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

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

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.

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.

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.

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.)

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.

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.

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.

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.

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.

Room temperature Young's modulus, shear modulus, Poisson's ratio and hardness of PbTe-PbS thermoelectric materials

Energy Technology Data Exchange (ETDEWEB)

Ni, Jennifer E [Chemical Engineering and Materials Science Department, Michigan State University, East Lansing, MI 48824 (United States); Case, Eldon D., E-mail: casee@egr.msu.edu [Chemical Engineering and Materials Science Department, Michigan State University, East Lansing, MI 48824 (United States); Khabir, Kristen N; Stewart, Ryan C [Chemical Engineering and Materials Science Department, Michigan State University, East Lansing, MI 48824 (United States); Wu, Chun-I; Hogan, Timothy P [Electrical and Computer Engineering Department, Michigan State University, East Lansing, MI 48824 (United States); Timm, Edward J [Mechanical Engineering Department, Michigan State University, East Lansing, MI 48824 (United States); Girard, Steven N; Kanatzidis, Mercouri G [Department of Chemistry, Northwestern University, Evanston, IL (United States)

2010-06-15

Two-phase PbTe-PbS materials, in which PbS is a nanostructured phase, are promising thermoelectric materials for the direct conversion of heat energy into electricity. In this study, a Vickers indentation mean hardness of 1.18 {+-} 0.09 GPa was measured for hot pressed specimens Pb{sub 0.95}Sn{sub 0.05}Te-PbS 8% while the mean hardness of cast specimens was 0.68 {+-} 0.07 GPa. The mean fracture toughness of the not pressed specimens was estimated as 0.35 {+-} 0.04 MPa m{sup 1/2} via Vickers indentation. Resonant Ultrasound Spectroscopy (RUS) measurements on hot pressed specimens gave mean values of Young's modulus, shear modulus and Poisson's ratio of 53.1 GPa, 21.4 GPa and 0.245, respectively while for the cast specimens the Young's and shear moduli were about 10% lower than for the hot pressed, with a mean value of Poisson's ratio of 0.245. The differences between the hardness and elastic moduli values for the cast and hot pressed specimens are discussed.

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.

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

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

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)

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.

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.

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.

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.

Formality theory from Poisson structures to deformation quantization

CERN Document Server

Esposito, Chiara

2015-01-01

This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.

Theory of melt polyelectrolyte blends and block copolymers: Phase behavior, surface tension, and microphase periodicity

Energy Technology Data Exchange (ETDEWEB)

Sing, Charles E. [Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208 (United States); Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Zwanikken, Jos W.; Olvera de la Cruz, Monica [Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208 (United States)

2015-01-21

Polymer mixtures such as blends or block copolymers are of great interest in energy applications and functional materials, and often, one or more of these species contain charges. The traditional fashion in which such materials are studied uses Self-Consistent Field Theory (SCFT) methods that incorporate electrostatics using Poisson-Boltzmann (PB) theory. We adapt a new and rigorous approach that does not rely on the mean-field assumptions inherent in the PB theory and instead uses Liquid State (LS) integral equation theory to articulate charge correlations that are completely neglected in PB. We use this theory to calculate phase diagrams for both blends and block copolyelectrolytes using SCFT-LS and demonstrate how their phase behavior is highly dependent on chain length, charge fraction, charge size, and the strength of Coulombic interactions. Beyond providing phase behavior of blends and block copolyelectrolytes, we can use this theory to investigate the interfacial properties such as surface tension and block copolyelectrolyte lamellar spacing. Lamellar spacing provides a way to directly compare the SCFT-LS theory to the results of experiments. SCFT-LS will provide conceptual and mathematical clarification of the role of charge correlations in these systems and aid in the design of materials based on charge polymers.

Theory of melt polyelectrolyte blends and block copolymers: Phase behavior, surface tension, and microphase periodicity

International Nuclear Information System (INIS)

Sing, Charles E.; Zwanikken, Jos W.; Olvera de la Cruz, Monica

2015-01-01

Polymer mixtures such as blends or block copolymers are of great interest in energy applications and functional materials, and often, one or more of these species contain charges. The traditional fashion in which such materials are studied uses Self-Consistent Field Theory (SCFT) methods that incorporate electrostatics using Poisson-Boltzmann (PB) theory. We adapt a new and rigorous approach that does not rely on the mean-field assumptions inherent in the PB theory and instead uses Liquid State (LS) integral equation theory to articulate charge correlations that are completely neglected in PB. We use this theory to calculate phase diagrams for both blends and block copolyelectrolytes using SCFT-LS and demonstrate how their phase behavior is highly dependent on chain length, charge fraction, charge size, and the strength of Coulombic interactions. Beyond providing phase behavior of blends and block copolyelectrolytes, we can use this theory to investigate the interfacial properties such as surface tension and block copolyelectrolyte lamellar spacing. Lamellar spacing provides a way to directly compare the SCFT-LS theory to the results of experiments. SCFT-LS will provide conceptual and mathematical clarification of the role of charge correlations in these systems and aid in the design of materials based on charge polymers

Scattering theory of the linear Boltzmann operator

International Nuclear Information System (INIS)

Hejtmanek, J.

1975-01-01

In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schroedinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moeller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space. (orig.) [de

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.

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+.

New Poisson–Boltzmann type equations: one-dimensional solutions

International Nuclear Information System (INIS)

Lee, Chiun-Chang; Lee, Hijin; Hyon, YunKyong; Lin, Tai-Chia; Liu, Chun

2011-01-01

The Poisson–Boltzmann (PB) equation is conventionally used to model the equilibrium of bulk ionic species in different media and solvents. In this paper we study a new Poisson–Boltzmann type (PB n ) equation with a small dielectric parameter ε 2 and non-local nonlinearity which takes into consideration the preservation of the total amount of each individual ion. This equation can be derived from the original Poisson–Nernst–Planck system. Under Robin-type boundary conditions with various coefficient scales, we demonstrate the asymptotic behaviours of one-dimensional solutions of PB n equations as the parameter ε approaches zero. In particular, we show that in case of electroneutrality, i.e. α = β, solutions of 1D PB n equations have a similar asymptotic behaviour as those of 1D PB equations. However, as α ≠ β (non-electroneutrality), solutions of 1D PB n equations may have blow-up behaviour which cannot be found in 1D PB equations. Such a difference between 1D PB and PB n equations can also be verified by numerical simulations

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

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.

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.

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

Transverse-momentum spectra and nuclear modification factor using Boltzmann Transport Equation with flow in Pb+Pb collisions at √(s{sub NN}) = 2.76 TeV

Energy Technology Data Exchange (ETDEWEB)

Tripathy, Sushanta; Khuntia, Arvind; Tiwari, Swatantra Kumar; Sahoo, Raghunath [Indian Institute of Technology Indore, Discipline of Physics, School of Basic Sciences, Indore (India)

2017-05-15

In the continuation of our previous work, the transverse-momentum (p{sub T}) spectra and nuclear modification factor (R{sub AA}) are derived using the relaxation time approximation of Boltzmann Transport Equation (BTE). The initial p{sub T}-distribution used to describe p + p collisions has been studied with the perturbative-Quantum Chromodynamics (pQCD) inspired power-law distribution, Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse-momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the p{sub T}-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at √(s{sub NN}) = 2.76 TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, K{sup *0} and φ. It is observed that the present formalism while explaining the transverse-momentum spectra up to 5 GeV/c, explains the nuclear modification factor very well up to 8 GeV/c in p{sub T} for all these particles except for protons. R{sub AA} is found to be independent of the degree of non-extensivity, q{sub pp} after p{sub T} ∝ 8 GeV/c. (orig.)

Remarks on 'Poisson ratio beyond the limits of the elasticity theory'

International Nuclear Information System (INIS)

Wojciechowski, K.W.

2002-12-01

The non-chiral, elastically isotropic model exhibits Poison ratios in the range -1 ≤ σ ≤ 1 without any molecular rotation. The centres of discs-atoms are replaced in the vertices of a perfect triangle of the side length equal to σ. The positive sign of the Lame constant λ is not necessary for the stability of an isotropic system at any dimensionality. As the upper limit for the Poisson ratio in 2D isotropic systems is 1, crystalline or polycrystalline 2D systems can be obtained having the Poisson ratio exceeding 1/2. Both the traditional theory of elasticity and the Cosserat one exclude Poisson ratios exceeding 1/2 in 3D isotropic systems. Neighter anisotropy nor rotation are necessary to obtain extreme values of the Poisson ratio (author)

Renormalized perturbation theory: Vlasov-Poisson System, weak turbulence limit and gyrokinetics

International Nuclear Information System (INIS)

Zhang, Y.Z.; Mahajan, S.M.

1987-10-01

The Self-consistency of the renormalized perturbation theory is demonstrated by applying it to the Vlasov-Poisson System and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-β gyrokinetic system. Comparison of our theory with other current theories is presented. 22 refs

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

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

Multiscale Multiphysics and Multidomain Models I: Basic Theory.

Science.gov (United States)

Wei, Guo-Wei

2013-12-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long

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.

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.)

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.

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.

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

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.

The Poisson algebra of the invariant charges of the Nambu-Goto theory: Casimir elements

International Nuclear Information System (INIS)

Pohlmeyer, K.

1988-01-01

The reparametrization invariant ''non-local'' conserved charges of the Nambu-Goto theory form an algebra under Poisson bracket operation. The center of the formal closure of this algebra is determined. The relation of the central elements to the constraints of the Nambu-Goto theory is clarified. (orig.)

Beatification: Flattening Poisson brackets for plasma theory and computation

Science.gov (United States)

Morrison, P. J.; Viscondi, T. F.; Caldas, I.

2017-10-01

A perturbative method called beatification is presented for producing nonlinear Hamiltonian fluid and plasma theories. Plasma Hamiltonian theories, fluid and kinetic, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding a transformation that removes the explicit variable dependence from a noncanonical Poisson bracket and replaces it with a fixed dependence on a chosen state in the phase space. As such, beatification is a major step toward casting the Hamiltonian system in its canonical form, thus enabling or facilitating the use of analytical and numerical techniques that require or favor a representation in terms of canonical, or beatified, Hamiltonian variables. Examples will be given. U.S. D.O.E No. #DE-FG02-04ER-54742.

Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations

CERN Document Server

Riotto, Antonio

1998-01-01

The closed time-path (CPT) formalism is a powerful Green's function formulation to describe nonequilibrium phenomena in field theory and it leads to a complete nonequilibrium quantum kinetic theory. In this paper we make use of the CPT formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest ``memory'' effects which are typical of the quantum transp ort t...

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.)

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)

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

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.)

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.

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

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...

Variational multiscale models for charge transport.

Science.gov (United States)

Wei, Guo-Wei; Zheng, Qiong; Chen, Zhan; Xia, Kelin

2012-01-01

This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle

Variational multiscale models for charge transport

Science.gov (United States)

Wei, Guo-Wei; Zheng, Qiong; Chen, Zhan; Xia, Kelin

2012-01-01

This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle

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

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.

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.

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.

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)

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

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

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

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.…

Energy flow in non-equilibrium conformal field theory

Science.gov (United States)

Bernard, Denis; Doyon, Benjamin

2012-09-01

We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.

The coupling of Poisson sigma models to topological backgrounds

Energy Technology Data Exchange (ETDEWEB)

Rosa, Dario [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of)

2016-12-13

We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.

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

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.

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.

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.)

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.

MPBEC, a Matlab Program for Biomolecular Electrostatic Calculations

OpenAIRE

Vergara-Perez, Sandra; Marucho, Marcelo

2015-01-01

One of the most used and efficient approaches to compute electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation. There are several software packages available that solve the PB equation for molecules in aqueous electrolyte solutions. Most of these software packages are useful for scientists with specialized training and expertise in computational biophysics. However, the user is usually required to manually take several important choices, de...

Effective charge versus bare charge: an analytical estimate for colloids in the infinite dilution limit

International Nuclear Information System (INIS)

Aubouy, Miguel; Trizac, Emmanuel; Bocquet, Lyderic

2003-01-01

We propose an analytical approximation for the dependence of the effective charge on the bare charge for spherical and cylindrical macro-ions as a function of the size of the colloid and salt content, for the situation of a unique colloid immersed in a sea of electrolyte (where the definition of an effective charge is non-ambiguous). Our approach is based on the Poisson-Boltzmann (PB) mean-field theory. Mathematically speaking, our estimate is asymptotically exact in the limit κa >> 1, where a is the radius of the colloid and κ is the inverse screening length. In practice, a careful comparison with effective charge parameters, obtained by numerically solving the full nonlinear PB theory, proves that our estimate is good down to κa ∼ 1. This is precisely the limit appropriate to treat colloidal suspensions. A particular emphasis is put on the range of parameters suitable to describe both single and double strand DNA molecules under physiological conditions

Exact mean-field theory of ionic solutions: non-Debye screening

International Nuclear Information System (INIS)

Varela, L.M.; Garcia, Manuel; Mosquera, Victor

2003-01-01

The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Hueckel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory

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

Ionic Liquids in Electro-active Devices (ILED)

Science.gov (United States)

2013-12-12

near a charged wall can be modeled by Poisson- Nernst -Planck (PNP) equations , Poisson-Boltzmann (PB) equations , and Gouy-Chapman-Stern (GCS) model...actuators can be calculated from the bending curvature к and the Young’s moduli of the ionic polymer layer Yi and the Au layer Ym by the equation below...Arrhenius equation exp a E p p RT (1) wherein p and aE are the conducting ion concentration as T and the activation energy for conducting

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

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...

Thermoelectric properties of fully hydrogenated graphene: Semi-classical Boltzmann theory

International Nuclear Information System (INIS)

Reshak, A. H.

2015-01-01

Based on the calculated band structure, the electronic transport coefficients of chair-/boat-like graphane were evaluated by using the semi-classical Boltzmann theory and rigid band model. The maximum value of electrical conductivity for chair (boat)-like graphane of about 1.4 (0.6) × 10 19 (Ωms) −1 is achieved at 600 K. The charge carrier concentration and the electrical conductivity linearly increase with increasing the temperature in agreement with the experimental work for graphene. The investigated materials exhibit the highest value of Seebeck coefficient at 300 K. We should emphasize that in the chemical potential between ∓0.125 μ(eV) the investigated materials exhibit minimum value of electronic thermal conductivity, therefore, maximum efficiency. As the temperature increases, the electronic thermal conductivity increases exponentially, in agreement with the experimental data of graphene. We also calculated the power factor of chair-/boat-like graphane at 300 and 600 K as a function of chemical potential between ∓0.25 μ(eV)

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

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

Revisiting Wiedemann-Franz law through Boltzmann transport equations and ab-initio density functional theory

Science.gov (United States)

Nag, Abhinav; Kumari, Anuja; Kumar, Jagdish

2018-05-01

We have investigated structural, electronic and transport properties of the alkali metals using ab-initio density functional theory. The electron energy dispersions are found parabolic free electron like which is expected for alkali metals. The lattice constants for all the studied metals are also in good agreement within 98% with experiments. We have further computed their transport properties using semi-classical Boltzmann transport equations with special focus on electrical and thermal conductivity. Our objective was to obtain Wiedemann-Franz law and hence Lorenz number. The motivation to do these calculations is to see that how the incorporation of different interactions such as electron-lattice, electron-electron interaction affect the Wiedeman-Franz law. By solving Boltzmann transport equations, we have obtained electrical conductivity (σ/τ) and thermal conductivity (κ0 /τ) at different temperatures and then calculated Lorenz number using L = κ0 /(σT). The obtained value of Lorenz number has been found to match with value derived for free electron Fermi gas 2.44× 10-8 WΩK-2. Our results prove that the Wiedemann-Franz law as derived for free electron gas does not change much for alkali metals, even when one incorporates interaction of electrons with atomic nuclei and other electrons. However, at lower temperatures, the Lorenz number, was found to be deviating from its theoretical value.

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

M5-brane as a Nambu-Poisson geometry of a multi-D1-brane theory

International Nuclear Information System (INIS)

De Castro, A.; Garcia del Moral, M.P.; Martin, I.; Restuccia, A.

