boltzmann transport equation. Monte Carlo estimates of these quantities are called non-Boltzmann tallies and have become increasingly important recently. Standard Monte Carlo variance reduction techniques were designed for tallies based on individual particles rather than groups of particles. Experience with non-Boltzmann tallies and analog Monte Carlo has demonstrated the severe limitations of analog Monte Carlo for many non-Boltzmann tallies. In fact, many calculations absolutely require variance reduction methods to achieve practical computation times. Three different approaches to variance reduction for non-Boltzmann tallies are described and shown to be unbiased. The advantages and disadvantages of each of the approaches are discussed

  10. Non-equal-time Poisson brackets

    OpenAIRE

    Nikolic, H.

    1998-01-01

    The standard definition of the Poisson brackets is generalized to the non-equal-time Poisson brackets. Their relationship to the equal-time Poisson brackets, as well as to the equal- and non-equal-time commutators, is discussed.

  11. A comparative study of the lattice Boltzmann and volume of fluid method for the rising bubble flows

    Energy Technology Data Exchange (ETDEWEB)

    Ryu, Seung Yeob; Park, Cheon Tae; Choi, Suhn [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2010-10-15

    Recently, the lattice Boltzmann method (LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with the way multiphase flows, complex geometries and interfacial dynamics may be treated. Nevertheless, the LBM is considered as a mere alternative CFD tools, not a promising approach. The motion of the bubbles in a liquid has been the focus of both academic and practical interest. The central problem is the relationship between the rise velocity, bubble shape due to the interface deformation and flow field. The buoyancy effect due to density difference in the two phase flows is characterized with Eotvos and Morton numbers. In this study, a single bubble rising under a buoyancy is simulated with LBM and VOF based on conventional CFD method. The two simulation results are compared with the previous experiments. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows

  12. A comparative study of the lattice Boltzmann and volume of fluid method for the rising bubble flows

    International Nuclear Information System (INIS)

    Ryu, Seung Yeob; Park, Cheon Tae; Choi, Suhn

    2010-01-01

    Recently, the lattice Boltzmann method (LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with the way multiphase flows, complex geometries and interfacial dynamics may be treated. Nevertheless, the LBM is considered as a mere alternative CFD tools, not a promising approach. The motion of the bubbles in a liquid has been the focus of both academic and practical interest. The central problem is the relationship between the rise velocity, bubble shape due to the interface deformation and flow field. The buoyancy effect due to density difference in the two phase flows is characterized with Eotvos and Morton numbers. In this study, a single bubble rising under a buoyancy is simulated with LBM and VOF based on conventional CFD method. The two simulation results are compared with the previous experiments. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows

  13. Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels

    International Nuclear Information System (INIS)

    Liu, Jinn-Liang; Eisenberg, Bob

    2014-01-01

    A Poisson-Nernst-Planck-Fermi (PNPF) theory is developed for studying ionic transport through biological ion channels. Our goal is to deal with the finite size of particle using a Fermi like distribution without calculating the forces between the particles, because they are both expensive and tricky to compute. We include the steric effect of ions and water molecules with nonuniform sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of water molecules in an inhomogeneous aqueous electrolyte. Including the finite volume of water and the voids between particles is an important new part of the theory presented here. Fermi like distributions of all particle species are derived from the volume exclusion of classical particles. Volume exclusion and the resulting saturation phenomena are especially important to describe the binding and permeation mechanisms of ions in a narrow channel pore. The Gibbs free energy of the Fermi distribution reduces to that of a Boltzmann distribution when these effects are not considered. The classical Gibbs entropy is extended to a new entropy form — called Gibbs-Fermi entropy — that describes mixing configurations of all finite size particles and voids in a thermodynamic system where microstates do not have equal probabilities. The PNPF model describes the dynamic flow of ions, water molecules, as well as voids with electric fields and protein charges. The model also provides a quantitative mean-field description of the charge/space competition mechanism of particles within the highly charged and crowded channel pore. The PNPF results are in good accord with experimental currents recorded in a 10 8 -fold range of Ca 2+ concentrations. The results illustrate the anomalous mole fraction effect, a signature of L-type calcium channels. Moreover, numerical results concerning water density, dielectric permittivity, void volume, and steric energy provide useful details to

  14. Branes in Poisson sigma models

    International Nuclear Information System (INIS)

    Falceto, Fernando

    2010-01-01

    In this review we discuss possible boundary conditions (branes) for the Poisson sigma model. We show how to carry out the perturbative quantization in the presence of a general pre-Poisson brane and how this is related to the deformation quantization of Poisson structures. We conclude with an open problem: the perturbative quantization of the system when the boundary has several connected components and we use a different pre-Poisson brane in every component.

  15. 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 ...

  16. Extended Poisson Exponential Distribution

    Directory of Open Access Journals (Sweden)

    Anum Fatima

    2015-09-01

    Full Text Available A new mixture of Modified Exponential (ME and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.

  17. Poisson branching point processes

    International Nuclear Information System (INIS)

    Matsuo, K.; Teich, M.C.; Saleh, B.E.A.

    1984-01-01

    We investigate the statistical properties of a special branching point process. The initial process is assumed to be a homogeneous Poisson point process (HPP). The initiating events at each branching stage are carried forward to the following stage. In addition, each initiating event independently contributes a nonstationary Poisson point process (whose rate is a specified function) located at that point. The additional contributions from all points of a given stage constitute a doubly stochastic Poisson point process (DSPP) whose rate is a filtered version of the initiating point process at that stage. The process studied is a generalization of a Poisson branching process in which random time delays are permitted in the generation of events. Particular attention is given to the limit in which the number of branching stages is infinite while the average number of added events per event of the previous stage is infinitesimal. In the special case when the branching is instantaneous this limit of continuous branching corresponds to the well-known Yule--Furry process with an initial Poisson population. The Poisson branching point process provides a useful description for many problems in various scientific disciplines, such as the behavior of electron multipliers, neutron chain reactions, and cosmic ray showers

  18. Non linear Euler-Poisson system. Part 1: global existence of low entropy solutions

    International Nuclear Information System (INIS)

    Cordier, S.

    1995-05-01

    In this work a 1-D model of electrons and ions plasma is considered. Electrons are supposed to be in Maxwell-Boltzmann thermodynamic equilibrium while ions are described with an isothermal flow model of charged particles submitted to a self-consistent electric field. A collision term between neutral particles and ions simulates the presence of neutral particles. This work demonstrates the existence of low entropy solutions for this simple model with arbitrary initial conditions. Most of the paper is devoted to the demonstration of this theorem and follows the successive steps: construction of a numerical scheme, recall of the classical properties of Riemann problem solutions using Glimm method, uniform estimations for the whole variation norm, and finally, convergence of the constructed solutions towards a low entropy solution for the non-linear Euler/Poisson system. Domains of application for this type of model are listed in the conclusion. (J.S.). 18 refs

  19. Flavored quantum Boltzmann equations

    International Nuclear Information System (INIS)

    Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean

    2010-01-01

    We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.

  20. Long-range correlations in Boltzmann-Langevin model

    International Nuclear Information System (INIS)

    Ayik, S.

    1994-01-01

    The average phase-space density described by the Boltzmann-Langevin model can largely deviate from the one provided by the Boltzmann-Uhling-Uhlenbeck model, due to the non-linear evolution of density fluctuations. This aspect is investigated for long-wavelength, small density fluctuations in the framework of a memory incorporated Boltzmann-Langevin model. It is shown that the correlations associated with density fluctuations yield a collision term describing coupling between the collective vibrations and the single-particle degrees of freedom, which may play an important role in damping of collective motion in both the stable and unstable regions. (orig.)

  1. Boltzmann-Gaussian transition under specific noise effect

    International Nuclear Information System (INIS)

    Anh, Chu Thuy; Lan, Nguyen Tri; Viet, Nguyen Ai

    2014-01-01

    It is observed that a short time data set of market returns presents almost symmetric Boltzmann distribution whereas a long time data set tends to show a Gaussian distribution. To understand this universal phenomenon, many hypotheses which are spreading in a wide range of interdisciplinary research were proposed. In current work, the effects of background fluctuations on symmetric Boltzmann distribution is investigated. The numerical calculation is performed to show that the Gaussian noise may cause the transition from initial Boltzmann distribution to Gaussian one. The obtained results would reflect non-dynamic nature of the transition under consideration.

  2. Biomolecular surface construction by PDE transform.

    Science.gov (United States)

    Zheng, Qiong; Yang, Siyang; Wei, Guo-Wei

    2012-03-01

    This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high-order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the spatial resolution. The present work provides a new variational derivation of high-order PDE transforms. The fast Fourier transform is utilized to accomplish the PDE transform so as to avoid stringent stability constraints in solving high-order PDEs. As a consequence, the time integration of high-order PDEs can be done efficiently with the fast Fourier transform. The present approach is validated with a variety of test examples in two-dimensional and three-dimensional settings. We explore the impact of the PDE transform parameters, such as the PDE order and propagation time, on the quality of resulting surfaces. Additionally, we utilize a set of 10 proteins to compare the computational efficiency of the present surface generation method and a standard approach in Cartesian meshes. Moreover, we analyze the present method by examining some benchmark indicators of biomolecular surface, that is, surface area, surface-enclosed volume, solvation free energy, and surface electrostatic potential. A test set of 13 protein molecules is used in the present investigation. The electrostatic analysis is carried out via the Poisson-Boltzmann equation model. To further demonstrate the utility of the present PDE transform-based surface method, we solve the Poisson-Nernst-Planck equations with a PDE transform surface of a protein. Second-order convergence is observed for the electrostatic potential and concentrations. Finally, to test the capability and efficiency of the present PDE transform-based surface generation method, we apply it to the construction of an excessively large biomolecule, a

  3. On (co)homology of Frobenius Poisson algebras

    OpenAIRE

    Zhu, Can; Van Oystaeyen, Fred; ZHANG, Yinhuo

    2014-01-01

    In this paper, we study Poisson (co)homology of a Frobenius Poisson algebra. More precisely, we show that there exists a duality between Poisson homology and Poisson cohomology of Frobenius Poisson algebras, similar to that between Hochschild homology and Hochschild cohomology of Frobenius algebras. Then we use the non-degenerate bilinear form on a unimodular Frobenius Poisson algebra to construct a Batalin-Vilkovisky structure on the Poisson cohomology ring making it into a Batalin-Vilkovisk...

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

    International Nuclear Information System (INIS)

    Yan-Yan, Chen; Hua-Bing, Li; Hou-Hui, Yi

    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

  5. Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena

    International Nuclear Information System (INIS)

    Lin Chuan-Dong; Li Ying-Jun; Xu Ai-Guo; Zhang Guang-Cai

    2014-01-01

    A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier—Stokes equations, including contribution of chemical reaction, via the Chapman—Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  6. Normal forms in Poisson geometry

    NARCIS (Netherlands)

    Marcut, I.T.

    2013-01-01

    The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric

  7. Lattice Boltzmann method used to simulate particle motion in a conduit

    Czech Academy of Sciences Publication Activity Database

    Dolanský, Jindřich; Chára, Zdeněk; Vlasák, Pavel; Kysela, Bohuš

    2017-01-01

    Roč. 65, č. 2 (2017), s. 105-113 ISSN 0042-790X R&D Projects: GA ČR GA15-18870S Institutional support: RVO:67985874 Keywords : Lattice Boltzmann method * particle motion * particle–fluid interaction * PIV * particle tracking Subject RIV: BK - Fluid Dynamics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.654, year: 2016

  8. Drying paint: from micro-scale dynamics to mechanical instabilities

    Science.gov (United States)

    Goehring, Lucas; Li, Joaquim; Kiatkirakajorn, Pree-Cha

    2017-04-01

    Charged colloidal dispersions make up the basis of a broad range of industrial and commercial products, from paints to coatings and additives in cosmetics. During drying, an initially liquid dispersion of such particles is slowly concentrated into a solid, displaying a range of mechanical instabilities in response to highly variable internal pressures. Here we summarize the current appreciation of this process by pairing an advection-diffusion model of particle motion with a Poisson-Boltzmann cell model of inter-particle interactions, to predict the concentration gradients in a drying colloidal film. We then test these predictions with osmotic compression experiments on colloidal silica, and small-angle X-ray scattering experiments on silica dispersions drying in Hele-Shaw cells. Finally, we use the details of the microscopic physics at play in these dispersions to explore how two macroscopic mechanical instabilities-shear-banding and fracture-can be controlled. This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

  9. Hypersonic Shock Wave Computations Using the Generalized Boltzmann Equation

    Science.gov (United States)

    Agarwal, Ramesh; Chen, Rui; Cheremisin, Felix G.

    2006-11-01

    Hypersonic shock structure in diatomic gases is computed by solving the Generalized Boltzmann Equation (GBE), where the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively [1]. The computational framework available for the standard Boltzmann equation [2] is extended by including both the rotational and vibrational degrees of freedom in the GBE. There are two main difficulties encountered in computation of high Mach number flows of diatomic gases with internal degrees of freedom: (1) a large velocity domain is needed for accurate numerical description of the distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 energy levels are needed for accurate representation of the rotational spectrum of the gas. Our methodology addresses these problems, and as a result the efficiency of calculations has increased by several orders of magnitude. The code has been validated by computing the shock structure in Nitrogen for Mach numbers up to 25 including the translational and rotational degrees of freedom. [1] Beylich, A., ``An Interlaced System for Nitrogen Gas,'' Proc. of CECAM Workshop, ENS de Lyon, France, 2000. [2] Cheremisin, F., ``Solution of the Boltzmann Kinetic Equation for High Speed Flows of a Rarefied Gas,'' Proc. of the 24th Int. Symp. on Rarefied Gas Dynamics, Bari, Italy, 2004.

  10. Ludwig Boltzmann - The Man and His Work

    International Nuclear Information System (INIS)

    Broda, E.

    1982-01-01

    It is argued that Ludwig Boltzmann was, along with Newton and Maxwell, one of the three greatest theoretical physicists of classical times. It is less generally known that he was also a powerful realist-materialist philosopher and a keen opponent of Ernst Mach's positivism and of the philosophical idealism of Berkeley, Hegel and Schopenhauer. Boltzmann was also opposed to Kant. Moreover, he had a lively interest in biology and especially in Darwinian evolution, and he should be taken as one of the founders of biophysics. Boltzmann discussed the origin of life and of the mind. Finally, he also was a most vigorous, colourful and attractive person. (author)

  11. Modeling and analysis of surface potential of single gate fully depleted SOI MOSFET using 2D-Poisson's equation

    Science.gov (United States)

    Mani, Prashant; Tyagi, Chandra Shekhar; Srivastav, Nishant

    2016-03-01

    In this paper the analytical solution of the 2D Poisson's equation for single gate Fully Depleted SOI (FDSOI) MOSFET's is derived by using a Green's function solution technique. The surface potential is calculated and the threshold voltage of the device is minimized for the low power consumption. Due to minimization of threshold voltage the short channel effect of device is suppressed and after observation we obtain the device is kink free. The structure and characteristics of SingleGate FDSOI MOSFET were matched by using MathCAD and silvaco respectively.

  12. Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes

    Science.gov (United States)

    Orsingher, Enzo; Polito, Federico

    2012-08-01

    In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes N α ( t), N β ( t), t>0, we have that N_{α}(N_{β}(t)) stackrel{d}{=} sum_{j=1}^{N_{β}(t)} Xj, where the X j s are Poisson random variables. We present a series of similar cases, where the outer process is Poisson with different inner processes. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form N_{α}(tauk^{ν}), ν∈(0,1], where tauk^{ν} is the inverse of the fractional Poisson process, and we show how these compositions can be represented as random sums. Furthermore we study compositions of the form Θ( N( t)), t>0, which can be represented as random products. The last section is devoted to studying continued fractions of Cauchy random variables with a Poisson number of levels. We evaluate the exact distribution and derive the scale parameter in terms of ratios of Fibonacci numbers.

  13. Boltzmann hierarchy for interacting neutrinos I: formalism

    International Nuclear Information System (INIS)

    Oldengott, Isabel M.; Rampf, Cornelius; Wong, Yvonne Y.Y.

    2015-01-01

    Starting from the collisional Boltzmann equation, we derive for the first time and from first principles the Boltzmann hierarchy for neutrinos including interactions with a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. We study two limits of the scalar mass: (i) An extremely massive scalar whose only role is to mediate an effective 4-fermion neutrino-neutrino interaction, and (ii) a massless scalar that can be produced in abundance and thus demands its own Boltzmann hierarchy. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino/scalar Boltzmann hierarchies contain additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino-neutrino and neutrino-scalar interactions. This necessitates that we track each momentum mode of the phase space distributions individually, even if the particles were massless. Comparing our hierarchy with the commonly used (c eff 2 ,c vis 2 )-parameterisation, we find no formal correspondence between the two approaches, which raises the question of whether the latter parameterisation even has an interpretation in terms of particle scattering. Lastly, although we have invoked majoron-like models as a motivation for our study, our treatment is in fact generally applicable to all scenarios in which the neutrino and/or other ultrarelativistic fermions interact with scalar particles

  14. Derivation of the Second Law of Thermodynamics from Boltzmann's Distribution Law.

    Science.gov (United States)

    Nelson, P. G.

    1988-01-01

    Shows how the thermodynamic condition for equilibrium in an isolated system can be derived by the application of Boltzmann's law to a simple physical system. States that this derivation could be included in an introductory course on chemical equilibrium to help prepare students for a statistical mechanical treatment presented in the curriculum.…

  15. Collisionless Boltzmann equation approach for the study of stellar discs within barred galaxies

    Science.gov (United States)

    Bienaymé, Olivier

    2018-04-01

    We have studied the kinematics of stellar disc populations within the solar neighbourhood in order to find the imprints of the Galactic bar. We carried out the analysis by developing a numerical resolution of the 2D2V (two-dimensional in the physical space, 2D, and two-dimensional in the velocity motion, 2V) collisionless Boltzmann equation and modelling the stellar motions within the plane of the Galaxy within the solar neighbourhood. We recover similar results to those obtained by other authors using N-body simulations, but we are also able to numerically identify faint structures thanks to the cancelling of the Poisson noise. We find that the ratio of the bar pattern speed to the local circular frequency is in the range ΩB/Ω = 1.77 to 1.91. If the Galactic bar angle orientation is within the range from 24 to 45 degrees, the bar pattern speed is between 46 and 49 km s-1 kpc-1.

  16. Pseudopotential multi-relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio

    International Nuclear Information System (INIS)

    Shan Ming-Lei; Zhu Chang-Ping; Yao Cheng; Yin Cheng; Jiang Xiao-Yan

    2016-01-01

    The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multi-relaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling. (paper)

  17. A twisted generalization of Novikov-Poisson algebras

    OpenAIRE

    Yau, Donald

    2010-01-01

    Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products and several kinds of twistings. Necessary and sufficient conditions are given under which Hom-Novikov-Poisson algebras give rise to Hom-Poisson algebras.

  18. Poisson hierarchy of discrete strings

    International Nuclear Information System (INIS)

    Ioannidou, Theodora; Niemi, Antti J.

    2016-01-01

    The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

  19. Poisson hierarchy of discrete strings

    Energy Technology Data Exchange (ETDEWEB)

    Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)

    2016-01-28

    The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

  20. Accurate Solution of Multi-Region Continuum Biomolecule Electrostatic Problems Using the Linearized Poisson-Boltzmann Equation with Curved Boundary Elements

    Science.gov (United States)

    Altman, Michael D.; Bardhan, Jaydeep P.; White, Jacob K.; Tidor, Bruce

    2009-01-01

    We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson–Boltzmann equation. Motivating this implementation is the desire to create a solver capable of precisely describing the geometries and topologies prevalent in continuum models of biological molecules. This implementation is enabled by the synthesis of four technologies developed or implemented specifically for this work. First, molecular and accessible surfaces used to describe dielectric and ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce molecular geometries. Second, we avoided explicitly forming the dense BEM matrices and instead solved the linear systems with a preconditioned iterative method (GMRES), using a matrix compression algorithm (FFTSVD) to accelerate matrix-vector multiplication. Third, robust numerical integration methods were employed to accurately evaluate singular and near-singular integrals over the curved boundary elements. Finally, we present a general boundary-integral approach capable of modeling an arbitrary number of embedded homogeneous dielectric regions with differing dielectric constants, possible salt treatment, and point charges. A comparison of the presented BEM implementation and standard finite-difference techniques demonstrates that for certain classes of electrostatic calculations, such as determining absolute electrostatic solvation and rigid-binding free energies, the improved convergence properties of the BEM approach can have a significant impact on computed energetics. We also demonstrate that the improved accuracy offered by the curved-element BEM is important when more sophisticated techniques, such as non-rigid-binding models, are used to compute the relative electrostatic effects of molecular modifications. In addition, we show that electrostatic calculations requiring multiple solves using the same molecular geometry

  1. Global existence proof for relativistic Boltzmann equation

    International Nuclear Information System (INIS)

    Dudynski, M.; Ekiel-Jezewska, M.L.

    1992-01-01

    The existence and causality of solutions to the relativistic Boltzmann equation in L 1 and in L loc 1 are proved. The solutions are shown to satisfy physically natural a priori bounds, time-independent in L 1 . The results rely upon new techniques developed for the nonrelativistic Boltzmann equation by DiPerna and Lions

  2. Quantization of the Poisson SU(2) and its Poisson homogeneous space - the 2-sphere

    International Nuclear Information System (INIS)

    Sheu, A.J.L.

    1991-01-01

    We show that deformation quantizations of the Poisson structures on the Poisson Lie group SU(2) and its homogeneous space, the 2-sphere, are compatible with Woronowicz's deformation quantization of SU(2)'s group structure and Podles' deformation quantization of 2-sphere's homogeneous structure, respectively. So in a certain sense the multiplicativity of the Lie Poisson structure on SU(2) at the classical level is preserved under quantization. (orig.)

  3. Cumulative Poisson Distribution Program

    Science.gov (United States)

    Bowerman, Paul N.; Scheuer, Ernest M.; Nolty, Robert

    1990-01-01

    Overflow and underflow in sums prevented. Cumulative Poisson Distribution Program, CUMPOIS, one of two computer programs that make calculations involving cumulative Poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), used independently of one another. CUMPOIS determines cumulative Poisson distribution, used to evaluate cumulative distribution function (cdf) for gamma distributions with integer shape parameters and cdf for X (sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Written in C.

  4. Quantum Heat Engine and Negative Boltzmann Temperature

    International Nuclear Information System (INIS)

    Xi Jing-Yi; Quan Hai-Tao

    2017-01-01

    To clarify the ambiguity on negative Boltzmann temperature in literature, we study the Carnot and the Otto cycle with one of the heat reservoirs at the negative Boltzmann temperature based on a canonical ensemble description. The work extraction, entropy production and the efficiency of these cycles are explored. Conditions for constructing and properties of these thermodynamic cycles are elucidated. We find that the apparent “violation” of the second law of thermodynamics in these cycles are due to the fact that the traditional definition of thermodynamic efficiency is inappropriate in this situation. When properly understanding the efficiency and the adiabatic processes, in which the system crosses over “absolute ZERO” in a limit sense, the Carnot cycle with one of the heat reservoirs at a negative Boltzmann temperature can be understood straightforwardly, and it contradicts neither the second nor the third law of thermodynamics. Hence, negative Boltzmann temperature is a consistent concept in thermodynamics. We use a two-level system and an Ising spin system to illustrate our central results. (paper)

  5. Nonlinear Poisson equation for heterogeneous media.

    Science.gov (United States)

    Hu, Langhua; Wei, Guo-Wei

    2012-08-22

    The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  6. Influence of Poisson's ratio variation on lateral spring constant of atomic force microscopy cantilevers

    International Nuclear Information System (INIS)

    Yeh, M.-K.; Tai, N.-Ha; Chen, B.-Y.

    2008-01-01

    Atomic force microscopy (AFM) can be used to measure the surface morphologies and the mechanical properties of nanostructures. The force acting on the AFM cantilever can be obtained by multiplying the spring constant of AFM cantilever and the corresponding deformation. To improve the accuracy of force experiments, the spring constant of AFM cantilever must be calibrated carefully. Many methods, such as theoretical equations, the finite element method, and the use of reference cantilever, were reported to obtain the spring constant of AFM cantilevers. For the cantilever made of single crystal, the Poisson's ratio varies with different cantilever-crystal angles. In this paper, the influences of Poisson's ratio variation on the lateral spring constant and axial spring constant of rectangular and V-shaped AFM cantilevers, with different tilt angles and normal forces, were investigated by the finite element analysis. When the cantilever's tilt angle is 20 deg. and the Poisson's ratio varies from 0.02 to 0.4, the finite element results show that the lateral spring constants decrease 11.75% for the rectangular cantilever with 1 μN landing force and decrease 18.60% for the V-shaped cantilever with 50 nN landing force, respectively. The influence of Poisson's ratio variation on axial spring constant is less than 3% for both rectangular and V-shaped cantilevers. As the tilt angle increases, the axial spring constants for rectangular and V-shaped cantilevers decrease substantially. The results obtained can be used to improve the accuracy of the lateral force measurement when using atomic force microscopy

  7. Boltzmann machines as a model for parallel annealing

    NARCIS (Netherlands)

    Aarts, E.H.L.; Korst, J.H.M.

    1991-01-01

    The potential of Boltzmann machines to cope with difficult combinatorial optimization problems is investigated. A discussion of various (parallel) models of Boltzmann machines is given based on the theory of Markov chains. A general strategy is presented for solving (approximately) combinatorial

  8. 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.

  9. Ionic Size Effects: Generalized Boltzmann Distributions, Counterion Stratification, and Modified Debye Length.

    Science.gov (United States)

    Liu, Bo; Liu, Pei; Xu, Zhenli; Zhou, Shenggao

    2013-10-01

    Near a charged surface, counterions of different valences and sizes cluster; and their concentration profiles stratify. At a distance from such a surface larger than the Debye length, the electric field is screened by counterions. Recent studies by a variational mean-field approach that includes ionic size effects and by Monte Carlo simulations both suggest that the counterion stratification is determined by the ionic valence-to-volume ratios. Central in the mean-field approach is a free-energy functional of ionic concentrations in which the ionic size effects are included through the entropic effect of solvent molecules. The corresponding equilibrium conditions define the generalized Boltzmann distributions relating the ionic concentrations to the electrostatic potential. This paper presents a detailed analysis and numerical calculations of such a free-energy functional to understand the dependence of the ionic charge density on the electrostatic potential through the generalized Boltzmann distributions, the role of ionic valence-to-volume ratios in the counterion stratification, and the modification of Debye length due to the effect of ionic sizes.

  10. Poisson equation in the Kohn-Sham Coulomb problem

    OpenAIRE

    Manby, F. R.; Knowles, Peter James

    2001-01-01

    We apply the Poisson equation to the quantum mechanical Coulomb problem for many-particle systems. By introducing a suitable basis set, the two-electron Coulomb integrals become simple overlaps. This offers the possibility of very rapid linear-scaling treatment of the Coulomb contribution to Kohn-Sham theory.

