basic particle equations: Topics by Science.gov

Sample records for basic particle equations

Internally electrodynamic particle model: Its experimental basis and its predictions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng-Johansson, J. X., E-mail: jxzj@iofpr.or

2010-03-15

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts: (a) electric charges present with all material particles, (b) an accelerated charge generates electromagnetic waves according to Maxwell's equations and Planck energy equation, and (c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schroedinger equation, mass, Einstein mass-energy relation, Newton's law of gravity,more » single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A conditioned solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.« less
Internally electrodynamic particle model: Its experimental basis and its predictions

NASA Astrophysics Data System (ADS)

Zheng-Johansson, J. X.

2010-03-01

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts: (a) electric charges present with all material particles, (b) an accelerated charge generates electromagnetic waves according to Maxwell’s equations and Planck energy equation, and (c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schrödinger equation, mass, Einstein mass-energy relation, Newton’s law of gravity, single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A conditioned solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.
An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1988-01-01

An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..
Particles, Waves, and the Interpretation of Quantum Mechanics

ERIC Educational Resources Information Center

Christoudouleas, N. D.

1975-01-01

Presents an explanation, without mathematical equations, of the basic principles of quantum mechanics. Includes wave-particle duality, the probability character of the wavefunction, and the uncertainty relations. (MLH)
Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.
Moment equations for chromatography using superficially porous spherical particles.

PubMed

Miyabe, Kanji

2011-01-01

New moment equations were developed for chromatography using superficially porous (shell-type) spherical particles, which have recently attracted much attention as one of separation media for fast separation with high efficiency. At first, the moment equations of the first absolute and second central moments in the real time domain were derived from the analytical solution in the Laplace domain of a set of basic equations of the general rate model of chromatography, which represent the mass balance, mass-transfer rate, and reaction kinetics in the column packed with shell-type particles. Then, the moment equations were used for analyzing the experimental data of chromatography of kallidin in a Halo column, which were published in a previous paper written by other researchers. It was tried to predict the chromatographic behavior of shell-type particles having different shell thicknesses. The new moment equations are useful for a detailed analysis of the chromatographic behavior of shell-type spherical particles. It is also concluded that they can be used for the preliminarily optimization of their structural characteristics.
Coagulation algorithms with size binning

NASA Technical Reports Server (NTRS)

Statton, David M.; Gans, Jason; Williams, Eric

1994-01-01

The Smoluchowski equation describes the time evolution of an aerosol particle size distribution due to aggregation or coagulation. Any algorithm for computerized solution of this equation requires a scheme for describing the continuum of aerosol particle sizes as a discrete set. One standard form of the Smoluchowski equation accomplishes this by restricting the particle sizes to integer multiples of a basic unit particle size (the monomer size). This can be inefficient when particle concentrations over a large range of particle sizes must be calculated. Two algorithms employing a geometric size binning convention are examined: the first assumes that the aerosol particle concentration as a function of size can be considered constant within each size bin; the second approximates the concentration as a linear function of particle size within each size bin. The output of each algorithm is compared to an analytical solution in a special case of the Smoluchowski equation for which an exact solution is known . The range of parameters more appropriate for each algorithm is examined.
Experimental Basis for IED Particle Model

NASA Astrophysics Data System (ADS)

Zheng-Johansson, J.

2009-03-01

The internally electrodynamic (IED) particle model is built on three experimental facts: a) electric charges present in all matter particles, b) an accelerated charge generates electromagnetic (EM) waves by Maxwell's equations and Planck energy equation, and c) source motion gives Doppler effect. A set of well-kwon basic particle equations have been predicted based on first-principles solutions for IED particle (e.g. J Phys CS128, 012019, 2008); the equations are long experimentally validated. A critical review of the key experiments suggests that the IED process underlies these equations not just sufficiently but also necessarily. E.g.: 1) A free IED electron solution is a plane wave ψ= Ce^i(kdX-φT) requisite for producing the diffraction fringe in a Davisson-Germer experiment, and of also all basic point-like attributes facilitated by a linear momentum kd and the model structure. It needs not further be a wave packet which produces not a diffraction fringe. 2)The radial partial EM waves, hence the total ψ, of an IED electron will, on both EM theory and experiment basis -not by assumption, enter two slits at the same time, as is requisite for an electron to interfere with itself as shown in double slit experiments. 3) On annihilation, an electron converts (from mass m) to a radiation energy φ without an acceleration which is externally observable and yet requisite by EM theory. So a charge oscillation of frequency φ and its EM waves must regularly present internal of a normal electron, whence the IED model.
The ultimate limits of the relativistic rocket equation. The Planck photon rocket

NASA Astrophysics Data System (ADS)

Haug, Espen Gaarder

2017-07-01

In this paper we look at the ultimate limits of a photon propulsion rocket. The maximum velocity for a photon propulsion rocket is just below the speed of light and is a function of the reduced Compton wavelength of the heaviest subatomic particles in the rocket. We are basically combining the relativistic rocket equation with Haug's new insight on the maximum velocity for anything with rest mass. An interesting new finding is that in order to accelerate any subatomic "fundamental" particle to its maximum velocity, the particle rocket basically needs two Planck masses of initial load. This might sound illogical until one understands that subatomic particles with different masses have different maximum velocities. This can be generalized to large rockets and gives us the maximum theoretical velocity of a fully-efficient and ideal rocket. Further, no additional fuel is needed to accelerate a Planck mass particle to its maximum velocity; this also might sound absurd, but it has a very simple and logical solution that is explained in this paper.
Relativistic Kinetic Theory

NASA Astrophysics Data System (ADS)

Vereshchagin, Gregory V.; Aksenov, Alexey G.

2017-02-01

Preface; Acknowledgements; Acronyms and definitions; Introduction; Part I. Theoretical Foundations: 1. Basic concepts; 2. Kinetic equation; 3. Averaging; 4. Conservation laws and equilibrium; 5. Relativistic BBGKY hierarchy; 6. Basic parameters in gases and plasmas; Part II. Numerical Methods: 7. The basics of computational physics; 8. Direct integration of Boltzmann equations; 9. Multidimensional hydrodynamics; Part III. Applications: 10. Wave dispersion in relativistic plasma; 11. Thermalization in relativistic plasma; 12. Kinetics of particles in strong fields; 13. Compton scattering in astrophysics and cosmology; 14. Self-gravitating systems; 15. Neutrinos, gravitational collapse and supernovae; Appendices; Bibliography; Index.
Engineering mechanics: statics and dynamics. [Textbook

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sandor, B.I.

1983-01-01

The purpose of this textbook is to provide engineering students with basic learning material about statics and dynamics which are fundamental engineering subjects. The chapters contain information on: an introduction to engineering mechanics; forces on particles, rigid bodies, and structures; kinetics of particles, particle systems, and rigid bodies in motion; kinematics; mechanical vibrations; and friction, work, moments of inertia, and potential energy. Each chapter contains introductory material, the development of the essential equations, worked-out example problems, homework problems, and, finally, summaries of the essential methods and equations, graphically illustrated where appropriate. (LCL)
Experimental Basis for IED Particle Model

NASA Astrophysics Data System (ADS)

Zheng-Johansson, J.

2009-05-01

The internally electrodynamic (IED) particle model is built on three experimental facts: a) electric charges present in all matter particles, b) an accelerated charge generates electromagnetic (EM) waves by Maxwell's equations and Planck energy equation, and c) source motion gives Doppler effect. A set of well-kwon basic particle equations have been predicted based on first-principles solutions for IED particle (e.g. arxiv:0812.3951, J Phys CS128, 012019, 2008); the equations are long experimentally validated. A critical review of the key experiments suggests that the IED process underlies these equations not just sufficiently but also necessarily. E.g.: 1) A free IED electron solution is a plane wave ψ= Ce^i(kdX-φT) requisite for producing the diffraction fringe in a Davisson-Germer experiment, and of also all basic point-like attributes facilitated by a linear momentum kd and the model structure. It needs not further be a wave packet which produces not a diffraction fringe. 2)The radial partial EM waves, hence the total ψ, of an IED electron will, on both EM theory and experiment basis -not by assumption, enter two slits at the same time, as is requisite for an electron to interfere with itself as shown in double slit experiments. 3) On annihilation, an electron converts (from mass m) to a radiation energy φ without an acceleration which is externally observable and yet requisite by EM theory. So a charge oscillation of frequency φ and its EM waves must regularly present internal of a normal electron, whence the IED model.
A Study of Green's Function Methods Applied to Space Radiation Protection

NASA Technical Reports Server (NTRS)

Heinbockel, John H.

2001-01-01

The purpose of this research was to study the propagation of galactic ions through various materials. Galactic light ions result from the break up of heavy ion particles and their propagation through materials is modeled using the one-dimensional Boltzmann equation. When ions enter materials there can occur (i) the interaction of ions with orbital electrons which causes ionization within the material and (ii) ions collide with atoms causing production of secondary particles which penetrate deeper within the material. These processes are modeled by a continuum model. The basic idea is to place a control volume within the material and examine the change in ion flux across this control volume. In this way on can derive the basic equations for the transport of light and heavy ions in matter. Green's function perturbation methods can then be employed to solve the resulting equations using energy dependent nuclear cross sections.
α-quantized Einstein masses for leptons, quarks, hadrons, gauge bosons, and Higgs constants

NASA Astrophysics Data System (ADS)

Mac Gregor, Malcolm

2011-11-01

The Einstein particle mass ɛi is defined by the equation ɛi = Ei / c^2. The basic particle ground states have unique additive Einstein masses (energies), and they interleave in α-quantized (α-1 = 137) energy plots to form distinctive excitation patterns. The ɛu,d,s,c,b,t Einstein masses are constituent-quark masses. Particle generation proceeds via ``α-boosted'' boson, fermion, and gauge-boson ``unit masses,'' which are ``bundled'' together to form particles and quarks. The Einstein mass equations extend throughout the entire range of particle masses. Lederman and HillootnotetextL. M. Lederman and C. T. Hill, Symmetry (Prometheus Books, Amherst, 2004), p. 282. note that the scalar Higgs and Fermi fields are at the 175 GeV energy scale of the top quark t, and they suggest the Higgs coupling constant equation ge=me/mt = 0.0000029, which matches the Einstein mass expression ge=α^2/18.
Spin waves in fluids

NASA Technical Reports Server (NTRS)

Kistler, E. L.

1972-01-01

A working report is presented in order to document early results of research on the stability of laminar boundary layers. The report shows that constitutive equations for a structured continua may be derived by the technique of reinterpreting velocity in the conventional stress to rate-of-strain relationship so as to account for effects of particle rotation. It is demonstrated that accounting for particle structure even at a molecular level makes the fluid viscoelastic with the ability to propagate vector waves. It is shown that particle structure modifies the basic stability equation for the system, which in turn would alter values for critical Reynolds number.
Zubarev's Nonequilibrium Statistical Operator Method in the Generalized Statistics of Multiparticle Systems

NASA Astrophysics Data System (ADS)

Glushak, P. A.; Markiv, B. B.; Tokarchuk, M. V.

2018-01-01

We present a generalization of Zubarev's nonequilibrium statistical operator method based on the principle of maximum Renyi entropy. In the framework of this approach, we obtain transport equations for the basic set of parameters of the reduced description of nonequilibrium processes in a classical system of interacting particles using Liouville equations with fractional derivatives. For a classical systems of particles in a medium with a fractal structure, we obtain a non-Markovian diffusion equation with fractional spatial derivatives. For a concrete model of the frequency dependence of a memory function, we obtain generalized Kettano-type diffusion equation with the spatial and temporal fractality taken into account. We present a generalization of nonequilibrium thermofield dynamics in Zubarev's nonequilibrium statistical operator method in the framework of Renyi statistics.
Particle circulation and solids transport in large bubbling fluidized beds. Progress report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Homsy, G.M.

1982-04-01

We have undertaken a theoretical study of the possibility of the formation of plumes or channeling when coal particles volatilize upon introduction to a fluidized bed, Fitzgerald (1980). We have completed the analysis of the basic state of uniform flow and are currently completing a stability analysis. We have modified the continuum equations of fluidization, Homsy et al. (1980), to include the source of gas due to volatilization, which we assume to be uniformly distributed spatially. Simplifying these equations and solving leads to the prediction of a basic state analogous to the state of uniform fluidization found when no sourcemore » is present within the medium. We are currently completing a stability analysis of this basic state which will give the critical volatilization rate above which the above simple basic state is unstable. Because of the experimental evidence of Jewett and Lawless (1981), who observed regularly spaced plume-like instabilities upon drying a bed of saturated silica gel, we are considering two-dimensional periodic disturbances. The analysis is similar to that given by Homsy, et al. (1980) and Medlin et al. (1974). We hope to determine the stability limits for this system shortly.« less
Absorbing Boundary Conditions in Quantum Relativistic Mechanics for Spinless Particles Subject to a Classical Electromagnetic Field

NASA Astrophysics Data System (ADS)

Sater, Julien

The theory of Artificial Boundary Conditions described by Antoine et al. [2,4-6] for the Schrodinger equation is applied to the Klein-Gordon (KG) in two-dimensions (2-D) for spinless particles subject to electromagnetic fields. We begin by providing definitions for a basic understanding of the theory of operators, differential geometry and wave front sets needed to discuss the factorization theorem thanks to Nirenberg and Hormander [14, 16]. The laser-free Klein-Gordon equation in 1-D is then discussed, followed by the case including electrodynamics potentials, concluding with the KG equation in 2-D space with electrodynamics potentials. We then consider numerical simulations of the laser-particle KG equation, which includes a brief analysis of a finite difference scheme. The conclusion integrates a discussion of the numerical results, the successful completion of the objective set forth, a declaration of the unanswered encountered questions and a suggestion of subjects for further research.
Artificial magnetic field for the space station (Protecting space stations in future space missions)

NASA Astrophysics Data System (ADS)

Ahmadi Tara, Miss

Problem Explanation Strong solar storms and cosmic rays make great disturbances for equip-ment outside the magnetosphere. Also these disturbances are so harmful for biological process of living cells. If one decides to stay more outside the Earth, one's healthy is in a great danger. To investigate space station situation against strong solar storms, 5 recent strong solar storms have been selected. Dst of these storms are more than -300 nT. Each one of these storms has an accurate danger percentage. These data has been shown in Tab I. Tab I. strong solar storms during 1989-2003 and their danger percentage for space equipments and astronauts on outside the magnetic field As has been shown in Tab I. these strong storms are so dangerous and make problem for human outside the Earth layers. Basic on [13] solar activities in next century will be more than this century. That paper shows that the average number of sunspots in this century is less than 77 and this average will be more than 150 sunspots in a century. So we have only 70 years to prepare a suitable space station in other wise building this centre wills has many problem such as health security and long travels. Method explanation Only method to face with energetic particles is magnetic field. Space station is bereft of strong magnetic field to protect herself from energetic particles that released from the Sun and other types of stars in other galaxies (cosmic rays). Therefore the existence of an artificial magnetic field is necessary, this is not important that this field will be for the space station or its inner space because this field performs as magnetosphere. It does not allow energetic particles to enter the field. Also this field loads up to solar magnetic field as magnetosphere. Position of this artificial field is not important because basic on the simulations this field could repulse 85.6Modeling Important feature of this artificial field is its situation against solar magnetic field, i.e. these fields always are anti-aligned because artificial field could change direction by itself basic on the situation of Sun. Relationship between artificial field and solar storm has two types: 1) Artifi-cial field loads up to solar storm's magnetic field and makes magnetic reconnection 2) artificial field repulses energetic solar particles. These below equations show situation of artificial field against magnetic reconnection with magnetic field of solar storm and repulsing particles. Basic on the volume of repulsed particles the strength of field could be: Each one of these storms has an accurate danger percentage. These data has been shown in Tab I. Tab I. strong solar storms during 1989-2003 and their danger percentage for space equipments and astronauts on outside the magnetic field As has been shown in Tab I. these strong storms are so dangerous and make problem for human outside the Earth layers. Basic on [13] solar activities in next century will be more than this century. That paper shows that the average number of sunspots in this century is less than 77 and this average will be more than 150 sunspots in a century. So we have only 70 years to prepare a suitable space station in other wise building this centre wills has many problem such as health security and long travels. Method explanation Only method to face with energetic particles is magnetic field. Space station is bereft of strong magnetic field to protect herself from energetic particles that released from the Sun and other types of stars in other galaxies (cosmic rays). Therefore the existence of an artificial magnetic field is necessary, this is not important that this field will be for the space station or its inner space because this field performs as magnetosphere. It does not allow energetic particles to enter the field. Also this field loads up to solar magnetic field as magnetosphere. Position of this artificial field is not important because basic on the simulations this field could repulse 85.6Modeling Important feature of this artificial field is its situation against solar magnetic field, i.e. these fields always are anti-aligned because artificial field could change direction by itself basic on the situation of Sun. Relationship between artificial field and solar storm has two types: 1) Artificial field loads up to solar storm's magnetic field and makes magnetic reconnection 2) ar-tificial field repulses energetic solar particles. These below equations show situation of artificial field against magnetic reconnection with magnetic field of solar storm and repulsing particles. Basic on the volume of repulsed particles the strength of field could be: General equation of artificial field: Equations of artificial field basic on the magnetic reconnection: Also equation of balance of electrical energy is: That , V and P are denoting respectively density, velocity and pressure. is plasma energy density. J= current density, Bo =artificial magnetic field, B,E=plasma magnetic and electric field. Vs=volume of a sphere with r radius and =resistance General equation of artificial field: Equations of artificial field basic on the magnetic reconnec-tion: Also equation of balance of electrical energy is: That , V and P are denoting respectively density, velocity and pressure. is plasma energy density. J= current density, Bo =artificial magnetic field, B,E=plasma magnetic and electric field. Vs=volume of a sphere with r radius and =resistance Results Tab II. Danger percentage of 5 strong solar storms for equipment and astronauts in the future space station within the influence on artificial field As has been shown in Tab II artificial magnetic field could pass great dangers of solar storms and protect space station wherever of free space. FIG.2) Upper panel shows X-ray flux at two wavelengths 0.5-4 ˚ and 1-8 ˚. Lower Panel shows Proton flux in various energy levels received on the Moon's A A surface from solar storm 2000(obtained from simulation) 0-14(UT) obtained from outside the field, 14-7(UT) obtained from receiver in the field, 7-0(UT) obtained from receiver behind in-strument Conclusion In this brief paper, I describe a way to protect future space station from energetic particles. This field could reduce damage of solar storms and cosmic rays that arrived to the space station outside the Earth magnetic field. This field performs as magnetosphere for space station. It could change its situation and make easy live on the space station. This strong magnetic field must be generated by low-temperature superconductors. They are suit-able material to use at generating a strong magnetic field. These materials could be used in the structure of spacecrafts during long duration space travels in future
Radiation effects in accelerator components

NASA Astrophysics Data System (ADS)

Borden, M. J.

1995-05-01

A review of basic radiation effects is presented. The fundamental definitions of radioactivity are given for alpha, beta, positron decay, gamma-ray emission and electron capture. The interaction of neutrons with material is covered including: absorption through radiative capture, neutron-proton interaction, alpha particle emission, neutron-multi-neutron reactions and fission. Basic equations defining inelastic and elastic scattering are presented with examples of neutron energy loss per collision for several elements. Photon interactions are considered for gamma-rays and x-rays. Photoelectric collisions, the Compton effect and pair production are reviewed. Electron-proton interactions are discussed with emphasis placed on defect production. Basic displacement damage mechanisms for photon and particle interaction are presented. Several examples of radiation effects to plastics, electronics and ceramics are presented. Extended references are given for each example.

Relativistic theory of particles in a scattering flow I: basic equations, diffusion and drift.

NASA Astrophysics Data System (ADS)

Achterberg, A.; Norman, C. A.

2018-06-01

We reconsider the theory of particle transport in a scattering medium, allowing for relativistic flow velocities. The theory uses a mixed set of variables, with position and time measured in the Laboratory Frame, and particle energy and momentum measured in the Fluid Rest Frame, the reference frame where scattering is assumed to be elastic. We give a new derivation for the fictitious force terms in the equation of motion that are present if the Fluid Rest Frame is not an inertial frame. By using a 3+1 notation we discuss the physical interpretation of the different terms in the fictitious force. It is shown that different approaches to the problem of particle propagation in a magnetized medium due to Skilling (1975) and Kulsrud (1983) are largely equivalent. We extend known results for non-relativistic flows to include the effects of cross-field diffusion for cosmic rays in a magnetized plasma. We also carefully consider the correct form of the diffusion approximation for scattering, and show that the resulting equations can be cast in conservation form.
Charged particle concepts for fog dispersion

NASA Technical Reports Server (NTRS)

Frost, W.; Collins, F. G.; Koepf, D.

1981-01-01

Charged particle techniques hold promise for dispersing warm fog in the terminal area of commercial airports. This report focuses on features of the charged particle technique which require further study. The basic physical principles of the technique and the major verification experiments carried out in the past are described. The fundamentals of the nozzle operation are given. The nozzle characteristics and the theory of particle charging in the nozzle are discussed, including information from extensive literature on electrostatic precipitation relative to environmental pollution control and a description of some preliminary reported analyses on the jet characteristics and interaction with neighboring jets. The equation governing the transfer of water substances and of electrical charge is given together with a brief description of several semi-empirical, mathematical expressions necessary for the governing equations. The necessary ingredients of a field experiment to verify the system once a prototype is built are described.
A Concise Introduction to Quantum Mechanics

NASA Astrophysics Data System (ADS)

Swanson, Mark S.

2018-02-01

Assuming a background in basic classical physics, multivariable calculus, and differential equations, A Concise Introduction to Quantum Mechanics provides a self-contained presentation of the mathematics and physics of quantum mechanics. The relevant aspects of classical mechanics and electrodynamics are reviewed, and the basic concepts of wave-particle duality are developed as a logical outgrowth of experiments involving blackbody radiation, the photoelectric effect, and electron diffraction. The Copenhagen interpretation of the wave function and its relation to the particle probability density is presented in conjunction with Fourier analysis and its generalization to function spaces. These concepts are combined to analyze the system consisting of a particle confined to a box, developing the probabilistic interpretation of observations and their associated expectation values. The Schrödinger equation is then derived by using these results and demanding both Galilean invariance of the probability density and Newtonian energy-momentum relations. The general properties of the Schrödinger equation and its solutions are analyzed, and the theory of observables is developed along with the associated Heisenberg uncertainty principle. Basic applications of wave mechanics are made to free wave packet spreading, barrier penetration, the simple harmonic oscillator, the Hydrogen atom, and an electric charge in a uniform magnetic field. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented and used to analyze coherent states, the linear potential, two state oscillations, and electron diffraction. Applications are made to photon and electron spin and the addition of angular momentum, and direct product multiparticle states are used to formulate both the Pauli exclusion principle and quantum decoherence. The book concludes with an introduction to the rotation group and the general properties of angular momentum.
A Gas-Kinetic Scheme for Reactive Flows

NASA Technical Reports Server (NTRS)

Lian,Youg-Sheng; Xu, Kun

1998-01-01

In this paper, the gas-kinetic BGK scheme for the compressible flow equations is extended to chemical reactive flow. The mass fraction of the unburnt gas is implemented into the gas kinetic equation by assigning a new internal degree of freedom to the particle distribution function. The new variable can be also used to describe fluid trajectory for the nonreactive flows. Due to the gas-kinetic BGK model, the current scheme basically solves the Navier-Stokes chemical reactive flow equations. Numerical tests validate the accuracy and robustness of the current kinetic method.
Freak oscillation in a dusty plasma.

PubMed

Zhang, Heng; Yang, Yang; Hong, Xue-Ren; Qi, Xin; Duan, Wen-Shan; Yang, Lei

2017-05-01

The freak oscillation in one-dimensional dusty plasma is studied numerically by particle-in-cell method. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the rogue waves in dusty plasma. Additionally, the application scope of the analytical solution of the rogue wave described by the NLSE is given.
Supersonic Flow of Chemically Reacting Gas-Particle Mixtures. Volume 2: RAMP - A Computer Code for Analysis of Chemically Reacting Gas-Particle Flows

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Anderson, P. G.; Sulyma, P. R.; Pearson, M. L.

1976-01-01

A computer program written in conjunction with the numerical solution of the flow of chemically reacting gas-particle mixtures was documented. The solution to the set of governing equations was obtained by utilizing the method of characteristics. The equations cast in characteristic form were shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The characteristic directions for the gas-particle system are found to be the conventional gas Mach lines, the gas streamlines and the particle streamlines. The basic mesh construction for the flow solution is along streamlines and normals to the streamlines for axisymmetric or two-dimensional flow. The analysis gives detailed information of the supersonic flow and provides for a continuous solution of the nozzle and exhaust plume flow fields. Boundary conditions for the flow solution are either the nozzle wall or the exhaust plume boundary.
A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu

2016-07-15

Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished bymore » allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.« less
Visual Basic VPython Interface: Charged Particle in a Magnetic Field

NASA Astrophysics Data System (ADS)

Prayaga, Chandra

2006-12-01

A simple Visual Basic (VB) to VPython interface is described and illustrated with the example of a charged particle in a magnetic field. This interface allows data to be passed to Python through a text file read by Python. The first component of the interface is a user-friendly data entry screen designed in VB, in which the user can input values of the charge, mass, initial position and initial velocity of the particle, and the magnetic field. Next, a command button is coded to write these values to a text file. Another command button starts the VPython program, which reads the data from the text file, numerically solves the equation of motion, and provides the 3d graphics animation. Students can use the interface to run the program several times with different data and observe changes in the motion.
Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface

NASA Astrophysics Data System (ADS)

Shao, Songdong; Lo, Edmond Y. M.

An incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces. The basic equations solved are the incompressible mass conservation and Navier-Stokes equations. The method uses prediction-correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting deviation of particle density is then implicitly projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. Various SPH formulations are employed in the discretization of the relevant gradient, divergence and Laplacian terms. Free surfaces are identified by the particles whose density is below a set point. Wall boundaries are represented by particles whose positions are fixed. The SPH formulation is also extended to non-Newtonian flows and demonstrated using the Cross rheological model. The incompressible SPH method is tested by typical 2-D dam-break problems in which both water and fluid mud are considered. The computations are in good agreement with available experimental data. The different flow features between Newtonian and non-Newtonian flows after the dam-break are discussed.
Dilation and breakage dissipation of granular soils subjected to monotonic loading

NASA Astrophysics Data System (ADS)

Sun, Yifei; Xiao, Yang; Ji, Hua

2016-12-01

Dilation and breakage energy dissipation of four different granular soils are investigated by using an energy balance equation. Due to particle breakage, the dilation curve does not necessarily pass through the origin of coordinates. Breakage energy dissipation is found to increase significantly at the initial loading stage and then gradually become stabilised. The incremental dissipation ratio between breakage energy and plastic work exhibits almost independence of the confining pressure. Accordingly, a plastic flow rule considering the effect of particle breakage is suggested. The critical state friction angle is found to be a combination of the basic friction between particles and the friction contributed by particle breakage.
Steady-State Ion Beam Modeling with MICHELLE

NASA Astrophysics Data System (ADS)

Petillo, John

2003-10-01

There is a need to efficiently model ion beam physics for ion implantation, chemical vapor deposition, and ion thrusters. Common to all is the need for three-dimensional (3D) simulation of volumetric ion sources, ion acceleration, and optics, with the ability to model charge exchange of the ion beam with a background neutral gas. The two pieces of physics stand out as significant are the modeling of the volumetric source and charge exchange. In the MICHELLE code, the method for modeling the plasma sheath in ion sources assumes that the electron distribution function is a Maxwellian function of electrostatic potential over electron temperature. Charge exchange is the process by which a neutral background gas with a "fast" charged particle streaming through exchanges its electron with the charged particle. An efficient method for capturing this is essential, and the model presented is based on semi-empirical collision cross section functions. This appears to be the first steady-state 3D algorithm of its type to contain multiple generations of charge exchange, work with multiple species and multiple charge state beam/source particles simultaneously, take into account the self-consistent space charge effects, and track the subsequent fast neutral particles. The solution used by MICHELLE is to combine finite element analysis with particle-in-cell (PIC) methods. The basic physics model is based on the equilibrium steady-state application of the electrostatic particle-in-cell (PIC) approximation employing a conformal computational mesh. The foundation stems from the same basic model introduced in codes such as EGUN. Here, Poisson's equation is used to self-consistently include the effects of space charge on the fields, and the relativistic Lorentz equation is used to integrate the particle trajectories through those fields. The presentation will consider the complexity of modeling ion thrusters.
Fractional Klein-Gordon equation composed of Jumarie fractional derivative and its interpretation by a smoothness parameter

NASA Astrophysics Data System (ADS)

Ghosh, Uttam; Banerjee, Joydip; Sarkar, Susmita; Das, Shantanu

2018-06-01

Klein-Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein-Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein-Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein-Gordon equation, we can overcome the problem. The fractional Klein-Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases.
A stratospheric aerosol model with perturbations induced by the space shuttle particulate effluents

NASA Technical Reports Server (NTRS)

Rosen, J. M.; Hofmann, D. J.

1977-01-01

A one dimensional steady state stratospheric aerosol model is developed that considers the subsequent perturbations caused by including the expected space shuttle particulate effluents. Two approaches to the basic modeling effort were made: in one, enough simplifying assumptions were introduced so that a more or less exact solution to the descriptive equations could be obtained; in the other approach very few simplifications were made and a computer technique was used to solve the equations. The most complex form of the model contains the effects of sedimentation, diffusion, particle growth and coagulation. Results of the perturbation calculations show that there will probably be an immeasurably small increase in the stratospheric aerosol concentration for particles larger than about 0.15 micrometer radius.
Separated spin-up and spin-down quantum hydrodynamics of degenerated electrons: Spin-electron acoustic wave appearance.

PubMed

Andreev, Pavel A

2015-03-01

The quantum hydrodynamic (QHD) model of charged spin-1/2 particles contains physical quantities defined for all particles of a species including particles with spin-up and with spin-down. Different populations of states with different spin directions are included in the spin density (the magnetization). In this paper I derive a QHD model, which separately describes spin-up electrons and spin-down electrons. Hence electrons with different projections of spins on the preferable direction are considered as two different species of particles. It is shown that the numbers of particles with different spin directions do not conserve. Hence the continuity equations contain sources of particles. These sources are caused by the interactions of the spins with the magnetic field. Terms of similar nature arise in the Euler equation. The z projection of the spin density is no longer an independent variable. It is proportional to the difference between the concentrations of the electrons with spin-up and the electrons with spin-down. The propagation of waves in the magnetized plasmas of degenerate electrons is considered. Two regimes for the ion dynamics, the motionless ions and the motion of the degenerate ions as the single species with no account of the spin dynamics, are considered. It is shown that this form of the QHD equations gives all solutions obtained from the traditional form of QHD equations with no distinction of spin-up and spin-down states. But it also reveals a soundlike solution called the spin-electron acoustic wave. Coincidence of most solutions is expected since this derivation was started with the same basic equation: the Pauli equation. Solutions arise due to the different Fermi pressures for the spin-up electrons and the spin-down electrons in the magnetic field. The results are applied to degenerate electron gas of paramagnetic and ferromagnetic metals in the external magnetic field. The dispersion of the spin-electron acoustic waves in the partially spin-polarized degenerate neutron matter are also considered.
A technique to remove the tensile instability in weakly compressible SPH

NASA Astrophysics Data System (ADS)

Xu, Xiaoyang; Yu, Peng

2018-01-01

When smoothed particle hydrodynamics (SPH) is directly applied for the numerical simulations of transient viscoelastic free surface flows, a numerical problem called tensile instability arises. In this paper, we develop an optimized particle shifting technique to remove the tensile instability in SPH. The basic equations governing free surface flow of an Oldroyd-B fluid are considered, and approximated by an improved SPH scheme. This includes the implementations of the correction of kernel gradient and the introduction of Rusanov flux into the continuity equation. To verify the effectiveness of the optimized particle shifting technique in removing the tensile instability, the impacting drop, the injection molding of a C-shaped cavity, and the extrudate swell, are conducted. The numerical results obtained are compared with those simulated by other numerical methods. A comparison among different numerical techniques (e.g., the artificial stress) to remove the tensile instability is further performed. All numerical results agree well with the available data.
SEDIDAT: A BASIC program for the collection and statistical analysis of particle settling velocity data

NASA Astrophysics Data System (ADS)

Wright, Robyn; Thornberg, Steven M.

SEDIDAT is a series of compiled IBM-BASIC (version 2.0) programs that direct the collection, statistical calculation, and graphic presentation of particle settling velocity and equivalent spherical diameter for samples analyzed using the settling tube technique. The programs follow a menu-driven format that is understood easily by students and scientists with little previous computer experience. Settling velocity is measured directly (cm,sec) and also converted into Chi units. Equivalent spherical diameter (reported in Phi units) is calculated using a modified Gibbs equation for different particle densities. Input parameters, such as water temperature, settling distance, particle density, run time, and Phi;Chi interval are changed easily at operator discretion. Optional output to a dot-matrix printer includes a summary of moment and graphic statistical parameters, a tabulation of individual and cumulative weight percents, a listing of major distribution modes, and cumulative and histogram plots of a raw time, settling velocity. Chi and Phi data.
QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

NASA Astrophysics Data System (ADS)

Kiršanskas, Gediminas; Pedersen, Jonas Nyvold; Karlström, Olov; Leijnse, Martin; Wacker, Andreas

2017-12-01

QmeQ is an open-source Python package for numerical modeling of transport through quantum dot devices with strong electron-electron interactions using various approximate master equation approaches. The package provides a framework for calculating stationary particle or energy currents driven by differences in chemical potentials or temperatures between the leads which are tunnel coupled to the quantum dots. The electronic structures of the quantum dots are described by their single-particle states and the Coulomb matrix elements between the states. When transport is treated perturbatively to lowest order in the tunneling couplings, the possible approaches are Pauli (classical), first-order Redfield, and first-order von Neumann master equations, and a particular form of the Lindblad equation. When all processes involving two-particle excitations in the leads are of interest, the second-order von Neumann approach can be applied. All these approaches are implemented in QmeQ. We here give an overview of the basic structure of the package, give examples of transport calculations, and outline the range of applicability of the different approximate approaches.
Test particle propagation in magnetostatic turbulence. 2: The local approximation method

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Sandri, G.; Scudder, J. D.; Howell, D. R.

1976-01-01

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.
Some examples of exact and approximate solutions in small particle scattering - A progress report

NASA Technical Reports Server (NTRS)

Greenberg, J. M.

1974-01-01

The formulation of basic equations from which the scattering of radiation by a localized variation in a medium is discussed. These equations are developed in both the differential and the integral form. Primary interest is in the scattering of electromagnetic waves for which the solution of the vector wave equation with appropriate boundary conditions must be considered. Scalar scattering by an infinite homogeneous isotropic circular cylinder, and scattering of electromagnetic waves by infinite circular cylinders are treated, and the case of the finite circular cylinder is considered. A procedure is given for obtaining angular scattering distributions from spheroids.
Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Physics, mathematics and numerics of particle adsorption on fluid interfaces

NASA Astrophysics Data System (ADS)

Schmuck, Markus; Pavliotis, Grigorios A.; Kalliadasis, Serafim

2012-11-01

We study two arbitrary immiscible fuids where one phase contains small particles of the size of the interface and smaller. We primarily focus on charge-free particles with wetting characteristics described by the contact angle formed at the interface between the two phases and the particles. Based on the experimental observation that particles are adsorbed on the interface to reduce the interfacial energy and hence the surface tension as well, we formulate a free-energy functional that accounts for these physical effects. Using elements from calculus of variations and formal gradient flow theory, we derive partial differential equations describing the location of the interface and the density of the particles in the fluid phases. Via numerical experiments we analyse the time evolution of the surface tension, the particle concentration, and the free energy over time and reflect basic experimentally observed phenomena.
Basic Equations Interrelate Atomic and Nuclear Properties to Patterns at the Size Scales of the Cosmos, Extended Clusters of Galaxies, Galaxies, and Nebulae

NASA Astrophysics Data System (ADS)

Allen, Rob

2016-09-01

Structures within molecules and nuclei have relationships to astronomical patterns. The COBE cosmic scale plots, and large scale surveys of galaxy clusters have patterns also repeating and well known at atomic scales. The Induction, Strong Force, and Nuclear Binding Energy Periods within the Big Bang are revealed to have played roles in the formation of these large scale distributions. Equations related to the enormous patterns also model chemical bonds and likely nucleus and nucleon substructures. ratios of the forces that include gravity are accurately calculated from the distributions and shapes. In addition, particle masses and a great many physical constants can be derived with precision and accuracy from astrophysical shapes. A few very basic numbers can do modelling from nucleon internals to molecules to super novae, and up to the Visible Universe. Equations are also provided along with possible structural configurations for some Cold Dark Matter and Dark Energy.
STEADY-STATE MODEL OF SOLAR WIND ELECTRONS REVISITED

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoon, Peter H.; Kim, Sunjung; Choe, G. S., E-mail: yoonp@umd.edu

2015-10-20

In a recent paper, Kim et al. put forth a steady-state model for the solar wind electrons. The model assumed local equilibrium between the halo electrons, characterized by an intermediate energy range, and the whistler-range fluctuations. The basic wave–particle interaction is assumed to be the cyclotron resonance. Similarly, it was assumed that a dynamical steady state is established between the highly energetic superhalo electrons and high-frequency Langmuir fluctuations. Comparisons with the measured solar wind electron velocity distribution function (VDF) during quiet times were also made, and reasonable agreements were obtained. In such a model, however, only the steady-state solution for themore » Fokker–Planck type of electron particle kinetic equation was considered. The present paper complements the previous analysis by considering both the steady-state particle and wave kinetic equations. It is shown that the model halo and superhalo electron VDFs, as well as the assumed wave intensity spectra for the whistler and Langmuir fluctuations, approximately satisfy the quasi-linear wave kinetic equations in an approximate sense, thus further validating the local equilibrium model constructed in the paper by Kim et al.« less
The quantum universe

NASA Astrophysics Data System (ADS)

Hey, Anthony J. G.; Walters, Patrick

This book provides a descriptive, popular account of quantum physics. The basic topics addressed include: waves and particles, the Heisenberg uncertainty principle, the Schroedinger equation and matter waves, atoms and nuclei, quantum tunneling, the Pauli exclusion principle and the elements, quantum cooperation and superfluids, Feynman rules, weak photons, quarks, and gluons. The applications of quantum physics to astrophyics, nuclear technology, and modern electronics are addressed.
General equations for the motions of ice crystals and water drops in gravitational and electric fields

NASA Technical Reports Server (NTRS)

Nisbet, John S.

1988-01-01

General equations for the Reynolds number of a variety of types of ice crystals and water drops are given in terms of the Davies, Bond, and Knudsen numbers. The equations are in terms of the basic physical parameters of the system and are valid for calculating velocities in gravitational and electric fields over a very wide range of sizes and atmospheric conditions. The equations are asymptotically matched at the bottom and top of the size spectrum, useful when checking large computer codes. A numerical system for specifying the dimensional properties of ice crystals is introduced. Within the limits imposed by such variables as particle density, which have large deviations, the accuracy of velocities appears to be within 10 percent over the entire range of sizes of interest.
Book Review: Book review

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.

2017-01-01

The second - revised and enlarged - edition of this popular monograph is co-authored by Michael Kahnert and is published as Volume 145 of the Springer Series in Optical Sciences. As in the first edition, the main emphasis is on the mathematics of electromagnetic scattering and on numerically exact computer solutions of the frequency-domain macroscopic Maxwell equations for particles with complex shapes. The book is largely centered on Green-function solution of relevant boundary value problems and the T-matrix methodology, although other techniques (the method of lines, integral equation methods, and Lippmann-Schwinger equations) are also covered. The first four chapters serve as a thorough overview of key theoretical aspects of electromagnetic scattering intelligible to readers with undergraduate training in mathematics. A separate chapter provides an instructive analysis of the Rayleigh hypothesis which is still viewed by many as a highly controversial aspect of electromagnetic scattering by nonspherical objects. Another dedicated chapter introduces basic quantities serving as optical observables in practical applications. A welcome extension of the first edition is the new chapter on group theoretical aspects of electromagnetic scattering by particles with discrete symmetries. An essential part of the book is the penultimate chapter describing in detail popular public-domain computer programs mieschka and Tsym which can be applied to a wide range of particle shapes. The final chapter provides a general overview of available literature on electromagnetic scattering by particles and gives useful reading advice.
Introducing the Dimensional Continuous Space-Time Theory

NASA Astrophysics Data System (ADS)

Martini, Luiz Cesar

2013-04-01

This article is an introduction to a new theory. The name of the theory is justified by the dimensional description of the continuous space-time of the matter, energy and empty space, that gathers all the real things that exists in the universe. The theory presents itself as the consolidation of the classical, quantum and relativity theories. A basic equation that describes the formation of the Universe, relating time, space, matter, energy and movement, is deduced. The four fundamentals physics constants, light speed in empty space, gravitational constant, Boltzmann's constant and Planck's constant and also the fundamentals particles mass, the electrical charges, the energies, the empty space and time are also obtained from this basic equation. This theory provides a new vision of the Big-Bang and how the galaxies, stars, black holes and planets were formed. Based on it, is possible to have a perfect comprehension of the duality between wave-particle, which is an intrinsic characteristic of the matter and energy. It will be possible to comprehend the formation of orbitals and get the equationing of atomics orbits. It presents a singular comprehension of the mass relativity, length and time. It is demonstrated that the continuous space-time is tridimensional, inelastic and temporally instantaneous, eliminating the possibility of spatial fold, slot space, worm hole, time travels and parallel universes. It is shown that many concepts, like dark matter and strong forces, that hypothetically keep the cohesion of the atomics nucleons, are without sense.
Digital quantum simulation of Dirac equation with a trapped ion

NASA Astrophysics Data System (ADS)

Shen, Yangchao; Zhang, Xiang; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jingning; Kim, Kihwan; Department Of Physical Chemistry Collaboration

2014-05-01

Recently there has been growing interest in simulating relativistic effects in controllable physical system. We digitally simulate the Dirac equation in 3 +1 dimensions with a single trapped ion. We map four internal levels of 171Yb+ ion to the Dirac bispinor. The time evolution of the Dirac equation is implemented by trotter expansion. In the 3 +1 dimension, we can observe a helicoidal motion of a free Dirac particle which reduces to Zitterbewegung in 1 +1 dimension. This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00301, the National Natural Science Foundation of China Grant 61033001, 61061130540. KK acknowledge the support from the recruitment program of global youth experts.
Oblique Propagation of Electrostatic Waves in a Magnetized Electron-Positron-Ion Plasma in the Presence of Heavy Particles

NASA Astrophysics Data System (ADS)

Sarker, M.; Hossen, M. R.; Shah, M. G.; Hosen, B.; Mamun, A. A.

2018-06-01

A theoretical investigation is carried out to understand the basic features of nonlinear propagation of heavy ion-acoustic (HIA) waves subjected to an external magnetic field in an electron-positron-ion plasma that consists of cold magnetized positively charged heavy ion fluids and superthermal distributed electrons and positrons. In the nonlinear regime, the Korteweg-de Vries (K-dV) and modified K-dV (mK-dV) equations describing the propagation of HIA waves are derived. The latter admits a solitary wave solution with both positive and negative potentials (for K-dV equation) and only positive potential (for mK-dV equation) in the weak amplitude limit. It is observed that the effects of external magnetic field (obliqueness), superthermal electrons and positrons, different plasma species concentration, heavy ion dynamics, and temperature ratio significantly modify the basic features of HIA solitary waves. The application of the results in a magnetized EPI plasma, which occurs in many astrophysical objects (e.g. pulsars, cluster explosions, and active galactic nuclei) is briefly discussed.
Computational Science: Ensuring America’s Competitiveness

DTIC Science & Technology

2005-06-01

Supercharging U. S. Innovation & Competitiveness, Washington, D.C. , July 2004. Davies, C. T. H. , et al. , “High-Precision Lattice QCD Confronts Experiment...together to form a class of particles call hadrons (that include protons and neutrons) . For 30 years, researchers in lattice QCD have been trying to use...the basic QCD equations to calculate the properties of hadrons, especially their masses, using numerical lattice gauge theory calculations in order to
Developments in the kinetic theories of ion and electron swarms in the 1960s and 70s

NASA Astrophysics Data System (ADS)

Skullerud, H. R.

2017-04-01

The two decades between 1960 to 1980 saw quite a fantastic development in diverse areas in physics, and so also in the quantitative theoretical treatment and deeper understanding of the behaviour of isolated electrons and ions in gases—that is ‘charged particle swarm physics’. The evolution in swarm theory was strongly correlated with the contemporary advances in computer technology and the emergence of new and accurate experimental methods for finding charged particle transport parameters, as drift velocities, diffusion coefficients and reaction rates, and also with developments in neighbouring fields as plasma physics and the physics of electronic and molecular collisions. In 1960, low energy electron behaviour could already be calculated with reasonable accuracy in the so-called two-term approximation, while ion behaviour could only be treated at weak electric fields. By 1980, reasonably complete theories had been developed for perhaps most cases in interest—which is reflected in a number of reviews, books and journal articles published in the early 1980s. We will present a journey through the developments in this period and the basic theories behind the Boltzmann equation and Maxwell’s transfer equations. We will also indicate how the interaction between different studies of the same basic processes have led to the elimination of shortcomings and a better understanding.
Hyperunified field theory and gravitational gauge-geometry duality

NASA Astrophysics Data System (ADS)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.
An initial physical mechanism in the treatment of neurologic disorders with externally applied pico Tesla magnetic fields.

PubMed

Jacobson, J I; Yamanashi, W S

1995-04-01

The recent clinical studies describing the treatment of some neurological disorders with an externally applied pico Tesla (10(-12) Tesla, or 10(-8) gauss) magnetic field are considered from a physical view point. An equation relating the intrinsic (or rest) energy of a charged particle of mass m with its energy of interaction in an externally applied magnetic field B is presented. The equation represents an initial basic physical interaction as a part of a more complex biological mechanism to explain the therapeutic effects of externally applied magnetic fields in these and other neurologic disorders.
A physical mechanism in the treatment of neurologic disorders with externally applied pico Tesla magnetic fields.

PubMed

Jacobson, J I; Yamanashi, W S

1995-06-01

The clinical studies describing the treatment of some neurological disorders with an externally applied pico Tesla (10R Tesla, or 10(-8) gauss) magnetic field are considered from a physical view point. An equation relating the intrinsic or "rest" energy of a charged particle of mass with its energy of interaction in an externally applied magnetic field B is presented. The equation is proposed to represent an initial basic physical interaction as a part of a more complex biological mechanism to explain the therapeutic effects of externally applied magnetic fields in these and other neurologic disorders.
Effective friction of granular flows made of non-spherical particles

NASA Astrophysics Data System (ADS)

Somfai, Ellák; Nagy, Dániel B.; Claudin, Philippe; Favier, Adeline; Kálmán, Dávid; Börzsönyi, Tamás

2017-06-01

Understanding the rheology of dense granular matter is a long standing problem and is important both from the fundamental and the applied point of view. As the basic building blocks of granular materials are macroscopic particles, the nature of both the response to deformations and the dissipation is very different from that of molecular materials. In the absence of large gradients, the best approach formulates the constitutive equation as an effective friction: for sheared granular matter the ratio of the off-diagonal and the diagonal elements of the stress tensor depends only on dynamical parameters, in particular the inertial number. In this work we employ numerical simulations to extend this formalism to granular packings made of frictionless elongated particles. We measured how the shape of the particles affects the effective friction, volume fraction and first normal stress difference, and compared it to the spherical particle case. We had to introduce polydispersity in particle size in order to keep the systems of the more elongated particles disordered.
FLRW Cosmology from Yang-Mills Gravity

NASA Astrophysics Data System (ADS)

Katz, Daniel

2013-04-01

We extend to basic cosmology the subject of Yang-Mills gravity - a theory of gravity based on local translational gauge invariance in flat spacetime. It has been shown that this particular gauge invariance leads to tensor factors in the macroscopic limit of the equations of motion of particles which plays the same role as the metric tensor of General Relativity. The assumption that this ``effective metric" tensor takes on the standard FLRW form is our starting point. Equations analogous to the Friedman equations are derived and then solved in closed form for the three special cases of a universe dominated by 1) matter, 2) radiation, and 3) dark energy. We find that the solutions for the scale factor are similar to, but distinct from, those found in the corresponding GR based treatment.
Influence of Non-Maxwellian Particles on Dust Acoustic Waves in a Dusty Magnetized Plasma

NASA Astrophysics Data System (ADS)

M. Nouri, Kadijani; Zareamoghaddam, H.

2013-11-01

In this paper an investigation into dust acoustic solitary waves (DASWs) in the presence of superthermal electrons and ions in a magnetized plasma with cold dust grains and trapped electrons is discussed. The dynamic of both electrons and ions is simulated by the generalized Lorentzian (κ) distribution function (DF). The dust grains are cold and their dynamics are studied by hydrodynamic equations. The basic set of fluid equations is reduced to modified Korteweg-de Vries (mKdV) equation using Reductive Perturbation Theory (RPT). Two types of solitary waves, fast and slow dust acoustic soliton (DAS) exist in this plasma. Calculations reveal that compressive solitary structures are possibly propagated in the plasma where dust grains are negatively (or positively) charged. The properties of DASs are also investigated numerically.
Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply

NASA Astrophysics Data System (ADS)

Gavrilov, S. N.; Krivtsov, A. M.; Tsvetkov, D. V.

2018-05-01

We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear partial differential equations for covariance variables. An exact analytic solution describing unsteady ballistic heat transfer in the crystal is obtained. It is shown that the stationary spatial profile of the kinetic temperature caused by a point source of heat supply of constant intensity is described by the Macdonald function of zero order. A comparison with the results obtained in the framework of the classical heat equation is presented. We expect that the results obtained in the paper can be verified by experiments with laser excitation of low-dimensional nanostructures.
Cosmic-ray streaming perpendicular to the mean magnetic field. II - The gyrophase distribution function

NASA Technical Reports Server (NTRS)

Forman, M. A.; Jokipii, J. R.

1978-01-01

The distribution function of cosmic rays streaming perpendicular to the mean magnetic field in a turbulent medium is reexamined. Urch's (1977) discovery that in quasi-linear theory, the flux is due to particles at 90 deg pitch angle is discussed and shown to be consistent with previous formulations of the theory. It is pointed out that this flux of particles at 90 deg cannot be arbitrarily set equal to zero, and hence the alternative theory which proceeds from this premise is dismissed. A further, basic inconsistency in Urch's transport equation is demonstrated, and the connection between quasi-linear theory and compound diffusion is discussed.
Foundations of modelling of nonequilibrium low-temperature plasmas

NASA Astrophysics Data System (ADS)

Alves, L. L.; Bogaerts, A.; Guerra, V.; Turner, M. M.

2018-02-01

This work explains the need for plasma models, introduces arguments for choosing the type of model that better fits the purpose of each study, and presents the basics of the most common nonequilibrium low-temperature plasma models and the information available from each one, along with an extensive list of references for complementary in-depth reading. The paper presents the following models, organised according to the level of multi-dimensional description of the plasma: kinetic models, based on either a statistical particle-in-cell/Monte-Carlo approach or the solution to the Boltzmann equation (in the latter case, special focus is given to the description of the electron kinetics); multi-fluid models, based on the solution to the hydrodynamic equations; global (spatially-average) models, based on the solution to the particle and energy rate-balance equations for the main plasma species, usually including a very complete reaction chemistry; mesoscopic models for plasma-surface interaction, adopting either a deterministic approach or a stochastic dynamical Monte-Carlo approach. For each plasma model, the paper puts forward the physics context, introduces the fundamental equations, presents advantages and limitations, also from a numerical perspective, and illustrates its application with some examples. Whenever pertinent, the interconnection between models is also discussed, in view of multi-scale hybrid approaches.

Gravity and Zero Point Energy

NASA Astrophysics Data System (ADS)

Massie, U. W.

When Planck introduced the 1/2 hv term to his 1911 black body equation he showed that there is a residual energy remaining at zero degree K after all thermal energy ceased. Other investigators, including Lamb, Casimir, and Dirac added to this information. Today zero point energy (ZPE) is accepted as an established condition. The purpose of this paper is to demonstrate that the density of the ZPE is given by the gravity constant (G) and the characteristics of its particles are revealed by the cosmic microwave background (CMB). Eddies of ZPE particles created by flow around mass bodies reduce the pressure normal to the eddy flow and are responsible for the force of gravity. Helium atoms resonate with ZPE particles at low temperature to produce superfluid helium. High velocity micro vortices of ZPE particles about a basic particle or particles are responsible for electromagnetic forces. The speed of light is the speed of the wave front in the ZPE and its value is a function of the temperature and density of the ZPE.
Importance sampling variance reduction for the Fokker–Planck rarefied gas particle method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Collyer, B.S., E-mail: benjamin.collyer@gmail.com; London Mathematical Laboratory, 14 Buckingham Street, London WC2N 6DF; Connaughton, C.