2004-01-01

We introduce a Nambu-Poisson bracket in the geometrical description of the D=11 M5-brane. This procedure allows us, under some assumptions, to eliminate the local degrees of freedom of the antisymmetric field in the M5-brane Hamiltonian and to express it as a D=11 p-brane theory invariant under symplectomorphisms. The explicit expression of the Hamiltonian is obtained. The existence of nontrivial physical configurations annihilating the energy density is shown. Finally, a regularization of the M5-brane in terms of a multi D1-brane theory invariant under the SU(N)xSU(N) group in the limit when N→∞ is constructed

An introduction to the Boltzmann equation and transport processes in gases

CERN Document Server

Kremer, Gilberto M; Colton, David

2010-01-01

This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.

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

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.

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.

Structure and osmotic pressure of ionic microgel dispersions

Energy Technology Data Exchange (ETDEWEB)

Hedrick, Mary M. [Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050 (United States); Department of Chemistry and Biochemistry, North Dakota State University, Fargo, North Dakota 58108-6050 (United States); Chung, Jun Kyung; Denton, Alan R., E-mail: alan.denton@ndsu.edu [Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050 (United States)

2015-01-21

We investigate structural and thermodynamic properties of aqueous dispersions of ionic microgels—soft colloidal gel particles that exhibit unusual phase behavior. Starting from a coarse-grained model of microgel macroions as charged spheres that are permeable to microions, we perform simulations and theoretical calculations using two complementary implementations of Poisson-Boltzmann (PB) theory. Within a one-component model, based on a linear-screening approximation for effective electrostatic pair interactions, we perform molecular dynamics simulations to compute macroion-macroion radial distribution functions, static structure factors, and macroion contributions to the osmotic pressure. For the same model, using a variational approximation for the free energy, we compute both macroion and microion contributions to the osmotic pressure. Within a spherical cell model, which neglects macroion correlations, we solve the nonlinear PB equation to compute microion distributions and osmotic pressures. By comparing the one-component and cell model implementations of PB theory, we demonstrate that the linear-screening approximation is valid for moderately charged microgels. By further comparing cell model predictions with simulation data for osmotic pressure, we chart the cell model’s limits in predicting osmotic pressures of salty dispersions.

Structure and osmotic pressure of ionic microgel dispersions

International Nuclear Information System (INIS)

Hedrick, Mary M.; Chung, Jun Kyung; Denton, Alan R.

2015-01-01

We investigate structural and thermodynamic properties of aqueous dispersions of ionic microgels—soft colloidal gel particles that exhibit unusual phase behavior. Starting from a coarse-grained model of microgel macroions as charged spheres that are permeable to microions, we perform simulations and theoretical calculations using two complementary implementations of Poisson-Boltzmann (PB) theory. Within a one-component model, based on a linear-screening approximation for effective electrostatic pair interactions, we perform molecular dynamics simulations to compute macroion-macroion radial distribution functions, static structure factors, and macroion contributions to the osmotic pressure. For the same model, using a variational approximation for the free energy, we compute both macroion and microion contributions to the osmotic pressure. Within a spherical cell model, which neglects macroion correlations, we solve the nonlinear PB equation to compute microion distributions and osmotic pressures. By comparing the one-component and cell model implementations of PB theory, we demonstrate that the linear-screening approximation is valid for moderately charged microgels. By further comparing cell model predictions with simulation data for osmotic pressure, we chart the cell model’s limits in predicting osmotic pressures of salty dispersions

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

Diverse carrier mobility of monolayer BNCx: A combined density functional theory and Boltzmann transport theory study.

Science.gov (United States)

Wu, Tao; Deng, Kaiming; Deng, Wei-Qiao; Lu, Ruifeng

2017-09-19

BNCX monolayer as a kind of two-dimensional material has numerous chemical atomic ratios and arrangements with different electronic structures. Via calculations on the basis of density functional theory and Boltzmann transport theory under deformation potential approximation, the band structures and carrier mobilities of BNCX (x=1,2,3,4) nanosheets are systematically investigated. The calculated results show that BNC2-1 is a material with very small band gap (0.02 eV) among all the structures while other BNCX monolayers are semiconductors with band gap ranging from 0.51 to 1.32 eV. The carrier mobility of BNCX varies considerably from tens to millions of cm2 V-1 s-1. For BNC2-1, the hole mobility and electron mobility along both x and y directions can reach 105 orders of magnitude, which is similar to the carrier mobility of graphene. Besides, all studied BNCX monolayers obviously have anisotropic hole mobility and electron mobility. In particular, for semiconductor BNC4, its hole mobility along y direction and electron mobility along x direction unexpectedly reach 106 orders of magnitude, even higher than that of graphene. Our findings suggest that BNCX layered materials with proper ratio and arrangement of carbon atoms will possess desirable charge transport properties, exhibiting potential applications in nanoelectronic devices. © 2017 IOP Publishing Ltd.

The effects of pH, salt and bond stiffness on charged dendrimers

International Nuclear Information System (INIS)

Huissmann, Sebastian; Wynveen, Aaron; Likos, Christos N; Blaak, Ronald

2010-01-01

We have performed molecular dynamics simulations of charged dendrimers with various charge distributions, and including both rigid and soft bonds between the monomers. Whereas the rigid bonds result in a shell-like structure, the soft bonds lead to a larger dendrimer size and a more homogeneous monomer distribution. The measured density profiles of counter-ions and co-ions are compared with those stemming from Poisson-Boltzmann theory. The latter is in very good agreement with simulations for the soft-bond model, whereas for rigid bonds, significant discrepancies arise caused by the fact that Poisson-Boltzmann theory neglects finite-size ion effects. The addition of monovalent salt has no significant influence on the behavior of the dendrimers. (fast track communication)

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..

Dilaton gravity, Poisson sigma models and loop quantum gravity

International Nuclear Information System (INIS)

Bojowald, Martin; Reyes, Juan D

2009-01-01

Spherically symmetric gravity in Ashtekar variables coupled to Yang-Mills theory in two dimensions and its relation to dilaton gravity and Poisson sigma models are discussed. After introducing its loop quantization, quantum corrections for inverse triad components are shown to provide a consistent deformation without anomalies. The relation to Poisson sigma models provides a covariant action principle of the quantum-corrected theory with effective couplings. Results are also used to provide loop quantizations of spherically symmetric models in arbitrary D spacetime dimensions.

Dissipative Boltzmann-Robertson-Walker cosmologies

International Nuclear Information System (INIS)

Hiscock, W.A.; Salmonson, J.

1991-01-01

The equations governing a flat Robertson-Walker cosmological model containing a dissipative Boltzmann gas are integrated numerically. The bulk viscous stress is modeled using the Eckart and Israel-Stewart theories of dissipative relativistic fluids; the resulting cosmologies are compared and contrasted. The Eckart models are shown to always differ in a significant quantitative way from the Israel-Stewart models. It thus appears inappropriate to use the pathological (nonhyperbolic) Eckart theory for cosmological applications. For large bulk viscosities, both cosmological models approach asymptotic nonequilibrium states; in the Eckart model the total pressure is negative, while in the Israel-Stewart model the total pressure is asymptotically zero. The Eckart model also expands more rapidly than the Israel-Stewart models. These results suggest that ''bulk-viscous'' inflation may be an artifact of using a pathological fluid theory such as the Eckart theory

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.

Irreversible processes kinetic theory

CERN Document Server

Brush, Stephen G

2013-01-01

Kinetic Theory, Volume 2: Irreversible Processes deals with the kinetic theory of gases and the irreversible processes they undergo. It includes the two papers by James Clerk Maxwell and Ludwig Boltzmann in which the basic equations for transport processes in gases are formulated, together with the first derivation of Boltzmann's ""H-theorem"" and a discussion of this theorem, along with the problem of irreversibility.Comprised of 10 chapters, this volume begins with an introduction to the fundamental nature of heat and of gases, along with Boltzmann's work on the kinetic theory of gases and s

Alkaline earth lead and tin compounds Ae2Pb, Ae2Sn, Ae = Ca, Sr, Ba, as thermoelectric materials

Science.gov (United States)

Parker, David; Singh, David J

2013-01-01

We present a detailed theoretical study of three alkaline earth compounds Ca2Pb, Sr2Pb and Ba2Pb, which have undergone little previous study, calculating electronic band structures and Boltzmann transport and bulk moduli using density functional theory. We also study the corresponding tin compounds Ca2Sn, Sr2Sn and Ba2Sn. We find that these are all narrow band gap semiconductors with an electronic structure favorable for thermoelectric performance, with substantial thermopowers for the lead compounds at temperature ranges from 300 to 800 K. For the lead compounds, we further find very low calculated bulk moduli—roughly half of the values for the lead chalcogenides, suggestive of soft phonons and hence low lattice thermal conductivity. All these facts indicate that these materials merit experimental investigation as potential high performance thermoelectrics. We find good potential for thermoelectric performance in the environmentally friendly stannide materials, particularly at high temperature. PMID:27877610

Alkaline earth lead and tin compounds Ae2Pb, Ae2Sn, Ae = Ca, Sr, Ba, as thermoelectric materials

Directory of Open Access Journals (Sweden)

David Parker and David J Singh

2013-01-01

Full Text Available We present a detailed theoretical study of three alkaline earth compounds Ca2Pb, Sr2Pb and Ba2Pb, which have undergone little previous study, calculating electronic band structures and Boltzmann transport and bulk moduli using density functional theory. We also study the corresponding tin compounds Ca2Sn, Sr2Sn and Ba2Sn. We find that these are all narrow band gap semiconductors with an electronic structure favorable for thermoelectric performance, with substantial thermopowers for the lead compounds at temperature ranges from 300 to 800 K. For the lead compounds, we further find very low calculated bulk moduli—roughly half of the values for the lead chalcogenides, suggestive of soft phonons and hence low lattice thermal conductivity. All these facts indicate that these materials merit experimental investigation as potential high performance thermoelectrics. We find good potential for thermoelectric performance in the environmentally friendly stannide materials, particularly at high temperature.

Electron confinement in quantum nanostructures: Self-consistent Poisson-Schroedinger theory

International Nuclear Information System (INIS)

Luscombe, J.H.; Bouchard, A.M.; Luban, M.

1992-01-01

We compute the self-consistent electron states and confining potential, V(r,T), for laterally confined cylindrical quantum wires at a temperature T from a numerical solution of the coupled Poisson and Schroedinger (PS) equations. Finite-temperature effects are included in the electron density function, n(r,T), via the single-particle density matrix in the grand-canonical ensemble using the self-consistent bound states. We compare our results for a GaAs quantum wire with those obtained previously [J. H. Luscombe and M. Luban, Appl. Phys. Lett. 57, 61 (1990)] from a finite-temperature Thomas-Fermi (TF) approximation. We find that the TF results agree well with those of the more realistic, but also more computationally intensive PS theory, except for low temperatures or for cases where the quantum wire is almost, but not totally, depleted due to a combination of either small geometry, surface boundary conditions, or low doping concentrations. In the latter situations, the number of subbands that are populated is relatively small, and both n(r,T) and V(r,T) exhibit Friedel-type oscillations. Otherwise the TF theory, which is based on free-particle states, is remarkably accurate. We also present results for the partial electron density functions associated with the angular momentum quantum numbers, and discuss their role in populating the quantum wire

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...

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

MPBEC, a Matlab Program for Biomolecular Electrostatic Calculations.

Science.gov (United States)

Vergara-Perez, Sandra; Marucho, Marcelo

2016-01-01

One of the most used and efficient approaches to compute electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation. There are several software packages available that solve the PB equation for molecules in aqueous electrolyte solutions. Most of these software packages are useful for scientists with specialized training and expertise in computational biophysics. However, the user is usually required to manually take several important choices, depending on the complexity of the biological system, to successfully obtain the numerical solution of the PB equation. This may become an obstacle for researchers, experimentalists, even students with no special training in computational methodologies. Aiming to overcome this limitation, in this article we present MPBEC, a free, cross-platform, open-source software that provides non-experts in the field an easy and efficient way to perform biomolecular electrostatic calculations on single processor computers. MPBEC is a Matlab script based on the Adaptative Poisson Boltzmann Solver, one of the most popular approaches used to solve the PB equation. MPBEC does not require any user programming, text editing or extensive statistical skills, and comes with detailed user-guide documentation. As a unique feature, MPBEC includes a useful graphical user interface (GUI) application which helps and guides users to configure and setup the optimal parameters and approximations to successfully perform the required biomolecular electrostatic calculations. The GUI also incorporates visualization tools to facilitate users pre- and post- analysis of structural and electrical properties of biomolecules.

MPBEC, a Matlab Program for Biomolecular Electrostatic Calculations

Science.gov (United States)

Vergara-Perez, Sandra; Marucho, Marcelo

2016-01-01

One of the most used and efficient approaches to compute electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation. There are several software packages available that solve the PB equation for molecules in aqueous electrolyte solutions. Most of these software packages are useful for scientists with specialized training and expertise in computational biophysics. However, the user is usually required to manually take several important choices, depending on the complexity of the biological system, to successfully obtain the numerical solution of the PB equation. This may become an obstacle for researchers, experimentalists, even students with no special training in computational methodologies. Aiming to overcome this limitation, in this article we present MPBEC, a free, cross-platform, open-source software that provides non-experts in the field an easy and efficient way to perform biomolecular electrostatic calculations on single processor computers. MPBEC is a Matlab script based on the Adaptative Poisson-Boltzmann Solver, one of the most popular approaches used to solve the PB equation. MPBEC does not require any user programming, text editing or extensive statistical skills, and comes with detailed user-guide documentation. As a unique feature, MPBEC includes a useful graphical user interface (GUI) application which helps and guides users to configure and setup the optimal parameters and approximations to successfully perform the required biomolecular electrostatic calculations. The GUI also incorporates visualization tools to facilitate users pre- and post-analysis of structural and electrical properties of biomolecules.

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

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

Contributions to the spectral theory of the linear Boltzmann operator for various geometries

International Nuclear Information System (INIS)

Protopopescu, V.

1975-01-01

The linear monoenergetic Boltzmann operator with isotropic scattering is studied for various geometries and boundary conditions as the infinitesimal generator of a positivity preserving contractive semigroup in an appropriate Hilbert space. General results about the existence and the uniqueness of the solutions of the corresponding evolution problems are reviewed. The spectrum of the Boltzmann operator is analyzed for semi-infinite, slab and parallelepipedic geometries with vacuum, periodic, perfectly reflecting, generalized and diffusely reflecting boundary condition respectively. The main features of these spectra, their importance for determining the asymptotic evolution and possible generalizations to more realistic models are put together in a final section. (author)

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…

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.

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.

Complete synchronization of the global coupled dynamical network induced by Poisson noises.

Science.gov (United States)

Guo, Qing; Wan, Fangyi

2017-01-01

The different Poisson noise-induced complete synchronization of the global coupled dynamical network is investigated. Based on the stability theory of stochastic differential equations driven by Poisson process, we can prove that Poisson noises can induce synchronization and sufficient conditions are established to achieve complete synchronization with probability 1. Furthermore, numerical examples are provided to show the agreement between theoretical and numerical analysis.

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.

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.

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.

APBSmem: a graphical interface for electrostatic calculations at the membrane.

Directory of Open Access Journals (Sweden)

Keith M Callenberg

2010-09-01

Full Text Available Electrostatic forces are one of the primary determinants of molecular interactions. They help guide the folding of proteins, increase the binding of one protein to another and facilitate protein-DNA and protein-ligand binding. A popular method for computing the electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB equation, and there are several easy-to-use software packages available that solve the PB equation for soluble proteins. Here we present a freely available program, called APBSmem, for carrying out these calculations in the presence of a membrane. The Adaptive Poisson-Boltzmann Solver (APBS is used as a back-end for solving the PB equation, and a Java-based graphical user interface (GUI coordinates a set of routines that introduce the influence of the membrane, determine its placement relative to the protein, and set the membrane potential. The software Jmol is embedded in the GUI to visualize the protein inserted in the membrane before the calculation and the electrostatic potential after completing the computation. We expect that the ease with which the GUI allows one to carry out these calculations will make this software a useful resource for experimenters and computational researchers alike. Three examples of membrane protein electrostatic calculations are carried out to illustrate how to use APBSmem and to highlight the different quantities of interest that can be calculated.