  11. Poisson's ratio of fiber-reinforced composites

    Science.gov (United States)

    Christiansson, Henrik; Helsing, Johan

    1996-05-01

    Poisson's ratio flow diagrams, that is, the Poisson's ratio versus the fiber fraction, are obtained numerically for hexagonal arrays of elastic circular fibers in an elastic matrix. High numerical accuracy is achieved through the use of an interface integral equation method. Questions concerning fixed point theorems and the validity of existing asymptotic relations are investigated and partially resolved. Our findings for the transverse effective Poisson's ratio, together with earlier results for random systems by other authors, make it possible to formulate a general statement for Poisson's ratio flow diagrams: For composites with circular fibers and where the phase Poisson's ratios are equal to 1/3, the system with the lowest stiffness ratio has the highest Poisson's ratio. For other choices of the elastic moduli for the phases, no simple statement can be made.

  12. Soft network materials with isotropic negative Poisson's ratios over large strains.

    Science.gov (United States)

    Liu, Jianxing; Zhang, Yihui

    2018-01-31

    Auxetic materials with negative Poisson's ratios have important applications across a broad range of engineering areas, such as biomedical devices, aerospace engineering and automotive engineering. A variety of design strategies have been developed to achieve artificial auxetic materials with controllable responses in the Poisson's ratio. The development of designs that can offer isotropic negative Poisson's ratios over large strains can open up new opportunities in emerging biomedical applications, which, however, remains a challenge. Here, we introduce deterministic routes to soft architected materials that can be tailored precisely to yield the values of Poisson's ratio in the range from -1 to 1, in an isotropic manner, with a tunable strain range from 0% to ∼90%. The designs rely on a network construction in a periodic lattice topology, which incorporates zigzag microstructures as building blocks to connect lattice nodes. Combined experimental and theoretical studies on broad classes of network topologies illustrate the wide-ranging utility of these concepts. Quantitative mechanics modeling under both infinitesimal and finite deformations allows the development of a rigorous design algorithm that determines the necessary network geometries to yield target Poisson ratios over desired strain ranges. Demonstrative examples in artificial skin with both the negative Poisson's ratio and the nonlinear stress-strain curve precisely matching those of the cat's skin and in unusual cylindrical structures with engineered Poisson effect and shape memory effect suggest potential applications of these network materials.

  13. Acoustic Phonons and Mechanical Properties of Ultra-Thin Porous Low-k Films: A Surface Brillouin Scattering Study

    Science.gov (United States)

    Zizka, J.; King, S.; Every, A.; Sooryakumar, R.

    2018-04-01

    To reduce the RC (resistance-capacitance) time delay of interconnects, a key development of the past 20 years has been the introduction of porous low-k dielectrics to replace the traditional use of SiO2. Moreover, in keeping pace with concomitant reduction in technology nodes, these low-k materials have reached thicknesses below 100 nm wherein the porosity becomes a significant fraction of the film volume. The large degree of porosity not only reduces mechanical strength of the dielectric layer but also renders a need for non-destructive approaches to measure the mechanical properties of such ultra-thin films within device configurations. In this study, surface Brillouin scattering (SBS) is utilized to determine the elastic constants, Poisson's ratio, and Young's modulus of these porous low-k SiOC:H films (˜ 25-250 nm thick) grown on Si substrates by probing surface acoustic phonons and their dispersions.

  14. Poisson processes on groups and Feynman path integrals

    International Nuclear Information System (INIS)

    Combe, P.; Rodriguez, R.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille; Sirugue, M.

    1979-09-01

    An expression is given for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems

  15. Coordination of Conditional Poisson Samples

    Directory of Open Access Journals (Sweden)

    Grafström Anton

    2015-12-01

    Full Text Available Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP sampling is a modification of the classical Poisson sampling that produces a fixed-size πps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.

  16. Poisson processes on groups and Feynamn path integrals

    International Nuclear Information System (INIS)

    Combe, P.; Rodriguez, R.; Aix-Marseille-2 Univ., 13 - Marseille; Sirugue, M.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille; Hoegh-Krohn, R.

    1980-01-01

    We give an expression for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems. (orig.)

  17. 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

  18. Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

    CERN Document Server

    Farhat, Hassan; Kondaraju, Sasidhar

    2014-01-01

    Colloids are ubiquitous in the food, medical, cosmetics, polymers, water purification, and pharmaceutical industries. The thermal, mechanical, and storage properties of colloids are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a convenient and reliable tool for the study of colloids. Accelerated Lattice Boltzmann Model for Colloidal Suspensions introduce the main building-blocks for an improved lattice Boltzmann–based numerical tool designed for the study of colloidal rheology and interface morphology. This book also covers the migrating multi-block used to simulate single component, multi-component, multiphase, and single component multiphase flows and their validation by experimental, numerical, and analytical solutions.   Among other topics discussed are the hybrid lattice Boltzmann method (LBM) for surfactant-covered droplets; biological suspensions such as blood; used in conjunction with the suppression of coalescence for investigating the...

  19. The charge effect on the hindrance factors for diffusion and convection of a solute in pores: II

    Energy Technology Data Exchange (ETDEWEB)

    Akinaga, Takeshi; O-tani, Hideyuki; Sugihara-Seki, Masako, E-mail: r091077@kansai-u.ac.jp [Department of Pure and Applied Physics, Kansai University, Yamate-cho, Suita, Osaka 564-8680 (Japan)

    2012-10-15

    The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e. the Debye-Hueckel equation. (paper)

  20. Computational Study of the Binding Mechanism of Actin-Depolymerizing Factor 1 with Actin in Arabidopsis thaliana.

    Directory of Open Access Journals (Sweden)

    Juan Du

    Full Text Available Actin is a highly conserved protein. It plays important roles in cellular function and exists either in the monomeric (G-actin or polymeric form (F-actin. Members of the actin-depolymerizing factor (ADF/cofilin protein family bind to both G-actin and F-actin and play vital roles in actin dynamics by manipulating the rates of filament polymerization and depolymerization. It has been reported that the S6D and R98A/K100A mutants of actin-depolymerizing factor 1 (ADF1 in Arabidopsis thaliana decreased the binding affinity of ADF for the actin monomer. To investigate the binding mechanism and dynamic behavior of the ADF1-actin complex, we constructed a homology model of the AtADF1-actin complex based on the crystal structure of AtADF1 and the twinfilin C-terminal ADF-H domain in a complex with a mouse actin monomer. The model was then refined for subsequent molecular dynamics simulations. Increased binding energy of the mutated system was observed using the Molecular Mechanics Generalized Born Surface Area and Poisson-Boltzmann Surface Area (MM-GB/PBSA methods. To determine the residues that make decisive contributions to the ADF1 actin-binding affinity, per-residue decomposition and computational alanine scanning analyses were performed, which provided more detailed information on the binding mechanism. Root-mean-square fluctuation and principal component analyses confirmed that the S6D and R98A/K100A mutants induced an increased conformational flexibility. The comprehensive molecular insight gained from this study is of great importance for understanding the binding mechanism of ADF1 and G-actin.

  1. 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

  2. Application of Lattice Boltzmann Methods in Complex Mass Transfer Systems

    Science.gov (United States)

    Sun, Ning

    Lattice Boltzmann Method (LBM) is a novel computational fluid dynamics method that can easily handle complex and dynamic boundaries, couple local or interfacial interactions/reactions, and be easily parallelized allowing for simulation of large systems. While most of the current studies in LBM mainly focus on fluid dynamics, however, the inherent power of this method makes it an ideal candidate for the study of mass transfer systems involving complex/dynamic microstructures and local reactions. In this thesis, LBM is introduced to be an alternative computational method for the study of electrochemical energy storage systems (Li-ion batteries (LIBs) and electric double layer capacitors (EDLCs)) and transdermal drug design on mesoscopic scale. Based on traditional LBM, the following in-depth studies have been carried out: (1) For EDLCs, the simulation of diffuse charge dynamics is carried out for both the charge and the discharge processes on 2D systems of complex random electrode geometries (pure random, random spheres and random fibers). Steric effect of concentrated solutions is considered by using modified Poisson-Nernst-Plank (MPNP) equations and compared with regular Poisson-Nernst-Plank (PNP) systems. The effects of electrode microstructures (electrode density, electrode filler morphology, filler size, etc.) on the net charge distribution and charge/discharge time are studied in detail. The influence of applied potential during discharging process is also discussed. (2) For the study of dendrite formation on the anode of LIBs, it is shown that the Lattice Boltzmann model can capture all the experimentally observed features of microstructure evolution at the anode, from smooth to mossy to dendritic. The mechanism of dendrite formation process in mesoscopic scale is discussed in detail and compared with the traditional Sand's time theories. It shows that dendrite formation is closely related to the inhomogeneous reactively at the electrode-electrolyte interface

  3. Two Experiments to Approach the Boltzmann Factor: Chemical Reaction and Viscous Flow

    Science.gov (United States)

    Fazio, Claudio; Battaglia, Onofrio R.; Guastella, Ivan

    2012-01-01

    In this paper we discuss a pedagogical approach aimed at pointing out the role played by the Boltzmann factor in describing phenomena usually perceived as regulated by different mechanisms of functioning. Experimental results regarding some aspects of a chemical reaction and of the viscous flow of some liquids are analysed and described in terms…

  4. Charged plate in asymmetric electrolytes: One-loop renormalization of surface charge density and Debye length due to ionic correlations.

    Science.gov (United States)

    Ding, Mingnan; Lu, Bing-Sui; Xing, Xiangjun

    2016-10-01

    Self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a m:-n electrolyte. A perturbation series is developed in terms of g=4πκb, where band1/κ are Bjerrum length and bare Debye length, respectively. To the zeroth order, we obtain the nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes (m≠n), the first order (one-loop) correction to mean potential contains a secular term, which indicates the breakdown of the regular perturbation method. Using a renormalizaton group transformation, we remove the secular term and obtain a globally well-behaved one-loop approximation with a renormalized Debye length and a renormalized surface charge density. Furthermore, we find that if the counterions are multivalent, the surface charge density is renormalized substantially downwards and may undergo a change of sign, if the bare surface charge density is sufficiently large. Our results agrees with large MC simulation even when the density of electrolytes is relatively high.

  5. Re-dispersion of alumina particles in water: influence of the surface state

    International Nuclear Information System (INIS)

    Desset, Sabine

    1999-01-01

    The aim of this work was to determine the mechanisms by which suspensions of alpha alumina particles may be dried and then re-dispersed spontaneously in water. To get reproducible results, we designed appropriate protocols: (i) for preparing the surface state, and for generating controlled interparticle contacts (presence of water or complexing agents); (ii) for measuring the amount of re-dispersed material with a proper averaging over all interparticle bonds (turbidity). These results show that there are thresholds, determined by the conditions of drying and re-dispersion, where all the powder goes from the aggregated state to the dispersed state. With hydrated powders, it was found that mild changes in the chemical conditions (pH) and application of very weak mechanical forces (sedimentation) were enough to cause significant change in re-dispersion. According to these thresholds, a re-dispersion mechanism could be identified. Re-dispersion is ruled, indeed, by a balance of forces and the displacement of the re-dispersion thresholds indicates a shift in the balance of forces. These forces are the well known forces that control colloidal stability: van der Waals attraction, electrostatic repulsion and hydration forces. We found that hydration acts as a repulsive wall corresponding to one or two monolayers of water on each surface and depends on the Relative Humidity of drying. We also found that electrostatic repulsions at short separations are much weaker than the predictions based on the Poisson Boltzmann equation, but should be modelled according to the triple layer model. Repulsions to be considered are those calculated with the screened charges of the particles. Another aim of this work was to facilitate re-dispersion by using complexing agents that bind to the surfaces and add a steric repulsion We have found that molecules with carboxylic and hydroxyl groups can be efficient in this respect, if they are bound to surfaces before aggregation, if they are not

  6. Re-dispersion of alumina particles in water: influence of the surface state

    International Nuclear Information System (INIS)

    Desset, Sabine

    1999-01-01

    The aim of this work was to determine the mechanisms by which suspensions of alpha alumina particles may be dried and then re-dispersed spontaneously in water. To get reproducible results, we designed appropriate protocols: (i) for preparing the surface state, and for generating controlled interparticle contacts (presence of water or complexing agents); (ii) for measuring the amount of re-dispersed material with a proper averaging over all interparticle bonds (turbidity). These results show that there are thresholds, determined by the conditions of drying and re-dispersion, where all the powder goes from the aggregated state to the dispersed state. With hydrated powders, it was found that mild changes in the chemical conditions (pH) and application of very weak mechanical forces (sedimentation) were enough to cause significant change in re-dispersion. According to these thresholds, a re-dispersion mechanism could be identified. Re-dispersion is ruled, indeed, by a balance of forces and the displacement of the re-dispersion thresholds indicates a shift in the balance of forces. These forces are the well-known forces that control colloidal stability: van der Waals attraction, electrostatic repulsion and hydration forces. We found that hydration acts as a repulsive wall corresponding to one or two monolayers of water on each surface and depends on the Relative Humidity of drying. We also found that electrostatic repulsions at short separations are much weaker than the predictions based on the Poisson Boltzmann equation, but should be modelled according to the triple layer model. Repulsions to be considered are those calculated with the screened charges of the particles. Another aim of this work was to facilitate re-dispersion by using complexing agents that bind to the surfaces and add a steric repulsion We have found that molecules with carboxylic and hydroxyl groups can be efficient in this respect, if they are bound to surfaces before aggregation, if they are not

  7. On some asymptotic relations in the Boltzmann-Enskog model

    International Nuclear Information System (INIS)

    Sadovnikov, B.I.; Inozemtseva, N.G.

    1977-04-01

    The coefficients in the tsup(-3/2) asymptotics of the time autocorrelation functions are successively determined in the framework of the non-linear Boltzmann-Enskog model. The left and right eigenfunction systems are constructed for the Boltzmann-Enskog operator

  8. Poisson brackets of orthogonal polynomials

    OpenAIRE

    Cantero, María José; Simon, Barry

    2009-01-01

    For the standard symplectic forms on Jacobi and CMV matrices, we compute Poisson brackets of OPRL and OPUC, and relate these to other basic Poisson brackets and to Jacobians of basic changes of variable.

  9. Fully coupled Lattice Boltzmann simulation of fiber reinforced self compacting concrete flow

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skocek, Jan; Stang, Henrik

    accurately the most important phenomena is introduced. A conventional Lattice Boltzmann method has been chosen as a fluid dynamics solver of the non-Newtonian fluid. A Mass Tracking Algorithm has been implemented to correctly represent a free surface and a modified Immersed Boundary Method (IBM) with direct...

  10. 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...

  11. 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.

  12. Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

    Science.gov (United States)

    Lu, Benzhuo; Zhou, Y.C.

    2011-01-01

    The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

  13. Thermal equation of state for lattice Boltzmann gases

    International Nuclear Information System (INIS)

    Zheng, Ran

    2009-01-01

    The Galilean invariance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar–Gross–Krook model are 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

  14. A pedagogical approach to the Boltzmann factor through experiments and simulations

    International Nuclear Information System (INIS)

    Battaglia, O R; Bonura, A; Sperandeo-Mineo, R M

    2009-01-01

    The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment that, besides having a user-friendly interface, allows an easy interaction with the algorithm. The approach supplies pedagogical support for the introduction of the Boltzmann factor at the undergraduate level to students without a background in statistical mechanics.

  15. A pedagogical approach to the Boltzmann factor through experiments and simulations

    Energy Technology Data Exchange (ETDEWEB)

    Battaglia, O R; Bonura, A; Sperandeo-Mineo, R M [University of Palermo Physics Education Research Group, Dipartimento di Fisica e Tecnologie Relative, Universita di Palermo (Italy)], E-mail: sperandeo@difter.unipa.it

    2009-09-15

    The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment that, besides having a user-friendly interface, allows an easy interaction with the algorithm. The approach supplies pedagogical support for the introduction of the Boltzmann factor at the undergraduate level to students without a background in statistical mechanics.

  16. Nonlocal Poisson-Fermi model for ionic solvent.

    Science.gov (United States)

    Xie, Dexuan; Liu, Jinn-Liang; Eisenberg, Bob

    2016-07-01

    We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-like kernel function. The Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.

  17. The time-dependent development of electric double-layers in saline solutions

    International Nuclear Information System (INIS)

    Morrow, R; McKenzie, D R; Bilek, M M M

    2006-01-01

    We have studied the time-dependent development of electric double-layers (ionic sheaths) in saline solutions by simultaneously solving the sodium and chlorine ion continuity equations coupled with Poisson's equation in one dimension. The study of the effects of time-varying electric fields in solution is relevant to the possible health effect of radio-frequency electric fields on cells in the human body and to assessing the potential of using external electric fields to orient proteins for attachment to surfaces for biosensing applications. Our calculations, for applied voltages of 10-175 mV between the electrode and the solution, predict time scales of ∼0.1-110 μs for the formation of double-layers in solutions of concentration between 0.001 and 1.0 M. We develop an empirical equation that can predict the double-layer formation time to within 10% over this wide parameter range. The method has been validated by comparing the solutions obtained, once the program has run to a steady state, with the standard non-linear Poisson-Boltzmann equations. Excellent agreement is found with the Gouy-Chapman solution of the non-linear Poisson-Boltzmann equation. Thus the method is not restricted in accuracy and applicability as is the case for the linear Poisson-Boltzmann equation. The method can also provide solutions for cases where there are orders of magnitude changes in the ion densities; this has not been the case for previous studies where small perturbation analysis has been employed. The method developed here can readily be extended to two and three dimensions using time-splitting methods

  18. CMB spectral distortions as solutions to the Boltzmann equations

    Energy Technology Data Exchange (ETDEWEB)

    Ota, Atsuhisa, E-mail: a.ota@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)

    2017-01-01

    We propose to re-interpret the cosmic microwave background spectral distortions as solutions to the Boltzmann equation. This approach makes it possible to solve the second order Boltzmann equation explicitly, with the spectral y distortion and the momentum independent second order temperature perturbation, while generation of μ distortion cannot be explained even at second order in this framework. We also extend our method to higher order Boltzmann equations systematically and find new type spectral distortions, assuming that the collision term is linear in the photon distribution functions, namely, in the Thomson scattering limit. As an example, we concretely construct solutions to the cubic order Boltzmann equation and show that the equations are closed with additional three parameters composed of a cubic order temperature perturbation and two cubic order spectral distortions. The linear Sunyaev-Zel'dovich effect whose momentum dependence is different from the usual y distortion is also discussed in the presence of the next leading order Kompaneets terms, and we show that higher order spectral distortions are also generated as a result of the diffusion process in a framework 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.

  19. 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.

  20. L2-stability of the Vlasov-Maxwell-Boltzmann system near global Maxwellians

    International Nuclear Information System (INIS)

    Ha, Seung-Yeal; Xiao, Qinghua; Xiong, Linjie; Zhao, Huijiang

    2013-01-01

    We present a L 2 -stability theory of the Vlasov-Maxwell-Boltzmann system for the two-species collisional plasma. We show that in a perturbative regime of a global Maxwellian, the L 2 -distance between two strong solutions can be controlled by that between initial data in a Lipschitz manner. Our stability result extends earlier results [Ha, S.-Y. and Xiao, Q.-H., “A revisiting to the L 2 -stability theory of the Boltzmann equation near global Maxwellians,” (submitted) and Ha, S.-Y., Yang, X.-F., and Yun, S.-B., “L 2 stability theory of the Boltzmann equation near a global Maxwellian,” Arch. Ration. Mech. Anal. 197, 657–688 (2010)] on the L 2 -stability of the Boltzmann equation to the Boltzmann equation coupled with self-consistent external forces. As a direct application of our stability result, we show that classical solutions in Duan et al. [“Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space,” Commun. Pure Appl. Math. 24, 1497–1546 (2011)] and Guo [“The Vlasov-Maxwell-Boltzmann system near Maxwellians,” Invent. Math. 153(3), 593–630 (2003)] satisfy a uniform L 2 -stability estimate. This is the first result on the L 2 -stability of the Boltzmann equation coupled with self-consistent field equations in three dimensions

  1. 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.

  2. Analysis of spectral methods for the homogeneous Boltzmann equation

    KAUST Repository

    Filbet, Francis; Mouhot, Clé ment

    2011-01-01

    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.

  3. 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.

  4. Insight into interaction mechanism of the inhibitor pDI5W with MDM2 based on molecular dynamics

    International Nuclear Information System (INIS)

    Chen Jianzhong; Liang Zhiqiang; Wang Wei; Liu Jinqing; Zhang Qinggang; Liu Xiaoyang

    2012-01-01

    The p53-MDM2 interaction has been an important target of drug design curing cancers. In this work, molecular dynamics (MD) simulation coupled with molecular mechanics/Poisson Boltzmann surface area method (MM-PBSA) was performed to calculate the binding free energy of peptide inhibitor pDI6W to MDM2. The results show that van der Waals energy is the dominant factor of the pDI6W— MDM2 interaction. Cross-correlation matrix calculated suggests that the main motion of the residues in MMDM2 induced by the inhibitor binding is anti-correlation motion. The calculations of residue-residue interactions between pDI6W and MDM2 not only prove that five residues Phe19', Trp22', Trp23', Leu26' and Thr27' from pDI6W can produce strong interaction with MDM2, but also show that CH-π, CH-CH and π-π interactions drive the binding of pDI6W in the hydrophobic cleft of MDM2. This study can provide theoretical helps for anti-cancer drug designs. (authors)

  5. Understanding colloidal charge renormalization from surface chemistry: Experiment and theory

    Science.gov (United States)

    Gisler, T.; Schulz, S. F.; Borkovec, M.; Sticher, H.; Schurtenberger, P.; D'Aguanno, B.; Klein, R.

    1994-12-01

    In this paper we report on the charging behavior of latex particles in aqueous suspensions. We use static light scattering and acid-base titrations as complementary techniques to observe both effective and bare particle charges. Acid-base titrations at various ionic strengths provide the pH dependent charging curves. The surface chemical parameters (dissociation constant of the acidic carboxylic groups, total density of ionizable sites and Stern capacitance) are determined from fits of a Stern layer model to the titration data. We find strong evidence that the dissociation of protons is the only specific adsorption process. Effective particle charges are determined by fits of integral equation calculations of the polydisperse static structure factor to the static light scattering data. A generalization of the Poisson-Boltzmann cell model including the dissociation of the acidic surface groups and the autodissociation of water is used to predict effective particle charges from the surface chemical parameters determined by the titration experiments. We find that the light scattering data are best described by a model where a small fraction of the ionizable surface sites are sulfate groups which are completely dissociated at moderate pH. These effective charges are comparable to the predictions by a basic cell model where charge regulation is absent.

  6. Simulation of Cavity Flow by the Lattice Boltzmann Method using Multiple-Relaxation-Time scheme

    International Nuclear Information System (INIS)

    Ryu, Seung Yeob; Kang, Ha Nok; Seo, Jae Kwang; Yun, Ju Hyeon; Zee, Sung Quun

    2006-01-01

    Recently, the lattice Boltzmann method(LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for pressure, and (3) ease with multiphase flows, complex geometries and interfacial dynamics may be treated. The LBM using relaxation technique was introduced by Higuerea and Jimenez to overcome some drawbacks of lattice gas automata(LGA) such as large statistical noise, limited range of physical parameters, non- Galilean invariance, and implementation difficulty in three-dimensional problem. The simplest LBM is the lattice Bhatnager-Gross-Krook(LBGK) equation, which based on a single-relaxation-time(SRT) approximation. Due to its extreme simplicity, the lattice BGK(LBGK) equation has become the most popular lattice Boltzmann model in spite of its well-known deficiencies, for example, in simulating high-Reynolds numbers flow. The Multiple-Relaxation-Time(MRT) LBM was originally developed by D'Humieres. Lallemand and Luo suggests that the use of a Multiple-Relaxation-Time(MRT) models are much more stable than LBGK, because the different relaxation times can be individually tuned to achieve 'optimal' stability. A lid-driven cavity flow is selected as the test problem because it has geometrically singular points in the flow, but geometrically simple. Results are compared with those using SRT, MRT model in the LBGK method and previous simulation data using Navier-Stokes equations for the same flow conditions. In summary, LBM using MRT model introduces much less spatial oscillations near geometrical singular points, which is important for the successful simulation of higher Reynolds number flows

  7. A weighted multiple-relaxation-time lattice Boltzmann method for multiphase flows and its application to partial coalescence cascades

    Science.gov (United States)

    Fakhari, Abbas; Bolster, Diogo; Luo, Li-Shi

    2017-07-01

    We present a lattice Boltzmann method (LBM) with a weighted multiple-relaxation-time (WMRT) collision model and an adaptive mesh refinement (AMR) algorithm for direct numerical simulation of two-phase flows in three dimensions. The proposed WMRT model enhances the numerical stability of the LBM for immiscible fluids at high density ratios, particularly on the D3Q27 lattice. The effectiveness and efficiency of the proposed WMRT-LBM-AMR is validated through simulations of (a) buoyancy-driven motion and deformation of a gas bubble rising in a viscous liquid; (b) the bag-breakup mechanism of a falling drop; (c) crown splashing of a droplet on a wet surface; and (d) the partial coalescence mechanism of a liquid drop at a liquid-liquid interface. The numerical simulations agree well with available experimental data and theoretical approximations where applicable.

  8. Singular reduction of Nambu-Poisson manifolds

    Science.gov (United States)

    Das, Apurba

    The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.

  9. Student learning of upper-level thermal and statistical physics: The derivation and use of the Boltzmann factor

    Science.gov (United States)

    Thompson, John

    2015-04-01

    As the Physical Review Focused Collection demonstrates, recent frontiers in physics education research include systematic investigations at the upper division. As part of a collaborative project, we have examined student understanding of several topics in upper-division thermal and statistical physics. A fruitful context for research is the Boltzmann factor in statistical mechanics: the standard derivation involves several physically justified mathematical steps as well as the invocation of a Taylor series expansion. We have investigated student understanding of the physical significance of the Boltzmann factor as well as its utility in various circumstances, and identified various lines of student reasoning related to the use of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students do not use the Boltzmann factor when answering questions related to probability in applicable physical situations, even after lecture instruction. We designed an inquiry-based tutorial activity to guide students through a derivation of the Boltzmann factor and to encourage deep connections between the physical quantities involved and the mathematics. Observations of students working through the tutorial suggest that many students at this level can recognize and interpret Taylor series expansions, but they often lack fluency in creating and using Taylor series appropriately, despite previous exposure in both calculus and physics courses. Our findings also suggest that tutorial participation not only increases the prevalence of relevant invocation of the Boltzmann factor, but also helps students gain an appreciation of the physical implications and meaning of the mathematical formalism behind the formula. Supported in part by NSF Grants DUE-0817282, DUE-0837214, and DUE-1323426.