The Fokker–Planck approximation to the Boltzmann equation, solved numerically by stochastic particle schemes, is used to provide estimates for rarefied gas flows. This paper presents a variance reduction technique for a stochastic particle method that is able to greatly reduce the uncertainty of the estimated flow fields when the characteristic speed of the flow is small in comparison to the thermal velocity of the gas. The method relies on importance sampling, requiring minimal changes to the basic stochastic particle scheme. We test the importance sampling scheme on a homogeneous relaxation, planar Couette flow and a lid-driven-cavity flow, and find thatmore » our method is able to greatly reduce the noise of estimated quantities. Significantly, we find that as the characteristic speed of the flow decreases, the variance of the noisy estimators becomes independent of the characteristic speed.« less
FLRW Cosmology from Yang-Mills Gravity with Translational Gauge Symmetry

NASA Astrophysics Data System (ADS)

Katz, Daniel

2013-03-01

We extend to basic cosmology the subject of Yang-Mills gravity — a theory of gravity based on local translational gauge invariance in flat space-time. It has been shown that this particular gauge invariance leads to tensor factors in the macroscopic limit of the equations of motion of particles which plays the same role as the metric tensor of general relativity (GR). The assumption that this "effective metric" tensor takes on the standard FLRW form is our starting point. Equations analogous to the Friedmann equations are derived and then solved in closed form for the three special cases of a universe dominated by (1) matter, (2) radiation and (3) dark energy. We find that the solutions for the scale factor are similar to, but distinct from, those found in the corresponding GR based treatment.
A Review of Positive Ion Sensitivities for the SIMS Analysis of CMT

DTIC Science & Technology

1991-05-01

microprobe. Inter-laboratory exercises organised by NRL using standardised glasses and steels’ s showed considerable agreement usually within a factor...would be sufficient oxygen to convert all the remaining matrix atoms to oxides, TeO2 and CdO. Any general theory of the lonisation of sputtered particles...Eggert equation which works well for many other matrices, such as metals, glasses and ceramics. Despite decades of basic studies there is still no
Entropy-based separation of yeast cells using a microfluidic system of conjoined spheres

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Kai-Jian; Qin, S.-J., E-mail: shuijie.qin@gmail.com; Bai, Zhong-Chen

2013-11-21

A physical model is derived to create a biological cell separator that is based on controlling the entropy in a microfluidic system having conjoined spherical structures. A one-dimensional simplified model of this three-dimensional problem in terms of the corresponding effects of entropy on the Brownian motion of particles is presented. This dynamic mechanism is based on the Langevin equation from statistical thermodynamics and takes advantage of the characteristics of the Fokker-Planck equation. This mechanism can be applied to manipulate biological particles inside a microfluidic system with identical, conjoined, spherical compartments. This theoretical analysis is verified by performing a rapid andmore » a simple technique for separating yeast cells in these conjoined, spherical microfluidic structures. The experimental results basically match with our theoretical model and we further analyze the parameters which can be used to control this separation mechanism. Both numerical simulations and experimental results show that the motion of the particles depends on the geometrical boundary conditions of the microfluidic system and the initial concentration of the diffusing material. This theoretical model can be implemented in future biophysics devices for the optimized design of passive cell sorters.« less
Lectures on gravitation

NASA Astrophysics Data System (ADS)

Das, Ashok

1. Basics of geometry and relativity. 1.1. Two dimensional geometry. 1.2. Inertial and gravitational masses. 1.3. Relativity -- 2. Relativistic dynamics. 2.1. Relativistic point particle. 2.2. Current and charge densities. 2.3. Maxwell's equations in the presence of sources. 2.4. Motion of a charged particle in EM field. 2.5. Energy-momentum tensor. 2.6. Angular momentum -- 3. Principle of general covariance. 3.1. Principle of equivalence. 3.2. Principle of general covariance. 3.3. Tensor densities -- 4. Affine connection and covariant derivative. 4.1. Parallel transport of a vector. 4.2. Christoffel symbol. 4.3. Covariant derivative of contravariant tensors. 4.4. Metric compatibility. 4.5. Covariant derivative of covariant and mixed tensors. 4.6. Electromagnetic analogy. 4.7. Gradient, divergence and curl -- 5. Geodesic equation. 5.1. Covariant differentiation along a curve. 5.2. Curvature from derivatives. 5.3. Parallel transport along a closed curve. 5.4. Geodesic equation. 5.5. Derivation of geodesic equation from a Lagrangian -- 6. Applications of the geodesic equation. 6.1. Geodesic as representing gravitational effect. 6.2. Rotating coordinate system and the Coriolis force. 6.3. Gravitational red shift. 6.4. Twin paradox and general covariance. 6.5. Other equations in the presence of gravitation -- 7. Curvature tensor and Einstein's equation. 7.1. Curvilinear coordinates versus gravitational field. 7.2. Definition of an inertial coordinate frame. 7.3. Geodesic deviation. 7.4. Properties of the curvature tensor. 7.5. Einstein's equation. 7.6. Cosmological constant. 7.7. Initial value problem. 7.8. Einstein's equation from an action -- 8. Schwarzschild solution. 8.1. Line element. 8.2. Connection. 8.3. Solution of the Einstein equation. 8.4. Properties of the Schwarzschild solution. 8.5. Isotropic coordinates -- 9. Tests of general relativity. 9.1. Radar echo experiment. 9.2. Motion of a particle in a Schwarzschild background. 9.3. Motion of light rays in a Schwarzschild background. 9.4. Perihelion advance of Mercury -- 10. Black holes. 10.1. Singularities of the metric. 10.2. Singularities of the Schwarzschild metric. 10.3. Black holes -- 11. Cosmological models and the big bang theory. 11.1. Homogeneity and isotropy. 11.2. Different models of the universe. 11.3. Hubble's law. 11.4. Evolution equation. 11.5. Big bang theory and blackbody radiation.
Theory and observation of electromagnetic ion cyclotron triggered emissions in the magnetosphere

NASA Astrophysics Data System (ADS)

Omura, Yoshiharu; Pickett, Jolene; Grison, Benjamin; Santolik, Ondrej; Dandouras, Iannis; Engebretson, Mark; Décréau, Pierrette M. E.; Masson, Arnaud

2010-07-01

We develop a nonlinear wave growth theory of electromagnetic ion cyclotron (EMIC) triggered emissions observed in the inner magnetosphere. We first derive the basic wave equations from Maxwell's equations and the momentum equations for the electrons and ions. We then obtain equations that describe the nonlinear dynamics of resonant protons interacting with an EMIC wave. The frequency sweep rate of the wave plays an important role in forming the resonant current that controls the wave growth. Assuming an optimum condition for the maximum growth rate as an absolute instability at the magnetic equator and a self-sustaining growth condition for the wave propagating from the magnetic equator, we obtain a set of ordinary differential equations that describe the nonlinear evolution of a rising tone emission generated at the magnetic equator. Using the physical parameters inferred from the wave, particle, and magnetic field data measured by the Cluster spacecraft, we determine the dispersion relation for the EMIC waves. Integrating the differential equations numerically, we obtain a solution for the time variation of the amplitude and frequency of a rising tone emission at the equator. Assuming saturation of the wave amplitude, as is found in the observations, we find good agreement between the numerical solutions and the wave spectrum of the EMIC triggered emissions.
The Capra Research Program for Modelling Extreme Mass Ratio Inspirals

NASA Astrophysics Data System (ADS)

Thornburg, Jonathan

2011-02-01

Suppose a small compact object (black hole or neutron star) of mass m orbits a large black hole of mass M ≫ m. This system emits gravitational waves (GWs) that have a radiation-reaction effect on the particle's motion. EMRIs (extreme-mass-ratio inspirals) of this type will be important GW sources for LISA. To fully analyze these GWs, and to detect weaker sources also present in the LISA data stream, will require highly accurate EMRI GW templates. In this article I outline the ``Capra'' research program to try to model EMRIs and calculate their GWs ab initio, assuming only that m ≪ M and that the Einstein equations hold. Because m ≪ M the timescale for the particle's orbit to shrink is too long for a practical direct numerical integration of the Einstein equations, and because this orbit may be deep in the large black hole's strong-field region, a post-Newtonian approximation would be inaccurate. Instead, we treat the EMRI spacetime as a perturbation of the large black hole's ``background'' (Schwarzschild or Kerr) spacetime and use the methods of black-hole perturbation theory, expanding in the small parameter m/M. The particle's motion can be described either as the result of a radiation-reaction ``self-force'' acting in the background spacetime or as geodesic motion in a perturbed spacetime. Several different lines of reasoning lead to the (same) basic O(m/M) ``MiSaTaQuWa'' equations of motion for the particle. In particular, the MiSaTaQuWa equations can be derived by modelling the particle as either a point particle or a small Schwarzschild black hole. The latter is conceptually elegant, but the former is technically much simpler and (surprisingly for a nonlinear field theory such as general relativity) still yields correct results. Modelling the small body as a point particle, its own field is singular along the particle worldline, so it's difficult to formulate a meaningful ``perturbation'' theory or equations of motion there. Detweiler and Whiting found an elegant decomposition of the particle's metric perturbation into a singular part which is spherically symmetric at the particle and a regular part which is smooth (and non-symmetric) at the particle. If we assume that the singular part (being spherically symmetric at the particle) exerts no force on the particle, then the MiSaTaQuWa equations follow immediately. The MiSaTaQuWa equations involve gradients of a (curved-spacetime) Green function, integrated over the particle's entire past worldline. These expressions aren't amenable to direct use in practical computations. By carefully analysing the singularity structure of each term in a spherical-harmonic expansion of the particle's field, Barack and Ori found that the self-force can be written as an infinite sum of modes, each of which can be calculated by (numerically) solving a set of wave equations in 1{+}1 dimensions, summing the gradients of the resulting fields at the particle position, and then subtracting certain analytically-calculable ``regularization parameters''. This ``mode-sum'' regularization scheme has been the basis for much further research including explicit numerical calculations of the self-force in a variety of situations, initially for Schwarzschild spacetime and more recently extending to Kerr spacetime. Recently Barack and Golbourn developed an alternative ``m-mode'' regularization scheme. This regularizes the physical metric perturbation by subtracting from it a suitable ``puncture function'' approximation to the Detweiler-Whiting singular field. The residual is then decomposed into a Fourier sum over azimuthal (e^{imϕ}) modes, and the resulting equations solved numerically in 2{+}1 dimensions. Vega and Detweiler have developed a related scheme that uses the same puncture-function regularization but then solves the regularized perturbation equation numerically in 3{+}1 dimensions, avoiding a mode-sum decomposition entirely. A number of research projects are now using these puncture-function regularization schemes, particularly for calculations in Kerr spacetime. Most Capra research to date has used 1st order perturbation theory, with the particle moving on a fixed (usually geodesic) worldline. Much current research is devoted to generalizing this to allow the particle worldline to be perturbed by the self-force, and to obtain approximation schemes which remain valid over long (EMRI-inspiral) timescales. To obtain the very high accuracies needed to fully exploit LISA's observations of the strongest EMRIs, 2nd order perturbation theory will probably also be needed; both this and long-time approximations remain frontiers for future Capra research.
A Time-Space Symmetry Based Cylindrical Model for Quantum Mechanical Interpretations

NASA Astrophysics Data System (ADS)

Vo Van, Thuan

2017-12-01

Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time-space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space-time curvatures. Interpretation of some important issues of quantum mechanical reality is carried out in comparison with the 5D space-time-matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally.
A B-B-G-K-Y framework for fluid turbulence

NASA Technical Reports Server (NTRS)

Montgomery, D.

1975-01-01

A kinetic theory for fluid turbulence is developed from the Liouville equation and the associated BBGKY hierarchy. Real and imaginary parts of Fourier coefficients of fluid variables play the roles of particles. Closure is achieved by the assumption of negligible five-coefficient correlation functions and probability distributions of Fourier coefficients are the basic variables of the theory. An additional approximation leads to a closed-moment description similar to the so-called eddy-damped Markovian approximation. A kinetic equation is derived for which conservation laws and an H-theorem can be rigorously established, the H-theorem implying relaxation of the absolute equilibrium of Kraichnan. The equation can be cast in the Fokker-Planck form, and relaxation times estimated from its friction and diffusion coefficients. An undetermined parameter in the theory is the free decay time for triplet correlations. Some attention is given to the inclusion of viscous damping and external driving forces.
Space Flows and Disturbances Due to Bodies in Motion Through the Magnetoplasma

NASA Astrophysics Data System (ADS)

Ponomarjov, Maxim G.

2000-10-01

In this paper a method is concerned which makes it possible to describe numerically and analytically the most famous structures in the non-equilibrium ionosphere, such as stratified and yacht sail like structures, flute jets, wakes and clouds. These problems are of practical interest in space sciences, astrophysics and in turbulence theory, and also of fundamental interest since they enable one to concentrate on the effects of the ambient electric and magnetic fields. Disturbances of charged particle flows due to the ambient flow interactions with bodies are simulated with taking into account the ambient magnetic field effect. The effects of interactions between solid surfaces and the flows was simulated by making use of an original image method. The flow disturbances were described by the Boltzmann equation. In the case of the ambient homogeneous magnetic field the Boltzmann equation is solved analytically. The case of diffuse reflection of particles by surface is considered in detail. The disturbances of charged particle concentration are calculated in 3D space. The contours of constant particle concentration obtained from numerical simulations illustrate the dynamics of developing stratifications and flute structures in charged particle jets and wakes under the ambient magnetic field effect. The basic goal of this paper is to present the method and to demonstate its possibility for simulations of turbulence, plasma jets, wakes and clouds in the ionosphere and Space when effects of electric and magnetic fields are taken into account.
Understanding the Magnetosphere: The Counter-intuitive Simplicity of Cosmic Electrodynamics

NASA Astrophysics Data System (ADS)

Vasyliūnas, V. M.

2008-12-01

Planetary magnetospheres exhibit an amazing variety of phenomena, unlimited in complexity if followed into endlessly fine detail. The challenge of theory is to understand this variety and complexity, ultimately by seeing how the observed effects follow from the basic equations of physics (a point emphasized by Eugene Parker). The basic equations themselves are remarkably simple, only their consequences being exceedingly complex (a point emphasized by Fred Hoyle). In this lecture I trace the development of electrodynamics as an essential ingredient of magnetospheric physics, through the three stages it has undergone to date. Stage I is the initial application of MHD concepts and constraints (sometimes phrased in equivalent single-particle terms). Stage II is the classical formulation of self-consistent coupling between magnetosphere and ionosphere. Stage III is the more recent recognition that properly elucidating time sequence and cause-effect relations requires Maxwell's equations combined with the unique constraints of large-scale plasma. Problems and controversies underlie the transition from each stage to the following. For each stage, there are specific observed aspects of the magnetosphere that can be understood at its level; also, each stage implies a specific way to formulate unresolved questions (particularly important in this age of extensive multi-point observations and ever-more-detailed numerical simulations).
Modeling of Particle Acceleration at Multiple Shocks via Diffusive Shock Acceleration: Preliminary Results

NASA Technical Reports Server (NTRS)

Parker, L. Neergaard; Zank, G. P.

2013-01-01

Successful forecasting of energetic particle events in space weather models require algorithms for correctly predicting the spectrum of ions accelerated from a background population of charged particles. We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box. We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (E(sub max)) appropriate for quasi-parallel and quasi-perpendicular shocks and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).
Approche Kaluza-Klein et Supersymetrie de Jauge

NASA Astrophysics Data System (ADS)

Pare, Jean-Pierre

This thesis presents a non-Abelian gauge-supersymmetric Kaluza-Klein approach for charged spinning particles and strings in a background of gravitational and Yang-Mills fields. In the classical Kaluza-Klein approach, the basic mathematical structure is a principal bundle of which the base manifold is space-time. This principal bundle is endowed with a pseudo-Riemannian metric, invariant under the action of the structural group of the bundle, and a connection. Geodesic equations on the bundle lead to the Maxwell-Lorentz equation for curved space-time and Yang -Mills fields, and to a conservation law of a non-Abelian (bosonic) charge. This conservation law originates from the invariance of the free-particle action on the bundle under the action of the structural group of the bundle (gauge group). Firstly, we generalize this approach for a spinning particle. The spin of the particle is described by Grassmannian variables added to the principal bundle. This supersymmetrization gives rise, in addition to the bosonic non-Abelian charge, a fermionic one. This leads to a search for a supergroup action on the superprincipal bundle which leaves invariant the action of the spinning particle. The invariance of this action would lead to the conservation of a non-Abelian super-charge, generalizing the conservation law obtained for particles without spin. We present Lagrangian and Hamiltonian formulations, both invariant under a super -group action. The equations of motion are derived and discussed. Different terms in these equations are well known in the literature. The invariance of these formulations under a supergroup action leads to a conservation law of a non-Abelian supercharge. The bosonic part of this supercharge corresponds to the non-Abelian (bosonic) charge obtained for a particle without spin. The fermionic part is a non -physical charge. It turns out in the supersymmetric case that this decouples from all other dynamical variables, and hence it does not influence trajectories of spinning particles. It is interesting to mention how this gauge -supersymmetry is introduced in the dynamics. It arises by choosing the unique metric connection on the principal bundle with torsion given by the Chern-Simons 3-form. We then proceed to extend these formulations for spinning strings. We present Lagrangian and Hamiltonian gauge-supersymmetric formulations in a superloop space setting. The same connection corresponding to the Chern -Simons 3-form is used here. Equations of motion are derived and discussed. In the appendix, we discuss the effect of using this connection in a non-Abelian Kaluza-Klein field theory. Using the same connection, we present a non-Abelian Kaluza-Klein approach leading to a zero cosmological constant.
Fundamental equations of a mixture of gas and small spherical solid particles from simple kinetic theory.

NASA Technical Reports Server (NTRS)

Pai, S. I.

1973-01-01

The fundamental equations of a mixture of a gas and pseudofluid of small spherical solid particles are derived from the Boltzmann equation of two-fluid theory. The distribution function of the gas molecules is defined in the same manner as in the ordinary kinetic theory of gases, but the distribution function for the solid particles is different from that of the gas molecules, because it is necessary to take into account the different size and physical properties of solid particles. In the proposed simple kinetic theory, two additional parameters are introduced: one is the radius of the spheres and the other is the instantaneous temperature of the solid particles in the distribution of the solid particles. The Boltzmann equation for each species of the mixture is formally written, and the transfer equations of these Boltzmann equations are derived and compared to the well-known fundamental equations of the mixture of a gas and small solid particles from continuum theory. The equations obtained reveal some insight into various terms in the fundamental equations. For instance, the partial pressure of the pseudofluid of solid particles is not negligible if the volume fraction of solid particles is not negligible as in the case of lunar ash flow.
A Variational Assimilation Method for Satellite and Conventional Data: Development of Basic Model for Diagnosis of Cyclone Systems

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Scott, Robert W.; Chen, J.

1991-01-01

A summary is presented of the progress toward the completion of a comprehensive diagnostic objective analysis system based upon the calculus of variations. The approach was to first develop the objective analysis subject to the constraints that the final product satisfies the five basic primitive equations for a dry inviscid atmosphere: the two nonlinear horizontal momentum equations, the continuity equation, the hydrostatic equation, and the thermodynamic equation. Then, having derived the basic model, there would be added to it the equations for moist atmospheric processes and the radiative transfer equation.
Generalized Boltzmann-Type Equations for Aggregation in Gases

NASA Astrophysics Data System (ADS)

Adzhiev, S. Z.; Vedenyapin, V. V.; Volkov, Yu. A.; Melikhov, I. V.

2017-12-01

The coalescence and fragmentation of particles in a dispersion system are investigated by applying kinetic theory methods, namely, by generalizing the Boltzmann kinetic equation to coalescence and fragmentation processes. Dynamic equations for the particle concentrations in the system are derived using the kinetic equations of motion. For particle coalescence and fragmentation, equations for the particle momentum, coordinate, and mass distribution functions are obtained and the coalescence and fragmentation coefficients are calculated. The equilibrium mass and velocity distribution functions of the particles in the dispersion system are found in the approximation of an active terminal group (Becker-Döring-type equation). The transition to a continuum description is performed.
Drift-based scrape-off particle width in X-point geometry

NASA Astrophysics Data System (ADS)

Reiser, D.; Eich, T.

2017-04-01

The Goldston heuristic estimate of the scrape-off layer width (Goldston 2012 Nucl. Fusion 52 013009) is reconsidered using a fluid description for the plasma dynamics. The basic ingredient is the inclusion of a compressible diamagnetic drift for the particle cross field transport. Instead of testing the heuristic model in a sophisticated numerical simulation including several physical mechanisms working together, the purpose of this work is to point out basic consequences for a drift-dominated cross field transport using a reduced fluid model. To evaluate the model equations and prepare them for subsequent numerical solution a specific analytical model for 2D magnetic field configurations with X-points is employed. In a first step parameter scans in high-resolution grids for isothermal plasmas are done to assess the basic formulas of the heuristic model with respect to the functional dependence of the scrape-off width on the poloidal magnetic field and plasma temperature. Particular features in the 2D-fluid calculations—especially the appearance of supersonic parallel flows and shock wave like bifurcational jumps—are discussed and can be understood partly in the framework of a reduced 1D model. The resulting semi-analytical findings might give hints for experimental proof and implementation in more elaborated fluid simulations.
A comparative study of different ferrofluid constitutive equations.

NASA Astrophysics Data System (ADS)

Kaloni, Purna

2011-11-01

Ferrofluids are stable colloidal suspensions of fine ferromagnetic monodomain nanoparticles in a non-conducting carrier fluid. The particles are coated with a surfacant to avoid agglomeration and coagulation.Brownian motion keeps the nanoparticles from settling under gravity. In recent years these fluids have found several applications including in liquid seals in rotary shafts for vacuum system and in hard disk drives of personal computers, in cooling and damping of loud speakers, in shock absorbers and in biomedical applications. A continuum description of ferrofluids was initiated by Neuringer and Rosensweig but the theory had some limitations. In subsequent years,several authors have proposed generalization of the above theory.Some of these are based upon the internal particle rotation concept, some are phemonological, some are based upon a thermodynamic framework, some employ statistical approach and some have used the dynamic mean field approach. The results based upon these theories ane in early stages and inconclusive. Our purpose is, first, to critically examine the basic foundations of these equations and then study the pedictions obtained in all the theories related to an experimental as well as a theoretical study.
Fundamentals of Polarized Light

NASA Technical Reports Server (NTRS)

Mishchenko, Michael

2003-01-01

The analytical and numerical basis for describing scattering properties of media composed of small discrete particles is formed by the classical electromagnetic theory. Although there are several excellent textbooks outlining the fundamentals of this theory, it is convenient for our purposes to begin with a summary of those concepts and equations that are central to the subject of this book and will be used extensively in the following chapters. We start by formulating Maxwell's equations and constitutive relations for time- harmonic macroscopic electromagnetic fields and derive the simplest plane-wave solution that underlies the basic optical idea of a monochromatic parallel beam of light. This solution naturally leads to the introduction of such fundamental quantities as the refractive index and the Stokes parameters. Finally, we define the concept of a quasi-monochromatic beam of light and discuss its implications.

Space–time and spatial geodesic orbits in Schwarzschild geometry

NASA Astrophysics Data System (ADS)

Resca, Lorenzo

2018-05-01

Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.
Basic lubrication equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.
Sectional methods for aggregation problems: application to volcanic eruptions

NASA Astrophysics Data System (ADS)

Rossi, E.

2016-12-01

Particle aggregation is a general problem that is common to several scientific disciplines such as planetary formation, food industry and aerosol sciences. So far the ordinary approach to this class of problems relies on the solution of the Smoluchowski Coagulation Equations (SCE), a set of Ordinary Differential Equations (ODEs) derived from the Population Balance Equations (PBE), which basically describe the change in time of an initial grain-size distribution due to the interaction of "single" particles. The frequency of particles collisions and their sticking efficiencies depend on the specific problem under analysis, but the mathematical framework and the possible solutions to the ODEs seem to be somehow discipline-independent and very general. In this work we will focus on the problem of volcanic ash aggregation, since it represents an extreme case of complexity that can be relevant also to other disciplines. In fact volcanic ash aggregates observed during the fallouts are characterized by relevant porosities and they do not fit with simplified descriptions based on monomer-like structures or fractal geometries. In this work we propose a bidimensional approach to the PBEs which uses additive (mass) and non-additive (volume) internal descriptors in order to better characterize the evolution of volcanic ash aggregation. In particular we used sectional methods (fixed-pivot) to discretize the internal parameters space. This algorithm has been applied to a one dimensional volcanic plume model in order to investigate how the Total Grain Size Distribution (TGSD) changes throughout the erupted column in real scenarios (i.e. Eyjafjallajokull 2010, Sakurajima 2013 and Mt. Saint Helens 1980).
A New Look into the Effect of Large Drops on Radiative Transfer Process

NASA Technical Reports Server (NTRS)

Marshak, Alexander

2003-01-01

Recent studies indicate that a cloudy atmosphere absorbs more solar radiation than any current 1D or 3D radiation model can predict. The excess absorption is not large, perhaps 10-15 W/sq m or less, but any such systematic bias is of concern since radiative transfer models are assumed to be sufficiently accurate for remote sensing applications and climate modeling. The most natural explanation would be that models do not capture real 3D cloud structure and, as a consequence, their photon path lengths are too short. However, extensive calculations, using increasingly realistic 3D cloud structures, failed to produce photon paths long enough to explain the excess absorption. Other possible explanations have also been unsuccessful so, at this point, conventional models seem to offer no solution to this puzzle. The weakest link in conventional models is the way a size distribution of cloud particles is mathematically handled. Basically, real particles are replaced with a single average particle. This "ensemble assumption" assumes that all particle sizes are well represented in any given elementary volume. But the concentration of larger particles can be so low that this assumption is significantly violated. We show how a different mathematical route, using the concept of a cumulative distribution, avoids the ensemble assumption. The cumulative distribution has jumps, or steps, corresponding to the rarer sizes. These jumps result in an additional term, a kind of Green's function, in the solution of the radiative transfer equation. Solving the cloud radiative transfer equation with the measured particle distributions, described in a cumulative rather than an ensemble fashion, may lead to increased cloud absorption of the magnitude observed.
Two dimensional numerical prediction of deflagration-to-detonation transition in porous energetic materials.

PubMed

Narin, B; Ozyörük, Y; Ulas, A

2014-05-30

This paper describes a two-dimensional code developed for analyzing two-phase deflagration-to-detonation transition (DDT) phenomenon in granular, energetic, solid, explosive ingredients. The two-dimensional model is constructed in full two-phase, and based on a highly coupled system of partial differential equations involving basic flow conservation equations and some constitutive relations borrowed from some one-dimensional studies that appeared in open literature. The whole system is solved using an optimized high-order accurate, explicit, central-difference scheme with selective-filtering/shock capturing (SF-SC) technique, to augment central-diffencing and prevent excessive dispersion. The sources of the equations describing particle-gas interactions in terms of momentum and energy transfers make the equation system quite stiff, and hence its explicit integration difficult. To ease the difficulties, a time-split approach is used allowing higher time steps. In the paper, the physical model for the sources of the equation system is given for a typical explosive, and several numerical calculations are carried out to assess the developed code. Microscale intergranular and/or intragranular effects including pore collapse, sublimation, pyrolysis, etc. are not taken into account for ignition and growth, and a basic temperature switch is applied in calculations to control ignition in the explosive domain. Results for one-dimensional DDT phenomenon are in good agreement with experimental and computational results available in literature. A typical shaped-charge wave-shaper case study is also performed to test the two-dimensional features of the code and it is observed that results are in good agreement with those of commercial software. Copyright © 2014 Elsevier B.V. All rights reserved.
Modeling of Particle Acceleration at Multiple Shocks Via Diffusive Shock Acceleration: Preliminary Results

NASA Technical Reports Server (NTRS)

Parker, Linda Neergaard; Zank, Gary P.

2013-01-01

We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al., 1999) in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box (Melrose and Pope, 1993; Zank et al., 2000). We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (Emax) appropriate for quasi-parallel and quasi-perpendicular shocks (Zank et al., 2000, 2006; Dosch and Shalchi, 2010) and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).
Remote sensing of environmental particulate pollutants - Optical methods for determinations of size distribution and complex refractive index

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1978-01-01

A unifying approach, based on a generalization of Pearson's differential equation of statistical theory, is proposed for both the representation of particulate size distribution and the interpretation of radiometric measurements in terms of this parameter. A single-parameter gamma-type distribution is introduced, and it is shown that inversion can only provide the dimensionless parameter, r/ab (where r = particle radius, a = effective radius, b = effective variance), at least when the distribution vanishes at both ends. The basic inversion problem in reconstructing the particle size distribution is analyzed, and the existing methods are reviewed (with emphasis on their capabilities) and classified. A two-step strategy is proposed for simultaneously determining the complex refractive index and reconstructing the size distribution of atmospheric particulates.
The combustion of large particles of char in bubbling fluidized beds: The dependence of Sherwood number and the rate of burning on particle diameter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dennis, J.S.; Hayhurst, A.N.; Scott, S.A.

Particles of char derived from a variety of fuels (e.g., biomass, sewage sludge, coal, or graphite), with diameters in excess of {approx}1.5mm, burn in fluidized bed combustors containing smaller particles of, e.g., sand, such that the rate is controlled by the diffusion both of O{sub 2} to the burning solid and of the products CO and CO{sub 2} away from it into the particulate phase. It is therefore important to characterize these mass transfer processes accurately. Measurements of the burning rate of char particles made from sewage sludge suggest that the Sherwood number, Sh, increases linearly with the diameter ofmore » the fuel particle, d{sub char} (for d{sub char}>{approx}1.5mm). This linear dependence of Sh on d{sub char} is expected from the basic equation Sh=2{epsilon}{sub mf}(1+d{sub char}/2{delta}{sub diff})/{tau}, provided the thickness of the boundary layer for mass transfer, {delta}{sub diff}, is constant in the region of interest (d{sub char}>{approx}1.5mm). Such a dependence is not seen in the empirical equations currently used and based on the Frossling expression. It is found here that for chars made from sewage sludge (for d{sub char}>{approx}1.5mm), the thickness of the boundary layer for mass transfer in a fluidized bed, {delta}{sub diff}, is less than that predicted by empirical correlations based on the Frossling expression. In fact, {delta}{sub diff} is not more than the diameter of the fluidized sand particles. Finally, the experiments in this study indicate that models based on surface renewal theory should be rejected for a fluidized bed, because they give unrealistically short contact times for packets of fluidized particles at the surface of a burning sphere. The result is the new correlation Sh = 2{epsilon}{sub mf}/{tau} + (A{sub cush}/A{sub char})(d{sub char}/ {delta}{sub diff}) for the dependence of Sh on d{sub char}, the diameter of a burning char particle. This equation is based on there being a gas-cushion of fluidizing gas underneath a burning char particle; the implication of this correlation is that a completely new picture emerges for the combustion of a char particle in a hot fluidized bed. (author)« less
Theoretical astrophysics in the 19th century (Homage to Radó von Kövesligethy)

NASA Astrophysics Data System (ADS)

Balázs, Lajos G.

The nature of astronomical information is determined mostly by the incoming light. Theoretical astrophysics means basically the theory of light emission and its relation to the physical constitution of the emitting celestial bodies. The necessary physical disciplines include theory of gravitation, theory of radiation, thermodynamics, matter--radiation interaction. The most significant theoretical achievement in the 17th - 18th century was the axiomatic foundation of mechanics and the law of gravitation. In the context of the nature of light, there were two conceptions: Newton contra Huygens, i.e. particle versus wave phenomenon. Using the theory of gravitation, first speculations appeared on black holes (Michell, Laplace), cosmogony (Kant-Laplace theory), the structure of the Milky Way (Kant), and the explanation of motion of the celestial bodies. The Olbers Paradox, formulated in the 19th century, is still one of the most significant constraints on observational cosmology. The development of thermodynamics, matter-radiation interaction, development of the theory of electromagnetism became important milestones. Maxwell's theory was the classical framework of the interaction between matter and radiation. Kirchhoff and Bunsen's revolutionary discovery of spectral analysis (1859) showed that observation of spectra makes it possible to study the chemical composition of emitting bodies. Thermodynamics predicted the existence of the black body radiation. It did not succeed, however, to determine the functional form of the wavelength dependence. A combination of the thermodynamic equation of state with the equation of hydrostatics resulted in the first stellar models (Lane, Ritter, Schuster). The first successful spectral equation of black body radiation was the theory of continuous spectra of celestial bodies by Radó von Kövesligethy (published 1885 in Hungarian, 1890 in German). Kövesligethy made several assumptions on the matter-radiation interaction: radiating matter consists of interacting particles, the form of interaction is an inverse power law, the radiation field is represented by the aether, aether is made also from interacting particles, light is the propagation of the oscillation of the aether particles, there is an equipartition between the oscillations energy of material and aetheric particles. Based on these assumptions, he derived a spectral equation with the following properties: the spectral distribution of radiation depends only on the temperature, the total irradiated energy is finite (15 years before Planck!), the wavelength of the intensity maximum is inversely proportional to the temperature (eight years before Wien!). Using his spectral equation, he estimated the temperature of several celestial bodies, including the Sun.
Monte Carlo based NMR simulations of open fractures in porous media

NASA Astrophysics Data System (ADS)

Lukács, Tamás; Balázs, László

2014-05-01

According to the basic principles of nuclear magnetic resonance (NMR), a measurement's free induction decay curve has an exponential characteristic and its parameter is the transversal relaxation time, T2, given by the Bloch equations in rotating frame. In our simulations we are observing that particular case when the bulk's volume is neglectable to the whole system, the vertical movement is basically zero, hence the diffusion part of the T2 relation can be editted out. This small-apertured situations are common in sedimentary layers, and the smallness of the observed volume enable us to calculate with just the bulk relaxation and the surface relaxation. The simulation uses the Monte-Carlo method, so it is based on a random-walk generator which provides the brownian motions of the particles by uniformly distributed, pseudorandom generated numbers. An attached differential equation assures the bulk relaxation, the initial and the iterated conditions guarantee the simulation's replicability and enable having consistent estimations. We generate an initial geometry of a plain segment with known height, with given number of particles, the spatial distribution is set to equal to each simulation, and the surface-volume ratio remains at a constant value. It follows that to the given thickness of the open fracture, from the fitted curve's parameter, the surface relaxivity is determinable. The calculated T2 distribution curves are also indicating the inconstancy in the observed fracture situations. The effect of varying the height of the lamina at a constant diffusion coefficient also produces characteristic anomaly and for comparison we have run the simulation with the same initial volume, number of particles and conditions in spherical bulks, their profiles are clear and easily to understand. The surface relaxation enables us to estimate the interaction beetwen the materials of boundary with this two geometrically well-defined bulks, therefore the distribution takes as a basis in estimation of the porosity and can be use of identifying small-grained porous media.
Tendency to occupy a statistically dominant spatial state of the flow as a driving force for turbulent transition.

PubMed

Chekmarev, Sergei F

2013-03-01

The transition from laminar to turbulent fluid motion occurring at large Reynolds numbers is generally associated with the instability of the laminar flow. On the other hand, since the turbulent flow characteristically appears in the form of spatially localized structures (e.g., eddies) filling the flow field, a tendency to occupy such a structured state of the flow cannot be ruled out as a driving force for turbulent transition. To examine this possibility, we propose a simple analytical model that treats the flow as a collection of localized spatial structures, each of which consists of elementary cells in which the behavior of the particles (atoms or molecules) is uncorrelated. This allows us to introduce the Reynolds number, associating it with the ratio between the total phase volume for the system and that for the elementary cell. Using the principle of maximum entropy to calculate the most probable size distribution of the localized structures, we show that as the Reynolds number increases, the elementary cells group into the localized structures, which successfully explains turbulent transition and some other general properties of turbulent flows. An important feature of the present model is that a bridge between the spatial-statistical description of the flow and hydrodynamic equations is established. We show that the basic assumptions underlying the model, i.e., that the particles are indistinguishable and elementary volumes of phase space exist in which the state of the particles is uncertain, are involved in the derivation of the Navier-Stokes equation. Taking into account that the model captures essential features of turbulent flows, this suggests that the driving force for the turbulent transition is basically the same as in the present model, i.e., the tendency of the system to occupy a statistically dominant state plays a key role. The instability of the flow at high Reynolds numbers can then be a mechanism to initiate structural rearrangement of the flow to find this state.
A relativistic dissipative hydrodynamic description for systems including particle number changing processes

NASA Astrophysics Data System (ADS)

El, Andrej; Muronga, Azwinndini; Xu, Zhe; Greiner, Carsten

2010-12-01

Relativistic dissipative hydrodynamic equations are extended by taking into account particle number changing processes in a gluon system, which expands in one dimension boost-invariantly. Chemical equilibration is treated by a rate equation for the particle number density based on Boltzmann equation and Grad's ansatz for the off-equilibrium particle phase space distribution. We find that not only the particle production, but also the temperature and the momentum spectra of the gluon system, obtained from the hydrodynamic calculations, are sensitive to the rates of particle number changing processes. Comparisons of the hydrodynamic calculations with the transport ones employing the parton cascade BAMPS show the inaccuracy of the rate equation at large shear viscosity to entropy density ratio. To improve the rate equation, Grad's ansatz has to be modified beyond the second moments in momentum.
Simulating propagation of coherent light in random media using the Fredholm type integral equation

NASA Astrophysics Data System (ADS)

Kraszewski, Maciej; Pluciński, Jerzy

2017-06-01

Studying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g. Radiative Transfer Theory and Monte Carlo methods) but they do not treat coherence properties of light directly. Some variations of these methods allows to predict behavior of coherent light but only for an averaged realization of the scattering medium. This limits their application in studying many physical phenomena connected to a specific distribution of scattering particles (e.g. laser speckle). In general, numerical simulation of coherent light propagation in a specific realization of random medium is a time- and memory-consuming problem. The goal of the presented research was to develop new efficient method for solving this problem. The method, presented in our earlier works, is based on solving the Fredholm type integral equation, which describes multiple light scattering process. This equation can be discretized and solved numerically using various algorithms e.g. by direct solving the corresponding linear equations system, as well as by using iterative or Monte Carlo solvers. Here we present recent development of this method including its comparison with well-known analytical results and a finite-difference type simulations. We also present extension of the method for problems of multiple scattering of a polarized light on large spherical particles that joins presented mathematical formalism with Mie theory.
MPPhys—A many-particle simulation package for computational physics education

NASA Astrophysics Data System (ADS)

Müller, Thomas

2014-03-01

In a first course to classical mechanics elementary physical processes like elastic two-body collisions, the mass-spring model, or the gravitational two-body problem are discussed in detail. The continuation to many-body systems, however, is deferred to graduate courses although the underlying equations of motion are essentially the same and although there is a strong motivation for high-school students in particular because of the use of particle systems in computer games. The missing link between the simple and the more complex problem is a basic introduction to solve the equations of motion numerically which could be illustrated, however, by means of the Euler method. The many-particle physics simulation package MPPhys offers a platform to experiment with simple particle simulations. The aim is to give a principle idea how to implement many-particle simulations and how simulation and visualization can be combined for interactive visual explorations. Catalogue identifier: AERR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERR_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 111327 No. of bytes in distributed program, including test data, etc.: 608411 Distribution format: tar.gz Programming language: C++, OpenGL, GLSL, OpenCL. Computer: Linux and Windows platforms with OpenGL support. Operating system: Linux and Windows. RAM: Source Code 4.5 MB Complete package 242 MB Classification: 14, 16.9. External routines: OpenGL, OpenCL Nature of problem: Integrate N-body simulations, mass-spring models Solution method: Numerical integration of N-body-simulations, 3D-Rendering via OpenGL. Running time: Problem dependent
Characterizing property distributions of polymeric nanogels by size-exclusion chromatography.

PubMed

Mourey, Thomas H; Leon, Jeffrey W; Bennett, James R; Bryan, Trevor G; Slater, Lisa A; Balke, Stephen T

2007-03-30

Nanogels are highly branched, swellable polymer structures with average diameters between 1 and 100nm. Size-exclusion chromatography (SEC) fractionates materials in this size range, and it is commonly used to measure nanogel molar mass distributions. For many nanogel applications, it may be more important to calculate the particle size distribution from the SEC data than it is to calculate the molar mass distribution. Other useful nanogel property distributions include particle shape, area, and volume, as well as polymer volume fraction per particle. All can be obtained from multi-detector SEC data with proper calibration and data analysis methods. This work develops the basic equations for calculating several of these differential and cumulative property distributions and applies them to SEC data from the analysis of polymeric nanogels. The methods are analogous to those used to calculate the more familiar SEC molar mass distributions. Calibration methods and characteristics of the distributions are discussed, and the effects of detector noise and mismatched concentration and molar mass sensitive detector signals are examined.
Ordinary differential equations.

PubMed

Lebl, Jiří

2013-01-01

In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.
Continuous time random walk with local particle-particle interaction

NASA Astrophysics Data System (ADS)

Xu, Jianping; Jiang, Guancheng

2018-05-01

The continuous time random walk (CTRW) is often applied to the study of particle motion in disordered media. Yet most such applications do not allow for particle-particle (walker-walker) interaction. In this paper, we consider a CTRW with particle-particle interaction; however, for simplicity, we restrain the interaction to be local. The generalized Chapman-Kolmogorov equation is modified by introducing a perturbation function that fluctuates around 1, which models the effect of interaction. Subsequently, a time-fractional nonlinear advection-diffusion equation is derived from this walking system. Under the initial condition of condensed particles at the origin and the free-boundary condition, we numerically solve this equation with both attractive and repulsive particle-particle interactions. Moreover, a Monte Carlo simulation is devised to verify the results of the above numerical work. The equation and the simulation unanimously predict that this walking system converges to the conventional one in the long-time limit. However, for systems where the free-boundary condition and long-time limit are not simultaneously satisfied, this convergence does not hold.
Generalized Landau Equation for a System with a Self-Consistent Mean Field - Derivation from an N-Particle Liouville Equation

NASA Astrophysics Data System (ADS)

Kandrup, H.

1981-02-01

Assume that the evolution of a system is determined by an N-particle Liouville equation. Suppose, moreover, that the particles which compose the system interact via a long range force like gravity so that the system will be spatially inhomogeneous. In this case, the mean force acting upon a test particle does not vanish, so that one wishes to isolate a self-consistent mean field and distinguish its "systematic" effects from the effects of "fluctuations." This is done here. The time-dependent projection operator formalism of Willis and Picard is used to obtain an exact equation for the time evolution of an appropriately defined one-particle probability density. If one implements the assumption that the "fluctuation" time scale is much shorter than both the relaxation and dynamical time scales, this exact equation can be approximated as a closed Markovian equation. In the limiting case of spatial homogeneity, one recovers precisely the standard Landau equation, which is customarily derived by a stochastic binary-encounter argument. This equation is contrasted with the standard heuristic equation for a mean field theory, as formulated for a Newtonian r-1 gravitational potential in stellar dynamics.
Trapping of quantum particles and light beams by switchable potential wells

NASA Astrophysics Data System (ADS)

Sonkin, Eduard; Malomed, Boris A.; Granot, Er'El; Marchewka, Avi

2010-09-01

We consider basic dynamical effects in settings based on a pair of local potential traps that may be effectively switched on and off, or suddenly displaced, by means of appropriate control mechanisms, such as scanning tunneling microscopy or photo-switchable quantum dots. The same models, based on the linear Schrödinger equation with time-dependent trapping potentials, apply to the description of optical planar systems designed for the switching of trapped light beams. The analysis is carried out in the analytical form, using exact solutions of the Schrödinger equation. The first dynamical problem considered in this work is the retention of a particle released from a trap which was suddenly turned off, while another local trap was switched on at a distance—immediately or with a delay. In this case, we demonstrate that the maximum of the retention rate is achieved at a specific finite value of the strength of the new trap, and at a finite value of the temporal delay, depending on the distance between the two traps. Another problem is retrapping of the bound particle when the addition of the second trap transforms the single-well setting into a double-well potential (DWP). In that case, we find probabilities for the retrapping into the ground or first excited state of the DWP. We also analyze effects entailed by the application of a kick to a bound particle, the most interesting one being a kick-induced transition between the DWP’s ground and excited states. In the latter case, the largest transition probability is achieved at a particular strength of the kick.
Sedimentation of Inertialess Particles in Stokes Flows

NASA Astrophysics Data System (ADS)

Höfer, Richard M.

2018-05-01

We investigate the sedimentation of a cloud of rigid, spherical particles of identical radii under gravity in a Stokes fluid. Both inertia and rotation of particles are neglected. We consider the homogenization limit of many small particles in the case of a dilute system in which interactions between particles are still important. In the relevant time scale, we rigorously prove convergence of the dynamics to the solution of a macroscopic equation. This macroscopic equation resembles the Stokes equations for a fluid of variable density subject to gravitation.

Modeling of Particle Acceleration at Multiple Shocks Via Diffusive Shock Acceleration: Preliminary Results

NASA Astrophysics Data System (ADS)

Parker, L. N.; Zank, G. P.

2013-12-01

Successful forecasting of energetic particle events in space weather models require algorithms for correctly predicting the spectrum of ions accelerated from a background population of charged particles. We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al., 1999) in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box (Melrose and Pope, 1993; Zank et al., 2000). We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (Emax) appropriate for quasi-parallel and quasi-perpendicular shocks (Zank et al., 2000, 2006; Dosch and Shalchi, 2010) and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).
Mode coupling theory for nonequilibrium glassy dynamics of thermal self-propelled particles.

PubMed

Feng, Mengkai; Hou, Zhonghuai

2017-06-28

We present a mode coupling theory study for the relaxation and glassy dynamics of a system of strongly interacting self-propelled particles, wherein the self-propulsion force is described by Ornstein-Uhlenbeck colored noise and thermal noises are included. Our starting point is an effective Smoluchowski equation governing the distribution function of particle positions, from which we derive a memory function equation for the time dependence of density fluctuations in nonequilibrium steady states. With the basic assumption of the absence of macroscopic currents and standard mode coupling approximation, we can obtain expressions for the irreducible memory function and other relevant dynamic terms, wherein the nonequilibrium character of the active system is manifested through an averaged diffusion coefficient D[combining macron] and a nontrivial structural function S 2 (q) with q being the magnitude of wave vector q. D[combining macron] and S 2 (q) enter the frequency term and the vertex term for the memory function, and thus influence both the short time and the long time dynamics of the system. With these equations obtained, we study the glassy dynamics of this thermal self-propelled particle system by investigating the Debye-Waller factor f q and relaxation time τ α as functions of the persistence time τ p of self-propulsion, the single particle effective temperature T eff as well as the number density ρ. Consequently, we find the critical density ρ c for given τ p shifts to larger values with increasing magnitude of propulsion force or effective temperature, in good accordance with previously reported simulation work. In addition, the theory facilitates us to study the critical effective temperature T for fixed ρ as well as its dependence on τ p . We find that T increases with τ p and in the limit τ p → 0, it approaches the value for a simple passive Brownian system as expected. Our theory also well recovers the results for passive systems and can be easily extended to more complex systems such as active-passive mixtures.
Drift-free kinetic equations for turbulent dispersion

NASA Astrophysics Data System (ADS)

Bragg, A.; Swailes, D. C.; Skartlien, R.

2012-11-01

The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.
Drift-free kinetic equations for turbulent dispersion.

PubMed

Bragg, A; Swailes, D C; Skartlien, R

2012-11-01

The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.
General theory of the multistage geminate reactions of the isolated pairs of reactants. II. Detailed balance and universal asymptotes of kinetics.

PubMed

Kipriyanov, Alexey A; Doktorov, Alexander B

2014-10-14

The analysis of general (matrix) kinetic equations for the mean survival probabilities of any of the species in a sample (or mean concentrations) has been made for a wide class of the multistage geminate reactions of the isolated pairs. These kinetic equations (obtained in the frame of the kinetic approach based on the concept of "effective" particles in Paper I) take into account various possible elementary reactions (stages of a multistage reaction) excluding monomolecular, but including physical and chemical processes of the change in internal quantum states carried out with the isolated pairs of reactants (or isolated reactants). The general basic principles of total and detailed balance have been established. The behavior of the reacting system has been considered on macroscopic time scales, and the universal long-term kinetics has been determined.
Spatial averaging of a dissipative particle dynamics model for active suspensions

NASA Astrophysics Data System (ADS)

Panchenko, Alexander; Hinz, Denis F.; Fried, Eliot

2018-03-01

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving-Kirkwood-Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.
Dynamics and Structure of Dusty Reacting Flows: Inert Particles in Strained, Laminar, Premixed Flames

NASA Technical Reports Server (NTRS)

Egolfopoulos, Fokion N.; Campbell, Charles S.

1999-01-01

A detailed numerical study was conducted on the dynamics and thermal response of inert, spherical particles in strained, laminar, premixed hydrogen/air flames. The modeling included the solution of the steady conservation equations for both the gas and particle phases along and around the stagnation streamline of an opposed-jet configuration, and the use of detailed descriptions of chemical kinetics and molecular transport, For the gas phase, the equations of mass, momentum, energy, and species are considered, while for the particle phase, the model is based on conservation equations of the particle momentum balance in the axial and radial direction, the particle number density, and the particle thermal energy equation. The particle momentum equation includes the forces as induced by drag, thermophoresis, and gravity. The particle thermal energy equation includes the convective/conductive heat exchange between the two phases, as well as radiation emission and absorption by the particle. A one-point continuation method is also included in the code that allows for the description of turning points, typical of ignition and extinction behavior. As expected, results showed that the particle velocity can be substantially different than the gas phase velocity, especially in the presence of large temperature gradients and large strain rates. Large particles were also found to cross the gas stagnation plane, stagnate, and eventually reverse as a result of the opposing gas phase velocity. It was also shown that the particle number density varies substantially throughout the flowfield, as a result of the straining of the flow and the thermal expansion. Finally, for increased values of the particle number density, substantial flame cooling to extinction states and modification of the gas phase fluid mechanics were observed. As also expected, the effect of gravity was shown to be important for low convective velocities and heavy particles. Under such conditions, simulations indicate that the magnitude and direction of the gravitational force can substantially affect the profiles of the particle velocity, number density, mass flux, and temperature.
Dynamics and Structure of Dusty Reacting Flows: Inert Particles in Strained, Laminar, Premixed Flames

NASA Technical Reports Server (NTRS)

Egolfopoulos, Fokion N.; Campbell, Charles S.; Wu, Ming-Shin (Technical Monitor)

1999-01-01

A detailed numerical study was conducted on the dynamics and thermal response of inert spherical particles in strained, laminar, premixed hydrogen/air flames. The modeling included the solution of the steady conservation equations for both the gas and particle phases along and around the stagnation streamline of an opposed-jet configuration, and the use of detailed descriptions of chemical kinetics and molecular transport. For the gas phase, the equations of mass, momentum, energy, and species are considered, while for the particle phase, the model is based on conservation equations of the particle momentum balance in the axial and radial direction, the particle number density, and the particle thermal energy equation. The particle momentum equation includes the forces as induced by drag, thermophoresis, and gravity. The particle thermal energy equation includes the convective/conductive heat exchange between the two phases, as well as radiation emission and absorption by the particle. A one-point continuation method is also included in the code that allows for the description of turning points, typical of ignition and extinction behavior. As expected, results showed that the particle velocity can be substantially different than the gas phase velocity, especially in the presence of large temperature gradients and large strain rates. Large particles were also found to cross the gas stagnation plane, stagnate, and eventually reverse as a result of the opposing gas phase velocity. It was also shown that the particle number density varies substantially throughout the flowfield, as a result of the straining of the flow and the thermal expansion. Finally, for increased values of the particle number density, substantial flame cooling to extinction states and modification of the gas phase fluid mechanics were observed. As also expected, the effect of gravity was shown to be important for low convective velocities and heavy particles. Under such conditions, simulations indicate that the magnitude and direction of the gravitational force can substantially affect the profiles of the particle velocity, number density, mass flux, and temperature.
Behavior of a spin-1/2 massive charged particle in Schwarzschild immersed in an electromagnetic universe

NASA Astrophysics Data System (ADS)

Al-Badawi, A.

2018-02-01

The Dirac equation is considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic field. Due to the presence of electromagnetic field from the surroundings, the interaction with the spin-1/2 massive charged particle is considered. The equations of the spin-1/2 massive charged particle are separated into radial and angular equations by adopting the Newman-Penrose formalism. The angular equations obtained are similar to the Schwarzschild geometry. For the radial equations we manage to obtain the one dimensional Schrödinger-type wave equations with effective potentials. Finally, we study the behavior of the potentials by plotting them as a function of radial distance and expose the effect of the external parameter, charge and the frequency of the particle on them.
On the reduced dynamics of a subset of interacting bosonic particles

NASA Astrophysics Data System (ADS)

Gessner, Manuel; Buchleitner, Andreas

2018-03-01

The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an N-particle system produces a hierarchical expansion for the subdynamics of M ≤ N particles. Truncating this hierarchy with a pure product state ansatz yields the general, nonlinear coherent mean-field equation of motion. In the special case of a contact interaction potential, this reproduces the Gross-Pitaevskii equation. To account for incoherent effects on top of the mean-field evolution, we discuss possible extensions towards a second-order perturbation theory that accounts for interaction-induced decoherence in form of a nonlinear Lindblad-type master equation.
Deterministic analysis of extrinsic and intrinsic noise in an epidemiological model.