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.

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.

Inverse problems with Poisson data: statistical regularization theory, applications and algorithms

International Nuclear Information System (INIS)

Hohage, Thorsten; Werner, Frank

2016-01-01

Inverse problems with Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. The design of regularization methods and estimators for such problems has been studied intensively over the last two decades. In this review we give an overview of statistical regularization theory for such problems, the most important applications, and the most widely used algorithms. The focus is on variational regularization methods in the form of penalized maximum likelihood estimators, which can be analyzed in a general setup. Complementing a number of recent convergence rate results we will establish consistency results. Moreover, we discuss estimators based on a wavelet-vaguelette decomposition of the (necessarily linear) forward operator. As most prominent applications we briefly introduce Positron emission tomography, inverse problems in fluorescence microscopy, and phase retrieval problems. The computation of a penalized maximum likelihood estimator involves the solution of a (typically convex) minimization problem. We also review several efficient algorithms which have been proposed for such problems over the last five years. (topical review)

Diverse carrier mobility of monolayer BNC x : a combined density functional theory and Boltzmann transport theory study.

Science.gov (United States)

Wu, Tao; Deng, Kaiming; Deng, Weiqiao; Lu, Ruifeng

2017-10-19

BNC x monolayer as a kind of two-dimensional material has numerous chemical atomic ratios and arrangements with different electronic structures. Via calculations on the basis of density functional theory and Boltzmann transport theory under deformation potential approximation, the band structures and carrier mobilities of BNC x (x  =  1,2,3,4) nanosheets are systematically investigated. The calculated results show that BNC 2 -1 is a material with very small band gap (0.02 eV) among all the structures while other BNC x monolayers are semiconductors with band gap ranging from 0.51 eV to 1.32 eV. The carrier mobility of BNC x varies considerably from tens to millions of cm 2 V -1 s -1 . For BNC 2 -1, the hole mobility and electron mobility along both x and y directions can reach 10 5 orders of magnitude, which is similar to the carrier mobility of graphene. Besides, all studied BNC x monolayers obviously have anisotropic hole mobility and electron mobility. In particular, for semiconductor BNC 4 , its hole mobility along the y direction and electron mobility along the x direction unexpectedly reach 10 6 orders of magnitude, even higher than that of graphene. Our findings suggest that BNC x layered materials with the proper ratio and arrangement of carbon atoms will possess desirable charge transport properties, exhibiting potential applications in nanoelectronic devices.

The polaron problem and the Boltzmann equation

International Nuclear Information System (INIS)

Devreese, J.

1979-01-01

A mobility theory for the Feynman polaron is developed. It is shown that the Boltzmann equation for polarons is valid for weak coupling and not too high electric fields. The analytical results indicate that for E → 0 the relaxation time approximation is valid. A comparison is made of three methods to calculate the mobility in a linear electron transport theory. An approximation to the Kubo formula, a mobility calculation using path integrals by Feynman and a calculation based on the displaced Maxwell distribution function are considered. The three methods lead to equivalent results in the weak scattering and small electric field limit

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)

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)

First principles density functional theory study of Pb doped α-MnO2 catalytic materials

Science.gov (United States)

Song, Zilin; Yan, Zhiguo; Yang, Xiaojun; Bai, Hang; Duan, Yuhua; Yang, Bin; Leng, Li

2018-03-01

The impact of Pb in the tunnels of manganese oxide octahedral molecular sieves on chemical state of Mn species and lattice oxygen were investigated utilizing density functional theory calculations. The results show that the Pb dopant in the tunnels of OMS-2 could reduce the average valence states of Mn. The lower energy required for bulk oxygen defects formation in Pb-OMS-2 validates the activation of lattice oxygen by inclusion of tunnel dopant. The inclusion of Pb promotes the catalytic oxidation activity of OMS-2 by reducing the energy required for the surface lattice oxygen migration during the Mars - van Krevelen oxidation process.

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

Development of a Generalized Version of the Poisson-Nernst-Planck Equations Using the Hybrid Mixture Theory: Presentation of 2D Numerical Examples

DEFF Research Database (Denmark)

Johannesson, Björn

2010-01-01

A numerical scheme for the transient solution of generalized version of the Poisson-Nernst-Planck equations is presented. The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present problem iteratively. The Poisson......-scale and that it includes the volume fractions of phases in its structure. The background to the Poisson-Nernst-Planck equations can by the HMT approach be described by using the postulates of mass conservation of constituents together with the Gauss’ law used together with consistent constitutive laws. The HMT theory......-Nernst-Planck equations represent a set of diffusion equations for charged species, i.e. dissolved ions. These equations are coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The Nernst-Planck equations describing the diffusion of the ionic species and the Gauss’ law in used are...

Modelling and nonlinear shock waves for binary gas mixtures by the discrete Boltzmann equation with multiple collisions

International Nuclear Information System (INIS)

Bianchi, M.P.

1991-01-01

The discrete Boltzmann equation is a mathematical model in the kinetic theory of gases which defines the time and space evolution of a system of gas particles with a finite number of selected velocities. Discrete kinetic theory is an interesting field of research in mathematical physics and applied mathematics for several reasons. One of the relevant fields of application of the discrete Boltzmann equation is the analysis of nonlinear shock wave phenomena. Here, a new multiple collision regular plane model for binary gas mixtures is proposed within the discrete theory of gases and applied to the analysis of the classical problems of shock wave propagation

Efficient information transfer by Poisson neurons

Czech Academy of Sciences Publication Activity Database

Košťál, Lubomír; Shinomoto, S.

2016-01-01

Roč. 13, č. 3 (2016), s. 509-520 ISSN 1547-1063 R&D Projects: GA ČR(CZ) GA15-08066S Institutional support: RVO:67985823 Keywords : information capacity * Poisson neuron * metabolic cost * decoding error Subject RIV: BD - Theory of Information Impact factor: 1.035, year: 2016

(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.

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

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.

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)

Quantization of Poisson Manifolds from the Integrability of the Modular Function

Science.gov (United States)

Bonechi, F.; Ciccoli, N.; Qiu, J.; Tarlini, M.

2014-10-01

We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on , seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU( n + 1). We show that a bihamiltonian system on defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras.

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...

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...

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.

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

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

Ostwald ripening of Pb nanocrystalline phase in mechanically milled Al-Pb alloys and the influence of Cu additive

International Nuclear Information System (INIS)

Wu, Z.F.; Zeng, M.Q.; Ouyang, L.Z.; Zhang, X.P.; Zhu, M.

2005-01-01

The coarsening behavior of nanosized Pb phase in both Al-10%Pb and Al-10%Pb-4.5%Cu alloys has been studied by X-ray diffraction and transmission electron microscopy analysis. The coarsening of Pb nanophase in Al-Pb alloys still follows the classical ripening theory (the LSW theory) and the addition of Cu decreases the coarsening rate of Pb nanophase

? filtering for stochastic systems driven by Poisson processes

Science.gov (United States)

Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya

2015-01-01

This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

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.

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.

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

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.

Null canonical formalism 1, Maxwell field. [Poisson brackets, boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Wodkiewicz, K [Warsaw Univ. (Poland). Inst. Fizyki Teoretycznej

1975-01-01

The purpose of this paper is to formulate the canonical formalism on null hypersurfaces for the Maxwell electrodynamics. The set of the Poisson brackets relations for null variables of the Maxwell field is obtained. The asymptotic properties of the theory are investigated. The Poisson bracket relations for the news-functions of the Maxwell field are computed. The Hamiltonian form of the asymptotic Maxwell equations in terms of these news-functions is obtained.

Independent production and Poisson distribution

International Nuclear Information System (INIS)

Golokhvastov, A.I.

1994-01-01

The well-known statement of factorization of inclusive cross-sections in case of independent production of particles (or clusters, jets etc.) and the conclusion of Poisson distribution over their multiplicity arising from it do not follow from the probability theory in any way. Using accurately the theorem of the product of independent probabilities, quite different equations are obtained and no consequences relative to multiplicity distributions are obtained. 11 refs

Boltzmann, Darwin and Directionality theory

Energy Technology Data Exchange (ETDEWEB)

Demetrius, Lloyd A., E-mail: ldemetr@oeb.harvard.edu

2013-09-01

Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and

Boltzmann, Darwin and Directionality theory

International Nuclear Information System (INIS)

Demetrius, Lloyd A.

2013-01-01

Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and

POISSON SUPERFISH, Poisson Equation Solver for Radio Frequency Cavity

International Nuclear Information System (INIS)

Colman, J.

2001-01-01

1 - Description of program or function: POISSON, SUPERFISH is a group of (1) codes that solve Poisson's equation and are used to compute field quality for both magnets and fixed electric potentials and (2) RF cavity codes that calculate resonant frequencies and field distributions of the fundamental and higher modes. The group includes: POISSON, PANDIRA, SUPERFISH, AUTOMESH, LATTICE, FORCE, MIRT, PAN-T, TEKPLOT, SF01, and SHY. POISSON solves Poisson's (or Laplace's) equation for the vector (scalar) potential with nonlinear isotropic iron (dielectric) and electric current (charge) distributions for two-dimensional Cartesian or three-dimensional cylindrical symmetry. It calculates the derivatives of the potential, the stored energy, and performs harmonic (multipole) analysis of the potential. PANDIRA is similar to POISSON except it allows anisotropic and permanent magnet materials and uses a different numerical method to obtain the potential. SUPERFISH solves for the accelerating (TM) and deflecting (TE) resonant frequencies and field distributions in an RF cavity with two-dimensional Cartesian or three-dimensional cylindrical symmetry. Only the azimuthally symmetric modes are found for cylindrically symmetric cavities. AUTOMESH prepares input for LATTICE from geometrical data describing the problem, (i.e., it constructs the 'logical' mesh and generates (x,y) coordinate data for straight lines, arcs of circles, and segments of hyperbolas). LATTICE generates an irregular triangular (physical) mesh from the input data, calculates the 'point current' terms at each mesh point in regions with distributed current density, and sets up the mesh point relaxation order needed to write the binary problem file for the equation-solving POISSON, PANDIRA, or SUPERFISH. FORCE calculates forces and torques on coils and iron regions from POISSON or PANDIRA solutions for the potential. MIRT optimizes magnet profiles, coil shapes, and current densities from POISSON output based on a

Boltzmann, Darwin and Directionality theory

Science.gov (United States)

Demetrius, Lloyd A.

2013-09-01

Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and

A Simple PB/LIE Free Energy Function Accurately Predicts the Peptide Binding Specificity of the Tiam1 PDZ Domain.

Science.gov (United States)

Panel, Nicolas; Sun, Young Joo; Fuentes, Ernesto J; Simonson, Thomas

2017-01-01

PDZ domains generally bind short amino acid sequences at the C-terminus of target proteins, and short peptides can be used as inhibitors or model ligands. Here, we used experimental binding assays and molecular dynamics simulations to characterize 51 complexes involving the Tiam1 PDZ domain and to test the performance of a semi-empirical free energy function. The free energy function combined a Poisson-Boltzmann (PB) continuum electrostatic term, a van der Waals interaction energy, and a surface area term. Each term was empirically weighted, giving a Linear Interaction Energy or "PB/LIE" free energy. The model yielded a mean unsigned deviation of 0.43 kcal/mol and a Pearson correlation of 0.64 between experimental and computed free energies, which was superior to a Null model that assumes all complexes have the same affinity. Analyses of the models support several experimental observations that indicate the orientation of the α 2 helix is a critical determinant for peptide specificity. The models were also used to predict binding free energies for nine new variants, corresponding to point mutants of the Syndecan1 and Caspr4 peptides. The predictions did not reveal improved binding; however, they suggest that an unnatural amino acid could be used to increase protease resistance and peptide lifetimes in vivo . The overall performance of the model should allow its use in the design of new PDZ ligands in the future.

A Simple PB/LIE Free Energy Function Accurately Predicts the Peptide Binding Specificity of the Tiam1 PDZ Domain

Directory of Open Access Journals (Sweden)

Nicolas Panel

2017-09-01

Full Text Available PDZ domains generally bind short amino acid sequences at the C-terminus of target proteins, and short peptides can be used as inhibitors or model ligands. Here, we used experimental binding assays and molecular dynamics simulations to characterize 51 complexes involving the Tiam1 PDZ domain and to test the performance of a semi-empirical free energy function. The free energy function combined a Poisson-Boltzmann (PB continuum electrostatic term, a van der Waals interaction energy, and a surface area term. Each term was empirically weighted, giving a Linear Interaction Energy or “PB/LIE” free energy. The model yielded a mean unsigned deviation of 0.43 kcal/mol and a Pearson correlation of 0.64 between experimental and computed free energies, which was superior to a Null model that assumes all complexes have the same affinity. Analyses of the models support several experimental observations that indicate the orientation of the α2 helix is a critical determinant for peptide specificity. The models were also used to predict binding free energies for nine new variants, corresponding to point mutants of the Syndecan1 and Caspr4 peptides. The predictions did not reveal improved binding; however, they suggest that an unnatural amino acid could be used to increase protease resistance and peptide lifetimes in vivo. The overall performance of the model should allow its use in the design of new PDZ ligands in the future.

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.

Comparison of Einstein-Boltzmann solvers for testing general relativity

Science.gov (United States)

Bellini, E.; Barreira, A.; Frusciante, N.; Hu, B.; Peirone, S.; Raveri, M.; Zumalacárregui, M.; Avilez-Lopez, A.; Ballardini, M.; Battye, R. A.; Bolliet, B.; Calabrese, E.; Dirian, Y.; Ferreira, P. G.; Finelli, F.; Huang, Z.; Ivanov, M. M.; Lesgourgues, J.; Li, B.; Lima, N. A.; Pace, F.; Paoletti, D.; Sawicki, I.; Silvestri, A.; Skordis, C.; Umiltà, C.; Vernizzi, F.

2018-01-01

We compare Einstein-Boltzmann solvers that include modifications to general relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f (R ) gravity, a code that models covariant Galileons, a code that models Hořava-Lifschitz gravity, and two codes that model nonlocal models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the subpercent level. This means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.

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.

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...

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.

Inelastic Quantum Transport in Superlattices: Success and Failure of the Boltzmann Equation

DEFF Research Database (Denmark)

Wacker, Andreas; Jauho, Antti-Pekka; Rott, Stephan

1999-01-01

the whole held range from linear response to negative differential conductivity. The quantum results are compared with the respective results obtained from a Monte Carlo solution of the Boltzmann equation. Our analysis thus sets the limits of validity for the semiclassical theory in a nonlinear transport...

Fiber-wise linear Poisson structures related to W∗-algebras

Science.gov (United States)

Odzijewicz, Anatol; Jakimowicz, Grzegorz; Sliżewska, Aneta

2018-01-01

In the framework of Banach differential geometry we investigate the fiber-wise linear Poisson structures as well as the Lie groupoid and Lie algebroid structures which are defined in the canonical way by the structure of a W∗-algebra (von Neumann algebra) M. The main role in this theory is played by the complex Banach-Lie groupoid G(M) ⇉ L(M) of partially invertible elements of M over the lattice L(M) of orthogonal projections of M. The Atiyah sequence and the predual Atiyah sequence corresponding to this groupoid are investigated from the point of view of Banach Poisson geometry. In particular we show that the predual Atiyah sequence fits in a short exact sequence of complex Banach sub-Poisson V B-groupoids with G(M) ⇉ L(M) as the side groupoid.

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.

A physiologically based nonhomogeneous Poisson counter model of visual identification

DEFF Research Database (Denmark)

Christensen, Jeppe H; Markussen, Bo; Bundesen, Claus

2018-01-01

A physiologically based nonhomogeneous Poisson counter model of visual identification is presented. The model was developed in the framework of a Theory of Visual Attention (Bundesen, 1990; Kyllingsbæk, Markussen, & Bundesen, 2012) and meant for modeling visual identification of objects that are ......A physiologically based nonhomogeneous Poisson counter model of visual identification is presented. The model was developed in the framework of a Theory of Visual Attention (Bundesen, 1990; Kyllingsbæk, Markussen, & Bundesen, 2012) and meant for modeling visual identification of objects...... that mimicked the dynamics of receptive field selectivity as found in neurophysiological studies. Furthermore, the initial sensory response yielded theoretical hazard rate functions that closely resembled empirically estimated ones. Finally, supplied with a Naka-Rushton type contrast gain control, the model...