  10. 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.

  11. Boltzmann and Einstein: Statistics and dynamics –An unsolved ...

    Indian Academy of Sciences (India)

    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 ...

  12. Lattice Boltzmann simulation of antiplane shear loading of a stationary crack

    Science.gov (United States)

    Schlüter, Alexander; Kuhn, Charlotte; Müller, Ralf

    2018-01-01

    In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61-69, 2000) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu's work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.

  13. Poisson-Box Sampling algorithms for three-dimensional Markov binary mixtures

    Science.gov (United States)

    Larmier, Coline; Zoia, Andrea; Malvagi, Fausto; Dumonteil, Eric; Mazzolo, Alain

    2018-02-01

    Particle transport in Markov mixtures can be addressed by the so-called Chord Length Sampling (CLS) methods, a family of Monte Carlo algorithms taking into account the effects of stochastic media on particle propagation by generating on-the-fly the material interfaces crossed by the random walkers during their trajectories. Such methods enable a significant reduction of computational resources as opposed to reference solutions obtained by solving the Boltzmann equation for a large number of realizations of random media. CLS solutions, which neglect correlations induced by the spatial disorder, are faster albeit approximate, and might thus show discrepancies with respect to reference solutions. In this work we propose a new family of algorithms (called 'Poisson Box Sampling', PBS) aimed at improving the accuracy of the CLS approach for transport in d-dimensional binary Markov mixtures. In order to probe the features of PBS methods, we will focus on three-dimensional Markov media and revisit the benchmark problem originally proposed by Adams, Larsen and Pomraning [1] and extended by Brantley [2]: for these configurations we will compare reference solutions, standard CLS solutions and the new PBS solutions for scalar particle flux, transmission and reflection coefficients. PBS will be shown to perform better than CLS at the expense of a reasonable increase in computational time.

  14. On the fractal characterization of Paretian Poisson processes

    Science.gov (United States)

    Eliazar, Iddo I.; Sokolov, Igor M.

    2012-06-01

    Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto's law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of 'fractal processes' exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes-with respect to physical randomness-based measures of statistical heterogeneity-is characterized by exponential Poissonian intensities.

  15. NEWTPOIS- NEWTON POISSON DISTRIBUTION PROGRAM

    Science.gov (United States)

    Bowerman, P. N.

    1994-01-01

    The cumulative poisson distribution program, NEWTPOIS, is one of two programs which make calculations involving cumulative poisson distributions. Both programs, NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714), can be used independently of one another. NEWTPOIS determines percentiles for gamma distributions with integer shape parameters and calculates percentiles for chi-square distributions with even degrees of freedom. It can be used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. NEWTPOIS determines the Poisson parameter (lambda), that is; the mean (or expected) number of events occurring in a given unit of time, area, or space. Given that the user already knows the cumulative probability for a specific number of occurrences (n) it is usually a simple matter of substitution into the Poisson distribution summation to arrive at lambda. However, direct calculation of the Poisson parameter becomes difficult for small positive values of n and unmanageable for large values. NEWTPOIS uses Newton's iteration method to extract lambda from the initial value condition of the Poisson distribution where n=0, taking successive estimations until some user specified error term (epsilon) is reached. The NEWTPOIS program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly on most C compilers. The program format is interactive, accepting epsilon, n, and the cumulative probability of the occurrence of n as inputs. It has been implemented under DOS 3.2 and has a memory requirement of 30K. NEWTPOIS was developed in 1988.

  16. Avoiding negative populations in explicit Poisson tau-leaping.

    Science.gov (United States)

    Cao, Yang; Gillespie, Daniel T; Petzold, Linda R

    2005-08-01

    The explicit tau-leaping procedure attempts to speed up the stochastic simulation of a chemically reacting system by approximating the number of firings of each reaction channel during a chosen time increment tau as a Poisson random variable. Since the Poisson random variable can have arbitrarily large sample values, there is always the possibility that this procedure will cause one or more reaction channels to fire so many times during tau that the population of some reactant species will be driven negative. Two recent papers have shown how that unacceptable occurrence can be avoided by replacing the Poisson random variables with binomial random variables, whose values are naturally bounded. This paper describes a modified Poisson tau-leaping procedure that also avoids negative populations, but is easier to implement than the binomial procedure. The new Poisson procedure also introduces a second control parameter, whose value essentially dials the procedure from the original Poisson tau-leaping at one extreme to the exact stochastic simulation algorithm at the other; therefore, the modified Poisson procedure will generally be more accurate than the original Poisson procedure.

  17. Accelerating Electrostatic Surface Potential Calculation with Multiscale Approximation on Graphics Processing Units

    Science.gov (United States)

    Anandakrishnan, Ramu; Scogland, Tom R. W.; Fenley, Andrew T.; Gordon, John C.; Feng, Wu-chun; Onufriev, Alexey V.

    2010-01-01

    Tools that compute and visualize biomolecular electrostatic surface potential have been used extensively for studying biomolecular function. However, determining the surface potential for large biomolecules on a typical desktop computer can take days or longer using currently available tools and methods. Two commonly used techniques to speed up these types of electrostatic computations are approximations based on multi-scale coarse-graining and parallelization across multiple processors. This paper demonstrates that for the computation of electrostatic surface potential, these two techniques can be combined to deliver significantly greater speed-up than either one separately, something that is in general not always possible. Specifically, the electrostatic potential computation, using an analytical linearized Poisson Boltzmann (ALPB) method, is approximated using the hierarchical charge partitioning (HCP) multiscale method, and parallelized on an ATI Radeon 4870 graphical processing unit (GPU). The implementation delivers a combined 934-fold speed-up for a 476,040 atom viral capsid, compared to an equivalent non-parallel implementation on an Intel E6550 CPU without the approximation. This speed-up is significantly greater than the 42-fold speed-up for the HCP approximation alone or the 182-fold speed-up for the GPU alone. PMID:20452792

  18. Effect of surface bilayer charges on the magnetic field around ionic channels

    Energy Technology Data Exchange (ETDEWEB)

    Gomes Soares, Marília Amável [Post-graduation in Computational Sciences, Rio de Janeiro State University (Brazil); Cortez, Celia Martins, E-mail: ccortezs@ime.uerj.br [Post-graduation in Computational Sciences, Rio de Janeiro State University (Brazil); Department of Applied Mathematics, Rio de Janeiro State University (Brazil); Oliveira Cruz, Frederico Alan de [Post-graduation in Computational Sciences, Rio de Janeiro State University (Brazil); Department of Physics, Rural Federal University of Rio de Janeiro (Brazil); Silva, Dilson [Post-graduation in Computational Sciences, Rio de Janeiro State University (Brazil); Department of Applied Mathematics, Rio de Janeiro State University (Brazil)

    2017-01-01

    In this work, we present a physic-mathematical model for representing the ion transport through membrane channels, in special Na{sup +} and K{sup +}-channels, and discuss the influence of surface bilayer charges on the magnetic field behavior around the ionic current. The model was composed of a set of equations, including: a nonlinear differential Poisson-Boltzmann equation which usually allows to estimate the surface potentials and electric potential profile across membrane; equations for the ionic flux through channel and the ionic current density based on Armstrong's model for Na{sup +} and K{sup +} permeability and other Physics concepts; and a magnetic field expression derived from the classical Ampère equation. Results from computational simulations using the finite element method suggest that the ionic permeability is strongly dependent of surface bilayer charges, the current density through a K{sup +}-channel is very less sensible to temperature changes than the current density through a Na{sup +}- channel, active Na{sup +}-channels do not directly interfere with the K{sup +}-channels around, and vice-versa, since the magnetic perturbation generated by an active channel is of short-range.

  19. Elastic properties of a material composed of alternating layers of negative and positive Poisson's ratio

    International Nuclear Information System (INIS)

    Kocer, C.; McKenzie, D.R.; Bilek, M.M.

    2009-01-01

    The theory of elasticity predicts a variety of phenomena associated with solids that possess a negative Poisson's ratio. The fabrication of metamaterials with a 'designed' microstructure that exhibit a Poisson's ratio approaching the thermodynamic limits of 1/2 and -1 increases the likelihood of realising these phenomena for applications. In this work, we investigate the properties of a layered composite, with alternating layers of materials with negative and positive Poisson's ratio approaching the thermodynamic limits. Using the finite element method to simulate uniaxial loading and indentation of a free standing composite, we observed an increase in the resistance to mechanical deformation above the average value of the two materials. Even though the greatest increase in stiffness is gained as the thermodynamic limits are approached, a significant amount of added stiffness can be attained, provided that the Young's modulus of the negative Poisson's ratio material is not less than that of the positive Poisson's ratio material

  20. 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.

  1. Tomography and generative training with quantum Boltzmann machines

    Science.gov (United States)

    Kieferová, Mária; Wiebe, Nathan

    2017-12-01

    The promise of quantum neural nets, which utilize quantum effects to model complex data sets, has made their development an aspirational goal for quantum machine learning and quantum computing in general. Here we provide methods of training quantum Boltzmann machines. Our work generalizes existing methods and provides additional approaches for training quantum neural networks that compare favorably to existing methods. We further demonstrate that quantum Boltzmann machines enable a form of partial quantum state tomography that further provides a generative model for the input quantum state. Classical Boltzmann machines are incapable of this. This verifies the long-conjectured connection between tomography and quantum machine learning. Finally, we prove that classical computers cannot simulate our training process in general unless BQP=BPP , provide lower bounds on the complexity of the training procedures and numerically investigate training for small nonstoquastic Hamiltonians.

  2. Poisson Mixture Regression Models for Heart Disease Prediction.

    Science.gov (United States)

    Mufudza, Chipo; Erol, Hamza

    2016-01-01

    Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.

  3. Poisson Mixture Regression Models for Heart Disease Prediction

    Science.gov (United States)

    Erol, Hamza

    2016-01-01

    Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model. PMID:27999611

  4. 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.…

  5. Singularities of Poisson structures and Hamiltonian bifurcations

    NARCIS (Netherlands)

    Meer, van der J.C.

    2010-01-01

    Consider a Poisson structure on C8(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} =<¿C, (¿g x ¿f) > is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom

  6. Boltzmann Solver with Adaptive Mesh in Velocity Space

    International Nuclear Information System (INIS)

    Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.

    2011-01-01

    We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.

  7. Decomposition of almost-Poisson structure of generalised Chaplygin's nonholonomic systems

    International Nuclear Information System (INIS)

    Chang, Liu; Peng, Chang; Shi-Xing, Liu; Yong-Xin, Guo

    2010-01-01

    This paper constructs an almost-Poisson structure for the non-self-adjoint dynamical systems, which can be decomposed into a sum of a Poisson bracket and the other almost-Poisson bracket. The necessary and sufficient condition for the decomposition of the almost-Poisson bracket to be two Poisson ones is obtained. As an application, the almost-Poisson structure for generalised Chaplygin's systems is discussed in the framework of the decomposition theory. It proves that the almost-Poisson bracket for the systems can be decomposed into the sum of a canonical Poisson bracket and another two noncanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion

  8. Poisson's ratio of collagen fibrils measured by small angle X-ray scattering of strained bovine pericardium

    Energy Technology Data Exchange (ETDEWEB)

    Wells, Hannah C.; Sizeland, Katie H.; Kayed, Hanan R.; Haverkamp, Richard G., E-mail: r.haverkamp@massey.ac.nz [School of Engineering and Advanced Technology, Massey University, Private Bag 11222, Palmerston North 4442 (New Zealand); Kirby, Nigel; Hawley, Adrian; Mudie, Stephen T. [Australian Synchrotron, 800 Blackburn Road, Clayton, Victoria 3168 (Australia)

    2015-01-28

    Type I collagen is the main structural component of skin, tendons, and skin products, such as leather. Understanding the mechanical performance of collagen fibrils is important for understanding the mechanical performance of the tissues that they make up, while the mechanical properties of bulk tissue are well characterized, less is known about the mechanical behavior of individual collagen fibrils. In this study, bovine pericardium is subjected to strain while small angle X-ray scattering (SAXS) patterns are recorded using synchrotron radiation. The change in d-spacing, which is a measure of fibril extension, and the change in fibril diameter are determined from SAXS. The tissue is strained 0.25 (25%) with a corresponding strain in the collagen fibrils of 0.045 observed. The ratio of collagen fibril width contraction to length extension, or the Poisson's ratio, is 2.1 ± 0.7 for a tissue strain from 0 to 0.25. This Poisson's ratio indicates that the volume of individual collagen fibrils decreases with increasing strain, which is quite unlike most engineering materials. This high Poisson's ratio of individual fibrils may contribute to high Poisson's ratio observed for tissues, contributing to some of the remarkable properties of collagen-based materials.

  9. Poisson Spot with Magnetic Levitation

    Science.gov (United States)

    Hoover, Matthew; Everhart, Michael; D'Arruda, Jose

    2010-01-01

    In this paper we describe a unique method for obtaining the famous Poisson spot without adding obstacles to the light path, which could interfere with the effect. A Poisson spot is the interference effect from parallel rays of light diffracting around a solid spherical object, creating a bright spot in the center of the shadow.

  10. Entropy à la Boltzmann

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034 ...

  11. 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

  12. Riemann-Theta Boltzmann Machine arXiv

    CERN Document Server

    Krefl, Daniel; Haghighat, Babak; Kahlen, Jens

    A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques.

  13. Newton/Poisson-Distribution Program

    Science.gov (United States)

    Bowerman, Paul N.; Scheuer, Ernest M.

    1990-01-01

    NEWTPOIS, one of two computer programs making calculations involving cumulative Poisson distributions. NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714) used independently of one another. NEWTPOIS determines Poisson parameter for given cumulative probability, from which one obtains percentiles for gamma distributions with integer shape parameters and percentiles for X(sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Program written in C.

  14. Collision group and renormalization of the Boltzmann collision integral

    Science.gov (United States)

    Saveliev, V. L.; Nanbu, K.

    2002-05-01

    On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

  15. A Martingale Characterization of Mixed Poisson Processes.

    Science.gov (United States)

    1985-10-01

    03LA A 11. TITLE (Inciuae Security Clanafication, ",A martingale characterization of mixed Poisson processes " ________________ 12. PERSONAL AUTHOR... POISSON PROCESSES Jostification .......... . ... . . Di.;t ib,,jtion by Availability Codes Dietmar Pfeifer* Technical University Aachen Dist Special and...Mixed Poisson processes play an important role in many branches of applied probability, for instance in insurance mathematics and physics (see Albrecht

  16. Numerical simulations of a family of the coupled viscous Burgers, equation using the lattice Boltzmann method

    International Nuclear Information System (INIS)

    He, Y B; Tang, X H

    2016-01-01

    In this paper, in order to extend the lattice Boltzmann method (LBM) to deal with more nonlinear systems, a one-dimensional and five-velocity lattice Boltzmann scheme with an amending function for a family of the coupled viscous Burgers’ equation (CVBE) is proposed. With the Taylor and Chapman–Enskog expansion, a family of the CVBE is recovered correctly from the lattice Boltzmann equation through selecting the equilibrium distribution functions and amending functions properly. The method is applied to some test examples with an analytical solution. The results are compared with those obtained by the finite difference method (FDM); it is shown that the numerical solutions agree well with the analytical solutions and the errors obtained by the present method are smaller than the FDM. Furthermore, some problems without analytical solutions are numerically studied by the present method and the FDM. The results show that the numerical solutions of the LBM are in good agreement with those obtained by the FDM, which can validate the effectiveness and stability of the LBM. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

  17. A modified SOR method for the Poisson equation in unsteady free-surface flow calculations.

    NARCIS (Netherlands)

    Botta, E.F.F.; Ellenbroek, Marcellinus Hermannus Maria

    1985-01-01

    Convergence difficulties that sometimes occur if the successive overrelaxation (SOR) method is applied to the Poisson equation on a region with irregular free boundaries are analyzed. It is shown that these difficulties are related to the treatment of the free boundaries and caused by the appearance

  18. Poisson-Hopf limit of quantum algebras

    International Nuclear Information System (INIS)

    Ballesteros, A; Celeghini, E; Olmo, M A del

    2009-01-01

    The Poisson-Hopf analogue of an arbitrary quantum algebra U z (g) is constructed by introducing a one-parameter family of quantizations U z,ℎ (g) depending explicitly on ℎ and by taking the appropriate ℎ → 0 limit. The q-Poisson analogues of the su(2) algebra are discussed and the novel su q P (3) case is introduced. The q-Serre relations are also extended to the Poisson limit. This approach opens the perspective for possible applications of higher rank q-deformed Hopf algebras in semiclassical contexts

  19. Reduction of Nambu-Poisson Manifolds by Regular Distributions

    Science.gov (United States)

    Das, Apurba

    2018-03-01

    The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibáñez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduction theorem for Nambu-Poisson manifolds. Finally, we define gauge transformations of Nambu-Poisson structures and show that these transformations commute with the reduction procedure.

  20. Scale-free, axisymmetry galaxy models with little angular momentum

    International Nuclear Information System (INIS)

    Richstone, D.O.

    1980-01-01

    Two scale-free models of elliptical galaxies are constructed using a self-consistent field approach developed by Schwarschild. Both models have concentric, oblate spheroidal, equipotential surfaces, with a logarithmic potential dependence on central distance. The axial ratio of the equipotential surfaces is 4:3, and the extent ratio of density level surfaces id 2.5:1 (corresponding to an E6 galaxy). Each model satisfies the Poisson and steady state Boltzmann equaion for time scales of order 100 galactic years

  1. A Generalized QMRA Beta-Poisson Dose-Response Model.

    Science.gov (United States)

    Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie

    2016-10-01

    Quantitative microbial risk assessment (QMRA) is widely accepted for characterizing the microbial risks associated with food, water, and wastewater. Single-hit dose-response models are the most commonly used dose-response models in QMRA. Denoting PI(d) as the probability of infection at a given mean dose d, a three-parameter generalized QMRA beta-Poisson dose-response model, PI(d|α,β,r*), is proposed in which the minimum number of organisms required for causing infection, K min , is not fixed, but a random variable following a geometric distribution with parameter 0Poisson model, PI(d|α,β), is a special case of the generalized model with K min = 1 (which implies r*=1). The generalized beta-Poisson model is based on a conceptual model with greater detail in the dose-response mechanism. Since a maximum likelihood solution is not easily available, a likelihood-free approximate Bayesian computation (ABC) algorithm is employed for parameter estimation. By fitting the generalized model to four experimental data sets from the literature, this study reveals that the posterior median r* estimates produced fall short of meeting the required condition of r* = 1 for single-hit assumption. However, three out of four data sets fitted by the generalized models could not achieve an improvement in goodness of fit. These combined results imply that, at least in some cases, a single-hit assumption for characterizing the dose-response process may not be appropriate, but that the more complex models may be difficult to support especially if the sample size is small. The three-parameter generalized model provides a possibility to investigate the mechanism of a dose-response process in greater detail than is possible under a single-hit model. © 2016 Society for Risk Analysis.

  2. On a Boltzmann-type price formation model

    KAUST Repository

    Burger, Martin; Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie Therese

    2013-01-01

    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.

  3. 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.

  4. Poisson's spot and Gouy phase

    Science.gov (United States)

    da Paz, I. G.; Soldati, Rodolfo; Cabral, L. A.; de Oliveira, J. G. G.; Sampaio, Marcos

    2016-12-01

    Recently there have been experimental results on Poisson spot matter-wave interferometry followed by theoretical models describing the relative importance of the wave and particle behaviors for the phenomenon. We propose an analytical theoretical model for Poisson's spot with matter waves based on the Babinet principle, in which we use the results for free propagation and single-slit diffraction. We take into account effects of loss of coherence and finite detection area using the propagator for a quantum particle interacting with an environment. We observe that the matter-wave Gouy phase plays a role in the existence of the central peak and thus corroborates the predominantly wavelike character of the Poisson's spot. Our model shows remarkable agreement with the experimental data for deuterium (D2) molecules.

  5. Mechanics of active surfaces

    Science.gov (United States)

    Salbreux, Guillaume; Jülicher, Frank

    2017-09-01

    We derive a fully covariant theory of the mechanics of active surfaces. This theory provides a framework for the study of active biological or chemical processes at surfaces, such as the cell cortex, the mechanics of epithelial tissues, or reconstituted active systems on surfaces. We introduce forces and torques acting on a surface, and derive the associated force balance conditions. We show that surfaces with in-plane rotational symmetry can have broken up-down, chiral, or planar-chiral symmetry. We discuss the rate of entropy production in the surface and write linear constitutive relations that satisfy the Onsager relations. We show that the bending modulus, the spontaneous curvature, and the surface tension of a passive surface are renormalized by active terms. Finally, we identify active terms which are not found in a passive theory and discuss examples of shape instabilities that are related to active processes in the surface.

  6. Nonequilibrium statistical mechanics ensemble method

    CERN Document Server

    Eu, Byung Chan

    1998-01-01

    In this monograph, nonequilibrium statistical mechanics is developed by means of ensemble methods on the basis of the Boltzmann equation, the generic Boltzmann equations for classical and quantum dilute gases, and a generalised Boltzmann equation for dense simple fluids The theories are developed in forms parallel with the equilibrium Gibbs ensemble theory in a way fully consistent with the laws of thermodynamics The generalised hydrodynamics equations are the integral part of the theory and describe the evolution of macroscopic processes in accordance with the laws of thermodynamics of systems far removed from equilibrium Audience This book will be of interest to researchers in the fields of statistical mechanics, condensed matter physics, gas dynamics, fluid dynamics, rheology, irreversible thermodynamics and nonequilibrium phenomena

  7. Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

    Science.gov (United States)

    Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

    2017-08-01

    This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

  8. Operational derivation of Boltzmann distribution with Maxwell's demon model.

    Science.gov (United States)

    Hosoya, Akio; Maruyama, Koji; Shikano, Yutaka

    2015-11-24

    The resolution of the Maxwell's demon paradox linked thermodynamics with information theory through information erasure principle. By considering a demon endowed with a Turing-machine consisting of a memory tape and a processor, we attempt to explore the link towards the foundations of statistical mechanics and to derive results therein in an operational manner. Here, we present a derivation of the Boltzmann distribution in equilibrium as an example, without hypothesizing the principle of maximum entropy. Further, since the model can be applied to non-equilibrium processes, in principle, we demonstrate the dissipation-fluctuation relation to show the possibility in this direction.

  9. A lattice Boltzmann model for solute transport in open channel flow

    Science.gov (United States)

    Wang, Hongda; Cater, John; Liu, Haifei; Ding, Xiangyi; Huang, Wei

    2018-01-01

    A lattice Boltzmann model of advection-dispersion problems in one-dimensional (1D) open channel flows is developed for simulation of solute transport and pollutant concentration. The hydrodynamics are calculated based on a previous lattice Boltzmann approach to solving the 1D Saint-Venant equations (LABSVE). The advection-dispersion model is coupled with the LABSVE using the lattice Boltzmann method. Our research recovers the advection-dispersion equations through the Chapman-Enskog expansion of the lattice Boltzmann equation. The model differs from the existing schemes in two points: (1) the lattice Boltzmann numerical method is adopted to solve the advection-dispersion problem by meso-scopic particle distribution; (2) and the model describes the relation between discharge, cross section area and solute concentration, which increases the applicability of the water quality model in practical engineering. The model is verified using three benchmark tests: (1) instantaneous solute transport within a short distance; (2) 1D point source pollution with constant velocity; (3) 1D point source pollution in a dam break flow. The model is then applied to a 50-year flood point source pollution accident on the Yongding River, which showed good agreement with a MIKE 11 solution and gauging data.

  10. A review of spurious currents in the lattice Boltzmann method for multiphase flows

    Energy Technology Data Exchange (ETDEWEB)

    Conning Ton, Kevin; Lee, Tae Hun [The City College of the City Univ. of New York, New York (United States)

    2012-12-15

    A spurious current is a small amplitude artificial velocity field which arises from an imbalance between discretized forces in multiphase/multi component flows. If it occurs, the velocity field may persist indefinitely, preventing the achievement of a true equilibrium state. Spurious velocities can sometimes be as large as the characteristic velocities of the problem, causing severe instability and ambiguity between physical and spurious velocities. They are typically exacerbated by large values of numerical surface tension or when the two fluids being simulated have large density ratios. The resulting instability can restrict what parameters may be simulated. To varying degrees, spurious currents are found in all multiphase flow models of the lattice Boltzmann method (LBM). There have been many studies of the occurrence of the phenomenon, and many suggestions on how to eliminate it. This paper reviews the three main models of simulating multiphase/multi component flow in the lattice Boltzmann method, as well as the subsequent modifications made in order to reduce or eliminate spurious currents.

  11. Unimodularity criteria for Poisson structures on foliated manifolds

    Science.gov (United States)

    Pedroza, Andrés; Velasco-Barreras, Eduardo; Vorobiev, Yury

    2018-03-01

    We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria for regular Poisson manifolds related to the notion of the Reeb class. In particular, we show that the unimodularity of the transverse Poisson structure of the leaf is a necessary condition for the semilocal unimodular property. Our main tool is an explicit formula for a bigraded decomposition of modular vector fields of a coupling Poisson structure on a foliated manifold. Moreover, we also exploit the notion of the modular class of a Poisson foliation and its relationship with the Reeb class.

  12. Non-isothermal Smoluchowski-Poisson equation as a singular limit of the Navier-Stokes-Fourier-Poisson system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Laurençot, P.

    2007-01-01

    Roč. 88, - (2007), s. 325-349 ISSN 0021-7824 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier- Poisson system * Smoluchowski- Poisson system * singular limit Subject RIV: BA - General Mathematics Impact factor: 1.118, year: 2007

  13. A novel method for the accurate evaluation of Poisson's ratio of soft polymer materials.

    Science.gov (United States)

    Lee, Jae-Hoon; Lee, Sang-Soo; Chang, Jun-Dong; Thompson, Mark S; Kang, Dong-Joong; Park, Sungchan; Park, Seonghun

    2013-01-01

    A new method with a simple algorithm was developed to accurately measure Poisson's ratio of soft materials such as polyvinyl alcohol hydrogel (PVA-H) with a custom experimental apparatus consisting of a tension device, a micro X-Y stage, an optical microscope, and a charge-coupled device camera. In the proposed method, the initial positions of the four vertices of an arbitrarily selected quadrilateral from the sample surface were first measured to generate a 2D 1st-order 4-node quadrilateral element for finite element numerical analysis. Next, minimum and maximum principal strains were calculated from differences between the initial and deformed shapes of the quadrilateral under tension. Finally, Poisson's ratio of PVA-H was determined by the ratio of minimum principal strain to maximum principal strain. This novel method has an advantage in the accurate evaluation of Poisson's ratio despite misalignment between specimens and experimental devices. In this study, Poisson's ratio of PVA-H was 0.44 ± 0.025 (n = 6) for 2.6-47.0% elongations with a tendency to decrease with increasing elongation. The current evaluation method of Poisson's ratio with a simple measurement system can be employed to a real-time automated vision-tracking system which is used to accurately evaluate the material properties of various soft materials.