PubMed

Bayati, Basil S

2016-05-01

We couple a stochastic collocation method with an analytical expansion of the canonical epidemiological master equation to analyze the effects of both extrinsic and intrinsic noise. It is shown that depending on the distribution of the extrinsic noise, the master equation yields quantitatively different results compared to using the expectation of the distribution for the stochastic parameter. This difference is incident to the nonlinear terms in the master equation, and we show that the deviation away from the expectation of the extrinsic noise scales nonlinearly with the variance of the distribution. The method presented here converges linearly with respect to the number of particles in the system and exponentially with respect to the order of the polynomials used in the stochastic collocation calculation. This makes the method presented here more accurate than standard Monte Carlo methods, which suffer from slow, nonmonotonic convergence. In epidemiological terms, the results show that extrinsic fluctuations should be taken into account since they effect the speed of disease breakouts and that the gamma distribution should be used to model the basic reproductive number.
A high-order gas-kinetic Navier-Stokes flow solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Qibing, E-mail: lqb@tsinghua.edu.c; Xu Kun, E-mail: makxu@ust.h; Fu Song, E-mail: fs-dem@tsinghua.edu.c

2010-09-20

The foundation for the development of modern compressible flow solver is based on the Riemann solution of the inviscid Euler equations. The high-order schemes are basically related to high-order spatial interpolation or reconstruction. In order to overcome the low-order wave interaction mechanism due to the Riemann solution, the temporal accuracy of the scheme can be improved through the Runge-Kutta method, where the dynamic deficiencies in the first-order Riemann solution is alleviated through the sub-step spatial reconstruction in the Runge-Kutta process. The close coupling between the spatial and temporal evolution in the original nonlinear governing equations seems weakened due to itsmore » spatial and temporal decoupling. Many recently developed high-order methods require a Navier-Stokes flux function under piece-wise discontinuous high-order initial reconstruction. However, the piece-wise discontinuous initial data and the hyperbolic-parabolic nature of the Navier-Stokes equations seem inconsistent mathematically, such as the divergence of the viscous and heat conducting terms due to initial discontinuity. In this paper, based on the Boltzmann equation, we are going to present a time-dependent flux function from a high-order discontinuous reconstruction. The theoretical basis for such an approach is due to the fact that the Boltzmann equation has no specific requirement on the smoothness of the initial data and the kinetic equation has the mechanism to construct a dissipative wave structure starting from an initially discontinuous flow condition on a time scale being larger than the particle collision time. The current high-order flux evaluation method is an extension of the second-order gas-kinetic BGK scheme for the Navier-Stokes equations (BGK-NS). The novelty for the easy extension from a second-order to a higher order is due to the simple particle transport and collision mechanism on the microscopic level. This paper will present a hierarchy to construct such a high-order method. The necessity to couple spatial and temporal evolution nonlinearly in the flux evaluation can be clearly observed through the numerical performance of the scheme for the viscous flow computations.« less
Effects of turbulence on mixed-phase deep convective clouds under different basic-state winds and aerosol concentrations

NASA Astrophysics Data System (ADS)

Lee, Hyunho; Baik, Jong-Jin; Han, Ji-Young

2014-12-01

The effects of turbulence-induced collision enhancement (TICE) on mixed-phase deep convective clouds are numerically investigated using a 2-D cloud model with bin microphysics for uniform and sheared basic-state wind profiles and different aerosol concentrations. Graupel particles account for the most of the cloud mass in all simulation cases. In the uniform basic-state wind cases, graupel particles with moderate sizes account for some of the total graupel mass in the cases with TICE, whereas graupel particles with large sizes account for almost all the total graupel mass in the cases without TICE. This is because the growth of ice crystals into small graupel particles is enhanced due to TICE. The changes in the size distributions of graupel particles due to TICE result in a decrease in the mass-averaged mean terminal velocity of graupel particles. Therefore, the downward flux of graupel mass, and thus the melting of graupel particles, is reduced due to TICE, leading to a decrease in the amount of surface precipitation. Moreover, under the low aerosol concentration, TICE increases the sublimation of ice particles, consequently playing a partial role in reducing the amount of surface precipitation. The effects of TICE are less pronounced in the sheared basic-state wind cases than in the uniform basic-state wind cases because the number of ice crystals is much smaller in the sheared basic-state wind cases than in the uniform basic-state wind cases. Thus, the size distributions of graupel particles in the cases with and without TICE show little difference.
The Fokker-Planck equation for coupled Brown-Néel-rotation.

PubMed

Weizenecker, Jürgen

2018-01-22

Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.
The Fokker-Planck equation for coupled Brown-Néel-rotation

NASA Astrophysics Data System (ADS)

Weizenecker, Jürgen

2018-02-01

Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.
Depolarization of an Ultrashort Pulse in a Disordered Ensemble of Mie Particles

NASA Astrophysics Data System (ADS)

Gorodnichev, E. E.; Ivliev, S. V.; Kuzovlev, A. I.; Rogozkin, D. B.

2017-12-01

We study propagation of an ultrashort pulse of polarized light through a turbid medium with the Reynolds-McCormick phase function. Within the basic mode approach to the vector radiative transfer equation, the temporal profile of the degree of polarization is calculated analytically with the use of the small-angle approximation. The degree of polarization is shown to be described by the self-similar dependence on some combination of the transport scattering coefficient, the temporal delay and the sample thickness. Our results are in excellent agreement with the data of numerical simulations carried out previously for aqueous suspension of polystyrene microspheres.
Methods of applied dynamics

NASA Technical Reports Server (NTRS)

Rheinfurth, M. H.; Wilson, H. B.

1991-01-01

The monograph was prepared to give the practicing engineer a clear understanding of dynamics with special consideration given to the dynamic analysis of aerospace systems. It is conceived to be both a desk-top reference and a refresher for aerospace engineers in government and industry. It could also be used as a supplement to standard texts for in-house training courses on the subject. Beginning with the basic concepts of kinematics and dynamics, the discussion proceeds to treat the dynamics of a system of particles. Both classical and modern formulations of the Lagrange equations, including constraints, are discussed and applied to the dynamic modeling of aerospace structures using the modal synthesis technique.
A round trip from Caldirola to Bateman systems

NASA Astrophysics Data System (ADS)

Guerrero, J.; López-Ruiz, F. F.; Aldaya, V.; Cossío, F.

2011-03-01

For the quantum Caldirola-Kanai Hamiltonian, describing a quantum damped harmonic oscillator, a couple of constant of motion operators generating the Heisenberg algebra can be found. The inclusion in this algebra, in a unitary manner, of the standard time evolution generator , which is not a constant of motion, requires a non-trivial extension of this basic algebra and the physical system itself, which now includes a new dual particle. This enlarged algebra, when exponentiated, leads to a group, named the Bateman group, which admits unitary representations with support in the Hilbert space of functions satisfying the Schrodinger equation associated with the quantum Bateman Hamiltonian, either as a second order differential operator as well as a first order one. The classical Bateman Hamiltonian describes a dual system of a damped (losing energy) particle and a dual (gaining energy) particle. The classical Bateman system has a solution submanifold containing the trajectories of the original system as a submanifold. When restricted to this submanifold, the Bateman dual classical Hamiltonian leads to the Caldirola-Kanai Hamiltonian for a single damped particle. This construction can also be done at the quantum level, and the Caldirola-Kanai Hamiltonian operator can be derived from the Bateman Hamiltonian operator when appropriate constraints are imposed.
Chapman-Enskog expansion for the Vicsek model of self-propelled particles

NASA Astrophysics Data System (ADS)

Ihle, Thomas

2016-08-01

Using the standard Vicsek model, I show how the macroscopic transport equations can be systematically derived from microscopic collision rules. The approach starts with the exact evolution equation for the N-particle probability distribution and, after making the mean-field assumption of molecular chaos, leads to a multi-particle Enskog-type equation. This equation is treated by a non-standard Chapman-Enskog expansion to extract the macroscopic behavior. The expansion includes terms up to third order in a formal expansion parameter ɛ, and involves a fast time scale. A self-consistent closure of the moment equations is presented that leads to a continuity equation for the particle density and a Navier-Stokes-like equation for the momentum density. Expressions for all transport coefficients in these macroscopic equations are given explicitly in terms of microscopic parameters of the model. The transport coefficients depend on specific angular integrals which are evaluated asymptotically in the limit of infinitely many collision partners, using an analogy to a random walk. The consistency of the Chapman-Enskog approach is checked by an independent calculation of the shear viscosity using a Green-Kubo relation.
Steering particles by breaking symmetries

NASA Astrophysics Data System (ADS)

Bet, Bram; Samin, Sela; Georgiev, Rumen; Burak Eral, Huseyin; van Roij, René

2018-06-01

We derive general equations of motions for highly-confined particles that perform quasi-two-dimensional motion in Hele-Shaw channels, which we solve analytically, aiming to derive design principles for self-steering particles. Based on symmetry properties of a particle, its equations of motion can be simplified, where we retrieve an earlier-known equation of motion for the orientation of dimer particles consisting of disks (Uspal et al 2013 Nat. Commun. 4), but now in full generality. Subsequently, these solutions are compared with particle trajectories that are obtained numerically. For mirror-symmetric particles, excellent agreement between the analytical and numerical solutions is found. For particles lacking mirror symmetry, the analytic solutions provide means to classify the motion based on particle geometry, while we find that taking the side-wall interactions into account is important to accurately describe the trajectories.

On-line prognosis of fatigue crack propagation based on Gaussian weight-mixture proposal particle filter.

PubMed

Chen, Jian; Yuan, Shenfang; Qiu, Lei; Wang, Hui; Yang, Weibo

2018-01-01

Accurate on-line prognosis of fatigue crack propagation is of great meaning for prognostics and health management (PHM) technologies to ensure structural integrity, which is a challenging task because of uncertainties which arise from sources such as intrinsic material properties, loading, and environmental factors. The particle filter algorithm has been proved to be a powerful tool to deal with prognostic problems those are affected by uncertainties. However, most studies adopted the basic particle filter algorithm, which uses the transition probability density function as the importance density and may suffer from serious particle degeneracy problem. This paper proposes an on-line fatigue crack propagation prognosis method based on a novel Gaussian weight-mixture proposal particle filter and the active guided wave based on-line crack monitoring. Based on the on-line crack measurement, the mixture of the measurement probability density function and the transition probability density function is proposed to be the importance density. In addition, an on-line dynamic update procedure is proposed to adjust the parameter of the state equation. The proposed method is verified on the fatigue test of attachment lugs which are a kind of important joint components in aircraft structures. Copyright © 2017 Elsevier B.V. All rights reserved.
Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

NASA Astrophysics Data System (ADS)

Cremaschini, C.; Tessarotto, M.

2012-01-01

An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical N-body systems of mutually interacting particles. This refers, in particular, to charged particles subject to EM interactions, including both binary interactions and self-interactions ( EM-interacting N- body systems). The correct solution to the question represents an overriding prerequisite for the consistency between classical and quantum mechanics. In this paper it is shown that such a description can be consistently obtained in the context of classical electrodynamics, for the case of a N-body system of classical finite-size charged particles. A variational formulation of the problem is presented, based on the N -body hybrid synchronous Hamilton variational principle. Covariant Lagrangian and Hamiltonian equations of motion for the dynamics of the interacting N-body system are derived, which are proved to be delay-type ODEs. Then, a representation in both standard Lagrangian and Hamiltonian forms is proved to hold, the latter expressed by means of classical Poisson Brackets. The theory developed retains both the covariance with respect to the Lorentz group and the exact Hamiltonian structure of the problem, which is shown to be intrinsically non-local. Different applications of the theory are investigated. The first one concerns the development of a suitable Hamiltonian approximation of the exact equations that retains finite delay-time effects characteristic of the binary interactions and self-EM-interactions. Second, basic consequences concerning the validity of Dirac generator formalism are pointed out, with particular reference to the instant-form representation of Poincaré generators. Finally, a discussion is presented both on the validity and possible extension of the Dirac generator formalism as well as the failure of the so-called Currie "no-interaction" theorem for the non-local Hamiltonian system considered here.
The Equations of Oceanic Motions

NASA Astrophysics Data System (ADS)

Müller, Peter

2006-10-01

Modeling and prediction of oceanographic phenomena and climate is based on the integration of dynamic equations. The Equations of Oceanic Motions derives and systematically classifies the most common dynamic equations used in physical oceanography, from large scale thermohaline circulations to those governing small scale motions and turbulence. After establishing the basic dynamical equations that describe all oceanic motions, M|ller then derives approximate equations, emphasizing the assumptions made and physical processes eliminated. He distinguishes between geometric, thermodynamic and dynamic approximations and between the acoustic, gravity, vortical and temperature-salinity modes of motion. Basic concepts and formulae of equilibrium thermodynamics, vector and tensor calculus, curvilinear coordinate systems, and the kinematics of fluid motion and wave propagation are covered in appendices. Providing the basic theoretical background for graduate students and researchers of physical oceanography and climate science, this book will serve as both a comprehensive text and an essential reference.
Test-particle motion in the nonsymmetric gravitation theory

NASA Astrophysics Data System (ADS)

Moffat, J. W.

1987-06-01

A derivation of the motion of test particles in the nonsymmetric gravitational theory (NGT) is given using the field equations in the presence of matter. The motion of the particle is governed by the Christoffel symbols, which are formed from the symmetric part of the fundamental tensor gμν, as well as by a tensorial piece determined by the skew part of the contracted curvature tensor Rμν. Given the energy-momentum tensor for a perfect fluid and the definition of a test particle in the NGT, the equations of motion follow from the conservation laws. The tensorial piece in the equations of motion describes a new force in nature that acts on the conserved charge in a body. Particles that carry this new charge do not follow geodesic world lines in the NGT, whereas photons do satisfy geodesic equations of motion and the equivalence principle of general relativity. Astronomical predictions, based on the exact static, spherically symmetric solution of the field equations in a vacuum and the test-particle equations of motion, are derived in detail. The maximally extended coordinates that remove the event-horizon singularities in the static, spherically symmetric solution are presented. It is shown how an inward radially falling test particle can be prevented from forming an event horizon for a value greater than a specified critical value of the source charge. If a test particle does fall through an event horizon, then it must continue to fall until it reaches the singularity at r=0.
Relaxation dynamics of interacting skyrmions in thin films

NASA Astrophysics Data System (ADS)

Brown, Bart; Pleimling, Michel

Magnetic skyrmions are topologically protected spin textures which were recently observed in certain chiral magnets and thin films. Skyrmions can be moved by very low current densities which makes them very promising in spintronic applications such as data storage devices and logic gates. A thorough understanding of the relaxation processes for systems of interacting skyrmions far from equilibrium could prove invaluable in real world applications but is currently lacking in the literature. The dynamics are described by the Landau-Lifshitz-Gilbert (LLG) equation, however, simulating many interacting skyrmions by solving the LLG equation is computationally infeasible. We employ a suitable two-dimensional particle based model derived from Thiele's approach to study the two-time density correlation function and other quantities. The particle model differs most notably from similar models which describe vortices in type-II superconductors by the addition of the Magnus force which points perpendicular to the skyrmion velocity in the plane. Numerical studies reveal non-universal scaling of the correlation function where the scaling exponent is a function of the ratio of the Magnus force strength to damping coefficient as well as of the Gaussian noise. This research is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-09ER46613.
Interfacial dilatational deformation accelerates particle formation in monoclonal antibody solutions.

PubMed

Lin, Gigi L; Pathak, Jai A; Kim, Dong Hyun; Carlson, Marcia; Riguero, Valeria; Kim, Yoen Joo; Buff, Jean S; Fuller, Gerald G

2016-04-14

Protein molecules are amphiphilic moieties that spontaneously adsorb at the air/solution (A/S) interface to lower the surface energy. Previous studies have shown that hydrodynamic disruptions to these A/S interfaces can result in the formation of protein aggregates that are of concern to the pharmaceutical industry. Interfacial hydrodynamic stresses encountered by protein therapeutic solutions under typical manufacturing, filling, and shipping conditions will impact protein stability, prompting a need to characterize the contribution of basic fluid kinematics to monoclonal antibody (mAb) destabilization. We demonstrate that dilatational surface deformations are more important to antibody stability when compared to constant-area shear of the A/S interface. We have constructed a dilatational interfacial rheometer that utilizes simultaneous pressure and bubble shape measurements to study the mechanical stability of mAbs under interfacial aging. It has a distinct advantage over methods utilizing the Young-Laplace equation, which incorrectly describes viscoelastic interfaces. We provide visual evidence of particle ejection from dilatated A/S interfaces and spectroscopic data of ejected mAb particles. These rheological studies frame a molecular understanding of the protein-protein interactions at the complex-fluid interface.
The equation of motion for a radiating charged particle without self-interaction term

NASA Astrophysics Data System (ADS)

Herrera, L.

1990-03-01

The motion of a radiating charged particle is studied from the point of view of relativistic classical mechanics. Thus, the resulting equation of motion emerges from equating the total rate of change of momentum to the external force, without the introduction of a “self-force” term. Doing so, one is forced to abandon either one, or both, of the following restrictions: (a) the external force is non-dissipative, (b) the proper mass of the particle is constant. By abandoning (a) we obtain the Mo and Papas equation of motion, whereas allowing variations in the proper mass one is led, uniquely, to the Bonnor equation. A new equation of motion is proposed by abandoning both (a) and (b).
The analysis of influence of field of co-rotation on motion of submicronic particles in the Earth's plasmasphere

NASA Astrophysics Data System (ADS)

Yakovlev, A. B.

2018-05-01

The analysis of the motion of micro-particles with radii of several dozens of nanometers in the Earth's plasmasphere has confirmed that the earlier proved statement about conservation of the form for an orbit of a particle with constant electric charge which moves in superposition of the central gravitational field and the field of a magnetic dipole is true also for the case of a quasi-equilibrium electric charge. For a wide range of altitudes and the sizes of micro-particles other forces that act on the charged grain make considerably smaller impact on its motion. On the basis of numerical simulation it has been shown that for motion in an equatorial plane the field of co-rotation leads to very small monotonous growth of the semimajor axis and an orbit eccentricity, and for not-equatorial orbits there are fluctuations of the semimajor axis, an eccentricity and an inclination of an orbit with the period that considerably exceeds the period of orbital motion. In this paper, on the basis of the analysis of the canonical equations of the motion of a micro-particle in superposition of the central gravitational field and the field of co-rotation the explanation of the time dependences obtained numerically for the basic characteristics of an orbit of a micro-particle is proposed.
Exact analysis of surface field reduction due to field-emitted vacuum space charge, in parallel-plane geometry, using simple dimensionless equations

NASA Astrophysics Data System (ADS)

Forbes, Richard G.

2008-10-01

This paper reports (a) a simple dimensionless equation relating to field-emitted vacuum space charge (FEVSC) in parallel-plane geometry, namely 9ζ2θ2-3θ-4ζ+3=0, where ζ is the FEVSC "strength" and θ is the reduction in emitter surface field (θ =field-with/field-without FEVSC), and (b) the formula j =9θ2ζ/4, where j is the ratio of emitted current density JP to that predicted by Child's law. These equations apply to any charged particle, positive or negative, emitted with near-zero kinetic energy. They yield existing and additional basic formulas in planar FEVSC theory. The first equation also yields the well-known cubic equation describing the relationship between JP and applied voltage; a method of analytical solution is described. Illustrative FEVSC effects in a liquid metal ion source and in field electron emission are discussed. For Fowler-Nordheim plots, a "turn-over" effect is predicted in the high FEVSC limit. The higher the voltage-to-local-field conversion factor for the emitter concerned, then the higher is the field at which turn over occurs. Past experiments have not found complete turn over; possible reasons are noted. For real field emitters, planar theory is a worst-case limit; however, adjusting ζ on the basis of Monte Carlo calculations might yield formulae adequate for real situations.
A combined CFD-experimental method for developing an erosion equation for both gas-sand and liquid-sand flows

NASA Astrophysics Data System (ADS)

Mansouri, Amir

The surface degradation of equipment due to consecutive impacts of abrasive particles carried by fluid flow is called solid particle erosion. Solid particle erosion occurs in many industries including oil and gas. In order to prevent abrupt failures and costly repairs, it is essential to predict the erosion rate and identify the locations of the equipment that are mostly at risk. Computational Fluid Dynamics (CFD) is a powerful tool for predicting the erosion rate. Erosion prediction using CFD analysis includes three steps: (1) obtaining flow solution, (2) particle tracking and calculating the particle impact speed and angle, and (3) relating the particle impact information to mass loss of material through an erosion equation. Erosion equations are commonly generated using dry impingement jet tests (sand-air), since the particle impact speed and angle are assumed not to deviate from conditions in the jet. However, in slurry flows, a wide range of particle impact speeds and angles are produced in a single slurry jet test with liquid and sand particles. In this study, a novel and combined CFD/experimental method for developing an erosion equation in slurry flows is presented. In this method, a CFD analysis is used to characterize the particle impact speed, angle, and impact rate at specific locations on the test sample. Then, the particle impact data are related to the measured erosion depth to achieve an erosion equation from submerged testing. Traditionally, it was assumed that the erosion equation developed based on gas testing can be used for both gas-sand and liquid-sand flows. The erosion equations developed in this work were implemented in a CFD code, and CFD predictions were validated for various test conditions. It was shown that the erosion equation developed based on slurry tests can significantly improve the local thickness loss prediction in slurry flows. Finally, a generalized erosion equation is proposed which can be used to predict the erosion rate in gas-sand, water-sand and viscous liquid-sand flows with high accuracy. Furthermore, in order to gain a better understanding of the erosion mechanism, a comprehensive experimental study was conducted to investigate the important factors influencing the erosion rate in gas-sand and slurry flows. The wear pattern and total erosion ratio were measured in a direct impingement jet geometry (for both dry impact and submerged impingement jets). The effects of fluid viscosity, abrasive particle size, particle impact speed, jet inclination angle, standoff distance, sand concentration, and exposure time were investigated. Also, the eroded samples were studied with Scanning Electron Microscopy (SEM) to understand the erosion micro-structure. Also, the sand particle impact speed and angle were measured using a Particle Image Velocimetry (PIV) system. The measurements were conducted in two types of erosion testers (gas-solid and liquid-solid impinging jets). The Particle Tracking Velocimetry (PTV) technique was utilized which is capable of tracking individual small particles. Moreover, CFD modeling was performed to predict the particle impact data. Very good agreement between the CFD results and PTV measurements was observed.
Microcolumn studies of dye adsorption onto manganese oxides modified diatomite.

PubMed

Al-Ghouti, M A; Khraisheh, M A M; Ahmad, M N; Allen, S J

2007-07-19

The method described here cannot fully replace the analysis of large columns by small test columns (microcolumns). The procedure, however, is suitable for speeding up the determination of adsorption parameters of dye onto the adsorbent and for speeding up the initial screening of a large adsorbent collection that can be tedious if a several adsorbents and adsorption conditions must be tested. The performance of methylene blue (MB), a basic dye, Cibacron reactive black (RB) and Cibacron reactive yellow (RY) was predicted in this way and the influence of initial dye concentration and other adsorption conditions on the adsorption behaviour were demonstrated. On the basis of the experimental results, it can be concluded that the adsorption of RY onto manganese oxides modified diatomite (MOMD) exhibited a characteristic "S" shape and can be simulated effectively by the Thomas model. It is shown that the adsorption capacity increased as the initial dye concentration increased. The increase in the dye uptake capacity with the increase of the adsorbent mass in the column was due to the increase in the surface area of adsorbent, which provided more binding sites for the adsorption. It is shown that the use of high flow rates reduced the time that RY in the solution is in contact with the MOMD, thus allowing less time for adsorption to occur, leading to an early breakthrough of RY. A rapid decrease in the column adsorption capacity with an increase in particle size with an average 56% reduction in capacity resulting from an increase in the particle size from 106-250 microm to 250-500 microm. The experimental data correlated well with calculated data using the Thomas equation and the bed depth-service time (BDST) equation. Therefore, it might be concluded that the Thomas equation and the BDST equations can produce accurate predication for variation of dye concentration, mass of the adsorbent, flow rate and particle size. In general, the values of adsorption isotherm capacity obtained in a batch system show the maximum values and are considerably higher than those obtained in a fixed-bed.
CICART Center For Integrated Computation And Analysis Of Reconnection And Turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhattacharjee, Amitava

CICART is a partnership between the University of New Hampshire (UNH) and Dartmouth College. CICART addresses two important science needs of the DoE: the basic understanding of magnetic reconnection and turbulence that strongly impacts the performance of fusion plasmas, and the development of new mathematical and computational tools that enable the modeling and control of these phenomena. The principal participants of CICART constitute an interdisciplinary group, drawn from the communities of applied mathematics, astrophysics, computational physics, fluid dynamics, and fusion physics. It is a main premise of CICART that fundamental aspects of magnetic reconnection and turbulence in fusion devices, smaller-scalemore » laboratory experiments, and space and astrophysical plasmas can be viewed from a common perspective, and that progress in understanding in any of these interconnected fields is likely to lead to progress in others. The establishment of CICART has strongly impacted the education and research mission of a new Program in Integrated Applied Mathematics in the College of Engineering and Applied Sciences at UNH by enabling the recruitment of a tenure-track faculty member, supported equally by UNH and CICART, and the establishment of an IBM-UNH Computing Alliance. The proposed areas of research in magnetic reconnection and turbulence in astrophysical, space, and laboratory plasmas include the following topics: (A) Reconnection and secondary instabilities in large high-Lundquist-number plasmas, (B) Particle acceleration in the presence of multiple magnetic islands, (C) Gyrokinetic reconnection: comparison with fluid and particle-in-cell models, (D) Imbalanced turbulence, (E) Ion heating, and (F) Turbulence in laboratory (including fusion-relevant) experiments. These theoretical studies make active use of three high-performance computer simulation codes: (1) The Magnetic Reconnection Code, based on extended two-fluid (or Hall MHD) equations, in an Adaptive Mesh Refinement (AMR) framework, (2) the Particle Simulation Code, a fully electromagnetic 3D Particle-In-Cell (PIC) code that includes a collision operator, and (3) GS2, an Eulerian, electromagnetic, kinetic code that is widely used in the fusion program, and simulates the nonlinear gyrokinetic equations, together with a self-consistent set of Maxwell’s equations.« less
When is quasi-linear theory exact. [particle acceleration

NASA Technical Reports Server (NTRS)

Jones, F. C.; Birmingham, T. J.

1975-01-01

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.
A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lindesay, James V

2001-05-11

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' ormore » ''dressing'' of these parameters to connect them to the boundary states.« less
A particle-particle hybrid method for kinetic and continuum equations

NASA Astrophysics Data System (ADS)

Tiwari, Sudarshan; Klar, Axel; Hardt, Steffen

2009-10-01

We present a coupling procedure for two different types of particle methods for the Boltzmann and the Navier-Stokes equations. A variant of the DSMC method is applied to simulate the Boltzmann equation, whereas a meshfree Lagrangian particle method, similar to the SPH method, is used for simulations of the Navier-Stokes equations. An automatic domain decomposition approach is used with the help of a continuum breakdown criterion. We apply adaptive spatial and time meshes. The classical Sod's 1D shock tube problem is solved for a large range of Knudsen numbers. Results from Boltzmann, Navier-Stokes and hybrid solvers are compared. The CPU time for the hybrid solver is 3-4 times faster than for the Boltzmann solver.
The new finite temperature Schrödinger equations with strong or weak interaction

NASA Astrophysics Data System (ADS)

Li, Heling; Yang, Bin; Shen, Hongjun

2017-07-01

Implanting the thoughtway of thermostatistics into quantum mechanics, we formulate new Schrödinger equations of multi-particle and single-particle respectively at finite temperature. To get it, the pure-state free energies and the microscopic entropy operators are introduced and meantime the pure-state free energies take the places of mechanical energies at finite temperature. The definition of microscopic entropy introduced by Wu was also revised, and the strong or weak interactions dependent on temperature are considered in multi-particle Schrödinger Equations. Based on the new Schrödinger equation at finite temperature, two simple cases were analyzed. The first one is concerning some identical harmonic oscillators in N lattice points and the other one is about N unrelated particles in three dimensional in finite potential well. From the results gotten, we conclude that the finite temperature Schrödinger equation is particularly important for mesoscopic systems.
Gyrokinetic theory for particle and energy transport in fusion plasmas

NASA Astrophysics Data System (ADS)

Falessi, Matteo Valerio; Zonca, Fulvio

2018-03-01

A set of equations is derived describing the macroscopic transport of particles and energy in a thermonuclear plasma on the energy confinement time. The equations thus derived allow studying collisional and turbulent transport self-consistently, retaining the effect of magnetic field geometry without postulating any scale separation between the reference state and fluctuations. Previously, assuming scale separation, transport equations have been derived from kinetic equations by means of multiple-scale perturbation analysis and spatio-temporal averaging. In this work, the evolution equations for the moments of the distribution function are obtained following the standard approach; meanwhile, gyrokinetic theory has been used to explicitly express the fluctuation induced fluxes. In this way, equations for the transport of particles and energy up to the transport time scale can be derived using standard first order gyrokinetics.
Nonlinear data assimilation using synchronization in a particle filter

NASA Astrophysics Data System (ADS)

Rodrigues-Pinheiro, Flavia; Van Leeuwen, Peter Jan

2017-04-01

Current data assimilation methods still face problems in strongly nonlinear cases. A promising solution is a particle filter, which provides a representation of the model probability density function by a discrete set of particles. However, the basic particle filter does not work in high-dimensional cases. The performance can be improved by considering the proposal density freedom. A potential choice of proposal density might come from the synchronisation theory, in which one tries to synchronise the model with the true evolution of a system using one-way coupling via the observations. In practice, an extra term is added to the model equations that damps growth of instabilities on the synchronisation manifold. When only part of the system is observed synchronization can be achieved via a time embedding, similar to smoothers in data assimilation. In this work, two new ideas are tested. First, ensemble-based time embedding, similar to an ensemble smoother or 4DEnsVar is used on each particle, avoiding the need for tangent-linear models and adjoint calculations. Tests were performed using Lorenz96 model for 20, 100 and 1000-dimension systems. Results show state-averaged synchronisation errors smaller than observation errors even in partly observed systems, suggesting that the scheme is a promising tool to steer model states to the truth. Next, we combine these efficient particles using an extension of the Implicit Equal-Weights Particle Filter, a particle filter that ensures equal weights for all particles, avoiding filter degeneracy by construction. Promising results will be shown on low- and high-dimensional Lorenz96 models, and the pros and cons of these new ideas will be discussed.
Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.
Exploring synchronisation in nonlinear data assimilation

NASA Astrophysics Data System (ADS)

Rodrigues-Pinheiro, Flavia; van Leeuwen, Peter Jan

2016-04-01

Present-day data assimilation methods are based on linearizations and face serious problems in strongly nonlinear cases such as convection. A promising solution to this problem is a particle filter, which provides a representation of the model probability density function (pdf) by a discrete set of model states, or particles. The basic particle filter uses Bayes's theorem directly, but does not work in high-dimensional cases. The performance can be improved by considering the proposal density freedom. This allows one to change the model equations to bring the particles closer to the observations, resulting in very efficient update schemes at observation times, but extending these schemes between observation times is computationally expensive. Simple solutions like nudging have been shown to be not powerful enough. A potential solution might be synchronization, in which one tries to synchronise the model of a system with the true evolution of the system via the observations. In practice this means that an extra term is added to the model equations that hampers growth of instabilities on the synchronization manifold. Especially the delayed versions, where observations are allowed to influence the state in the past have shown some remarkable successes. Unfortunately, all efforts ignore errors in the observations, and as soon as these are introduced the performance degrades considerably. There is a close connection between time-delayed synchronization and a Kalman Smoother, which does allow for observational (and other) errors. In this presentation we will explore this connection to the full, with a view to extend synchronization to more realistic settings. Specifically performance of the spread of information from observed to unobserved variables is studied in detail. The results indicate that this extended synchronisation is a promising tool to steer the model states towards the observations efficiently. If time permits, we will show initial results of embedding the new synchronization method into a particle filter.

Kappa Distribution in a Homogeneous Medium: Adiabatic Limit of a Super-diffusive Process?

NASA Astrophysics Data System (ADS)

Roth, I.

2015-12-01

The classical statistical theory predicts that an ergodic, weakly interacting system like charged particles in the presence of electromagnetic fields, performing Brownian motions (characterized by small range deviations in phase space and short-term microscopic memory), converges into the Gibbs-Boltzmann statistics. Observation of distributions with a kappa-power-law tails in homogeneous systems contradicts this prediction and necessitates a renewed analysis of the basic axioms of the diffusion process: characteristics of the transition probability density function (pdf) for a single interaction, with a possibility of non-Markovian process and non-local interaction. The non-local, Levy walk deviation is related to the non-extensive statistical framework. Particles bouncing along (solar) magnetic field with evolving pitch angles, phases and velocities, as they interact resonantly with waves, undergo energy changes at undetermined time intervals, satisfying these postulates. The dynamic evolution of a general continuous time random walk is determined by pdf of jumps and waiting times resulting in a fractional Fokker-Planck equation with non-integer derivatives whose solution is given by a Fox H-function. The resulting procedure involves the known, although not frequently used in physics fractional calculus, while the local, Markovian process recasts the evolution into the standard Fokker-Planck equation. Solution of the fractional Fokker-Planck equation with the help of Mellin transform and evaluation of its residues at the poles of its Gamma functions results in a slowly converging sum with power laws. It is suggested that these tails form the Kappa function. Gradual vs impulsive solar electron distributions serve as prototypes of this description.
Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves

NASA Astrophysics Data System (ADS)

Tobita, Miwa; Omura, Yoshiharu

2018-03-01

We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.
One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Ishibashi, Kazuya

2018-06-01

We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.
Smooth particle hydrodynamics: theory and application to the origin of the moon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benz, W.

1986-01-01

The origin of the moon is modeled by the so-called smooth particle hydrodynamics (SPH) method (Lucy, 1977, Monaghan 1985) which substitutes to the fluid a finite set of extended particles, the hydrodynamics equations reduce to the equation of motion of individual particles. These equations of motion differ only from the standard gravitational N-body problem insofar that pressure gradients and viscosity terms have to be added to the gradient of the potential to derive the forces between the particles. The numerical tools developed for ''classical'' N-body problems can therefore be readily applied to solve 3 dimensional hydroynamical problems. 12 refs., 1more » fig.« less
Lattice gas models for particle systems in an underdamped hopping regime

NASA Astrophysics Data System (ADS)

Gobron, Thierry

A model in which the state of the particle is described by a multicomponent vector, each possible kinetic state for the particle being associated with one of the components is presented. A master equation describes the evolution of the probability distribution in an independent particle model. From the master equation and with the help of the symmetry group that leaves the state transition operator invariant, physical quantities such as the diffusion constant are explicitly calculated for several lattices in one, two, and three dimensions. A Boltzmann equation is established and compared to the Rice and Roth proposal.
On the Mo-Papas equation

NASA Astrophysics Data System (ADS)

Aguirregabiria, J. M.; Chamorro, A.; Valle, M. A.

1982-05-01

A new heuristic derivation of the Mo-Papas equation for charged particles is given. It is shown that this equation cannot be derived for a point particle by closely following Dirac's classical treatment of the problem. The Mo-Papas theory and the Bonnor-Rowe-Marx variable mass dynamics are not compatible.
Gravitational Agglomeration of Post-HCDA LMFBR Nonspherical Aerosols.

DTIC Science & Technology

1980-12-01

equations for two particle motions are developed . A computer program NGCEFF is constructed., the Navier-Stokes equation is solved by the finite difference...dynamic equations for two particle motions are developed . A computer program NGCEFF I is constructed, the Navier-Stokes equation is solved by the...spatial inhomogeneities for the aerosol. Thus, following an HCDA, an aerosol mixture of sodium compounds, fuel and core structural materials will
Transport equations for low-energy solar particles in evolving interplanetary magnetic fields

NASA Technical Reports Server (NTRS)

Ng, C. K.

1988-01-01

Two new forms of a simplified Fokker-Planck equation are derived for the transport of low-energy solar energetic particles in an evolving interplanetary magnetic field, carried by a variable radial solar wind. An idealized solution suggests that the 'invariant' anisotropy direction reported by Allum et al. (1974) may be explained within the conventional theoretical framework. The equations may be used to relate studies of solar particle propagation to solar wind transients, and vice versa.
Dynamical density functional theory for arbitrary-shape colloidal fluids including inertia and hydrodynamic interactions

NASA Astrophysics Data System (ADS)

Duran-Olivencia, Miguel A.; Goddard, Ben; Kalliadasis, Serafim

2015-11-01

Over the last few decades the classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become a remarkably powerful tool in the study of colloidal fluids. Recently there has been extensive research to generalise all previous DDFTs finally yielding a general DDFT equation (for spherical particles) which takes into account both inertia and hydrodynamic interactions (HI) which strongly influence non-equilibrium properties. The present work will be devoted to a further generalisation of such a framework to systems of anisotropic particles. To this end, the kinetic equation for the Brownian particle distribution function is derived starting from the Liouville equation and making use of Zwanzig's projection-operator techniques. By averaging over all but one particle, a DDFT equation is finally obtained with some similarities to that for spherical colloids. However, there is now an inevitable translational-rotational coupling which affects the diffusivity of asymmetric particles. Lastly, in the overdamped (high friction) limit the theory is notably simplified leading to a DDFT equation which agrees with previous derivations. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.
Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donker, H.C., E-mail: h.donker@science.ru.nl; Katsnelson, M.I.; De Raedt, H.

2016-09-15

The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds. - Highlights: • Logical inference applied to relativistic, massive, charged, and spinless particle experiments leads to the Klein–Gordon equation. • The relativistic Hamilton–Jacobi is scrutinized by employing a field description formore » the four-velocity. • Logical inference allows analysis of experiments with uncertainty in detection events and experimental conditions.« less
The centripetal force law and the equation of motion for a particle on a curved hypersurface

NASA Astrophysics Data System (ADS)

Hu, L. D.; Lian, D. K.; Liu, Q. H.

2016-12-01

It is pointed out that the current form of the extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version; for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once this fact is taken into consideration, the equation takes the same form as that for the centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is preferable.
Nonresonant interaction of heavy ions with electromagnetic ion cyclotron waves

NASA Technical Reports Server (NTRS)

Berchem, J.; Gendrin, R.

1985-01-01

The motion of a heavy ion in the presence of an intense ultralow-frequency electromagnetic wave propagating along the dc magnetic field is analyzed. Starting from the basic equations of motion and from their associated two invariants, the heavy ion velocity-space trajectories are drawn. It is shown that after a certain time, particles whose initial phase angles are randomly distributed tend to bunch together, provided that the wave intensity b-sub-1 is sufficiently large. The importance of these results for the interpretation of the recently observed acceleration of singly charged He ions in conjunction with the occurrence of large-amplitude ion cyclotron waves in the equatorial magnetosphere is discussed.
Effects of high-energy particles on accretion flows onto a super massive black hole

NASA Astrophysics Data System (ADS)

Kimura, Shigeo

We study effects of high-energy particles on the accretion flow onto a supermassive black hole and luminosities of escaping particles such as protons, neutrons, gamma-rays, and neutrinos. We formulate a one-dimensional model of the two-component accretion flow consisting of thermal particles and high-energy particles, supposing that some fraction of viscous dissipation energy is converted to the acceleration of high-energy particles. The thermal component is governed by fluid dynamics while the high-energy particles obey the moment equations of the diffusion-convection equation. By solving the time evolution of these equations, we obtain advection dominated flows as steady state solutions. Effects of the high-energy particles on the flow structure turn out to be very small because the compressional heating is so effective that the thermal component always provides the major part of the pressure. We calculate luminosities of escaping particles for these steady solutions. For a broad range of mass accretion rates, escaping particles can extract the energy about one-thousandth of the accretion energy. We also discuss some implications on relativistic jet production by escaping particles.
Langevin equation versus kinetic equation: Subdiffusive behavior of charged particles in a stochastic magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balescu, R.; Wang, H.; Misguich, J.H.

1994-12-01

The running diffusion coefficient [ital D]([ital t]) is evaluated for a system of charged particles undergoing the effect of a fluctuating magnetic field and of their mutual collisions. The latter coefficient can be expressed either in terms of the mean square displacement (MSD) of a test particle, or in terms of a correlation between a fluctuating distribution function and the magnetic field fluctuation. In the first case a stochastic differential equation of Langevin type for the position of a test particle must be solved; the second problem requires the determination of the distribution function from a kinetic equation. Using suitablemore » simplifications, both problems are amenable to exact analytic solution. The conclusion is that the equivalence of the two approaches is by no means automatically guaranteed. A new type of object, the hybrid kinetic equation'' is constructed: it automatically ensures the equivalence with the Langevin results. The same conclusion holds for the generalized Fokker--Planck equation. The (Bhatnagar--Gross--Krook) (BGK) model for the collisions yields a completely wrong result. A linear approximation to the hybrid kinetic equation yields an inexact behavior, but represents an acceptable approximation in the strongly collisional limit.« less
Lagrangian equations of motion of particles and photons in a Schwarzschild field

NASA Astrophysics Data System (ADS)

Ritus, V. I.

2015-11-01

The equations of motion of a particle in the gravitational field of a black hole are considered in a formulation that uses generalized coordinates, velocities, and accelerations and is convenient for finding the integrals of motion. The equations are rewritten in terms of the physical velocities and accelerations measured in the Schwarzschild frame by a stationary observer using proper local length and time standards. The attractive force due to the field and the centripetal acceleration of a particle is proportional to the particle kinetic energy m/\\sqrt{1 - v^2}, consistently with the fact that the particle kinetic energy and the photon energy \\hbarω in the field increase by the same factor compared with their values without a field. The attraction exerted on particles and photons by a gravitational field source is proportional to their kinetic energies. The particle trajectory in the ultrarelativistic limit v \\to 1 coincides with the photon trajectory.
Statistical description and transport in stochastic magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vanden Eijnden, E.; Balescu, R.

1996-03-01

The statistical description of particle motion in a stochastic magnetic field is presented. Starting form the stochastic Liouville equation (or, hybrid kinetic equation) associated with the equations of motion of a test particle, the probability distribution function of the system is obtained for various magnetic fields and collisional processes. The influence of these two ingredients on the statistics of the particle dynamics is stressed. In all cases, transport properties of the system are discussed. {copyright} {ital 1996 American Institute of Physics.}
General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Elhanbaly, A.; Schlickeiser, Reinhard

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.
Application of Microrheology in Food Science.

PubMed

Yang, Nan; Lv, Ruihe; Jia, Junji; Nishinari, Katsuyoshi; Fang, Yapeng

2017-02-28

Microrheology provides a technique to probe the local viscoelastic properties and dynamics of soft materials at the microscopic level by observing the motion of tracer particles embedded within them. It is divided into passive and active microrheology according to the force exerted on the embedded particles. Particles are driven by thermal fluctuations in passive microrheology, and the linear viscoelasticity of samples can be obtained on the basis of the generalized Stokes-Einstein equation. In active microrheology, tracer particles are controlled by external forces, and measurements can be extended to the nonlinear regime. Microrheology techniques have many advantages such as the need for only small sample amounts and a wider measurable frequency range. In particular, microrheology is able to examine the spatial heterogeneity of samples at the microlevel, which is not possible using traditional rheology. Therefore, microrheology has considerable potential for studying the local mechanical properties and dynamics of soft matter, particularly complex fluids, including solutions, dispersions, and other colloidal systems. Food products such as emulsions, foams, or gels are complex fluids with multiple ingredients and phases. Their macroscopic properties, such as stability and texture, are closely related to the structure and mechanical properties at the microlevel. In this article, the basic principles and methods of microrheology are reviewed, and the latest developments and achievements of microrheology in the field of food science are presented.
Turbulent fluid motion 3: Basic continuum equations

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1991-01-01

A derivation of the continuum equations used for the analysis of turbulence is given. These equations include the continuity equation, the Navier-Stokes equations, and the heat transfer or energy equation. An experimental justification for using a continuum approach for the study of turbulence is given.
A continuum theory of a lubrication problem with solid particles

NASA Technical Reports Server (NTRS)

Dai, Fuling; Khonsari, M. M.

1993-01-01

The governing equations for a two-dimensional lubrication problem involving the mixture of a Newtonian fluid with solid particles at an arbitrary volume fraction are developed using the theory of interacting continuua (mixture theory). The equations take the interaction between the fluid and the particles into consideration. Provision is made for the possibility of particle slippage at the boundaries. The equations are simplified assuming that the solid volume fraction varies in the sliding direction alone. Equations are solved for the velocity of the fluid phase and that of the solid phase of the mixture flow in the clearance space of an arbitrary shaped bearing. It is shown that the classical pure fluid case can be recovered as a special case of the solutions presented. Extensive numerical solutions are presented to quantify the effect of particulate solid for a number of pertinent performance parameters for both slider and journal bearings. Included in the results are discussions on the influence of particle slippage on the boundaries as well as the role of the interacting body force between the fluid and solid particles.

INTRODUCTION OF MANY-PARTICLE VARIABLES FOR THE TREATMENT OF SPECIAL TRANSLATIONALLY INVARIANT MANY-BODY PROBLEMS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mobius, P.

1960-05-01

An attempt is raade to treat special translationally invariant many-body problems by coordinate transformations introducing many-particle variables. These are adapted coordinates of such kind that the condition of translational invariance and the Pauli principle can be satisfied automatically. They are homogeneous functions of the particle coordinates obeying certain differential equations. The Schrodinger equation is transformed into these variables. There exist examples of systems of interacting particles which can be separated exactly in the many-particle variables but not in the particle coordinates. (auth)
Analysis of the correlation dimension for inertial particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gustavsson, Kristian; Department of Physics, Göteborg University, 41296 Gothenburg; Mehlig, Bernhard

2015-07-15

We obtain an implicit equation for the correlation dimension which describes clustering of inertial particles in a complex flow onto a fractal measure. Our general equation involves a propagator of a nonlinear stochastic process in which the velocity gradient of the fluid appears as additive noise. When the long-time limit of the propagator is considered our equation reduces to an existing large-deviation formalism from which it is difficult to extract concrete results. In the short-time limit, however, our equation reduces to a solvability condition on a partial differential equation. In the case where the inertial particles are much denser thanmore » the fluid, we show how this approach leads to a perturbative expansion of the correlation dimension, for which the coefficients can be obtained exactly and in principle to any order. We derive the perturbation series for the correlation dimension of inertial particles suspended in three-dimensional spatially smooth random flows with white-noise time correlations, obtaining the first 33 non-zero coefficients exactly.« less
Theory of diffusion of active particles that move at constant speed in two dimensions.

PubMed

Sevilla, Francisco J; Gómez Nava, Luis A

2014-08-01

Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the coarse-grained probability density of finding a particle at a given location and at a given time in arbitrary short-time regimes. By going beyond the diffusive limit, we derive a generalization of the telegrapher equation. Such generalization preserves the hyperbolic structure of the equation and incorporates memory effects in the diffusive term. While no difference is observed for the mean-square displacement computed from the two-dimensional telegrapher equation and from our generalization, the kurtosis results in a sensible parameter that discriminates between both approximations. We carry out a comparative analysis in Fourier space that sheds light on why the standard telegrapher equation is not an appropriate model to describe the propagation of particles with constant speed in dispersive media.
From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

NASA Astrophysics Data System (ADS)

Plastino, A. R.; Curado, E. M. F.; Nobre, F. D.; Tsallis, C.

2018-02-01

Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q -Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.
Role of magnetic fields in physics and astrophysics; Proceedings of the Conference, Copenhagen, Denmark, June 5-7, 1974

NASA Technical Reports Server (NTRS)

Canuto, V.

1975-01-01

The papers deal with the role of magnetism in astrophysics and the properties of matter in the presence of unusually large magnetic fields. Topics include a quantum-mechanical treatment of high-energy charged particles radiating in a homogeneous magnetic field, the solution and properties of the Dirac equation for magnetic fields of any strength up to 10 to the 13th power gauss, experimental difficulties encountered and overcome in generating megagauss fields, the effect of strong radiation damping for an ultrarelativistic charge in an external electromagnetic field, magnetic susceptibilities of nuclei and elementary particles, and Compton scattering in strong external electromagnetic fields. Other papers examine static uniform electric and magnetic polarizabilities of the vacuum in arbitrarily strong magnetic fields, quantum-mechanical processes in neutron stars, basic ideas of mean-field magnetohydrodynamics, helical MHD turbulence, relations between cosmic and laboratory plasma physics, and insights into the nature of magnetism provided by relativity and cosmology. Individual items are announced in this issue.
ME(SSY)**2: Monte Carlo Code for Star Cluster Simulations

NASA Astrophysics Data System (ADS)

Freitag, Marc Dewi

2013-02-01

ME(SSY)**2 stands for “Monte-carlo Experiments with Spherically SYmmetric Stellar SYstems." This code simulates the long term evolution of spherical clusters of stars; it was devised specifically to treat dense galactic nuclei. It is based on the pioneering Monte Carlo scheme proposed by Hénon in the 70's and includes all relevant physical ingredients (2-body relaxation, stellar mass spectrum, collisions, tidal disruption, ldots). It is basically a Monte Carlo resolution of the Fokker-Planck equation. It can cope with any stellar mass spectrum or velocity distribution. Being a particle-based method, it also allows one to take stellar collisions into account in a very realistic way. This unique code, featuring most important physical processes, allows million particle simulations, spanning a Hubble time, in a few CPU days on standard personal computers and provides a wealth of data only rivalized by N-body simulations. The current version of the software requires the use of routines from the "Numerical Recipes in Fortran 77" (http://www.nrbook.com/a/bookfpdf.php).
Modelling electro-active polymers with a dispersion-type anisotropy

NASA Astrophysics Data System (ADS)

Hossain, Mokarram; Steinmann, Paul

2018-02-01

We propose a novel constitutive framework for electro-active polymers (EAPs) that can take into account anisotropy with a chain dispersion. To enhance actuation behaviour, particle-filled EAPs become promising candidates nowadays. Recent studies suggest that particle-filled EAPs, which can be cured under an electric field during the manufacturing time, do not necessarily form perfect anisotropic composites, rather they create composites with dispersed chains. Hence in this contribution, an electro-mechanically coupled constitutive model is devised that considers the chain dispersion with a probability distribution function in an integral form. To obtain relevant quantities in discrete form, numerical integration over the unit sphere is utilized. Necessary constitutive equations are derived exploiting the basic laws of thermodynamics that result in a thermodynamically consistent formulation. To demonstrate the performance of the proposed electro-mechanically coupled framework, we analytically solve a non-homogeneous boundary value problem, the extension and inflation of an axisymmetric cylindrical tube under electro-mechanically coupled load. The results capture various electro-mechanical couplings with the formulation proposed for EAP composites.
Spatially-Dependent Modelling of Pulsar Wind Nebula G0.9+0.1

NASA Astrophysics Data System (ADS)

van Rensburg, C.; Krüger, P. P.; Venter, C.

2018-03-01

We present results from a leptonic emission code that models the spectral energy distribution of a pulsar wind nebula by solving a Fokker-Planck-type transport equation and calculating inverse Compton and synchrotron emissivities. We have created this time-dependent, multi-zone model to investigate changes in the particle spectrum as they traverse the pulsar wind nebula, by considering a time and spatially-dependent B-field, spatially-dependent bulk particle speed implying convection and adiabatic losses, diffusion, as well as radiative losses. Our code predicts the radiation spectrum at different positions in the nebula, yielding the surface brightness versus radius and the nebular size as function of energy. We compare our new model against more basic models using the observed spectrum of pulsar wind nebula G0.9+0.1, incorporating data from H.E.S.S. as well as radio and X-ray experiments. We show that simultaneously fitting the spectral energy distribution and the energy-dependent source size leads to more stringent constraints on several model parameters.
Spatially dependent modelling of pulsar wind nebula G0.9+0.1

NASA Astrophysics Data System (ADS)

van Rensburg, C.; Krüger, P. P.; Venter, C.

2018-07-01

We present results from a leptonic emission code that models the spectral energy distribution of a pulsar wind nebula by solving a Fokker-Planck-type transport equation and calculating inverse Compton and synchrotron emissivities. We have created this time-dependent, multizone model to investigate changes in the particle spectrum as they traverse the pulsar wind nebula, by considering a time and spatially dependent B-field, spatially dependent bulk particle speed implying convection and adiabatic losses, diffusion, as well as radiative losses. Our code predicts the radiation spectrum at different positions in the nebula, yielding the surface brightness versus radius and the nebular size as function of energy. We compare our new model against more basic models using the observed spectrum of pulsar wind nebula G0.9+0.1, incorporating data from H.E.S.S. as well as radio and X-ray experiments. We show that simultaneously fitting the spectral energy distribution and the energy-dependent source size leads to more stringent constraints on several model parameters.
Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.
Current of interacting particles inside a channel of exponential cavities: Application of a modified Fick-Jacobs equation.