Poisson structure of the equations of ideal multispecies fluid electrodynamics

International Nuclear Information System (INIS)

Spencer, R.G.

1984-01-01

The equations of the two- (or multi-) fluid model of plasma physics are recast in Hamiltonian form, following general methods of symplectic geometry. The dynamical variables are the fields of physical interest, but are noncanonical, so that the Poisson bracket in the theory is not the standard one. However, it is a skew-symmetric bilinear form which, from the method of derivation, automatically satisfies the Jacobi identity; therefore, this noncanonical structure has all the essential properties of a canonical Poisson bracket

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.

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

Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations.

Science.gov (United States)

Kilic, Mustafa Sabri; Bazant, Martin Z; Ajdari, Armand

2007-02-01

In situations involving large potentials or surface charges, the Poisson-Boltzman (PB) equation has shortcomings because it neglects ion-ion interactions and steric effects. This has been widely recognized by the electrochemistry community, leading to the development of various alternative models resulting in different sets "modified PB equations," which have had at least qualitative success in predicting equilibrium ion distributions. On the other hand, the literature is scarce in terms of descriptions of concentration dynamics in these regimes. Here, adapting strategies developed to modify the PB equation, we propose a simple modification of the widely used Poisson-Nernst-Planck (PNP) equations for ionic transport, which at least qualitatively accounts for steric effects. We analyze numerical solutions of these modified PNP equations on the model problem of the charging of a simple electrolyte cell, and compare the outcome to that of the standard PNP equations. Finally, we repeat the asymptotic analysis of Bazant, Thornton, and Ajdari [Phys. Rev. E 70, 021506 (2004)] for this new system of equations to further document the interest and limits of validity of the simpler equivalent electrical circuit models introduced in Part I [Kilic, Bazant, and Ajdari, Phys. Rev. E 75, 021502 (2007)] for such problems.

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

Novel diagrammatic method for computing transport coefficients - beyond the Boltzmann approximation

International Nuclear Information System (INIS)

Hidaka, Y.; Kunihiro, T.

2010-01-01

We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. Our method is based on a reformulation and extension of the diagrammatic method by Eliashberg given in the imaginary-time formalism to the relativistic quantum field theory in the real-time formalism, in which the cumbersome analytical continuation problem can be avoided. The transport coefficients are obtained from a two-point function via Kubo formula. It is know that naive perturbation theory breaks down owing to a so called pinch singularity, and hence a resummation is required for getting a finite and sensible result. As a novel resummation method, we first decompose the two point function into the singular part and the regular part, and then reconstruct the diagrams. We find that a self-consistent equation for the two-point function has the same structure as the linearized Boltzmann equation. It is known that the two-point function at the leading order is equivalent to the linearized Boltzmann equation. We find the higher order corrections are nicely summarized as a renormalization of the vertex function, spectral function, and collision term. We also discuss the critical behavior of the transport coefficients near a phase transition, applying our method. (author)

Celebrating Cercignani's conjecture for the Boltzmann equation

KAUST Repository

Villani, Cé dric; Mouhot, Clé ment; Desvillettes, Laurent

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.

Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions

KAUST Repository

Reis, Tim; Dellar, Paul J.

2012-01-01

lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier

Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

Directory of Open Access Journals (Sweden)

Diem Dang Huan

2015-12-01

Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

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

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

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

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...

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

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

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...

Natural Poisson structures of nonlinear plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1982-01-01

Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering. (Auth.)

Natural Poisson structures of nonlinear plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1982-06-01

Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering

An advanced kinetic theory for morphing continuum with inner structures

Science.gov (United States)

Chen, James

2017-12-01

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

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...

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.

Models, Their Application, and Scientific Anticipation: Ludwig Boltzmann's Work as Tacit Knowing

Science.gov (United States)

Schmitt, Richard Henry

2011-01-01

Ludwig Boltzmann's work in theoretical physics exhibits an approach to the construction of theory that he transmitted to the succeeding generation by example. It involved the construction of clear models, allowed more than one, and was not based solely on the existing facts, with the intent of examining and criticizing the assumptions that made…

Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation

OpenAIRE

Wu, Lei

2014-01-01

We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.

Boltzmann equation and hydrodynamics beyond Navier-Stokes.

Science.gov (United States)

Bobylev, A V

2018-04-28

We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

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.

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

A generalized Poisson solver for first-principles device simulations

Energy Technology Data Exchange (ETDEWEB)

Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost, E-mail: joost.vandevondele@mat.ethz.ch [Nanoscale Simulations, ETH Zürich, 8093 Zürich (Switzerland); Brück, Sascha; Luisier, Mathieu [Integrated Systems Laboratory, ETH Zürich, 8092 Zürich (Switzerland)

2016-01-28

Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.

Existence theory for a Poisson-Nernst-Planck model of electrophoresis

OpenAIRE

Bedin, Luciano; Thompson, Mark

2011-01-01

A system modeling the electrophoretic motion of a charged rigid macromolecule immersed in a incompressible ionized fluid is considered. The ionic concentration is governing by the Nernst-Planck equation coupled with the Poisson equation for the electrostatic potential, Navier-Stokes and Newtonian equations for the fluid and the macromolecule dynamics, respectively. A local in time existence result for suitable weak solutions is established, following the approach of Desjardins and Esteban [Co...

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)

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)

Dynamic state estimation based on Poisson spike trains—towards a theory of optimal encoding

International Nuclear Information System (INIS)

Susemihl, Alex; Opper, Manfred; Meir, Ron

2013-01-01

Neurons in the nervous system convey information to higher brain regions by the generation of spike trains. An important question in the field of computational neuroscience is how these sensory neurons encode environmental information in a way which may be simply analyzed by subsequent systems. Many aspects of the form and function of the nervous system have been understood using the concepts of optimal population coding. Most studies, however, have neglected the aspect of temporal coding. Here we address this shortcoming through a filtering theory of inhomogeneous Poisson processes. We derive exact relations for the minimal mean squared error of the optimal Bayesian filter and, by optimizing the encoder, obtain optimal codes for populations of neurons. We also show that a class of non-Markovian, smooth stimuli are amenable to the same treatment, and provide results for the filtering and prediction error which hold for a general class of stochastic processes. This sets a sound mathematical framework for a population coding theory that takes temporal aspects into account. It also formalizes a number of studies which discussed temporal aspects of coding using time-window paradigms, by stating them in terms of correlation times and firing rates. We propose that this kind of analysis allows for a systematic study of temporal coding and will bring further insights into the nature of the neural code. (paper)

Equal-Time and Equal-Space Poisson Brackets of the N -Component Coupled NLS Equation

International Nuclear Information System (INIS)

Zhou Ru-Guang; Li Pei-Yao; Gao Yuan

2017-01-01

Two Poisson brackets for the N-component coupled nonlinear Schrödinger (NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation. (paper)

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.

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.

Nonlinear poisson brackets geometry and quantization

CERN Document Server

Karasev, M V

2012-01-01

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.

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.

A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution.

Science.gov (United States)

Inouye, David; Yang, Eunho; Allen, Genevera; Ravikumar, Pradeep

2017-01-01

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section.

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

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

A temperature and mass dependence of the linear Boltzmann collision operator from group theory point of view

International Nuclear Information System (INIS)

Saveliev, V.

1996-01-01

The Lie group of the transformations affecting the parameters of the linear Boltzmann collision operator such as temperature of background gas and ratio of masses of colliding particles and molecules is discovered. The group also describes the conservation laws for collisions and main symmetries of the collision operator. New algebraic properties of the collision operator are derived. Transformations acting on the variables and parameters and leaving the linear Boltzmann kinetic equation invariant are found. For the constant collision frequency the integral representation of solutions for nonuniform case in terms of the distribution function of particles drifting in a gas with zero temperature is deduced. The new exact relaxation solutions are obtained too. copyright 1996 American Institute of Physics

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.

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

Classical r-matrices and Poisson bracket structures on infinite-dimensional groups

International Nuclear Information System (INIS)

Aratyn, H.; Nissimov, E.; Pacheva, S.

1992-01-01

Starting with a canonical symplectic structure defined on the contangent bundle T * G we derive, via Dirac hamiltonian reduction, Poisson brackets (PBs) on an arbitrary infinite-dimensional group G (admitting central extension). The PB structures are given in terms of an r-operator kernel related to the two-cocycle of the underlying Lie algebra and satisfying a differential classical Yang-Baxter equation. The explicit expressions of the PBs among the group variables for the (N, 0) for N=0, 1, ..., 4 (super-) Virasoro groups and the group of area-preserving diffeomorphisms on the torus are presented. (orig.)

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...

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

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.

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

Testing and application of the nuclear field theory: the nuclei 91Nb and 211Pb

International Nuclear Information System (INIS)

Liotta, R.J.; Silvestre-Brac, B.A.

1978-01-01

A method is presented for summing up the whole nuclear field theory series for the case of three particles outside a closed shell. The method is first illustrated within a simple model and then applied to the nucleus 91 Nb. In all the cases it is shown that the theory properly corrects the Pauli principle violations and the resulting overcompleteness of the basis. Finally, the application of the method in the analysis of the spectrum of 211 Pb gives a reasonable account of the experimental features. This last application also shows that the first-order perturbation method is in good agreement with the full application of the theory. (Auth.)

Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems

Directory of Open Access Journals (Sweden)

Florian Thüroff

2014-11-01

Full Text Available Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system’s dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system’s ordered state nematic, despite purely polar interactions on the level of single particles.

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.

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

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

Electronic and thermoelectric properties of InN studied using ab initio density functional theory and Boltzmann transport calculations

Energy Technology Data Exchange (ETDEWEB)

Borges, P. D., E-mail: pdborges@gmail.com, E-mail: lscolfaro@txstate.edu; Scolfaro, L., E-mail: pdborges@gmail.com, E-mail: lscolfaro@txstate.edu [Department of Physics, Texas State University, San Marcos, Texas 78666 (United States)

2014-12-14

The thermoelectric properties of indium nitride in the most stable wurtzite phase (w-InN) as a function of electron and hole concentrations and temperature were studied by solving the semiclassical Boltzmann transport equations in conjunction with ab initio electronic structure calculations, within Density Functional Theory. Based on maximally localized Wannier function basis set and the ab initio band energies, results for the Seebeck coefficient are presented and compared with available experimental data for n-type as well as p-type systems. Also, theoretical results for electric conductivity and power factor are presented. Most cases showed good agreement between the calculated properties and experimental data for w-InN unintentionally and p-type doped with magnesium. Our predictions for temperature and concentration dependences of electrical conductivity and power factor revealed a promising use of InN for intermediate and high temperature thermoelectric applications. The rigid band approach and constant scattering time approximation were utilized in the calculations.

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.

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 ...

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.

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

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.

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.

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

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.)

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.

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...

A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins

Science.gov (United States)

Xu, Jingjie; Lu, Benzhuo

2018-01-01

Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson–Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the z-axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations. PMID:29495644

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.

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

The Lattice Boltzmann method principles and practice

CERN Document Server

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

2017-01-01

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

Moments analysis of concurrent Poisson processes

International Nuclear Information System (INIS)

McBeth, G.W.; Cross, P.

1975-01-01

A moments analysis of concurrent Poisson processes has been carried out. Equations are given which relate combinations of distribution moments to sums of products involving the number of counts associated with the processes and the mean rate of the processes. Elimination of background is discussed and equations suitable for processing random radiation, parent-daughter pairs in the presence of background, and triple and double correlations in the presence of background are given. The theory of identification of the four principle radioactive series by moments analysis is discussed. (Auth.)

Developments in perturbation theory

International Nuclear Information System (INIS)

Greenspan, E.

1976-01-01

Included are sections dealing with perturbation expressions for reactivity, methods for the calculation of perturbed fluxes, integral transport theory formulations for reactivity, generalized perturbation theory, sensitivity and optimization studies, multigroup calculations of bilinear functionals, and solution of inhomogeneous Boltzmann equations with singular operators

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

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)

Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy.

Science.gov (United States)

Ansumali, S; Karlin, I V; Arcidiacono, S; Abbas, A; Prasianakis, N I

2007-03-23

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.

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.

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

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.

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.

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.

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.

Kinetic theory of Jean instability in Eddington-inspired Born-Infeld gravity

Energy Technology Data Exchange (ETDEWEB)

Martino, Ivan de [University of the Basque Country UPV/EHU, Department of Theoretical Physics and History of Science, Faculty of Science and Technology, Leioa (Spain); Capolupo, Antonio [Universita di Salerno, Dipartimento di Fisica E.R. Caianiello, Fisciano (Italy); INFN Gruppo Collegato di Salerno, Fisciano (Italy)

2017-10-15

We analyze the stability of self-gravitating systems which dynamics is investigated using the collisionless Boltzmann equation, and the modified Poisson equation of Eddington-inspired Born-Infield gravity. These equations provide a description of the Jeans paradigm used to determine the critical scale above which such systems collapse. At equilibrium, the systems are described using the time-independent Maxwell-Boltzmann distribution function f{sub 0}(v). Considering small perturbations to this equilibrium state, we obtain a modified dispersion relation, and we find a new characteristic scale length. Our results indicate that the dynamics of self-gravitating astrophysical systems can be fully addressed in the Eddington-inspired Born-Infeld gravity. The latter modifies the Jeans instability in high densities environments, while its effects become negligible in star formation regions. (orig.)

Lattice Boltzmann model for numerical relativity.

Science.gov (United States)

Ilseven, E; Mendoza, M

2016-02-01

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

Superdeformation in Pb isotopes

International Nuclear Information System (INIS)

Naz, Tabassum; Ahmad, Shakeb

2017-01-01

The Relatvistic Hartree-Bogoliubov (RHB) theory is used to explore the structure of superdeformed (SD) 190,212 Pb isotopes using the non-linear NL3* and density dependent (DD-ME2, DD-PC1) interactions. We have studied the the excitation energy, the potential depth and the deformation of these Pb isotopes

Coagulation kinetics beyond mean field theory using an optimised Poisson representation

Energy Technology Data Exchange (ETDEWEB)

Burnett, James [Department of Mathematics, UCL, Gower Street, London WC1E 6BT (United Kingdom); Ford, Ian J. [Department of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT (United Kingdom)

2015-05-21

Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable “gauge” transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.

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)

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

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.)

Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras

Directory of Open Access Journals (Sweden)

Lothar Schlafer

2008-05-01

Full Text Available C*-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is found in the construction of Poisson algebras and non-commutative twisted Banach-*-algebras on the stage of measures on the not locally compact test function space. Already within this frame strict deformation quantization is obtained, but in terms of Banach-*-algebras instead of C*-algebras. Fourier transformation and representation theory of the measure Banach-*-algebras are combined with the theory of continuous projective group representations to arrive at the genuine C*-algebraic strict deformation quantization in the sense of Rieffel and Landsman. Weyl quantization is recognized to depend in the first step functorially on the (in general infinite dimensional, pre-symplectic test function space; but in the second step one has to select a family of representations, indexed by the deformation parameter h. The latter ambiguity is in the present investigation connected with the choice of a folium of states, a structure, which does not necessarily require a Hilbert space representation.

Cellular solutions for the Poisson equation in extended systems

International Nuclear Information System (INIS)

Zhang, X.; Butler, W.H.; MacLaren, J.M.; van Ek, J.

1994-01-01

The Poisson equation for the electrostatic potential in a solid is solved using three different cellular techniques. The relative merits of these different approaches are discussed for two test charge densities for which an analytic solution to the Poisson equation is known. The first approach uses full-cell multiple-scattering theory and results in the famililar structure constant and multipole moment expansion. This solution is shown to be valid everywhere inside the cell, although for points outside the muffin-tin sphere but inside the cell the sums must be performed in the correct order to yield meaningful results. A modification of the multiple-scattering-theory approach yields a second method, a Green-function cellular method, which only requires the solution of a nearest-neighbor linear system of equations. A third approach, a related variational cellular method, is also derived. The variational cellular approach is shown to be the most accurate and reliable, and to have the best convergence in angular momentum of the three methods. Coulomb energies accurate to within 10 -6 hartree are easily achieved with the variational cellular approach, demonstrating the practicality of the approach in electronic structure calculations

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.