  14. Perturbation-induced emergence of Poisson-like behavior in non-Poisson systems

    International Nuclear Information System (INIS)

    Akin, Osman C; Grigolini, Paolo; Paradisi, Paolo

    2009-01-01

    The response of a system with ON–OFF intermittency to an external harmonic perturbation is discussed. ON–OFF intermittency is described by means of a sequence of random events, i.e., the transitions from the ON to the OFF state and vice versa. The unperturbed waiting times (WTs) between two events are assumed to satisfy a renewal condition, i.e., the WTs are statistically independent random variables. The response of a renewal model with non-Poisson ON–OFF intermittency, associated with non-exponential WT distribution, is analyzed by looking at the changes induced in the WT statistical distribution by the harmonic perturbation. The scaling properties are also studied by means of diffusion entropy analysis. It is found that, in the range of fast and relatively strong perturbation, the non-Poisson system displays a Poisson-like behavior in both WT distribution and scaling. In particular, the histogram of perturbed WTs becomes a sequence of equally spaced peaks, with intensity decaying exponentially in time. Further, the diffusion entropy detects an ordinary scaling (related to normal diffusion) instead of the expected unperturbed anomalous scaling related to the inverse power-law decay. Thus, an analysis based on the WT histogram and/or on scaling methods has to be considered with some care when dealing with perturbed intermittent systems

  15. Flux Limiter Lattice Boltzmann for Compressible Flows

    International Nuclear Information System (INIS)

    Chen Feng; Li Yingjun; Xu Aiguo; Zhang Guangcai

    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. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  16. Principles of applying Poisson units in radiology

    International Nuclear Information System (INIS)

    Benyumovich, M.S.

    2000-01-01

    The probability that radioactive particles hit particular space patterns (e.g. cells in the squares of a count chamber net) and time intervals (e.g. radioactive particles hit a given area per time unit) follows the Poisson distribution. The mean is the only parameter from which all this distribution depends. A metrological base of counting the cells and radioactive particles is a property of the Poisson distribution assuming equality of a standard deviation to a root square of mean (property 1). The application of Poisson units in counting of blood formed elements and cultured cells was proposed by us (Russian Federation Patent No. 2126230). Poisson units relate to the means which make the property 1 valid. In a case of cells counting, the square of these units is equal to 1/10 of one of count chamber net where they count the cells. Thus one finds the means from the single cell count rate divided by 10. Finding the Poisson units when counting the radioactive particles should assume determination of a number of these particles sufficient to make equality 1 valid. To this end one should subdivide a time interval used in counting a single particle count rate into different number of equal portions (count numbers). Next one should pick out the count number ensuring the satisfaction of equality 1. Such a portion is taken as a Poisson unit in the radioactive particles count. If the flux of particles is controllable one should set up a count rate sufficient to make equality 1 valid. Operations with means obtained by with the use of Poisson units are performed on the base of approximation of the Poisson distribution by a normal one. (author)

  17. A Seemingly Unrelated Poisson Regression Model

    OpenAIRE

    King, Gary

    1989-01-01

    This article introduces a new estimator for the analysis of two contemporaneously correlated endogenous event count variables. This seemingly unrelated Poisson regression model (SUPREME) estimator combines the efficiencies created by single equation Poisson regression model estimators and insights from "seemingly unrelated" linear regression models.

  18. Poisson geometry from a Dirac perspective

    Science.gov (United States)

    Meinrenken, Eckhard

    2018-03-01

    We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.

  19. Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

    Science.gov (United States)

    Chen, Z.; Shu, C.; Tan, D.

    2018-05-01

    An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

  20. Classifying images using restricted Boltzmann machines and convolutional neural networks

    Science.gov (United States)

    Zhao, Zhijun; Xu, Tongde; Dai, Chenyu

    2017-07-01

    To improve the feature recognition ability of deep model transfer learning, we propose a hybrid deep transfer learning method for image classification based on restricted Boltzmann machines (RBM) and convolutional neural networks (CNNs). It integrates learning abilities of two models, which conducts subject classification by exacting structural higher-order statistics features of images. While the method transfers the trained convolutional neural networks to the target datasets, fully-connected layers can be replaced by restricted Boltzmann machine layers; then the restricted Boltzmann machine layers and Softmax classifier are retrained, and BP neural network can be used to fine-tuned the hybrid model. The restricted Boltzmann machine layers has not only fully integrated the whole feature maps, but also learns the statistical features of target datasets in the view of the biggest logarithmic likelihood, thus removing the effects caused by the content differences between datasets. The experimental results show that the proposed method has improved the accuracy of image classification, outperforming other methods on Pascal VOC2007 and Caltech101 datasets.

  1. Lattice Boltzmann simulation on the liquid junction potential in a concentration fuel cell. Paper no. IGEC-1-060

    International Nuclear Information System (INIS)

    Park, J.; Huh, K.Y.; Li, X.

    2005-01-01

    The lattice Boltzmann method (LBM) is applied to investigate the liquid junction potential (LJP) at an interface between two electrolyte layers. The Poisson equation for electrostatic field is solved to extend the applicable range to micro and nano scales in which electroneutrality does not hold. The LBM solutions are validated against analytical and finite difference method (FDM) results for evolution of concentration, net charge density and electrostatic potential. Noticeable separation of the concentration profiles of positive and negative ions occurs for kd less than 67 in simulation, where k is the inverse of the thickness of electrical double layer and d is the system length. Parametric study is performed for the peak potential and the time to reach the peak with respect to kd and ξ which is the initial thickness ratio of the lower concentration to entire stream. Simple coding and easy parallelization will allow the LBM to make an efficient analysis tool for complex electrochemical systems. (author)

  2. Lattice Boltzmann simulations of liquid crystalline fluids: active gels and blue phases

    OpenAIRE

    Cates, M. E.; Henrich, O.; Marenduzzo, D.; Stratford, K.

    2010-01-01

    Lattice Boltzmann simulations have become a method of choice to solve the hydrodynamic equations of motion of a number of complex fluids. Here we review some recent applications of lattice Boltzmann to study the hydrodynamics of liquid crystalline materials. In particular, we focus on the study of (a) the exotic blue phases of cholesteric liquid crystals, and (b) active gels - a model system for actin plus myosin solutions or bacterial suspensions. In both cases lattice Boltzmann studies have...

  3. QSPR models based on molecular mechanics and quantum chemical calculations. 1. Construction of Boltzmann averaged descriptors for alkanes, alcohols, diols, ethers and cyclic compounds

    DEFF Research Database (Denmark)

    Dyekjær, Jane Dannow; Rasmussen, Kjeld; Jonsdottir, Svava Osk

    2002-01-01

    Values for nine descriptors for QSPR (quantitative structure-property relationships) modeling of physical properties of 96 alkanes, alcohols, ethers, diols, triols and cyclic alkanes and alcohols in conjunction with the program Codessa are presented. The descriptors are Boltzmann-averaged by sele......Values for nine descriptors for QSPR (quantitative structure-property relationships) modeling of physical properties of 96 alkanes, alcohols, ethers, diols, triols and cyclic alkanes and alcohols in conjunction with the program Codessa are presented. The descriptors are Boltzmann...

  4. Lattice Boltzmann simulations of droplet formation in confined channels with thermocapillary flows

    Science.gov (United States)

    Gupta, A.; Sbragaglia, M.; Belardinelli, D.; Sugiyama, K.

    2016-12-01

    Based on mesoscale lattice Boltzmann simulations with the "Shan-Chen" model, we explore the influence of thermocapillarity on the breakup properties of fluid threads in a microfluidic T-junction, where a dispersed phase is injected perpendicularly into a main channel containing a continuous phase, and the latter induces periodic breakup of droplets due to the cross-flowing. Temperature effects are investigated by switching on-off both positive-negative temperature gradients along the main channel direction, thus promoting a different thread dynamics with anticipated-delayed breakup. Numerical simulations are performed at changing the flow rates of both the continuous and dispersed phases, as well as the relative importance of viscous forces, surface tension forces, and thermocapillary stresses. The range of parameters is broad enough to characterize the effects of thermocapillarity on different mechanisms of breakup in the confined T-junction, including the so-called "squeezing" and "dripping" regimes, previously identified in the literature. Some simple scaling arguments are proposed to rationalize the observed behavior, and to provide quantitative guidelines on how to predict the droplet size after breakup.

  5. Non-chiral, molecular model of negative Poisson ratio in two dimensions

    International Nuclear Information System (INIS)

    Wojciechowski, K W

    2003-01-01

    A two-dimensional model of tri-atomic molecules (in which 'atoms' are distributed on vertices of equilateral triangles, and which are further referred to as cyclic trimers) is solved exactly in the static (zero-temperature) limit for the nearest-neighbour site-site interactions. It is shown that the cyclic trimers form a mechanically stable and elastically isotropic non-chiral phase of negative Poisson ratio. The properties of the system are illustrated by three examples of atom-atom interaction potentials: (i) the purely repulsive (n-inverse-power) potential, (ii) the purely attractive (n-power) potential and (iii) the Lennard-Jones potential which shows both the repulsive and the attractive part. The analytic form of the dependence of the Poisson ratio on the interatomic potential is obtained. It is shown that the Poisson ratio depends, in a universal way, only on the trimer anisotropy parameter both (1) in the limit of n → ∞ for cases (i) and (ii), as well as (2) at the zero external pressure for any potential with a doubly differentiable minimum, case (iii) is an example

  6. Some properties of the Boltzmann elastic collision operator; Quelques proprietes particulieres de l'operateur de collision elastique de Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    Delcroix, J. L. [Ecole Normale Superieure (France); Salmon, J. [Commissariat a l' energie atomique et aux energies alternatives - CEA (France)

    1959-07-01

    The authors point out some properties (an important one is a variational property) of the Boltzmann elastic collision operator, valid in a more general framework than that of the Lorentz gas. Reprint of a paper published in 'Le journal de physique et le radium', tome 20, Jun 1959, p. 594-596 [French] Les auteurs mettent en evidence quelques proprietes (dont notamment une propriete variationnelle) de l'operateur de collision elastique de Boltzmann valables dans un cadre plus general que celui du gaz de Lorentz. Reproduction d'un article publie dans 'Le journal de physique et le radium', tome 20, Jun 1959, p. 594-596.

  7. Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

    Science.gov (United States)

    Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua

    2018-01-01

    The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model (DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation. It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model. Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model. To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified. Support of National Natural Science Foundation of China under Grant Nos. 11475028, 11772064, and 11502117 Science Challenge Project under Grant Nos. JCKY2016212A501 and TZ2016002

  8. Lattice Boltzmann method for weakly ionized isothermal plasmas

    International Nuclear Information System (INIS)

    Li Huayu; Ki, Hyungson

    2007-01-01

    In this paper, a lattice Boltzmann method (LBM) for weakly ionized isothermal plasmas is presented by introducing a rescaling scheme for the Boltzmann transport equation. Without using this rescaling, we found that the nondimensional relaxation time used in the LBM is too large and the LBM does not produce physically realistic results. The developed model was applied to the electrostatic wave problem and the diffusion process of singly ionized helium plasmas with a 1-3% degree of ionization under an electric field. The obtained results agree well with theoretical values

  9. A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide

    KAUST Repository

    Allen, Rebecca

    2013-01-01

    The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer\\'s cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently

  10. Simulation of bubble motion under gravity by lattice Boltzmann method

    International Nuclear Information System (INIS)

    Takada, Naoki; Misawa, Masaki; Tomiyama, Akio; Hosokawa, Shigeo

    2001-01-01

    We describe the numerical simulation results of bubble motion under gravity by the lattice Boltzmann method (LBM), which assumes that a fluid consists of mesoscopic fluid particles repeating collision and translation and a multiphase interface is reproduced in a self-organizing way by repulsive interaction between different kinds of particles. The purposes in this study are to examine the applicability of LBM to the numerical analysis of bubble motions, and to develop a three-dimensional version of the binary fluid model that introduces a free energy function. We included the buoyancy terms due to the density difference in the lattice Boltzmann equations, and simulated single-and two-bubble motions, setting flow conditions according to the Eoetvoes and Morton numbers. The two-dimensional results by LBM agree with those by the Volume of Fluid method based on the Navier-Stokes equations. The three-dimensional model possesses the surface tension satisfying the Laplace's law, and reproduces the motion of single bubble and the two-bubble interaction of their approach and coalescence in circular tube. There results prove that the buoyancy terms and the 3D model proposed here are suitable, and that LBM is useful for the numerical analysis of bubble motion under gravity. (author)

  11. Determination of maximum negative Poisson's ratio for laminated fiber composites

    Energy Technology Data Exchange (ETDEWEB)

    Shokrieh, M.M.; Assadi, A. [Composites Research Laboratory, Mechanical Engineering Department, Center of Excellence in Experimental Solid Mechanics and Dynamics, Iran University of Science and Technology, Tehran 16846-13114 (Iran, Islamic Republic of)

    2011-05-15

    Contrary to isotropic materials, composites always show complicated mechanical behavior under external loadings. In this article, an efficient algorithm is employed to obtain the maximum negative Poisson's ratio for laminated composite plates. We try to simplify the problem based on normalization of parameters and some manufacturing constraints to overlook the additional constraint of the optimization procedure. A genetic algorithm is used to find the optimal thickness of each lamina with a specified fiber direction. It is observed that the laminated composite with the configuration of (15/60/15) has the maximum negative Poisson's ratio. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  12. The Interaction of Boltzmann with Mach, Ostwald and Planck, and his influence on Nernst and Einstein

    International Nuclear Information System (INIS)

    Broda, E.

    1981-01-01

    Boltzmann esteemed both Mach and Ostwald personally and as experimentalists, but consistently fought them in epistemology. He represented atomism and realism against energism and positivism. In the early period Boltzmann also had to struggle against Planck as a phenomenologist, but he welcomed his quantum hypothesis. As a scientist Nernst was also under Boltzmann's influence. Einstein learned atomism from (Maxwell and) Boltzmann. After Einstein had overcome Mach's positivist influence, he unknowingly approached Boltzmann's philosophical views. Some sociopolitlcal aspects of the lives of the great physicists will be discussed. It will be shown how they all, and many of Boltzmann's most eminent students, in one way or other conflicted with evil tendencies and developments in existing society. (author)

  13. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations; Application de la decomposition de Littlewood-Paley a la regularite pour des equations cinetiques de type Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    EL Safadi, M

    2007-03-15

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  14. Universal Property of Quantum Gravity implied by Bekenstein-Hawking Entropy and Boltzmann formula

    International Nuclear Information System (INIS)

    Saida, Hiromi

    2013-01-01

    We search for a universal property of quantum gravity. By u niversal , we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we try to put the basis of our discussion on theories established by some experiments. Thus, we focus our attention on thermodynamical and statistical-mechanical basis of the black hole thermodynamics: Let us assume that the Bekenstein-Hawking entropy is given by the Boltzmann formula applied to the underlying theory of quantum gravity. Under this assumption, the conditions justifying Boltzmann formula together with uniqueness of Bekenstein-Hawking entropy imply a reasonable universal property of quantum gravity. The universal property indicates a repulsive gravity at Planck length scale, otherwise stationary black holes can not be regarded as thermal equilibrium states of gravity. Further, in semi-classical level, we discuss a possible correction of Einstein equation which generates repulsive gravity at Planck length scale.

  15. Grafting and Poisson Structure in (2+1)-Gravity with Vanishing Cosmological Constant

    Science.gov (United States)

    Meusburger, C.

    2006-09-01

    We relate the geometrical construction of (2+1)-spacetimes via grafting to phase space and Poisson structure in the Chern-Simons formulation of (2+1)-dimensional gravity with vanishing cosmological constant on manifolds of topology mathbb{R} × S_g, where S g is an orientable two-surface of genus g>1. We show how grafting along simple closed geodesics λ is implemented in the Chern-Simons formalism and derive explicit expressions for its action on the holonomies of general closed curves on S g .We prove that this action is generated via the Poisson bracket by a gauge invariant observable associated to the holonomy of λ. We deduce a symmetry relation between the Poisson brackets of observables associated to the Lorentz and translational components of the holonomies of general closed curves on S g and discuss its physical interpretation. Finally, we relate the action of grafting on the phase space to the action of Dehn twists and show that grafting can be viewed as a Dehn twist with a formal parameter θ satisfying θ2 = 0.

  16. 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.

  17. Boltzmann-Fokker-Planck calculations using standard discrete-ordinates codes

    International Nuclear Information System (INIS)

    Morel, J.E.

    1987-01-01

    The Boltzmann-Fokker-Planck (BFP) equation can be used to describe both neutral and charged-particle transport. Over the past several years, the author and several collaborators have developed methods for representing Fokker-Planck operators with standard multigroup-Legendre cross-section data. When these data are input to a standard S/sub n/ code such as ONETRAN, the code actually solves the Boltzmann-Fokker-Planck equation rather than the Boltzmann equation. This is achieved wihout any modification to the S/sub n/ codes. Because BFP calculations can be more demanding from a numerical viewpoint than standard neutronics calculations, we have found it useful to implement new quadrature methods ad convergence acceleration methods in the standard discrete-ordinates code, ONETRAN. We discuss our BFP cross-section representation techniques, our improved quadrature and acceleration techniques, and present results from BFP coupled electron-photon transport calculations performed with ONETRAN. 19 refs., 7 figs

  18. Poisson structure and symmetry in the Chern-Simons formulation of (2 + 1)-dimensional gravity

    International Nuclear Information System (INIS)

    Meusburger, C; Schroers, B J

    2003-01-01

    In the formulation of (2 + 1)-dimensional gravity as a Chern-Simons gauge theory, the phase space is the moduli space of flat Poincare group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincare transformations in a nontrivial fashion. We derive the conserved quantities associated with the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms

  19. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations

    International Nuclear Information System (INIS)

    EL Safadi, M.

    2007-03-01

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  20. The Fractional Poisson Process and the Inverse Stable Subordinator

    OpenAIRE

    Meerschaert, Mark; Nane, Erkan; Vellaisamy, P.

    2011-01-01

    The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two main approaches in the stochastic theory of time-fractional diffusion equations. The equivalence extend...

  1. Semiclassical corrections to the interaction energy of a hard-sphere Boltzmann gas

    Energy Technology Data Exchange (ETDEWEB)

    Bhaduri, R K [Department of Physics and Astronomy, McMaster University, Hamilton, L8S 4M1 (Canada); Dijk, W van [Department of Physics and Astronomy, McMaster University, Hamilton, L8S 4M1 (Canada); Srivastava, M K [Institute Instrumentation Center, IIT, Roorkee 247 667 (India)

    2006-11-01

    Quantum effects in statistical mechanics are important when the thermal wavelength is of the order of, or greater than, the mean interatomic spacing. This is examined in depth taking the example of a hard-sphere Boltzmann gas. Using the virial expansion for the equation of state, it is shown that the interaction energy of a classical hard-sphere gas is exactly zero. When the (second) virial coefficient of such a gas is obtained quantum mechanically, however, the quantum contribution to the interaction energy is shown to be substantial. The importance of the semiclassical corrections to the interaction energy shows up dramatically in such a system.

  2. Semiclassical corrections to the interaction energy of a hard-sphere Boltzmann gas

    International Nuclear Information System (INIS)

    Bhaduri, R K; Dijk, W van; Srivastava, M K

    2006-01-01

    Quantum effects in statistical mechanics are important when the thermal wavelength is of the order of, or greater than, the mean interatomic spacing. This is examined in depth taking the example of a hard-sphere Boltzmann gas. Using the virial expansion for the equation of state, it is shown that the interaction energy of a classical hard-sphere gas is exactly zero. When the (second) virial coefficient of such a gas is obtained quantum mechanically, however, the quantum contribution to the interaction energy is shown to be substantial. The importance of the semiclassical corrections to the interaction energy shows up dramatically in such a system

  3. Mass and heat transfer between evaporation and condensation surfaces: Atomistic simulation and solution of Boltzmann kinetic equation.

    Science.gov (United States)

    Zhakhovsky, Vasily V; Kryukov, Alexei P; Levashov, Vladimir Yu; Shishkova, Irina N; Anisimov, Sergey I

    2018-04-16

    Boundary conditions required for numerical solution of the Boltzmann kinetic equation (BKE) for mass/heat transfer between evaporation and condensation surfaces are analyzed by comparison of BKE results with molecular dynamics (MD) simulations. Lennard-Jones potential with parameters corresponding to solid argon is used to simulate evaporation from the hot side, nonequilibrium vapor flow with a Knudsen number of about 0.02, and condensation on the cold side of the condensed phase. The equilibrium density of vapor obtained in MD simulation of phase coexistence is used in BKE calculations for consistency of BKE results with MD data. The collision cross-section is also adjusted to provide a thermal flux in vapor identical to that in MD. Our MD simulations of evaporation toward a nonreflective absorbing boundary show that the velocity distribution function (VDF) of evaporated atoms has the nearly semi-Maxwellian shape because the binding energy of atoms evaporated from the interphase layer between bulk phase and vapor is much smaller than the cohesive energy in the condensed phase. Indeed, the calculated temperature and density profiles within the interphase layer indicate that the averaged kinetic energy of atoms remains near-constant with decreasing density almost until the interphase edge. Using consistent BKE and MD methods, the profiles of gas density, mass velocity, and temperatures together with VDFs in a gap of many mean free paths between the evaporation and condensation surfaces are obtained and compared. We demonstrate that the best fit of BKE results with MD simulations can be achieved with the evaporation and condensation coefficients both close to unity.

  4. Beyond the continuum: how molecular solvent structure affects electrostatics and hydrodynamics at solid-electrolyte interfaces.

    Science.gov (United States)

    Bonthuis, Douwe Jan; Netz, Roland R

    2013-10-03

    Standard continuum theory fails to predict several key experimental results of electrostatic and electrokinetic measurements at aqueous electrolyte interfaces. In order to extend the continuum theory to include the effects of molecular solvent structure, we generalize the equations for electrokinetic transport to incorporate a space dependent dielectric profile, viscosity profile, and non-electrostatic interaction potential. All necessary profiles are extracted from atomistic molecular dynamics (MD) simulations. We show that the MD results for the ion-specific distribution of counterions at charged hydrophilic and hydrophobic interfaces are accurately reproduced using the dielectric profile of pure water and a non-electrostatic repulsion in an extended Poisson-Boltzmann equation. The distributions of Na(+) at both surface types and Cl(-) at hydrophilic surfaces can be modeled using linear dielectric response theory, whereas for Cl(-) at hydrophobic surfaces it is necessary to apply nonlinear response theory. The extended Poisson-Boltzmann equation reproduces the experimental values of the double-layer capacitance for many different carbon-based surfaces. In conjunction with a generalized hydrodynamic theory that accounts for a space dependent viscosity, the model captures the experimentally observed saturation of the electrokinetic mobility as a function of the bare surface charge density and the so-called anomalous double-layer conductivity. The two-scale approach employed here-MD simulations and continuum theory-constitutes a successful modeling scheme, providing basic insight into the molecular origins of the static and kinetic properties of charged surfaces, and allowing quantitative modeling at low computational cost.

  5. Evaluating the double Poisson generalized linear model.

    Science.gov (United States)

    Zou, Yaotian; Geedipally, Srinivas Reddy; Lord, Dominique

    2013-10-01

    The objectives of this study are to: (1) examine the applicability of the double Poisson (DP) generalized linear model (GLM) for analyzing motor vehicle crash data characterized by over- and under-dispersion and (2) compare the performance of the DP GLM with the Conway-Maxwell-Poisson (COM-Poisson) GLM in terms of goodness-of-fit and theoretical soundness. The DP distribution has seldom been investigated and applied since its first introduction two decades ago. The hurdle for applying the DP is related to its normalizing constant (or multiplicative constant) which is not available in closed form. This study proposed a new method to approximate the normalizing constant of the DP with high accuracy and reliability. The DP GLM and COM-Poisson GLM were developed using two observed over-dispersed datasets and one observed under-dispersed dataset. The modeling results indicate that the DP GLM with its normalizing constant approximated by the new method can handle crash data characterized by over- and under-dispersion. Its performance is comparable to the COM-Poisson GLM in terms of goodness-of-fit (GOF), although COM-Poisson GLM provides a slightly better fit. For the over-dispersed data, the DP GLM performs similar to the NB GLM. Considering the fact that the DP GLM can be easily estimated with inexpensive computation and that it is simpler to interpret coefficients, it offers a flexible and efficient alternative for researchers to model count data. Copyright © 2013 Elsevier Ltd. All rights reserved.

  6. 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.

  7. Lattice Boltzmann method with the cell-population equilibrium

    International Nuclear Information System (INIS)

    Zhou Xiaoyang; Cheng Bing; Shi Baochang

    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 non-negative 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

  8. A test of inflated zeros for Poisson regression models.

    Science.gov (United States)

    He, Hua; Zhang, Hui; Ye, Peng; Tang, Wan

    2017-01-01

    Excessive zeros are common in practice and may cause overdispersion and invalidate inference when fitting Poisson regression models. There is a large body of literature on zero-inflated Poisson models. However, methods for testing whether there are excessive zeros are less well developed. The Vuong test comparing a Poisson and a zero-inflated Poisson model is commonly applied in practice. However, the type I error of the test often deviates seriously from the nominal level, rendering serious doubts on the validity of the test in such applications. In this paper, we develop a new approach for testing inflated zeros under the Poisson model. Unlike the Vuong test for inflated zeros, our method does not require a zero-inflated Poisson model to perform the test. Simulation studies show that when compared with the Vuong test our approach not only better at controlling type I error rate, but also yield more power.

  9. Stabilization of the Lattice Boltzmann Method Using Information Theory

    OpenAIRE

    Wilson, Tyler L; Pugh, Mary; Dawson, Francis

    2018-01-01

    A novel Lattice Boltzmann method is derived using the Principle of Minimum Cross Entropy (MinxEnt) via the minimization of Kullback-Leibler Divergence (KLD). By carrying out the actual single step Newton-Raphson minimization (MinxEnt-LBM) a more accurate and stable Lattice Boltzmann Method can be implemented. To demonstrate this, 1D shock tube and 2D lid-driven cavity flow simulations are carried out and compared to Single Relaxation Time LBM, Two Relaxation Time LBM, Multiple Relaxation Time...

  10. Simplified simulation of Boltzmann-Langevin equation

    International Nuclear Information System (INIS)

    Ayik, S.; Randrup, J.

    1994-01-01

    We briefly recall the Boltzmann-Langevin model of nuclear dynamics. We then summarize recent progress in deriving approximate analytical expressions for the associated transport coefficients and describe a numerical method for simulating the stochastic evolution of the phase-space density. (orig.)