PubMed

Suárez, G; Hoyuelos, M; Mártin, H

2016-06-01

Recently a nonlinear Fick-Jacobs equation has been proposed for the description of transport and diffusion of particles interacting through a hard-core potential in tubes or channels of varying cross section [Suárez et al., Phys. Rev. E 91, 012135 (2015)]PLEEE81539-375510.1103/PhysRevE.91.012135. Here we focus on the analysis of the current and mobility when the channel is composed by a chain of asymmetric cavities and a force is applied in one or the opposite direction, for both interacting and noninteracting particles, and compare analytical and Monte Carlo simulation results. We consider a cavity with a shape given by exponential functions; the linear Fick-Jacobs equation for noninteracting particles can be exactly solved in this case. The results of the current difference (when a force is applied in opposite directions) are more accurate for the modified Fick-Jacobs equation for particles with hard-core interaction than for noninteracting ones.
Earth Sciences Push Radiative Transfer Theory

NASA Astrophysics Data System (ADS)

Davis, Anthony; Mishchenko, Michael

2009-12-01

2009 International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics; Saratoga Springs, New York, 4-7 May 2009; The theories of radiative transfer and particle—particularly neutron—transport are grounded in distinctive microscale physics that deals with either optics or particle dynamics. However, it is not practical to track every wave or particle in macroscopic systems, nor do all of these details matter. That is why Newton's laws, which describe individual particles, are replaced by those of Euler, Navier-Stokes, Maxwell, Boltzmann, Gibbs, and others, which describe the collective behavior of vast numbers of particles. And that is why the radiative transfer (RT) equation is used to describe the flow of radiation through geophysical-scale systems, leaving to Maxwell's wave equations only the task of providing the optical properties of the medium, be it air, water, snow, ice, or biomass. Interestingly, particle transport is determined by the linear transport equation, which is mathematically identical to the RT equation, so geophysicists and nuclear scientists are interested in the same mathematics and computational techniques.
Evolution of the concentration PDF in random environments modeled by global random walk

NASA Astrophysics Data System (ADS)

Suciu, Nicolae; Vamos, Calin; Attinger, Sabine; Knabner, Peter

2013-04-01

The evolution of the probability density function (PDF) of concentrations of chemical species transported in random environments is often modeled by ensembles of notional particles. The particles move in physical space along stochastic-Lagrangian trajectories governed by Ito equations, with drift coefficients given by the local values of the resolved velocity field and diffusion coefficients obtained by stochastic or space-filtering upscaling procedures. A general model for the sub-grid mixing also can be formulated as a system of Ito equations solving for trajectories in the composition space. The PDF is finally estimated by the number of particles in space-concentration control volumes. In spite of their efficiency, Lagrangian approaches suffer from two severe limitations. Since the particle trajectories are constructed sequentially, the demanded computing resources increase linearly with the number of particles. Moreover, the need to gather particles at the center of computational cells to perform the mixing step and to estimate statistical parameters, as well as the interpolation of various terms to particle positions, inevitably produce numerical diffusion in either particle-mesh or grid-free particle methods. To overcome these limitations, we introduce a global random walk method to solve the system of Ito equations in physical and composition spaces, which models the evolution of the random concentration's PDF. The algorithm consists of a superposition on a regular lattice of many weak Euler schemes for the set of Ito equations. Since all particles starting from a site of the space-concentration lattice are spread in a single numerical procedure, one obtains PDF estimates at the lattice sites at computational costs comparable with those for solving the system of Ito equations associated to a single particle. The new method avoids the limitations concerning the number of particles in Lagrangian approaches, completely removes the numerical diffusion, and speeds up the computation by orders of magnitude. The approach is illustrated for the transport of passive scalars in heterogeneous aquifers, with hydraulic conductivity modeled as a random field.
Analytical solutions of the space-time fractional Telegraph and advection-diffusion equations

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Schlickeiser, Reinhard; Elhanbaly, A.

2018-02-01

The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection-diffusion equation. Analytical solutions of the space-time fractional Telegraph equation and space-time fractional advection-diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace-Fourier technique. The solutions are given in terms of Fox's H function. As an illustration they are applied to the case of solar energetic particles.
Gravity and the Spin-2 Planar Schrödinger Equation

NASA Astrophysics Data System (ADS)

Bergshoeff, Eric A.; Rosseel, Jan; Townsend, Paul K.

2018-04-01

A Schrödinger equation proposed for the Girvin-MacDonald-Platzman gapped spin-2 mode of fractional quantum Hall states is found from a novel nonrelativistic limit, applicable only in 2 +1 dimensions, of the massive spin-2 Fierz-Pauli field equations. It is also found from a novel null reduction of the linearized Einstein field equations in 3 +1 dimensions, and in this context a uniform distribution of spin-2 particles implies, via a Brinkmann-wave solution of the nonlinear Einstein equations, a confining harmonic oscillator potential for the individual particles.
A novel quantum-mechanical interpretation of the Dirac equation

NASA Astrophysics Data System (ADS)

K-H Kiessling, M.; Tahvildar-Zadeh, A. S.

2016-04-01

A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit G\\to 0, where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.
Vector solution for the mean electromagnetic fields in a layer of random particles

NASA Technical Reports Server (NTRS)

Lang, R. H.; Seker, S. S.; Levine, D. M.

1986-01-01

The mean electromagnetic fields are found in a layer of randomly oriented particles lying over a half space. A matrix-dyadic formulation of Maxwell's equations is employed in conjunction with the Foldy-Lax approximation to obtain equations for the mean fields. A two variable perturbation procedure, valid in the limit of small fractional volume, is then used to derive uncoupled equations for the slowly varying amplitudes of the mean wave. These equations are solved to obtain explicit expressions for the mean electromagnetic fields in the slab region in the general case of arbitrarily oriented particles and arbitrary polarization of the incident radiation. Numerical examples are given for the application to remote sensing of vegetation.
Multiphysics modelling of the separation of suspended particles via frequency ramping of ultrasonic standing waves.

PubMed

Trujillo, Francisco J; Eberhardt, Sebastian; Möller, Dirk; Dual, Jurg; Knoerzer, Kai

2013-03-01

A model was developed to determine the local changes of concentration of particles and the formations of bands induced by a standing acoustic wave field subjected to a sawtooth frequency ramping pattern. The mass transport equation was modified to incorporate the effect of acoustic forces on the concentration of particles. This was achieved by balancing the forces acting on particles. The frequency ramping was implemented as a parametric sweep for the time harmonic frequency response in time steps of 0.1s. The physics phenomena of piezoelectricity, acoustic fields and diffusion of particles were coupled and solved in COMSOL Multiphysics™ (COMSOL AB, Stockholm, Sweden) following a three step approach. The first step solves the governing partial differential equations describing the acoustic field by assuming that the pressure field achieves a pseudo steady state. In the second step, the acoustic radiation force is calculated from the pressure field. The final step allows calculating the locally changing concentration of particles as a function of time by solving the modified equation of particle transport. The diffusivity was calculated as function of concentration following the Garg and Ruthven equation which describes the steep increase of diffusivity when the concentration approaches saturation. However, it was found that this steep increase creates numerical instabilities at high voltages (in the piezoelectricity equations) and high initial particle concentration. The model was simplified to a pseudo one-dimensional case due to computation power limitations. The predicted particle distribution calculated with the model is in good agreement with the experimental data as it follows accurately the movement of the bands in the centre of the chamber. Crown Copyright © 2012. Published by Elsevier B.V. All rights reserved.
Vertical Distribution Characteristics of PM2.5 Observed by a Mobile Vehicle Lidar in Tianjin, China in 2016

NASA Astrophysics Data System (ADS)

Lyu, Lihui; Dong, Yunsheng; Zhang, Tianshu; Liu, Cheng; Liu, Wenqing; Xie, Zhouqing; Xiang, Yan; Zhang, Yi; Chen, Zhenyi; Fan, Guangqiang; Zhang, Leibo; Liu, Yang; Shi, Yuchen; Shu, Xiaowen

2018-02-01

We present mobile vehicle lidar observations in Tianjin, China during the spring, summer, and winter of 2016. Mobile observations were carried out along the city border road of Tianjin to obtain the vertical distribution characteristics of PM2.5. Hygroscopic growth was not considered since relative humidity was less than 60% during the observation experiments. PM2.5 profile was obtained with the linear regression equation between the particle extinction coefficient and PM2.5 mass concentration. In spring, the vertical distribution of PM2.5 exhibited a hierarchical structure. In addition to a layer of particles that gathered near the ground, a portion of particles floated at 0.6-2.5-km height. In summer and winter, the fine particles basically gathered below 1 km near the ground. In spring and summer, the concentration of fine particles in the south was higher than that in the north because of the influence of south wind. In winter, the distribution of fine particles was opposite to that measured during spring and summer. High concentrations of PM2.5 were observed in the rural areas of North Tianjin with a maximum of 350 μg m-3 on 13 December 2016. It is shown that industrial and ship emissions in spring and summer and coal combustion in winter were the major sources of fine particles that polluted Tianjin. The results provide insights into the mechanisms of haze formation and the effects of meteorological conditions during haze-fog pollution episodes in the Tianjin area.
A paradigm for modeling and computation of gas dynamics

NASA Astrophysics Data System (ADS)

Xu, Kun; Liu, Chang

2017-02-01

In the continuum flow regime, the Navier-Stokes (NS) equations are usually used for the description of gas dynamics. On the other hand, the Boltzmann equation is applied for the rarefied flow. These two equations are based on distinguishable modeling scales for flow physics. Fortunately, due to the scale separation, i.e., the hydrodynamic and kinetic ones, both the Navier-Stokes equations and the Boltzmann equation are applicable in their respective domains. However, in real science and engineering applications, they may not have such a distinctive scale separation. For example, around a hypersonic flying vehicle, the flow physics at different regions may correspond to different regimes, where the local Knudsen number can be changed significantly in several orders of magnitude. With a variation of flow physics, theoretically a continuous governing equation from the kinetic Boltzmann modeling to the hydrodynamic Navier-Stokes dynamics should be used for its efficient description. However, due to the difficulties of a direct modeling of flow physics in the scale between the kinetic and hydrodynamic ones, there is basically no reliable theory or valid governing equations to cover the whole transition regime, except resolving flow physics always down to the mean free path scale, such as the direct Boltzmann solver and the Direct Simulation Monte Carlo (DSMC) method. In fact, it is an unresolved problem about the exact scale for the validity of the NS equations, especially in the small Reynolds number cases. The computational fluid dynamics (CFD) is usually based on the numerical solution of partial differential equations (PDEs), and it targets on the recovering of the exact solution of the PDEs as mesh size and time step converging to zero. This methodology can be hardly applied to solve the multiple scale problem efficiently because there is no such a complete PDE for flow physics through a continuous variation of scales. For the non-equilibrium flow study, the direct modeling methods, such as DSMC, particle in cell, and smooth particle hydrodynamics, play a dominant role to incorporate the flow physics into the algorithm construction directly. It is fully legitimate to combine the modeling and computation together without going through the process of constructing PDEs. In other words, the CFD research is not only to obtain the numerical solution of governing equations but to model flow dynamics as well. This methodology leads to the unified gas-kinetic scheme (UGKS) for flow simulation in all flow regimes. Based on UGKS, the boundary for the validation of the Navier-Stokes equations can be quantitatively evaluated. The combination of modeling and computation provides a paradigm for the description of multiscale transport process.

The influence of particle shape on dielectric enhancement in metal-insulator composites

NASA Astrophysics Data System (ADS)

Doyle, W. T.; Jacobs, I. S.

1992-04-01

Disordered suspensions of conducting particles exhibit substantial permittivity enhancements beyond the predictions of the Clausius-Mossotti equation and other purely dipolar approximations. The magnitude of the enhancement depends upon the shape of the particles. A recently developed effective cluster model for spherical particles [Phys. Rev. B 42, 9319 (1990)] that treats a disordered suspension as a mixture, or mesosuspension, of isolated spheres and close-packed spherical clusters of arbitrary size is in excellent agreement with experiments on well-stirred suspensions of spheres over the entire accessible range of volume loading. In this paper, the effective cluster model is extended to be applicable to disordered suspensions of arbitrarily shaped conducting particles. Two physical parameters are used to characterize a general suspension: the angular average polarizability of an isolated particle, and the volume loading at closest packing of the suspension. Multipole interactions within the clusters are treated exactly. External particle-shape-dependent interactions between clusters and isolated particles are treated in the dipole approximation in two ways: explicitly, using the Clausius-Mossotti equation, and implicitly, using the Wiener equation. Both versions of the model are used to find the permittivity of a monodisperse suspension of conducting spheroids, for which the model parameters can be determined independently. The two versions are in good agreement when the axial ratio of the particles is not extreme. The Clausius-Mossotti version of the model yields a mesoscopic analogue of the dielectric virial expansion. It is limited to small volume loadings when the particles have an extremely nonspherical shape. The Wiener equation version of the model holds at all volume loadings for particles of arbitrary shape. Comparison of the two versions of the model leads to a simple physical interpretation of Wiener's equation. The models are compared with experiments of Kelly, Stenoien, and Isbell [J. Appl. Phys. 24, 258 (1953)] on aluminum and zinc particles in paraffin, with Nasuhoglu's experiments on iron particles in oil [Commun. Fac. Sci. Univ. Ankara 4, 108 (1952)], and with new X-band and Kα-band permittivity measurements on Ni-Cr alloy particles in a polyurethane binder.
Theoretical approaches to the steady-state statistical physics of interacting dissipative units

NASA Astrophysics Data System (ADS)

Bertin, Eric

2017-02-01

The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative ‘units’. The latter notion includes, e.g. inelastic grains, active or self-propelled particles, bubbles in a foam, low-dimensional dynamical systems like driven oscillators, or even spatially extended modes like Fourier modes of the velocity field in a fluid. We first review methods based on the statistical properties of a single unit, starting with elementary mean-field approximations, either static or dynamic, that describe a unit embedded in a ‘self-consistent’ environment. We then discuss how this basic mean-field approach can be extended to account for spatial dependences, in the form of space-dependent mean-field Fokker-Planck equations, for example. We also briefly review the use of kinetic theory in the framework of the Boltzmann equation, which is an appropriate description for dilute systems. We then turn to descriptions in terms of the full N-body distribution, starting from exact solutions of one-dimensional models, using a matrix-product ansatz method when correlations are present. Since exactly solvable models are scarce, we also present some approximation methods which can be used to determine the N-body distribution in a large system of dissipative units. These methods include the Edwards approach for dense granular matter and the approximate treatment of multiparticle Langevin equations with colored noise, which models systems of self-propelled particles. Throughout this review, emphasis is put on methodological aspects of the statistical modeling and on formal similarities between different physical problems, rather than on the specific behavior of a given system.
Justifying quasiparticle self-consistent schemes via gradient optimization in Baym-Kadanoff theory.

PubMed

Ismail-Beigi, Sohrab

2017-09-27

The question of which non-interacting Green's function 'best' describes an interacting many-body electronic system is both of fundamental interest as well as of practical importance in describing electronic properties of materials in a realistic manner. Here, we study this question within the framework of Baym-Kadanoff theory, an approach where one locates the stationary point of a total energy functional of the one-particle Green's function in order to find the total ground-state energy as well as all one-particle properties such as the density matrix, chemical potential, or the quasiparticle energy spectrum and quasiparticle wave functions. For the case of the Klein functional, our basic finding is that minimizing the length of the gradient of the total energy functional over non-interacting Green's functions yields a set of self-consistent equations for quasiparticles that is identical to those of the quasiparticle self-consistent GW (QSGW) (van Schilfgaarde et al 2006 Phys. Rev. Lett. 96 226402-4) approach, thereby providing an a priori justification for such an approach to electronic structure calculations. In fact, this result is general, applies to any self-energy operator, and is not restricted to any particular approximation, e.g., the GW approximation for the self-energy. The approach also shows that, when working in the basis of quasiparticle states, solving the diagonal part of the self-consistent Dyson equation is of primary importance while the off-diagonals are of secondary importance, a common observation in the electronic structure literature of self-energy calculations. Finally, numerical tests and analytical arguments show that when the Dyson equation produces multiple quasiparticle solutions corresponding to a single non-interacting state, minimizing the length of the gradient translates into choosing the solution with largest quasiparticle weight.
Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems

NASA Astrophysics Data System (ADS)

Thüroff, Florian; Weber, Christoph A.; Frey, Erwin

2014-10-01

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.
Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Kok Foong; Patterson, Robert I.A.; Wagner, Wolfgang

2015-12-15

Graphical abstract: -- Highlights: •Problems concerning multi-compartment population balance equations are studied. •A class of fragmentation weight transfer functions is presented. •Three stochastic weighted algorithms are compared against the direct simulation algorithm. •The numerical errors of the stochastic solutions are assessed as a function of fragmentation rate. •The algorithms are applied to a multi-dimensional granulation model. -- Abstract: This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. Themore » weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.« less
Thermodynamics and emergent universe

NASA Astrophysics Data System (ADS)

Ghosh, Saumya; Gangopadhyay, Sunandan

2017-05-01

We show that in the isentropic scenario, the first-order thermodynamical particle creation model gives an emergent universe solution even when the chemical potential is nonzero. However, there exists no emergent universe scenario in the second-order non-equilibrium theory for the particle creation model. We then point out a correspondence between the particle creation model with barotropic equation of state and the equation of state giving rise to an emergent universe without particle creation in spatially flat FRW cosmology.
Integrable particle systems vs solutions to the KP and 2D Toda equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruijsenaars, S.N.

Starting from the relation between integrable relativistic N-particle systems with hyperbolic interactions and elementary N-soliton solutions to the KP and 2D Toda equations, we show how fusion properties of the soliton solutions are mirrored by fusion properties of the Poisson commuting particle dynamics. We also obtain previously known relations between elliptic solutions and integrable N-particle systems with elliptic interactions, without invoking finite-gap integration theory. {copyright} 1997 Academic Press, Inc.
Studies of Fundamental Particle Dynamics in Microgravity

NASA Technical Reports Server (NTRS)

Rangel, Roger; Trolinger, James D.; Coimbra, Carlos F. M.; Witherow, William; Rogers, Jan; Rose, M. Franklin (Technical Monitor)

2001-01-01

This work summarizes theoretical and experimental concepts used to design the flight experiment mission for SHIVA - Spaceflight Holography Investigation in a Virtual Apparatus. SHIVA is a NASA project that exploits a unique, holography-based, diagnostics tool to understand the behavior of small particles subjected to transient accelerations. The flight experiments are designed for testing model equations, measuring g, g-jitter, and other microgravity phenomena. Data collection will also include experiments lying outside of the realm of existing theory. The regime under scrutiny is the low Reynolds number, Stokes regime or creeping flow, which covers particles and bubbles moving at very low velocity. The equations describing this important regime have been under development and investigation for over 100 years and yet a complete analytical solution of the general equation had remained elusive yielding only approximations and numerical solutions. In the course of the ongoing NASA NRA, the first analytical solution of the general equation was produced by members of the investigator team using the mathematics of fractional derivatives. This opened the way to an even more insightful and important investigation of the phenomena in microgravity. Recent results include interacting particles, particle-wall interactions, bubbles, and Reynolds numbers larger than unity. The Space Station provides an ideal environment for SHIVA. Limited ground experiments have already confirmed some aspects of the theory. In general the space environment is required for the overall experiment, especially for cases containing very heavy particles, very light particles, bubbles, collections of particles and for characterization of the space environment and its effect on particle experiments. Lightweight particles and bubbles typically rise too fast in a gravitational field and heavy particles sink too fast. In a microgravity environment, heavy and light particles can be studied side-by-side for long periods of time.
Geometrical approach to tumor growth.

PubMed

Escudero, Carlos

2006-08-01

Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells and particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former paper [C. Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend our analysis and try to shed light on the possible geometrical principles that drive tumor growth. We present two-dimensional models that reproduce the experimental observations, and analyze the unexplored three-dimensional case, for which interesting conclusions on tumor growth are derived.
Simulation and phases of macroscopic particles in vortex flow

NASA Astrophysics Data System (ADS)

Rice, Heath Eric

Granular materials are an interesting class of media in that they exhibit many disparate characteristics depending on conditions. The same set of particles may behave like a solid, liquid, gas, something in-between, or something completely unique depending on the conditions. Practically speaking, granular materials are used in many aspects of manufacturing, therefore any new information gleaned about them may help refine these techniques. For example, learning of a possible instability may help avoid it in practical application, saving machinery, money, and even personnel. To that end, we intend to simulate a granular medium under tornado-like vortex airflow by varying particle parameters and observing the behaviors that arise. The simulation itself was written in Python from the ground up, starting from the basic simulation equations in Poschel [1]. From there, particle spin, viscous friction, and vertical and tangential airflow were added. The simulations were then run in batches on a local cluster computer, varying the parameters of radius, flow force, density, and friction. Phase plots were created after observing the behaviors of the simulations and the regions and borders were analyzed. Most of the results were as expected: smaller particles behaved more like a gas, larger particles behaved more like a solid, and most intermediate simulations behaved like a liquid. A small subset formed an interesting crossover region in the center, and under moderate forces began to throw a few particles at a time upward from the center in a fountain-like effect. Most borders between regions appeared to agree with analysis, following a parabolic critical rotational velocity at which the parabolic surface of the material dips to the bottom of the mass of particles. The fountain effects seemed to occur at speeds along and slightly faster than this division. [1] Please see thesis for references.
Gyrokinetic equations and full f solution method based on Dirac's constrained Hamiltonian and inverse Kruskal iteration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heikkinen, J. A.; Nora, M.

2011-02-15

Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J= as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allowsmore » direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.« less
Ion composition and temperature in the topside ionosphere.

NASA Technical Reports Server (NTRS)

Brace, L. H.; Dunham, G. S.; Mayr, H. G.

1967-01-01

Particle and energy continuity equations derived and solved by computer method ion composition and plasma temperature measured by Explorer XXII PARTICLE and energy continuity equations derived and solved by computer method for ion composition and plasma temperature measured by Explorer XXII
Inhalers and nebulizers: basic principles and preliminary measurements

NASA Astrophysics Data System (ADS)

Misik, Ondrej; Lizal, Frantisek; Asl, Vahid Farhikhteh; Belka, Miloslav; Jedelsky, Jan; Elcner, Jakub; Jicha, Miroslav

2018-06-01

Inhalers are hand-held devices which are used for administration of therapeutic aerosols via inhalation. Nebulizers are larger devices serving for home and hospital care using inhaled medication. This contribution describes the basic principles of dispersion of aerosol particles used in various types of inhalers and nebulizers, and lists the basic physical mechanisms contributing to the deposition of inhaled particles in the human airways. The second part of this article presents experimental setup, methodology and preliminary results of particle size distributions produced by several selected inhalers and nebulizers.
Analytical Model of Advection and Erosion in a Rectangular Channel

NASA Astrophysics Data System (ADS)

Kaufman, Miron

2007-03-01

We consider the Boussinesq pressure driven creeping flow in a rectangular channel. We assume a particle to be made of primary fragments bound together. Particles are advected by the flow and they erode because of the shear stresses imparted by the fluid. The time evolution of the numbers of particles of different sizes is described by the Bateman equations of nuclear radioactivity. We find, by solving these differential equations, the numbers of particles of each possible size as functions of time.
Size distribution spectrum of noninertial particles in turbulence

NASA Astrophysics Data System (ADS)

Saito, Izumi; Gotoh, Toshiyuki; Watanabe, Takeshi

2018-05-01

Collision-coalescence growth of noninertial particles in three-dimensional homogeneous isotropic turbulence is studied. Smoluchowski's coagulation equation describes the evolution of the size distribution of particles in this system. By applying a methodology based on turbulence theory, the equation is shown to have a steady-state solution, which corresponds to the Kolmogorov-type power-law spectrum. Direct numerical simulations of turbulence and Lagrangian particles are conducted. The result shows that the size distribution in a statistically steady state agrees accurately with the theoretical prediction.
Effects of solar radiation on the orbits of small particles

NASA Technical Reports Server (NTRS)

Lyttleton, R. A.

1976-01-01

A modification of the Robertson (1937) equations of particle motion in the presence of solar radiation is developed which allows for partial reflection of sunlight as a result of rapid and varying particle rotations caused by interaction with the solar wind. The coefficients and forces in earlier forms of the equations are compared with those in the present equations, and secular rates of change of particle orbital elements are determined. Orbital dimensions are calculated in terms of time, probable sizes and densities of meteoric and cometary particles are estimated, and times of infall to the sun are computed for a particle moving in an almost circular orbit and a particle moving in an elliptical orbit of high eccentricity. Changes in orbital elements are also determined for particles from a long-period sun-grazing comet. The results show that the time of infall to the sun from a highly eccentric orbit is substantially shorter than from a circular orbit with a radius equal to the mean distance in the eccentric orbit. The possibility is considered that the free orbital kinetic energy of particles drawn into the sun may be the energy source for the solar corona.
Comparisons of Multilevel Modeling and Structural Equation Modeling Approaches to Actor-Partner Interdependence Model.

PubMed

Hong, Sehee; Kim, Soyoung

2018-01-01

There are basically two modeling approaches applicable to analyzing an actor-partner interdependence model: the multilevel modeling (hierarchical linear model) and the structural equation modeling. This article explains how to use these two models in analyzing an actor-partner interdependence model and how these two approaches work differently. As an empirical example, marital conflict data were used to analyze an actor-partner interdependence model. The multilevel modeling and the structural equation modeling produced virtually identical estimates for a basic model. However, the structural equation modeling approach allowed more realistic assumptions on measurement errors and factor loadings, rendering better model fit indices.
The nature of the sunspot phenomenon. I - Solutions of the heat transport equation

NASA Technical Reports Server (NTRS)

Parker, E. N.

1974-01-01

It is pointed out that sunspots represent a disruption in the uniform flow of heat through the convective zone. The basic sunspot structure is, therefore, determined by the energy transport equation. The solutions of this equation for the case of stochastic heat transport are examined. It is concluded that a sunspot is basically a region of enhanced, rather than inhibited, energy transport and emissivity. The heat flow equations are discussed and attention is given to the shallow depth of the sunspot phenomenon. The sunspot is seen as a heat engine of high efficiency which converts most of the heat flux into hydromagnetic waves.
Dirac-Kähler particle in Riemann spherical space: boson interpretation

NASA Astrophysics Data System (ADS)

Ishkhanyan, A. M.; Florea, O.; Ovsiyuk, E. M.; Red'kov, V. M.

2015-11-01

In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself one may expect to have a discrete energy spectrum. In the case of the minimal value of the total angular momentum, $j=0$, the radial equations are reduced to second-order ordinary differential equations, which are straightforwardly solved in terms of the hypergeometric functions. For non-zero values of the total angular momentum, however, the radial equations are reduced to a pair of complicated fourth-order differential equations. Employing the factorization approach, we derive the general solution of these equations involving four independent fundamental solutions written in terms of combinations of the hypergeometric functions. The corresponding discrete energy spectrum is then determined via termination of the involved hypergeometric series, resulting in quasi-polynomial wave-functions. The constructed solutions lead to notable observations when compared with those for the ordinary Dirac particle. The energy spectrum for the Dirac-K\\"ahler particle in spherical space is much more complicated. Its structure substantially differs from that for the Dirac particle since it consists of two paralleled energy level series each of which is twofold degenerate. Besides, none of the two separate series coincides with the series for the Dirac particle. Thus, the Dirac--K\\"ahler field cannot be interpreted as a system of four Dirac fermions. Additional arguments supporting this conclusion are discussed.
Solar wind and the motion of dust grains

NASA Astrophysics Data System (ADS)

Klačka, J.; Petržala, J.; Pástor, P.; Kómar, L.

2012-04-01

In this paper, we investigate the action of solar wind on an arbitrarily shaped interplanetary dust particle. The final relativistically covariant equation of motion of the particle also contains the change of the particle's mass. The non-radial solar wind velocity vector is also included. The covariant equation of motion reduces to the Poynting-Robertson effect in the limiting case when a spherical particle is treated, when the speed of the incident solar wind corpuscles tends to the speed of light and when the corpuscles spread radially from the Sun. The results of quantum mechanics have to be incorporated into the physical considerations, in order to obtain the limiting case. If the solar wind affects the motion of a spherical interplanetary dust particle, then ?. Here, p'in and p'out are the incoming and outgoing radiation momenta (per unit time), respectively, measured in the proper frame of reference of the particle, and ? and ? are the solar wind pressure and the total scattering cross-sections, respectively. An analytical solution of the derived equation of motion yields a qualitative behaviour consistent with numerical calculations. This also holds if we consider a decrease of the particle's mass. Using numerical integration of the derived equation of motion, we confirm our analytical result that the non-radial solar wind (with a constant value of angle between the radial direction and the direction of the solar wind velocity) causes outspiralling of the dust particle from the Sun for large values of the particle's semimajor axis. The non-radial solar wind also increases the time the particle spirals towards the Sun. If we consider the periodical variability of the solar wind with the solar cycle, then there are resonances between the particle's orbital period and the period of the solar cycle.

Hydrodynamics of sediment threshold

NASA Astrophysics Data System (ADS)

Ali, Sk Zeeshan; Dey, Subhasish

2016-07-01

A novel hydrodynamic model for the threshold of cohesionless sediment particle motion under a steady unidirectional streamflow is presented. The hydrodynamic forces (drag and lift) acting on a solitary sediment particle resting over a closely packed bed formed by the identical sediment particles are the primary motivating forces. The drag force comprises of the form drag and form induced drag. The lift force includes the Saffman lift, Magnus lift, centrifugal lift, and turbulent lift. The points of action of the force system are appropriately obtained, for the first time, from the basics of micro-mechanics. The sediment threshold is envisioned as the rolling mode, which is the plausible mode to initiate a particle motion on the bed. The moment balance of the force system on the solitary particle about the pivoting point of rolling yields the governing equation. The conditions of sediment threshold under the hydraulically smooth, transitional, and rough flow regimes are examined. The effects of velocity fluctuations are addressed by applying the statistical theory of turbulence. This study shows that for a hindrance coefficient of 0.3, the threshold curve (threshold Shields parameter versus shear Reynolds number) has an excellent agreement with the experimental data of uniform sediments. However, most of the experimental data are bounded by the upper and lower limiting threshold curves, corresponding to the hindrance coefficients of 0.2 and 0.4, respectively. The threshold curve of this study is compared with those of previous researchers. The present model also agrees satisfactorily with the experimental data of nonuniform sediments.
A computational study of the discretization error in the solution of the Spencer-Lewis equation by doubling applied to the upwind finite-difference approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nelson, P.; Seth, D.L.; Ray, A.K.

A detailed and systematic study of the nature of the discretization error associated with the upwind finite-difference method is presented. A basic model problem has been identified and based upon the results for this problem, a basic hypothesis regarding the accuracy of the computational solution of the Spencer-Lewis equation is formulated. The basic hypothesis is then tested under various systematic single complexifications of the basic model problem. The results of these tests provide the framework of the refined hypothesis presented in the concluding comments. 27 refs., 3 figs., 14 tabs.
Eulerian velocity reconstruction in ideal atmospheric dynamics using potential vorticity and potential temperature

NASA Astrophysics Data System (ADS)

Blender, R.

2009-04-01

An approach for the reconstruction of atmospheric flow is presented which uses space- and time-dependent fields of density ?, potential vorticity Q and potential temperature Î& cedil;[J. Phys. A, 38, 6419 (2005)]. The method is based on the fundamental equations without approximation. The basic idea is to consider the time-dependent continuity equation as a condition for zero divergence of momentum in four dimensions (time and space, with unit velocity in time). This continuity equation is solved by an ansatz for the four-dimensional momentum using three conserved stream functions, the potential vorticity, potential temperature and a third field, denoted as ?-potential. In zonal flows, the ?-potential identifies the initial longitude of particles, whereas potential vorticity and potential temperature identify mainly meridional and vertical positions. Since the Lagrangian tracers Q, Î&,cedil; and ? determine the Eulerian velocity field, the reconstruction combines the Eulerian and the Lagrangian view of hydrodynamics. In stationary flows, the ?-potential is related to the Bernoulli function. The approach requires that the gradients of the potential vorticity and potential temperature do not vanish when the velocity remains finite. This behavior indicates a possible interrelation with stability conditions. Examples with analytical solutions are presented for a Rossby wave and zonal and rotational shear flows.
Relativistic particle in a box: Klein-Gordon versus Dirac equations

NASA Astrophysics Data System (ADS)

Alberto, Pedro; Das, Saurya; Vagenas, Elias C.

2018-03-01

The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.
Steady-state configuration and tension calculations of marine cables under complex currents via separated particle swarm optimization

NASA Astrophysics Data System (ADS)

Xu, Xue-song

2014-12-01

Under complex currents, the motion governing equations of marine cables are complex and nonlinear, and the calculations of cable configuration and tension become difficult compared with those under the uniform or simple currents. To obtain the numerical results, the usual Newton-Raphson iteration is often adopted, but its stability depends on the initial guessed solution to the governing equations. To improve the stability of numerical calculation, this paper proposed separated the particle swarm optimization, in which the variables are separated into several groups, and the dimension of search space is reduced to facilitate the particle swarm optimization. Via the separated particle swarm optimization, these governing nonlinear equations can be solved successfully with any initial solution, and the process of numerical calculation is very stable. For the calculations of cable configuration and tension of marine cables under complex currents, the proposed separated swarm particle optimization is more effective than the other particle swarm optimizations.
Environmental solid particle effects on compressor cascade performance

NASA Technical Reports Server (NTRS)

Tabakoff, W.; Balan, C.

1982-01-01

The effect of suspended solid particles on the performance of the compressor cascade was investigated experimentally in a specially built cascade tunnel, using quartz sand particles. The cascades were made of NACA 65(10)10 airfoils. Three cascades were tested, one accelerating cascade and two diffusing cascades. The theoretical analysis assumes inviscid and incompressible two dimensional flow. The momentum exchange between the fluid and the particle is accounted for by the interphase force terms in the fluid momentum equation. The modified fluid phase momentum equations and the continuity equation are reduced to the conventional stream function vorticity formulation. The method treats the fluid phase in the Eulerian system and the particle phase in Lagrangian system. The experimental results indicate a small increase in the blade surface static pressures, while the theoretical results indicate a small decrease. The theoretical analysis, also predicts the loss in total pressure associated with the particulate flow through the cascade.
Temperature effects on drift of suspended single-domain particles induced by the Magnus force

NASA Astrophysics Data System (ADS)

Denisov, S. I.; Lyutyy, T. V.; Reva, V. V.; Yermolenko, A. S.

2018-03-01

We study the temperature dependence of the drift velocity of single-domain ferromagnetic particles induced by the Magnus force in a dilute suspension. A set of stochastic equations describing the translational and rotational dynamics of particles is derived, and the particle drift velocity that depends on components of the average particle magnetization is introduced. The Fokker-Planck equation for the probability density of magnetization orientations is solved analytically in the limit of strong thermal fluctuations for both the planar rotor and general models. Using these solutions, we calculate the drift velocity and show that the out-of-plane fluctuations of magnetization, which are not accounted for in the planar rotor model, play an important role. In the general case of arbitrary fluctuations, we investigate the temperature dependence of the drift velocity by numerically simulating a set of effective stochastic differential equations for the magnetization dynamics.
A Persistent Feature of Multiple Scattering of Waves in the Time-Domain: A Tutorial

NASA Technical Reports Server (NTRS)

Lock, James A.; Mishchenko, Michael I.

2015-01-01

The equations for frequency-domain multiple scattering are derived for a scalar or electromagnetic plane wave incident on a collection of particles at known positions, and in the time-domain for a plane wave pulse incident on the same collection of particles. The calculation is carried out for five different combinations of wave types and particle types of increasing geometrical complexity. The results are used to illustrate and discuss a number of physical and mathematical characteristics of multiple scattering in the frequency- and time-domains. We argue that frequency-domain multiple scattering is a purely mathematical construct since there is no temporal sequencing information in the frequency-domain equations and since the multi-particle path information can be dispelled by writing the equations in another mathematical form. However, multiple scattering becomes a definite physical phenomenon in the time-domain when the collection of particles is illuminated by an appropriately short localized pulse.
An integral equation formulation for rigid bodies in Stokes flow in three dimensions

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Greengard, Leslie; Rachh, Manas; Veerapaneni, Shravan

2017-03-01

We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials, so that only a small number of spatial discretization points per particle are required. The resulting discrete sums are computed in O (n) time, where n denotes the number of particles, using the fast multipole method (FMM). The particle positions and orientations are updated by a high-order time-stepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples.
Speciation dynamics of metals in dispersion of nanoparticles with discrete distribution of charged binding sites.

PubMed

Polyakov, Pavel D; Duval, Jérôme F L

2014-02-07

We report a comprehensive theory to evaluate the kinetics of complex formation between metal ions and charged spherical nanoparticles. The latter consist of an ion-impermeable core surrounded by a soft shell layer characterized by a discrete axisymmetric 2D distribution of charged sites that bind metal ions. The theory explicitly integrates the conductive diffusion of metal ions from bulk solution toward the respective locations of the reactive sites within the particle shell volume. The kinetic constant k for outer-sphere nanoparticle-metal association is obtained from the sum of the contributions stemming from all reactive sites, each evaluated from the corresponding incoming flux of metal ions derived from steady-state Poisson-Nernst-Planck equations. Illustrations are provided to capture the basic intertwined impacts of particle size, overall particle charge, spatial heterogeneity in site distribution, type of particle (hard, core-shell or porous) and concentration of the background electrolyte on k. As a limit, k converges with predictions from previously reported analytical expressions derived for porous particles with low and high charge density, cases that correspond to coulombic and mean-field (smeared-out) electrostatic treatments, respectively. The conditions underlying the applicability of these latter approaches are rigorously identified in terms of (i) the extent of overlap between electric double layers around charged neighbouring sites, and (ii) the magnitude of the intraparticulate metal concentration gradient. For the first time, the proposed theory integrates the differentiated impact of the local potential around the charged binding sites amidst the overall particle field, together with that of the so-far discarded intraparticulate flux of metal ions.
Anomalous segregation dynamics of self-propelled particles

NASA Astrophysics Data System (ADS)

Mones, Enys; Czirók, András; Vicsek, Tamás

2015-06-01

A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider the adhesion difference-driven segregation of actively moving units, a fundamental but still poorly explored aspect of collective motility. In particular, we propose a model in which particles have a tendency to adhere through a mechanism which makes them both stay in touch and synchronize their direction of motion—but the interaction is limited to particles of the same kind. The calculations corresponding to the related differential equations can be made in parallel, thus a powerful GPU card allows large scale simulations. We find that in a very large system of particles, interacting without explicit alignment rule, three basic segregation regimes seem to exist as a function of time: (i) at the beginning the time dependence of the correlation length is analogous to that predicted by the Cahn-Hilliard theory, (ii) next rapid segregation occurs characterized with a separation of the different kinds of units being faster than any previously suggested speed, finally, (iii) the growth of the characteristic sizes in the system slows down due to a new regime in which self-confined, rotating, splitting and re-joining clusters appear. Our results can explain recent observations of segregating tissue cells in vitro.
Steady-State Electrodiffusion from the Nernst-Planck Equation Coupled to Local Equilibrium Monte Carlo Simulations.

PubMed

Boda, Dezső; Gillespie, Dirk

2012-03-13

We propose a procedure to compute the steady-state transport of charged particles based on the Nernst-Planck (NP) equation of electrodiffusion. To close the NP equation and to establish a relation between the concentration and electrochemical potential profiles, we introduce the Local Equilibrium Monte Carlo (LEMC) method. In this method, Grand Canonical Monte Carlo simulations are performed using the electrochemical potential specified for the distinct volume elements. An iteration procedure that self-consistently solves the NP and flux continuity equations with LEMC is shown to converge quickly. This NP+LEMC technique can be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concentrations and small applied voltages that are difficult for other particle simulation techniques.
A deterministic particle method for one-dimensional reaction-diffusion equations

NASA Technical Reports Server (NTRS)

Mascagni, Michael

1995-01-01

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.
Particle connectedness and cluster formation in sequential depositions of particles: integral-equation theory.

PubMed

Danwanichakul, Panu; Glandt, Eduardo D

2004-11-15

We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.
Particle connectedness and cluster formation in sequential depositions of particles: Integral-equation theory

NASA Astrophysics Data System (ADS)

Danwanichakul, Panu; Glandt, Eduardo D.

2004-11-01

We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.
Spectral modeling of radiation in combustion systems

NASA Astrophysics Data System (ADS)

Pal, Gopalendu

Radiation calculations are important in combustion due to the high temperatures encountered but has not been studied in sufficient detail in the case of turbulent flames. Radiation calculations for such problems require accurate, robust, and computationally efficient models for the solution of radiative transfer equation (RTE), and spectral properties of radiation. One more layer of complexity is added in predicting the overall heat transfer in turbulent combustion systems due to nonlinear interactions between turbulent fluctuations and radiation. The present work is aimed at the development of finite volume-based high-accuracy thermal radiation modeling, including spectral radiation properties in order to accurately capture turbulence-radiation interactions (TRI) and predict heat transfer in turbulent combustion systems correctly and efficiently. The turbulent fluctuations of temperature and chemical species concentrations have strong effects on spectral radiative intensities, and TRI create a closure problem when the governing partial differential equations are averaged. Recently, several approaches have been proposed to take TRI into account. Among these attempts the most promising approaches are the probability density function (PDF) methods, which can treat nonlinear coupling between turbulence and radiative emission exactly, i.e., "emission TRI". The basic idea of the PDF method is to treat physical variables as random variables and to solve the PDF transport equation stochastically. The actual reacting flow field is represented by a large number of discrete stochastic particles each carrying their own random variable values and evolving with time. The mean value of any function of those random variables, such as the chemical source term, can be evaluated exactly by taking the ensemble average of particles. The local emission term belongs to this class and thus, can be evaluated directly and exactly from particle ensembles. However, the local absorption term involves interactions between the local particle and energy emitted by all other particles and, hence, cannot be obtained from particle ensembles directly. To close the nonlinear coupling between turbulence and absorption, i.e., "absorption TRI", an optically thin fluctuation approximation can be applied to virtually all combustion problems and obtain acceptable accuracy. In the present study a composition-PDF method is applied, in which only the temperature and the species concentrations are treated as random variables. A closely coupled hybrid finite-volume/Monte Carlo scheme is adopted, in which the Monte Carlo method is used to solve the composition-PDF for chemical reactions and the finite volume method is used to solve for the flow field and radiation. Spherical harmonics method-based finite volume solvers (P-1 and P-3) are developed using the data structures of the high fidelity open-source code flow software OpenFOAM. Spectral radiative properties of the participating medium are modeled using full-spectrum k-distribution methods. Advancements of basic k-distribution methods are performed for nongray nonhomogeneous gas- and particulate-phase (soot, fuel droplets, ash, etc.) participating media using multi-scale and multi-group based approaches. These methods achieve close-to benchmark line-by-line (LBL) accuracy in strongly inhomogeneous media at a tiny fraction of LBL's computational cost. A portable spectral module is developed, which includes all the basic to advanced k-distribution methods along with the precompiled accurate and compact k-distribution databases. The P-1 /P-3 RTE solver coupled with the spectral module is used in conjunction with the combined Reynolds-averaged Navier-Stokes (RANS) and composition-PDF-based turbulence-chemistry solver to investigate TRI in multiphase turbulent combustion systems. The combustion solvers developed in this study is employed to simulate several turbulent jet flames, such as Sandia Flame D, and artificial nonsooting and sooting flames derived from Flame D. The effects of combustion chemistry, radiation and TRI on total heat transfer and pollutant (such as NO x) generation are studied for the above flames. The accuracy of the overall combustion solver is assessed by comparing it with the experimental data for Flame D. Comparison of the accuracy and the computational cost among various spectral models and RTE solvers is extensively done on the artificial flames derived from Flame D to demonstrate the necessity of accurate modeling of radiation in combustion problems.
A geometric viewpoint on generalized hydrodynamics

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Spohn, Herbert; Yoshimura, Takato

2018-01-01

Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective ("dressed") velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles; in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.
Coarse-grained computation for particle coagulation and sintering processes by linking Quadrature Method of Moments with Monte-Carlo

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zou Yu, E-mail: yzou@Princeton.ED; Kavousanakis, Michail E., E-mail: mkavousa@Princeton.ED; Kevrekidis, Ioannis G., E-mail: yannis@Princeton.ED

2010-07-20

The study of particle coagulation and sintering processes is important in a variety of research studies ranging from cell fusion and dust motion to aerosol formation applications. These processes are traditionally simulated using either Monte-Carlo methods or integro-differential equations for particle number density functions. In this paper, we present a computational technique for cases where we believe that accurate closed evolution equations for a finite number of moments of the density function exist in principle, but are not explicitly available. The so-called equation-free computational framework is then employed to numerically obtain the solution of these unavailable closed moment equations bymore » exploiting (through intelligent design of computational experiments) the corresponding fine-scale (here, Monte-Carlo) simulation. We illustrate the use of this method by accelerating the computation of evolving moments of uni- and bivariate particle coagulation and sintering through short simulation bursts of a constant-number Monte-Carlo scheme.« less
Pressure evolution equation for the particulate phase in inhomogeneous compressible disperse multiphase flows

NASA Astrophysics Data System (ADS)

Annamalai, Subramanian; Balachandar, S.; Sridharan, P.; Jackson, T. L.

2017-02-01

An analytical expression describing the unsteady pressure evolution of the dispersed phase driven by variations in the carrier phase is presented. In this article, the term "dispersed phase" represents rigid particles, droplets, or bubbles. Letting both the dispersed and continuous phases be inhomogeneous, unsteady, and compressible, the developed pressure equation describes the particle response and its eventual equilibration with that of the carrier fluid. The study involves impingement of a plane traveling wave of a given frequency and subsequent volume-averaged particle pressure calculation due to a single wave. The ambient or continuous fluid's pressure and density-weighted normal velocity are identified as the source terms governing the particle pressure. Analogous to the generalized Faxén theorem, which is applicable to the particle equation of motion, the pressure expression is also written in terms of the surface average of time-varying incoming flow properties. The surface average allows the current formulation to be generalized for any complex incident flow, including situations where the particle size is comparable to that of the incoming flow. Further, the particle pressure is also found to depend on the dispersed-to-continuous fluid density ratio and speed of sound ratio in addition to dynamic viscosities of both fluids. The model is applied to predict the unsteady pressure variation inside an aluminum particle subjected to normal shock waves. The results are compared against numerical simulations and found to be in good agreement. Furthermore, it is shown that, although the analysis is conducted in the limit of negligible flow Reynolds and Mach numbers, it can be used to compute the density and volume of the dispersed phase to reasonable accuracy. Finally, analogous to the pressure evolution expression, an equation describing the time-dependent particle radius is deduced and is shown to reduce to the Rayleigh-Plesset equation in the linear limit.
Preparation and characterization of corn cob activated carbon coated with nano-sized magnetite particles for the removal of Cr(VI).

PubMed

Nethaji, S; Sivasamy, A; Mandal, A B

2013-04-01

Activated carbon prepared from corn cob biomass, magnetized by magnetite nanoparticles (MCCAC) was used for the adsorption of hexavalent chromium from aqueous solution. The adsorbent was characterized by SEM, TEM, XRD, VSM, surface functionality and zero-point charge. The iron oxide nanoparticles were of 50 nm sizes and the saturation magnetization value for the adsorbent is 48.43 emu/g. Adsorption was maximum at pH 2. Isotherm data were modeled using Langmuir, Freundlich and Temkin isotherm. The prepared MCCAC had a heterogeneous surface. The maximum monolayer adsorption capacity was 57.37 mg/g. Kinetic studies were carried out and the data fitted the pseudo second-order equation. The mechanism of the adsorption process was studied by incorporating the kinetic data with intraparticle diffusion model, Bangham equation and Boyd plot. The adsorption was by chemisorption and the external mass transfer was the rate-determining step. A micro column was designed and the basic column parameters were estimated. Copyright © 2013 Elsevier Ltd. All rights reserved.

Size Effect on Specific Energy Distribution in Particle Comminution

NASA Astrophysics Data System (ADS)

Xu, Yongfu; Wang, Yidong

A theoretical study is made to derive an energy distribution equation for the size reduction process from the fractal model for the particle comminution. Fractal model is employed as a valid measure of the self-similar size distribution of comminution daughter products. The tensile strength of particles varies with particle size in the manner of a power function law. The energy consumption for comminuting single particle is found to be proportional to the 5(D-3)/3rd order of the particle size, D being the fractal dimension of particle comminution daughter. The Weibull statistics is applied to describe the relationship between the breakage probability and specific energy of particle comminution. A simple equation is derived for the breakage probability of particles in view of the dependence of fracture energy on particle size. The calculated exponents and Weibull coefficients are generally in conformity with published data for fracture of particles.
Unveiling the relationships among the viscosity equations of glass liquids and colloidal suspensions for obtaining universal equations with the generic free volume concept.

PubMed

Hao, Tian

2015-09-14

The underlying relationships among viscosity equations of glass liquids and colloidal suspensions are explored with the aid of free volume concept. Viscosity equations of glass liquids available in literature are focused and found to have a same physical basis but different mathematical expressions for the free volume. The glass transitions induced by temperatures in glass liquids and the percolation transition induced by particle volume fractions in colloidal suspensions essentially are a second order phase transition: both those two transitions could induce the free volume changes, which in turn determines how the viscosities are going to change with temperatures and/or particle volume fractions. Unified correlations of the free volume to both temperatures and particle volume fractions are thus proposed. The resulted viscosity equations are reducible to many popular viscosity equations currently widely used in literature; those equations should be able to cover many different types of materials over a wide temperature range. For demonstration purpose, one of the simplified versions of those newly developed equations is compared with popular viscosity equations and the experimental data: it can well fit the experimental data over a wide temperature range. The current work reveals common physical grounds among various viscosity equations, deepening our understanding on viscosity and unifying the free volume theory across many different systems.
Group theoretical derivation of the minimal coupling principle

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2017-04-01

The group theoretical methods worked out by Bargmann, Mackey and Wigner, which deductively establish the Quantum Theory of a free particle for which Galileian transformations form a symmetry group, are extended to the case of an interacting particle. In doing so, the obstacles caused by loss of symmetry are overcome. In this approach, specific forms of the wave equation of an interacting particle, including the equation derived from the minimal coupling principle, are implied by particular first-order invariance properties that characterize the interaction with respect to specific subgroups of Galileian transformations; moreover, the possibility of yet unknown forms of the wave equation is left open.
Fluctuating chemohydrodynamics and the stochastic motion of self-diffusiophoretic particles

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Kapral, Raymond

2018-04-01

The propulsion of active particles by self-diffusiophoresis is driven by asymmetric catalytic reactions on the particle surface that generate a mechanochemical coupling between the fluid velocity and the concentration fields of fuel and product in the surrounding solution. Because of thermal and molecular fluctuations in the solution, the motion of micrometric or submicrometric active particles is stochastic. Coupled Langevin equations describing the translation, rotation, and reaction of such active particles are deduced from fluctuating chemohydrodynamics and fluctuating boundary conditions at the interface between the fluid and the particle. These equations are consistent with microreversibility and the Onsager-Casimir reciprocal relations between affinities and currents and provide a thermodynamically consistent basis for the investigation of the dynamics of active particles propelled by diffusiophoretic mechanisms.
A volume-filtered formulation to capture particle-shock interactions in multiphase compressible flows

NASA Astrophysics Data System (ADS)

Shallcross, Gregory; Capecelatro, Jesse

2017-11-01

Compressible particle-laden flows are common in engineering systems. Applications include but are not limited to water injection in high-speed jet flows for noise suppression, rocket-plume surface interactions during planetary landing, and explosions during coal mining operations. Numerically, it is challenging to capture these interactions due to the wide range of length and time scales. Additionally, there are many forms of the multiphase compressible flow equations with volume fraction effects, some of which are conflicting in nature. The purpose of this presentation is to develop the capability to accurately capture particle-shock interactions in systems with a large number of particles from dense to dilute regimes. A thorough derivation of the volume filtered equations is presented. The volume filtered equations are then implemented in a high-order, energy-stable Eulerian-Lagrangian framework. We show this framework is capable of decoupling the fluid mesh from the particle size, enabling arbitrary particle size distributions in the presence of shocks. The proposed method is then assessed against particle-laden shock tube data. Quantities of interest include fluid-phase pressure profiles and particle spreading rates. The effect of collisions in 2D and 3D are also evaluated.
The nature and role of advection in advection-diffusion equations used for modelling bed load transport

NASA Astrophysics Data System (ADS)

Ancey, Christophe; Bohorquez, Patricio; Heyman, Joris

2016-04-01

The advection-diffusion equation arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Stochastic models can also be used to derive this equation, with the significant advantage that they provide information on the statistical properties of particle activity. Stochastic models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. We develop an approach based on birth-death Markov processes, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received little attention. We show that particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.
The Influence of Turbulent Coherent Structure on Suspended Sediment Transport

NASA Astrophysics Data System (ADS)

Huang, S. H.; Tsai, C.