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)

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.

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.

A theory for viral capsid assembly around electrostatic cores

Science.gov (United States)

Hagan, Michael F.

2009-03-01

We develop equilibrium and kinetic theories that describe the assembly of viral capsid proteins on a charged central core, as seen in recent experiments in which brome mosaic virus capsids assemble around nanoparticles functionalized with polyelectrolyte. We model interactions between capsid proteins and nanoparticle surfaces as the interaction of polyelectrolyte brushes with opposite charge using the nonlinear Poisson Boltzmann equation. The models predict that there is a threshold density of functionalized charge, above which capsids efficiently assemble around nanoparticles, and that light scatter intensity increases rapidly at early times without the lag phase characteristic of empty capsid assembly. These predictions are consistent with and enable interpretation of preliminary experimental data. However, the models predict a stronger dependence of nanoparticle incorporation efficiency on functionalized charge density than measured in experiments and do not completely capture a logarithmic growth phase seen in experimental light scatter. These discrepancies may suggest the presence of metastable disordered states in the experimental system. In addition to discussing future experiments for nanoparticle-capsid systems, we discuss broader implications for understanding assembly around charged cores such as nucleic acids.

Dirichlet forms methods for Poisson point measures and Lévy processes with emphasis on the creation-annihilation techniques

CERN Document Server

Bouleau, Nicolas

2015-01-01

A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the “lent particle method” it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: it consists in adding a particle and then removing it after computing the gradient. Using this method, one can establish absolute continuity of Poisson functionals such as Lévy areas, solutions of SDEs driven by Poisson measure and, by iteration, obtain regularity of laws. The authors also give applications to error calcul...

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.

High-spin states in the 192Pb and 193Pb isotopes

International Nuclear Information System (INIS)

Lagrange, J.M.; Pautrat, M.

1991-01-01

The 193 Pb and 192 Pb isotopes are produced through the 182 W( 16 O, 5n, 6n) reactions. The de-excitation γ-ray and conversion electron spectra lead to the conversion coefficients for most transitions. With the results of the γ-γ and e - -γ coincidences, the half-lives measured for several states, the angular distribution coefficients for the odd isotope and the transition multipolarities, the data on the 192 Pb level scheme has been much enhanced and the 193 Pb one studied for the first time. The experimental schemes are compared to those given by microscopic calculations, in a two or three quasi-particle approximation using a surface delta interaction with a reduced pairing component. The discrepancies between theory and experiment are attributed to the increasing influence of proton configurations

Reliability Analysis of a Cold Standby System with Imperfect Repair and under Poisson Shocks

Directory of Open Access Journals (Sweden)

Yutian Chen

2014-01-01

Full Text Available This paper considers the reliability analysis of a two-component cold standby system with a repairman who may have vacation. The system may fail due to intrinsic factors like aging or deteriorating, or external factors such as Poisson shocks. The arrival time of the shocks follows a Poisson process with the intensity λ>0. Whenever the magnitude of a shock is larger than the prespecified threshold of the operating component, the operating component will fail. The paper assumes that the intrinsic lifetime and the repair time on the component are an extended Poisson process, the magnitude of the shock and the threshold of the operating component are nonnegative random variables, and the vacation time of the repairman obeys the general continuous probability distribution. By using the vector Markov process theory, the supplementary variable method, Laplace transform, and Tauberian theory, the paper derives a number of reliability indices: system availability, system reliability, the rate of occurrence of the system failure, and the mean time to the first failure of the system. Finally, a numerical example is given to validate the derived indices.

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

Poisson structure of dynamical systems with three degrees of freedom

Science.gov (United States)

Gümral, Hasan; Nutku, Yavuz

1993-12-01

It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one-form in three dimensions. Advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability. Techniques for finding Poisson structures are presented and applied to various examples such as the Halphen system which has been studied as the two-monopole problem by Atiyah and Hitchin. It is shown that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a nontrivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of three-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the SL(2,R) structure is a quadratic unfolding of an integrable one-form in 3+1 dimensions. It is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of Poisson structure and some new techniques for incorporating arbitrary constants into the Poisson one-form are presented herein. This leads to some extensions, analogous to q extensions, of Poisson structure. The Kermack-McKendrick model and some of its generalizations describing the spread of epidemics, as well as the integrable cases of the Lorenz, Lotka-Volterra, May-Leonard, and Maxwell-Bloch systems admit globally integrable bi-Hamiltonian structure.

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.

Planar screening by charge polydisperse counterions

Science.gov (United States)

Trulsson, M.; Trizac, E.; Šamaj, L.

2018-01-01

We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane (plate), when the counterions are characterised by a distribution of charges (or valence), n(q) . We work out analytically the one-plate and two-plate cases, at the level of non-linear Poisson-Boltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full Poisson-Boltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions n(q) , for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous n(q) behaviour are already featured by discrete mixtures with a relatively small number of constituents.

W and Z bosons in pp, pPb and PbPb with CMS

CERN Document Server

AUTHOR|(CDS)2079475

2016-01-01

Electroweak boson production is an important benchmark process in high-energy heavy-ion collisions at the LHC. W and Z bosons do not participate in the strong interaction and their leptonic decays provide medium-blind probes of the initial state of the collisions. The final results on the W and Z production in pPb collisions at 5.02 TeV, combining both the muon and electron channels, will be presented. When compared to theory calculations that include nuclear modifications to the parton distributions, data show a clear sensitivity to this type of effects. The final results in PbPb collisions at 2.76 TeV, compared to pp collisions at the same center of mass energy, will also be presented. The centrality dependence confirms the binary scaling of hard probes in heavy-ion collisions, while the differential cross sections points to initial state effects small compared to the statistical precision of the available data.

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

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.

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)

Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks

Science.gov (United States)

Frahm, Klaus M.; Shepelyansky, Dima L.

2014-04-01

We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.

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...

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

Ion distributions, exclusion coefficients, and separation factors of electrolytes in a charged cylindrical nanopore: a partially perturbative density functional theory study.

Science.gov (United States)

Peng, Bo; Yu, Yang-Xin

2009-10-07

The structural and thermodynamic properties for charge symmetric and asymmetric electrolytes as well as mixed electrolyte system inside a charged cylindrical nanopore are investigated using a partially perturbative density functional theory. The electrolytes are treated in the restricted primitive model and the internal surface of the cylindrical nanopore is considered to have a uniform charge density. The proposed theory is directly applicable to the arbitrary mixed electrolyte solution containing ions with the equal diameter and different valences. Large amount of simulation data for ion density distributions, separation factors, and exclusion coefficients are used to determine the range of validity of the partially perturbative density functional theory for monovalent and multivalent counterion systems. The proposed theory is found to be in good agreement with the simulations for both mono- and multivalent counterion systems. In contrast, the classical Poisson-Boltzmann equation only provides reasonable descriptions of monovalent counterion system at low bulk density, and is qualitatively and quantitatively wrong in the prediction for the multivalent counterion systems due to its neglect of the strong interionic correlations in these systems. The proposed density functional theory has also been applied to an electrolyte absorbed into a pore that is a model of the filter of a physiological calcium channel.

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.

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.

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.

Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework

KAUST Repository

Neumann, Philipp

2012-01-01

We present simulation results of flows in the finite Knudsen range, which is in the slip and transition flow regime. Our implementations are based on the Lattice Boltzmann method and are accomplished within the Peano framework. We validate our code by solving two- and three-dimensional channel flow problems and compare our results with respective experiments from other research groups. We further apply our Lattice Boltzmann solver to the geometrical setup of a microreactor consisting of differently sized channels and a reactor chamber. Here, we apply static adaptive grids to fur-ther reduce computational costs. We further investigate the influence of using a simple BGK collision kernel in coarse grid regions which are further away from the slip boundaries. Our results are in good agreement with theory and non-adaptive simulations, demonstrating the validity and the capabilities of our adaptive simulation software for flow problems at finite Knudsen numbers.

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

Lectures on gas theory

CERN Document Server

Boltzmann, Ludwig

2011-01-01

One of the great masterpieces of theoretical physics, this classic work contains a comprehensive exposition of the kinetic theory of gases that is still relevant today, nearly 100 years after its first publication. Although the modifications of quantum mechanics have rendered some parts of the work obsolete, many of the topics dealt with still yield to the classical-mechanics approach outlined by Boltzmann; moreover, a variety of problems in aerodynamics, nuclear reactors, and thermonuclear power generation are best solved by Boltzmann's famous transport equation.The work is divided into two

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

Local order and concentration fluctuations in K-Pb and Rb-Pb alloys

International Nuclear Information System (INIS)

Akinlade, O.

1992-08-01

The concentration fluctuations in the long wavelength limit S cc (0), short range order parameter and free energy of mixing of K-Pb and Rb-Pb alloys have been studied within the framework of the quasi-chemical theory. It is observed that the simple model could be used to shed more insight into the nature of chemical ordering that exists in such strongly compound forming binary alloys. (author). 19 refs, 6 figs, 1 tab

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.

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.

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.

W and Z bosons with CMS in pp, pPb and PbPb collisions

Energy Technology Data Exchange (ETDEWEB)

Chapon, Émilien, E-mail: emilien.chapon@cern.ch

2016-12-15

Electroweak boson production is an important benchmark process in high-energy heavy-ion collisions at the LHC. W and Z bosons do not participate in the strong interaction and their leptonic decays provide medium-blind probes of the initial state of the collisions. The final results on the W and Z production in pPb collisions at 5.02 TeV, combining both the muon and electron channels, will be presented. When compared to theory calculations that include nuclear modifications to the parton distributions, data show a clear sensitivity to this type of effects. The final results in PbPb collisions at 2.76 TeV, compared to pp collisions at the same centre of mass energy, will also be presented. The centrality dependence confirms the binary scaling of hard probes in heavy-ion collisions, while the differential cross sections points to initial state effects small compared to the statistical precision of the available data.

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.

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.

All orders Boltzmann collision term from the multiple scattering expansion of the self-energy

International Nuclear Information System (INIS)

Fillion-Gourdeau, F.; Gagnon, J.-S.; Jeon, S.

2007-01-01

We summarize our main findings in deriving the Boltzmann collision term from the Kadanoff-Baym relativistic transport equation and the multiple scattering expansion of the self-energy within a quasi-particle approximation. Our collision term is valid to all orders in perturbation theory and contains processes with any number of participating particles. This work completes a program initiated by Carrington and Mrowczynski and developed further by present authors and Weinstock in recent literature

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

Anomalous X-ray diffraction from self-assembled PbSe/PbEuTe quantum dots

International Nuclear Information System (INIS)

Holy, V.; Schuelli, T.U.; Lechner, R.T.; Springholz, G.; Bauer, G.

2005-01-01

Anomalous X-ray scattering from self-assembled PbSe quantum dots embedded in Pb 1-x Eu x Te was used for the study of their structure. The measured reciprocal-space distributions of diffracted intensity were compared with simulations based on kinematical scattering theory and continuum elasticity. From the comparison, the mean chemical composition of the dots and their aspect ratio (height/width) were estimated

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

Boltzmann babies in the proper time measure

Energy Technology Data Exchange (ETDEWEB)

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

2007-12-20

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

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.

Maslov indices, Poisson brackets, and singular differential forms

Science.gov (United States)

Esterlis, I.; Haggard, H. M.; Hedeman, A.; Littlejohn, R. G.

2014-06-01

Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the 6j-symbol, which is important in angular-momentum theory and in quantum gravity.

Experimental test of proximity effect theories by surface impedance measurements on the Pb-Sn system

International Nuclear Information System (INIS)

Hook, J.R.; Battilana, J.A.

1976-01-01

The proximity effect in the Pb-Sn system in zero magnetic field has been studied by measuring the surface impedance at 3 GHz of a thin film of tin evaporated on to a bulk lead substrate. The results are compared with the predictions of theories of the proximity effect. It is found that good agreement can be obtained by using a theory due to Hook and Waldram of the spatial variation of the superconducting order parameter Δ inside each metal together with suitable boundary conditions on Δ at the interface between the metals. The required boundary conditions are a generalization to the case of non-zero electron reflection at the interface of the boundary conditions given by Zaitsev for the Ginsburg-Landau equation. (author)

Essentially Entropic Lattice Boltzmann Model

Science.gov (United States)

Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh

2017-12-01

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.

Solution of spatially homogeneous model Boltzmann equations by means of Lie groups of transformations

International Nuclear Information System (INIS)

Foroutan, A.

1992-05-01

The essential mathematical challenge in transport theory is based on the nonlinearity of the integro-differential equations governing classical thermodynamic systems on molecular kinetic level. It is the aim of this thesis to gain exact analytical solutions to the model Boltzmann equation suggested by Tjon and Wu. Such solutions afford a deeper insight into the dynamics of rarefied gases. Tjon and Wu have provided a stochastic model of a Boltzmann equation. Its transition probability depends only on the relative speed of the colliding particles. This assumption leads in the case of two translational degrees of freedom to an integro-differential equation of convolution type. According to this convolution structure the integro-differential equation is Laplace transformed. The result is a nonlinear partial differential equation. The investigation of the symmetries of this differential equation by means of Lie groups of transformation enables us to transform the originally nonlinear partial differential equation into ordinary differential equation into ordinary differential equations of Bernoulli type. (author)

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.

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 ...

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.

Information content of poisson images

International Nuclear Information System (INIS)

Cederlund, J.

1979-04-01

One major problem when producing images with the aid of Poisson distributed quanta is how best to compromise between spatial and contrast resolution. Increasing the number of image elements improves spatial resolution, but at the cost of fewer quanta per image element, which reduces contrast resolution. Information theory arguments are used to analyse this problem. It is argued that information capacity is a useful concept to describe an important property of the imaging device, but that in order to compute the information content of an image produced by this device some statistical properties (such as the a priori probability of the densities) of the object to be depicted must be taken into account. If these statistical properties are not known one cannot make a correct choice between spatial and contrast resolution. (author)

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.

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.

Poisson-Fermi modeling of ion activities in aqueous single and mixed electrolyte solutions at variable temperature

Science.gov (United States)

Liu, Jinn-Liang; Eisenberg, Bob

2018-02-01

The combinatorial explosion of empirical parameters in tens of thousands presents a tremendous challenge for extended Debye-Hückel models to calculate activity coefficients of aqueous mixtures of the most important salts in chemistry. The explosion of parameters originates from the phenomenological extension of the Debye-Hückel theory that does not take steric and correlation effects of ions and water into account. By contrast, the Poisson-Fermi theory developed in recent years treats ions and water molecules as nonuniform hard spheres of any size with interstitial voids and includes ion-water and ion-ion correlations. We present a Poisson-Fermi model and numerical methods for calculating the individual or mean activity coefficient of electrolyte solutions with any arbitrary number of ionic species in a large range of salt concentrations and temperatures. For each activity-concentration curve, we show that the Poisson-Fermi model requires only three unchanging parameters at most to well fit the corresponding experimental data. The three parameters are associated with the Born radius of the solvation energy of an ion in electrolyte solution that changes with salt concentrations in a highly nonlinear manner.

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.

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.

Theory of conductivity of chiral particles

International Nuclear Information System (INIS)

Kailasvuori, Janik; Šopík, Břetislav; Trushin, Maxim

2013-01-01

In this methodology focused paper we scrutinize the application of the band-coherent Boltzmann equation approach to calculating the conductivity of chiral particles. As the ideal testing ground we use the two-band kinetic Hamiltonian with an N-fold chiral twist that arises in a low-energy description of charge carriers in rhombohedrally stacked multilayer graphene. To understand the role of chirality in the conductivity of such particles we also consider the artificial model with the chiral winding number decoupled from the power of the dispersion. We first utilize the approximate but analytically solvable band-coherent Boltzmann approach including the ill-understood principal value terms that are a byproduct of several quantum many-body theory derivations of Boltzmann collision integrals. Further on, we employ the finite-size Kubo formula with the exact diagonalization of the total Hamiltonian perturbed by disorder. Finally, we compare several choices of Ansatz in the derivation of the Boltzmann equation according to the qualitative agreement between the Boltzmann and Kubo conductivities. We find that the best agreement can be reached in the approach where the principal value terms in the collision integral are absent. (paper)

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.