  11. Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes.

    Science.gov (United States)

    Hougaard, P; Lee, M L; Whitmore, G A

    1997-12-01

    Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.

  12. On the effects of the reactive terms in the Boltzmann equation

    Directory of Open Access Journals (Sweden)

    C. J. Zamlutti

    Full Text Available The effects of the production and loss mechanisms that affect the Boltzmann equations are considered by the inclusion of a reactive term. The necessary elements to develop a proper form for this term are revised and the current trends analyzed. Although no accurate theoretical treatment of the problem is possible due to the many body nature of it, important relations can be derived which, besides being representative of the quantitative aspects of the matter, are illustrative of the qualitative features of the phenomenon. The overall procedure is detailed in this revision.

  13. Relaxed Poisson cure rate models.

    Science.gov (United States)

    Rodrigues, Josemar; Cordeiro, Gauss M; Cancho, Vicente G; Balakrishnan, N

    2016-03-01

    The purpose of this article is to make the standard promotion cure rate model (Yakovlev and Tsodikov, ) more flexible by assuming that the number of lesions or altered cells after a treatment follows a fractional Poisson distribution (Laskin, ). It is proved that the well-known Mittag-Leffler relaxation function (Berberan-Santos, ) is a simple way to obtain a new cure rate model that is a compromise between the promotion and geometric cure rate models allowing for superdispersion. So, the relaxed cure rate model developed here can be considered as a natural and less restrictive extension of the popular Poisson cure rate model at the cost of an additional parameter, but a competitor to negative-binomial cure rate models (Rodrigues et al., ). Some mathematical properties of a proper relaxed Poisson density are explored. A simulation study and an illustration of the proposed cure rate model from the Bayesian point of view are finally presented. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  14. Poisson denoising on the sphere

    Science.gov (United States)

    Schmitt, J.; Starck, J. L.; Fadili, J.; Grenier, I.; Casandjian, J. M.

    2009-08-01

    In the scope of the Fermi mission, Poisson noise removal should improve data quality and make source detection easier. This paper presents a method for Poisson data denoising on sphere, called Multi-Scale Variance Stabilizing Transform on Sphere (MS-VSTS). This method is based on a Variance Stabilizing Transform (VST), a transform which aims to stabilize a Poisson data set such that each stabilized sample has an (asymptotically) constant variance. In addition, for the VST used in the method, the transformed data are asymptotically Gaussian. Thus, MS-VSTS consists in decomposing the data into a sparse multi-scale dictionary (wavelets, curvelets, ridgelets...), and then applying a VST on the coefficients in order to get quasi-Gaussian stabilized coefficients. In this present article, the used multi-scale transform is the Isotropic Undecimated Wavelet Transform. Then, hypothesis tests are made to detect significant coefficients, and the denoised image is reconstructed with an iterative method based on Hybrid Steepest Descent (HST). The method is tested on simulated Fermi data.

  15. Lattice Boltzmann Methods to Address Fundamental Boiling and Two-Phase Problems

    Energy Technology Data Exchange (ETDEWEB)

    Uddin, Rizwan

    2012-01-01

    This report presents the progress made during the fourth (no cost extension) year of this three-year grant aimed at the development of a consistent Lattice Boltzmann formulation for boiling and two-phase flows. During the first year, a consistent LBM formulation for the simulation of a two-phase water-steam system was developed. Results of initial model validation in a range of thermo-dynamic conditions typical for Boiling Water Reactors (BWRs) were shown. Progress was made on several fronts during the second year. Most important of these included the simulation of the coalescence of two bubbles including the surface tension effects. Work during the third year focused on the development of a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model) for the 3 simulation of two-phase dynamics. The model is based on the principle of free energy minimization and invokes the Gibbs-Duhem equation in the formulation of non-ideal forcing function. This was reported in detail in the last progress report. Part of the efforts during the last (no-cost extension) year were focused on developing a parallel capability for the 2D as well as for the 3D codes developed in this project. This will be reported in the final report. Here we report the work carried out on testing the AILB model for conditions including the thermal effects. A simplified thermal LB model, based on the thermal energy distribution approach, was developed. The simplifications are made after neglecting the viscous heat dissipation and the work done by pressure in the original thermal energy distribution model. Details of the model are presented here, followed by a discussion of the boundary conditions, and then results for some two-phase thermal problems.

  16. On hamiltonian systems with even and odd Poisson brackets and on the duality of their conservation laws

    International Nuclear Information System (INIS)

    Volkov, D.V.; Pashnev, A.I.; Soroka, V.A.; Tkach, V.I.

    1986-01-01

    Taking as example the Witten supersymmetric mechanics it is shown that the hamiltonian system with equal number of even and odd canonical variables admits simultaneously the introduction of even and odd Poisson brackets. When using bracket operations of different graduation the canonical variable equations are not varied whereas the motion integrals with opposite Grassman graduation become dual transforming into each other at the transition to Poisson bracket with opposite graduation

  17. Selective Contrast Adjustment by Poisson Equation

    Directory of Open Access Journals (Sweden)

    Ana-Belen Petro

    2013-09-01

    Full Text Available Poisson Image Editing is a new technique permitting to modify the gradient vector field of an image, and then to recover an image with a gradient approaching this modified gradient field. This amounts to solve a Poisson equation, an operation which can be efficiently performed by Fast Fourier Transform (FFT. This paper describes an algorithm applying this technique, with two different variants. The first variant enhances the contrast by increasing the gradient in the dark regions of the image. This method is well adapted to images with back light or strong shadows, and reveals details in the shadows. The second variant of the same Poisson technique enhances all small gradients in the image, thus also sometimes revealing details and texture.

  18. Simple dead-time corrections for discrete time series of non-Poisson data

    International Nuclear Information System (INIS)

    Larsen, Michael L; Kostinski, Alexander B

    2009-01-01

    The problem of dead time (instrumental insensitivity to detectable events due to electronic or mechanical reset time) is considered. Most existing algorithms to correct for event count errors due to dead time implicitly rely on Poisson counting statistics of the underlying phenomena. However, when the events to be measured are clustered in time, the Poisson statistics assumption results in underestimating both the true event count and any statistics associated with count variability; the 'busiest' part of the signal is partially missed. Using the formalism associated with the pair-correlation function, we develop first-order correction expressions for the general case of arbitrary counting statistics. The results are verified through simulation of a realistic clustering scenario

  19. PENERAPAN REGRESI BINOMIAL NEGATIF UNTUK MENGATASI OVERDISPERSI PADA REGRESI POISSON

    Directory of Open Access Journals (Sweden)

    PUTU SUSAN PRADAWATI

    2013-09-01

    Full Text Available Poisson regression was used to analyze the count data which Poisson distributed. Poisson regression analysis requires state equidispersion, in which the mean value of the response variable is equal to the value of the variance. However, there are deviations in which the value of the response variable variance is greater than the mean. This is called overdispersion. If overdispersion happens and Poisson Regression analysis is being used, then underestimated standard errors will be obtained. Negative Binomial Regression can handle overdispersion because it contains a dispersion parameter. From the simulation data which experienced overdispersion in the Poisson Regression model it was found that the Negative Binomial Regression was better than the Poisson Regression model.

  20. Accelerating electrostatic surface potential calculation with multi-scale approximation on graphics processing units.

    Science.gov (United States)

    Anandakrishnan, Ramu; Scogland, Tom R W; Fenley, Andrew T; Gordon, John C; Feng, Wu-chun; Onufriev, Alexey V

    2010-06-01

    Tools that compute and visualize biomolecular electrostatic surface potential have been used extensively for studying biomolecular function. However, determining the surface potential for large biomolecules on a typical desktop computer can take days or longer using currently available tools and methods. Two commonly used techniques to speed-up these types of electrostatic computations are approximations based on multi-scale coarse-graining and parallelization across multiple processors. This paper demonstrates that for the computation of electrostatic surface potential, these two techniques can be combined to deliver significantly greater speed-up than either one separately, something that is in general not always possible. Specifically, the electrostatic potential computation, using an analytical linearized Poisson-Boltzmann (ALPB) method, is approximated using the hierarchical charge partitioning (HCP) multi-scale method, and parallelized on an ATI Radeon 4870 graphical processing unit (GPU). The implementation delivers a combined 934-fold speed-up for a 476,040 atom viral capsid, compared to an equivalent non-parallel implementation on an Intel E6550 CPU without the approximation. This speed-up is significantly greater than the 42-fold speed-up for the HCP approximation alone or the 182-fold speed-up for the GPU alone. Copyright (c) 2010 Elsevier Inc. All rights reserved.

  1. Boltzmann brains and the scale-factor cutoff measure of the multiverse

    International Nuclear Information System (INIS)

    De Simone, Andrea; Guth, Alan H.; Linde, Andrei; Noorbala, Mahdiyar; Salem, Michael P.; Vilenkin, Alexander

    2010-01-01

    To make predictions for an eternally inflating 'multiverse', one must adopt a procedure for regulating its divergent spacetime volume. Recently, a new test of such spacetime measures has emerged: normal observers - who evolve in pocket universes cooling from hot big bang conditions - must not be vastly outnumbered by 'Boltzmann brains' - freak observers that pop in and out of existence as a result of rare quantum fluctuations. If the Boltzmann brains prevail, then a randomly chosen observer would be overwhelmingly likely to be surrounded by an empty world, where all but vacuum energy has redshifted away, rather than the rich structure that we observe. Using the scale-factor cutoff measure, we calculate the ratio of Boltzmann brains to normal observers. We find the ratio to be finite, and give an expression for it in terms of Boltzmann brain nucleation rates and vacuum decay rates. We discuss the conditions that these rates must obey for the ratio to be acceptable, and we discuss estimates of the rates under a variety of assumptions.

  2. Analyzing hospitalization data: potential limitations of Poisson regression.

    Science.gov (United States)

    Weaver, Colin G; Ravani, Pietro; Oliver, Matthew J; Austin, Peter C; Quinn, Robert R

    2015-08-01

    Poisson regression is commonly used to analyze hospitalization data when outcomes are expressed as counts (e.g. number of days in hospital). However, data often violate the assumptions on which Poisson regression is based. More appropriate extensions of this model, while available, are rarely used. We compared hospitalization data between 206 patients treated with hemodialysis (HD) and 107 treated with peritoneal dialysis (PD) using Poisson regression and compared results from standard Poisson regression with those obtained using three other approaches for modeling count data: negative binomial (NB) regression, zero-inflated Poisson (ZIP) regression and zero-inflated negative binomial (ZINB) regression. We examined the appropriateness of each model and compared the results obtained with each approach. During a mean 1.9 years of follow-up, 183 of 313 patients (58%) were never hospitalized (indicating an excess of 'zeros'). The data also displayed overdispersion (variance greater than mean), violating another assumption of the Poisson model. Using four criteria, we determined that the NB and ZINB models performed best. According to these two models, patients treated with HD experienced similar hospitalization rates as those receiving PD {NB rate ratio (RR): 1.04 [bootstrapped 95% confidence interval (CI): 0.49-2.20]; ZINB summary RR: 1.21 (bootstrapped 95% CI 0.60-2.46)}. Poisson and ZIP models fit the data poorly and had much larger point estimates than the NB and ZINB models [Poisson RR: 1.93 (bootstrapped 95% CI 0.88-4.23); ZIP summary RR: 1.84 (bootstrapped 95% CI 0.88-3.84)]. We found substantially different results when modeling hospitalization data, depending on the approach used. Our results argue strongly for a sound model selection process and improved reporting around statistical methods used for modeling count data. © The Author 2015. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

  3. The quantum poisson-Lie T-duality and mirror symmetry

    International Nuclear Information System (INIS)

    Parkhomenko, S.E.

    1999-01-01

    Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the quantum Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also

  4. The lattice Boltzmann model for the second-order Benjamin–Ono equations

    International Nuclear Information System (INIS)

    Lai, Huilin; Ma, Changfeng

    2010-01-01

    In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin–Ono equation. With the Taylor expansion and the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations

  5. Statistics of weighted Poisson events and its applications

    International Nuclear Information System (INIS)

    Bohm, G.; Zech, G.

    2014-01-01

    The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or relevance to a certain type of reaction. The sum is described by the compound Poisson distribution (CPD) which is shortly reviewed. It is shown that the CPD can be approximated by a scaled Poisson distribution (SPD). The SPD is applied to parameter estimation in situations where the data are distorted by resolution effects. It performs considerably better than the normal approximation that is usually used. A special Poisson bootstrap technique is presented which permits to derive confidence limits for observations following the CPD

  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. Lyapunov stability and poisson structure of the thermal TDHF and RPA equations

    International Nuclear Information System (INIS)

    Balian, R.; Veneroni, M.

    1989-01-01

    The thermal TDHF equation is analyzed in the Liouville representation of quantum mechanics, where the matrix elements of the single-particle (s.p) density ρ behave as classical dynamical variables. By introducing the Lie--Poisson bracket associated with the unitary group of the s.p. Hilbert space, we show that TDHF has a Hamiltonian, but non-canonical, classical form. Within this Poisson structure, either the s.p. energy or the s.p. grand potential Ω(ρ) act as a Hamilton function. The Lyapunov stability of both the TDHF and RPA equations around a HF state then follows, since the HF approximation for thermal equilibrium is determined by minimizing Ω(ρ). The RPA matrix in the Liouville space is expressed as the product of the Poisson tensor with the HF stability matrix, interpreted as a metric tensor generated by the entropy. This factorization displays the roles of the energy and entropy terms arising from Ω(ρ) in the RPA dynamics, and it helps to construct the RPA modes. Several extensions are considered. copyright 1989 Academic Press, Inc

  8. Lyapunov stability and Poisson structure of the thermal TDHF and RPA equations

    International Nuclear Information System (INIS)

    Veneroni, M.; Balian, R.

    1989-01-01

    The thermal TDHF equation is analyzed in the Liouville representation of quantum mechanics, where the matrix elements of the single-particle (s.p.) density ρ behave as classical dynamical variables. By introducing the Lie-Poisson bracket associated with the unitary group of the s.p. Hilbert space, we show that TDHF has a hamiltonian, but non-canonical, classical form. Within this Poisson structure, either the s.p. energy or the s.p. grand potential Ω(ρ) act as a Hamilton function. The Lyapunov stability of both the TDHF and RPA equations around a HF state then follows, since the HF approximation for thermal equilibrium is determined by minimizing Ω(ρ). The RPA matrix in the Liouville space is expressed as the product of the Poisson tensor with the HF stability matrix, interpreted as a metric tensor generated by the entropy. This factorization displays the roles of the energy and entropy terms arising from Ω(ρ) in the RPA dynamics, and it helps to construct the RPA modes. Several extensions are considered

  9. Boltzmann Oracle for Combinatorial Systems

    OpenAIRE

    Pivoteau , Carine; Salvy , Bruno; Soria , Michèle

    2008-01-01

    International audience; Boltzmann random generation applies to well-defined systems of recursive combinatorial equations. It relies on oracles giving values of the enumeration generating series inside their disk of convergence. We show that the combinatorial systems translate into numerical iteration schemes that provide such oracles. In particular, we give a fast oracle based on Newton iteration.

  10. Investigation of Random Switching Driven by a Poisson Point Process

    DEFF Research Database (Denmark)

    Simonsen, Maria; Schiøler, Henrik; Leth, John-Josef

    2015-01-01

    This paper investigates the switching mechanism of a two-dimensional switched system, when the switching events are generated by a Poisson point process. A model, in the shape of a stochastic process, for such a system is derived and the distribution of the trajectory's position is developed...... together with marginal density functions for the coordinate functions. Furthermore, the joint probability distribution is given explicitly....

  11. Noncommutative gauge theory for Poisson manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

    2000-09-25

    A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

  12. Noncommutative gauge theory for Poisson manifolds

    International Nuclear Information System (INIS)

    Jurco, Branislav; Schupp, Peter; Wess, Julius

    2000-01-01

    A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem

  13. Entropic multirelaxation lattice Boltzmann models for turbulent flows

    Science.gov (United States)

    Bösch, Fabian; Chikatamarla, Shyam S.; Karlin, Ilya V.

    2015-10-01

    We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014), 10.1103/PhysRevE.90.031302] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.

  14. A stochastic model of multiple scattering of charged particles: process, transport equation and solutions

    International Nuclear Information System (INIS)

    Papiez, L.; Moskvin, V.; Tulovsky, V.

    2001-01-01

    The process of angular-spatial evolution of multiple scattering of charged particles can be described by a special case of Boltzmann integro-differential equation called Lewis equation. The underlying stochastic process for this evolution is the compound Poisson process on the surface of the unit sphere. The significant portion of events that constitute compound Poisson process that describes multiple scattering have diffusional character. This property allows to analyze the process of angular-spatial evolution of multiple scattering of charged particles as combination of soft and hard collision processes and compute appropriately its transition densities. These computations provide a method of the approximate solution to the Lewis equation. (orig.)

  15. Generic Schemes for Single-Molecule Kinetics. 2: Information Content of the Poisson Indicator.

    Science.gov (United States)

    Avila, Thomas R; Piephoff, D Evan; Cao, Jianshu

    2017-08-24

    Recently, we described a pathway analysis technique (paper 1) for analyzing generic schemes for single-molecule kinetics based upon the first-passage time distribution. Here, we employ this method to derive expressions for the Poisson indicator, a normalized measure of stochastic variation (essentially equivalent to the Fano factor and Mandel's Q parameter), for various renewal (i.e., memoryless) enzymatic reactions. We examine its dependence on substrate concentration, without assuming all steps follow Poissonian kinetics. Based upon fitting to the functional forms of the first two waiting time moments, we show that, to second order, the non-Poissonian kinetics are generally underdetermined but can be specified in certain scenarios. For an enzymatic reaction with an arbitrary intermediate topology, we identify a generic minimum of the Poisson indicator as a function of substrate concentration, which can be used to tune substrate concentration to the stochastic fluctuations and to estimate the largest number of underlying consecutive links in a turnover cycle. We identify a local maximum of the Poisson indicator (with respect to substrate concentration) for a renewal process as a signature of competitive binding, either between a substrate and an inhibitor or between multiple substrates. Our analysis explores the rich connections between Poisson indicator measurements and microscopic kinetic mechanisms.

  16. 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.)

  17. Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.

    Science.gov (United States)

    Schuss, Z; Nadler, B; Eisenberg, R S

    2001-09-01

    Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately

  18. Boltzmann machines for travelling salesman problems

    NARCIS (Netherlands)

    Aarts, E.H.L.; Korst, J.H.M.

    1989-01-01

    Boltzmann machines are proposed as a massively parallel alternative to the (sequential) simulated annealing algorithm. Our approach is tailored to the travelling salesman problem, but it can also be applied to a more general class of combinatorial optimization problems. For two distinct 0–1

  19. Compound Poisson Approximations for Sums of Random Variables

    OpenAIRE

    Serfozo, Richard F.

    1986-01-01

    We show that a sum of dependent random variables is approximately compound Poisson when the variables are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. We give several upper bounds on the total-variation distance between the distribution of such a sum and a compound Poisson distribution. Included is an example for Markovian occurrences of a rare event. Our bounds are consistent with those that are known for Poisson approximations for sums of...

  20. Square root approximation to the poisson channel

    NARCIS (Netherlands)

    Tsiatmas, A.; Willems, F.M.J.; Baggen, C.P.M.J.

    2013-01-01

    Starting from the Poisson model we present a channel model for optical communications, called the Square Root (SR) Channel, in which the noise is additive Gaussian with constant variance. Initially, we prove that for large peak or average power, the transmission rate of a Poisson Channel when coding

  1. Duality and modular class of a Nambu-Poisson structure

    International Nuclear Information System (INIS)

    Ibanez, R.; Leon, M. de; Lopez, B.; Marrero, J.C.; Padron, E.

    2001-01-01

    In this paper we introduce cohomology and homology theories for Nambu-Poisson manifolds. Also we study the relation between the existence of a duality for these theories and the vanishing of a particular Nambu-Poisson cohomology class, the modular class. The case of a regular Nambu-Poisson structure and some singular examples are discussed. (author)

  2. 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

  3. Poisson goodness-of-fit tests for radiation-induced chromosome aberrations

    International Nuclear Information System (INIS)

    Merkle, W.

    1981-01-01

    Asymptotic and exact Poisson goodness-to-fit tests have been reviewed with regard to their applicability in analysing distributional properties of data on chromosome aberrations. It has been demonstrated that for typical cytogenetic samples, i.e. when the average number of aberrations per cell is smaller than one, results of asymptotic tests, especially of the most commonly used u-test, differ greatly from results of corresponding exact tests. While the u-statistic can serve as a qualitative index to indicate a tendency towards under- or over-dispersion, exact tests should be used if the assumption of a Poisson distribution is crucial, e.g. in investigating induction mechanisms. If the main interest is to detect a difference between the mean and the variance of a sample it is furthermore important to realize that a much larger sample size is required to detect underdispersion than it is to detect overdispersion. (author)

  4. Scaling the Poisson Distribution

    Science.gov (United States)

    Farnsworth, David L.

    2014-01-01

    We derive the additive property of Poisson random variables directly from the probability mass function. An important application of the additive property to quality testing of computer chips is presented.

  5. Background stratified Poisson regression analysis of cohort data.

    Science.gov (United States)

    Richardson, David B; Langholz, Bryan

    2012-03-01

    Background stratified Poisson regression is an approach that has been used in the analysis of data derived from a variety of epidemiologically important studies of radiation-exposed populations, including uranium miners, nuclear industry workers, and atomic bomb survivors. We describe a novel approach to fit Poisson regression models that adjust for a set of covariates through background stratification while directly estimating the radiation-disease association of primary interest. The approach makes use of an expression for the Poisson likelihood that treats the coefficients for stratum-specific indicator variables as 'nuisance' variables and avoids the need to explicitly estimate the coefficients for these stratum-specific parameters. Log-linear models, as well as other general relative rate models, are accommodated. This approach is illustrated using data from the Life Span Study of Japanese atomic bomb survivors and data from a study of underground uranium miners. The point estimate and confidence interval obtained from this 'conditional' regression approach are identical to the values obtained using unconditional Poisson regression with model terms for each background stratum. Moreover, it is shown that the proposed approach allows estimation of background stratified Poisson regression models of non-standard form, such as models that parameterize latency effects, as well as regression models in which the number of strata is large, thereby overcoming the limitations of previously available statistical software for fitting background stratified Poisson regression models.

  6. Poisson-Lie T-plurality

    International Nuclear Information System (INIS)

    Unge, Rikard von

    2002-01-01

    We extend the path-integral formalism for Poisson-Lie T-duality to include the case of Drinfeld doubles which can be decomposed into bi-algebras in more than one way. We give the correct shift of the dilaton, correcting a mistake in the literature. We then use the fact that the six dimensional Drinfeld doubles have been classified to write down all possible conformal Poisson-Lie T-duals of three dimensional space times and we explicitly work out two duals to the constant dilaton and zero anti-symmetric tensor Bianchi type V space time and show that they satisfy the string equations of motion. This space-time was previously thought to have no duals because of the tracefulness of the structure constants. (author)

  7. 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.

  8. 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.

  9. Associative and Lie deformations of Poisson algebras

    OpenAIRE

    Remm, Elisabeth

    2011-01-01

    Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations which preserves the underlying associative structure and we study deformations which preserve the underlying Lie algebra.

  10. Toward negative Poisson's ratio composites: Investigation of the auxetic behavior of fibrous networks

    Science.gov (United States)

    Tatlier, Mehmet Seha

    Random fibrous can be found among natural and synthetic materials. Some of these random fibrous networks possess negative Poisson's ratio and they are extensively called auxetic materials. The governing mechanisms behind this counter intuitive property in random networks are yet to be understood and this kind of auxetic material remains widely under-explored. However, most of synthetic auxetic materials suffer from their low strength. This shortcoming can be rectified by developing high strength auxetic composites. The process of embedding auxetic random fibrous networks in a polymer matrix is an attractive alternate route to the manufacture of auxetic composites, however before such an approach can be developed, a methodology for designing fibrous networks with the desired negative Poisson's ratios must first be established. This requires an understanding of the factors which bring about negative Poisson's ratios in these materials. In this study, a numerical model is presented in order to investigate the auxetic behavior in compressed random fiber networks. Finite element analyses of three-dimensional stochastic fiber networks were performed to gain insight into the effects of parameters such as network anisotropy, network density, and degree of network compression on the out-of-plane Poisson's ratio and Young's modulus. The simulation results suggest that the compression is the critical parameter that gives rise to negative Poisson's ratio while anisotropy significantly promotes the auxetic behavior. This model can be utilized to design fibrous auxetic materials and to evaluate feasibility of developing auxetic composites by using auxetic fibrous networks as the reinforcing layer.

  11. Boltzmann rovibrational collisional coarse-grained model for internal energy excitation and dissociation in hypersonic flows.

    Science.gov (United States)

    Munafò, A; Panesi, M; Magin, T E

    2014-02-01

    A Boltzmann rovibrational collisional coarse-grained model is proposed to reduce a detailed kinetic mechanism database developed at NASA Ames Research Center for internal energy transfer and dissociation in N(2)-N interactions. The coarse-grained model is constructed by lumping the rovibrational energy levels of the N(2) molecule into energy bins. The population of the levels within each bin is assumed to follow a Boltzmann distribution at the local translational temperature. Excitation and dissociation rate coefficients for the energy bins are obtained by averaging the elementary rate coefficients. The energy bins are treated as separate species, thus allowing for non-Boltzmann distributions of their populations. The proposed coarse-grained model is applied to the study of nonequilibrium flows behind normal shock waves and within converging-diverging nozzles. In both cases, the flow is assumed inviscid and steady. Computational results are compared with those obtained by direct solution of the master equation for the rovibrational collisional model and a more conventional multitemperature model. It is found that the proposed coarse-grained model is able to accurately resolve the nonequilibrium dynamics of internal energy excitation and dissociation-recombination processes with only 20 energy bins. Furthermore, the proposed coarse-grained model provides a superior description of the nonequilibrium phenomena occurring in shock heated and nozzle flows when compared with the conventional multitemperature models.

  12. A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

    Directory of Open Access Journals (Sweden)

    Zhen Chen

    2017-03-01

    Full Text Available An unconditionally stable thermal lattice Boltzmann method (USTLBM is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE through Chapman–Enskog (C-E expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM. Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

  13. Gap processing for adaptive maximal poisson-disk sampling

    KAUST Repository

    Yan, Dongming; Wonka, Peter

    2013-01-01

    In this article, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or when their radii are changed.We build on the concepts of regular triangulations and the power diagram. Third, we show how our analysis contributes to the state-of-the-art in surface remeshing. © 2013 ACM.

  14. Gap processing for adaptive maximal poisson-disk sampling

    KAUST Repository

    Yan, Dongming

    2013-10-17

    In this article, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or when their radii are changed.We build on the concepts of regular triangulations and the power diagram. Third, we show how our analysis contributes to the state-of-the-art in surface remeshing. © 2013 ACM.