2017-12-01

The anomalous diffusion of turbulent sedimentation has received more and more attention in recent years. With the advent of new instruments and technologies, researchers have found that sediment behavior may deviate from Fickian assumptions when particles are heavier. In particle-laden flow, bursting phenomena affects instantaneous local concentrations, and seems to carry suspended particles for a longer distance. Instead of the pure diffusion process in an analogy to Brownian motion, Levy flight which allows particles to move in response to bursting phenomena is suspected to be more suitable for describing particle movement in turbulence. And the fractional differential equation is a potential candidate to improve the concentration profile. However, stochastic modeling (the Differential Chapmen-Kolmogorov Equation) also provides an alternative mathematical framework to describe system transits between different states through diffusion/the jump processes. Within this framework, the stochastic particle tracking model linked with advection diffusion equation is a powerful tool to simulate particle locations in the flow field. By including the jump process to this model, a more comprehensive description for suspended sediment transport can be provided with a better physical insight. This study also shows the adaptability and expandability of the stochastic particle tracking model for suspended sediment transport modeling.
Predictive Capability of the Compressible MRG Equation for an Explosively Driven Particle with Validation

NASA Astrophysics Data System (ADS)

Garno, Joshua; Ouellet, Frederick; Koneru, Rahul; Balachandar, Sivaramakrishnan; Rollin, Bertrand

2017-11-01

An analytic model to describe the hydrodynamic forces on an explosively driven particle is not currently available. The Maxey-Riley-Gatignol (MRG) particle force equation generalized for compressible flows is well-studied in shock-tube applications, and captures the evolution of particle force extracted from controlled shock-tube experiments. In these experiments only the shock-particle interaction was examined, and the effects of the contact line were not investigated. In the present work, the predictive capability of this model is considered for the case where a particle is explosively ejected from a rigid barrel into ambient air. Particle trajectory information extracted from simulations is compared with experimental data. This configuration ensures that both the shock and contact produced by the detonation will influence the motion of the particle. The simulations are carried out using a finite volume, Euler-Lagrange code using the JWL equation of state to handle the explosive products. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program,under Contract No. DE-NA0002378.
Smoothed Particle Hydrodynamics and its applications for multiphase flow and reactive transport in porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tartakovsky, Alexandre M.; Trask, Nathaniel; Pan, K.

2016-03-11

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and Advection-Diffusion-Reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.
Relationships between basic soils-engineering equations and basic ground-water flow equations

USGS Publications Warehouse

Jorgensen, Donald G.

1980-01-01

The many varied though related terms developed by ground-water hydrologists and by soils engineers are useful to each discipline, but their differences in terminology hinder the use of related information in interdisciplinary studies. Equations for the Terzaghi theory of consolidation and equations for ground-water flow are identical under specific conditions. A combination of the two sets of equations relates porosity to void ratio and relates the modulus of elasticity to the coefficient of compressibility, coefficient of volume compressibility, compression index, coefficient of consolidation, specific storage, and ultimate compaction. Also, transient ground-water flow is related to coefficient of consolidation, rate of soil compaction, and hydraulic conductivity. Examples show that soils-engineering data and concepts are useful to solution of problems in ground-water hydrology.
Grid adaption based on modified anisotropic diffusion equations formulated in the parametic domain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagmeijer, R.

1994-11-01

A new grid-adaption algorithm for problems in computational fluid dynamics is presented. The basic equations are derived from a variational problem formulated in the parametric domain of the mapping that defines the existing grid. Modification of the basic equations provides desirable properties in boundary layers. The resulting modified anisotropic diffusion equations are solved for the computational coordinates as functions of the parametric coordinates and these functions are numerically inverted. Numerical examples show that the algorithm is robust, that shocks and boundary layers are well-resolved on the adapted grid, and that the flow solution becomes a globally smooth function of themore » computational coordinates.« less
A momentum-space formulation without partial wave decomposition for scattering of two spin-half particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fachruddin, Imam, E-mail: imam.fachruddin@sci.ui.ac.id; Salam, Agus

2016-03-11

A new momentum-space formulation for scattering of two spin-half particles, both either identical or unidentical, is formulated. As basis states the free linear-momentum states are not expanded into the angular-momentum states, the system’s spin states are described by the product of the spin states of the two particles, and the system’s isospin states by the total isospin states of the two particles. We evaluate the Lippmann-Schwinger equations for the T-matrix elements in these basis states. The azimuthal behavior of the potential and of the T-matrix elements leads to a set of coupled integral equations for the T-matrix elements in twomore » variables only, which are the magnitude of the relative momentum and the scattering angle. Some symmetry relations for the potential and the T-matrix elements reduce the number of the integral equations to be solved. A set of six spin operators to express any interaction of two spin-half particles is introduced. We show the spin-averaged differential cross section as being calculated in terms of the solution of the set of the integral equations.« less
A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Chang, E-mail: cliuaa@ust.hk; Xu, Kun, E-mail: makxu@ust.hk; Sun, Quanhua, E-mail: qsun@imech.ac.cn

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, themore » dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the non-equilibrium flow study. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well.« less
Mechanical modeling for magnetorheological elastomer isolators based on constitutive equations and electromagnetic analysis

NASA Astrophysics Data System (ADS)

Wang, Qi; Dong, Xufeng; Li, Luyu; Ou, Jinping

2018-06-01

As constitutive models are too complicated and existing mechanical models lack universality, these models are beyond satisfaction for magnetorheological elastomer (MRE) devices. In this article, a novel universal method is proposed to build concise mechanical models. Constitutive model and electromagnetic analysis were applied in this method to ensure universality, while a series of derivations and simplifications were carried out to obtain a concise formulation. To illustrate the proposed modeling method, a conical MRE isolator was introduced. Its basic mechanical equations were built based on equilibrium, deformation compatibility, constitutive equations and electromagnetic analysis. An iteration model and a highly efficient differential equation editor based model were then derived to solve the basic mechanical equations. The final simplified mechanical equations were obtained by re-fitting the simulations with a novel optimal algorithm. In the end, verification test of the isolator has proved the accuracy of the derived mechanical model and the modeling method.
Nonstationary stochastic charge fluctuations of a dust particle in plasmas.

PubMed

Shotorban, B

2011-06-01

Stochastic charge fluctuations of a dust particle that are due to discreteness of electrons and ions in plasmas can be described by a one-step process master equation [T. Matsoukas and M. Russell, J. Appl. Phys. 77, 4285 (1995)] with no exact solution. In the present work, using the system size expansion method of Van Kampen along with the linear noise approximation, a Fokker-Planck equation with an exact Gaussian solution is developed by expanding the master equation. The Gaussian solution has time-dependent mean and variance governed by two ordinary differential equations modeling the nonstationary process of dust particle charging. The model is tested via the comparison of its results to the results obtained by solving the master equation numerically. The electron and ion currents are calculated through the orbital motion limited theory. At various times of the nonstationary process of charging, the model results are in a very good agreement with the master equation results. The deviation is more significant when the standard deviation of the charge is comparable to the mean charge in magnitude.
Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.

ERIC Educational Resources Information Center

Hwang, Chi-en; Cleary, T. Anne

The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…
Single-Particle Quantum Dynamics in a Magnetic Lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Venturini, Marco

2001-02-01

We study the quantum dynamics of a spinless charged-particle propagating through a magnetic lattice in a transport line or storage ring. Starting from the Klein-Gordon equation and by applying the paraxial approximation, we derive a Schroedinger-like equation for the betatron motion. A suitable unitary transformation reduces the problem to that of a simple harmonic oscillator. As a result we are able to find an explicit expression for the particle wavefunction.
Antigravity: Spin-gravity coupling in action

NASA Astrophysics Data System (ADS)

Plyatsko, Roman; Fenyk, Mykola

2016-08-01

The typical motions of a spinning test particle in Schwarzschild's background which show the strong repulsive action of the highly relativistic spin-gravity coupling are considered using the exact Mathisson-Papapetrou equations. An approximated approach to choice solutions of these equations which describe motions of the particle's proper center of mass is developed.
Comparison of stochastic lung deposition fractions with experimental data.

PubMed

Majid, Hussain; Hofmann, Werner; Winkler-Heil, Renate

2012-04-01

Deposition fractions of inhaled particles predicted by different computational models vary with respect to physical and biological factors and mathematical modeling techniques. These models must be validated by comparison with available experimental data. Experimental data supplied by different deposition studies with surrogate airway models or lung casts were used in this study to evaluate the stochastic deposition model Inhalation, Deposition and Exhalation of Aerosols in the Lung at the airway generation level. Furthermore, different analytical equations derived for the three major deposition mechanisms, diffusion, impaction, and sedimentation, were applied to different cast or airway models to quantify their effect on calculated particle deposition fractions. The experimental results for ultrafine particles (0.00175 and 0.01) were found to be in close agreement with the stochastic model predictions; however, for coarse particles (3 and 8 μm), experimental deposition fractions became higher with increasing flow rate. An overall fair agreement among the calculated deposition fractions for the different cast geometries was found. However, alternative deposition equations resulted in up to 300% variation in predicted deposition fractions, although all equations predicted the same trends as functions of particle diameter and breathing conditions. From this comparative study, it can be concluded that structural differences in lung morphologies among different individuals are responsible for the apparent variability in particle deposition in each generation. The use of different deposition equations yields varying deposition results caused primarily by (i) different lung morphometries employed in their derivation and the choice of the central bifurcation zone geometry, (ii) the assumption of specific flow profiles, and (iii) different methods used in the derivation of these equations.
Gas Flux and Density Surrounding a Cylindrical Aperture in the Free Molecular Flow Regime

NASA Technical Reports Server (NTRS)

Soulas, George C.

2011-01-01

The equations for rigorously calculating the particle flux and density surrounding a cylindrical aperture in the free molecular flow regime are developed and presented. The fundamental equations for particle flux and density from a reservoir and a diffusely reflecting surface will initially be developed. Assumptions will include a Maxwell-Boltzmann speed distribution, equal particle and wall temperatures, and a linear flux distribution along the cylindrical aperture walls. With this information, the equations for axial flux and density surrounding a cylindrical aperture will be developed. The cylindrical aperture will be divided into multiple volumes and regions to rigorously determine the surrounding axial flux and density, and appropriate limits of integration will be determined. The results of these equations will then be evaluated. The linear wall flux distribution assumption will be assessed. The axial flux and density surrounding a cylindrical aperture with a thickness-to-radius ratio of 1.25 will be presented. Finally, the equations determined in this study will be verified using multiple methods.

Equations of motion of test particles for solving the spin-dependent Boltzmann–Vlasov equation

DOE PAGES

Xia, Yin; Xu, Jun; Li, Bao-An; ...

2016-06-16

A consistent derivation of the equations of motion (EOMs) of test particles for solving the spin-dependent Boltzmann–Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg picture of quantum mechanics. Considering further the quantum nature of spin and choosing the direction of total angular momentum in heavy-ion reactions as a reference of measuring nucleon spin, the EOMs of spin-up and spin-down nucleons are given separately. The key elements affecting the spin dynamics in heavy-ion collisions are identified. Themore » resulting EOMs provide a solid foundation for using the test-particle approach in studying spin dynamics in heavy-ion collisions at intermediate energies. Future comparisons of model simulations with experimental data will help to constrain the poorly known in-medium nucleon spin–orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.« less
DOE Office of Scientific and Technical Information (OSTI.GOV)

B.B. Rokhman

A two-dimensional stationary model of motion, heat and mass exchange, and chemical reaction of polydisperse coke and ash particles in ascending gas-suspension flow has been constructed with allowance for the turbulent and pseudo turbulent mechanisms of transfer in the dispersed phase. The system of equations that describes motion and heat transfer in the solid phase has been closed at the level of the equations for the second moments of velocity and temperature pulsations, whereas the momentum equations of the carrying medium have been closed using the equation for turbulent gas energy, which allows for the influence of the particles andmore » heterogeneous reactions.« less
Relationship Between Integro-Differential Schrodinger Equation with a Symmetric Kernel and Position-Dependent Effective Mass

NASA Astrophysics Data System (ADS)

Khosropour, B.; Moayedi, S. K.; Sabzali, R.

2018-07-01

The solution of integro-differential Schrodinger equation (IDSE) which was introduced by physicists has a great role in the fields of science. The purpose of this paper comes in two parts. First, studying the relationship between integro-differential Schrodinger equation with a symmetric non-local potential and one-dimensional Schrodinger equation with a position-dependent effective mass. Second, we show that the quantum Hamiltonian for a particle with position-dependent mass after applying Liouville-Green transformations will be converted to a quantum Hamiltonian for a particle with constant mass.
Navier-Stokes Dynamics by a Discrete Boltzmann Model

NASA Technical Reports Server (NTRS)

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.
Introduction to Physical Intelligence

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

A slight deviation from Newtonian dynamics can lead to new effects associated with the concept of physical intelligence. Non-Newtonian effects such as deviation from classical thermodynamic as well as quantum-like properties have been analyzed. A self-supervised (intelligent) particle that can escape from Brownian motion autonomously is introduced. Such a capability is due to a coupling of the particle governing equation with its own Liouville equation via an appropriate feedback. As a result, the governing equation is self-stabilized, and random oscillations are suppressed, while the Liouville equation takes the form of the Fokker-Planck equation with negative diffusion. Non- Newtonian properties of such a dynamical system as well as thermodynamical implications have been evaluated.
Development of a size reduction equation for woody biomass: The influence of branch wood properties on Rittinger's constant

DOE PAGES

Naimi, Ladan J.; Sokhansanj, Shahabaddine; Bi, Xiaotao; ...

2015-11-25

Size reduction is an essential but energy-intensive process for preparing biomass for conversion processes. Three well-known scaling equations (Bond, Kick, and Rittinger) are used to estimate energy input for grinding minerals and food particles. Previous studies have shown that the Rittinger equation has the best fit to predict energy input for grinding cellulosic biomass. In the Rittinger equation, Rittinger's constant (k R) is independent of the size of ground particles, yet we noted large variations in k R among similar particle size ranges. In this research, the dependence of k R on the physical structure and chemical composition of amore » number of woody materials was explored. Branches from two softwood species (Douglas fir and pine) and two hardwood species (aspen and poplar) were ground in a laboratory knife mill. The recorded data included power input, mass flow rate, and particle size before and after grinding. Nine material properties were determined: particle density, solid density (pycnometer and x-ray diffraction methods), microfibril angle, fiber coarseness, fiber length, and composition (lignin and cellulose glucan contents). The correlation matrix among the nine properties revealed high degrees of interdependence between properties. The k R value had the largest positive correlation (+0.60) with particle porosity across the species tested. As a result, particle density was strongly correlated with lignin content (0.85), microfibril angle (0.71), fiber length (0.87), and fiber coarseness (0.78). An empirical model relating k R to particle density was developed.« less
Development of a size reduction equation for woody biomass: The influence of branch wood properties on Rittinger's constant

DOE Office of Scientific and Technical Information (OSTI.GOV)

Naimi, Ladan J.; Sokhansanj, Shahabaddine; Bi, Xiaotao

Size reduction is an essential but energy-intensive process for preparing biomass for conversion processes. Three well-known scaling equations (Bond, Kick, and Rittinger) are used to estimate energy input for grinding minerals and food particles. Previous studies have shown that the Rittinger equation has the best fit to predict energy input for grinding cellulosic biomass. In the Rittinger equation, Rittinger's constant (k R) is independent of the size of ground particles, yet we noted large variations in k R among similar particle size ranges. In this research, the dependence of k R on the physical structure and chemical composition of amore » number of woody materials was explored. Branches from two softwood species (Douglas fir and pine) and two hardwood species (aspen and poplar) were ground in a laboratory knife mill. The recorded data included power input, mass flow rate, and particle size before and after grinding. Nine material properties were determined: particle density, solid density (pycnometer and x-ray diffraction methods), microfibril angle, fiber coarseness, fiber length, and composition (lignin and cellulose glucan contents). The correlation matrix among the nine properties revealed high degrees of interdependence between properties. The k R value had the largest positive correlation (+0.60) with particle porosity across the species tested. As a result, particle density was strongly correlated with lignin content (0.85), microfibril angle (0.71), fiber length (0.87), and fiber coarseness (0.78). An empirical model relating k R to particle density was developed.« less
Functional differentiability in time-dependent quantum mechanics.

PubMed

Penz, Markus; Ruggenthaler, Michael

2015-03-28

In this work, we investigate the functional differentiability of the time-dependent many-body wave function and of derived quantities with respect to time-dependent potentials. For properly chosen Banach spaces of potentials and wave functions, Fréchet differentiability is proven. From this follows an estimate for the difference of two solutions to the time-dependent Schrödinger equation that evolve under the influence of different potentials. Such results can be applied directly to the one-particle density and to bounded operators, and present a rigorous formulation of non-equilibrium linear-response theory where the usual Lehmann representation of the linear-response kernel is not valid. Further, the Fréchet differentiability of the wave function provides a new route towards proving basic properties of time-dependent density-functional theory.
Saturation behavior: a general relationship described by a simple second-order differential equation.

PubMed

Kepner, Gordon R

2010-04-13

The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical constants governing the behavior of these phenomena led to an alternative perspective on saturation behavior kinetics. Their essential commonality was revealed by this analysis, based on the second-order differential equation.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

DOE PAGES

Ku, S.; Hager, R.; Chang, C. S.; ...

2016-04-01

In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. In conclusion, the numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ku, S.; Hager, R.; Chang, C. S.

In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. In conclusion, the numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ku, S., E-mail: sku@pppl.gov; Hager, R.; Chang, C.S.

In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less
Analytical treatment of particle motion in circularly polarized slab-mode wave fields

NASA Astrophysics Data System (ADS)

Schreiner, Cedric; Vainio, Rami; Spanier, Felix

2018-02-01

Wave-particle interaction is a key process in particle diffusion in collisionless plasmas. We look into the interaction of single plasma waves with individual particles and discuss under which circumstances this is a chaotic process, leading to diffusion. We derive the equations of motion for a particle in the fields of a magnetostatic, circularly polarized, monochromatic wave and show that no chaotic particle motion can arise under such circumstances. A novel and exact analytic solution for the equations is presented. Additional plasma waves lead to a breakdown of the analytic solution and chaotic particle trajectories become possible. We demonstrate this effect by considering a linearly polarized, monochromatic wave, which can be seen as the superposition of two circularly polarized waves. Test particle simulations are provided to illustrate and expand our analytical considerations.
Transport of inertial anisotropic particles under surface gravity waves

NASA Astrophysics Data System (ADS)

Dibenedetto, Michelle; Koseff, Jeffrey; Ouellette, Nicholas

2016-11-01

The motion of neutrally and almost-neutrally buoyant particles under surface gravity waves is relevant to the transport of microplastic debris and other small particulates in the ocean. Consequently, a number of studies have looked at the transport of spherical particles or mobile plankton in these conditions. However, the effects of particle-shape anisotropy on the trajectories and behavior of irregularly shaped particles in this type of oscillatory flow are still relatively unknown. To better understand these issues, we created an idealized numerical model which simulates the three-dimensional behavior of anisotropic spheroids in flow described by Airy wave theory. The particle's response is calculated using a simplified Maxey-Riley equation coupled with Jeffery's equation for particle rotation. We show that the particle dynamics are strongly dependent on their initial conditions and shape, with some some additional dependence on Stokes number.
Chemically Reacting One-Dimensional Gas-Particle Flows

NASA Technical Reports Server (NTRS)

Tevepaugh, J. A.; Penny, M. M.

1975-01-01

The governing equations for the one-dimensional flow of a gas-particle system are discussed. Gas-particle effects are coupled via the system momentum and energy equations with the gas assumed to be chemically frozen or in chemical equilibrium. A computer code for calculating the one-dimensional flow of a gas-particle system is discussed and a user's input guide presented. The computer code provides for the expansion of the gas-particle system from a specified starting velocity and nozzle inlet geometry. Though general in nature, the final output of the code is a startline for initiating the solution of a supersonic gas-particle system in rocket nozzles. The startline includes gasdynamic data defining gaseous startline points from the nozzle centerline to the nozzle wall and particle properties at points along the gaseous startline.
Can phoretic particles swim in two dimensions?

NASA Astrophysics Data System (ADS)

Sondak, David; Hawley, Cory; Heng, Siyu; Vinsonhaler, Rebecca; Lauga, Eric; Thiffeault, Jean-Luc

2016-12-01

Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows, and ultimately the swimming velocity may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Péclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.
A Generalization of the Einstein-Maxwell Equations

NASA Astrophysics Data System (ADS)

Cotton, Fredrick

2016-03-01

The proposed modifications of the Einstein-Maxwell equations include: (1) the addition of a scalar term to the electromagnetic side of the equation rather than to the gravitational side, (2) the introduction of a 4-dimensional, nonlinear electromagnetic constitutive tensor and (3) the addition of curvature terms arising from the non-metric components of a general symmetric connection. The scalar term is defined by the condition that a spherically symmetric particle be force-free and mathematically well-behaved everywhere. The constitutive tensor introduces two auxiliary fields which describe the particle structure. The additional curvature terms couple both to particle solutions and to electromagnetic and gravitational wave solutions. http://sites.google.com/site/fwcotton/em-30.pdf
Turbulence kinetic energy equation for dilute suspensions

NASA Technical Reports Server (NTRS)

Abou-Arab, T. W.; Roco, M. C.

1989-01-01

A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.
Importance of core electrostatic properties on the electrophoresis of a soft particle

NASA Astrophysics Data System (ADS)

De, Simanta; Bhattacharyya, Somnath; Gopmandal, Partha P.

2016-08-01

The impact of the volumetric charged density of the dielectric rigid core on the electrophoresis of a soft particle is analyzed numerically. The volume charge density of the inner core of a soft particle can arise for a dendrimer structure or bacteriophage MS2. We consider the electrokinetic model based on the conservation principles, thus no conditions for Debye length or applied electric field is imposed. The fluid flow equations are coupled with the ion transport equations and the equation for the electric field. The occurrence of the induced nonuniform surface charge density on the outer surface of the inner core leads to a situation different from the existing analysis of a soft particle electrophoresis. The impact of this induced surface charge density together with the double-layer polarization and relaxation due to ion convection and electromigration is analyzed. The dielectric permittivity and the charge density of the core have a significant impact on the particle electrophoresis when the Debye length is in the order of the particle size. We find that by varying the ionic concentration of the electrolyte, the particle can exhibit reversal in its electrophoretic velocity. The role of the polymer layer softness parameter is addressed in the present analysis.
Relaxation of polar order in suspensions with Quincke effect.

PubMed

Belovs, M; Cēbers, A

2014-05-01

The Quincke effect--spontaneous rotation of dielectric particles in a liquid with low conductivity under the action of an electric field--is considered. The distribution functions for the orientation of particle rotation planes are introduced and a set of nonlinear kinetic equations is derived in the mean field approximation considering the dynamics of their orientation in the flow induced by rotating particles. As a result the nonequilibrium phase transition to the polar order, if the concentration of the particles is sufficiently high, is predicted and the condition of the synchronization of particle rotations is established. Two cases are considered: the layer of the Quincke suspension with one free boundary and the ensemble of the particles rolling on the solid wall under the action of a torque in an electric field. It is shown that in both cases the synchronization of particle rotations occurs due to the hydrodynamic interactions. In the limit of small spatial nonhomogeneity a set of nonlinear partial differential equations for the macroscopic variables--the concentration and the director of the polar order--is derived from the kinetic equation. Its properties are analyzed and compared with available recent experimental results.

Relaxation of polar order in suspensions with Quincke effect

NASA Astrophysics Data System (ADS)

Belovs, M.; CÄ`bers, A.

2014-05-01

The Quincke effect—spontaneous rotation of dielectric particles in a liquid with low conductivity under the action of an electric field—is considered. The distribution functions for the orientation of particle rotation planes are introduced and a set of nonlinear kinetic equations is derived in the mean field approximation considering the dynamics of their orientation in the flow induced by rotating particles. As a result the nonequilibrium phase transition to the polar order, if the concentration of the particles is sufficiently high, is predicted and the condition of the synchronization of particle rotations is established. Two cases are considered: the layer of the Quincke suspension with one free boundary and the ensemble of the particles rolling on the solid wall under the action of a torque in an electric field. It is shown that in both cases the synchronization of particle rotations occurs due to the hydrodynamic interactions. In the limit of small spatial nonhomogeneity a set of nonlinear partial differential equations for the macroscopic variables—the concentration and the director of the polar order—is derived from the kinetic equation. Its properties are analyzed and compared with available recent experimental results.
Radiation reaction effect on laser driven auto-resonant particle acceleration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sagar, Vikram; Sengupta, Sudip; Kaw, P. K.

2015-12-15

The effects of radiation reaction force on laser driven auto-resonant particle acceleration scheme are studied using Landau-Lifshitz equation of motion. These studies are carried out for both linear and circularly polarized laser fields in the presence of static axial magnetic field. From the parametric study, a radiation reaction dominated region has been identified in which the particle dynamics is greatly effected by this force. In the radiation reaction dominated region, the two significant effects on particle dynamics are seen, viz., (1) saturation in energy gain by the initially resonant particle and (2) net energy gain by an initially non-resonant particlemore » which is caused due to resonance broadening. It has been further shown that with the relaxation of resonance condition and with optimum choice of parameters, this scheme may become competitive with the other present-day laser driven particle acceleration schemes. The quantum corrections to the Landau-Lifshitz equation of motion have also been taken into account. The difference in the energy gain estimates of the particle by the quantum corrected and classical Landau-Lifshitz equation is found to be insignificant for the present day as well as upcoming laser facilities.« less
Investigation of unsteadiness in Shock-particle cloud interaction: Fully resolved two-dimensional simulation and one-dimensional modeling

NASA Astrophysics Data System (ADS)

Hosseinzadeh-Nik, Zahra; Regele, Jonathan D.

2015-11-01

Dense compressible particle-laden flow, which has a complex nature, exists in various engineering applications. Shock waves impacting a particle cloud is a canonical problem to investigate this type of flow. It has been demonstrated that large flow unsteadiness is generated inside the particle cloud from the flow induced by the shock passage. It is desirable to develop models for the Reynolds stress to capture the energy contained in vortical structures so that volume-averaged models with point particles can be simulated accurately. However, the previous work used Euler equations, which makes the prediction of vorticity generation and propagation innacurate. In this work, a fully resolved two dimensional (2D) simulation using the compressible Navier-Stokes equations with a volume penalization method to model the particles has been performed with the parallel adaptive wavelet-collocation method. The results still show large unsteadiness inside and downstream of the particle cloud. A 1D model is created for the unclosed terms based upon these 2D results. The 1D model uses a two-phase simple low dissipation AUSM scheme (TSLAU) developed by coupled with the compressible two phase kinetic energy equation.
APPROACH TO EQUILIBRIUM OF A QUANTUM PLASMA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balescu, R.

1961-01-01

The treatment of irreversible processes in a classical plasma (R. Balescu, Phys. Fluids 3, 62(1960)) was extended to a gas of charged particles obeying quantum statistics. The various contributions to the equation of evolution for the reduced one-particle Wigner function were written in a form analogous to the classical formalism. The summation was then performed in a straightforward manner. The resulting equation describes collisions between particles "dressed" by their polarization clouds, exactly as in the classical situation. (auth)
Particle Size Distributions in Atmospheric Clouds

NASA Technical Reports Server (NTRS)

Paoli, Roberto; Shariff, Karim

2003-01-01

In this note, we derive a transport equation for a spatially integrated distribution function of particles size that is suitable for sparse particle systems, such as in atmospheric clouds. This is done by integrating a Boltzmann equation for a (local) distribution function over an arbitrary but finite volume. A methodology for evolving the moments of the integrated distribution is presented. These moments can be either tracked for a finite number of discrete populations ('clusters') or treated as continuum variables.
Modelling the behaviour of additives in gun barrels

NASA Astrophysics Data System (ADS)

Rhodes, N.; Ludwig, J. C.

1986-01-01

A mathematical model which predicts the flow and heat transfer in a gun barrel is described. The model is transient, two-dimensional and equations are solved for velocities and enthalpies of a gas phase, which arises from the combustion of propellant and cartridge case, for particle additives which are released from the case; volume fractions of the gas and particles. Closure of the equations is obtained using a two-equation turbulence model. Preliminary calculations are described in which the proportions of particle additives in the cartridge case was altered. The model gives a good prediction of the ballistic performance and the gas to wall heat transfer. However, the expected magnitude of reduction in heat transfer when particles are present is not predicted. The predictions of gas flow invalidate some of the assumptions made regarding case and propellant behavior during combustion and further work is required to investigate these effects and other possible interactions, both chemical and physical, between gas and particles.
Calculation of two-dimension radial electric field in boundary plasmas by using BOUT++

NASA Astrophysics Data System (ADS)

Li, N. M.; Xu, X. Q.; Rognlien, T. D.; Gui, B.; Sun, J. Z.; Wang, D. Z.

2018-07-01

The steady state radial electric field (Er) is calculated by coupling a plasma transport model with the quasi-neutrality constraint and the vorticity equation within the BOUT++ framework. Based on the experimentally measured plasma density and temperature profiles in Alcator C-Mod discharges, the effective radial particle and heat diffusivities are inferred from the set of plasma transport equations. The effective diffusivities are then extended into the scrape-off layer (SOL) to calculate the plasma density, temperature and flow profiles across the separatrix into the SOL with the electrostatic sheath boundary conditions (SBC) applied on the divertor plates. Given these diffusivities, the electric field can be calculated self-consistently across the separatrix from the vorticity equation with SBC coupled to the plasma transport equations. The sheath boundary conditions act to generate a large and positive Er in the SOL, which is consistent with experimental measurements. The effect of magnetic particle drifts is shown to play a significant role on local particle transport and Er by inducing a net particle flow in both the edge and SOL regions.
Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.

2007-01-01

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.
Diffusion coefficients in organic-water solutions and comparison with Stokes-Einstein predictions

NASA Astrophysics Data System (ADS)

Evoy, E.; Kamal, S.; Bertram, A. K.

2017-12-01

Diffusion coefficients of organic species in particles containing secondary organic material (SOM) are necessary for predicting the growth and reactivity of these particles in the atmosphere. Previously, the Stokes-Einstein equation combined with viscosity measurements have been used to predict these diffusion coefficients. However, the accuracy of the Stokes-Einstein equation for predicting diffusion coefficients in SOM-water particles has not been quantified. To test the Stokes-Einstein equation, diffusion coefficients of fluorescent organic probe molecules were measured in citric acid-water and sorbitol-water solutions. These solutions were used as proxies for SOM-water particles found in the atmosphere. Measurements were performed as a function of water activity, ranging from 0.26-0.86, and as a function of viscosity ranging from 10-3 to 103 Pa s. Diffusion coefficients were measured using fluorescence recovery after photobleaching. The measured diffusion coefficients were compared with predictions made using the Stokes-Einstein equation combined with literature viscosity data. Within the uncertainties of the measurements, the measured diffusion coefficients agreed with the predicted diffusion coefficients, in all cases.
Catmull-Rom Curve Fitting and Interpolation Equations

ERIC Educational Resources Information Center

Jerome, Lawrence

2010-01-01

Computer graphics and animation experts have been using the Catmull-Rom smooth curve interpolation equations since 1974, but the vector and matrix equations can be derived and simplified using basic algebra, resulting in a simple set of linear equations with constant coefficients. A variety of uses of Catmull-Rom interpolation are demonstrated,…
Insights.

ERIC Educational Resources Information Center

Bogner, Donna, Ed.

1990-01-01

Presented is an approach to solving oxidation-reduction reactions. The advantage of this procedure for both acidic and basic equations is stressed and emphasizes the electrical nature of redox equations. (KR)
Higher-order geodesic deviation for charged particles and resonance induced by gravitational waves

NASA Astrophysics Data System (ADS)

Heydari-Fard, M.; Hasani, S. N.

We generalize the higher-order geodesic deviation for the structure-less test particles to the higher-order geodesic deviation equations of the charged particles [R. Kerner, J. W. van Holten and R. Colistete Jr., Class. Quantum Grav. 18 (2001) 4725]. By solving these equations for charged particles moving in a constant magnetic field in the spacetime of a gravitational wave, we show for both cases when the gravitational wave is parallel and perpendicular to the constant magnetic field, a magnetic resonance appears at wg = Ω. This feature might be useful to detect the gravitational wave with high frequencies.
A structural equation modeling analysis of students' understanding in basic mathematics

NASA Astrophysics Data System (ADS)

Oktavia, Rini; Arif, Salmawaty; Ferdhiana, Ridha; Yuni, Syarifah Meurah; Ihsan, Mahyus

2017-11-01

This research, in general, aims to identify incoming students' understanding and misconceptions of several basic concepts in mathematics. The participants of this study are the 2015 incoming students of Faculty of Mathematics and Natural Science of Syiah Kuala University, Indonesia. Using an instrument that were developed based on some anecdotal and empirical evidences on students' misconceptions, a survey involving 325 participants was administered and several quantitative and qualitative analysis of the survey data were conducted. In this article, we discuss the confirmatory factor analysis using Structural Equation Modeling (SEM) on factors that determine the new students' overall understanding of basic mathematics. The results showed that students' understanding on algebra, arithmetic, and geometry were significant predictors for their overall understanding of basic mathematics. This result supported that arithmetic and algebra are not the only predictors of students' understanding of basic mathematics.
Quasi-linear theory via the cumulant expansion approach

NASA Technical Reports Server (NTRS)

Jones, F. C.; Birmingham, T. J.

1974-01-01

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate.
An exact solution of the Currie-Hill equations in 1 + 1 dimensional Minkowski space

NASA Astrophysics Data System (ADS)

Balog, János

2014-11-01

We present an exact two-particle solution of the Currie-Hill equations of Predictive Relativistic Mechanics in 1 + 1 dimensional Minkowski space. The instantaneous accelerations are given in terms of elementary functions depending on the relative particle position and velocities. The general solution of the equations of motion is given and by studying the global phase space of this system it is shown that this is a subspace of the full kinematic phase space.
The linear Boltzmann equation in slab geometry - Development and verification of a reliable and efficient solution

NASA Technical Reports Server (NTRS)

Stamnes, K.; Lie-Svendsen, O.; Rees, M. H.

1991-01-01

The linear Boltzmann equation can be cast in a form mathematically identical to the radiation-transport equation. A multigroup procedure is used to reduce the energy (or velocity) dependence of the transport equation to a series of one-speed problems. Each of these one-speed problems is equivalent to the monochromatic radiative-transfer problem, and existing software is used to solve this problem in slab geometry. The numerical code conserves particles in elastic collisions. Generic examples are provided to illustrate the applicability of this approach. Although this formalism can, in principle, be applied to a variety of test particle or linearized gas dynamics problems, it is particularly well-suited to study the thermalization of suprathermal particles interacting with a background medium when the thermal motion of the background cannot be ignored. Extensions of the formalism to include external forces and spherical geometry are also feasible.
Hydrodynamic Stability Analysis of Particle-Laden Solid Rocket Motors

NASA Astrophysics Data System (ADS)

Elliott, T. S.; Majdalani, J.

2014-11-01

Fluid-wall interactions within solid rocket motors can result in parietal vortex shedding giving rise to hydrodynamic instabilities, or unsteady waves, that translate into pressure oscillations. The oscillations can result in vibrations observed by the rocket, rocket subsystems, or payload, which can lead to changes in flight characteristics, design failure, or other undesirable effects. For many years particles have been embedded in solid rocket propellants with the understanding that their presence increases specific impulse and suppresses fluctuations in the flowfield. This study utilizes a two dimensional framework to understand and quantify the aforementioned two-phase flowfield inside a motor case with a cylindrical grain perforation. This is accomplished through the use of linearized Navier-Stokes equations with the Stokes drag equation and application of the biglobal ansatz. Obtaining the biglobal equations for analysis requires quantification of the mean flowfield within the solid rocket motor. To that end, the extended Taylor-Culick form will be utilized to represent the gaseous phase of the mean flowfield while the self-similar form will be employed for the particle phase. Advancing the mean flowfield by quantifying the particle mass concentration with a semi-analytical solution the finalized mean flowfield is combined with the biglobal equations resulting in a system of eight partial differential equations. This system is solved using an eigensolver within the framework yielding the entire spectrum of eigenvalues, frequency and growth rate components, at once. This work will detail the parametric analysis performed to demonstrate the stabilizing and destabilizing effects of particles within solid rocket combustion.
EMPHASIS/Nevada UTDEM user guide. Version 2.0.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turner, C. David; Seidel, David Bruce; Pasik, Michael Francis

The Unstructured Time-Domain ElectroMagnetics (UTDEM) portion of the EMPHASIS suite solves Maxwell's equations using finite-element techniques on unstructured meshes. This document provides user-specific information to facilitate the use of the code for applications of interest. UTDEM is a general-purpose code for solving Maxwell's equations on arbitrary, unstructured tetrahedral meshes. The geometries and the meshes thereof are limited only by the patience of the user in meshing and by the available computing resources for the solution. UTDEM solves Maxwell's equations using finite-element method (FEM) techniques on tetrahedral elements using vector, edge-conforming basis functions. EMPHASIS/Nevada Unstructured Time-Domain ElectroMagnetic Particle-In-Cell (UTDEM PIC) ismore » a superset of the capabilities found in UTDEM. It adds the capability to simulate systems in which the effects of free charge are important and need to be treated in a self-consistent manner. This is done by integrating the equations of motion for macroparticles (a macroparticle is an object that represents a large number of real physical particles, all with the same position and momentum) being accelerated by the electromagnetic forces upon the particle (Lorentz force). The motion of these particles results in a current, which is a source for the fields in Maxwell's equations.« less
FAST TRACK COMMUNICATION: Semiclassical Klein Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential

NASA Astrophysics Data System (ADS)

Coffey, W. T.; Kalmykov, Yu P.; Titov, S. V.; Mulligan, B. P.

2007-01-01

The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(planck4) and in the classical limit, planck → 0, reduces to the Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived.
Particle-size segregation and diffusive remixing in shallow granular avalanches

NASA Astrophysics Data System (ADS)

Gray, J. M. N. T.; Chugunov, V. A.

2006-12-01

Segregation and mixing of dissimilar grains is a problem in many industrial and pharmaceutical processes, as well as in hazardous geophysical flows, where the size-distribution can have a major impact on the local rheology and the overall run-out. In this paper, a simple binary mixture theory is used to formulate a model for particle-size segregation and diffusive remixing of large and small particles in shallow gravity-driven free-surface flows. This builds on a recent theory for the process of kinetic sieving, which is the dominant mechanism for segregation in granular avalanches provided the density-ratio and the size-ratio of the particles are not too large. The resulting nonlinear parabolic segregation remixing equation reduces to a quasi-linear hyperbolic equation in the no-remixing limit. It assumes that the bulk velocity is incompressible and that the bulk pressure is lithostatic, making it compatible with most theories used to compute the motion of shallow granular free-surface flows. In steady-state, the segregation remixing equation reduces to a logistic type equation and the ‘S’-shaped solutions are in very good agreement with existing particle dynamics simulations for both size and density segregation. Laterally uniform time-dependent solutions are constructed by mapping the segregation remixing equation to Burgers equation and using the Cole Hopf transformation to linearize the problem. It is then shown how solutions for arbitrary initial conditions can be constructed using standard methods. Three examples are investigated in which the initial concentration is (i) homogeneous, (ii) reverse graded with the coarse grains above the fines, and, (iii) normally graded with the fines above the coarse grains. Time-dependent two-dimensional solutions are also constructed for plug-flow in a semi-infinite chute.

HST3D; a computer code for simulation of heat and solute transport in three-dimensional ground-water flow systems

USGS Publications Warehouse

Kipp, K.L.

1987-01-01

The Heat- and Soil-Transport Program (HST3D) simulates groundwater flow and associated heat and solute transport in three dimensions. The three governing equations are coupled through the interstitial pore velocity, the dependence of the fluid density on pressure, temperature, the solute-mass fraction , and the dependence of the fluid viscosity on temperature and solute-mass fraction. The solute transport equation is for only a single, solute species with possible linear equilibrium sorption and linear decay. Finite difference techniques are used to discretize the governing equations using a point-distributed grid. The flow-, heat- and solute-transport equations are solved , in turn, after a particle Gauss-reduction scheme is used to modify them. The modified equations are more tightly coupled and have better stability for the numerical solutions. The basic source-sink term represents wells. A complex well flow model may be used to simulate specified flow rate and pressure conditions at the land surface or within the aquifer, with or without pressure and flow rate constraints. Boundary condition types offered include specified value, specified flux, leakage, heat conduction, and approximate free surface, and two types of aquifer influence functions. All boundary conditions can be functions of time. Two techniques are available for solution of the finite difference matrix equations. One technique is a direct-elimination solver, using equations reordered by alternating diagonal planes. The other technique is an iterative solver, using two-line successive over-relaxation. A restart option is available for storing intermediate results and restarting the simulation at an intermediate time with modified boundary conditions. This feature also can be used as protection against computer system failure. Data input and output may be in metric (SI) units or inch-pound units. Output may include tables of dependent variables and parameters, zoned-contour maps, and plots of the dependent variables versus time. (Lantz-PTT)
Investigations of the effects of particle properties on the wear resistance of the particle reinforced composites using a novel wear model

NASA Astrophysics Data System (ADS)

Prabhu, T. Ram

2016-08-01

A wear model is developed based on the discrete lattice spring-mass approach to study the effects of particle volume fraction, size, and stiffness on the wear resistance of particle reinforced composites. To study these effects, we have considered three volume fractions (10%, 20% and 30%), two sizes (10 × 10 and 4 × 4 sites), and two different stiffness of particles embedded in the matrix in a regular pattern. In this model, we have discretized the composite system (400 × 100 sites) into the lumped masses connected with interaction spring elements in two dimensions. The interaction elements are assumed as linear elastic and ideal plastic under applied forces. Each mass is connected to its first and second nearest neighbors by springs. The matrix and particles sites are differentiated by choosing the different stiffness values. The counter surface is simulated as a rigid body that moves on the composite material at a constant sliding speed along the horizontal direction. The governing equations are formed by equating the spring force between the pair of sites given by Hooke’s law plus external contact forces and the force due to the motion of the site given by the equation of motion. The equations are solved for the plastic strain accumulated in the springs using an explicit time stepping procedure based on a finite difference form of the above equations. If the total strain accumulated in the spring elements connected to a lump mass site exceeds the failure strain, the springs are considered to be broken, and the mass site is removed or worn away from the lattice and accounts as a wear loss. The model predicts that (i) increasing volume fraction, reducing particle size and increasing particle stiffness enhance the wear resistance of the particle reinforced composites, (ii) the particle stiffness is the most significant factor affecting the wear resistance of the composites, and (iii) the wear resistance reduced above the critical volume fraction (Vc), and Vc increases with increasing particle size. Finally, we have qualitatively compared the model results with our previously published experimental results to prove the effectiveness of the model to analysis the complex wear systems.
Numerical investigation of the dynamics of Janus magnetic particles in a rotating magnetic field

NASA Astrophysics Data System (ADS)

Kim, Hui Eun; Kim, Kyoungbeom; Ma, Tae Yeong; Kang, Tae Gon

2017-02-01

We investigated the rotational dynamics of Janus magnetic particles suspended in a viscous liquid, in the presence of an externally applied rotating magnetic field. A previously developed two-dimensional direct simulation method, based on the finite element method and a fictitious domain method, is employed to solve the magnetic particulate flow. As for the magnetic problem, the two Maxwell equations are converted to a differential equation using the magnetic potential. The magnetic forces acting on the particles are treated by a Maxwell stress tensor formulation, enabling us to consider the magnetic interactions among the particles without any approximation. The dynamics of a single particle in the rotating field is studied to elucidate the effect of the Mason number and the magnetic susceptibility on the particle motions. Then, we extended our interest to a two-particle problem, focusing on the effect of the initial configuration of the particles on the particle motions. In three-particle interaction problems, the particle dynamics and the fluid flow induced by the particle motions are significantly affected by the particle configuration and the orientation of each particle.
A purely Lagrangian method for simulating the shallow water equations on a sphere using smooth particle hydrodynamics

NASA Astrophysics Data System (ADS)

Capecelatro, Jesse

2018-03-01

It has long been suggested that a purely Lagrangian solution to global-scale atmospheric/oceanic flows can potentially outperform tradition Eulerian schemes. Meanwhile, a demonstration of a scalable and practical framework remains elusive. Motivated by recent progress in particle-based methods when applied to convection dominated flows, this work presents a fully Lagrangian method for solving the inviscid shallow water equations on a rotating sphere in a smooth particle hydrodynamics framework. To avoid singularities at the poles, the governing equations are solved in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the surface of the sphere. An underlying grid in spherical coordinates is used to facilitate efficient neighbor detection and parallelization. The method is applied to a suite of canonical test cases, and conservation, accuracy, and parallel performance are assessed.
Experimental and numerical analysis of the constitutive equation of rubber composites reinforced with random ceramic particle

NASA Astrophysics Data System (ADS)

Luo, D. M.; Xie, Y.; Su, X. R.; Zhou, Y. L.

2018-01-01

Based on the four classical models of Mooney-Rivlin (M-R), Yeoh, Ogden and Neo-Hookean (N-H) model, a strain energy constitutive equation with large deformation for rubber composites reinforced with random ceramic particles is proposed from the angle of continuum mechanics theory in this paper. By decoupling the interaction between matrix and random particles, the strain energy of each phase is obtained to derive the explicit constitutive equation for rubber composites. The tests results of uni-axial tensile, pure shear and equal bi-axial tensile are simulated by the non-linear finite element method on the ANSYS platform. The results from finite element method are compared with those from experiment, and the material parameters are determined by fitting the results from different test conditions, and the influence of radius of random ceramic particles on the effective mechanical properties are analyzed.
Stochastic analysis of pitch angle scattering of charged particles by transverse magnetic waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lemons, Don S.; Liu Kaijun; Winske, Dan

2009-11-15

This paper describes a theory of the velocity space scattering of charged particles in a static magnetic field composed of a uniform background field and a sum of transverse, circularly polarized, magnetic waves. When that sum has many terms the autocorrelation time required for particle orbits to become effectively randomized is small compared with the time required for the particle velocity distribution to change significantly. In this regime the deterministic equations of motion can be transformed into stochastic differential equations of motion. The resulting stochastic velocity space scattering is described, in part, by a pitch angle diffusion rate that ismore » a function of initial pitch angle and properties of the wave spectrum. Numerical solutions of the deterministic equations of motion agree with the theory at all pitch angles, for wave energy densities up to and above the energy density of the uniform field, and for different wave spectral shapes.« less
Continuum theories for fluid-particle flows: Some aspects of lift forces and turbulence

NASA Technical Reports Server (NTRS)

Mctigue, David F.; Givler, Richard C.; Nunziato, Jace W.

1988-01-01

A general framework is outlined for the modeling of fluid particle flows. The momentum exchange between the constituents embodies both lift and drag forces, constitutive equations for which can be made explicit with reference to known single particle analysis. Relevant results for lift are reviewed, and invariant representations are posed. The fluid and particle velocities and the particle volume fraction are then decomposed into mean and fluctuating parts to characterize turbulent motions, and the equations of motion are averaged. In addition to the Reynolds stresses, further correlations between concentration and velocity fluctuations appear. These can be identified with turbulent transport processes such as eddy diffusion of the particles. When the drag force is dominant, the classical convection dispersion model for turbulent transport of particles is recovered. When other interaction forces enter, particle segregation effects can arise. This is illustrated qualitatively by consideration of turbulent channel flow with lift effects included.
Superalgebras for three interacting particles in an external magnetic field

NASA Astrophysics Data System (ADS)

Sadeghi, J.

2006-04-01

In this paper we discuss interacting particles in an external magnetic field. By comparing the Schrödinger equation of three interacting particles with the associated Laguerre differential equation, we obtain the energy spectrum which corresponds to indices ni and mi. Finally by using the so called factorization method we obtain the raising and lowering operators. These operators are supersymmetric structures related to the Hamiltonian partner. Also these operators lead to the realization of Heisenberg Lie superalgebras with two, four and six supercharges.
A general mixture model and its application to coastal sandbar migration simulation

NASA Astrophysics Data System (ADS)

Liang, Lixin; Yu, Xiping

2017-04-01

A mixture model for general description of sediment laden flows is developed and then applied to coastal sandbar migration simulation. Firstly the mixture model is derived based on the Eulerian-Eulerian approach of the complete two-phase flow theory. The basic equations of the model include the mass and momentum conservation equations for the water-sediment mixture and the continuity equation for sediment concentration. The turbulent motion of the mixture is formulated for the fluid and the particles respectively. A modified k-ɛ model is used to describe the fluid turbulence while an algebraic model is adopted for the particles. A general formulation for the relative velocity between the two phases in sediment laden flows, which is derived by manipulating the momentum equations of the enhanced two-phase flow model, is incorporated into the mixture model. A finite difference method based on SMAC scheme is utilized for numerical solutions. The model is validated by suspended sediment motion in steady open channel flows, both in equilibrium and non-equilibrium state, and in oscillatory flows as well. The computed sediment concentrations, horizontal velocity and turbulence kinetic energy of the mixture are all shown to be in good agreement with experimental data. The mixture model is then applied to the study of sediment suspension and sandbar migration in surf zones under a vertical 2D framework. The VOF method for the description of water-air free surface and topography reaction model is coupled. The bed load transport rate and suspended load entrainment rate are all decided by the sea bed shear stress, which is obtained from the boundary layer resolved mixture model. The simulation results indicated that, under small amplitude regular waves, erosion occurred on the sandbar slope against the wave propagation direction, while deposition dominated on the slope towards wave propagation, indicating an onshore migration tendency. The computation results also shows that the suspended load will also make great contributions to the topography change in the surf zone, which is usually neglected in some previous researches.
Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.
Comet Gas and Dust Dynamics Modeling

NASA Technical Reports Server (NTRS)

Von Allmen, Paul A.; Lee, Seungwon

2010-01-01

This software models the gas and dust dynamics of comet coma (the head region of a comet) in order to support the Microwave Instrument for Rosetta Orbiter (MIRO) project. MIRO will study the evolution of the comet 67P/Churyumov-Gerasimenko's coma system. The instrument will measure surface temperature, gas-production rates and relative abundances, and velocity and excitation temperatures of each species along with their spatial temporal variability. This software will use these measurements to improve the understanding of coma dynamics. The modeling tool solves the equation of motion of a dust particle, the energy balance equation of the dust particle, the continuity equation for the dust and gas flow, and the dust and gas mixture energy equation. By solving these equations numerically, the software calculates the temperature and velocity of gas and dust as a function of time for a given initial gas and dust production rate, and a dust characteristic parameter that measures the ability of a dust particle to adjust its velocity to the local gas velocity. The software is written in a modular manner, thereby allowing the addition of more dynamics equations as needed. All of the numerical algorithms are added in-house and no third-party libraries are used.
Modelling Solar Energetic Particle Propagation in Realistic Heliospheric Solar Wind Conditions Using a Combined MHD and Stochastic Differential Equation Approach

NASA Astrophysics Data System (ADS)

Wijsen, N.; Poedts, S.; Pomoell, J.

2017-12-01

Solar energetic particles (SEPs) are high energy particles originating from solar eruptive events. These particles can be energised at solar flare sites during magnetic reconnection events, or in shock waves propagating in front of coronal mass ejections (CMEs). These CME-driven shocks are in particular believed to act as powerful accelerators of charged particles throughout their propagation in the solar corona. After escaping from their acceleration site, SEPs propagate through the heliosphere and may eventually reach our planet where they can disrupt the microelectronics on satellites in orbit and endanger astronauts among other effects. Therefore it is of vital importance to understand and thereby build models capable of predicting the characteristics of SEP events. The propagation of SEPs in the heliosphere can be described by the time-dependent focused transport equation. This five-dimensional parabolic partial differential equation can be solved using e.g., a finite difference method or by integrating a set of corresponding first order stochastic differential equations. In this work we take the latter approach to model SEP events under different solar wind and scattering conditions. The background solar wind in which the energetic particles propagate is computed using a magnetohydrodynamic model. This allows us to study the influence of different realistic heliospheric configurations on SEP transport. In particular, in this study we focus on exploring the influence of high speed solar wind streams originating from coronal holes that are located close to the eruption source region on the resulting particle characteristics at Earth. Finally, we discuss our upcoming efforts towards integrating our particle propagation model with time-dependent heliospheric MHD space weather modelling.
Radiation reaction on a classical charged particle: a modified form of the equation of motion.

PubMed

Alcaine, Guillermo García; Llanes-Estrada, Felipe J

2013-09-01

We present and numerically solve a modified form of the equation of motion for a charged particle under the influence of an external force, taking into account the radiation reaction. This covariant equation is integro-differential, as Dirac-Röhrlich's, but has several technical improvements. First, the equation has the form of Newton's second law, with acceleration isolated on the left hand side and the force depending only on positions and velocities: Thus, the equation is linear in the highest derivative. Second, the total four-force is by construction perpendicular to the four-velocity. Third, if the external force vanishes for all future times, the total force and the acceleration automatically vanish at the present time. We show the advantages of this equation by solving it numerically for several examples of external force.
Radiation reaction on a classical charged particle: A modified form of the equation of motion

NASA Astrophysics Data System (ADS)

Alcaine, Guillermo García; Llanes-Estrada, Felipe J.

2013-09-01

We present and numerically solve a modified form of the equation of motion for a charged particle under the influence of an external force, taking into account the radiation reaction. This covariant equation is integro-differential, as Dirac-Röhrlich's, but has several technical improvements. First, the equation has the form of Newton's second law, with acceleration isolated on the left hand side and the force depending only on positions and velocities: Thus, the equation is linear in the highest derivative. Second, the total four-force is by construction perpendicular to the four-velocity. Third, if the external force vanishes for all future times, the total force and the acceleration automatically vanish at the present time. We show the advantages of this equation by solving it numerically for several examples of external force.
Is the kinetic equation for turbulent gas-particle flows ill posed?