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.

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

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.

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

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.

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.

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 ...

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

Charged-particle calculations using Boltzmann transport methods

International Nuclear Information System (INIS)

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

1981-01-01

Several aspects of radiation damage effects in fusion reactor neutron and ion irradiation environments are amenable to treatment by transport theory methods. In this paper, multigroup transport techniques are developed for the calculation of charged particle range distributions, reflection coefficients, and sputtering yields. The Boltzmann transport approach can be implemented, with minor changes, in standard neutral particle computer codes. With the multigroup discrete ordinates code, ANISN, determination of ion and target atom distributions as functions of position, energy, and direction can be obtained without the stochastic error associated with atomistic computer codes such as MARLOWE and TRIM. With the multigroup Monte Carlo code, MORSE, charged particle effects can be obtained for problems associated with very complex geometries. Results are presented for several charged particle problems. Good agreement is obtained between quantities calculated with the multigroup approach and those obtained experimentally or by atomistic computer codes

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.

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.

Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions

KAUST Repository

Reis, Tim

2012-01-01

We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity the pressure relative to asymptotic solutions of the compressible Navier-Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier-Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself. © 2012 American Institute of Physics.

X-ray spectroscopic study of amorphous and polycrystalline PbO films, α-PbO, and β-PbO for direct conversion imaging.

Science.gov (United States)

Qamar, A; LeBlanc, K; Semeniuk, O; Reznik, A; Lin, J; Pan, Y; Moewes, A

2017-10-13

We investigated the electronic structure of Lead Oxide (PbO) - one of the most promising photoconductor materials for direct conversion x-ray imaging detectors, using soft x-ray emission and absorption spectroscopy. Two structural configurations of thin PbO layers, namely the polycrystalline and the amorphous phase, were studied, and compared to the properties of powdered α-PbO and β-PbO samples. In addition, we performed calculations within the framework of density functional theory and found an excellent agreement between the calculated and the measured absorption and emission spectra, which indicates high accuracy of our structural models. Our work provides strong evidence that the electronic structure of PbO layers, specifically the width of the band gap and the presence of additional interband and intraband states in both conduction and valence band, depend on the deposition conditions. We tested several model structures using DFT simulations to understand what the origin of these states is. The presence of O vacancies is the most plausible explanation for these additional electronic states. Several other plausible models were ruled out including interstitial O, dislocated O and the presence of significant lattice stress in PbO.

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.

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

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

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.

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.

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.

A physiologically based nonhomogeneous Poisson counter model of visual identification.

Science.gov (United States)

Christensen, Jeppe H; Markussen, Bo; Bundesen, Claus; Kyllingsbæk, Søren

2018-04-30

A physiologically based nonhomogeneous Poisson counter model of visual identification is presented. The model was developed in the framework of a Theory of Visual Attention (Bundesen, 1990; Kyllingsbæk, Markussen, & Bundesen, 2012) and meant for modeling visual identification of objects that are mutually confusable and hard to see. The model assumes that the visual system's initial sensory response consists in tentative visual categorizations, which are accumulated by leaky integration of both transient and sustained components comparable with those found in spike density patterns of early sensory neurons. The sensory response (tentative categorizations) feeds independent Poisson counters, each of which accumulates tentative object categorizations of a particular type to guide overt identification performance. We tested the model's ability to predict the effect of stimulus duration on observed distributions of responses in a nonspeeded (pure accuracy) identification task with eight response alternatives. The time courses of correct and erroneous categorizations were well accounted for when the event-rates of competing Poisson counters were allowed to vary independently over time in a way that mimicked the dynamics of receptive field selectivity as found in neurophysiological studies. Furthermore, the initial sensory response yielded theoretical hazard rate functions that closely resembled empirically estimated ones. Finally, supplied with a Naka-Rushton type contrast gain control, the model provided an explanation for Bloch's law. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

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.

Propriedades eletrônicas e estruturais do PbTiO3: teoria do funcional de densidade aplicada a modelos periódicos Structural and electronic properties of PbTio3: density functional theory applied to periodic models

Directory of Open Access Journals (Sweden)

Sérgio Ricardo de Lázaro

2005-02-01

Full Text Available Calculations based on density functional theory at the B3LYP hybrid functional level applied to periodic models have been performed to characterize the structural and electronic properties of PbTiO3. Two different slab terminations (PbO and TiO2 have been considered to obtain and discuss the results of band structure, density of states, charge distribution on bulk and surface relaxation. It is observed that the relaxation processes are most prominent for the Ti and Pb surface atoms. The electron density maps confirm the partial covalent character of the Ti-O bonds. The calculated optical band gap and other results are in agreement with experimental data.

Ray-theory approach to electrical-double-layer interactions.

Science.gov (United States)

Schnitzer, Ory

2015-02-01

A novel approach is presented for analyzing the double-layer interaction force between charged particles in electrolyte solution, in the limit where the Debye length is small compared with both interparticle separation and particle size. The method, developed here for two planar convex particles of otherwise arbitrary geometry, yields a simple asymptotic approximation limited to neither small zeta potentials nor the "close-proximity" assumption underlying Derjaguin's approximation. Starting from the nonlinear Poisson-Boltzmann formulation, boundary-layer solutions describing the thin diffuse-charge layers are asymptotically matched to a WKBJ expansion valid in the bulk, where the potential is exponentially small. The latter expansion describes the bulk potential as superposed contributions conveyed by "rays" emanating normally from the boundary layers. On a special curve generated by the centers of all circles maximally inscribed between the two particles, the bulk stress-associated with the ray contributions interacting nonlinearly-decays exponentially with distance from the center of the smallest of these circles. The force is then obtained by integrating the traction along this curve using Laplace's method. We illustrate the usefulness of our theory by comparing it, alongside Derjaguin's approximation, with numerical simulations in the case of two parallel cylinders at low potentials. By combining our result and Derjaguin's approximation, the interaction force is provided at arbitrary interparticle separations. Our theory can be generalized to arbitrary three-dimensional geometries, nonideal electrolyte models, and other physical scenarios where exponentially decaying fields give rise to forces.

Multiple-relaxation-time lattice Boltzmann model for compressible fluids

International Nuclear Information System (INIS)

Chen Feng; Xu Aiguo; Zhang Guangcai; Li Yingjun

2011-01-01

We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. The collision step is first calculated in the moment space and then mapped back to the velocity space. The moment space and corresponding transformation matrix are constructed according to the group representation theory. Equilibria of the nonconserved moments are chosen according to the need of recovering compressible Navier-Stokes equations through the Chapman-Enskog expansion. Numerical experiments showed that compressible flows with strong shocks can be well simulated by the present model. The new model works for both low and high speeds compressible flows. It contains more physical information and has better numerical stability and accuracy than its single-relaxation-time version. - Highlights: → We present an energy-conserving MRT finite-difference LB model. → The moment space is constructed according to the group representation theory. → The new model works for both low and high speeds compressible flows. → It has better numerical stability and wider applicable range than its SRT version.

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.

Infrared and dc conductivity in metals with strong scattering: Nonclassical behavior from a generalized Boltzmann equation containing band-mixing effects

International Nuclear Information System (INIS)

Allen, P.B.; Chakraborty, B.

1981-01-01

Metals with high resistivity (approx.100 μΩ cm) seem to show weaker variation of resistivity (as a function of temperature and perhaps also static disorder) than predicted by semiclassical (Bloch-Boltzmann) theory (SBT). We argue that the effect is not closely related to Anderson localization, and therefore does not necessarily signify a failure of the independent collision approximation. Instead we propose a failure of the semiclassical acceleration and conduction approximations. A generalization of Boltzmann theory is made which includes quantum (interband) acceleration and conduction, as well as a complete treatment of interband-collision effects (within the independent-collision approximation). The interband terms enhance short-time response to E fields (because the theory satisfies the exact f-sum rule instead of the semiclassical approximation to it). This suggests that the additional conductivity, as expressed phenomenologically by the shunt resistor model, is explained by interband effects. The scattering operator is complex, its imaginary parts being related to energy-band renormalization caused by the disorder. Charge conservation is respected and thermal equilibrium is restored by the collision operator. The theory is formally solved for the leading corrections to SBT, which have the form of a shunt resistor model. At infrared frequencies, the conductivity mostly obeys the Drude law sigma(ω)approx.sigma(0)(1-iωtau) -1 , except for one term which goes as (1-iωtau) -2

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.

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

Chapman--Enskog approach to flux-limited diffusion theory

International Nuclear Information System (INIS)

Levermore, C.D.

1979-01-01

Using the technique developed by Chapman and Enskog for deriving the Navier--Stokes equations from the Boltzmann equation, a framework is set up for deriving diffusion theories from the transport equation. The procedure is first applied to give a derivation of isotropic diffusion theory and then of a completely new theory which is naturally flux-limited. This new flux-limited diffusion theory is then compared with asymptotic diffusion theory

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.

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

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)

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.

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.

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.

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.

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)

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...

Podolsky electromagnetism and a modification in Stefan-Boltzmann law

Energy Technology Data Exchange (ETDEWEB)

Bonin, Carlos Alberto; Bufalo, Rodrigo Santos; Escobar, Bruto Max Pimentel; Zambrano, German Enrique Ramos [Instituto de Fisica Teorica (IFT/UNESP), Sao Paulo, SP (Brazil)

2009-07-01

Full text. As it is well-known, gauge fields that emerge from the gauge principle are massless vector fields. Considering the photon as a Proca particle, experience sets an upper limit on its mass. This limit is m{sub Proca} < 6X10{sup -17}eV (PDG 2006). However, a mass term, regardless how small, breaks the gauge symmetry. Nevertheless, there exists a theory in which is possible to introduce a mass term preserving all symmetries of Maxwell electromagnetism, including the gauge one: such theory is known as Podolsky Electromagnetism. Podolsky theory is a second- order-derivative theory and has some remarkable properties, despite those already mentioned: the theory has two sectors, a massive one and massless one, it depends on a free parameter (which happens to be the mass of the massive sector) that, like all other elementary particles's masses of the Standard Model, must be fixed through experiences, and the fact that the electrostatic potential is finite everywhere, including over a punctual charge. Just like Maxwell electromagnetism, Podolsky's is a constrained theory and, since it is of second order in the derivatives, it consists in a much richer theoretical structure. Therefore, from both, theoretical and experimental points of view, Podolsky electromagnetism is a very attractive theory. In this work we study a gas of Podolsky photons at finite temperature through path integration. We show that the massless sector leads to the famous Planck's law for black-body radiation and, therefore, to the Stefan-Boltzmann law. We also show that the massive sector of the Podolsky theory induces a modification in both these laws. It is possible to set limits on the Podolsky parameter through comparison of our results with data from cosmic microwave background radiation. (author)

Nonequilibrium quantum field theories

International Nuclear Information System (INIS)

Niemi, A.J.

1988-01-01

Combining the Feynman-Vernon influence functional formalism with the real-time formulation of finite-temperature quantum field theories we present a general approach to relativistic quantum field theories out of thermal equilibrium. We clarify the physical meaning of the additional fields encountered in the real-time formulation of quantum statistics and outline diagrammatic rules for perturbative nonequilibrium computations. We derive a generalization of Boltzmann's equation which gives a complete characterization of relativistic nonequilibrium phenomena. (orig.)

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

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

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.

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

Log-normal frailty models fitted as Poisson generalized linear mixed models.

Science.gov (United States)

Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver

2016-12-01

The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

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)

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)

A transferable force field for CdS-CdSe-PbS-PbSe solid systems

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Fan, Zhaochuan; Koster, Rik S.; Wang, Shuaiwei; Fang, Changming; Yalcin, Anil O.; Tichelaar, Frans D.; Zandbergen, Henny W.; van Huis, Marijn A.; Vlugt, Thijs J. H.

2014-12-01

A transferable force field for the PbSe-CdSe solid system using the partially charged rigid ion model has been successfully developed and was used to study the cation exchange in PbSe-CdSe heteronanocrystals [A. O. Yalcin et al., "Atomic resolution monitoring of cation exchange in CdSe-PbSe heteronanocrystals during epitaxial solid-solid-vapor growth," Nano Lett. 14, 3661-3667 (2014)]. In this work, we extend this force field by including another two important binary semiconductors, PbS and CdS, and provide detailed information on the validation of this force field. The parameterization combines Bader charge analysis, empirical fitting, and ab initio energy surface fitting. When compared with experimental data and density functional theory calculations, it is shown that a wide range of physical properties of bulk PbS, PbSe, CdS, CdSe, and their mixed phases can be accurately reproduced using this force field. The choice of functional forms and parameterization strategy is demonstrated to be rational and effective. This transferable force field can be used in various studies on II-VI and IV-VI semiconductor materials consisting of CdS, CdSe, PbS, and PbSe. Here, we demonstrate the applicability of the force field model by molecular dynamics simulations whereby transformations are initiated by cation exchange.

A transferable force field for CdS-CdSe-PbS-PbSe solid systems

Energy Technology Data Exchange (ETDEWEB)

Fan, Zhaochuan; Vlugt, Thijs J. H., E-mail: t.j.h.vlugt@tudelft.nl [Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft,The Netherlands (Netherlands); Koster, Rik S.; Fang, Changming; Huis, Marijn A. van [Debye Institute for Nanomaterials Science and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); Wang, Shuaiwei [Institute of Nanostructured Functional Materials, Huanghe Science and Technology College, Zhengzhou, Henan 450006 (China); Yalcin, Anil O.; Tichelaar, Frans D.; Zandbergen, Henny W. [Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft (Netherlands)

2014-12-28

A transferable force field for the PbSe-CdSe solid system using the partially charged rigid ion model has been successfully developed and was used to study the cation exchange in PbSe-CdSe heteronanocrystals [A. O. Yalcin et al., “Atomic resolution monitoring of cation exchange in CdSe-PbSe heteronanocrystals during epitaxial solid-solid-vapor growth,” Nano Lett. 14, 3661–3667 (2014)]. In this work, we extend this force field by including another two important binary semiconductors, PbS and CdS, and provide detailed information on the validation of this force field. The parameterization combines Bader charge analysis, empirical fitting, and ab initio energy surface fitting. When compared with experimental data and density functional theory calculations, it is shown that a wide range of physical properties of bulk PbS, PbSe, CdS, CdSe, and their mixed phases can be accurately reproduced using this force field. The choice of functional forms and parameterization strategy is demonstrated to be rational and effective. This transferable force field can be used in various studies on II-VI and IV-VI semiconductor materials consisting of CdS, CdSe, PbS, and PbSe. Here, we demonstrate the applicability of the force field model by molecular dynamics simulations whereby transformations are initiated by cation exchange.

Lattice Boltzmann simulations of bubble formation in a microfluidic T-junction.

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Amaya-Bower, Luz; Lee, Taehun

2011-06-28

A lattice Boltzmann equation method based on the Cahn-Hilliard diffuse interface theory is developed to investigate the bubble formation process in a microchannel with T-junction mixing geometry. The bubble formation process has different regimes, namely, squeezing, dripping and jetting regimes, which correspond to the primary forces acting on the system. Transition from regime to regime is generally dictated by the capillary number Ca, volumetric flow ratio Q and viscosity ratio λ. A systematic analysis is performed to evaluate these effects. The computations are performed in the range of 10(-4)

Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)

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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.