  15. The Influence of Ernst Mach and Ludwig Boltzmann on Albert Einstein

    International Nuclear Information System (INIS)

    Broda, E.

    1979-01-01

    This document, written by Engelbert Broda in 1979, analyses the influence of Ernst Mach and Ludwig Boltzmann on Albert Einstein. Broda describes how Einstein and his scientific thinking benefited from Mach’s criticism on classical mechanics and its basic concepts like absolute time and absolute space. This criticism encouraged Einstein in the time he worked on his special relativity. On the other side Broda writes about the influence of Ludwig Boltzman, an atomist, whose scientific work and research prepared the ground for Einsteins work on the quantum-structure of electromagnetic radiation or the discovery of the photoelectric effect. (nowak)

  16. Adaptive Non-Boltzmann Monte Carlo

    International Nuclear Information System (INIS)

    Fitzgerald, M.; Picard, R.R.; Silver, R.N.

    1998-01-01

    This manuscript generalizes the use of transition probabilities (TPs) between states, which are efficient relative to histogram procedures in deriving system properties. The empirical TPs of the simulation depend on the importance weights and are temperature-specific, so they are not conducive to accumulating statistics as weights change or to extrapolating in temperature. To address these issues, the authors provide a method for inferring Boltzmann-weighted TPs for one temperature from simulations run at other temperatures and/or at different adaptively varying importance weights. They refer to these as canonical transition probabilities (CTPs). System properties are estimated from CTPs. Statistics on CTPs are gathered by inserting a low-cost easily-implemented bookkeeping step into the Metropolis algorithm for non-Boltzmann sampling. The CTP method is inherently adaptive, can take advantage of partitioning of the state space into small regions using either serial or (embarrassingly) parallel architectures, and reduces variance by avoiding histogramming. They also demonstrate how system properties may be extrapolated in temperature from CTPs without the extra memory required by using energy as a microstate label. Nor does it require the solution of non-linear equations used in histogram methods

  17. Adaptive Non-Boltzmann Monte Carlo

    Energy Technology Data Exchange (ETDEWEB)

    Fitzgerald, M.; Picard, R.R.; Silver, R.N.

    1998-06-01

    This manuscript generalizes the use of transition probabilities (TPs) between states, which are efficient relative to histogram procedures in deriving system properties. The empirical TPs of the simulation depend on the importance weights and are temperature-specific, so they are not conducive to accumulating statistics as weights change or to extrapolating in temperature. To address these issues, the authors provide a method for inferring Boltzmann-weighted TPs for one temperature from simulations run at other temperatures and/or at different adaptively varying importance weights. They refer to these as canonical transition probabilities (CTPs). System properties are estimated from CTPs. Statistics on CTPs are gathered by inserting a low-cost easily-implemented bookkeeping step into the Metropolis algorithm for non-Boltzmann sampling. The CTP method is inherently adaptive, can take advantage of partitioning of the state space into small regions using either serial or (embarrassingly) parallel architectures, and reduces variance by avoiding histogramming. They also demonstrate how system properties may be extrapolated in temperature from CTPs without the extra memory required by using energy as a microstate label. Nor does it require the solution of non-linear equations used in histogram methods.

  18. Laplace-Laplace analysis of the fractional Poisson process

    OpenAIRE

    Gorenflo, Rudolf; Mainardi, Francesco

    2013-01-01

    We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving probability densities.

  19. The child-Langmuir limit for semiconductors: a numerical validation

    International Nuclear Information System (INIS)

    Caceres, M.J.; Carrillo, J.A.; Degond, P.

    2002-01-01

    The Boltzmann-Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child-Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child-Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child-Langmuir regime by performing detailed numerical comparisons between the simulation of the Boltzmann-Poisson system and the Child-Langmuir equations in test problems. (authors)

  20. Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid.

    Science.gov (United States)

    Sahin, Buyukdagli; Ralf, Blossey

    2014-07-16

    We study a model Coulomb fluid consisting of dipolar solvent molecules of finite extent which generalizes the point-like dipolar Poisson-Boltzmann model (DPB) previously introduced by Coalson and Duncan (1996 J. Phys. Chem. 100 2612) and Abrashkin et al (2007 Phys. Rev. Lett. 99 077801). We formulate a nonlocal Poisson-Boltzmann equation (NLPB) and study both linear and nonlinear dielectric response in this model for the case of a single plane geometry. Our results shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.

  1. Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

    International Nuclear Information System (INIS)

    Ayissi, Raoul Domingo; Noutchegueme, Norbert

    2015-01-01

    Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the

  2. Background stratified Poisson regression analysis of cohort data

    International Nuclear Information System (INIS)

    Richardson, David B.; Langholz, Bryan

    2012-01-01

    Background stratified Poisson regression is an approach that has been used in the analysis of data derived from a variety of epidemiologically important studies of radiation-exposed populations, including uranium miners, nuclear industry workers, and atomic bomb survivors. We describe a novel approach to fit Poisson regression models that adjust for a set of covariates through background stratification while directly estimating the radiation-disease association of primary interest. The approach makes use of an expression for the Poisson likelihood that treats the coefficients for stratum-specific indicator variables as 'nuisance' variables and avoids the need to explicitly estimate the coefficients for these stratum-specific parameters. Log-linear models, as well as other general relative rate models, are accommodated. This approach is illustrated using data from the Life Span Study of Japanese atomic bomb survivors and data from a study of underground uranium miners. The point estimate and confidence interval obtained from this 'conditional' regression approach are identical to the values obtained using unconditional Poisson regression with model terms for each background stratum. Moreover, it is shown that the proposed approach allows estimation of background stratified Poisson regression models of non-standard form, such as models that parameterize latency effects, as well as regression models in which the number of strata is large, thereby overcoming the limitations of previously available statistical software for fitting background stratified Poisson regression models. (orig.)

  3. On Poisson Nonlinear Transformations

    Directory of Open Access Journals (Sweden)

    Nasir Ganikhodjaev

    2014-01-01

    Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.

  4. Theoretical model for the detection of charged proteins with a silicon-on-insulator sensor

    International Nuclear Information System (INIS)

    Birner, S; Uhl, C; Bayer, M; Vogl, P

    2008-01-01

    For a bio-sensor device based on a silicon-on-insulator structure, we calculate the sensitivity to specific charge distributions in the electrolyte solution that arise from protein binding to the semiconductor surface. This surface is bio-functionalized with a lipid layer so that proteins can specifically bind to the headgroups of the lipids on the surface. We consider charged proteins such as the green fluorescent protein (GFP) and artificial proteins that consist of a variable number of aspartic acids. Specifically, we calculate self-consistently the spatial charge and electrostatic potential distributions for different ion concentrations in the electrolyte. We fully take into account the quantum mechanical charge density in the semiconductor. We determine the potential change at the binding sites as a function of protein charge and ionic strength. Comparison with experiment is generally very good. Furthermore, we demonstrate the superiority of the full Poisson-Boltzmann equation by comparing its results to the simplified Debye-Hueckel approximation

  5. Plasma immersion ion implantation of the interior surface of a large cylindrical bore using an auxiliary electrode

    International Nuclear Information System (INIS)

    Zeng, X.C.; Kwok, T.K.; Liu, A.G.; Chu, P.K.; Tang, B.Y.

    1998-01-01

    A model utilizing cold, unmagnetized, and collisionless fluid ions as well as Boltzmann electrons is used to comprehensively investigate the sheath expansion into a translationally invariant large bore in the presence of an auxiliary electrode during plasma immersion ion implantation (PIII) of a cylindrical bore sample. The governing equation of ion continuity, ion motion, and Poisson close-quote s equation are solved by using a numerical finite difference method for different cylindrical bore radii, auxiliary electrode radii, and voltage rise times. The ion density and ion impact energy at the cylindrical inner surface, as well as the ion energy distribution, maximum ion impact energy, and average ion impact energy for the various cases are obtained. Our results show a dramatic improvement in the impact energy when an auxiliary electrode is used and the recommended normalized auxiliary electrode radius is in the range of 0.1 endash 0.3. copyright 1998 American Institute of Physics

  6. Network Traffic Monitoring Using Poisson Dynamic Linear Models

    Energy Technology Data Exchange (ETDEWEB)

    Merl, D. M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2011-05-09

    In this article, we discuss an approach for network forensics using a class of nonstationary Poisson processes with embedded dynamic linear models. As a modeling strategy, the Poisson DLM (PoDLM) provides a very flexible framework for specifying structured effects that may influence the evolution of the underlying Poisson rate parameter, including diurnal and weekly usage patterns. We develop a novel particle learning algorithm for online smoothing and prediction for the PoDLM, and demonstrate the suitability of the approach to real-time deployment settings via a new application to computer network traffic monitoring.

  7. Test of Poisson Process for Earthquakes in and around Korea

    International Nuclear Information System (INIS)

    Noh, Myunghyun; Choi, Hoseon

    2015-01-01

    Since Cornell's work on the probabilistic seismic hazard analysis (hereafter, PSHA), majority of PSHA computer codes are assuming that the earthquake occurrence is Poissonian. To the author's knowledge, it is uncertain who first opened the issue of the Poisson process for the earthquake occurrence. The systematic PSHA in Korea, led by the nuclear industry, were carried out for more than 25 year with the assumption of the Poisson process. However, the assumption of the Poisson process has never been tested. Therefore, the test is of significance. We tested whether the Korean earthquakes follow the Poisson process or not. The Chi-square test with the significance level of 5% was applied. The test turned out that the Poisson process could not be rejected for the earthquakes of magnitude 2.9 or larger. However, it was still observed in the graphical comparison that some portion of the observed distribution significantly deviated from the Poisson distribution. We think this is due to the small earthquake data. The earthquakes of magnitude 2.9 or larger occurred only 376 times during 34 years. Therefore, the judgment on the Poisson process derived in the present study is not conclusive

  8. Kinematics of semiclassical spin and spin fiber bundle associated with so(n) Lie-Poisson manifold

    International Nuclear Information System (INIS)

    Deriglazov, A A

    2013-01-01

    We describe geometric construction underlying the Lagrangian actions for non-Grassmann spinning particles proposed in our recent works. If we discard the spatial variables (the case of frozen spin), the problem reduces to formulation of a variational problem for Hamiltonian system on a manifold with so(n) Lie-Poisson bracket. To achieve this, we identify dynamical variables of the problem with coordinates of the base of a properly constructed fiber bundle. In turn, the fiber bundle is embedded as a surface into the phase space equipped with canonical Poisson bracket. This allows us to formulate the variational problem using the standard methods of Dirac theory for constrained systems.

  9. A topological insight into restricted Boltzmann machines

    NARCIS (Netherlands)

    Mocanu, D.C.; Mocanu, E.; Nguyen, H.P.; Gibescu, M.; Liotta, A.

    Restricted Boltzmann Machines (RBMs) and models derived from them have been successfully used as basic building blocks in deep artificial neural networks for automatic features extraction, unsupervised weights initialization, but also as density estimators. Thus, their generative and discriminative

  10. Modeling surface roughness scattering in metallic nanowires

    Energy Technology Data Exchange (ETDEWEB)

    Moors, Kristof, E-mail: kristof@itf.fys.kuleuven.be [KU Leuven, Institute for Theoretical Physics, Celestijnenlaan 200D, B-3001 Leuven (Belgium); IMEC, Kapeldreef 75, B-3001 Leuven (Belgium); Sorée, Bart [IMEC, Kapeldreef 75, B-3001 Leuven (Belgium); Physics Department, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen (Belgium); KU Leuven, Electrical Engineering (ESAT) Department, Kasteelpark Arenberg 10, B-3001 Leuven (Belgium); Magnus, Wim [IMEC, Kapeldreef 75, B-3001 Leuven (Belgium); Physics Department, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen (Belgium)

    2015-09-28

    Ando's model provides a rigorous quantum-mechanical framework for electron-surface roughness scattering, based on the detailed roughness structure. We apply this method to metallic nanowires and improve the model introducing surface roughness distribution functions on a finite domain with analytical expressions for the average surface roughness matrix elements. This approach is valid for any roughness size and extends beyond the commonly used Prange-Nee approximation. The resistivity scaling is obtained from the self-consistent relaxation time solution of the Boltzmann transport equation and is compared to Prange-Nee's approach and other known methods. The results show that a substantial drop in resistivity can be obtained for certain diameters by achieving a large momentum gap between Fermi level states with positive and negative momentum in the transport direction.

  11. Method of Poisson's ratio imaging within a material part

    Science.gov (United States)

    Roth, Don J. (Inventor)

    1996-01-01

    The present invention is directed to a method of displaying the Poisson's ratio image of a material part. In the present invention longitudinal data is produced using a longitudinal wave transducer and shear wave data is produced using a shear wave transducer. The respective data is then used to calculate the Poisson's ratio for the entire material part. The Poisson's ratio approximations are then used to displayed the image.

  12. The applicability of the Poisson distribution in radiochemical measurements

    International Nuclear Information System (INIS)

    Luthardt, M.; Proesch, U.

    1980-01-01

    The fact that, on principle, the Poisson distribution describes the statistics of nuclear decay is generally accepted. The applicability of this distribution to nuclear radiation measurements has recently been questioned. Applying the chi-squared test for goodness of fit on the analogy of the moving average, at least 3 cases may be distinguished, which lead to an incorrect rejection of the Poisson distribution for measurements. Examples are given. Distributions, which make allowance for special parameters, should only be used after careful examination of the data with regard to other interfering effects. The Poisson distribution will further on be applicable to many simple measuring operations. Some basic equations for the analysis of poisson-distributed data are given. (author)

  13. Galilean-Invariant Lattice-Boltzmann Models with H Theorem

    National Research Council Canada - National Science Library

    Boghosian, Bruce

    2003-01-01

    The authors demonstrate that the requirement of Galilean invariance determines the choice of H function for a wide class of entropic lattice-Boltzmann models for the incompressible Navier-Stokes equations...

  14. Multivariate fractional Poisson processes and compound sums

    OpenAIRE

    Beghin, Luisa; Macci, Claudio

    2015-01-01

    In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.

  15. Contravariant gravity on Poisson manifolds and Einstein gravity

    International Nuclear Information System (INIS)

    Kaneko, Yukio; Watamura, Satoshi; Muraki, Hisayoshi

    2017-01-01

    A relation between gravity on Poisson manifolds proposed in Asakawa et al (2015 Fortschr. Phys . 63 683–704) and Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein–Hilbert-type action yields an equation of motion which is written in terms of the analog of the Einstein tensor, and it includes couplings between the metric and the Poisson tensor. The study of the Weyl transformation reveals properties of those interactions. It is argued that this theory can have an equivalent description as a system of Einstein gravity coupled to matter. As an example, it is shown that the contravariant gravity on a two-dimensional Poisson manifold can be described by a real scalar field coupled to the metric in a specific manner. (paper)

  16. Modified Regression Correlation Coefficient for Poisson Regression Model

    Science.gov (United States)

    Kaengthong, Nattacha; Domthong, Uthumporn

    2017-09-01

    This study gives attention to indicators in predictive power of the Generalized Linear Model (GLM) which are widely used; however, often having some restrictions. We are interested in regression correlation coefficient for a Poisson regression model. This is a measure of predictive power, and defined by the relationship between the dependent variable (Y) and the expected value of the dependent variable given the independent variables [E(Y|X)] for the Poisson regression model. The dependent variable is distributed as Poisson. The purpose of this research was modifying regression correlation coefficient for Poisson regression model. We also compare the proposed modified regression correlation coefficient with the traditional regression correlation coefficient in the case of two or more independent variables, and having multicollinearity in independent variables. The result shows that the proposed regression correlation coefficient is better than the traditional regression correlation coefficient based on Bias and the Root Mean Square Error (RMSE).

  17. A comparison of Poisson-one-inflated power series distributions for ...

    African Journals Online (AJOL)

    A class of Poisson-one-inflated power series distributions (the binomial, the Poisson, the negative binomial, the geometric, the log-series and the misrecorded Poisson) are proposed for modeling rural out-migration at the household level. The probability mass functions of the mixture distributions are derived and fitted to the ...

  18. Optimized aspect ratios of restrained thick-wall cylinders by virtue of Poisson's ratio selection. Part two: Temperature application

    International Nuclear Information System (INIS)

    Whitty, J.P.M.; Henderson, B.; Francis, J.

    2011-01-01

    Highlights: → Incontrovertible evidence is presented that thermal stresses in cylindrical components which include nuclear reactors and containment vessels are shown to be highly dependent on the Poisson's ratio of the materials. → The key novelty is concerned with the identification of a new potential thermal applications for negative Poisson's ratio (auxetic) materials; i.e. those that get fatter when they are stretched. → Negative Poisson's ratio (auxetic) materials exhibit lower thermal stress build-up than conventional positive Poisson's ratio materials, this conjecture being proven using thermal surface plots. - Abstract: Analytical and numerical modelling have been employed to show that the choice of Poisson's ratio is one of the principal design criteria in order to reduce thermal stress build-up in isotropic materials. The modelling procedures are all twofold; consisting of a solution to a steady-state heat conduction problem followed by a linear static solution. The models developed take the form of simplistic thick-wall cylinders such model systems are applicable at macro-structural and micro-structural levels as the underlining formulations are based on the classical theory of elasticity. Generally, the results show that the Poisson's ratio of the material has a greater effect on the magnitude of the principal stresses than the aspect ratio of the cylinders investigated. Constraining the outside of these models significantly increases the thermal stresses induced. The most significant and original finding presented is that the for both freely expanding and constrained thick-wall cylinders the optimum Poisson's ratio is minus unity.

  19. Monitoring Poisson observations using combined applications of Shewhart and EWMA charts

    Science.gov (United States)

    Abujiya, Mu'azu Ramat

    2017-11-01

    The Shewhart and exponentially weighted moving average (EWMA) charts for nonconformities are the most widely used procedures of choice for monitoring Poisson observations in modern industries. Individually, the Shewhart EWMA charts are only sensitive to large and small shifts, respectively. To enhance the detection abilities of the two schemes in monitoring all kinds of shifts in Poisson count data, this study examines the performance of combined applications of the Shewhart, and EWMA Poisson control charts. Furthermore, the study proposes modifications based on well-structured statistical data collection technique, ranked set sampling (RSS), to detect shifts in the mean of a Poisson process more quickly. The relative performance of the proposed Shewhart-EWMA Poisson location charts is evaluated in terms of the average run length (ARL), standard deviation of the run length (SDRL), median run length (MRL), average ratio ARL (ARARL), average extra quadratic loss (AEQL) and performance comparison index (PCI). Consequently, all the new Poisson control charts based on RSS method are generally more superior than most of the existing schemes for monitoring Poisson processes. The use of these combined Shewhart-EWMA Poisson charts is illustrated with an example to demonstrate the practical implementation of the design procedure.

  20. Poisson-Jacobi reduction of homogeneous tensors

    International Nuclear Information System (INIS)

    Grabowski, J; Iglesias, D; Marrero, J C; Padron, E; Urbanski, P

    2004-01-01

    The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold M, homogeneous with respect to a vector field Δ on M, and first-order polydifferential operators on a closed submanifold N of codimension 1 such that Δ is transversal to N. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on M to the Schouten-Jacobi bracket of first-order polydifferential operators on N and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can also be understood as a sort of reduction; in the standard case-a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between Δ-homogeneous symplectic structures on M and contact structures on N

  1. Limitations of Poisson statistics in describing radioactive decay.

    Science.gov (United States)

    Sitek, Arkadiusz; Celler, Anna M

    2015-12-01

    The assumption that nuclear decays are governed by Poisson statistics is an approximation. This approximation becomes unjustified when data acquisition times longer than or even comparable with the half-lives of the radioisotope in the sample are considered. In this work, the limits of the Poisson-statistics approximation are investigated. The formalism for the statistics of radioactive decay based on binomial distribution is derived. The theoretical factor describing the deviation of variance of the number of decays predicated by the Poisson distribution from the true variance is defined and investigated for several commonly used radiotracers such as (18)F, (15)O, (82)Rb, (13)N, (99m)Tc, (123)I, and (201)Tl. The variance of the number of decays estimated using the Poisson distribution is significantly different than the true variance for a 5-minute observation time of (11)C, (15)O, (13)N, and (82)Rb. Durations of nuclear medicine studies often are relatively long; they may be even a few times longer than the half-lives of some short-lived radiotracers. Our study shows that in such situations the Poisson statistics is unsuitable and should not be applied to describe the statistics of the number of decays in radioactive samples. However, the above statement does not directly apply to counting statistics at the level of event detection. Low sensitivities of detectors which are used in imaging studies make the Poisson approximation near perfect. Copyright © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

  2. Improvements to the APBS biomolecular solvation software suite.

    Science.gov (United States)

    Jurrus, Elizabeth; Engel, Dave; Star, Keith; Monson, Kyle; Brandi, Juan; Felberg, Lisa E; Brookes, David H; Wilson, Leighton; Chen, Jiahui; Liles, Karina; Chun, Minju; Li, Peter; Gohara, David W; Dolinsky, Todd; Konecny, Robert; Koes, David R; Nielsen, Jens Erik; Head-Gordon, Teresa; Geng, Weihua; Krasny, Robert; Wei, Guo-Wei; Holst, Michael J; McCammon, J Andrew; Baker, Nathan A

    2018-01-01

    The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that have provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses the three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suite of accompanying software since its release in 2001. In this article, we discuss the models and capabilities that have recently been implemented within the APBS software package including a Poisson-Boltzmann analytical and a semi-analytical solver, an optimized boundary element solver, a geometry-based geometric flow solvation model, a graph theory-based algorithm for determining pK a values, and an improved web-based visualization tool for viewing electrostatics. © 2017 The Protein Society.

  3. Improvements to the APBS biomolecular solvation software suite: Improvements to the APBS Software Suite

    Energy Technology Data Exchange (ETDEWEB)

    Jurrus, Elizabeth [Pacific Northwest National Laboratory, Richland Washington; Engel, Dave [Pacific Northwest National Laboratory, Richland Washington; Star, Keith [Pacific Northwest National Laboratory, Richland Washington; Monson, Kyle [Pacific Northwest National Laboratory, Richland Washington; Brandi, Juan [Pacific Northwest National Laboratory, Richland Washington; Felberg, Lisa E. [University of California, Berkeley California; Brookes, David H. [University of California, Berkeley California; Wilson, Leighton [University of Michigan, Ann Arbor Michigan; Chen, Jiahui [Southern Methodist University, Dallas Texas; Liles, Karina [Pacific Northwest National Laboratory, Richland Washington; Chun, Minju [Pacific Northwest National Laboratory, Richland Washington; Li, Peter [Pacific Northwest National Laboratory, Richland Washington; Gohara, David W. [St. Louis University, St. Louis Missouri; Dolinsky, Todd [FoodLogiQ, Durham North Carolina; Konecny, Robert [University of California San Diego, San Diego California; Koes, David R. [University of Pittsburgh, Pittsburgh Pennsylvania; Nielsen, Jens Erik [Protein Engineering, Novozymes A/S, Copenhagen Denmark; Head-Gordon, Teresa [University of California, Berkeley California; Geng, Weihua [Southern Methodist University, Dallas Texas; Krasny, Robert [University of Michigan, Ann Arbor Michigan; Wei, Guo-Wei [Michigan State University, East Lansing Michigan; Holst, Michael J. [University of California San Diego, San Diego California; McCammon, J. Andrew [University of California San Diego, San Diego California; Baker, Nathan A. [Pacific Northwest National Laboratory, Richland Washington; Brown University, Providence Rhode Island

    2017-10-24

    The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that has provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suite of accompanying software since its release in 2001. In this manuscript, we discuss the models and capabilities that have recently been implemented within the APBS software package including: a Poisson-Boltzmann analytical and a semi-analytical solver, an optimized boundary element solver, a geometry-based geometric flow solvation model, a graph theory based algorithm for determining pKa values, and an improved web-based visualization tool for viewing electrostatics.

  4. Singularities in the nonisotropic Boltzmann equation

    International Nuclear Information System (INIS)

    Garibotti, C.R.; Martiarena, M.L.; Zanette, D.

    1987-09-01

    We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs

  5. Poisson solvers for self-consistent multi-particle simulations

    International Nuclear Information System (INIS)

    Qiang, J; Paret, S

    2014-01-01

    Self-consistent multi-particle simulation plays an important role in studying beam-beam effects and space charge effects in high-intensity beams. The Poisson equation has to be solved at each time-step based on the particle density distribution in the multi-particle simulation. In this paper, we review a number of numerical methods that can be used to solve the Poisson equation efficiently. The computational complexity of those numerical methods will be O(N log(N)) or O(N) instead of O(N2), where N is the total number of grid points used to solve the Poisson equation

  6. Poisson image reconstruction with Hessian Schatten-norm regularization.

    Science.gov (United States)

    Lefkimmiatis, Stamatios; Unser, Michael

    2013-11-01

    Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupted by Poisson noise. In this paper, we propose an efficient framework for Poisson image reconstruction, under a regularization approach, which depends on matrix-valued regularization operators. In particular, the employed regularizers involve the Hessian as the regularization operator and Schatten matrix norms as the potential functions. For the solution of the problem, we propose two optimization algorithms that are specifically tailored to the Poisson nature of the noise. These algorithms are based on an augmented-Lagrangian formulation of the problem and correspond to two variants of the alternating direction method of multipliers. Further, we derive a link that relates the proximal map of an l(p) norm with the proximal map of a Schatten matrix norm of order p. This link plays a key role in the development of one of the proposed algorithms. Finally, we provide experimental results on natural and biological images for the task of Poisson image deblurring and demonstrate the practical relevance and effectiveness of the proposed framework.

  7. Seasonally adjusted birth frequencies follow the Poisson distribution.

    Science.gov (United States)

    Barra, Mathias; Lindstrøm, Jonas C; Adams, Samantha S; Augestad, Liv A

    2015-12-15

    Variations in birth frequencies have an impact on activity planning in maternity wards. Previous studies of this phenomenon have commonly included elective births. A Danish study of spontaneous births found that birth frequencies were well modelled by a Poisson process. Somewhat unexpectedly, there were also weekly variations in the frequency of spontaneous births. Another study claimed that birth frequencies follow the Benford distribution. Our objective was to test these results. We analysed 50,017 spontaneous births at Akershus University Hospital in the period 1999-2014. To investigate the Poisson distribution of these births, we plotted their variance over a sliding average. We specified various Poisson regression models, with the number of births on a given day as the outcome variable. The explanatory variables included various combinations of years, months, days of the week and the digit sum of the date. The relationship between the variance and the average fits well with an underlying Poisson process. A Benford distribution was disproved by a goodness-of-fit test (p Poisson process when monthly and day-of-the-week variation is included. The frequency is highest in summer towards June and July, Friday and Tuesday stand out as particularly busy days, and the activity level is at its lowest during weekends.