PubMed

Reeks, M; Swailes, D C; Bragg, A D

2018-02-01

This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.
Spinning particle and gauge theories as integrability conditions

NASA Astrophysics Data System (ADS)

Eisenberg, Yeshayahu

1992-02-01

Starting from a new four dimensional spinning point particle we obtain new representations of the standard four dimensional gauge field equations in terms of a generalized space (Minkowski + light cone). In terms of this new formulation we define linear systems whose integrability conditions imply the massive Dirac-Maxwell and the Yang-Mills equations. Research supported by the Rothschild Fellowship.
Generalized Spencer-Lewis equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Filippone, W.L.

The Spencer-Lewis equation, which describes electron transport in homogeneous media when continuous slowing down theory is valid, is derived from the Boltzmann equation. Also derived is a time-dependent generalized Spencer-Lewis equation valid for inhomogeneous media. An independent verification of this last equation is obtained for the one-dimensional case using particle balance considerations.
Derivation of stiffness matrix in constitutive modeling of magnetorheological elastomer

NASA Astrophysics Data System (ADS)

Leng, D.; Sun, L.; Sun, J.; Lin, Y.

2013-02-01

Magnetorheological elastomers (MREs) are a class of smart materials whose mechanical properties change instantly by the application of a magnetic field. Based on the specially orthotropic, transversely isotropic stress-strain relationships and effective permeability model, the stiffness matrix of constitutive equations for deformable chain-like MRE is considered. To valid the components of shear modulus in this stiffness matrix, the magnetic-structural simulations with finite element method (FEM) are presented. An acceptable agreement is illustrated between analytical equations and numerical simulations. For the specified magnetic field, sphere particle radius, distance between adjacent particles in chains and volume fractions of ferrous particles, this constitutive equation is effective to engineering application to estimate the elastic behaviour of chain-like MRE in an external magnetic field.
Upscaling the diffusion equations in particulate media made of highly conductive particles. I. Theoretical aspects.

PubMed

Vassal, J-P; Orgéas, L; Favier, D; Auriault, J-L; Le Corre, S

2008-01-01

Many analytical and numerical works have been devoted to the prediction of macroscopic effective transport properties in particulate media. Usually, structure and properties of macroscopic balance and constitutive equations are stated a priori. In this paper, the upscaling of the transient diffusion equations in concentrated particulate media with possible particle-particle interfacial barriers, highly conductive particles, poorly conductive matrix, and temperature-dependent physical properties is revisited using the homogenization method based on multiple scale asymptotic expansions. This method uses no a priori assumptions on the physics at the macroscale. For the considered physics and microstructures and depending on the order of magnitude of dimensionless Biot and Fourier numbers, it is shown that some situations cannot be homogenized. For other situations, three different macroscopic models are identified, depending on the quality of particle-particle contacts. They are one-phase media, following the standard heat equation and Fourier's law. Calculations of the effective conductivity tensor and heat capacity are proved to be uncoupled. Linear and steady state continuous localization problems must be solved on representative elementary volumes to compute the effective conductivity tensors for the two first models. For the third model, i.e., for highly resistive contacts, the localization problem becomes simpler and discrete whatever the shape of particles. In paper II [Vassal, Phys. Rev. E 77, 011303 (2008)], diffusion through networks of slender, wavy, entangled, and oriented fibers is considered. Discrete localization problems can then be obtained for all models, as well as semianalytical or fully analytical expressions of the corresponding effective conductivity tensors.
Full particle simulations of quasi-perpendicular shocks

NASA Astrophysics Data System (ADS)

Lembège, B.

This tutorial-style review is dedicated to the different strategies and constraints used for analysing the dynamics of a collisionless shocks with full particle simulations. Main results obtained with such simulations can be found in published materials (recent references are provided in this text); these will be only quoted herein in order to illustrate a few aspects of these simulations. Thanks to the large improvement of super computers, full particle simulations reveal to be quite helpful for analyzing in details the dynamics of collisionless shocks. The main characteristics of such codes can be shortly reminded as follows: one resolves the full set of Poisson and Maxwell's equations without any approximation. Two approaches are commonly used for resolving this equation's set, more precisely the space derivatives: (i) the finite difference approach and (ii) the use of FFT's (Fast Fourier Transform). Two advantages of approach (ii) are that FFT's are highly optimized in supercomputers libraries, and these allow to separate all fields components into two groups: the longitudinal electrostatic component El (solution of Poisson equation) and the transverse electromagnetic components Et and Bt solutions of the Maxwell's equations (so called "fields pusher"). Such a separation is quite helpful in the post processing stage necessary for the data analysis, as will be explained in the presentation. both ions and electrons populations are treated as individual finite-size particles and suffer the effects of all fields via the Lorentz force, so called "particle pusher", which is applied to each particle. Because of the large number of particles commonly used, the particle pusher represents the most expensive part of the calculations on which most efforts of optimisation needs to be performed (in terms of "vectorisation" or of "parallelism"). Relativistic effects may be included in this force via the use of particle momemtum. Each particle has three velocity components (vx, vy, vz), but may have 1, 2 or 3 space coordinates (x, y, z) according to the dimension of the code of concern.

Equations as Guides to Thinking and Problem Solving

ERIC Educational Resources Information Center

Hewitt, Paul G.

2011-01-01

Science is the study of nature's rules. The most basic of these are the laws of physics, most of which are expressed in equation form. Physics equations show how concepts connect to one another. But does a study of these equations enhance student understanding? Not always, for too often in an introductory course students are tempted (or even…
Foundations of radiation hydrodynamics

NASA Astrophysics Data System (ADS)

Mihalas, D.; Mihalas, B. W.

This book is the result of an attempt, over the past few years, to gather the basic tools required to do research on radiating flows in astrophysics. The microphysics of gases is discussed, taking into account the equation of state of a perfect gas, the first and second law of thermodynamics, the thermal properties of a perfect gas, the distribution function and Boltzmann's equation, the collision integral, the Maxwellian velocity distribution, Boltzmann's H-theorem, the time of relaxation, and aspects of classical statistical mechanics. Other subjects explored are related to the dynamics of ideal fluids, the dynamics of viscous and heat-conducting fluids, relativistic fluid flow, waves, shocks, winds, radiation and radiative transfer, the equations of radiation hydrodynamics, and radiating flows. Attention is given to small-amplitude disturbances, nonlinear flows, the interaction of radiation and matter, the solution of the transfer equation, acoustic waves, acoustic-gravity waves, basic concepts of special relativity, and equations of motion and energy.
Two-dimensional extended fluid model for a dc glow discharge with nonlocal ionization source term

NASA Astrophysics Data System (ADS)

Rafatov, Ismail; Bogdanov, Eugeny; Kudryavtsev, Anatoliy

2013-09-01

Numerical techniques applied to the gas discharge plasma modelling are generally grouped into fluid and kinetic (particle) methods, and their combinations which lead to the hybrid models. Hybrid models usually employ Monte Carlo method to simulate fast electron dynamics, while slow plasma species are described as fluids. However, since fast electrons contribution to these models is limited to deriving the ionization rate distribution, their effect can be expressed by the analytical approximation of the ionization source function, and then integrating it into the fluid model. In the context of this approach, we incorporated effect of fast electrons into the ``extended fluid model'' of glow discharge, using two spatial dimensions. Slow electrons, ions and excited neutral species are described by the fluid plasma equations. Slow electron transport (diffusion and mobility) coefficients as well as electron induced reaction rates are determined from the solutions of the electron Boltzmann equation. The self-consistent electric field is calculated using the Poisson equation. We carried out test calculations for the discharge in argon gas. Comparison with the experimental data as well as with the hybrid model results exhibits good applicability of the proposed model. The work was supported by the joint research grant from the Scientific and Technical Research Council of Turkey (TUBITAK) 212T164 and Russian Foundation for Basic Research (RFBR).
PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES Dust Acoustic Solitary Waves in Saturn F-ring's Region

NASA Astrophysics Data System (ADS)

E. K., El-Shewy; M. I. Abo el, Maaty; H. G., Abdelwahed; M. A., Elmessary

2011-01-01

Effect of hot and cold dust charge on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains has been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Kortewege-de Vries (KdV) equation. At the critical hot dusty plasma density Nh0, the KdV equation is not appropriate for describing the system. Hence, a set of stretched coordinates is considered to derive the modified KdV equation. It is found that the presence of hot and cold dust charge grains not only significantly modifies the basic properties of solitary structure, but also changes the polarity of the solitary profiles. In the vicinity of the critical hot dusty plasma density Nh0, neither KdV nor mKdV equation is appropriate for describing the DAWs. Therefore, a further modified KdV (fmKdV) equation is derived, which admits both soliton and double layer solutions.
Induced drag ideal efficiency factor of arbitrary lateral-vertical wing forms

NASA Technical Reports Server (NTRS)

Deyoung, J.

1980-01-01

A relatively simple equation is presented for estimating the induced drag ideal efficiency factor e for arbitrary cross sectional wing forms. This equation is based on eight basic but varied wing configurations which have exact solutions. The e function which relates the basic wings is developed statistically and is a continuous function of configuration geometry. The basic wing configurations include boxwings shaped as a rectangle, ellipse, and diamond; the V-wing; end-plate wing; 90 degree cruciform; circle dumbbell; and biplane. Example applications of the e equations are made to many wing forms such as wings with struts which form partial span rectangle dumbbell wings; bowtie, cruciform, winglet, and fan wings; and multiwings. Derivations are presented in the appendices of exact closed form solutions found of e for the V-wing and 90 degree cruciform wing and for an asymptotic solution for multiwings.
Dynamic sealing principles

NASA Technical Reports Server (NTRS)

Zuk, J.

1976-01-01

The fundamental principles governing dynamic sealing operation are discussed. Different seals are described in terms of these principles. Despite the large variety of detailed construction, there appear to be some basic principles, or combinations of basic principles, by which all seals function, these are presented and discussed. Theoretical and practical considerations in the application of these principles are discussed. Advantages, disadvantages, limitations, and application examples of various conventional and special seals are presented. Fundamental equations governing liquid and gas flows in thin film seals, which enable leakage calculations to be made, are also presented. Concept of flow functions, application of Reynolds lubrication equation, and nonlubrication equation flow, friction and wear; and seal lubrication regimes are explained.
Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth

NASA Technical Reports Server (NTRS)

Neitzel, G. P.; Chang, K.-T.; Jankowski, D. F.; Mittelmann, H. D.

1992-01-01

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.
Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Corato, M., E-mail: marco.decorato@unina.it; Slot, J.J.M., E-mail: j.j.m.slot@tue.nl; Hütter, M., E-mail: m.huetter@tue.nl

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered withinmore » the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.« less
Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koke, Christian, E-mail: christian.koke@stud.uni-heidelberg.de; Noh, Changsuk, E-mail: changsuk@kias.re.kr; Angelakis, Dimitris G., E-mail: dimitris.angelakis@gmail.com

When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogicalmore » introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.« less
Expendable Launch Vehicles Briefing and Basic Rocketry Physics

NASA Technical Reports Server (NTRS)

Delgado, Luis G.

2010-01-01

This slide presentation is composed of two parts. The first part shows pictures of launch vehicles and lift offs or in the case of the Pegasus launch vehicle separations. The second part discusses the basic physics of rocketry, starting with Newton's three physical laws that form the basis for classical mechanics. It includes a review of the basic equations that define the physics of rocket science, such as total impulse, specific impulse, effective exhaust velocity, mass ratio, propellant mass fraction, and the equations that combine to arrive at the thrust of the rocket. The effect of atmospheric pressure is reviewed, as is the effect of propellant mix on specific impulse.
Gaussian theory for spatially distributed self-propelled particles

NASA Astrophysics Data System (ADS)

Seyed-Allaei, Hamid; Schimansky-Geier, Lutz; Ejtehadi, Mohammad Reza

2016-12-01

Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model, we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatiotemporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.
Friction factor and heat transfer of nanofluids containing cylindrical nanoparticles in laminar pipe flow

NASA Astrophysics Data System (ADS)

Lin, Jianzhong; Xia, Yi; Ku, Xiaoke

2014-10-01

Numerical simulations of polyalphaolefins-Al2O3 nanofluids containing cylindrical nanoparticles in a laminar pipe flow are performed by solving the Navier-Stokes equation with term of cylindrical nanoparticles, the general dynamic equation for cylindrical nanoparticles, and equation for nanoparticle orientation. The distributions of particle number and volume concentration, the friction factor, and heat transfer are obtained and analyzed. The results show that distributions of nanoparticle number and volume concentration are non-uniform across the section, with larger and smaller values in the region near the pipe center and near the wall, respectively. The non-uniformity becomes significant with the increase in the axial distance from the inlet. The friction factor decreases with increasing Reynolds number. The relationships between the friction factor and the nanoparticle volume concentration as well as particle aspect ratio are dependent on the Reynolds number. The Nusselt number of nanofluids, directly proportional to the Reynolds number, particle volume concentration, and particle aspect ratio, is higher near the pipe entrance than at the downstream locations. The rate of increase in Nusselt number at lower particle volume concentration is more than that at higher concentration. Finally, the expressions of friction factor and Nusselt number as a function of particle volume concentration, particle aspect ratio, and Reynolds number are derived based on the numerical data.
Lie algebras and linear differential equations.

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Rahimi, A.

1972-01-01

Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.
Modeling the burnout of solid polydisperse fuel under the conditions of external heat transfer

NASA Astrophysics Data System (ADS)

Skorik, I. A.; Goldobin, Yu. M.; Tolmachev, E. M.; Gal'perin, L. G.

2013-11-01

A self-similar burnout mode of solid polydisperse fuel is considered taking into consideration heat transfer between fuel particles, gases, and combustion chamber walls. A polydisperse composition of fuel is taken into account by introducing particle distribution functions by radiuses obtained for the kinetic and diffusion combustion modes. Equations for calculating the temperatures of particles and gases are presented, which are written for particles average with respect to their distribution functions by radiuses taking into account the fuel burnout ratio. The proposed equations take into consideration the influence of fuel composition, air excess factor, and gas recirculation ratio. Calculated graphs depicting the variation of particle and gas temperatures, and the fuel burnout ratio are presented for an anthracite-fired boiler.
Linear study of the precessional fishbone instability

NASA Astrophysics Data System (ADS)

Idouakass, M.; Faganello, M.; Berk, H. L.; Garbet, X.; Benkadda, S.

2016-10-01

The precessional fishbone instability is an m = n = 1 internal kink mode destabilized by a population of trapped energetic particles. The linear phase of this instability is studied here, analytically and numerically, with a simplified model. This model uses the reduced magneto-hydrodynamics equations for the bulk plasma and the Vlasov equation for a population of energetic particles with a radially decreasing density. A threshold condition for the instability is found, as well as a linear growth rate and frequency. It is shown that the mode frequency is given by the precession frequency of the deeply trapped energetic particles at the position of strongest radial gradient. The growth rate is shown to scale with the energetic particle density and particle energy while it is decreased by continuum damping.
Computing diffusivities from particle models out of equilibrium

NASA Astrophysics Data System (ADS)

Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia

2018-04-01

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitrary out-of-equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation-dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero-range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.
Radiation torque on nonspherical particles in the transition matrix formalism

NASA Astrophysics Data System (ADS)

Borghese, Ferdinando; Denti, Paolo; Saija, Rosalba; Iatì, Maria A.

2006-10-01

The torque exerted by radiation on small particles is recognized to have a considerable relevance, e.g., on the dynamics of cosmic dust grains and for the manipulation of micro and nanoparticles under controlled conditions. In the present paper we derive, in the transition matrix formalism, the radiation torque applied by a plane polarized wave on nonspherical particles. In case of circularly polarized waves impinging on spherical particles our equations reproduce the findings of Marston and Crichton [Phys. Rev. A 30, 2508 2516 (1984)]. Our equations were applied to calculate the torque on a few model particles shaped as aggregates of identical spheres, both axially symmetric and lacking any symmetry, and the conditions for the stability of the induced rotational motion are discussed.
Particle trajectory computer program for icing analysis of axisymmetric bodies

NASA Technical Reports Server (NTRS)

Frost, Walter; Chang, Ho-Pen; Kimble, Kenneth R.

1982-01-01

General aviation aircraft and helicopters exposed to an icing environment can accumulate ice resulting in a sharp increase in drag and reduction of maximum lift causing hazardous flight conditions. NASA Lewis Research Center (LeRC) is conducting a program to examine, with the aid of high-speed computer facilities, how the trajectories of particles contribute to the ice accumulation on airfoils and engine inlets. This study, as part of the NASA/LeRC research program, develops a computer program for the calculation of icing particle trajectories and impingement limits relative to axisymmetric bodies in the leeward-windward symmetry plane. The methodology employed in the current particle trajectory calculation is to integrate the governing equations of particle motion in a flow field computed by the Douglas axisymmetric potential flow program. The three-degrees-of-freedom (horizontal, vertical, and pitch) motion of the particle is considered. The particle is assumed to be acted upon by aerodynamic lift and drag forces, gravitational forces, and for nonspherical particles, aerodynamic moments. The particle momentum equation is integrated to determine the particle trajectory. Derivation of the governing equations and the method of their solution are described in Section 2.0. General features, as well as input/output instructions for the particle trajectory computer program, are described in Section 3.0. The details of the computer program are described in Section 4.0. Examples of the calculation of particle trajectories demonstrating application of the trajectory program to given axisymmetric inlet test cases are presented in Section 5.0. For the examples presented, the particles are treated as spherical water droplets. In Section 6.0, limitations of the program relative to excessive computer time and recommendations in this regard are discussed.
[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].

PubMed

Murase, Kenya

2014-01-01

Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.
Numerical study of liquid-hydrogen droplet generation from a vibrating orifice

NASA Astrophysics Data System (ADS)

Xu, J.; Celik, D.; Hussaini, M. Y.; Van Sciver, S. W.

2005-08-01

Atomic hydrogen propellant feed systems for far-future spacecraft may utilize solid-hydrogen particle carriers for atomic species that undergo recombination to create hot rocket exhaust. Such technology will require the development of particle generation techniques. One such technique could involve the production of hydrogen droplets from a vibrating orifice that would then freeze in cryogenic helium vapor. Among other quantities, the shape and size of the droplet are of particular interest. The present paper addresses this problem within the framework of the incompressible Navier-Stokes equations for multiphase flows, in order to unravel the basic mechanisms of droplet formation with a view to control them. Surface tension, one of the most important mechanisms to determine droplet shape, is modeled as the source term in the momentum equation. Droplet shape is tracked using a volume-of-fluid approach. A dynamic meshing technique is employed to accommodate the vibration of the generator orifice. Numerically predicted droplet shapes show satisfactory agreement with photographs of droplets generated in experiments. A parametric study is carried out to understand the influence of injection velocity, nozzle vibrational frequency, and amplitude on the droplet shape and size. The computational model provides a definitive qualitative picture of the evolution of droplet shape as a function of the operating parameters. It is observed that, primarily, the orifice vibrational frequency affects the shape, the vibrational amplitude affects the time until droplet detachment from the orifice, and the injection velocity affects the size. However, it does not mean that, for example, there is no secondary effect of amplitude on shape or size.

Supersonic flow of chemically reacting gas-particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Anderson, P. G.; Sulyma, P. R.; Pearson, M. L.

1976-01-01

A numerical solution for chemically reacting supersonic gas-particle flows in rocket nozzles and exhaust plumes was described. The gas-particle flow solution is fully coupled in that the effects of particle drag and heat transfer between the gas and particle phases are treated. Gas and particles exchange momentum via the drag exerted on the gas by the particles. Energy is exchanged between the phases via heat transfer (convection and/or radiation). Thermochemistry calculations (chemical equilibrium, frozen or chemical kinetics) were shown to be uncoupled from the flow solution and, as such, can be solved separately. The solution to the set of governing equations is obtained by utilizing the method of characteristics. The equations cast in characteristic form are shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The particle distribution is represented in the numerical solution by a finite distribution of particle sizes.
Nonlocal birth-death competitive dynamics with volume exclusion

NASA Astrophysics Data System (ADS)

Khalil, Nagi; López, Cristóbal; Hernández-García, Emilio

2017-06-01

A stochastic birth-death competition model for particles with excluded volume is proposed. The particles move, reproduce, and die on a regular lattice. While the death rate is constant, the birth rate is spatially nonlocal and implements inter-particle competition by a dependence on the number of particles within a finite distance. The finite volume of particles is accounted for by fixing an upper value to the number of particles that can occupy a lattice node, compromising births and movements. We derive closed macroscopic equations for the density of particles and spatial correlation at two adjacent sites. Under different conditions, the description is further reduced to a single equation for the particle density that contains three terms: diffusion, a linear death, and a highly nonlinear and nonlocal birth term. Steady-state homogeneous solutions, their stability which reveals spatial pattern formation, and the dynamics of time-dependent homogeneous solutions are discussed and compared, in the one-dimensional case, with numerical simulations of the particle system.
Shock Interaction of Metal Particles in Condensed Explosive Detonation

NASA Astrophysics Data System (ADS)

Ripley, Robert; Zhang, Fan; Lien, Fue-Sang

2005-07-01

For detonation propagation in a condensed explosive with metal particles, a macro-scale physical model describing the momentum transfer between the explosive and particles has yet to be completely established. Previous 1D and 2D meso-scale modeling studies indicated that significant momentum transfer from the explosive to the particles occurs as the leading shock front crosses the particles, thus influencing the initiation and detonation structure. In this work, 3D meso-scale modeling is conducted to further study the two-phase momentum transfer during the shock diffraction and subsequent detonation in liquid nitromethane containing packed metal particles. Detonation of the condensed explosive is computed using an Arrhenius reaction model and a hybrid EOS model that combines the Mie-Gruneisen equation for reactants and the JWL equation for products. The compressible particles are modeled using the Tait EOS, where the material strength is negligible. The effect of particle packing configuration and inter-particle spacing is shown by parametric studies. Finally, a physical description of the momentum transfer is discussed.
Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C-Metric

NASA Astrophysics Data System (ADS)

Kar, Priyasri; Singh, Ritesh K.; Dasgupta, Ananda; Panigrahi, Prasanta K.

2018-03-01

The equation of motion of a massless Dirac particle in the C-metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, is cast in terms of a new set of su(1, 1) generators involving differential operators of degrees ±1/2 and 0. Additional Heun polynomials are obtained using this new algebraic structure and are used to construct some exact solutions for the radial and the polar parts of the Dirac equation.
Action principle for Coulomb collisions in plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hirvijoki, Eero

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.
Action principle for Coulomb collisions in plasmas

DOE PAGES

Hirvijoki, Eero

2016-09-14

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.
The Acceleration of Charged Particles at a Spherical Shock Moving through an Irregular Magnetic Field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giacalone, J.

We investigate the physics of charged-particle acceleration at spherical shocks moving into a uniform plasma containing a turbulent magnetic field with a uniform mean. This has applications to particle acceleration at astrophysical shocks, most notably, to supernovae blast waves. We numerically integrate the equations of motion of a large number of test protons moving under the influence of electric and magnetic fields determined from a kinematically defined plasma flow associated with a radially propagating blast wave. Distribution functions are determined from the positions and velocities of the protons. The unshocked plasma contains a magnetic field with a uniform mean andmore » an irregular component having a Kolmogorov-like power spectrum. The field inside the blast wave is determined from Maxwell’s equations. The angle between the average magnetic field and unit normal to the shock varies with position along its surface. It is quasi-perpendicular to the unit normal near the sphere’s equator, and quasi-parallel to it near the poles. We find that the highest intensities of particles, accelerated by the shock, are at the poles of the blast wave. The particles “collect” at the poles as they approximately adhere to magnetic field lines that move poleward from their initial encounter with the shock at the equator, as the shock expands. The field lines at the poles have been connected to the shock the longest. We also find that the highest-energy protons are initially accelerated near the equator or near the quasi-perpendicular portion of the shock, where the acceleration is more rapid.« less
Nonlinear longitudinal resonance interaction of energetic charged particles and VLF waves in the magnetosphere

NASA Technical Reports Server (NTRS)

Tkalcevic, S.

1982-01-01

The longitudinal resonance of waves and energetic electrons in the Earth's magnetosphere, and the possible role this resonance may play in generating various magnetospheric phenomena are studied. The derivation of time-averaged nonlinear equations of motion for energetic particles longitudinally resonant with a whistler mode wave propagating with nonzero wave normal is considered. It is shown that the wave magnetic forces can be neglected at lower particle pitch angles, while they become equal to or larger than the wave electric forces for alpha 20 deg. The time-averaged equations of motion were used in test particle simulation which were done for a wide range of wave amplitudes, wave normals, particle pitch angles, particle parallel velocities, and in an inhomogeneous medium such as the magnetosphere. It was found that there are two classes of particles, trapped and untrapped, and that the scattering and energy exchange for those two groups exhibit significantly different behavior.
A hybridized discontinuous Galerkin framework for high-order particle-mesh operator splitting of the incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Maljaars, Jakob M.; Labeur, Robert Jan; Möller, Matthias

2018-04-01

A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.
Predicting fractional bed load transport rates: Application of the Wilcock‐Crowe equations to a regulated gravel bed river

USGS Publications Warehouse

Gaeuman, David; Andrews, E.D.; Krause, Andreas; Smith, Wes

2009-01-01

Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock‐Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (τ*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between τ*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock‐Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock‐Crowe equations nonetheless consistently under‐predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of τ*rm estimated from bed load samples are up to 50% larger than those predicted with the Wilcock‐Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to the Wilcock‐Crowe equation for determining τ*rm and the hiding function used to scale τ*rm to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River.
Particulate Matter (PM) Basics

EPA Pesticide Factsheets

Particle pollution is the term for a mixture of solid particles and liquid droplets found in the air. These include inhalable coarse particles, with diameters between 2.5 micrometers and 10 micrometers, and fine particles, 2.5 micrometers and smaller.
Smoothed particle hydrodynamics method for simulating waterfall flow

NASA Astrophysics Data System (ADS)

Suwardi, M. G.; Jondri; Tarwidi, D.

2018-03-01

The existence of waterfall in many nations, such as Indonesia has a potential to develop and to fulfill the electricity demand in the nation. By utilizing mechanical flow energy of the waterfall, it would be able to generate electricity. The study of mechanical energy could be done by simulating waterfall flow using 2-D smoothed particle hydrodynamics (SPH) method. The SPH method is suitable to simulate the flow of the waterfall, because it has an advantage which could form particles movement that mimic the characteristics of fluid. In this paper, the SPH method is used to solve Navier-Stokes and continuity equation which are the main cores of fluid motion. The governing equations of fluid flow are used to obtain the acceleration, velocity, density, and position of the SPH particles as well as the completion of Leapfrog time-stepping method. With these equations, simulating a waterfall flow would be more attractive and able to complete the analysis of mechanical energy as desired. The mechanical energy that generated from the waterfall flow is calculated and analyzed based on the mass, height, and velocity of each SPH particle.
Impact of soil properties on selected pharmaceuticals adsorption in soils

NASA Astrophysics Data System (ADS)

Kodesova, Radka; Kocarek, Martin; Klement, Ales; Fer, Miroslav; Golovko, Oksana; Grabic, Roman; Jaksik, Ondrej

2014-05-01

The presence of human and veterinary pharmaceuticals in the environment has been recognized as a potential threat. Pharmaceuticals may contaminate soils and consequently surface and groundwater. Study was therefore focused on the evaluation of selected pharmaceuticals adsorption in soils, as one of the parameters, which are necessary to know when assessing contaminant transport in soils. The goals of this study were: (1) to select representative soils of the Czech Republic and to measure soil physical and chemical properties; (2) to measure adsorption isotherms of selected pharmaceuticals; (3) to evaluate impact of soil properties on pharmaceutical adsorptions and to propose pedotransfer rules for estimating adsorption coefficients from the measured soil properties. Batch sorption tests were performed for 6 selected pharmaceuticals (beta blockers Atenolol and Metoprolol, anticonvulsant Carbamazepin, and antibiotics Clarithromycin, Trimetoprim and Sulfamethoxazol) and 13 representative soils (soil samples from surface horizons of 11 different soil types and 2 substrates). The Freundlich equations were used to describe adsorption isotherms. The simple correlations between measured physical and chemical soil properties (soil particle density, soil texture, oxidable organic carbon content, CaCO3 content, pH_H2O, pH_KCl, exchangeable acidity, cation exchange capacity, hydrolytic acidity, basic cation saturation, sorption complex saturation, salinity), and the Freundlich adsorption coefficients were assessed using Pearson correlation coefficient. Then multiple-linear regressions were applied to predict the Freundlich adsorption coefficients from measured soil properties. The largest adsorption was measured for Clarithromycin (average value of 227.1) and decreased as follows: Trimetoprim (22.5), Metoprolol (9.0), Atenolol (6.6), Carbamazepin (2.7), Sulfamethoxazol (1.9). Absorption coefficients for Atenolol and Metoprolol closely correlated (R=0.85), and both were also related to absorption coefficients of Carbamazepin (R=0.67 and 0.68). Positive correlation was found between Trimetoprim absorption coefficients and Atenolol, Metoprolol or Carbamazepin absorption coefficients. The negative relationship was found between absorption coefficients of Sulfomethoxazol and Clarithromycin (R=-0.80). Sulfamethoxazol absorption coefficient was negatively related to pH_H2O, pH_KCL or sorption complex saturation and positively to the hydrolytic acidity or exchangeable acidity. Trimetoprim absorption coefficient was positively related to the oxidable organic carbon content, cation exchange capacity, basic cation saturation or silt content and negatively to particle density or sand content. Clarithromycin absorption coefficient was positively related to pH_H2O, pH_KCL, CaCO3 content, basic cation saturation or sorption complex saturation and negatively to hydrolytic acidity or exchangeable acidity. Atenolol and Metoprolol absorption coefficients were positively related to the oxidable organic carbon content, cation exchange capacity, basic cation saturation, salinity, clay content or silt content, and negatively to the particle density or sand content. Finally Carbamazepin absorption coefficient was positively related to the oxidable organic carbon content, cation exchange capacity or basic cation saturation, and negatively to the particle density or sand content. Evaluated pedotransfer rules for different pharmaceuticals included different sets of soil properties. Absorption coefficients could be predicted from: the hydrolytic acidity (Sulfamethoxazol), the oxidable organic carbon content (Trimetoprim and Carbamazepin), the oxidable organic carbon content, hydrolytic acidity and cation exchange capacity (Clarithromycin), the basic cation saturation (Atenolol and Metoprolol). Acknowledgement: Authors acknowledge the financial support of the Czech Science Foundation (Project No. 13-12477S).
ELECTROKINETIC PHENOMENA. II : THE FACTOR OF PROPORTIONALITY FOR CATAPHORETIC AND ELECTROENDOSMOTIC MOBILITIES.

PubMed

Abramson, H A

1930-07-20

Two theories which predict different values for the ratio of V(E), the electroendosmotic velocity of a liquid past a surface, to V(p), the electric mobility of a particle of the same surface through the same liquid are discussed. The theory demanding that See PDF for Equation was supported by certain data of van der Grinten for a glass surface. Re-calculation of van der Grinten's data reveals that the ratio varies between 2.1 and 2.8. These results are in accord with previous data of Abramson. It is pointed out that glass is unsuitable for the investigation. The ratio See PDF for Equation is here determined for a flat surface and particles when both are covered by the same proteins. Under these conditions See PDF for Equation The theory is similarly tested for a round surface using a micro-cataphoresis cell. It is shown that See PDF for Equation for a round surface is approximately 1.00. These findings are confirmatory of previous data supporting the view that cataphoretic mobility is independent of the size and shape of the particles when all particles compared have similar surface constitutions.
Building 1D resonance broadened quasilinear (RBQ) code for fast ions Alfvénic relaxations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

The performance of the burning plasma is limited by the confinement of superalfvenic fusion products, e.g. alpha particles, which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using a resonance line broadened diffusion coefficient. The interaction of fast ions and AEs is captured for cases where there are either isolated or overlapping modes. A new code RBQ1D is being built which constructs diffusion coefficients based on realistic eigenfunctions that are determined by the ideal MHD code NOVA. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the ion distribution function.
Dominant height-based height-diameter equations for trees in southern Indiana

Treesearch

John A., Jr. Kershaw; Robert C. Morrissey; Douglass F. Jacobs; John R. Seifert; James B. McCarter

2008-01-01

Height-diameter equations are developed based on dominant tree data collected in 1986 in 8- to 17-year-old clearcuts and the phase 2 Forest Inventory and Analysis plots on the Hoosier National Forest in south central Indiana. Two equation forms are explored: the basic, three-parameter Chapman-Richards function, and a modification of the three-parameter equation...
The method of averages applied to the KS differential equations

NASA Technical Reports Server (NTRS)

Graf, O. F., Jr.; Mueller, A. C.; Starke, S. E.

1977-01-01

A new approach for the solution of artificial satellite trajectory problems is proposed. The basic idea is to apply an analytical solution method (the method of averages) to an appropriate formulation of the orbital mechanics equations of motion (the KS-element differential equations). The result is a set of transformed equations of motion that are more amenable to numerical solution.
Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

NASA Astrophysics Data System (ADS)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.
Filling of a Poisson trap by a population of random intermittent searchers.

PubMed

Bressloff, Paul C; Newby, Jay M

2012-03-01

We extend the continuum theory of random intermittent search processes to the case of N independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi-infinite track. Each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state. We assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process. The hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target; the particle is removed from the system after delivering its cargo. As a further generalization of previous models, we assume that up to n successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as 1/N, we show that there exists a well-defined mean-field limit N→∞, in which the stochastic model reduces to a deterministic system of linear reaction-hyperbolic equations for the concentrations of particles in each of the internal states. These equations decouple from the stochastic process associated with filling the target with cargo. The latter can be modeled as a Poisson process in which the time-dependent rate of filling λ(t) depends on the concentration of stationary particles within the target domain. Hence, we refer to the target as a Poisson trap. We analyze the efficiency of filling the Poisson trap with n particles in terms of the waiting time density f(n)(t). The latter is determined by the integrated Poisson rate μ(t)=∫(0)(t)λ(s)ds, which in turn depends on the solution to the reaction-hyperbolic equations. We obtain an approximate solution for the particle concentrations by reducing the system of reaction-hyperbolic equations to a scalar advection-diffusion equation using a quasisteady-state analysis. We compare our analytical results for the mean-field model with Monte Carlo simulations for finite N. We thus determine how the mean first passage time (MFPT) for filling the target depends on N and n.
A boundary-layer model for Mars - Comparison with Viking lander and entry data

NASA Technical Reports Server (NTRS)

Haberle, Robert M.; Houben, Howard C.; Hertenstein, Rolf; Herdtle, Tomas

1993-01-01

A 1D boundary-layer model of Mars based on a momentum equation that describes friction, pressure gradient, and Coriolis forces is presented. Frictional forces and convective heating are computed using the level-2 turbulence closure theory of Mellor and Yamada (1974). The model takes into account the radiative effects of CO2 gas and suspended dust particles. Both radiation and convection depend on surface temperatures which are computed from a surface heat budget. Model predictions are compared with available observations from Viking landers. It is concluded that, in general, the model reproduces the basic features of the temperature data. The agreement is particularly good at entry time for the V L-2 site, where the model and observations are within several degrees at all levels for which data are available.

Tap density equations of granular powders based on the rate process theory and the free volume concept.

PubMed

Hao, Tian

2015-02-28

The tap density of a granular powder is often linked to the flowability via the Carr index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in the literature: the inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept under the assumption that particles will obey similar thermodynamic laws during the tapping process if the "granular temperature" is defined in a different way, we obtain the tap density equations, and they are reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environmental temperature are grouped into this parameter that weighs the pace of the packing process. The current results, in conjunction with our previous findings, may imply that both "dry" (granular) and "wet" (colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process).
Constraining ejecta particle size distributions with light scattering

NASA Astrophysics Data System (ADS)

Schauer, Martin; Buttler, William; Frayer, Daniel; Grover, Michael; Lalone, Brandon; Monfared, Shabnam; Sorenson, Daniel; Stevens, Gerald; Turley, William

2017-06-01

The angular distribution of the intensity of light scattered from a particle is strongly dependent on the particle size and can be calculated using the Mie solution to Maxwell's equations. For a collection of particles with a range of sizes, the angular intensity distribution will be the sum of the contributions from each particle size weighted by the number of particles in that size bin. The set of equations describing this pattern is not uniquely invertible, i.e. a number of different distributions can lead to the same scattering pattern, but with reasonable assumptions about the distribution it is possible to constrain the problem and extract estimates of the particle sizes from a measured scattering pattern. We report here on experiments using particles ejected by shockwaves incident on strips of triangular perturbations machined into the surface of tin targets. These measurements indicate a bimodal distribution of ejected particle sizes with relatively large particles (median radius 2-4 μm) evolved from the edges of the perturbation strip and smaller particles (median radius 200-600 nm) from the perturbations. We will briefly discuss the implications of these results and outline future plans.
The Marriage of Gas and Dust

NASA Astrophysics Data System (ADS)

Price, D. J.; Laibe, G.

2015-10-01

Dust-gas mixtures are the simplest example of a two fluid mixture. We show that when simulating such mixtures with particles or with particles coupled to grids a problem arises due to the need to resolve a very small length scale when the coupling is strong. Since this is occurs in the limit when the fluids are well coupled, we show how the dust-gas equations can be reformulated to describe a single fluid mixture. The equations are similar to the usual fluid equations supplemented by a diffusion equation for the dust-to-gas ratio or alternatively the dust fraction. This solves a number of numerical problems as well as making the physics clear.
Using Theoretical Descriptors in Structural Activity Relationships: 4. Molecular Orbital Basicity and Electrostatic Basicity

DTIC Science & Technology

1988-11-01

rates.6 The Hammet equation , also called the Linear Free Energy Relationship (LFER) because of the relationship of the Gibb’s Free Energy to the... equations for numerous biological and physicochemical properties. Linear Solvation Enery Relationship (LSER), a sub-set of QSAR have been used by...originates from thermodynamics, where Hammet recognized the relationship of structure to the Gibb’s Free Energy, and ultimately to equilibria and reaction
Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

NASA Astrophysics Data System (ADS)

Na, D.-Y.; Moon, H.; Omelchenko, Y. A.; Teixeira, F. L.

2018-01-01

Accurate modeling of relativistic particle motion is essential for physical predictions in many problems involving vacuum electronic devices, particle accelerators, and relativistic plasmas. A local, explicit, and charge-conserving finite-element time-domain (FETD) particle-in-cell (PIC) algorithm for time-dependent (non-relativistic) Maxwell-Vlasov equations on irregular (unstructured) meshes was recently developed by Moon et al. [Comput. Phys. Commun. 194, 43 (2015); IEEE Trans. Plasma Sci. 44, 1353 (2016)]. Here, we extend this FETD-PIC algorithm to the relativistic regime by implementing and comparing three relativistic particle-pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.
Estimation of CT-derived abdominal visceral and subcutaneous adipose tissue depots from anthropometry in Europeans, South Asians and African Caribbeans.

PubMed

Eastwood, Sophie V; Tillin, Therese; Wright, Andrew; Heasman, John; Willis, Joseph; Godsland, Ian F; Forouhi, Nita; Whincup, Peter; Hughes, Alun D; Chaturvedi, Nishi

2013-01-01

South Asians and African Caribbeans experience more cardiometabolic disease than Europeans. Risk factors include visceral (VAT) and subcutaneous abdominal (SAT) adipose tissue, which vary with ethnicity and are difficult to quantify using anthropometry. We developed and cross-validated ethnicity and gender-specific equations using anthropometrics to predict VAT and SAT. 669 Europeans, 514 South Asians and 227 African Caribbeans (70 ± 7 years) underwent anthropometric measurement and abdominal CT scanning. South Asian and African Caribbean participants were first-generation migrants living in London. Prediction equations were derived for CT-measured VAT and SAT using stepwise regression, then cross-validated by comparing actual and predicted means. South Asians had more and African Caribbeans less VAT than Europeans. For basic VAT prediction equations (age and waist circumference), model fit was better in men (R(2) range 0.59-0.71) than women (range 0.35-0.59). Expanded equations (+ weight, height, hip and thigh circumference) improved fit for South Asian and African Caribbean women (R(2) 0.35 to 0.55, and 0.43 to 0.56 respectively). For basic SAT equations, R(2) was 0.69-0.77, and for expanded equations it was 0.72-0.86. Cross-validation showed differences between actual and estimated VAT of <7%, and SAT of <8% in all groups, apart from VAT in South Asian women which disagreed by 16%. We provide ethnicity- and gender-specific VAT and SAT prediction equations, derived from a large tri-ethnic sample. Model fit was reasonable for SAT and VAT in men, while basic VAT models should be used cautiously in South Asian and African Caribbean women. These equations will aid studies of mechanisms of cardiometabolic disease in later life, where imaging data are not available.
BASIC INVESTIGATIONS IN PHOTOPOTENTIOMETRY.

DTIC Science & Technology

favorably with potentials calculated from the Nernst equation . The potentials are produced by a mechanism resembling a concentration cell with...transference. The effects of temperature and concentration are well defined by the Nernst equation . The observed potential at any time during the irradiation...is approximated by a potential calculated from the Nernst equation . (Author)
Effect of magnetic reconnection in stellar plasma

NASA Astrophysics Data System (ADS)

Hammoud, M.; El Eid, M.; Darwish, M.

2017-06-01

An important phenomenon in Astrophysics is the process of magnetic reconnection (MGR), which is envisaged to understand the solar flares, coronal mass ejection, interaction of the solar wind with the Earth’s magnetic field (so called geomagnetic storm) and other phenomena. In addition, it plays a role in the formation of stars. MGR involves topological change of a set of magnetic field lines leading to a new equilibrium configuration of lower magnetic energy. The MGR is basically described in the framework of the Maxwell’s equations linked to Navier-Stockes equations. Nevertheless, many details are still not understood. In this paper, we investigate the MGR process in the framework of the Magnetohydrodynamic (MHD) model of a single conducting fluid using a modern powerful computational tool (OpenFOAM). We will show that the MGR process takes place only if resistivity exists. However, despite the high conductivity of the plasma, resistivity becomes effective in a very thin layer generating sharp gradients of the magnetic field, and thus accelerating the reconnection process. The net effect of MGR is that magnetic energy is converted into thermal and kinetic energies leading to heating and acceleration of charged particles. The Sun’s coronal ejection is an example of the MGR process.
Steady Secondary Flows Generated by Periodic Compression and Expansion of an Ideal Gas in a Pulse Tube

NASA Technical Reports Server (NTRS)

Lee, Jeffrey M.

1999-01-01

This study establishes a consistent set of differential equations for use in describing the steady secondary flows generated by periodic compression and expansion of an ideal gas in pulse tubes. Also considered is heat transfer between the gas and the tube wall of finite thickness. A small-amplitude series expansion solution in the inverse Strouhal number is proposed for the two-dimensional axisymmetric mass, momentum and energy equations. The anelastic approach applies when shock and acoustic energies are small compared with the energy needed to compress and expand the gas. An analytic solution to the ordered series is obtained in the strong temperature limit where the zeroth-order temperature is constant. The solution shows steady velocities increase linearly for small Valensi number and can be of order I for large Valensi number. A conversion of steady work flow to heat flow occurs whenever temperature, velocity or phase angle gradients are present. Steady enthalpy flow is reduced by heat transfer and is scaled by the Prandtl times Valensi numbers. Particle velocities from a smoke-wire experiment were compared with predictions for the basic and orifice pulse tube configurations. The theory accurately predicted the observed steady streaming.
Numerical study of alfvénic wave activity in the solar wind as a cause for pitch angle scattering with focus on kinetic processes

NASA Astrophysics Data System (ADS)

Keilbach, D.; Berger, L.; Drews, C.; Marsch, E.; Wimmer-Schweingruber, R. F.

2017-12-01

Recent studies, that determined the inflow longitude of the local interstellar medium from the anisotropy of interstellar pickup ion (PUI) radial velocity, have once again raised the question, how transport effects and especially wave activity in the solar wind modifies the velocity distribution function of PUIs.This study investigates the modification of an oxygen PUI torus distribution by alfvénic waves qualitatively with a numerical approach. The focus of this study is to understand this modification kinetically, which means, that instead of describing the PUI transport through diffusion approaches, we trace the trajectories of test particles in pitch angle space with a time resolution of at least 100 time steps per gyro orbit in order to find first principles of wave particle interactions on the most basic scale.Therefore we have implemented a Leapfrog solver of the Lorentz-Newton equations of motion for a charged test particle in a electro-magnetic field. The alfvénic waves were represented through a continuous circularly polarized wave superimposed to a constant 5 nT background magnetic field. In addition an electric field arising from induction has been added to the simulation's boundary conditions. The simulation code computes the particles' trajectories in the solar wind bulk system.Upon interaction with mono frequent single-frequency waves, the particles are found to perform stationary trajectories in pitch angle space, so that the pitch angle distribution of a conglomerate of test particles does not experience a systematic broadening over time. Also the particles do not react most strongly with waves at resonant frequencies, since the pitch angle modification by the waves sweeps their parallel velocity out of resonance quickly. However, within frequencies close to first order resonance, strong interactions between waves and particles are observed.Altogether the framework of our simulation is readily expandable to simulate additional effects, which may modify the test particles' pitch angle distribution strongly (e.g. collisions with solar wind particles or gradient drifts). So far we have expanded the simulation to support intermittent waves, where we have observed, that the pitch angle distribution of the test particles broadens systematically over time.
Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements

NASA Astrophysics Data System (ADS)

Zander, C.; Plastino, A. R.; Díaz-Alonso, J.

2015-11-01

We investigate time-dependent solutions for a non-linear Schrödinger equation recently proposed by Nassar and Miret-Artés (NM) to describe the continuous measurement of the position of a quantum particle (Nassar, 2013; Nassar and Miret-Artés, 2013). Here we extend these previous studies in two different directions. On the one hand, we incorporate a potential energy term in the NM equation and explore the corresponding wave packet dynamics, while in the previous works the analysis was restricted to the free-particle case. On the other hand, we investigate time-dependent solutions while previous studies focused on a stationary one. We obtain exact wave packet solutions for linear and quadratic potentials, and approximate solutions for the Morse potential. The free-particle case is also revisited from a time-dependent point of view. Our analysis of time-dependent solutions allows us to determine the stability properties of the stationary solution considered in Nassar (2013), Nassar and Miret-Artés (2013). On the basis of these results we reconsider the Bohmian approach to the NM equation, taking into account the fact that the evolution equation for the probability density ρ =| ψ | 2 is not a continuity equation. We show that the effect of the source term appearing in the evolution equation for ρ has to be explicitly taken into account when interpreting the NM equation from a Bohmian point of view.
Dimensional reduction of a general advection–diffusion equation in 2D channels

NASA Astrophysics Data System (ADS)

Kalinay, Pavol; Slanina, František

2018-06-01

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick–Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient can be always found.
Composite anion-exchangers modified with nanoparticles of hydrated oxides of multivalent metals

NASA Astrophysics Data System (ADS)

Maltseva, T. V.; Kolomiets, E. O.; Dzyazko, Yu. S.; Scherbakov, S.

2018-02-01

Organic-inorganic composite ion-exchangers based on anion exchange resins have been obtained. Particles of one-component and two-component modifier were embedded using the approach, which allows us to realize purposeful control of a size of the embedded particles. The approach is based on Ostwald-Freundlich equation, which was adapted to deposition in ion exchange matrix. The equation was obtained experimentally. Hydrated oxides of zirconium and iron were applied to modification, concentration of the reagents were varied. The embedded particles accelerate sorption, the rate of which is fitted by the model equation of chemical reactions of pseudo-second order. When sorption of arsenate ions from very diluted solution (50 µg dm-3) occurs, the composites show higher distribution coefficients comparing with the pristine resin.
An Analysis of Processes in the Solar Wind in a Thin Layer Adjacent to the Front of the Shock Wave

NASA Astrophysics Data System (ADS)

Molotkov, I. A.; Atamaniuk, B.

2018-05-01

A two-dimensional stationary system of nonlinear magnetohydrodynamics (MHD) equations in a thin layer adjoining the front of the interplanetary shock wave has been solved. Previously, any available publications relied on linear transport equations. But the presence of high-energy particles in the solar wind (SW) requires taking into account the processes of self-interaction. Our analysis examines the nonlinear terms in the MHD equations. A solution has been constructed for three cases: (1) in the absence of magnetic reconnections; (2) for magnetic reconnections; and (3) with the simultaneous action of reconnections and junction of magnetic islands. In all three cases, expressions were found for the main parameters of the SW. The results obtained on the basis of the solution of the MHD equations are consistent with the conclusions based on the investigation of the particle velocity distribution functions. This makes it possible to confirm the previously established fraction of particles excited to energies above 1 MeV.
Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-07-29

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N 2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less
On Determination of the Equation of State of Colloidal Suspensions

NASA Astrophysics Data System (ADS)

Sirorattanakul, Krittanon; Huang, Hao; Uhl, Christopher; Ou-Yang, Daniel

Colloidal suspensions are the main ingredients for a variety of materials in our daily life, e.g., milk, salad dressing, skin lotions and paint for wall coatings. Material properties of these systems require an understanding of the equation of state of these materials. Our project aims to experimentally determine the equation of state of colloidal suspensions by microfluidics, dielectrophoresis (DEP) and optical imaging. We use fluorescent polystyrene latexes as a model system for this study. Placing semi-permeable membranes between microfluidics channels, which made from PDMS, we control the particle concentration and ionic strengths of the suspension. We use osmotic equilibrium equation to analyze the particle concentration distribution in a potential force field created by DEP. We use confocal optical imaging to measure the spatial distribution of the particle concentration. We compare the results of our experimental study with data obtained by computer simulation of osmotic equilibrium of interacting colloids. NSF DMR-0923299, Emulsion Polymer Institute, Department of Physics, Bioengineering Program of Lehigh University.
Available Energy via Nonequilibrium Thermodynamics.

ERIC Educational Resources Information Center

Woollett, E. L.

1979-01-01

Presents basic relations involving the concept of available energy that are derived from the local equations of nonequilibrium thermodynamics. The equations and applications of the local thermodynamic equilibrium LTD model are also presented. (HM)
a Study of Dynamic Powder Consolidation Based on a Particle-Level Mathematical Model.

NASA Astrophysics Data System (ADS)

Williamson, Richard L.

A mathematical model is developed to investigate the effects of large amplitude shock waves on powder materials during dynamic consolidation. The model is constructed at the particle level, focusing on a region containing a few powder particles and the surrounding interstices. The general equations of continuum mechanics are solved over this region, using initial and boundary conditions appropriate for the consolidation process. Closure of the equation system is obtained using an analytical equation of state; relations are included to account for solid to liquid phase changes. An elastic, perfectly-plastic constitutive law, specifically modified to describe material behavior at high-strain-rates, is applied to the solid materials. To reduce complexity, the model is restricted to two dimensions, therefore individual particles are approximated as infinitely long cylinders rather than spheres. The equation system is solved using standard finite-difference numerical techniques. It is demonstrated that for typical consolidation conditions, energy diffusion mechanisms are insignificant during the rapid densification phase of consolidation. Using type 304 stainless steel powder material, the particle-level model is used to investigate the mechanisms responsible for particle surface heating and metallurgical bonding during consolidation. It is demonstrated that energy deposition near particle surfaces results both from rapid particle deformation during interstitial filling and large localized impacts occurring at the final instant of interstitial closure; particle interior regions remain at sufficiently low temperatures to avoid microstructural modification. Nonuniform metallurgical bonding is predicted around the particle periphery, ranging from complete fusion to mechanical abutment. Simulation results are used to investigate the detailed wave propagation phenomena at the particle level, providing an improved understanding of this complex behavior. A variety of parametric studies are conducted including investigations of the effects of stress wave amplitude and rise time, the role of interstitial gases during consolidation, and various geometric aspects including the importance of initial void fraction. The model is applied to a metal matrix composite system to investigate the consolidation of mixtures of differing materials; results of a two-dimensional experiment are included. Available experimental data are compared with simulation results. In general, very good agreement between simulation results and data is obtained.
Nonlinear Gyro-Landau-Fluid Equations

NASA Astrophysics Data System (ADS)

Raskolnikov, I.; Mattor, Nathan; Parker, Scott E.