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

Pricing Zero-Coupon Catastrophe Bonds Using EVT with Doubly Stochastic Poisson Arrivals

Directory of Open Access Journals (Sweden)

Zonggang Ma

2017-01-01

Full Text Available The frequency and severity of climate abnormal change displays an irregular upward cycle as global warming intensifies. Therefore, this paper employs a doubly stochastic Poisson process with Black Derman Toy (BDT intensity to describe the catastrophic characteristics. By using the Property Claim Services (PCS loss index data from 2001 to 2010 provided by the US Insurance Services Office (ISO, the empirical result reveals that the BDT arrival rate process is superior to the nonhomogeneous Poisson and lognormal intensity process due to its smaller RMSE, MAE, MRPE, and U and larger E and d. Secondly, to depict extreme features of catastrophic risks, this paper adopts the Peak Over Threshold (POT in extreme value theory (EVT to characterize the tail characteristics of catastrophic loss distribution. And then the loss distribution is analyzed and assessed using a quantile-quantile (QQ plot to visually check whether the PCS index observations meet the generalized Pareto distribution (GPD assumption. Furthermore, this paper derives a pricing formula for zero-coupon catastrophe bonds with a stochastic interest rate environment and aggregate losses generated by a compound doubly stochastic Poisson process under the forward measure. Finally, simulation results verify pricing model predictions and show how catastrophic risks and interest rate risk affect the prices of zero-coupon catastrophe bonds.

Behavior of Poisson Bracket Mapping Equation in Studying Excitation Energy Transfer Dynamics of Cryptophyte Phycocyanin 645 Complex

International Nuclear Information System (INIS)

Lee, Weon Gyu; Kelly, Aaron; Rhee, Young Min

2012-01-01

Recently, it has been shown that quantum coherence appears in energy transfers of various photosynthetic light harvesting complexes at from cryogenic to even room temperatures. Because the photosynthetic systems are inherently complex, these findings have subsequently interested many researchers in the field of both experiment and theory. From the theoretical part, simplified dynamics or semiclassical approaches have been widely used. In these approaches, the quantum-classical Liouville equation (QCLE) is the fundamental starting point. Toward the semiclassical scheme, approximations are needed to simplify the equations of motion of various degrees of freedom. Here, we have adopted the Poisson bracket mapping equation (PBME) as an approximate form of QCLE and applied it to find the time evolution of the excitation in a photosynthetic complex from marine algae. The benefit of using PBME is its similarity to conventional Hamiltonian dynamics. Through this, we confirmed the coherent population transfer behaviors in short time domain as previously reported with a more accurate but more time-consuming iterative linearized density matrix approach. However, we find that the site populations do not behave according to the Boltzmann law in the long time limit. We also test the effect of adding spurious high frequency vibrations to the spectral density of the bath, and find that their existence does not alter the dynamics to any significant extent as long as the associated reorganization energy is changed not too drastically. This suggests that adopting classical trajectory based ensembles in semiclassical simulations should not influence the coherence dynamics in any practical manner, even though the classical trajectories often yield spurious high frequency vibrational features in the spectral density

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

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)

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.

Evaluating the double Poisson generalized linear model.

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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.

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

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.

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

Acidic-basic properties of three alanine-based peptides containing acidic and basic side chains: comparison between theory and experiment.

Science.gov (United States)

Makowska, Joanna; Bagińska, Katarzyna; Liwo, Adam; Chmurzyński, Lech; Scheraga, Harold A

2008-01-01

The purpose of this work was to evaluate the effect of the nature of the ionizable end groups, and the solvent, on their acid-base properties in alanine-based peptides. Hence, the acid-base properties of three alanine-based peptides: Ac-KK-(A)(7)-KK-NH(2) (KAK), Ac-OO-(A)(7)-DD-NH(2) (OAD), Ac-KK-(A)(7)-EE-NH(2) (KAE), where A, D, E, K, and O denote alanine, aspartic acid, glutamic acid, lysine, and ornithine, respectively, were determined in water and in methanol by potentiometry. With the availability of these data, the ability of two theoretical methods to simulate pH-metric titration of those peptides was assessed: (i) the electrostatically driven Monte Carlo method with the ECEPP/3 force field and the Poisson-Boltzmann approach to compute solvation energy (EDMC/PB/pH), and (ii) the molecular dynamics method with the AMBER force field and the Generalized Born model (MD/GB/pH). For OAD and KAE, pK(a1) and pK(a2) correspond to the acidic side chains. For all three compounds in both solvents, the pK(a1) value is remarkably lower than the pK(a) of a compound modeling the respective isolated side chain, which can be explained by the influence of the electrostatic field from positively charged ornithine or lysine side chains. The experimental titration curves are reproduced well by the MD/GB/pH approach, the agreement being better if restraints derived from NMR measurements are incorporated in the conformational search. Poorer agreement is achieved by the EDMC/PB/pH method.

Contribution to the study of conformal theories and integrable models

International Nuclear Information System (INIS)

Sochen, N.

1992-05-01

The purpose of this thesis is the 2-D physics study. The main tool is the conformal field theory with Kac-Moody and W algebra. This theory describes the 2-D models that have translation, rotation and dilatation symmetries, at their critical point. The expanded conformal theories describe models that have a larger symmetry than conformal symmetry. After a review of conformal theory methods, the author effects a detailed study of singular vector form in sl(2) affine algebra. With this important form, correlation functions can be calculated. The classical W algebra is studied and the relations between classical W algebra and quantum W algebra are specified. Bosonization method is presented and sl(2)/sl(2) topological model, studied. Partition function bosonization of different models is described. A program of rational theory classification is described linking rational conformal theories and spin integrable models, and interesting relations between Boltzmann weights of different models have been found. With these relations, the integrability of models by a direct calculation of their Boltzmann weights is proved

A test of inflated zeros for Poisson regression models.

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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.

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.)

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.

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.

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.

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.

PENERAPAN REGRESI BINOMIAL NEGATIF UNTUK MENGATASI OVERDISPERSI PADA REGRESI POISSON

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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.

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.

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.

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

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

Variance to mean ratio, R(t), for poisson processes on phylogenetic trees.

Science.gov (United States)

Goldman, N

1994-09-01

The ratio of expected variance to mean, R(t), of numbers of DNA base substitutions for contemporary sequences related by a "star" phylogeny is widely seen as a measure of the adherence of the sequences' evolution to a Poisson process with a molecular clock, as predicted by the "neutral theory" of molecular evolution under certain conditions. A number of estimators of R(t) have been proposed, all predicted to have mean 1 and distributions based on the chi 2. Various genes have previously been analyzed and found to have values of R(t) far in excess of 1, calling into question important aspects of the neutral theory. In this paper, I use Monte Carlo simulation to show that the previously suggested means and distributions of estimators of R(t) are highly inaccurate. The analysis is applied to star phylogenies and to general phylogenetic trees, and well-known gene sequences are reanalyzed. For star phylogenies the results show that Kimura's estimators ("The Neutral Theory of Molecular Evolution," Cambridge Univ. Press, Cambridge, 1983) are unsatisfactory for statistical testing of R(t), but confirm the accuracy of Bulmer's correction factor (Genetics 123: 615-619, 1989). For all three nonstar phylogenies studied, attained values of all three estimators of R(t), although larger than 1, are within their true confidence limits under simple Poisson process models. This shows that lineage effects can be responsible for high estimates of R(t), restoring some limited confidence in the molecular clock and showing that the distinction between lineage and molecular clock effects is vital.(ABSTRACT TRUNCATED AT 250 WORDS)

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

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...

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.

The physics of the photovoltaic effect

International Nuclear Information System (INIS)

Boeer, K.W.

1978-01-01

The main parts of a photovoltaic cell and their function are described. Photovoltaic cells are then classified in respect to their operation. The operation of typical cells is analyzed with the goal to obtain current-voltage characteristics in a self-consistent physical model. This is achieved by connecting the emitter diffusion current with the voltage drop in the junction by a doubly acting boundary condition, the electron density at the emitter-junction interface. The consequently obtained characteristics have near the open circuit voltage (Boltzmann range), the form of the commonly used shifted diode characteristic, however, with parameters in substantially improved agreement with the experiment. Outside the Boltzmann range, integration of transport and Poisson equation yields the shape of the characteristics. This theory is then extended to include photovoltaic cells with dominant interface recombination. Such interface recombination causes mostly a lowering of the open circuit voltage. The agreement between theory and experiment is surprisingly good for CdS/Cu 2 S solar cells. (author)

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.

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

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

Theoretical analysis of radiographic images by nonstationary Poisson processes

International Nuclear Information System (INIS)

Tanaka, Kazuo; Uchida, Suguru; Yamada, Isao.

1980-01-01

This paper deals with the noise analysis of radiographic images obtained in the usual fluorescent screen-film system. The theory of nonstationary Poisson processes is applied to the analysis of the radiographic images containing the object information. The ensemble averages, the autocorrelation functions, and the Wiener spectrum densities of the light-energy distribution at the fluorescent screen and of the film optical-density distribution are obtained. The detection characteristics of the system are evaluated theoretically. Numerical examples one-dimensional image are shown and the results are compared with those obtained under the assumption that the object image is related to the background noise by the additive process. (author)

The Poisson equation at second order in relativistic cosmology

International Nuclear Information System (INIS)

Hidalgo, J.C.; Christopherson, Adam J.; Malik, Karim A.

2013-01-01

We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field

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...

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

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

Thermodynamics of Highly Concentrated Aqueous Electrolytes: Based on Boltzmann's eponymous equation

Energy Technology Data Exchange (ETDEWEB)

Ally, Moonis Raza [ORNL

2018-05-01

This sharply focused book invites the reader to explore the chemical thermodynamics of highly concentrated aqueous electrolytes from a different vantage point than traditional methods. The book's foundation is deeply rooted in Ludwig Boltzmann's eponymous equation. The pathway from micro to macro thermodynamics is explained heuristically, in a step-by-step approach. Concepts and mathematical formalism are explained in detail to captivate and maintain interest as the algebra twists and turns. Every significant result is derived in a lucid and piecemeal fashion. Application of the theory is exemplified with examples. It is amazing to realize that Boltamann's simple equation contains sufficient information from which such an elaborate theory can emerge. This book is suitable for undergraduate and graduate level classes in chemical engineering, chemistry, geochemistry, environmental sciences, and those studying aerosol particles in the troposphere. Students interested in understanding how thermodynamic theories may be developed would be inspired by the methodology. The author wishes that readers get as much excitement reading this book as he did writing it.

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.

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.

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)

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.

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.

Multiscale molecular dynamics using the matched interface and boundary method

International Nuclear Information System (INIS)

Geng Weihua; Wei, G.W.

2011-01-01

The Poisson-Boltzmann (PB) equation is an established multiscale model for electrostatic analysis of biomolecules and other dielectric systems. PB based molecular dynamics (MD) approach has a potential to tackle large biological systems. Obstacles that hinder the current development of PB based MD methods are concerns in accuracy, stability, efficiency and reliability. The presence of complex solvent-solute interface, geometric singularities and charge singularities leads to challenges in the numerical solution of the PB equation and electrostatic force evaluation in PB based MD methods. Recently, the matched interface and boundary (MIB) method has been utilized to develop the first second order accurate PB solver that is numerically stable in dealing with discontinuous dielectric coefficients, complex geometric singularities and singular source charges. The present work develops the PB based MD approach using the MIB method. New formulation of electrostatic forces is derived to allow the use of sharp molecular surfaces. Accurate reaction field forces are obtained by directly differentiating the electrostatic potential. Dielectric boundary forces are evaluated at the solvent-solute interface using an accurate Cartesian-grid surface integration method. The electrostatic forces located at reentrant surfaces are appropriately assigned to related atoms. Extensive numerical tests are carried out to validate the accuracy and stability of the present electrostatic force calculation. The new PB based MD method is implemented in conjunction with the AMBER package. MIB based MD simulations of biomolecules are demonstrated via a few example systems.

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

An integrated Boltzmann+hydrodynamics approach to heavy ion collisions

International Nuclear Information System (INIS)

Petersen, Hannah

2009-01-01

In this thesis the first fully integrated Boltzmann+hydrodynamics approach to relativistic heavy ion reactions has been developed. After a short introduction that motivates the study of heavy ion reactions as the tool to get insights about the QCD phase diagram, the most important theoretical approaches to describe the system are reviewed. The hadron-string transport approach that this work is based on is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. Predictions for the charged particle multiplicities at LHC energies are made. The next step is the development of a new framework to calculate the baryon number density in a transport approach. Time evolutions of the net baryon number and the quark density have been calculated at AGS, SPS and RHIC energies. Studies of phase diagram trajectories using hydrodynamics are performed. The hybrid approach that has been developed as the main part of this thesis is based on the UrQMD transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The full (3+1) dimensional ideal relativistic one fluid dynamics evolution is solved using the SHASTA algorithm. Three different equations of state have been used, namely a hadron gas equation of state without a QGP phase transition, a chiral EoS and a bag model EoS including a strong first order phase transition. For the freeze-out transition from hydrodynamics to the cascade calculation two different set-ups are employed. The parameter dependences of the model are investigated and the time evolution of different quantities is explored. The hybrid model calculation is able to reproduce the experimentally measured integrated as well as transverse momentum dependent v 2 values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from E lab =2-160 A GeV. The HBT correlation of the negatively charged pion source created in

An integrated Boltzmann+hydrodynamics approach to heavy ion collisions

Energy Technology Data Exchange (ETDEWEB)

Petersen, Hannah

2009-04-22

In this thesis the first fully integrated Boltzmann+hydrodynamics approach to relativistic heavy ion reactions has been developed. After a short introduction that motivates the study of heavy ion reactions as the tool to get insights about the QCD phase diagram, the most important theoretical approaches to describe the system are reviewed. The hadron-string transport approach that this work is based on is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. Predictions for the charged particle multiplicities at LHC energies are made. The next step is the development of a new framework to calculate the baryon number density in a transport approach. Time evolutions of the net baryon number and the quark density have been calculated at AGS, SPS and RHIC energies. Studies of phase diagram trajectories using hydrodynamics are performed. The hybrid approach that has been developed as the main part of this thesis is based on the UrQMD transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The full (3+1) dimensional ideal relativistic one fluid dynamics evolution is solved using the SHASTA algorithm. Three different equations of state have been used, namely a hadron gas equation of state without a QGP phase transition, a chiral EoS and a bag model EoS including a strong first order phase transition. For the freeze-out transition from hydrodynamics to the cascade calculation two different set-ups are employed. The parameter dependences of the model are investigated and the time evolution of different quantities is explored. The hybrid model calculation is able to reproduce the experimentally measured integrated as well as transverse momentum dependent v{sub 2} values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from E{sub lab}=2-160 A GeV. The HBT correlation of the negatively charged pion source

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

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.

Electroweak bosons in Pb+Pb and $p$+Pb collisions

CERN Document Server

AUTHOR|(INSPIRE)INSPIRE-00356981; The ATLAS collaboration

2016-01-01

Electroweak boson ( W , Z , γ ) measurements in Pb+Pb collisions at sNN=2.76 TeV and in p +Pb collisions at sNN=5.02 TeV are presented with the ATLAS detector at the LHC. In Pb+Pb, electroweak boson yields are shown to be independent of centrality. Differential measurements in absolute pseudorapidity are used to investigate nuclear effects to the free-proton parton distribution function (PDF). The distributions lack the experimental precision to unambiguously identify the presence of nuclear modifications. In p +Pb, the Z boson cross section is measured as a function of center-of-mass rapidity yZ⁎ and the momentum fraction of the lead-going parton (Bjorken xPb ). The distributions are asymmetric and model predictions underestimate the data at large xPb . The overall shape is best described by including nuclear effects. The differential cross section is also measured in different centrality classes and shows evidence of spatially-dependent nuclear PDFs. The Z boson production yields are measured as a functi...

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.

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)

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.