  8. Boltzmann, Gibbs and Darwin-Fowler approaches in parastatistics

    International Nuclear Information System (INIS)

    Ponczek, R.L.; Yan, C.C.

    1976-01-01

    Derivations of the equilibrium values of occupation numbers are made using three approaches, namely, the Boltzmann 'elementary' one, the ensemble method of Gibbs, and that of Darwin and Fowler as well [pt

  9. Lattice Boltzmann simulation of droplet formation in T-junction geometries

    Science.gov (United States)

    Busuioc, Sergiu; Ambruş, Victor E.; Sofonea, Victor

    2017-01-01

    The formation of droplets in T-junction configurations is investigated using a two-dimensional Lattice Boltzmann model for liquid-vapor systems. We use an expansion of the equilibrium distribution function with respect to Hermite polynomials and an off-lattice velocity set. To evolve the distribution functions we use the second order corner transport upwind numerical scheme and a third order scheme is used to compute the gradient operators in the force term. The droplet formation successfully recovers the squeezing, dripping and jetting regimes. We find that the droplet length decreases proportionally with the flow rate of the continuous phase and increases with the flow rate of the dispersed phase in all simulation configurations and has a linear dependency on the surface tension parameter κ.

  10. Modeling laser velocimeter signals as triply stochastic Poisson processes

    Science.gov (United States)

    Mayo, W. T., Jr.

    1976-01-01

    Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.

  11. Particular solutions of generalized Euler-Poisson-Darboux equation

    Directory of Open Access Journals (Sweden)

    Rakhila B. Seilkhanova

    2015-01-01

    Full Text Available In this article we consider the generalized Euler-Poisson-Darboux equation $$ {u}_{tt}+\\frac{2\\gamma }{t}{{u}_{t}}={u}_{xx}+{u}_{yy} +\\frac{2\\alpha }{x}{{u}_{x}}+\\frac{2\\beta }{y}{{u}_y},\\quad x>0,\\;y>0,\\;t>0. $$ We construct particular solutions in an explicit form expressed by the Lauricella hypergeometric function of three variables. Properties of each constructed solutions have been investigated in sections of surfaces of the characteristic cone. Precisely, we prove that found solutions have singularity $1/r$ at $r\\to 0$, where ${{r}^2}={{( x-{{x}_0}}^2}+{{( y-{{y}_0}}^2}-{{( t-{{t}_0}}^2}$.

  12. Simultaneous estimation of Poisson's ratio and Young's modulus using a single indentation: a finite element study

    International Nuclear Information System (INIS)

    Zheng, Y P; Choi, A P C; Ling, H Y; Huang, Y P

    2009-01-01

    Indentation is commonly used to determine the mechanical properties of different kinds of biological tissues and engineering materials. With the force–deformation data obtained from an indentation test, Young's modulus of the tissue can be calculated using a linear elastic indentation model with a known Poisson's ratio. A novel method for simultaneous estimation of Young's modulus and Poisson's ratio of the tissue using a single indentation was proposed in this study. Finite element (FE) analysis using 3D models was first used to establish the relationship between Poisson's ratio and the deformation-dependent indentation stiffness for different aspect ratios (indentor radius/tissue original thickness) in the indentation test. From the FE results, it was found that the deformation-dependent indentation stiffness linearly increased with the deformation. Poisson's ratio could be extracted based on the deformation-dependent indentation stiffness obtained from the force–deformation data. Young's modulus was then further calculated with the estimated Poisson's ratio. The feasibility of this method was demonstrated in virtue of using the indentation models with different material properties in the FE analysis. The numerical results showed that the percentage errors of the estimated Poisson's ratios and the corresponding Young's moduli ranged from −1.7% to −3.2% and 3.0% to 7.2%, respectively, with the aspect ratio (indentor radius/tissue thickness) larger than 1. It is expected that this novel method can be potentially used for quantitative assessment of various kinds of engineering materials and biological tissues, such as articular cartilage

  13. Non-linear effects in the Boltzmann equation

    International Nuclear Information System (INIS)

    Barrachina, R.O.

    1985-01-01

    The Boltzmann equation is studied by defining an integral transformation of the energy distribution function for an isotropic and homogeneous gas. This transformation may be interpreted as a linear superposition of equilibrium states with variable temperatures. It is shown that the temporal evolution features of the distribution function are determined by the singularities of said transformation. This method is applied to Maxwell and Very Hard Particle interaction models. For the latter, the solution of the Boltzmann equation with the solution of its linearized version is compared, finding out many basic discrepancies and non-linear effects. This gives a hint to propose a new rational approximation method with a clear physical meaning. Applying this technique, the relaxation features of the BKW (Bobylev, Krook anf Wu) mode is analyzed, finding a conclusive counter-example for the Krook and Wu conjecture. The anisotropic Boltzmann equation for Maxwell models is solved as an expansion in terms of the eigenfunctions of the corresponding linearized collision operator, finding interesting transient overpopulation and underpopulation effects at thermal energies as well as a new preferential spreading effect. By analyzing the initial collision, a criterion is established to deduce the general features of the final approach to equilibrium. Finally, it is shown how to improve the convergence of the eigenfunction expansion for high energy underpopulated distribution functions. As an application of this theory, the linear cascade model for sputtering is analyzed, thus finding out that many differences experimentally observed are due to non-linear effects. (M.E.L.) [es

  14. Some applications of the fractional Poisson probability distribution

    International Nuclear Information System (INIS)

    Laskin, Nick

    2009-01-01

    Physical and mathematical applications of the recently invented fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we have developed the fractional generalization of Bell polynomials, Bell numbers, and Stirling numbers of the second kind. The appearance of fractional Bell polynomials is natural if one evaluates the diagonal matrix element of the evolution operator in the basis of newly introduced quantum coherent states. Fractional Stirling numbers of the second kind have been introduced and applied to evaluate the skewness and kurtosis of the fractional Poisson probability distribution function. A representation of the Bernoulli numbers in terms of fractional Stirling numbers of the second kind has been found. In the limit case when the fractional Poisson probability distribution becomes the Poisson probability distribution, all of the above listed developments and implementations turn into the well-known results of the quantum optics and the theory of combinatorial numbers.

  15. A comparison between Poisson and zero-inflated Poisson regression models with an application to number of black spots in Corriedale sheep

    Directory of Open Access Journals (Sweden)

    Rodrigues-Motta Mariana

    2008-07-01

    Full Text Available Abstract Dark spots in the fleece area are often associated with dark fibres in wool, which limits its competitiveness with other textile fibres. Field data from a sheep experiment in Uruguay revealed an excess number of zeros for dark spots. We compared the performance of four Poisson and zero-inflated Poisson (ZIP models under four simulation scenarios. All models performed reasonably well under the same scenario for which the data were simulated. The deviance information criterion favoured a Poisson model with residual, while the ZIP model with a residual gave estimates closer to their true values under all simulation scenarios. Both Poisson and ZIP models with an error term at the regression level performed better than their counterparts without such an error. Field data from Corriedale sheep were analysed with Poisson and ZIP models with residuals. Parameter estimates were similar for both models. Although the posterior distribution of the sire variance was skewed due to a small number of rams in the dataset, the median of this variance suggested a scope for genetic selection. The main environmental factor was the age of the sheep at shearing. In summary, age related processes seem to drive the number of dark spots in this breed of sheep.

  16. Generalized Stefan-Boltzmann Law

    Science.gov (United States)

    Montambaux, Gilles

    2018-03-01

    We reconsider the thermodynamic derivation by L. Boltzmann of the Stefan law and we generalize it for various different physical systems whose chemical potential vanishes. Being only based on classical arguments, therefore independent of the quantum statistics, this derivation applies as well to the saturated Bose gas in various geometries as to "compensated" Fermi gas near a neutrality point, such as a gas of Weyl Fermions. It unifies in the same framework the thermodynamics of many different bosonic or fermionic non-interacting gases which were until now described in completely different contexts.

  17. Learning Algorithm of Boltzmann Machine Based on Spatial Monte Carlo Integration Method

    Directory of Open Access Journals (Sweden)

    Muneki Yasuda

    2018-04-01

    Full Text Available The machine learning techniques for Markov random fields are fundamental in various fields involving pattern recognition, image processing, sparse modeling, and earth science, and a Boltzmann machine is one of the most important models in Markov random fields. However, the inference and learning problems in the Boltzmann machine are NP-hard. The investigation of an effective learning algorithm for the Boltzmann machine is one of the most important challenges in the field of statistical machine learning. In this paper, we study Boltzmann machine learning based on the (first-order spatial Monte Carlo integration method, referred to as the 1-SMCI learning method, which was proposed in the author’s previous paper. In the first part of this paper, we compare the method with the maximum pseudo-likelihood estimation (MPLE method using a theoretical and a numerical approaches, and show the 1-SMCI learning method is more effective than the MPLE. In the latter part, we compare the 1-SMCI learning method with other effective methods, ratio matching and minimum probability flow, using a numerical experiment, and show the 1-SMCI learning method outperforms them.

  18. Steered Molecular Dynamics for Investigating the Interactions Between Insulin Receptor Tyrosine Kinase (IRK) and Variants of Protein Tyrosine Phosphatase 1B (PTP1B).

    Science.gov (United States)

    Nguyen, Hung; Do, Nhat; Phan, Tuyn; Pham, Tri

    2018-02-01

    The aim of this study is to use steered molecular dynamics to investigate the dissociation process between IRK and PTP1Bs for wild type and five mutants (consisting of p.D181E, p.D181A, p.Q262A, p.D181A-Y46F, and p.D181A-Q262A). The gained results are observed not only the unbinding mechanism of IRK-PTP1B complexes came from pulling force profile, number of hydrogen bonds, and interaction energy between IRK and PTP1Bs but also described PTP1B's point mutations could variably change its binding affinity towards IRK. Additionally, the binding free energy calculated by Molecular Mechanics/Poisson-Boltzmann Surface Area (MM-PBSA) is also revealed that electrostatic energy and polar solvation energy mainly made up the binding free energy of PTP1B-IRK complexes.

  19. 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.

  20. Modeling and simulation of ocean wave propagation using lattice Boltzmann method

    Science.gov (United States)

    Nuraiman, Dian

    2017-10-01

    In this paper, we present on modeling and simulation of ocean wave propagation from the deep sea to the shoreline. This requires high computational cost for simulation with large domain. We propose to couple a 1D shallow water equations (SWE) model with a 2D incompressible Navier-Stokes equations (NSE) model in order to reduce the computational cost. The coupled model is solved using the lattice Boltzmann method (LBM) with the lattice Bhatnagar-Gross-Krook (BGK) scheme. Additionally, a special method is implemented to treat the complex behavior of free surface close to the shoreline. The result shows the coupled model can reduce computational cost significantly compared to the full NSE model.

  1. On the theory of electric double layer with explicit account of a polarizable co-solvent

    Energy Technology Data Exchange (ETDEWEB)

    Budkov, Yu. A., E-mail: urabudkov@rambler.ru [Laboratory of NMR Spectroscopy and Numerical Investigations of Liquids, G. A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo (Russian Federation); Department of Applied Mathematics, National Research University Higher School of Economics, Moscow (Russian Federation); Kolesnikov, A. L. [Institut für Nichtklassische Chemie e.V., Universität Leipzig, Leipzig (Germany); Kiselev, M. G. [Laboratory of NMR Spectroscopy and Numerical Investigations of Liquids, G. A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo (Russian Federation)

    2016-05-14

    We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer. We formulate a modified Poisson-Boltzmann theory, using the formalism of density functional approach on the level of local density approximation taking into account the electrostatic interactions of ions and co-solvent molecules as well as their excluded volume. We derive the modified Poisson-Boltzmann equation, considering the three-component symmetric lattice gas model as a reference system and minimizing the grand thermodynamic potential with respect to the electrostatic potential. We apply present modified Poisson-Boltzmann equation to the electric double layer theory, showing that accounting for the excluded volume of co-solvent molecules and ions slightly changes the main result of our previous simplified theory. Namely, in the case of small co-solvent polarizability with its increase under the enough small surface potentials of electrode, the differential capacitance undergoes the significant growth. Oppositely, when the surface potential exceeds some threshold value (which is slightly smaller than the saturation potential), the increase in the co-solvent polarizability results in a differential capacitance decrease. However, when the co-solvent polarizability exceeds some threshold value, its increase generates a considerable enhancement of the differential capacitance in a wide range of surface potentials. We demonstrate that two qualitatively different behaviors of the differential capacitance are related to the depletion and adsorption of co-solvent molecules at the charged electrode. We show that an additive of the strongly polarizable co-solvent to an electrolyte solution can shift significantly the saturation potential in two qualitatively different manners. Namely, a small additive of strongly polarizable co-solvent results in a shift of saturation potential to higher surface potentials. On

  2. On the theory of electric double layer with explicit account of a polarizable co-solvent

    International Nuclear Information System (INIS)

    Budkov, Yu. A.; Kolesnikov, A. L.; Kiselev, M. G.

    2016-01-01

    We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer. We formulate a modified Poisson-Boltzmann theory, using the formalism of density functional approach on the level of local density approximation taking into account the electrostatic interactions of ions and co-solvent molecules as well as their excluded volume. We derive the modified Poisson-Boltzmann equation, considering the three-component symmetric lattice gas model as a reference system and minimizing the grand thermodynamic potential with respect to the electrostatic potential. We apply present modified Poisson-Boltzmann equation to the electric double layer theory, showing that accounting for the excluded volume of co-solvent molecules and ions slightly changes the main result of our previous simplified theory. Namely, in the case of small co-solvent polarizability with its increase under the enough small surface potentials of electrode, the differential capacitance undergoes the significant growth. Oppositely, when the surface potential exceeds some threshold value (which is slightly smaller than the saturation potential), the increase in the co-solvent polarizability results in a differential capacitance decrease. However, when the co-solvent polarizability exceeds some threshold value, its increase generates a considerable enhancement of the differential capacitance in a wide range of surface potentials. We demonstrate that two qualitatively different behaviors of the differential capacitance are related to the depletion and adsorption of co-solvent molecules at the charged electrode. We show that an additive of the strongly polarizable co-solvent to an electrolyte solution can shift significantly the saturation potential in two qualitatively different manners. Namely, a small additive of strongly polarizable co-solvent results in a shift of saturation potential to higher surface potentials. On

  3. Intertime jump statistics of state-dependent Poisson processes.

    Science.gov (United States)

    Daly, Edoardo; Porporato, Amilcare

    2007-01-01

    A method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state-dependent Poisson noise is proposed. Such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis. A model for the timing of human activities shows the capability of state-dependent Poisson noise to generate power-law distributions. The application of the method to a model for neuron dynamics and to a hydrological model accounting for land-atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state-dependent Poisson models.

  4. Cluster X-varieties, amalgamation, and Poisson-Lie groups

    DEFF Research Database (Denmark)

    Fock, V. V.; Goncharov, A. B.

    2006-01-01

    In this paper, starting from a split semisimple real Lie group G with trivial center, we define a family of varieties with additional structures. We describe them as cluster χ-varieties, as defined in [FG2]. In particular they are Poisson varieties. We define canonical Poisson maps of these varie...

  5. 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.

  6. Grid refinement model in lattice Boltzmann method for stream function-vorticity formulations

    Energy Technology Data Exchange (ETDEWEB)

    Shin, Myung Seob [Dept. of Mechanical Engineering, Dongyang Mirae University, Seoul (Korea, Republic of)

    2015-03-15

    In this study, we present a grid refinement model in the lattice Boltzmann method (LBM) for two-dimensional incompressible fluid flow. That is, the model combines the desirable features of the lattice Boltzmann method and stream function-vorticity formulations. In order to obtain an accurate result, very fine grid (or lattice) is required near the solid boundary. Therefore, the grid refinement model is used in the lattice Boltzmann method for stream function-vorticity formulation. This approach is more efficient in that it can obtain the same accurate solution as that in single-block approach even if few lattices are used for computation. In order to validate the grid refinement approach for the stream function-vorticity formulation, the numerical simulations of lid-driven cavity flows were performed and good results were obtained.

  7. Modeling animal-vehicle collisions using diagonal inflated bivariate Poisson regression.

    Science.gov (United States)

    Lao, Yunteng; Wu, Yao-Jan; Corey, Jonathan; Wang, Yinhai

    2011-01-01

    Two types of animal-vehicle collision (AVC) data are commonly adopted for AVC-related risk analysis research: reported AVC data and carcass removal data. One issue with these two data sets is that they were found to have significant discrepancies by previous studies. In order to model these two types of data together and provide a better understanding of highway AVCs, this study adopts a diagonal inflated bivariate Poisson regression method, an inflated version of bivariate Poisson regression model, to fit the reported AVC and carcass removal data sets collected in Washington State during 2002-2006. The diagonal inflated bivariate Poisson model not only can model paired data with correlation, but also handle under- or over-dispersed data sets as well. Compared with three other types of models, double Poisson, bivariate Poisson, and zero-inflated double Poisson, the diagonal inflated bivariate Poisson model demonstrates its capability of fitting two data sets with remarkable overlapping portions resulting from the same stochastic process. Therefore, the diagonal inflated bivariate Poisson model provides researchers a new approach to investigating AVCs from a different perspective involving the three distribution parameters (λ(1), λ(2) and λ(3)). The modeling results show the impacts of traffic elements, geometric design and geographic characteristics on the occurrences of both reported AVC and carcass removal data. It is found that the increase of some associated factors, such as speed limit, annual average daily traffic, and shoulder width, will increase the numbers of reported AVCs and carcass removals. Conversely, the presence of some geometric factors, such as rolling and mountainous terrain, will decrease the number of reported AVCs. Published by Elsevier Ltd.

  8. Molecular modeling of human acidic mammalian chitinase in complex with the natural-product cyclopentapeptide chitinase inhibitor argifin.

    Science.gov (United States)

    Gouda, Hiroaki; Terashima, Shinichi; Iguchi, Kanami; Sugawara, Akihiro; Saito, Yoshifumi; Yamamoto, Tsuyoshi; Hirose, Tomoyasu; Shiomi, Kazuro; Sunazuka, Toshiaki; Omura, Satoshi; Hirono, Shuichi

    2009-09-01

    Human acidic mammalian chitinase (hAMCase) is an attractive target for developing anti-asthma medications. We used a variety of computational methods to investigate the interaction between hAMCase and the natural-product cyclopentapeptide chitinase inhibitor argifin. The three-dimensional structure of hAMCase was first constructed using homology modeling. The interaction mode and binding free energy between argifin and hAMCase were then examined by the molecular-docking calculation and the molecular mechanics Poisson-Boltzmann surface area method combined with molecular dynamics simulation, respectively. The results suggested that argifin binds to hAMCase in a similar fashion to the interaction mode observed in the crystal structure of argifin-human chitotriosidase complex, and possesses inhibitory activity against hAMCase in the micromolar range. We further designed argifin derivatives expected to be selective for hAMCase.

  9. Evolutionary inference via the Poisson Indel Process.

    Science.gov (United States)

    Bouchard-Côté, Alexandre; Jordan, Michael I

    2013-01-22

    We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114-124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments.

  10. Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets

    Science.gov (United States)

    Carlet, Guido; Casati, Matteo; Shadrin, Sergey

    2017-04-01

    We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D > 1. Hence, in contrast with the D = 1 case, the deformation theory in the multivariable case is non-trivial.

  11. Quantum algebras and Poisson geometry in mathematical physics

    CERN Document Server

    Karasev, M V

    2005-01-01

    This collection presents new and interesting applications of Poisson geometry to some fundamental well-known problems in mathematical physics. The methods used by the authors include, in addition to advanced Poisson geometry, unexpected algebras with non-Lie commutation relations, nontrivial (quantum) Kählerian structures of hypergeometric type, dynamical systems theory, semiclassical asymptotics, etc.

  12. Poisson's ratio and Young's modulus of lipid bilayers in different phases

    Directory of Open Access Journals (Sweden)

    Tayebeh eJadidi

    2014-04-01

    Full Text Available A general computational method is introduced to estimate the Poisson's ratio for membranes with small thickness.In this method, the Poisson's ratio is calculated by utilizing a rescaling of inter-particle distancesin one lateral direction under periodic boundary conditions. As an example for the coarse grained lipid model introduced by Lenz and Schmid, we calculate the Poisson's ratio in the gel, fluid, and interdigitated phases. Having the Poisson's ratio, enable us to obtain the Young's modulus for the membranes in different phases. The approach may be applied to other membranes such as graphene and tethered membranes in orderto predict the temperature dependence of its Poisson's ratio and Young's modulus.

  13. Estimating Bird / Aircraft Collision Probabilities and Risk Utilizing Spatial Poisson Processes

    Science.gov (United States)

    2012-06-10

    ESTIMATING BIRD/AIRCRAFT COLLISION PROBABILITIES AND RISK UTILIZING SPATIAL POISSON PROCESSES GRADUATE...AND RISK UTILIZING SPATIAL POISSON PROCESSES GRADUATE RESEARCH PAPER Presented to the Faculty Department of Operational Sciences...COLLISION PROBABILITIES AND RISK UTILIZING SPATIAL POISSON PROCESSES Brady J. Vaira, BS, MS Major, USAF Approved

  14. Estimation of Poisson noise in spatial domain

    Science.gov (United States)

    Švihlík, Jan; Fliegel, Karel; Vítek, Stanislav; Kukal, Jaromír.; Krbcová, Zuzana

    2017-09-01

    This paper deals with modeling of astronomical images in the spatial domain. We consider astronomical light images contaminated by the dark current which is modeled by Poisson random process. Dark frame image maps the thermally generated charge of the CCD sensor. In this paper, we solve the problem of an addition of two Poisson random variables. At first, the noise analysis of images obtained from the astronomical camera is performed. It allows estimating parameters of the Poisson probability mass functions in every pixel of the acquired dark frame. Then the resulting distributions of the light image can be found. If the distributions of the light image pixels are identified, then the denoising algorithm can be applied. The performance of the Bayesian approach in the spatial domain is compared with the direct approach based on the method of moments and the dark frame subtraction.

  15. Three-dimensional multi-relaxation-time lattice Boltzmann front-tracking method for two-phase flow

    International Nuclear Information System (INIS)

    Xie Hai-Qiong; Zeng Zhong; Zhang Liang-Qi

    2016-01-01

    We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop, and the drop deformation in a shear flow, were simulated to validate the present model. (paper)

  16. Towards a physical interpretation of the entropic lattice Boltzmann method

    Science.gov (United States)

    Malaspinas, Orestis; Deville, Michel; Chopard, Bastien

    2008-12-01

    The entropic lattice Boltzmann method (ELBM) is one among several different versions of the lattice Boltzmann method for the simulation of hydrodynamics. The collision term of the ELBM is characterized by a nonincreasing H function, guaranteed by a variable relaxation time. We propose here an analysis of the ELBM using the Chapman-Enskog expansion. We show that it can be interpreted as some kind of subgrid model, where viscosity correction scales like the strain rate tensor. We confirm our analytical results by the numerical computations of the relaxation time modifications on the two-dimensional dipole-wall interaction benchmark.

  17. Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

    Science.gov (United States)

    Feng, Wensen; Qiao, Peng; Chen, Yunjin; Wensen Feng; Peng Qiao; Yunjin Chen; Feng, Wensen; Chen, Yunjin; Qiao, Peng

    2018-06-01

    The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.

  18. On covariant Poisson brackets in classical field theory

    International Nuclear Information System (INIS)

    Forger, Michael; Salles, Mário O.

    2015-01-01

    How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra

  19. On covariant Poisson brackets in classical field theory

    Energy Technology Data Exchange (ETDEWEB)

    Forger, Michael [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Salles, Mário O. [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN (Brazil)

    2015-10-15

    How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.

  20. Monte Carlo method for random surfaces

    International Nuclear Information System (INIS)

    Berg, B.

    1985-01-01

    Previously two of the authors proposed a Monte Carlo method for sampling statistical ensembles of random walks and surfaces with a Boltzmann probabilistic weight. In the present paper we work out the details for several models of random surfaces, defined on d-dimensional hypercubic lattices. (orig.)

  1. Direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation.

    Science.gov (United States)

    Garcia, Alejandro L; Wagner, Wolfgang

    2003-11-01

    In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.

  2. Simulation of capillary infiltration into packing structures for the optimization of ceramic materials using the lattice Boltzmann method

    Directory of Open Access Journals (Sweden)

    Danilo Sergi

    2016-01-01

    Full Text Available This study uses the lattice Boltzmann method (LBM to simulate in 2D the capillary infiltration into porous structures obtained from the packing of particles. The experimental problem motivating the work is the densification of carbon preforms by reactive melt infiltration. The aim is to determine the optimization principles for the manufacturing of high-performance ceramics. Simulations are performed for packings with varying structural properties. The results suggest that the observed slow infiltrations can be ascribed to interface dynamics. Pinning represents the primary factor retarding fluid penetration. The mechanism responsible for this phenomenon is analyzed in detail. When surface growth is allowed, it is found that the phenomenon of pinning becomes stronger. Systems trying to reproduce typical experimental conditions are also investigated. It turns out that the standard for accurate simulations is challenging. The primary obstacle to overcome for enhanced accuracy seems to be the over-occurrence of pinning.

  3. Exact solution for the Poisson field in a semi-infinite strip.

    Science.gov (United States)

    Cohen, Yossi; Rothman, Daniel H

    2017-04-01

    The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.

  4. A Method of Poisson's Ration Imaging Within a Material Part

    Science.gov (United States)

    Roth, Don J. (Inventor)

    1994-01-01

    The present invention is directed to a method of displaying the Poisson's ratio image of a material part. In the present invention, longitudinal data is produced using a longitudinal wave transducer and shear wave data is produced using a shear wave transducer. The respective data is then used to calculate the Poisson's ratio for the entire material part. The Poisson's ratio approximations are then used to display the data.

  5. Fractional poisson--a simple dose-response model for human norovirus.

    Science.gov (United States)

    Messner, Michael J; Berger, Philip; Nappier, Sharon P

    2014-10-01

    This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures. © 2014 Society for Risk Analysis Published 2014. This article is a U.S. Government work and is in the public domain for the U.S.A.

  6. The Lattice Boltzmann Method applied to neutron transport

    International Nuclear Information System (INIS)

    Erasmus, B.; Van Heerden, F. A.

    2013-01-01

    In this paper the applicability of the Lattice Boltzmann Method to neutron transport is investigated. One of the main features of the Lattice Boltzmann method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. An iterative solution of the operator form of the neutron transport equation is presented here, with the first collision source as the starting point of the iteration scheme. A full description of the discretization scheme is given, along with the quadrature set used for the angular discretization. An angular refinement scheme is introduced to increase the angular coverage of the problem phase space and to mitigate lattice ray effects. The method is applied to a model problem to investigate its applicability to neutron transport and the results are compared to a reference solution calculated, using MCNP. (authors)

  7. Mechanism of formation of subnanosecond current front in high-voltage pulse open discharge

    Science.gov (United States)

    Schweigert, I. V.; Alexandrov, A. L.; Zakrevsky, Dm. E.; Bokhan, P. A.