1996-11-01

We present fluid equations which describe the effects of both linear and nonlinear Landau damping (wave-particle-wave effects). These are derived using a recently developed analytical method similar to renormalization group theory. (Scott E. Parker and Daniele Carati, Phys. Rev. Lett. 75), 441 (1995). In this technique, the phase space structure inherent in Landau damping is treated analytically by building a ``renormalized collisionality'' onto a bare collisionality (which may be taken as vanishingly small). Here we apply this technique to the nonlinear ion gyrokinetic equation in slab geometry, obtaining nonlinear fluid equations for density, parallel momentum and heat. Wave-particle resonances are described by two functions appearing in the heat equation: a renormalized ``collisionality'' and a renormalized nonlinear coupling coeffient. It will be shown that these new equations may correct a deficiency in existing gyrofluid equations, (G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990). which can severely underestimate the strength of nonlinear interaction in regimes where linear resonance is strong. (N. Mattor, Phys. Fluids B 4,) 3952 (1992).
Cosmic ray injection spectrum at the galactic sources

NASA Astrophysics Data System (ADS)

Lagutin, Anatoly; Tyumentsev, Alexander; Volkov, Nikolay

The spectra of cosmic rays measured at Earth are different from their source spectra. A key to understanding this difference, being crucial for solving the problem of cosmic-ray origin, is the determination of how cosmic-ray (CR) particles propagate through the turbulent interstellar medium (ISM). If the medium is a quasi-homogeneous the propagation process can be described by a normal diffusion model. However, during a last few decades many evidences, both from theory and observations, of the existence of multiscale structures in the Galaxy have been found. Filaments, shells, clouds are entities widely spread in the ISM. In such a highly non-homogeneous (fractal-like) ISM the normal diffusion model certainly is not kept valid. Generalization of this model leads to what is known as "anomalous diffusion". The main goal of the report is to retrieve the cosmic ray injection spectrum at the galactic sources in the framework of the anomalous diffusion (AD) model. The anomaly in this model results from large free paths ("Levy flights") of particles between galactic inhomogeneities. In order to evaluate the CR spectrum at the sources, we carried out new calculation of the CR spectra at Earth. AD equation in terms of fractional derivatives have been used to describe CR propagation from the nearby (r≤1 kpc) young (t≤ 1 Myr) and multiple old distant (r > 1 kpc) sources. The assessment of the key model parameters have been based on the results of the particles diffusion in the cosmic and laboratory plasma. We show that in the framework of the anomalous diffusion model the locally observed basic features of the cosmic rays (difference between spectral exponents of proton, He and other nuclei, "knee" problem, positron to electron ratio) can be explained if the injection spectrum at the main galactic sources of cosmic rays has spectral exponent p˜ 2.85. The authors acknowledge support from The Russian Foundation for Basic Research grant No. 14-02-31524.

Different Scalable Implementations of Collision and Streaming for Optimal Computational Performance of Lattice Boltzmann Simulations

NASA Astrophysics Data System (ADS)

Geneva, Nicholas; Wang, Lian-Ping

2015-11-01

In the past 25 years, the mesoscopic lattice Boltzmann method (LBM) has become an increasingly popular approach to simulate incompressible flows including turbulent flows. While LBM solves more solution variables compared to the conventional CFD approach based on the macroscopic Navier-Stokes equation, it also offers opportunities for more efficient parallelization. In this talk we will describe several different algorithms that have been developed over the past 10 plus years, which can be used to represent the two core steps of LBM, collision and streaming, more effectively than standard approaches. The application of these algorithms spans LBM simulations ranging from basic channel to particle laden flows. We will cover the essential detail on the implementation of each algorithm for simple 2D flows, to the challenges one faces when using a given algorithm for more complex simulations. The key is to explore the best use of data structure and cache memory. Two basic data structures will be discussed and the importance of effective data storage to maximize a CPU's cache will be addressed. The performance of a 3D turbulent channel flow simulation using these different algorithms and data structures will be compared along with important hardware related issues.
Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy.

PubMed

Shizgal, Bernie D

2018-05-01

This paper considers two nonequilibrium model systems described by linear Fokker-Planck equations for the time-dependent velocity distribution functions that yield steady state Kappa distributions for specific system parameters. The first system describes the time evolution of a charged test particle in a constant temperature heat bath of a second charged particle. The time dependence of the distribution function of the test particle is given by a Fokker-Planck equation with drift and diffusion coefficients for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. A second system involves the Fokker-Planck equation for electrons dilutely dispersed in a constant temperature heat bath of atoms or ions and subject to an external time-independent uniform electric field. The momentum transfer cross section for collisions between the two components is assumed to be a power law in reduced speed. The time-dependent Fokker-Planck equations for both model systems are solved with a numerical finite difference method and the approach to equilibrium is rationalized with the Kullback-Leibler relative entropy. For particular choices of the system parameters for both models, the steady distribution is found to be a Kappa distribution. Kappa distributions were introduced as an empirical fitting function that well describe the nonequilibrium features of the distribution functions of electrons and ions in space science as measured by satellite instruments. The calculation of the Kappa distribution from the Fokker-Planck equations provides a direct physically based dynamical approach in contrast to the nonextensive entropy formalism by Tsallis [J. Stat. Phys. 53, 479 (1988)JSTPBS0022-471510.1007/BF01016429].
Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy

NASA Astrophysics Data System (ADS)

Shizgal, Bernie D.

2018-05-01

This paper considers two nonequilibrium model systems described by linear Fokker-Planck equations for the time-dependent velocity distribution functions that yield steady state Kappa distributions for specific system parameters. The first system describes the time evolution of a charged test particle in a constant temperature heat bath of a second charged particle. The time dependence of the distribution function of the test particle is given by a Fokker-Planck equation with drift and diffusion coefficients for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. A second system involves the Fokker-Planck equation for electrons dilutely dispersed in a constant temperature heat bath of atoms or ions and subject to an external time-independent uniform electric field. The momentum transfer cross section for collisions between the two components is assumed to be a power law in reduced speed. The time-dependent Fokker-Planck equations for both model systems are solved with a numerical finite difference method and the approach to equilibrium is rationalized with the Kullback-Leibler relative entropy. For particular choices of the system parameters for both models, the steady distribution is found to be a Kappa distribution. Kappa distributions were introduced as an empirical fitting function that well describe the nonequilibrium features of the distribution functions of electrons and ions in space science as measured by satellite instruments. The calculation of the Kappa distribution from the Fokker-Planck equations provides a direct physically based dynamical approach in contrast to the nonextensive entropy formalism by Tsallis [J. Stat. Phys. 53, 479 (1988), 10.1007/BF01016429].
Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

PubMed

Kanagawa, Tetsuya

2015-05-01

This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.
Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

NASA Astrophysics Data System (ADS)

Park, Brian T.; Petrosian, Vahe

1996-03-01

Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.
Kinetic Models for Topological Nearest-Neighbor Interactions

NASA Astrophysics Data System (ADS)

Blanchet, Adrien; Degond, Pierre

2017-12-01

We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal and human behavior. Precisely, the system consists of a finite number of particles characterized by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of its closest neighbor, the leader. We study the limit of a system size going to infinity and, under the assumption of propagation of chaos, show that the limit kinetic equation is a non-standard spatial diffusion equation for the particle distribution function. We also study the case wherein the particles interact with their K closest neighbors and show that the corresponding kinetic equation is the same. Finally, we prove that these models can be seen as a singular limit of the smooth rank-based model previously studied in Blanchet and Degond (J Stat Phys 163:41-60, 2016). The proofs are based on a combinatorial interpretation of the rank as well as some concentration of measure arguments.
Three kinds of particles on a single rationally parameterized world line

NASA Astrophysics Data System (ADS)

Kassandrov, V. V.; Markova, N. V.

2016-10-01

We consider the light cone (`retardation') equation (LCE) of an inertially moving observer and a single worldline parameterized by arbitrary rational functions. Then a set of apparent copies, R- or C-particles, defined by the (real or complex conjugate) roots of the LCE will be detected by the observer. For any rational worldline the collective R-C dynamics is manifestly Lorentz-invariant and conservative; the latter property follows directly from the structure of Vieta formulas for the LCE roots. In particular, two Lorentz invariants, the square of total 4-momentum and total rest mass, are distinct and both integer-valued. Asymptotically, at large values of the observer's proper time, one distinguishes three types of the LCE roots and associated R-C particles, with specific locations and evolutions; each of three kinds of particles can assemble into compact large groups - clusters. Throughout the paper, we make no use of differential equations of motion, field equations, etc.: the collective R-C dynamics is purely algebraic
On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion

NASA Astrophysics Data System (ADS)

Lim, Soon Hoe; Wehr, Jan; Lampo, Aniello; García-March, Miguel Ángel; Lewenstein, Maciej

2018-01-01

We study the small mass limit (or: the Smoluchowski-Kramers limit) of a class of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic bath spectral density with a Lorentz-Drude cutoff, we derive the Heisenberg-Langevin equations for the particle's observables using a quantum stochastic calculus approach. We set the mass of the particle to equal m = m0 ɛ , the reduced Planck constant to equal \\hbar = ɛ and the cutoff frequency to equal Λ = E_{Λ}/ɛ , where m_0 and E_{Λ} are positive constants, so that the particle's de Broglie wavelength and the largest energy scale of the bath are fixed as ɛ → 0. We study the limit as ɛ → 0 of the rescaled model and derive a limiting equation for the (slow) particle's position variable. We find that the limiting equation contains several drift correction terms, the quantum noise-induced drifts, including terms of purely quantum nature, with no classical counterparts.
Basic governing equations for the flight regimes of aeroassisted orbital transfer vehicles

NASA Technical Reports Server (NTRS)

Lee, J.-H.

1984-01-01

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are given explicitly. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, is derived by solving the system of master equations accounting for the multiple-level transitions.
Basic Governing Equations for the Flight Regimes of Aeroassisted Orbital Transfer Vehicles

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1985-01-01

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are explicitly given. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, are derived by solving the system of master equations accounting for the multiple-level transitions.
Vertical distribution of aerosol number concentration in the troposphere over Siberia derived from airborne in-situ measurements

NASA Astrophysics Data System (ADS)

Arshinov, Mikhail Yu.; Belan, Boris D.; Paris, Jean-Daniel; Machida, Toshinobu; Kozlov, Alexandr; Malyskin, Sergei; Simonenkov, Denis; Davydov, Denis; Fofonov, Alexandr

2016-04-01

Knowledge of the vertical distribution of aerosols particles is very important when estimating aerosol radiative effects. To date there are a lot of research programs aimed to study aerosol vertical distribution, but only a few ones exist in such insufficiently explored region as Siberia. Monthly research flights and several extensive airborne campaigns carried out in recent years in Siberian troposphere allowed the vertical distribution of aerosol number concentration to be summarized. In-situ aerosol measurements were performed in a wide range of particle sizes by means of improved version of the Novosibirsk-type diffusional particle sizer and GRIMM aerosol spectrometer Model 1.109. The data on aerosol vertical distribution enabled input parameters for the empirical equation of Jaenicke (1993) to be derived for Siberian troposphere up to 7 km. Vertical distributions of aerosol number concentration in different size ranges averaged for the main seasons of the year will be presented. This work was supported by Interdisciplinary integration projects of the Siberian Branch of the Russian Academy of Science No. 35, No. 70 and No. 131; the Branch of Geology, Geophysics and Mining Sciences of RAS (Program No. 5); and Russian Foundation for Basic Research (grant No. 14-05-00526). Jaenicke R. Tropospheric aerosols, in Aerosol-Cloud-Climate Interactions, edited by P.V. Hobs. -Academic Press, San Diego, CA, 1993.- P. 1-31.
DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems

NASA Astrophysics Data System (ADS)

Braun, Jean; Thieulot, Cédric; Fullsack, Philippe; DeKool, Marthijn; Beaumont, Christopher; Huismans, Ritske

2008-12-01

We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1- p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly irregular octree discretization and the tri-linear (or q1- p0) finite element. A three-dimensional cloud of particles is used to track material properties that depend on the integrated history of deformation (the integrated strain, for example); its density is variable and dynamically adapted to the computed flow. The large system of algebraic equations that results from the finite element discretization and linearization of the basic partial differential equations is solved using a multi-frontal massively parallel direct solver that can efficiently factorize poorly conditioned systems resulting from the highly non-linear rheology and the presence of the free surface. The code is almost entirely parallelized. We present example results including the onset of a Rayleigh-Taylor instability, the indentation of a rigid-plastic material and the formation of a fold beneath a free eroding surface, that demonstrate the accuracy, efficiency and appropriateness of the new code to solve complex geodynamical problems in three dimensions.
Lagrangian dynamics for classical, Brownian, and quantum mechanical particles

NASA Astrophysics Data System (ADS)

Pavon, Michele

1996-07-01

In the framework of Nelson's stochastic mechanics [E. Nelson, Dynamical Theories of Brownian Motion (Princeton University, Princeton, 1967); F. Guerra, Phys. Rep. 77, 263 (1981); E. Nelson, Quantum Fluctuations (Princeton University, Princeton, 1985)] we seek to develop the particle counterpart of the hydrodynamic results of M. Pavon [J. Math. Phys. 36, 6774 (1995); Phys. Lett. A 209, 143 (1995)]. In particular, a first form of Hamilton's principle is established. We show that this variational principle leads to the correct equations of motion for the classical particle, the Brownian particle in thermodynamical equilibrium, and the quantum particle. In the latter case, the critical process q satisfies a stochastic Newton law. We then introduce the momentum process p, and show that the pair (q,p) satisfies canonical-like equations.
Dispersive approaches for three-particle final state interaction

DOE PAGES

Guo, Peng; Danilkin, Igor V.; Szczepaniak, Adam P.

2015-10-30

In this work, we presented different representations of Khuri-Treiman equation, the advantage and disadvantage of each representations are discussed. With a scattering amplitude toy model, we also studied the sensitivity of solution of KT equation to left-hand cut of toy model and to the different approximate methods. At last, we give a brief discussion of Watson's theorem when three particles in final states are involved.
The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-09-01

We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.
A new class of exact solutions of the Klein-Gordon equation of a charged particle interacting with an electromagnetic plane wave in a medium

NASA Astrophysics Data System (ADS)

Varró, Sándor

2014-01-01

Exact solutions are presented of the Klein-Gordon equation of a charged particle moving in a transverse monochromatic plasmon wave of arbitrary high amplitude, which propagates in an underdense plasma. These solutions are expressed in terms of Ince polynomials, forming a doubly infinite set, parametrized by discrete momentum components of the charged particle’s de Broglie wave along the polarization vector and along the propagation direction of the plasmon radiation. The envelope of the exact wavefunctions describes a high-contrast periodic structure of the particle density on the plasma length scale, which may have relevance in novel particle acceleration mechanisms.
Non-Existence of Black Hole Solutionsfor a Spherically Symmetric, Static Einstein-Dirac-Maxwell System

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.
Multistep integration formulas for the numerical integration of the satellite problem

NASA Technical Reports Server (NTRS)

Lundberg, J. B.; Tapley, B. D.

1981-01-01

The use of two Class 2/fixed mesh/fixed order/multistep integration packages of the PECE type for the numerical integration of the second order, nonlinear, ordinary differential equation of the satellite orbit problem. These two methods are referred to as the general and the second sum formulations. The derivation of the basic equations which characterize each formulation and the role of the basic equations in the PECE algorithm are discussed. Possible starting procedures are examined which may be used to supply the initial set of values required by the fixed mesh/multistep integrators. The results of the general and second sum integrators are compared to the results of various fixed step and variable step integrators.
Normalization and extension of single-collector efficiency correlation equation

NASA Astrophysics Data System (ADS)

Messina, Francesca; Marchisio, Daniele; Sethi, Rajandrea

2015-04-01

The colloidal transport and deposition are important phenomena involved in many engineering problems. In the environmental engineering field the use of micro- and nano-scale zerovalent iron (M-NZVI) is one of the most promising technologies for groundwater remediation. Colloid deposition is normally studied from a micro scale point of view and the results are then implemented in macro scale models that are used to design field-scale applications. The single collector efficiency concept predicts particles deposition onto a single grain of a complex porous medium in terms of probability that an approaching particle would be retained on the solid grain. In literature, many different approaches and equations exist to predict it, but most of them fail under specific conditions (e.g. very small or very big particle size and very low fluid velocity) because they predict efficiency values exceeding unity. By analysing particle fluxes and deposition mechanisms and performing a mass balance on the entire domain, the traditional definition of efficiency was reformulated and a novel total flux normalized correlation equation is proposed for predicting single-collector efficiency under a broad range of parameters. It has been formulated starting from a combination of Eulerian and Lagrangian numerical simulations, performed under Smoluchowski-Levich conditions, in a geometry which consists of a sphere enveloped by a control volume. In order to guarantee the independence of each term, the correlation equation is derived through a rigorous hierarchical parameter estimation process, accounting for single and mutual interacting transport mechanisms. The correlation equation provides efficiency values lower than one over a wide range of parameters and is valid both for point and finite-size particles. A reduced form is also proposed by elimination of the less relevant terms. References 1. Yao, K. M.; Habibian, M. M.; Omelia, C. R., Water and Waste Water Filtration - Concepts and Applications. Environ Sci Technol 1971, 5, (11), 1105-&. 2. Tufenkji, N., and M. Elimelech, Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Environmental Science & Technology 2004 38(2):529-536. 3. Boccardo, G.; Marchisio, D. L.; Sethi, R., Microscale simulation of particle deposition in porous media. J Colloid Interface Sci 2014, 417, 227-37
Kinetic and dynamic probability-density-function descriptions of disperse turbulent two-phase flows

NASA Astrophysics Data System (ADS)

Minier, Jean-Pierre; Profeta, Christophe

2015-11-01

This article analyzes the status of two classical one-particle probability density function (PDF) descriptions of the dynamics of discrete particles dispersed in turbulent flows. The first PDF formulation considers only the process made up by particle position and velocity Zp=(xp,Up) and is represented by its PDF p (t ;yp,Vp) which is the solution of a kinetic PDF equation obtained through a flux closure based on the Furutsu-Novikov theorem. The second PDF formulation includes fluid variables into the particle state vector, for example, the fluid velocity seen by particles Zp=(xp,Up,Us) , and, consequently, handles an extended PDF p (t ;yp,Vp,Vs) which is the solution of a dynamic PDF equation. For high-Reynolds-number fluid flows, a typical formulation of the latter category relies on a Langevin model for the trajectories of the fluid seen or, conversely, on a Fokker-Planck equation for the extended PDF. In the present work, a new derivation of the kinetic PDF equation is worked out and new physical expressions of the dispersion tensors entering the kinetic PDF equation are obtained by starting from the extended PDF and integrating over the fluid seen. This demonstrates that, under the same assumption of a Gaussian colored noise and irrespective of the specific stochastic model chosen for the fluid seen, the kinetic PDF description is the marginal of a dynamic PDF one. However, a detailed analysis reveals that kinetic PDF models of particle dynamics in turbulent flows described by statistical correlations constitute incomplete stand-alone PDF descriptions and, moreover, that present kinetic-PDF equations are mathematically ill posed. This is shown to be the consequence of the non-Markovian characteristic of the stochastic process retained to describe the system and the use of an external colored noise. Furthermore, developments bring out that well-posed PDF descriptions are essentially due to a proper choice of the variables selected to describe physical systems and guidelines are formulated to emphasize the key role played by the notion of slow and fast variables.

Coincidence degree and periodic solutions of neutral equations

NASA Technical Reports Server (NTRS)

Hale, J. K.; Mawhin, J.

1973-01-01

The problem of existence of periodic solutions for some nonautonomous neutral functional differential equations is examined. It is an application of a basic theorem on the Fredholm alternative for periodic solutions of some linear neutral equations and of a generalized Leray-Schauder theory. Although proofs are simple, the results are nontrivial extensions to the neutral case of existence theorems for periodic solutions of functional differential equations.
Space-Plane Spreadsheet Program

NASA Technical Reports Server (NTRS)

Mackall, Dale

1993-01-01

Basic Hypersonic Data and Equations (HYPERDATA) spreadsheet computer program provides data gained from three analyses of performance of space plane. Equations used to perform analyses derived from Newton's second law of physics, derivation included. First analysis is parametric study of some basic factors affecting ability of space plane to reach orbit. Second includes calculation of thickness of spherical fuel tank. Third produces ratio between volume of fuel and total mass for each of various aircraft. HYPERDATA intended for use on Macintosh(R) series computers running Microsoft Excel 3.0.
A Theory of Preference Reversals.

DTIC Science & Technology

1984-08-01

the subject mst find sme way to transform-the basic evaluation, uCG ), into a monetary amonnt. we hypothesize that subjects do : this by a process of...the basic equations as follows; MS() = (1 - ()w 7) where, A -[C)- uCG )I/uCW)C) .. Furthermore, we can solve for ulC) by using equation (8); thus, u (a...monetary value of gambles by a method which avoids references to market -type behavior. Grether and Plott asked subjects to give Othe exact dollar
Modeling Particle Acceleration and Transport at a 2-D CME-Driven Shock

NASA Astrophysics Data System (ADS)

Hu, Junxiang; Li, Gang; Ao, Xianzhi; Zank, Gary P.; Verkhoglyadova, Olga

2017-11-01

We extend our earlier Particle Acceleration and Transport in the Heliosphere (PATH) model to study particle acceleration and transport at a coronal mass ejection (CME)-driven shock. We model the propagation of a CME-driven shock in the ecliptic plane using the ZEUS-3D code from 20 solar radii to 2 AU. As in the previous PATH model, the initiation of the CME-driven shock is simplified and modeled as a disturbance at the inner boundary. Different from the earlier PATH model, the disturbance is now longitudinally dependent. Particles are accelerated at the 2-D shock via the diffusive shock acceleration mechanism. The acceleration depends on both the parallel and perpendicular diffusion coefficients κ|| and κ⊥ and is therefore shock-obliquity dependent. Following the procedure used in Li, Shalchi, et al. (k href="#jgra53857-bib-0045"/>), we obtain the particle injection energy, the maximum energy, and the accelerated particle spectra at the shock front. Once accelerated, particles diffuse and convect in the shock complex. The diffusion and convection of these particles are treated using a refined 2-D shell model in an approach similar to Zank et al. (k href="#jgra53857-bib-0089"/>). When particles escape from the shock, they propagate along and across the interplanetary magnetic field. The propagation is modeled using a focused transport equation with the addition of perpendicular diffusion. We solve the transport equation using a backward stochastic differential equation method where adiabatic cooling, focusing, pitch angle scattering, and cross-field diffusion effects are all included. Time intensity profiles and instantaneous particle spectra as well as particle pitch angle distributions are shown for two example CME shocks.
Thermodynamic framework for compact q-Gaussian distributions

NASA Astrophysics Data System (ADS)

Souza, Andre M. C.; Andrade, Roberto F. S.; Nobre, Fernando D.; Curado, Evaldo M. F.

2018-02-01

Recent works have associated systems of particles, characterized by short-range repulsive interactions and evolving under overdamped motion, to a nonlinear Fokker-Planck equation within the class of nonextensive statistical mechanics, with a nonlinear diffusion contribution whose exponent is given by ν = 2 - q. The particular case ν = 2 applies to interacting vortices in type-II superconductors, whereas ν > 2 covers systems of particles characterized by short-range power-law interactions, where correlations among particles are taken into account. In the former case, several studies presented a consistent thermodynamic framework based on the definition of an effective temperature θ (presenting experimental values much higher than typical room temperatures T, so that thermal noise could be neglected), conjugated to a generalized entropy sν (with ν = 2). Herein, the whole thermodynamic scheme is revisited and extended to systems of particles interacting repulsively, through short-ranged potentials, described by an entropy sν, with ν > 1, covering the ν = 2 (vortices in type-II superconductors) and ν > 2 (short-range power-law interactions) physical examples. One basic requirement concerns a cutoff in the equilibrium distribution Peq(x) , approached due to a confining external harmonic potential, ϕ(x) = αx2 / 2 (α > 0). The main results achieved are: (a) The definition of an effective temperature θ conjugated to the entropy sν; (b) The construction of a Carnot cycle, whose efficiency is shown to be η = 1 -(θ2 /θ1) , where θ1 and θ2 are the effective temperatures associated with two isothermal transformations, with θ1 >θ2; (c) Thermodynamic potentials, Maxwell relations, and response functions. The present thermodynamic framework, for a system of interacting particles under the above-mentioned conditions, and associated to an entropy sν, with ν > 1, certainly enlarges the possibility of experimental verifications.
THE EFFECT OF DIFFUSION ON THE PARTICLE SPECTRA IN PULSAR WIND NEBULAE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vorster, M. J.; Moraal, H., E-mail: 12792322@nwu.ac.za

2013-03-01

A possible way to calculate particle spectra as a function of position in pulsar wind nebulae is to solve a Fokker-Planck transport equation. This paper presents numerical solutions to the transport equation with the processes of convection, diffusion, adiabatic losses, and synchrotron radiation included. In the first part of the paper, the steady-state version of the transport equation is solved as a function of position and energy. This is done to distinguish the various effects of the aforementioned processes on the solutions to the transport equation. The second part of the paper deals with a time-dependent solution to the transportmore » equation, specifically taking into account the effect of a moving outer boundary. The paper highlights the fact that diffusion can play a significant role in reducing the amount of synchrotron losses, leading to a modification in the expected particle spectra. These modified spectra can explain the change in the photon index of the synchrotron emission as a function of position. The solutions presented in this paper are not limited to pulsar wind nebulae, but can be applied to any similar central source system, e.g., globular clusters.« less
Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.
Decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio.

PubMed

Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

2016-10-01

A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.
Maximum Likelihood Analysis of Nonlinear Structural Equation Models with Dichotomous Variables

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lee, Sik-Yum

2005-01-01

In this article, a maximum likelihood approach is developed to analyze structural equation models with dichotomous variables that are common in behavioral, psychological and social research. To assess nonlinear causal effects among the latent variables, the structural equation in the model is defined by a nonlinear function. The basic idea of the…
Electrophoresis of a polarizable charged colloid with hydrophobic surface: A numerical study

NASA Astrophysics Data System (ADS)

Bhattacharyya, Somnath; Majee, Partha Sarathi

2017-04-01

We consider the electrophoresis of a charged colloid for a generalized situation in which the particle is considered to be polarizable and the surface exhibits hydrophobicity. The dielectric polarization of the particle creates a nonlinear dependence of the electrophoretic velocity on the applied electric field, and the core hydrophobicity amplifies the fluid convection in the Debye layer. Thus, a linear analysis is no longer applicable for this situation. The present analysis is based on the numerical solution of the nonlinear electrokinetic equations based on the Navier-Stokes-Nernst-Planck-Poisson equations coupled with the Laplace equation for the electric field within the dielectric particle. The hydrophobicity of the particle may influence its electric polarization by enhancing the convective transport of ions. The nonlinear effects, such as double-layer polarization and relaxation, are also influenced by the hydrophobicity of the particle surface. The present results compare well for a lower range of the applied electric field and surface charge density with the existing results for a perfectly dielectric particle with a hydrophobic surface based on the first-order perturbation analysis due to Khair and Squires [Phys. Fluids 21, 042001 (2009), 10.1063/1.3116664]. Dielectric polarization creates a reduction in particle electrophoretic velocity, and its impact is strong for a moderate range of Debye length. A quantitative measure of the nonlinear effects is demonstrated by comparing the electrophoretic velocity with an existing linear model.
Saturn Rings Origin: Quantum Trapping of Superconducting Iced Particles and Meissner Effect Lead to the Stable Rings System

NASA Astrophysics Data System (ADS)

Viktorovich Tchernyi, Vladimir

2018-06-01

Saturn Rings Origin: Quantum Trapping of Superconducting Iced Particles and Meissner Effect Lead to the Stable Rings System Vladimir V. Tchernyi (Cherny), Andrew Yu. Pospelov Modern Science Institute, SAIBR, Moscow, Russia. E-mail: chernyv@bk.ruAbstractIt is demonstrated how superconducting iced particles of the protoplanetary cloud of Saturn are coming to magnetic equator plane and create the stable enough rings disk. There are two steps. First, after appearance of the Saturn magnetic field due to Meissner phenomenon all particles orbits are moving to the magnetic equator plane. Finally they become distributed as rings and gaps like iron particles around magnet on laboratory table. And they are separated from each other by the magnetic field expelled from them. It takes up to few tens of thousands years with ten meters rings disk thickness. Second, due to their quantum trapping all particles become to be trapped within magnetic well at the magnetic equator plane due to Abrikosov vortex for superconductor. It works even when particles have small fraction of superconductor. During the rings evolution some contribution to the disk also could come from the collision-generated debris of the current moon and from the geysers like it happened due to magnetic coupling of Saturn and Enceladus. The rings are relict of the early days of the magnetic field of Saturn system.
Analytical solutions for the motion of a charged particle in electric and magnetic fields via non-singular fractional derivatives

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Taneco-Hernandez, M. A.

2017-12-01

In this work we propose fractional differential equations for the motion of a charged particle in electric, magnetic and electromagnetic fields. Exact solutions are obtained for the fractional differential equations by employing the Laplace transform method. The temporal fractional differential equations are considered in the Caputo-Fabrizio-Caputo and Atangana-Baleanu-Caputo sense. Application examples consider constant, ramp and harmonic fields. In addition, we present numerical results for different values of the fractional order. In all cases, when α = 1, we recover the standard electrodynamics.
Limitations on the applicability of FODO lattices for electron cooling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertsche, K.J.

1997-09-01

Assuming a KV beam distribution (a uniform distribution over an elliptical region of transverse phase space), the beam envelop equations are shown, where X and Y are the transverse beam sizes, {kappa} is the lens strength, K is the generalized beam perveance, and {epsilon} is the beam emittance. If we further assume operation in a space-charge dominated regime, the right most term can be ignored in each equation. In this case, particle flow will be laminar, and the above equations not only describe the envelope of the beam, but also the trajectory of the outermost particles.
Pressure oscillations and instability of working processes in the combustion chambers of solid rocket motors

NASA Astrophysics Data System (ADS)

Emelyanov, V. N.; Teterina, I. V.; Volkov, K. N.; Garkushev, A. U.

2017-06-01

Metal particles are widely used in space engineering to increase specific impulse and to supress acoustic instability of intra-champber processes. A numerical analysis of the internal injection-driven turbulent gas-particle flows is performed to improve the current understanding and modeling capabilities of the complex flow characteristics in the combustion chambers of solid rocket motors (SRMs) in presence of forced pressure oscillations. The two-phase flow is simulated with a combined Eulerian-Lagrangian approach. The Reynolds-averaged Navier-Stokes equations and transport equations of k - ε model are solved numerically for the gas. The particulate phase is simulated through a Lagrangian deterministic and stochastic tracking models to provide particle trajectories and particle concentration. The results obtained highlight the crucial significance of the particle dispersion in turbulent flowfield and high potential of statistical methods. Strong coupling between acoustic oscillations, vortical motion, turbulent fluctuations and particle dynamics is observed.
Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

PubMed

Shotorban, Babak

2010-04-01

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.
Clearing the waters: Evaluating the need for site-specific field fluorescence corrections based on turbidity measurements

USGS Publications Warehouse

Saraceno, John F.; Shanley, James B.; Downing, Bryan D.; Pellerin, Brian A.

2017-01-01

In situ fluorescent dissolved organic matter (fDOM) measurements have gained increasing popularity as a proxy for dissolved organic carbon (DOC) concentrations in streams. One challenge to accurate fDOM measurements in many streams is light attenuation due to suspended particles. Downing et al. (2012) evaluated the need for corrections to compensate for particle interference on fDOM measurements using a single sediment standard in a laboratory study. The application of those results to a large river improved unfiltered field fDOM accuracy. We tested the same correction equation in a headwater tropical stream and found that it overcompensated fDOM when turbidity exceeded ∼300 formazin nephelometric units (FNU). Therefore, we developed a site-specific, field-based fDOM correction equation through paired in situ fDOM measurements of filtered and unfiltered streamwater. The site-specific correction increased fDOM accuracy up to a turbidity as high as 700 FNU, the maximum observed in this study. The difference in performance between the laboratory-based correction equation of Downing et al. (2012) and our site-specific, field-based correction equation likely arises from differences in particle size distribution between the sediment standard used in the lab (silt) and that observed in our study (fine to medium sand), particularly during high flows. Therefore, a particle interference correction equation based on a single sediment type may not be ideal when field sediment size is significantly different. Given that field fDOM corrections for particle interference under turbid conditions are a critical component in generating accurate DOC estimates, we describe a way to develop site-specific corrections.
Enhanced Particle Swarm Optimization Algorithm: Efficient Training of ReaxFF Reactive Force Fields.

PubMed

Furman, David; Carmeli, Benny; Zeiri, Yehuda; Kosloff, Ronnie

2018-06-12

Particle swarm optimization (PSO) is a powerful metaheuristic population-based global optimization algorithm. However, when it is applied to nonseparable objective functions, its performance on multimodal landscapes is significantly degraded. Here we show that a significant improvement in the search quality and efficiency on multimodal functions can be achieved by enhancing the basic rotation-invariant PSO algorithm with isotropic Gaussian mutation operators. The new algorithm demonstrates superior performance across several nonlinear, multimodal benchmark functions compared with the rotation-invariant PSO algorithm and the well-established simulated annealing and sequential one-parameter parabolic interpolation methods. A search for the optimal set of parameters for the dispersion interaction model in the ReaxFF- lg reactive force field was carried out with respect to accurate DFT-TS calculations. The resulting optimized force field accurately describes the equations of state of several high-energy molecular crystals where such interactions are of crucial importance. The improved algorithm also presents better performance compared to a genetic algorithm optimization method in the optimization of the parameters of a ReaxFF- lg correction model. The computational framework is implemented in a stand-alone C++ code that allows the straightforward development of ReaxFF reactive force fields.
Multiscale modeling of a rectifying bipolar nanopore: Comparing Poisson-Nernst-Planck to Monte Carlo

NASA Astrophysics Data System (ADS)

Matejczyk, Bartłomiej; Valiskó, Mónika; Wolfram, Marie-Therese; Pietschmann, Jan-Frederik; Boda, Dezső

2017-03-01

In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the Nernst-Planck (NP) equation to compute ion transport in the framework of the implicit-water electrolyte model. The difference is that the Poisson-Boltzmann theory is used in the Poisson-Nernst-Planck (PNP) approach, while the Local Equilibrium Monte Carlo (LEMC) method is used in the particle simulation approach (NP+LEMC) to relate the concentration profile to the electrochemical potential profile. Since we consider a bipolar pore which is short and narrow, we perform simulations using two-dimensional PNP. In addition, results of a non-linear version of PNP that takes crowding of ions into account are shown. We observe that the mean field approximation applied in PNP is appropriate to reproduce the basic behavior of the bipolar nanopore (e.g., rectification) for varying parameters of the system (voltage, surface charge, electrolyte concentration, and pore radius). We present current data that characterize the nanopore's behavior as a device, as well as concentration, electrical potential, and electrochemical potential profiles.
Multiscale modeling of a rectifying bipolar nanopore: Comparing Poisson-Nernst-Planck to Monte Carlo.

PubMed

Matejczyk, Bartłomiej; Valiskó, Mónika; Wolfram, Marie-Therese; Pietschmann, Jan-Frederik; Boda, Dezső

2017-03-28

In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the Nernst-Planck (NP) equation to compute ion transport in the framework of the implicit-water electrolytemodel. The difference is that the Poisson-Boltzmann theory is used in the Poisson-Nernst-Planck (PNP) approach, while the Local Equilibrium Monte Carlo (LEMC) method is used in the particle simulation approach (NP+LEMC) to relate the concentration profile to the electrochemical potential profile. Since we consider a bipolar pore which is short and narrow, we perform simulations using two-dimensional PNP. In addition, results of a non-linear version of PNP that takes crowding of ions into account are shown. We observe that the mean field approximation applied in PNP is appropriate to reproduce the basic behavior of the bipolar nanopore (e.g., rectification) for varying parameters of the system (voltage, surface charge,electrolyte concentration, and pore radius). We present current data that characterize the nanopore's behavior as a device, as well as concentration, electrical potential, and electrochemical potential profiles.
Modeling of single film bubble and numerical study of the plateau structure in foam system

NASA Astrophysics Data System (ADS)

Sun, Zhong-guo; Ni, Ni; Sun, Yi-jie; Xi, Guang

2018-02-01

The single-film bubble has a special geometry with a certain amount of gas shrouded by a thin layer of liquid film under the surface tension force both on the inside and outside surfaces of the bubble. Based on the mesh-less moving particle semi-implicit (MPS) method, a single-film double-gas-liquid-interface surface tension (SDST) model is established for the single-film bubble, which characteristically has totally two gas-liquid interfaces on both sides of the film. Within this framework, the conventional surface free energy surface tension model is improved by using a higher order potential energy equation between particles, and the modification results in higher accuracy and better symmetry properties. The complex interface movement in the oscillation process of the single-film bubble is numerically captured, as well as typical flow phenomena and deformation characteristics of the liquid film. In addition, the basic behaviors of the coalescence and connection process between two and even three single-film bubbles are studied, and the cases with bubbles of different sizes are also included. Furthermore, the classic plateau structure in the foam system is reproduced and numerically proved to be in the steady state for multi-bubble connections.

SPH modeling and simulation of spherical particles interacting in a viscoelastic matrix

NASA Astrophysics Data System (ADS)

Vázquez-Quesada, A.; Ellero, M.

2017-12-01

In this work, we extend the three-dimensional Smoothed Particle Hydrodynamics (SPH) non-colloidal particulate model previously developed for Newtonian suspending media in Vázquez-Quesada and Ellero ["Rheology and microstructure of non-colloidal suspensions under shear studied with smoothed particle hydrodynamics," J. Non-Newtonian Fluid Mech. 233, 37-47 (2016)] to viscoelastic matrices. For the solvent medium, the coarse-grained SPH viscoelastic formulation proposed in Vázquez-Quesada, Ellero, and Español ["Smoothed particle hydrodynamic model for viscoelastic fluids with thermal fluctuations," Phys. Rev. E 79, 056707 (2009)] is adopted. The property of this particular set of equations is that they are entirely derived within the general equation for non-equilibrium reversible-irreversible coupling formalism and therefore enjoy automatically thermodynamic consistency. The viscoelastic model is derived through a physical specification of a conformation-tensor-dependent entropy function for the fluid particles. In the simple case of suspended Hookean dumbbells, this delivers a specific SPH discretization of the Oldroyd-B constitutive equation. We validate the suspended particle model by studying the dynamics of single and mutually interacting "noncolloidal" rigid spheres under shear flow and in the presence of confinement. Numerical results agree well with available numerical and experimental data. It is straightforward to extend the particulate model to Brownian conditions and to more complex viscoelastic solvents.
Electromagnetic scattering and emission by a fixed multi-particle object in local thermal equilibrium: General formalism.

PubMed

Mishchenko, Michael I

2017-10-01

The majority of previous studies of the interaction of individual particles and multi-particle groups with electromagnetic field have focused on either elastic scattering in the presence of an external field or self-emission of electromagnetic radiation. In this paper we apply semi-classical fluctuational electrodynamics to address the ubiquitous scenario wherein a fixed particle or a fixed multi-particle group is exposed to an external quasi-polychromatic electromagnetic field as well as thermally emits its own electromagnetic radiation. We summarize the main relevant axioms of fluctuational electrodynamics, formulate in maximally rigorous mathematical terms the general scattering-emission problem for a fixed object, and derive such fundamental corollaries as the scattering-emission volume integral equation, the Lippmann-Schwinger equation for the dyadic transition operator, the multi-particle scattering-emission equations, and the far-field limit. We show that in the framework of fluctuational electrodynamics, the computation of the self-emitted component of the total field is completely separated from that of the elastically scattered field. The same is true of the computation of the emitted and elastically scattered components of quadratic/bilinear forms in the total electromagnetic field. These results pave the way to the practical computation of relevant optical observables.
Effects of High-energy Particles on Accretion Flows onto a Supermassive Black Hole

NASA Astrophysics Data System (ADS)

Kimura, Shigeo S.; Toma, Kenji; Takahara, Fumio

2014-08-01

We study the effects of high-energy particles (HEPs) on the accretion flows onto a supermassive black hole and luminosities of escaping particles such as protons, neutrons, gamma rays, and neutrinos. We formulate a one-dimensional model of the two-component accretion flow consisting of thermal particles and HEPs, supposing that some fraction of the released energy is converted to the acceleration of HEPs. The thermal component is governed by fluid dynamics while the HEPs obey the moment equations of the diffusion-convection equation. By solving the time evolution of these equations, we obtain advection-dominated flows as the steady state solutions. The effects of the HEPs on the flow structures turn out to be small even if the pressure of the HEPs dominates over the thermal pressure. For a model in which the escaping protons take away almost all the energy released, the HEPs have a large enough influence to make the flow have a Keplerian angular velocity at the inner region. We calculate the luminosities of the escaping particles for these steady solutions. The escaping particles can extract the energy from about 10^{-4}\\dot{M} c^2 to 10^{-2}\\dot{M} c^2, where \\dot{M} is the mass accretion rate. The luminosities of the escaping particles depend on parameters such as the injection Lorentz factors, the mass accretion rates, and the diffusion coefficients. We also discuss some implications on the relativistic jet production by the escaping particles.
Suspension concentration distribution in turbulent flows: An analytical study using fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Kundu, Snehasis

2018-09-01

In this study vertical distribution of sediment particles in steady uniform turbulent open channel flow over erodible bed is investigated using fractional advection-diffusion equation (fADE). Unlike previous investigations on fADE to investigate the suspension distribution, in this study the modified Atangana-Baleanu-Caputo fractional derivative with a non-singular and non-local kernel is employed. The proposed fADE is solved and an analytical model for finding vertical suspension distribution is obtained. The model is validated against experimental as well as field measurements of Missouri River, Mississippi River and Rio Grande conveyance channel and is compared with the Rouse equation and other fractional model found in literature. A quantitative error analysis shows that the proposed model is able to predict the vertical distribution of particles more appropriately than previous models. The validation results shows that the fractional model can be equally applied to all size of particles with an appropriate choice of the order of the fractional derivative α. It is also found that besides particle diameter, parameter α depends on the mass density of particle and shear velocity of the flow. To predict this parameter, a multivariate regression is carried out and a relation is proposed for easy application of the model. From the results for sand and plastic particles, it is found that the parameter α is more sensitive to mass density than the particle diameter. The rationality of the dependence of α on particle and flow characteristics has been justified physically.
Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

NASA Technical Reports Server (NTRS)

Webb, G. M.; Jokipii, J. R.; Morfill, G. E.

1994-01-01

Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of aziuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega(sub 0)(omega(sub 0)/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from monoenergetic and truncated power-law sources. We conclude that it is possible to accelerate particles beyond the knee by galactic rotation, but not in sufficient number to adequately explain the observed spectrum.
Kinetic equation and nonequilibrium entropy for a quasi-two-dimensional gas.

PubMed

Brey, J Javier; Maynar, Pablo; García de Soria, M I

2016-10-01

A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle diameters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement on the particle collisions. A function S(t) is constructed by adding to the Boltzmann expression a confinement contribution. Then it is shown that for the solutions of the kinetic equation, S(t) increases monotonically in time, until the system reaches a stationary inhomogeneous state, when S becomes the equilibrium entropy of the confined system as derived from equilibrium statistical mechanics. From the entropy, other equilibrium properties are obtained, and molecular dynamics simulations are used to verify some of the theoretical predictions.
A Kinetic-MHD Theory for the Self-Consistent Energy Exchange Between Energetic Particles and Active Small-scale Flux Ropes

NASA Astrophysics Data System (ADS)

le Roux, J. A.

2017-12-01

We developed previously a focused transport kinetic theory formalism with Fokker-plank coefficients (and its Parker transport limit) to model large-scale energetic particle transport and acceleration in solar wind regions with multiple contracting and merging small-scale flux ropes on MHD (inertial) scales (Zank et al. 2014; le Roux et al. 2015). The theory unifies the main acceleration mechanisms identified in particle simulations for particles temporarily trapped in such active flux rope structures, such as acceleration by the parallel electric field in reconnection regions between merging flux ropes, curvature drift acceleration in incompressible/compressible contracting and merging flux ropes, and betatron acceleration (e.g., Dahlin et al 2016). Initial analytical solutions of the Parker transport equation in the test particle limit showed that the energetic particle pressure from efficient flux-rope energization can potentially be high in turbulent solar wind regions containing active flux-rope structures. This requires taking into account the back reaction of energetic particles on flux ropes to more accurately determine the efficiency of energetic particles acceleration by small-scale flux ropes. To accomplish this goal we developed recently an extension of the kinetic theory to a kinetic-MHD level. We will present the extended theory showing the focused transport equation to be coupled to a solar wind MHD transport equation for small-scale flux-rope energy density extracted from a recently published nearly incompressible theory for solar wind MHD turbulence with a plasma beta of 1 (Zank et al. 2017). In the flux-rope transport equation appears new expressions for the damping/growth rates of flux-rope energy derived from assuming energy conservation in the interaction between energetic particles and small-scale flux ropes for all the main flux-rope acceleration mechanisms, whereas previous expressions for average particle acceleration rates have been explored in more detail. Future applications will involve exploring the relative role of diffusive shock and flux-ropes acceleration in the vicinity of traveling shocks in the supersonic solar wind near Earth where many flux-rope structures were detected recently (Hu et al 2017, this session).
Geodesics In A Spinning String Spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Culetu, Hristu

2006-11-28

The geodesics equations for a rotating observer in a spinning string geometry are investigated using the Euler - Lagrange equations. For test particles with vanishing angular momentum, the radial equation of motion does not depend on the angular velocity {omega} but on the angular momentum of the string. A massless particle moves tachyonic but iteed tends asymptotically to unit velocity after a time of the order of few Planck time b. The spacetime has a horizon at r = 0, irrespective of the value of {omega} but its angular velocity is given by {omega} - 1/b. The Sagnac time delaymore » is computed proving to depend both on {omega} and the radius of the circular orbit. The velocity of an ingoing massive test particle approaches zero very close to the spinning string, as if it were rejected by it.« less
Variability simulations with a steady, linearized primitive equations model

NASA Technical Reports Server (NTRS)

Kinter, J. L., III; Nigam, S.

1985-01-01

Solutions of the steady, primitive equations on a sphere, linearized about a zonally symmetric basic state are computed for the purpose of simulating monthly mean variability in the troposphere. The basic states are observed, winter monthly mean, zonal means of zontal and meridional velocities, temperatures and surface pressures computed from the 15 year NMC time series. A least squares fit to a series of Legendre polynomials is used to compute the basic states between 20 H and the equator, and the hemispheres are assumed symmetric. The model is spectral in the zonal direction, and centered differences are employed in the meridional and vertical directions. Since the model is steady and linear, the solution is obtained by inversion of a block, pente-diagonal matrix. The model simulates the climatology of the GFDL nine level, spectral general circulation model quite closely, particularly in middle latitudes above the boundary layer. This experiment is an extension of that simulation to examine variability of the steady, linear solution.
Stability analysis of a Vlasov-Wave system describing particles interacting with their environment

NASA Astrophysics Data System (ADS)

De Bièvre, Stephan; Goudon, Thierry; Vavasseur, Arthur

2018-06-01

We study a kinetic equation of the Vlasov-Wave type, which arises in the description of the behavior of a large number of particles interacting weakly with an environment, composed of an infinite collection of local vibrational degrees of freedom, modeled by wave equations. We use variational techniques to establish the existence of large families of stationary states for this system, and analyze their stability.
Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.
Fluid equations with nonlinear wave-particle resonances^

NASA Astrophysics Data System (ADS)

Mattor, Nathan

1997-11-01

We have derived fluid equations that include linear and nonlinear wave-particle resonance effects. This greatly extends previous ``Landau-fluid'' closures, which include linear Landau damping. (G.W. Hammett and F.W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990).^, (Z. Chang and J. D. Callen, Phys. Fluids B 4,) 1167 (1992). The new fluid equations are derived with no approximation regarding nonlinear kinetic interaction, and so additionally include numerous nonlinear kinetic effects. The derivation starts with the electrostatic drift kinetic equation for simplicity, with a Maxwellian distribution function. Fluid closure is accomplished through a simple integration trick applied to the drift kinetic equation, using the property that the nth moment of Maxwellian distribution is related to the nth derivative. The result is a compact closure term appearing in the highest moment equation, a term which involves a plasma dispersion function of the electrostatic field and its derivatives. The new term reduces to the linear closures in appropriate limits, so both approaches retain linear Landau damping. But the nonlinearly closed equations have additional desirable properties. Unlike linear closures, the nonlinear closure retains the time-reversibility of the original kinetic equation. We have shown directly that the nonlinear closure retains at least two nonlinear resonance effects: wave-particle trapping and Compton scattering. Other nonlinear kinetic effects are currently under investigation. The new equations correct two previous discrepancies between kinetic and Landau-fluid predictions, including a propagator discrepancy (N. Mattor, Phys. Fluids B 4,) 3952 (1992). and a numerical discrepancy for the 3-mode shearless bounded slab ITG problem. (S. E. Parker et al.), Phys. Plasmas 1, 1461 (1994). ^* In collaboration with S. E. Parker, Department of Physics, University of Colorado, Boulder. ^ Work performed at LLNL under DoE contract No. W7405-ENG-48.
Schroedinger's Wave Structure of Matter (WSM)

NASA Astrophysics Data System (ADS)

Wolff, Milo; Haselhurst, Geoff

2009-10-01

The puzzling electron is due to the belief that it is a discrete particle. Einstein deduced this structure was impossible since Nature does not allow the discrete particle. Clifford (1876) rejected discrete matter and suggested structures in `space'. Schroedinger, (1937) also eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). He rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff and Geoff Haselhurst (SpaceAndMotion.com) using the Scalar Wave Equation to find spherical wave solutions in a 3D quantum space. This WSM, the origin of all the Natural Laws, contains all the electron's properties including the Schroedinger Equation. The origin of Newton's Law F=ma is no longer a puzzle; It originates from Mach's principle of inertia (1883) that depends on the space medium and the WSM. Carver Mead (1999) at CalTech used the WSM to design Intel micro-chips correcting errors of Maxwell's magnetic Equations. Applications of the WSM also describe matter at molecular dimensions: alloys, catalysts, biology and medicine, molecular computers and memories. See ``Schroedinger's Universe'' - at Amazon.com
Schroedinger's Wave Structure of Matter (WSM)

NASA Astrophysics Data System (ADS)

Wolff, Milo

2009-05-01

The puzzling electron is due to the belief that it is a discrete particle. Einstein deduced this structure impossible since Nature does not match the discrete particle. Clifford (1876) rejected discrete matter and suggested structures in `space'. Schroedinger, (1937) also eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). He rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff and Geoff Haselhurst (http://www.SpaceAndMotion.com) using the Scalar Wave Equation to find spherical wave solutions in a 3D quantum space. This WSM is the origin of all the Natural Laws; thus it contains all the electron's properties including the Schroedinger Equation. The origin of Newton's Law F=ma is no longer a puzzle; it is shown to originate from Mach's principle of inertia (1883) that depends on the space medium. Carver Mead (1999) applied the WSM to design Intel micro-chips correcting errors of Maxwell's magnetic Equations. Applications of the WSM describe matter at molecular dimensions: alloys, catalysts, the mechanisms of biology and medicine, molecular computers and memories. See http://www.amazon.com/Schro at Amazon.com.
A new fundamental model of moving particle for reinterpreting Schroedinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Umar, Muhamad Darwis

2012-06-20

The study of Schroedinger equation based on a hypothesis that every particle must move randomly in a quantum-sized volume has been done. In addition to random motion, every particle can do relative motion through the movement of its quantum-sized volume. On the other way these motions can coincide. In this proposed model, the random motion is one kind of intrinsic properties of the particle. The every change of both speed of randomly intrinsic motion and or the velocity of translational motion of a quantum-sized volume will represent a transition between two states, and the change of speed of randomly intrinsicmore » motion will generate diffusion process or Brownian motion perspectives. Diffusion process can take place in backward and forward processes and will represent a dissipative system. To derive Schroedinger equation from our hypothesis we use time operator introduced by Nelson. From a fundamental analysis, we find out that, naturally, we should view the means of Newton's Law F(vector sign) = ma(vector sign) as no an external force, but it is just to describe both the presence of intrinsic random motion and the change of the particle energy.« less
Rigid rotators. [deriving the time-independent energy states associated with rotational motions of the molecule

NASA Technical Reports Server (NTRS)

1976-01-01

The two-particle, steady-state Schroedinger equation is transformed to center of mass and internuclear distance vector coordinates, leading to the free particle wave equation for the kinetic energy motion of the molecule and a decoupled wave equation for a single particle of reduced mass moving in a spherical potential field. The latter describes the vibrational and rotational energy modes of the diatomic molecule. For fixed internuclear distance, this becomes the equation of rigid rotator motion. The classical partition function for the rotator is derived and compared with the quantum expression. Molecular symmetry effects are developed from the generalized Pauli principle that the steady-state wave function of any system of fundamental particles must be antisymmetric. Nuclear spin and spin quantum functions are introduced and ortho- and para-states of rotators, along with their degeneracies, are defined. Effects of nuclear spin on entropy are deduced. Next, rigid polyatomic rotators are considered and the partition function for this case is derived. The patterns of rotational energy levels for nonlinear molecules are discussed for the spherical symmetric top, for the prolate symmetric top, for the oblate symmetric top, and for the asymmetric top. Finally, the equilibrium energy and specific heat of rigid rotators are derived.
Generalized Langevin equation with tempered memory kernel

NASA Astrophysics Data System (ADS)

Liemert, André; Sandev, Trifce; Kantz, Holger

2017-01-01

We study a generalized Langevin equation for a free particle in presence of a truncated power-law and Mittag-Leffler memory kernel. It is shown that in presence of truncation, the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit. The case of harmonic oscillator is considered as well, and the relaxation functions and the normalized displacement correlation function are represented in an exact form. By considering external time-dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement. Additionally, the double-peak phenomenon in the imaginary part of the complex susceptibility is observed. It is obtained that the truncation parameter has a huge influence on the behavior of these quantities, and it is shown how the truncation parameter changes the critical frequencies. The normalized displacement correlation function for a fractional generalized Langevin equation is investigated as well. All the results are exact and given in terms of the three parameter Mittag-Leffler function and the Prabhakar generalized integral operator, which in the kernel contains a three parameter Mittag-Leffler function. Such kind of truncated Langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes.
Equating Two Forms of a Criterion-Referenced Test by Using Norm Referenced Data: An Illustration of Two Methods.