Etude d'un modele de Boltzmann sur reseau pour la simulation assistee par ordinateur des fluides a plusieurs phases immiscibles

Science.gov (United States)

Leclaire, Sebastien

The computer assisted simulation of the dynamics of fluid flow has been a highly rewarding topic of research for several decades now, in terms of the number of scientific problems that have been solved as a result, both in the academic world and in industry. In the fluid dynamics field, simulating multiphase immiscible fluid flow remains a challenge, because of the complexity of the interactions at the flow phase interfaces. Various numerical methods are available to study these phenomena, and, the lattice Boltzmann method has been shown in recent years to be well adapted to solving this type of complex flow. In this thesis, a lattice Boltzmann model for the simulation of two-phase immiscible flows is studied. The main objective of the thesis is to develop this promising method further, with a view to enhancing its validity. To achieve this objective, the research is divided into five distinct themes. The first two focus on correcting some of the deficiencies of the original model. The third generalizes the model to support the simulation of N-phase immiscible fluid flows. The fourth is aimed at modifying the model itself, to enable the simulation of immiscible fluid flows in which the density of the phases varies. With the lattice Boltzmann class of models studied here, this density variation has been inadequately modeled, and, after 20 years, the issue still has not been resolved. The fifth, which complements this thesis, is connected with the lattice Boltzmann method, in that it generalizes the theory of 2D and 3D isotropic gradients for a high order of spatial precision. These themes have each been the subject of a scientific article, as listed in the appendix to this thesis, and together they constitute a synthesis that explains the links between the articles, as well as their scientific contributions, and satisfy the main objective of this research. Globally, a number of qualitative and quantitative test cases based on the theory of multiphase fluid flows

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

Discrimination of shot-noise-driven Poisson processes by external dead time - Application of radioluminescence from glass

Science.gov (United States)

Saleh, B. E. A.; Tavolacci, J. T.; Teich, M. C.

1981-01-01

Ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching in the shot-noise-driven doubly stochastic Poisson point process (SNDP) are discussed. Interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects are investigated. It is demonstrated that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process can be obtained from the Laplace transform of the single-fold and joint-moment-generating functions for the driving rate process. The theory is in good agreement with experimental values for radioluminescence radiation in fused silica, quartz, and glass, and the process has many applications in pulse, particle, and photon detection.

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.)

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.

Stability, causality, and hyperbolicity in Carter's ''regular'' theory of relativistic heat-conducting fluids

International Nuclear Information System (INIS)

Olson, T.S.; Hiscock, W.A.

1990-01-01

Stability and causality are studied for linear perturbations about equilibrium in Carter's ''regular'' theory of relativistic heat-conducting fluids. The ''regular'' theory, when linearized around an equilibrium state having vanishing expansion and shear, is shown to be equivalent to the inviscid limit of the linearized Israel-Stewart theory of relativistic dissipative fluids for a particular choice of the second-order coefficients β 1 and γ 2 . A set of stability conditions is determined for linear perturbations of a general inviscid Israel-Stewart fluid using a monotonically decreasing energy functional. It is shown that, as in the viscous case, stability implies that the characteristic velocities are subluminal and that perturbations obey hyperbolic equations. The converse theorem is also true. We then apply this analysis to a nonrelativistic Boltzmann gas and to a strongly degenerate free Fermi gas in the ''regular'' theory. Carter's ''regular'' theory is shown to be incapable of correctly describing the nonrelativistic Boltzmann gas and the degenerate Fermi gas (at all temperatures)

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.

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

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

Jet Fragmentation in p+p, p+Pb and Pb+Pb at ATLAS

CERN Document Server

Slovak, Radim; The ATLAS collaboration

2017-01-01

Jets are an important tool to study the hot, dense matter produced in Pb+Pb collisions at the LHC. Due to the loss of some of the jet’s energy outside the jet cone, jet rates have been found to be reduced by approximately a factor of two, in the most central events and over a wide kinematic range. In order to understand precisely how the jets are modified, it is important to measure how the jet momentum is carried by its fragmentation products. The longitudinal momentum fraction of charged particles in jets from Pb+Pb, p+Pb, and p+p collisions have been measured using the ATLAS detector. Proton-proton and p+Pb collisions provide necessary baseline measurements for quantifying the modifications in Pb+Pb collisions. In Run 1, ATLAS collected samples of p+p and Pb+Pb collisions at a center of mass energy of 2.76 TeV and a sample of p+Pb collisions at 5.02 TeV. In Run 2, large samples of p+p and Pb+Pb collisions at 5.02 TeV have been collected providing a complete set of collision systems at 5.02 TeV. In this t...

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

Neutrons moderation theory; Theorie du ralentissement des neutrons

Energy Technology Data Exchange (ETDEWEB)

Vigier, J P

1949-07-01

This report gives a summarized presentation of the theory of fast neutrons diffusion and moderation in a given environment as elaborated by M. Langevin, E. Fermi, R. Marshak and others. This statistical theory is based on three assumptions: there is no inelastic diffusion, the elastic diffusion has a spherical symmetry with respect to the center of gravity of the neutron-nucleus system (s-scattering), and the effects of chemical bonds and thermal agitation of nuclei are neglected. The first chapter analyzes the Boltzmann equation of moderation, its first approximate solution (age-velocity equation) and its domain of validity, the extension of the age-velocity theory (general solution) and the boundary conditions, the upper order approximation (spherical harmonics method and Laplace transformation), the asymptotic solutions, and the theory of spatial momenta. The second chapter analyzes the energy distribution of delayed neutrons (stationary and non-stationary cases). (J.S.)

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.

Interplay of charge distribution and conformation in peptides: comparison of theory and experiment.

Science.gov (United States)

Makowska, Joanna; Bagińska, Katarzyna; Kasprzykowski, F; Vila, Jorge A; Jagielska, Anna; Liwo, Adam; Chmurzyński, Lech; Scheraga, Harold A

2005-01-01

We assessed the correlation between charge distribution and conformation of flexible peptides by comparing the theoretically calculated potentiometric-titration curves of two model peptides, Ac-Lys5-NHMe (a model of poly-L-lysine) and Ac-Lys-Ala11-Lys-Gly2-Tyr-NH2 (P1) in water and methanol, with the experimental curves. The calculation procedure consisted of three steps: (i) global conformational search of the peptide under study using the electrostatically driven Monte Carlo (EDMC) method with the empirical conformational energy program for peptides (ECEPP)/3 force field plus the surface-hydration (SRFOPT) or the generalized Born surface area (GBSA) solvation model as well as a molecular dynamics method with the assisted model building and energy refinement (AMBER)99/GBSA force field; (ii) reevaluation of the energy in the pH range considered by using the modified Poisson-Boltzmann approach and taking into account all possible protonation microstates of each conformation, and (iii) calculation of the average degree of protonation of the peptide at a given pH value by Boltzmann averaging over conformations. For Ac-Lys5-NHMe, the computed titration curve agrees qualitatively with the experimental curve of poly-L-lysine in 95% methanol. The experimental titration curves of peptide P1 in water and methanol indicate a remarkable downshift of the first pK(a) value compared to the values for reference compounds (n-butylamine and phenol, respectively), suggesting the presence of a hydrogen bond between the tyrosine hydroxyl oxygen and the H(epsilon) proton of a protonated lysine side chain. The theoretical titration curves agree well with the experimental curves, if conformations with such hydrogen bonds constitute a significant part of the ensemble; otherwise, the theory predicts too small a downward pH shift. Copyright 2005 Wiley Periodicals, Inc

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)

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...

Charmonium production in pp, pPb and PbPb collisions with CMS

International Nuclear Information System (INIS)

Ståhl, Andre Govinda

2017-01-01

The LHC Run 1 results of the analysis of charmonium production in pp, pPb and PbPb collisions with the CMS experiment are reported. The coherent J/ψ photoproduction cross section is measured as a function of rapidity in ultra-peripheral PbPb collisions at 2.76 TeV. The forward-backward ratio of prompt J/ψ yields in pPb collisions at 5.02 TeV is presented as a function of the event activity and p T . The nuclear modification factor of prompt J/ψ in PbPb collisions at 2.76 TeV is shown as a function of rapidity, centrality and p T . Finally, the ratio of ψ (2 S ) to J/ψ yields in PbPb collisions with respect to pp collisions at 2.76 TeV is analysed in different rapidity and centrality bins. (paper)

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.

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).

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 ...

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.

Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

Science.gov (United States)

Sels, Dries; Brosens, Fons

2013-10-01

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

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

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.

Gauge bridges in classical field theory

International Nuclear Information System (INIS)

Jakobs, S.

2009-03-01

In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called ''gauge bridges''are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)

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

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

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.

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.

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

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.

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....

Transition flow ion transport via integral Boltzmann equation

International Nuclear Information System (INIS)

Darcie, T.E.

1983-10-01

A new approach is developed to solve the Integral Boltzmann Equation for the evolving velocity distribution of a source of ions, undergoing electrostatic acceleration through a neutral gas target. The theory is applicable to arbitrarily strong electric fields, any ion/neutral mass ratio greater than unity, and is not limited to spatially isotropic gas targets. A hard sphere collision model is used, with a provision for inelasticity. Both axial and radial velocity distributions are calculated for applications where precollision radial velocities are negligible, as is the case for ion beam extractions from high pressure sources. Theoretical predictions are tested through an experiment in which an atmospheric pressure ion source is coupled to a high vacuum energy analyser. Excellent agreement results for configurations in which the radial velocity remains small. Velocity distributions are applied to predicting the efficiency of coupling an atmospheric pressure ion source to a quadrupole mass spectrometer and results clearly indicate the most desirable extracting configuration. A method is devised to calculate ion-molecule hard sphere collision cross sections for easily fragmented organic ions

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.

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.

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.

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.

Theoretical prediction and experimental confirmation of unusual ternary ordered semiconductor compounds in Sr-Pb-S system.

Science.gov (United States)

Hao, Shiqiang; Zhao, Li-Dong; Chen, Chang-Qiang; Dravid, Vinayak P; Kanatzidis, Mercouri G; Wolverton, Christopher M

2014-01-29

We examine the thermodynamics of phase separation and ordering in the ternary Ca(x)Pb(1-x)S and Sr(x)Pb(1-x)S systems by density-functional theory combined with a cluster expansion and Monte Carlo simulations. Similar to most other ternary III-V or IV-VI semiconductor alloys, we find that bulk phase separation is thermodynamically preferred for PbS-CaS. However, we predict the surprising existence of stable, ordered ternary compounds in the PbS-SrS system. These phases are previously unreported ordered rocksalt-based compounds: SrPb3S4, SrPbS2, and Sr3PbS4. The stability of these predicted ordered phases is confirmed by transmission electron microscopy observations and band gap measurements. We believe this work paves the way for a combined theory-experiment approach to decipher complex phase relations in multicomponent chalcogenide systems.

Electroweak bosons in Pb+Pb and p+Pb collisions from ATLAS

CERN Document Server

INSPIRE-00356981

2015-01-01

Electroweak boson ($W$, $Z$, $\\gamma$) measurements in Pb+Pb collisions at $\\sqrt{s_{NN}}=2.76$ TeV and in $p$+Pb collisions at $\\sqrt{s_{NN}}=5.02$ TeV are presented with the ATLAS detector at the LHC. In Pb+Pb, electroweak boson yields are shown to be independent of centrality. Differential measurements in absolute pseudorapidity are used to investigate nuclear effects to the free-proton parton distribution function (PDF). The distributions lack the experimental precision to unambiguously identify the presence of nuclear modifications. In $p$+Pb, the $Z$ boson cross section is measured as a function of center-of-mass rapidity $y_{Z}^{*}$ and the momentum fraction of the lead-going parton (Bjorken $x_{Pb}$). The distributions are asymmetric and model predictions underestimate the data at large $x_{Pb}$. The overall shape is best described by including nuclear effects. The differential cross section is also measured in different centrality classes and shows evidence of spatially-dependent nuclear PDFs. The $Z...

Noncommutative Geometry in M-Theory and Conformal Field Theory

International Nuclear Information System (INIS)

Morariu, Bogdan

1999-01-01

In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U q (SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun q (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models

Noncommutative Geometry in M-Theory and Conformal Field Theory

Energy Technology Data Exchange (ETDEWEB)

Morariu, Bogdan [Univ. of California, Berkeley, CA (United States)

1999-05-01

In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_q(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun_q (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.

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.

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...

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.

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.

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 ...

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

Ab initio study of point defects in PbSe and PbTe: Bulk and nanowire

Energy Technology Data Exchange (ETDEWEB)

Wrasse, E. O. [Instituto de Física, Universidade Federal de Uberlândia, 38408-100, Uberlândia, MG, Brazil and Departamento de Física, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS (Brazil); Venezuela, P. [Instituto de Física, Universidade Federal Fluminense, 24210-346, Niteroi, RJ (Brazil); Baierle, R. J., E-mail: rbaierle@smail.ufsm.br [Departamento de Física, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS (Brazil)

2014-11-14

First principles investigations, within the spin-polarized density functional theory, are performed to study energetic stability and electronic properties of point defects (vacancies and antisites) in PbSe and PbTe: bulk and nanowire (NW). Our results show that the energetic stability of these defects is ruled by relaxation process. These defects have lower formation energies in the nanowire structures as compared to the bulk, being more stable in the surface of the NWs. We also show that in the bulk system only one charge state is stable, otherwise, due to the larger band gaps, more than one charge state may be stable in the NWs. In addition, we have investigated how the presence of intrinsic defects affects the electronic properties of bulk and NW systems. Vacancies give rise to new electronic states near to the edges of the valence and conduction bands while the energetic position of the electronic states from antisites depends on the charge state, being localized inside the band gap or near the edges of the valence or conduction bands. We discuss how these changes in the electronic properties due to intrinsic defects may affect the thermoelectric properties of PbSe and PbTe NWs.

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.

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.

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.

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.

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

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...

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.

Electron kinetics modeling in a weakly ionized gas

International Nuclear Information System (INIS)

Boeuf, Jean-Pierre

1985-01-01

This work presents some features of electron kinetics in a weakly ionized gas. After a summary of the basis and recent developments of the kinetic theory, and a review of the most efficient numerical techniques for solving the Boltzmann equation, several aspects of electron motion in gases are analysed. Relaxation phenomena toward equilibrium under a uniform electric field, and the question of the existence of the hydrodynamic regime are first studied. The coupling between electron kinetics and chemical kinetics due to second kind collisions in Nitrogen is then analysed; a quantitative description of the evolution of the energy balance, accounting for electron-molecule as well as molecule-molecule energy transfer is also given. Finally, electron kinetics in space charge distorted, highly non uniform electric fields (glow discharges, streamers propagation) is investigated with microscopic numerical methods based on Boltzmann and Poisson equations. (author) [fr

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.

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...

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.

Experimental micro mechanics methods for conventional and negative Poisson's ratio cellular solids as Cosserat continua

Science.gov (United States)

Lakes, R.

1991-01-01

Continuum representations of micromechanical phenomena in structured materials are described, with emphasis on cellular solids. These phenomena are interpreted in light of Cosserat elasticity, a generalized continuum theory which admits degrees of freedom not present in classical elasticity. These are the rotation of points in the material, and a couple per unit area or couple stress. Experimental work in this area is reviewed, and other interpretation schemes are discussed. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. New experimental results are presented for foam materials with negative Poisson's ratios.

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.

The double-layer of penetrable ions: an alternative route to charge reversal.

Science.gov (United States)

Frydel, Derek; Levin, Yan

2013-05-07

We investigate a double-layer of penetrable ions near a charged wall. We find a new mechanism for charge reversal that occurs in the weak-coupling regime and, accordingly, the system is suitable for the mean-field analysis. The penetrability is achieved by smearing-out the ionic charge inside a sphere, so there is no need to introduce non-electrostatic forces and the system in the low coupling limit can be described by a modified version of the Poisson-Boltzmann equation. The predictions of the theory are compared with the Monte Carlo simulations.

Error-Rate Bounds for Coded PPM on a Poisson Channel

Science.gov (United States)

Moision, Bruce; Hamkins, Jon

2009-01-01

Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.

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.

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.

Kinetic theory of gases and plasmas

International Nuclear Information System (INIS)

Schram, P.P.J.M.

1991-01-01

Kinetic theory provides the link between the non-equilibrium statistical mechanics of many-particle systems and macroscopic or phenomenological physics. This volume deals with the derivation of kinetic equations, their limitations and generalizations,and with the applications of kinetic theory to physical phenomena and the calculation of transport coefficients. This book is divided in 12 chapters which discuss a wide range of topics such as balanced equations, the Klimontovich, Vlasov-Maxwell, and Boltzmann equations, Chapman-Enskog theory, the kinetic theory of plasmas, B.G.K. models, linear response theory, Brownian motion and renormalized kinetic theory. Each chapter is concluded with exercises, which not only enable the readers to test their understanding of the theory, but also present additional examples which complement the text. 151 refs.; 35 figs.; 5 tabs