    2014-11-01

    The mechanism of subnanosecond current front rise observed previously in the experiment in high-voltage pulse open discharge in helium is studied in kinetic particle-in-cell simulations. The Boltzmann equations for electrons, ions, and fast atoms are solved self-consistently with the Poisson equations for the electrical potential. The partial contributions to the secondary electron emission from the ions, fast atoms, photons, and electrons, bombarding the electrode, are calculated. In simulations, as in the experiment, the discharge glows between two symmetrical cathodes and the anode grid in the midplane at P =6 Torr and the applied voltage of 20 kV. The electron avalanche development is considered for two experimental situations during the last stage of breakdown: (i) with constant voltage and (ii) with decreasing voltage. For case (i), the subnanosecond current front rise is set by photons from the collisional excitation transfer reactions. For the case (ii), the energetic electrons swamp the cathode during voltage drop and provide the secondary electron emission for the subnanosecond current rise, observed in the experiment.

  8. Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation

    International Nuclear Information System (INIS)

    Dou, Nicholas G.; Minnich, Austin J.

    2016-01-01

    Materials that possess low density, low thermal conductivity, and high stiffness are desirable for engineering applications, but most materials cannot realize these properties simultaneously due to the coupling between them. Nanotrusses, which consist of hollow nanoscale beams architected into a periodic truss structure, can potentially break these couplings due to their lattice architecture and nanoscale features. In this work, we study heat conduction in the exact nanotruss geometry by solving the frequency-dependent Boltzmann transport equation using a variance-reduced Monte Carlo algorithm. We show that their thermal conductivity can be described with only two parameters, solid fraction and wall thickness. Our simulations predict that nanotrusses can realize unique combinations of mechanical and thermal properties that are challenging to achieve in typical materials

  9. Differentiated heated lid driven cavity interacting with tube: A lattice Boltzmann study

    Directory of Open Access Journals (Sweden)

    Bennacer Rachid

    2017-01-01

    Full Text Available The multiple-relaxation-time (MRT lattice-Boltzmann method is implemented to investigate combined natural and forced convection occurring in a two-dimensional square cavity. The top wall slides to the right at constant speed, while the other three remain stationary. The solution is performed for a left vertical wall at a constant temperature, which is higher than of the right wall. This yields a “cooperating” case, in which dynamic and buoyancy forces are added together. The enclosure is filled with air and contains a heat conducting circular cylinder, which is placed at various positions. The double distribution model used in lattice Boltzmann methods has been adopted to simulate the hydrodynamic and thermal fields, with the D2Q9 and D2Q5 lattices selected to perform the corresponding computations. Simulations have been conducted over a wide range of Rayleigh (Ra and Reynolds (Re numbers, and the features of dynamic and thermal fields are presented for the spectra of this mixed convection phenomenon. The flow and heat transfer characteristics of the cylinder position are described and analyzed in terms of the average Nusselt number (Nu. The computed results show the influence of the cylinder on the corresponding heat transfer in the enclosure. It has been found that the power (i.e. shear stress needed to lid the upper surface will depend on the governing parameters.

  10. Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation

    Energy Technology Data Exchange (ETDEWEB)

    Brull, S., E-mail: Stephane.Brull@math.u-bordeaux.fr; Charrier, P., E-mail: Pierre.Charrier@math.u-bordeaux.fr; Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux.fr [University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence (France)

    2016-08-15

    It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwell-like kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of mono-energetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified two-dimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a three-dimensional configuration. Finally, the case of non-elastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics of gas-surface interaction, at a reasonable computing cost, to improve kinetic simulations of micro- and nano-flows.

  11. Characterizing the performance of the Conway-Maxwell Poisson generalized linear model.

    Science.gov (United States)

    Francis, Royce A; Geedipally, Srinivas Reddy; Guikema, Seth D; Dhavala, Soma Sekhar; Lord, Dominique; LaRocca, Sarah

    2012-01-01

    Count data are pervasive in many areas of risk analysis; deaths, adverse health outcomes, infrastructure system failures, and traffic accidents are all recorded as count events, for example. Risk analysts often wish to estimate the probability distribution for the number of discrete events as part of doing a risk assessment. Traditional count data regression models of the type often used in risk assessment for this problem suffer from limitations due to the assumed variance structure. A more flexible model based on the Conway-Maxwell Poisson (COM-Poisson) distribution was recently proposed, a model that has the potential to overcome the limitations of the traditional model. However, the statistical performance of this new model has not yet been fully characterized. This article assesses the performance of a maximum likelihood estimation method for fitting the COM-Poisson generalized linear model (GLM). The objectives of this article are to (1) characterize the parameter estimation accuracy of the MLE implementation of the COM-Poisson GLM, and (2) estimate the prediction accuracy of the COM-Poisson GLM using simulated data sets. The results of the study indicate that the COM-Poisson GLM is flexible enough to model under-, equi-, and overdispersed data sets with different sample mean values. The results also show that the COM-Poisson GLM yields accurate parameter estimates. The COM-Poisson GLM provides a promising and flexible approach for performing count data regression. © 2011 Society for Risk Analysis.

  12. Boltzmann-Langevin equation, dynamical instability and multifragmentation

    International Nuclear Information System (INIS)

    Feng-Shou Zhang

    1993-02-01

    By using simulations of the Boltzmann-Langevin equation which incorporates dynamical fluctuations beyond usual transport theories and by coupling it with a coalescence model, we obtain information on multifragmentation in heavy-ion collisions. From a calculation of the 40 Ca + 40 Ca system, we recover some trends of recent multifragmentation data

  13. 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...

  14. Nonlocal Boltzmann theory of plasma channels

    International Nuclear Information System (INIS)

    Yu, S.S.; Melendez, R.E.

    1983-01-01

    The mathematical framework for the LLNL code NUTS is developed. This code is designed to study the evolution of an electron-beam-generated plasma channel at all pressures. The Boltzmann treatment of the secondary electrons presented include all inertial, nonlocal, electric and magnetic effects, as well as effects of atomic collisions. Field equations are advanced simultaneously and self-consistently with the evolving plasma currents

  15. Lattice Boltzmann Approach to Resistive MHD

    Czech Academy of Sciences Publication Activity Database

    Macnab, A.; Vahala, G.; Vahala, L.; Pavlo, Pavol; Soe, M.

    2002-01-01

    Roč. 47, č. 9 (2002), s. 51 ISSN 0003-0503. [Annual Meeting of the Division of Plasma Physics of the American Physical Society/44th./. Orlando , Florida, 11.11.2001-15.11.2001] R&D Projects: GA ČR GA202/00/1216 Institutional research plan: CEZ:AV0Z2043910 Keywords : Lattice Boltzmann, magnetic fields Subject RIV: BL - Plasma and Gas Discharge Physics

  16. Action-angle variables and a KAM theorem for b-Poisson manifolds

    OpenAIRE

    Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey

    2015-01-01

    In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.

  17. Transport of Multivalent Electrolyte Mixtures in Micro- and Nanochannels

    Science.gov (United States)

    2013-11-08

    equations for this process are the unsteady Navier-Stokes equations along with continuity and the Poisson- Nernst -Planck system for the electro- static part...about five times the Debye screening length D (the 1/e lengthscale for the potential from the solution of the linearized Poisson- Boltzmann equation

  18. 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...

  19. A lattice based solution of the collisional Boltzmann equation with applications to microchannel flows

    International Nuclear Information System (INIS)

    Green, B I; Vedula, Prakash

    2013-01-01

    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. (paper)

  20. Non-Poisson Processes: Regression to Equilibrium Versus Equilibrium Correlation Functions

    Science.gov (United States)

    2004-07-07

    ARTICLE IN PRESSPhysica A 347 (2005) 268–2880378-4371/$ - doi:10.1016/j Correspo E-mail adwww.elsevier.com/locate/physaNon- Poisson processes : regression...05.40.a; 89.75.k; 02.50.Ey Keywords: Stochastic processes; Non- Poisson processes ; Liouville and Liouville-like equations; Correlation function...which is not legitimate with renewal non- Poisson processes , is a correct property if the deviation from the exponential relaxation is obtained by time

  1. Multi-parameter full waveform inversion using Poisson

    KAUST Repository

    Oh, Juwon

    2016-07-21

    In multi-parameter full waveform inversion (FWI), the success of recovering each parameter is dependent on characteristics of the partial derivative wavefields (or virtual sources), which differ according to parameterisation. Elastic FWIs based on the two conventional parameterisations (one uses Lame constants and density; the other employs P- and S-wave velocities and density) have low resolution of gradients for P-wave velocities (or ). Limitations occur because the virtual sources for P-wave velocity or (one of the Lame constants) are related only to P-P diffracted waves, and generate isotropic explosions, which reduce the spatial resolution of the FWI for these parameters. To increase the spatial resolution, we propose a new parameterisation using P-wave velocity, Poisson\\'s ratio, and density for frequency-domain multi-parameter FWI for isotropic elastic media. By introducing Poisson\\'s ratio instead of S-wave velocity, the virtual source for the P-wave velocity generates P-S and S-S diffracted waves as well as P-P diffracted waves in the partial derivative wavefields for the P-wave velocity. Numerical examples of the cross-triangle-square (CTS) model indicate that the new parameterisation provides highly resolved descent directions for the P-wave velocity. Numerical examples of noise-free and noisy data synthesised for the elastic Marmousi-II model support the fact that the new parameterisation is more robust for noise than the two conventional parameterisations.

  2. Study on two-dimensional POISSON design of large-scale FFAG magnet

    International Nuclear Information System (INIS)

    Ouyang Huafu

    2006-01-01

    In order to decrease the edge effect of the field, the designed magnetic field distribution in a large-scale FFAG magnet is realized by both the trim coil and the shape of the magnet pole-face. Through two-dimensional POISSON simulations, the distribution about the current and the position of the trim coil and the shape of the magnet pole are determined. In order to facilitate the POISSON design, two codes are writteen to automatically adjust the current and the position of the trim coil and the shape of magnet pole-face appeared in the POISSON input file. With the two codes, the efficiency of POISSON simulations is improved and the mistakes which might occur in writing and adjusting the POISSON input file manually could be avoided. (authors)

  3. A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

    International Nuclear Information System (INIS)

    Gamba, Irene M.; Haack, Jeffrey R.

    2014-01-01

    We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation

  4. Influence of nonelectrostatic ion-ion interactions on double-layer capacitance

    Science.gov (United States)

    Zhao, Hui

    2012-11-01

    Recently a Poisson-Helmholtz-Boltzmann (PHB) model [Bohinc , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.031130 85, 031130 (2012)] was developed by accounting for solvent-mediated nonelectrostatic ion-ion interactions. Nonelectrostatic interactions are described by a Yukawa-like pair potential. In the present work, we modify the PHB model by adding steric effects (finite ion size) into the free energy to derive governing equations. The modified PHB model is capable of capturing both ion specificity and ion crowding. This modified model is then employed to study the capacitance of the double layer. More specifically, we focus on the influence of nonelectrostatic ion-ion interactions on charging a double layer near a flat surface in the presence of steric effects. We numerically compute the differential capacitance as a function of the voltage under various conditions. At small voltages and low salt concentrations (dilute solution), we find out that the predictions from the modified PHB model are the same as those from the classical Poisson-Boltzmann theory, indicating that nonelectrostatic ion-ion interactions and steric effects are negligible. At moderate voltages, nonelectrostatic ion-ion interactions play an important role in determining the differential capacitance. Generally speaking, nonelectrostatic interactions decrease the capacitance because of additional nonelectrostatic repulsion among excess counterions inside the double layer. However, increasing the voltage gradually favors steric effects, which induce a condensed layer with crowding of counterions near the electrode. Accordingly, the predictions from the modified PHB model collapse onto those computed by the modified Poisson-Boltzmann theory considering steric effects alone. Finally, theoretical predictions are compared and favorably agree with experimental data, in particular, in concentrated solutions, leading one to conclude that the modified PHB model adequately predicts the diffuse

  5. 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...

  6. Gaussian-Based Smooth Dielectric Function: A Surface-Free Approach for Modeling Macromolecular Binding in Solvents

    Directory of Open Access Journals (Sweden)

    Arghya Chakravorty

    2018-03-01

    Full Text Available Conventional modeling techniques to model macromolecular solvation and its effect on binding in the framework of Poisson-Boltzmann based implicit solvent models make use of a geometrically defined surface to depict the separation of macromolecular interior (low dielectric constant from the solvent phase (high dielectric constant. Though this simplification saves time and computational resources without significantly compromising the accuracy of free energy calculations, it bypasses some of the key physio-chemical properties of the solute-solvent interface, e.g., the altered flexibility of water molecules and that of side chains at the interface, which results in dielectric properties different from both bulk water and macromolecular interior, respectively. Here we present a Gaussian-based smooth dielectric model, an inhomogeneous dielectric distribution model that mimics the effect of macromolecular flexibility and captures the altered properties of surface bound water molecules. Thus, the model delivers a smooth transition of dielectric properties from the macromolecular interior to the solvent phase, eliminating any unphysical surface separating the two phases. Using various examples of macromolecular binding, we demonstrate its utility and illustrate the comparison with the conventional 2-dielectric model. We also showcase some additional abilities of this model, viz. to account for the effect of electrolytes in the solution and to render the distribution profile of water across a lipid membrane.

  7. Lattice Boltzmann equation calculation of internal, pressure-driven turbulent flow

    International Nuclear Information System (INIS)

    Hammond, L A; Halliday, I; Care, C M; Stevens, A

    2002-01-01

    We describe a mixing-length extension of the lattice Boltzmann approach to the simulation of an incompressible liquid in turbulent flow. The method uses a simple, adaptable, closure algorithm to bound the lattice Boltzmann fluid incorporating a law-of-the-wall. The test application, of an internal, pressure-driven and smooth duct flow, recovers correct velocity profiles for Reynolds number to 1.25 x 10 5 . In addition, the Reynolds number dependence of the friction factor in the smooth-wall branch of the Moody chart is correctly recovered. The method promises a straightforward extension to other curves of the Moody chart and to cylindrical pipe flow

  8. Boundary Lax pairs from non-ultra-local Poisson algebras

    International Nuclear Information System (INIS)

    Avan, Jean; Doikou, Anastasia

    2009-01-01

    We consider non-ultra-local linear Poisson algebras on a continuous line. Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or 'boundary' extensions. They are parametrized by a boundary scalar matrix and depend, in addition, on the choice of an antiautomorphism. The new algebras are the classical-linear counterparts of the known quadratic quantum boundary algebras. For any choice of parameters, the non-ultra-local contribution of the original Poisson algebra disappears. We also systematically construct the associated classical Lax pair. The classical boundary principal chiral model is examined as a physical example.

  9. Mathematical modeling of influence of ion size effects in an electrolyte in a nanoslit with overlapped EDL

    Science.gov (United States)

    Rajni, Kumar, Prashant

    2017-10-01

    Many nanofluidic systems are being used in a wide range of applications due to advances in nanotechnology. Due to nanoscale size of the system, the physics involved in the electric double layer and consequently the different phenomena related to it are different than those at microscale. The Poisson-Boltzmann equation governing the electric double layer in the system has many shortcomings such as point sized ions. The inclusion of finite size of ions give rise to various electrokinetic phenomena. Electrocapillarity is one such phenomena where the size effect plays an important role. Theeffect of asymmetric finite ion sizes in nano-confinement in the view of osmotic pressure and electrocapillarity is analyzed. As the confinement width of the system becomes comparable with the Debye length, the overlapped electric double layer (EDL) is influenced and significantly deformed by the steric effects. The osmotic pressure from the modified Poisson-Boltzmann equation in nanoslit is obtained. Due to nonlinear nature of the modified PB equation, the solution is obtained through numerical method. Afterwards, the electrocapillarity due to the steric effect is analyzed under constant surface potential condition at the walls of the nanoslit along with the flat interface assumption.

  10. Implementing the lattice Boltzmann method to electrohydrodynamics with the leaky dielectric theory

    International Nuclear Information System (INIS)

    Zhang, J.; Kwok, D.Y.

    2004-01-01

    The lattice Boltzmann method (LBM) and electrohydrodynamics are both active subjects in fluid mechanics research in recent years. In this paper, we present a method to apply a multicomponent LBM to electrohydrodynamics studies. A series of drop deformation simulations under the influence of an electric field were carried out and the results are in good agreement with other theoretical and experimental studies. Given that no special treatment of interfaces is required for LBM, our method could be an excellent alternative to electrohydrodynamics studies than traditional computational fluid dynamics methods. Further, our algorithm and simulation can be readily implemented to the more complex electrohydrodynamic systems. (author)

  11. Abrasive wear mechanisms and surface layer structure of refractory materials after mechanical working

    International Nuclear Information System (INIS)

    Milman, Y.V.; Lotsko, D.V.

    1989-01-01

    The mechanisms of abrasive wear and surface layer structure formation after different kinds of mechanical working are considered in terms of fracture and plastic deformation mechanisms for various refractory materials. The principles for classification of abrasive wear mechanisms are proposed, the four types of wear mechanisms are distinguished for various combinations of fractures and plastic deformation types. The concept of characteristic deformation temperature t * (knee temperature) is used. Detailed examples are given of investigating the surface layer structures in grinded crystals of sapphire and molybdenum. The amorphisation tendency of the thinnest surface layer while mechanical polishing is discussed separately. 19 refs., 11 figs., 2 tabs. (Author)

  12. Lattice-Boltzmann Method with Dynamic Grid Refinement for Simulating Particle Deposition on a Single Fibre

    Directory of Open Access Journals (Sweden)

    Helmut Schomburg

    2013-03-01

    Full Text Available In this work a numerical approach to predict the deposition behaviour of nano-scale particles on the surface of a single fibre by resolving the resulting dendrite-like particle structures in detail is presented. The gas flow simulation is carried out by a two-dimensional Lattice-Boltzmann method, which is coupled with a Lagrangian approach for the particle motion. To decrease calculation time and system requirements the Lattice-Boltzmann model is extended to allow for local grid refinement. Because of the a priori unknown location of deposition, the simulation procedure starts on a coarse mesh which is then locally refined in a fully adaptive way in regions of accumulated particles. After each deposition the fluid flow is recalculated in order to resolve the coupling of the flow with the growing particle structures correctly. For the purpose of avoiding unphysical blocking of flow by growing particle dendrites the Lattice-Boltzmann method is extended to permeable cells in these regions using the Brinkmann equation. This extended deposition model is compared to simpler approaches, where the deposit has no retroaction on the flow or is treated as a solid structure. It is clear that the permeable model is most realistic and allows considering the particle deposition on a fibre as two-dimensional problem. Comprehensive simulations were conducted for analysing the importance of different parameters, i.e. free-stream velocity and particle diameter on the deposit structure. The results of this sensitivity analysis agree qualitatively well with former published numerical and experimental results. Finally the structure of the particle deposit was quantitatively characterised by using a modified fractal dimension.

  13. The BRST complex of homological Poisson reduction

    Science.gov (United States)

    Müller-Lennert, Martin

    2017-02-01

    BRST complexes are differential graded Poisson algebras. They are associated with a coisotropic ideal J of a Poisson algebra P and provide a description of the Poisson algebra (P/J)^J as their cohomology in degree zero. Using the notion of stable equivalence introduced in Felder and Kazhdan (Contemporary Mathematics 610, Perspectives in representation theory, 2014), we prove that any two BRST complexes associated with the same coisotropic ideal are quasi-isomorphic in the case P = R[V] where V is a finite-dimensional symplectic vector space and the bracket on P is induced by the symplectic structure on V. As a corollary, the cohomology of the BRST complexes is canonically associated with the coisotropic ideal J in the symplectic case. We do not require any regularity assumptions on the constraints generating the ideal J. We finally quantize the BRST complex rigorously in the presence of infinitely many ghost variables and discuss the uniqueness of the quantization procedure.

  14. Poisson's Ratio and Auxetic Properties of Natural Rocks

    Science.gov (United States)

    Ji, Shaocheng; Li, Le; Motra, Hem Bahadur; Wuttke, Frank; Sun, Shengsi; Michibayashi, Katsuyoshi; Salisbury, Matthew H.

    2018-02-01

    Here we provide an appraisal of the Poisson's ratios (υ) for natural elements, common oxides, silicate minerals, and rocks with the purpose of searching for naturally auxetic materials. The Poisson's ratios of equivalently isotropic polycrystalline aggregates were calculated from dynamically measured elastic properties. Alpha-cristobalite is currently the only known naturally occurring mineral that has exclusively negative υ values at 20-1,500°C. Quartz and potentially berlinite (AlPO4) display auxetic behavior in the vicinity of their α-β structure transition. None of the crystalline igneous and metamorphic rocks (e.g., amphibolite, gabbro, granite, peridotite, and schist) display auxetic behavior at pressures of >5 MPa and room temperature. Our experimental measurements showed that quartz-rich sedimentary rocks (i.e., sandstone and siltstone) are most likely to be the only rocks with negative Poisson's ratios at low confining pressures (≤200 MPa) because their main constituent mineral, α-quartz, already has extremely low Poisson's ratio (υ = 0.08) and they contain microcracks, micropores, and secondary minerals. This finding may provide a new explanation for formation of dome-and-basin structures in quartz-rich sedimentary rocks in response to a horizontal compressional stress in the upper crust.

  15. Estimation of a Non-homogeneous Poisson Model: An Empirical ...

    African Journals Online (AJOL)

    This article aims at applying the Nonhomogeneous Poisson process to trends of economic development. For this purpose, a modified Nonhomogeneous Poisson process is derived when the intensity rate is considered as a solution of stochastic differential equation which satisfies the geometric Brownian motion. The mean ...

  16. A discontinuous Galerkin finite-element method for a 1D prototype of the Boltzmann equation

    NARCIS (Netherlands)

    Hoitinga, W.; Brummelen, van E.H.

    2011-01-01

    To develop and analyze new computational techniques for the Boltzmann equation based on model or approximation adaptivity, it is imperative to have disposal of a compliant model problem that displays the essential characteristics of the Boltzmann equation and that admits the extraction of highly

  17. NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes

    Directory of Open Access Journals (Sweden)

    Ana C. Cebrián

    2015-03-01

    Full Text Available NHPoisson is an R package for the modeling of nonhomogeneous Poisson processes in one dimension. It includes functions for data preparation, maximum likelihood estimation, covariate selection and inference based on asymptotic distributions and simulation methods. It also provides specific methods for the estimation of Poisson processes resulting from a peak over threshold approach. In addition, the package supports a wide range of model validation tools and functions for generating nonhomogenous Poisson process trajectories. This paper is a description of the package and aims to help those interested in modeling data using nonhomogeneous Poisson processes.

  18. Determination of oral mucosal Poisson's ratio and coefficient of friction from in-vivo contact pressure measurements.

    Science.gov (United States)

    Chen, Junning; Suenaga, Hanako; Hogg, Michael; Li, Wei; Swain, Michael; Li, Qing

    2016-01-01

    Despite their considerable importance to biomechanics, there are no existing methods available to directly measure apparent Poisson's ratio and friction coefficient of oral mucosa. This study aimed to develop an inverse procedure to determine these two biomechanical parameters by utilizing in vivo experiment of contact pressure between partial denture and beneath mucosa through nonlinear finite element (FE) analysis and surrogate response surface (RS) modelling technique. First, the in vivo denture-mucosa contact pressure was measured by a tactile electronic sensing sheet. Second, a 3D FE model was constructed based on the patient CT images. Third, a range of apparent Poisson's ratios and the coefficients of friction from literature was considered as the design variables in a series of FE runs for constructing a RS surrogate model. Finally, the discrepancy between computed in silico and measured in vivo results was minimized to identify the best matching Poisson's ratio and coefficient of friction. The established non-invasive methodology was demonstrated effective to identify such biomechanical parameters of oral mucosa and can be potentially used for determining the biomaterial properties of other soft biological tissues.

  19. Characterization and visualization of RNA secondary structure Boltzmann ensemble via information theory.

    Science.gov (United States)

    Lin, Luan; McKerrow, Wilson H; Richards, Bryce; Phonsom, Chukiat; Lawrence, Charles E

    2018-03-05

    The nearest neighbor model and associated dynamic programming algorithms allow for the efficient estimation of the RNA secondary structure Boltzmann ensemble. However because a given RNA secondary structure only contains a fraction of the possible helices that could form from a given sequence, the Boltzmann ensemble is multimodal. Several methods exist for clustering structures and finding those modes. However less focus is given to exploring the underlying reasons for this multimodality: the presence of conflicting basepairs. Information theory, or more specifically mutual information, provides a method to identify those basepairs that are key to the secondary structure. To this end we find most informative basepairs and visualize the effect of these basepairs on the secondary structure. Knowing whether a most informative basepair is present tells us not only the status of the particular pair but also provides a large amount of information about which other pairs are present or not present. We find that a few basepairs account for a large amount of the structural uncertainty. The identification of these pairs indicates small changes to sequence or stability that will have a large effect on structure. We provide a novel algorithm that uses mutual information to identify the key basepairs that lead to a multimodal Boltzmann distribution. We then visualize the effect of these pairs on the overall Boltzmann ensemble.

  20. Three-dimensional lattice Boltzmann model for compressible flows.

    Science.gov (United States)

    Sun, Chenghai; Hsu, Andrew T

    2003-07-01

    A three-dimensional compressible lattice Boltzmann model is formulated on a cubic lattice. A very large particle-velocity set is incorporated in order to enable a greater variation in the mean velocity. Meanwhile, the support set of the equilibrium distribution has only six directions. Therefore, this model can efficiently handle flows over a wide range of Mach numbers and capture shock waves. Due to the simple form of the equilibrium distribution, the fourth-order velocity tensors are not involved in the formulation. Unlike the standard lattice Boltzmann model, no special treatment is required for the homogeneity of fourth-order velocity tensors on square lattices. The Navier-Stokes equations were recovered, using the Chapman-Enskog method from the Bhatnagar-Gross-Krook (BGK) lattice Boltzmann equation. The second-order discretization error of the fluctuation velocity in the macroscopic conservation equation was eliminated by means of a modified collision invariant. The model is suitable for both viscous and inviscid compressible flows with or without shocks. Since the present scheme deals only with the equilibrium distribution that depends only on fluid density, velocity, and internal energy, boundary conditions on curved wall are easily implemented by an extrapolation of macroscopic variables. To verify the scheme for inviscid flows, we have successfully simulated a three-dimensional shock-wave propagation in a box and a normal shock of Mach number 10 over a wedge. As an application to viscous flows, we have simulated a flat plate boundary layer flow, flow over a cylinder, and a transonic flow over a NACA0012 airfoil cascade.