ERIC Educational Resources Information Center

Garcia-Quintana, Roan A.; Johnson, Lynne M.

Three different computational procedures for equating two forms of a test were applied to a pair of mathematics tests to compare the results of the three procedures. The tests that were being equated were two forms of the SRA Mastery Mathematics Tests. The common, linking test used for equating was the Comprehensive Tests of Basic Skills, Form S,…
Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1993-01-01

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.
On the stability of dust orbits in mean-motion resonances perturbed by from an interstellar wind

NASA Astrophysics Data System (ADS)

Pástor, Pavol

2014-09-01

Circumstellar dust particles can be captured in a mean-motion resonance (MMR) with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the MMR analytically using averaged resonant equations. We derive the averaged resonant equations from the equations of motion in near-canonical form. The secular variations of the particle orbit depending on the orientation of the orbit in space are taken into account. The averaged resonant equations can be derived/confirmed also from Lagrange's planetary equations. We apply the derived theory to the case when the non-gravitational effects are the Poynting-Robertson effect, the radial stellar wind, and an interstellar wind. The analytical and numerical results obtained are in excellent agreement. We found that the types of orbits correspond to libration centers of the conservative problem. The averaged resonant equations can lead to a system of equations which holds for stationary points in a subset of resonant variables. Using this system we show analytically that for the considered non-gravitational effects, all stationary points should correspond to orbits which are stationary in interplanetary space after an averaging over a synodic period. In an exact resonance, the stationary orbits are stable. The stability is achieved by a periodic repetition of the evolution during the synodic period. Numerical solutions of this system show that there are no stationary orbits for either the exact or non-exact resonances.

Thermal fluctuations and stability of a particle levitated by a repulsive Casimir force in a liquid.

PubMed

Inui, Norio; Goto, Kosuke

2013-11-01

We study the vertical Brownian motion of a gold particle levitated by a repulsive Casimir force to a silica plate immersed in bromobenzene. The time evolution of the particle distribution starting from an equilibrium position, where the Casimir force and gravitational force are balanced, is considered by solving the Langevin equation using the Monte Carlo method. When the gold particle is very close to the silica plate, the Casimir force changes from repulsive to attractive, and the particle eventually sticks to the surface. The escape rate from a metastable position is calculated by solving the Fokker-Plank equation; it agrees with the value obtained by Kramers' escape theory. The duration of levitation increases as the particle radius increases up to around 2.3 μm. As an example, we show that a 1-μm-diameter gold particle can be levitated for a significantly long time by the repulsive Casimir force at room temperature.
The ONR-602 experiment and investigation of particle precipitation near the equator

NASA Technical Reports Server (NTRS)

Miah, M. A.

1991-01-01

The global precipitation of radiation belt particles at low altitude was investigated, using the ONR-602 experiment on board U.S. Air Force mission S81-1. A combination of a main telescope, beginning analysis at a few MeV/nucleon, and a monitor system, giving results below 1 MeV/nucleon, was designed for measuring particle phenomena characterized by almost any energy spectrum. The monitor provides an indication of the presence of the particles at low energy, while the main telescope gives detailed flux and composition data for the higher energy events. Results of the instrument performance analysis indicate that, at the equator, the monitor telescope has the peak efficiency for particles of about 90 deg pitch angles. The large opening angle of 75 deg makes it possible to detect omnidirectional flux of quasi-trapped particles. The high-energy cosmic-ray background count is found to be very insignificant. It is demonstrated that the particle counting rates for the low-energy threshold have been almost entirely due to protons.
The evolution of energetic particles and the emitted radiation in solar flares. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lu, Edward Tsang

1989-01-01

The evolution of accelerated particle distributions in a magnetized plasma and the resulting radiation are calculated, and the results are applied to solar flares. To study the radiation on timescales of order the particle lifetimes, the evolution of the particle distribution is determined by the use of the Fokker-Planck equation including Coulomb collisions and magnetic mirroring. Analytic solution to the equations are obtained for limiting cases such as homogeneous injection in a homogeneous plasma, and for small pitch angle. These analytic solutions are then used to place constraints on flare parameters such as density, loop length, and the injection timescale for very short implusive solar flares. For general particle distributions in arbitrary magnetic field and background density, the equation is solved numerically. The relative timing of microwaves and X-rays during individual flares is investigated. A number of possible sources for excessive microwave flux are discussed including a flattening in the electron spectrum above hard X-ray energies, thermal synchrotron emission, and trapping of electron by converging magnetic fields. Over shorter timescales, the Fokker-Planck equation is solved numerically to calculate the temporal evolution of microwaves and X-rays from nonthermal thick target models. It is shown that magnetic trapping will not account for the observed correlation of microwaves of approximately 0.15 seconds behind X-rays in flares with rapid time variation, and thus higher energy electrons must be accelerated later than lower energy electrons.
Algebraic diagrammatic construction formalism with three-body interactions

NASA Astrophysics Data System (ADS)

Raimondi, Francesco; Barbieri, Carlo

2018-05-01

Background: Self-consistent Green's function theory has recently been extended to the basic formalism needed to account for three-body interactions [Carbone, Cipollone, Barbieri, Rios, and Polls, Phys. Rev. C 88, 054326 (2013), 10.1103/PhysRevC.88.054326]. The contribution of three-nucleon forces has so far been included in ab initio calculations on nuclear matter and finite nuclei only as averaged two-nucleon forces. Purpose: We derive the working equations for all possible two- and three-nucleon terms that enter the expansion of the self-energy up to the third order, thus including the interaction-irreducible (i.e., not averaged) diagrams with three-nucleon forces that have been previously neglected. Methods: We employ the algebraic diagrammatic construction up to the third order as an organization scheme for generating a nonperturbative self-energy, in which ring (particle-hole) and ladder (particle-particle) diagrams are resummed to all orders. Results: We derive expressions of the static and dynamic self-energy up to the third order, by taking into account the set of diagrams required when either the skeleton or nonskeleton expansions of the single-particle propagator are assumed. A hierarchy of importance among different diagrams is revealed, and a particular emphasis is given to a third-order diagram [see Fig. 2(c)] that is expected to play a significant role among those featuring an interaction-irreducible three-nucleon force. Conclusion: A consistent formalism to resum at infinite order correlations induced by three-nucleon forces in the self-consistent Green's function theory is now available and ready to be implemented in the many-body solvers.
Integrating Geochemical Reactions with a Particle-Tracking Approach to Simulate Nitrogen Transport and Transformation in Aquifers

NASA Astrophysics Data System (ADS)

Cui, Z.; Welty, C.; Maxwell, R. M.

2011-12-01

Lagrangian, particle-tracking models are commonly used to simulate solute advection and dispersion in aquifers. They are computationally efficient and suffer from much less numerical dispersion than grid-based techniques, especially in heterogeneous and advectively-dominated systems. Although particle-tracking models are capable of simulating geochemical reactions, these reactions are often simplified to first-order decay and/or linear, first-order kinetics. Nitrogen transport and transformation in aquifers involves both biodegradation and higher-order geochemical reactions. In order to take advantage of the particle-tracking approach, we have enhanced an existing particle-tracking code SLIM-FAST, to simulate nitrogen transport and transformation in aquifers. The approach we are taking is a hybrid one: the reactive multispecies transport process is operator split into two steps: (1) the physical movement of the particles including the attachment/detachment to solid surfaces, which is modeled by a Lagrangian random-walk algorithm; and (2) multispecies reactions including biodegradation are modeled by coupling multiple Monod equations with other geochemical reactions. The coupled reaction system is solved by an ordinary differential equation solver. In order to solve the coupled system of equations, after step 1, the particles are converted to grid-based concentrations based on the mass and position of the particles, and after step 2 the newly calculated concentration values are mapped back to particles. The enhanced particle-tracking code is capable of simulating subsurface nitrogen transport and transformation in a three-dimensional domain with variably saturated conditions. Potential application of the enhanced code is to simulate subsurface nitrogen loading to the Chesapeake Bay and its tributaries. Implementation details, verification results of the enhanced code with one-dimensional analytical solutions and other existing numerical models will be presented in addition to a discussion of implementation challenges.
Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Bart, Timothy J.; Kutler, Paul (Technical Monitor)

1998-01-01

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.
Slew maneuvers of Spacecraft Control Laboratory Experiment (SCOLE)

NASA Technical Reports Server (NTRS)

Kakad, Yogendra P.

1992-01-01

This is the final report on the dynamics and control of slew maneuvers of the Spacecraft Control Laboratory Experiment (SCOLE) test facility. The report documents the basic dynamical equation derivations for an arbitrary large angle slew maneuver as well as the basic decentralized slew maneuver control algorithm. The set of dynamical equations incorporate rigid body slew maneuver and three dimensional vibrations of the complete assembly comprising the rigid shuttle, the flexible beam, and the reflector with an offset mass. The analysis also includes kinematic nonlinearities of the entire assembly during the maneuver and the dynamics of the interactions between the rigid shuttle and the flexible appendage. The equations are simplified and evaluated numerically to include the first ten flexible modes to yield a model for designing control systems to perform slew maneuvers. The control problem incorporates the nonlinear dynamical equations and is expressed in terms of a two point boundary value problem.
General Boundary Conditions for a Majorana Single-Particle in a Box in (1 + 1) Dimensions

NASA Astrophysics Data System (ADS)

De Vincenzo, Salvatore; Sánchez, Carlet

2018-05-01

We consider the problem of a Majorana single-particle in a box in (1 + 1) dimensions. We show that the most general set of boundary conditions for the equation that models this particle is composed of two families of boundary conditions, each one with a real parameter. Within this set, we only have four confining boundary conditions—but infinite not confining boundary conditions. Our results are also valid when we include a Lorentz scalar potential in this equation. No other Lorentz potential can be added. We also show that the four confining boundary conditions for the Majorana particle are precisely the four boundary conditions that mathematically can arise from the general linear boundary condition used in the MIT bag model. Certainly, the four boundary conditions for the Majorana particle are also subject to the Majorana condition.
Second order upwind Lagrangian particle method for Euler equations

DOE PAGES

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

2016-06-01

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less
Second order upwind Lagrangian particle method for Euler equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less
Numerical Investigation of Two-Phase Flows With Charged Droplets in Electrostatic Field

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1996-01-01

A numerical method to solve two-phase turbulent flows with charged droplets in an electrostatic field is presented. The ensemble-averaged Navier-Stokes equations and the electrostatic potential equation are solved using a finite volume method. The transitional turbulence field is described using multiple-time-scale turbulence equations. The equations of motion of droplets are solved using a Lagrangian particle tracking scheme, and the inter-phase momentum exchange is described by the Particle-In-Cell scheme. The electrostatic force caused by an applied electrical potential is calculated using the electrostatic field obtained by solving a Laplacian equation and the force exerted by charged droplets is calculated using the Coulombic force equation. The method is applied to solve electro-hydrodynamic sprays. The calculated droplet velocity distributions for droplet dispersions occurring in a stagnant surrounding are in good agreement with the measured data. For droplet dispersions occurring in a two-phase flow, the droplet trajectories are influenced by aerodynamic forces, the Coulombic force, and the applied electrostatic potential field.
Flow of Combustion Products Containing Condensed-Phase Particles over a Recessed Vectorable Jet Nozzle

NASA Astrophysics Data System (ADS)

Volkov, K. N.; Denisikhin, S. V.; Emel'yanov, V. N.; Teterina, I. V.

2017-09-01

The flow of combustion products containing condensed-phase particles over the recessed vectorable nozzle of a solid-propellant rocket motor was investigated with the use of the Reynolds-averaged Navier-Stokes equations, equations of the k-ɛ model of turbulence, and the Lagrange approach. The fields of flows of combustion products and the mechanical trajectories of condensed-phase particles in the charge channel, the prenozzle space, and the nozzle unit of this motor were calculated for different angles of swing of the nozzle. The formation of vortices in the gas flow in the neighborhood of the downstream cover of the nozzle and their influence on the movement of particles different in size were considered.
Locating an atmospheric contamination source using slow manifolds

NASA Astrophysics Data System (ADS)

Tang, Wenbo; Haller, George; Baik, Jong-Jin; Ryu, Young-Hee

2009-04-01

Finite-size particle motion in fluids obeys the Maxey-Riley equations, which become singular in the limit of infinitesimally small particle size. Because of this singularity, finding the source of a dispersed set of small particles is a numerically ill-posed problem that leads to exponential blowup. Here we use recent results on the existence of a slow manifold in the Maxey-Riley equations to overcome this difficulty in source inversion. Specifically, we locate the source of particles by projecting their dispersed positions on a time-varying slow manifold, and by advecting them on the manifold in backward time. We use this technique to locate the source of a hypothetical anthrax release in an unsteady three-dimensional atmospheric wind field in an urban street canyon.
Quasiparticle Interactions in Neutron Matter for Applications in Neutron Stars

NASA Technical Reports Server (NTRS)

Wambach, J.; Anisworth, T. L.; Pines, D.

1993-01-01

A microscopic model for the quaisiparticle interaction in neutron matter is presented. Both particle-particle (pp) and particle-hole (ph) correlation are are included. The pp correlations are treated in semi-empirical way, while ph correlations are incorporated by solving coupled two-body equations for the particle hole interaction and the scattering amplitude on the Fermi sphere. The resulting integral equations self-consistently sum the ph reducible diagrams. Antisymmetry is kept at all stages and hence the forward-scattering sum rules are obeyed. Results for Landau parameters and transport coefficients in a density regime representing the crust of a neutron star are presented. We also estimate the S-1 gap parameter for neutron superfluidity and comment briefly on neutron-star implications.
Simulation of moving flat plate with unsteady translational motion using vortex method

NASA Astrophysics Data System (ADS)

Widodo, A. F.; Zuhal, L. R.

2013-10-01

This paper presents simulation of moving flate plate with unsteady translational motion using Lagrangianmeshless numerical simulation named vortex method. The method solves Navier-Stokes equations in term of vorticity. The solving strategy is splitting the equation into diffusion and convection term to be solved separately. The diffusion term is modeled by particles strength exchange(PSE) which is the most accurate of diffusion modeling in vortex method. The convection term that represents transport of particles is calculated by time step integration of velocity. Velocity of particles is natively calculated using Biot-Savart relation but for acceleration, fastmultiple method(FMM) is employed. The simulation is validated experimentally using digital particle image velocimetry(DPIV) and the results give good agreement.
General solution for diffusion-controlled dissolution of spherical particles. 1. Theory.

PubMed

Wang, J; Flanagan, D R

1999-07-01

Three classical particle dissolution rate expressions are commonly used to interpret particle dissolution rate phenomena. Our analysis shows that an assumption used in the derivation of the traditional cube-root law may not be accurate under all conditions for diffusion-controlled particle dissolution. Mathematical analysis shows that the three classical particle dissolution rate expressions are approximate solutions to a general diffusion layer model. The cube-root law is most appropriate when particle size is much larger than the diffusion layer thickness, the two-thirds-root expression applies when the particle size is much smaller than the diffusion layer thickness. The square-root expression is intermediate between these two models. A general solution to the diffusion layer model for monodispersed spherical particles dissolution was derived for sink and nonsink conditions. Constant diffusion layer thickness was assumed in the derivation. Simulated dissolution data showed that the ratio between particle size and diffusion layer thickness (a0/h) is an important factor in controlling the shape of particle dissolution profiles. A new semiempirical general particle dissolution equation is also discussed which encompasses the three classical particle dissolution expressions. The success of the general equation in explaining limitations of traditional particle dissolution expressions demonstrates the usefulness of the general diffusion layer model.
Dynamically orthogonal field equations for stochastic flows and particle dynamics

DTIC Science & Technology

2011-02-01

where uncertainty ‘lives’ as well as a system of Stochastic Di erential Equations that de nes how the uncertainty evolves in the time varying stochastic ... stochastic dynamical component that are both time and space dependent, we derive a system of field equations consisting of a Partial Differential Equation...a system of Stochastic Differential Equations that defines how the stochasticity evolves in the time varying stochastic subspace. These new
The breakdown of the weakly-nonlinear regime for kinetic instabilities

NASA Astrophysics Data System (ADS)

Sanz-Orozco, David; Berk, Herbert; Wang, Ge

2017-10-01

The evolution of marginally-unstable waves that interact resonantly with populations of energetic particles is governed by a well-known cubic integro-differential equation for the mode amplitude. One of the outcomes predicted by the equation is the so-called ``explosive'' regime, where the amplitude grows indefinitely, eventually taking the equation outside of its domain of validity. Beyond this point, only full Vlasov simulations will accurately describe the evolution of the mode amplitude. In this work, we study the breakdown of the cubic equation in detail. We find that, while the cubic equation is still valid, the distribution function of the energetic particles locally flattens or ``folds'' in phase space. This feature is unexpected in view of the assumptions of the theory that are given in. We also derive fifth-order terms in the wave equation, which not only give us a more accurate description of the marginally-unstable modes, but they also allow us to predict the breakdown of the cubic equation. Our findings allow us to better understand the transition between weakly-nonlinear modes and the long-term chirping modes that ultimately emerge.
Effect of anisotropic dust pressure and superthermal electrons on propagation and stability of dust acoustic solitary waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bashir, M. F., E-mail: frazbashir@yahoo.com; Behery, E. E., E-mail: eebehery@gmail.com; Department of Physics, Faculty of Science, Damietta University, P.O. 34517, New Damietta

2015-06-15

Employing the reductive perturbation technique, Zakharov–Kuznetzov (ZK) equation is derived for dust acoustic (DA) solitary waves in a magnetized plasma which consists the effects of dust anisotropic pressure, arbitrary charged dust particles, Boltzmann distributed ions, and Kappa distributed superthermal electrons. The ZK solitary wave solution is obtained. Using the small-k expansion method, the stability analysis for DA solitary waves is also discussed. The effects of the dust pressure anisotropy and the electron superthermality on the basic characteristics of DA waves as well as on the three-dimensional instability criterion are highlighted. It is found that the DA solitary wave is rarefactivemore » (compressive) for negative (positive) dust. In addition, the growth rate of instability increases rapidly as the superthermal spectral index of electrons increases with either positive or negative dust grains. A brief discussion for possible applications is included.« less
Introduction to big bang nucleosynthesis and modern cosmology

NASA Astrophysics Data System (ADS)

Mathews, Grant J.; Kusakabe, Motohiko; Kajino, Toshitaka

Primordial nucleosynthesis remains as one of the pillars of modern cosmology. It is the testing ground upon which many cosmological models must ultimately rest. It is our only probe of the universe during the important radiation-dominated epoch in the first few minutes of cosmic expansion. This paper reviews the basic equations of space-time, cosmology, and big bang nucleosynthesis. We also summarize the current state of observational constraints on primordial abundances along with the key nuclear reactions and their uncertainties. We summarize which nuclear measurements are most crucial during the big bang. We also review various cosmological models and their constraints. In particular, we analyze the constraints that big bang nucleosynthesis places upon the possible time variation of fundamental constants, along with constraints on the nature and origin of dark matter and dark energy, long-lived supersymmetric particles, gravity waves, and the primordial magnetic field.

Development of Sediment Deposition Height Capacity Equation in Sewer Networks

NASA Astrophysics Data System (ADS)

Song, Yangho; Jo, Deokjun; Lee, Jungho

2017-04-01

Sediment characteristics and transport processes in sewers are markedly different from river. There is a wide range of particle densities and smaller particle size variation in sewers. Sediment supply and the available erodible material are more limited in sewers, and the diverse hydraulic characteristics in sewer systems are more unsteady. Prevention of sewer sediment accumulation, which can cause major sewer operational problems, is imperative and has been an immense concern for engineers. The effects of sediment formation in sewer systems, an appropriate sediment transport modelling with the ability to determine the location and depth of sediment deposit is needed. It is necessary to design efficiently considering the transfer and settling phenomena of the sediment coming into the sewer systems. During transport in the sewer, the minimum shear flow velocity and possible shear stress at which the sediment is transported smoothly. However, the interaction of sediment and fluid within the sewer systems has been very complex and the rigorous theoretical handling of this problem has not been developed. It is derived from the empirical values obtained from the river bed. The basic theory that particles float is based on the balance between sedimentation of particles by gravity and turbulent diffusion of fluids. There are many variables related. Representative parameters include complex phenomena due to collisions between particles, particles and fluids, and interactions between particles and tube walls. In general, the main parameters that form the boundary between the main transport and sediment are particle size, density, volume fraction, pipe diameter and gravity. As the particle size and volume concentration increase, the minimum feed rate increases and the same tendency is observed for the change of the capillary diameter. Based on this tendency, this study has developed a sediment deposition height capacity formula to take into consideration the sewer discharge capacity. The main objective in undertaking this research is the assessment of the sediment scouring and transporting capacity of the discharged. Acknowledgements This research was supported by a grant(13AWMP-B066744-01) from Advanced Water Management Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government.
A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method

PubMed Central

Kojic, Milos; Filipovic, Nenad; Tsuda, Akira

2012-01-01

A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249–274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier–Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only. The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examples – simple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method. PMID:23814322
Electromagnetic banana kinetic equation and its applications in tokamaks

NASA Astrophysics Data System (ADS)

Shaing, K. C.; Chu, M. S.; Sabbagh, S. A.; Seol, J.

2018-03-01

A banana kinetic equation in tokamaks that includes effects of the finite banana width is derived for the electromagnetic waves with frequencies lower than the gyro-frequency and the bounce frequency of the trapped particles. The radial wavelengths are assumed to be either comparable to or shorter than the banana width, but much wider than the gyro-radius. One of the consequences of the banana kinetics is that the parallel component of the vector potential is not annihilated by the orbit averaging process and appears in the banana kinetic equation. The equation is solved to calculate the neoclassical quasilinear transport fluxes in the superbanana plateau regime caused by electromagnetic waves. The transport fluxes can be used to model electromagnetic wave and the chaotic magnetic field induced thermal particle or energetic alpha particle losses in tokamaks. It is shown that the parallel component of the vector potential enhances losses when it is the sole transport mechanism. In particular, the fact that the drift resonance can cause significant transport losses in the chaotic magnetic field in the hitherto unknown low collisionality regimes is emphasized.
State-of-charge estimation in lithium-ion batteries: A particle filter approach

NASA Astrophysics Data System (ADS)

Tulsyan, Aditya; Tsai, Yiting; Gopaluni, R. Bhushan; Braatz, Richard D.

2016-11-01

The dynamics of lithium-ion batteries are complex and are often approximated by models consisting of partial differential equations (PDEs) relating the internal ionic concentrations and potentials. The Pseudo two-dimensional model (P2D) is one model that performs sufficiently accurately under various operating conditions and battery chemistries. Despite its widespread use for prediction, this model is too complex for standard estimation and control applications. This article presents an original algorithm for state-of-charge estimation using the P2D model. Partial differential equations are discretized using implicit stable algorithms and reformulated into a nonlinear state-space model. This discrete, high-dimensional model (consisting of tens to hundreds of states) contains implicit, nonlinear algebraic equations. The uncertainty in the model is characterized by additive Gaussian noise. By exploiting the special structure of the pseudo two-dimensional model, a novel particle filter algorithm that sweeps in time and spatial coordinates independently is developed. This algorithm circumvents the degeneracy problems associated with high-dimensional state estimation and avoids the repetitive solution of implicit equations by defining a 'tether' particle. The approach is illustrated through extensive simulations.
General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.
The effect of shear flow on the rotational diffusivity of a single axisymmetric particle

NASA Astrophysics Data System (ADS)

Leahy, Brian; Koch, Donald; Cohen, Itai

2014-11-01

Colloidal suspensions of nonspherical particles abound in the world around us, from red blood cells in arteries to kaolinite discs in clay. Understanding the orientation dynamics of these particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in simple shear flow, the orientation dynamics of Brownian nonspherical particles are poorly understood at large shear rates. Here, we analytically calculate the time-dependent orientation distributions of particles confined to the flow-gradient plane when the rotary diffusion is small but nonzero. For both startup and oscillatory shear flows, we find a coordinate change that maps the convection-diffusion equation to a simple diffusion equation with an enhanced diffusion constant, simplifying the orientation dynamics. For oscillatory shear, this enhanced diffusion drastically alters the quasi-steady orientation distributions. Our theory of the unsteady orientation dynamics provides an understanding of a nonspherical particle suspension's rheology for a large class of unsteady flows. For particles with aspect ratio 10 under oscillatory shear, the rotary diffusion and intrinsic viscosity vary with amplitude by a factor of ~ 40 and ~ 2 , respectively.
Gas-particle partitioning of alcohol vapors on organic aerosols.

PubMed

Chan, Lap P; Lee, Alex K Y; Chan, Chak K

2010-01-01

Single particle levitation using an electrodynamic balance (EDB) has been found to give accurate and direct hygroscopic measurements (gas-particle partitioning of water) for a number of inorganic and organic aerosol systems. In this paper, we extend the use of an EDB to examine the gas-particle partitioning of volatile to semivolatile alcohols, including methanol, n-butanol, n-octanol, and n-decanol, on levitated oleic acid particles. The measured K(p) agreed with Pankow's absorptive partitioning model. At high n-butanol vapor concentrations (10(3) ppm), the uptake of n-butanol reduced the average molecular-weight of the oleic acid particle appreciably and hence increased the K(p) according to Pankow's equation. Moreover, the hygroscopicity of mixed oleic acid/n-butanol particles was higher than the predictions given by the UNIFAC model (molecular group contribution method) and the ZSR equation (additive rule), presumably due to molecular interactions between the chemical species in the mixed particles. Despite the high vapor concentrations used, these findings warrant further research on the partitioning of atmospheric organic vapors (K(p)) near sources and how collectively they affect the hygroscopic properties of organic aerosols.
Shock interaction with deformable particles using a constrained interface reinitialization scheme

NASA Astrophysics Data System (ADS)

Sridharan, P.; Jackson, T. L.; Zhang, J.; Balachandar, S.; Thakur, S.

2016-02-01

In this paper, we present axisymmetric numerical simulations of shock propagation in nitromethane over an aluminum particle for post-shock pressures up to 10 GPa. We use the Mie-Gruneisen equation of state to describe both the medium and the particle. The numerical method is a finite-volume based solver on a Cartesian grid, that allows for multi-material interfaces and shocks, and uses a novel constrained reinitialization scheme to precisely preserve particle mass and volume. We compute the unsteady inviscid drag coefficient as a function of time, and show that when normalized by post-shock conditions, the maximum drag coefficient decreases with increasing post-shock pressure. We also compute the mass-averaged particle pressure and show that the observed oscillations inside the particle are on the particle-acoustic time scale. Finally, we present simplified point-particle models that can be used for macroscale simulations. In the Appendix, we extend the isothermal or isentropic assumption concerning the point-force models to non-ideal equations of state, thus justifying their use for the current problem.
Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E. N.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account.
Exact solutions of the population balance equation including particle transport, using group analysis

NASA Astrophysics Data System (ADS)

Lin, Fubiao; Meleshko, Sergey V.; Flood, Adrian E.

2018-06-01

The population balance equation (PBE) has received an unprecedented amount of attention in recent years from both academics and industrial practitioners because of its long history, widespread use in engineering, and applicability to a wide variety of particulate and discrete-phase processes. However it is typically impossible to obtain analytical solutions, although in almost every case a numerical solution of the PBEs can be obtained. In this article, the symmetries of PBEs with homogeneous coagulation kernels involving aggregation, breakage and growth processes and particle transport in one dimension are found by direct solving the determining equations. Using the optimal system of one and two-dimensional subalgebras, all invariant solutions and reduced equations are obtained. In particular, an explicit analytical physical solution is also presented.
Variational principles for relativistic smoothed particle hydrodynamics

NASA Astrophysics Data System (ADS)

Monaghan, J. J.; Price, D. J.

2001-12-01

In this paper we show how the equations of motion for the smoothed particle hydrodynamics (SPH) method may be derived from a variational principle for both non-relativistic and relativistic motion when there is no dissipation. Because the SPH density is a function of the coordinates the derivation of the equations of motion through variational principles is simpler than in the continuum case where the density is defined through the continuity equation. In particular, the derivation of the general relativistic equations is more direct and simpler than that of Fock. The symmetry properties of the Lagrangian lead immediately to the familiar additive conservation laws of linear and angular momentum and energy. In addition, we show that there is an approximately conserved quantity which, in the continuum limit, is the circulation.
Discrete and continuous models for tissue growth and shrinkage.

PubMed

Yates, Christian A

2014-06-07

The incorporation of domain growth into stochastic models of biological processes is of increasing interest to mathematical modellers and biologists alike. In many situations, especially in developmental biology, the growth of the underlying tissue domain plays an important role in the redistribution of particles (be they cells or molecules) which may move and react atop the domain. Although such processes have largely been modelled using deterministic, continuum models there is an increasing appetite for individual-based stochastic models which can capture the fine details of the biological movement processes which are being elucidated by modern experimental techniques, and also incorporate the inherent stochasticity of such systems. In this work we study a simple stochastic model of domain growth. From a basic version of this model, Hywood et al. (2013) were able to derive a Fokker-Plank equation (FPE) (in this case an advection-diffusion partial differential equation on a growing domain) which describes the evolution of the probability density of some tracer particles on the domain. We extend their work so that a variety of different domain growth mechanisms can be incorporated and demonstrate a good agreement between the mean tracer density and the solution of the FPE in each case. In addition we incorporate domain shrinkage (via element death) into our individual-level model and demonstrate that we are able to derive coefficients for the FPE in this case as well. For situations in which the drift and diffusion coefficients are not readily available we introduce a numerical coefficient estimation approach and demonstrate the accuracy of this approach by comparing it with situations in which an analytical solution is obtainable. Copyright © 2014 Elsevier Ltd. All rights reserved.
Collisionless tearing instability of a bi-Maxwellian neutral sheet - An integrodifferential treatment with exact particle orbits

NASA Technical Reports Server (NTRS)

Burkhart, G. R.; Chen, J.

1989-01-01

The integrodifferential equation describing the linear tearing instability in the bi-Maxwellian neutral sheet is solved without approximating the particle orbits or the eigenfunction psi. Results of this calculation are presented. Comparison between the exact solution and the three-region approximation motivates the piecewise-straight-line approximation, a simplification that allows faster solution of the integrodifferential equation, yet retains the important features of the exact solution.
Plasma Theory and Simulation

DTIC Science & Technology

1988-06-30

equation using finite difference methods. The distribution function is represented by a large number of particles. The particle’s velocities change as a...Small angle Coulomb collisions The FP equation for describing small angle Coulomb collisions can be solved numerically using finite difference techniques...A finite Fourrier transform (FT) is made in z, then we can solve for each k using the following finite difference scheme [5]: 2{r 1 +l1 2 (,,+ 1 - fj
Modeling thermionic emission from laser-heated nanoparticles

DOE PAGES

Mitrani, J. M.; Shneider, M. N.; Stratton, B. C.; ...

2016-02-01

An adjusted form of thermionic emission is applied to calculate emitted current from laser-heated nanoparticles and to interpret time-resolved laser-induced incandescence (TR-LII) signals. This adjusted form of thermionic emission predicts significantly lower values of emitted current compared to the commonly used Richardson-Dushman equation, since the buildup of positive charge in a laser-heated nanoparticle increases the energy barrier for further emission of electrons. Thermionic emission influences the particle's energy balance equation, which can influence TR-LII signals. Additionally, reports suggest that thermionic emission can induce disintegration of nanoparticle aggregates when the electrostatic Coulomb repulsion energy between two positively charged primary particles ismore » greater than the van der Waals bond energy. Furthermore, since the presence and size of aggregates strongly influences the particle's energy balance equation, using an appropriate form of thermionic emission to calculate emitted current may improve interpretation of TR-LII signals.« less
Group Theoretical Characterization of Wave Equations

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2017-12-01

Group theoretical methods, worked out in particular by Mackey and Wigner, allow to attain the explicit Quantum Theory of a free particle through a purely deductive development based on symmetry principles. The extension of these methods to the case of an interacting particle finds a serious obstacle in the loss of the symmetry condition for the transformations of Galilei's group. The known attempts towards such an extension introduce restrictions which lead to theories empirically too limited. In the present article we show how the difficulties raised by the loss of symmetry can be overcome without the restrictions that affect tha past attempts. According to our results, the different specific forms of the wave equation of an interacting particle are implied by particular first order invariance properties that characterize the interaction with respect to specific sub-groups of galileian transformations. Moreover, the possibility of yet unknown forms of the wave equation is left open.
Real time visualization of quantum walk

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miyazaki, Akihide; Hamada, Shinji; Sekino, Hideo

2014-02-20

Time evolution of quantum particles like electrons is described by time-dependent Schrödinger equation (TDSE). The TDSE is regarded as the diffusion equation of electrons with imaginary diffusion coefficients. And the TDSE is solved by quantum walk (QW) which is regarded as a quantum version of a classical random walk. The diffusion equation is solved in discretized space/time as in the case of classical random walk with additional unitary transformation of internal degree of freedom typical for quantum particles. We call the QW for solution of the TDSE a Schrödinger walk (SW). For observation of one quantum particle evolution under amore » given potential in atto-second scale, we attempt a successive computation and visualization of the SW. Using Pure Data programming, we observe the correct behavior of a probability distribution under the given potential in real time for observers of atto-second scale.« less
Anomalous transport in fluid field with random waiting time depending on the preceding jump length

NASA Astrophysics Data System (ADS)

Zhang, Hong; Li, Guo-Hua

2016-11-01

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. Project supported by the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414) and the Opening Foundation of Geomathematics Key Laboratory of Sichuan Province, China (Grant No. scsxdz2013009).
Fast computation of radiation pressure force exerted by multiple laser beams on red blood cell-like particles

NASA Astrophysics Data System (ADS)

Gou, Ming-Jiang; Yang, Ming-Lin; Sheng, Xin-Qing

2016-10-01

Mature red blood cells (RBC) do not contain huge complex nuclei and organelles, makes them can be approximately regarded as homogeneous medium particles. To compute the radiation pressure force (RPF) exerted by multiple laser beams on this kind of arbitrary shaped homogenous nano-particles, a fast electromagnetic optics method is demonstrated. In general, based on the Maxwell's equations, the matrix equation formed by the method of moment (MOM) has many right hand sides (RHS's) corresponding to the different laser beams. In order to accelerate computing the matrix equation, the algorithm conducts low-rank decomposition on the excitation matrix consisting of all RHS's to figure out the so-called skeleton laser beams by interpolative decomposition (ID). After the solutions corresponding to the skeletons are obtained, the desired responses can be reconstructed efficiently. Some numerical results are performed to validate the developed method.
REVIEWS OF TOPICAL PROBLEMS: Particle kinetics in highly turbulent plasmas (renormalization and self-consistent field methods)

NASA Astrophysics Data System (ADS)

Bykov, Andrei M.; Toptygin, Igor'N.

1993-11-01

This review presents methods available for calculating transport coefficients for impurity particles in plasmas with strong long-wave MHD-type velocity and magnetic-field fluctuations, and random ensembles of strong shock fronts. The renormalization of the coefficients of the mean-field equation of turbulent dynamo theory is also considered. Particular attention is devoted to the renormalization method developed by the authors in which the renormalized transport coefficients are calculated from a nonlinear transcendental equation (or a set of such equations) and are expressed in the form of explicit functions of pair correlation tensors describing turbulence. Numerical calculations are reproduced for different turbulence spectra. Spatial transport in a magnetic field and particle acceleration by strong turbulence are investigated. The theory can be used in a wide range of practical problems in plasma physics, atmospheric physics, ocean physics, astrophysics, cosmic-ray physics, and so on.

The free-electron laser - Maxwell's equations driven by single-particle currents

NASA Technical Reports Server (NTRS)

Colson, W. B.; Ride, S. K.

1980-01-01

It is shown that if single particle currents are coupled to Maxwell's equations, the resulting set of self-consistent nonlinear equations describes the evolution of the electron beam and the amplitude and phase of the free-electron-laser field. The formulation is based on the slowly varying amplitude and phase approximation, and the distinction between microscopic and macroscopic scales, which distinguishes the microscopic bunching from the macroscopic pulse propagation. The capabilities of this new theoretical approach become apparent when its predictions for the ultrashort pulse free-electron laser are compared to experimental data; the optical pulse evolution, determined simply and accurately, agrees well with observations.
A survey of implicit particle filters for data assimilation [Implicit particle filters for data assimilation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chorin, Alexandre J.; Morzfeld, Matthias; Tu, Xuemin

Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles one by one to the high probability domain. We provide a detailed description of these filters, with illustrative examples, together with new, more general, methods for solving the algebraic equations and with a new algorithm for parameter identification.
Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Litvinenko, Yuri E.; Fichtner, Horst; Walter, Dominik

2017-05-20

We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatmentmore » of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.« less
On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.
Equations for hydraulic conductivity estimation from particle size distribution: A dimensional analysis

NASA Astrophysics Data System (ADS)

Wang, Ji-Peng; François, Bertrand; Lambert, Pierre

2017-09-01

Estimating hydraulic conductivity from particle size distribution (PSD) is an important issue for various engineering problems. Classical models such as Hazen model, Beyer model, and Kozeny-Carman model usually regard the grain diameter at 10% passing (d10) as an effective grain size and the effects of particle size uniformity (in Beyer model) or porosity (in Kozeny-Carman model) are sometimes embedded. This technical note applies the dimensional analysis (Buckingham's ∏ theorem) to analyze the relationship between hydraulic conductivity and particle size distribution (PSD). The porosity is regarded as a dependent variable on the grain size distribution in unconsolidated conditions. It indicates that the coefficient of grain size uniformity and a dimensionless group representing the gravity effect, which is proportional to the mean grain volume, are the main two determinative parameters for estimating hydraulic conductivity. Regression analysis is then carried out on a database comprising 431 samples collected from different depositional environments and new equations are developed for hydraulic conductivity estimation. The new equation, validated in specimens beyond the database, shows an improved prediction comparing to using the classic models.
BHR equations re-derived with immiscible particle effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schwarzkopf, John Dennis; Horwitz, Jeremy A.

2015-05-01

Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied tomore » the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.« less
Comparison of formulas for resonant interactions between energetic electrons and oblique whistler-mode waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Jinxing, E-mail: lijx@pku.edu.cn; Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095; Bortnik, Jacob

2015-05-15

Test particle simulation is a useful method for studying both linear and nonlinear wave-particle interactions in the magnetosphere. The gyro-averaged equations of particle motion for first-order and other cyclotron harmonic resonances with oblique whistler-mode waves were first derived by Bell [J. Geophys. Res. 89, 905 (1984)] and the most recent relativistic form was given by Ginet and Albert [Phys. Fluids B 3, 2994 (1991)], and Bortnik [Ph.D. thesis (Stanford University, 2004), p. 40]. However, recently we found there was a (−1){sup l−1} term difference between their formulas of perpendicular motion for the lth-order resonance. This article presents the detailed derivationmore » process of the generalized resonance formulas, and suggests a check of the signs for self-consistency, which is independent of the choice of conventions, that is, the energy variation equation resulting from the momentum equations should not contain any wave magnetic components, simply because the magnetic field does not contribute to changes of particle energy. In addition, we show that the wave centripetal force, which was considered small and was neglect in previous studies of nonlinear interactions, has a profound time derivative and can significantly enhance electron phase trapping especially in high frequency waves. This force can also bounce the low pitch angle particles out of the loss cone. We justify both the sign problem and the missing wave centripetal force by demonstrating wave-particle interaction examples, and comparing the gyro-averaged particle motion to the full particle motion under the Lorentz force.« less
Comparison of formulas for resonant interactions between energetic electrons and oblique whistler-mode waves

NASA Astrophysics Data System (ADS)

Li, Jinxing; Bortnik, Jacob; Xie, Lun; Pu, Zuyin; Chen, Lunjin; Ni, Binbin; Tao, Xin; Thorne, Richard M.; Fu, Suiyan; Yao, Zhonghua; Guo, Ruilong

2015-05-01

Test particle simulation is a useful method for studying both linear and nonlinear wave-particle interactions in the magnetosphere. The gyro-averaged equations of particle motion for first-order and other cyclotron harmonic resonances with oblique whistler-mode waves were first derived by Bell [J. Geophys. Res. 89, 905 (1984)] and the most recent relativistic form was given by Ginet and Albert [Phys. Fluids B 3, 2994 (1991)], and Bortnik [Ph.D. thesis (Stanford University, 2004), p. 40]. However, recently we found there was a ( - 1 ) l - 1 term difference between their formulas of perpendicular motion for the lth-order resonance. This article presents the detailed derivation process of the generalized resonance formulas, and suggests a check of the signs for self-consistency, which is independent of the choice of conventions, that is, the energy variation equation resulting from the momentum equations should not contain any wave magnetic components, simply because the magnetic field does not contribute to changes of particle energy. In addition, we show that the wave centripetal force, which was considered small and was neglect in previous studies of nonlinear interactions, has a profound time derivative and can significantly enhance electron phase trapping especially in high frequency waves. This force can also bounce the low pitch angle particles out of the loss cone. We justify both the sign problem and the missing wave centripetal force by demonstrating wave-particle interaction examples, and comparing the gyro-averaged particle motion to the full particle motion under the Lorentz force.
Statistical Extremes of Turbulence and a Cascade Generalisation of Euler's Gyroscope Equation

NASA Astrophysics Data System (ADS)

Tchiguirinskaia, Ioulia; Scherzer, Daniel

2016-04-01

Turbulence refers to a rather well defined hydrodynamical phenomenon uncovered by Reynolds. Nowadays, the word turbulence is used to designate the loss of order in many different geophysical fields and the related fundamental extreme variability of environmental data over a wide range of scales. Classical statistical techniques for estimating the extremes, being largely limited to statistical distributions, do not take into account the mechanisms generating such extreme variability. An alternative approaches to nonlinear variability are based on a fundamental property of the non-linear equations: scale invariance, which means that these equations are formally invariant under given scale transforms. Its specific framework is that of multifractals. In this framework extreme variability builds up scale by scale leading to non-classical statistics. Although multifractals are increasingly understood as a basic framework for handling such variability, there is still a gap between their potential and their actual use. In this presentation we discuss how to dealt with highly theoretical problems of mathematical physics together with a wide range of geophysical applications. We use Euler's gyroscope equation as a basic element in constructing a complex deterministic system that preserves not only the scale symmetry of the Navier-Stokes equations, but some more of their symmetries. Euler's equation has been not only the object of many theoretical investigations of the gyroscope device, but also generalised enough to become the basic equation of fluid mechanics. Therefore, there is no surprise that a cascade generalisation of this equation can be used to characterise the intermittency of turbulence, to better understand the links between the multifractal exponents and the structure of a simplified, but not simplistic, version of the Navier-Stokes equations. In a given way, this approach is similar to that of Lorenz, who studied how the flap of a butterfly wing could generate a cyclone with the help of a 3D ordinary differential system. Being well supported by the extensive numerical results, the cascade generalisation of Euler's gyroscope equation opens new horizons for predictability and predictions of processes having long-range dependences.
Numerical Limitations of 1D Hydraulic Models Using MIKE11 or HEC-RAS software - Case study of Baraolt River, Romania

NASA Astrophysics Data System (ADS)

Andrei, Armas; Robert, Beilicci; Erika, Beilicci

2017-10-01

MIKE 11 is an advanced hydroinformatic tool, a professional engineering software package for simulation of one-dimensional flows in estuaries, rivers, irrigation systems, channels and other water bodies. MIKE 11 is a 1-dimensional river model. It was developed by DHI Water · Environment · Health, Denmark. The basic computational procedure of HEC-RAS for steady flow is based on the solution of the one-dimensional energy equation. Energy losses are evaluated by friction and contraction / expansion. The momentum equation may be used in situations where the water surface profile is rapidly varied. These situations include hydraulic jumps, hydraulics of bridges, and evaluating profiles at river confluences. For unsteady flow, HEC-RAS solves the full, dynamic, 1-D Saint Venant Equation using an implicit, finite difference method. The unsteady flow equation solver was adapted from Dr. Robert L. Barkau’s UNET package. Fluid motion is controlled by the basic principles of conservation of mass, energy and momentum, which form the basis of fluid mechanics and hydraulic engineering. Complex flow situations must be solved using empirical approximations and numerical models, which are based on derivations of the basic principles (backwater equation, Navier-Stokes equation etc.). All numerical models are required to make some form of approximation to solve these principles, and consequently all have their limitations. The study of hydraulics and fluid mechanics is founded on the three basic principles of conservation of mass, energy and momentum. Real-life situations are frequently too complex to solve without the aid of numerical models. There is a tendency among some engineers to discard the basic principles taught at university and blindly assume that the results produced by the model are correct. Regardless of the complexity of models and despite the claims of their developers, all numerical models are required to make approximations. These may be related to geometric limitations, numerical simplification, or the use of empirical correlations. Some are obvious: one-dimensional models must average properties over the two remaining directions. It is the less obvious and poorly advertised approximations that pose the greatest threat to the novice user. Some of these, such as the inability of one-dimensional unsteady models to simulate supercritical flow can cause significant inaccuracy in the model predictions.
CRPropa 3.1—a low energy extension based on stochastic differential equations

NASA Astrophysics Data System (ADS)

Merten, Lukas; Becker Tjus, Julia; Fichtner, Horst; Eichmann, Björn; Sigl, Günter

2017-06-01

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ∥ and perpendicular κ⊥ diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.
Thermophoresis of a spherical particle: Modeling through moment-based, macroscopic transport equations

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Sprittles, James; Lockerby, Duncan

2017-11-01

Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).
Particle Acceleration and Fractional Transport in Turbulent Reconnection

NASA Astrophysics Data System (ADS)

Isliker, Heinz; Pisokas, Theophilos; Vlahos, Loukas; Anastasiadis, Anastasios

2017-11-01

We consider a large-scale environment of turbulent reconnection that is fragmented into a number of randomly distributed unstable current sheets (UCSs), and we statistically analyze the acceleration of particles within this environment. We address two important cases of acceleration mechanisms when particles interact with the UCS: (a) electric field acceleration and (b) acceleration by reflection at contracting islands. Electrons and ions are accelerated very efficiently, attaining an energy distribution of power-law shape with an index 1-2, depending on the acceleration mechanism. The transport coefficients in energy space are estimated from test-particle simulation data, and we show that the classical Fokker-Planck (FP) equation fails to reproduce the simulation results when the transport coefficients are inserted into it and it is solved numerically. The cause for this failure is that the particles perform Levy flights in energy space, while the distributions of the energy increments exhibit power-law tails. We then use the fractional transport equation (FTE) derived by Isliker et al., whose parameters and the order of the fractional derivatives are inferred from the simulation data, and solving the FTE numerically, we show that the FTE successfully reproduces the kinetic energy distribution of the test particles. We discuss in detail the analysis of the simulation data and the criteria that allow one to judge the appropriateness of either an FTE or a classical FP equation as a transport model.
Particle Acceleration and Fractional Transport in Turbulent Reconnection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Isliker, Heinz; Pisokas, Theophilos; Vlahos, Loukas

We consider a large-scale environment of turbulent reconnection that is fragmented into a number of randomly distributed unstable current sheets (UCSs), and we statistically analyze the acceleration of particles within this environment. We address two important cases of acceleration mechanisms when particles interact with the UCS: (a) electric field acceleration and (b) acceleration by reflection at contracting islands. Electrons and ions are accelerated very efficiently, attaining an energy distribution of power-law shape with an index 1–2, depending on the acceleration mechanism. The transport coefficients in energy space are estimated from test-particle simulation data, and we show that the classical Fokker–Planckmore » (FP) equation fails to reproduce the simulation results when the transport coefficients are inserted into it and it is solved numerically. The cause for this failure is that the particles perform Levy flights in energy space, while the distributions of the energy increments exhibit power-law tails. We then use the fractional transport equation (FTE) derived by Isliker et al., whose parameters and the order of the fractional derivatives are inferred from the simulation data, and solving the FTE numerically, we show that the FTE successfully reproduces the kinetic energy distribution of the test particles. We discuss in detail the analysis of the simulation data and the criteria that allow one to judge the appropriateness of either an FTE or a classical FP equation as a transport model.« less
Estimation of CT-Derived Abdominal Visceral and Subcutaneous Adipose Tissue Depots from Anthropometry in Europeans, South Asians and African Caribbeans

PubMed Central

Eastwood, Sophie V.; Tillin, Therese; Wright, Andrew; Heasman, John; Willis, Joseph; Godsland, Ian F.; Forouhi, Nita; Whincup, Peter; Hughes, Alun D.; Chaturvedi, Nishi

2013-01-01

Background South Asians and African Caribbeans experience more cardiometabolic disease than Europeans. Risk factors include visceral (VAT) and subcutaneous abdominal (SAT) adipose tissue, which vary with ethnicity and are difficult to quantify using anthropometry. Objective We developed and cross-validated ethnicity and gender-specific equations using anthropometrics to predict VAT and SAT. Design 669 Europeans, 514 South Asians and 227 African Caribbeans (70±7 years) underwent anthropometric measurement and abdominal CT scanning. South Asian and African Caribbean participants were first-generation migrants living in London. Prediction equations were derived for CT-measured VAT and SAT using stepwise regression, then cross-validated by comparing actual and predicted means. Results South Asians had more and African Caribbeans less VAT than Europeans. For basic VAT prediction equations (age and waist circumference), model fit was better in men (R2 range 0.59-0.71) than women (range 0.35-0.59). Expanded equations (+ weight, height, hip and thigh circumference) improved fit for South Asian and African Caribbean women (R2 0.35 to 0.55, and 0.43 to 0.56 respectively). For basic SAT equations, R2 was 0.69-0.77, and for expanded equations it was 0.72-0.86. Cross-validation showed differences between actual and estimated VAT of <7%, and SAT of <8% in all groups, apart from VAT in South Asian women which disagreed by 16%. Conclusion We provide ethnicity- and gender-specific VAT and SAT prediction equations, derived from a large tri-ethnic sample. Model fit was reasonable for SAT and VAT in men, while basic VAT models should be used cautiously in South Asian and African Caribbean women. These equations will aid studies of mechanisms of cardiometabolic disease in later life, where imaging data are not available. PMID:24069381
Big Bang Day: 5 Particles - 2. The Quark

ScienceCinema

None

2017-12-09

Simon Singh looks at the stories behind the discovery of 5 of the universe's most significant subatomic particles: the Electron, the Quark, the Anti-particle, the Neutrino and the "next particle". 2. The Quark "Three Quarks for Master Mark! Sure he hasn't got much of a bark." James Joyce's Finnegans Wake left its mark on modern physics when physicist Murray Gell Mann proposed this name for a group of hypothetical subatomic particles that were revealed in 1960 as the fundamental units of matter. Basic particles it seems are made up of even more basic units called quarks that make up 99.9% of visible material in the universe.. But why do we know so little about them? Quarks have never been seen as free particles but instead, inextricably bound together by the Strong Force that in turn holds the atomic nucleus together. This is the hardest of Nature's fundamental forces to crack, but recent theoretical advances, mean that the properties of the quark are at last being revealed.
Lock and Key Colloids through Polymerization-Induced Buckling of Monodispersed Silicon Oil Droplets

NASA Astrophysics Data System (ADS)

Sacanna, Stefano; Irvine, William T. M.; Chaikin, Paul M.; Pine, David J.

2010-03-01

Colloidal particles can spontaneously associate into larger structured aggregates when driven by selective and directional interactions. Colloidal organization can be programmed by engineering shapes and interactions of basic building blocks in a manner similar to molecular self-assembly. Examples of successful strategies that allow non-trivial assembly of particles include template-directed patterning, capillary forces and, most commonly, the functionalization of the particle surfaces with ``sticky patches'' of biological or synthetic molecules. The level of complexity of the realizable assemblies, increases when particles with well defined shape anisotropies are used. In particular depletion forces and specific surface treatments in combination with non spherical particles have proven to be powerful tools to self-assembly complex microstructures. We describe a simple, high yield, synthetic pathway to fabricate monodisperse hybrid silica spheres with well defined cavities. Because the particle morphologies are reproducible and tunable with precision, the resulting particles can be used as basic building blocks in the assembly of larger monodisperse clusters. This is demonstrated using depletion to drive the self-assembly.
Big Bang Day: 5 Particles - 2. The Quark

DOE Office of Scientific and Technical Information (OSTI.GOV)

None

2009-10-07

Simon Singh looks at the stories behind the discovery of 5 of the universe's most significant subatomic particles: the Electron, the Quark, the Anti-particle, the Neutrino and the "next particle". 2. The Quark "Three Quarks for Master Mark! Sure he hasn't got much of a bark." James Joyce's Finnegans Wake left its mark on modern physics when physicist Murray Gell Mann proposed this name for a group of hypothetical subatomic particles that were revealed in 1960 as the fundamental units of matter. Basic particles it seems are made up of even more basic units called quarks that make up 99.9%more » of visible material in the universe.. But why do we know so little about them? Quarks have never been seen as free particles but instead, inextricably bound together by the Strong Force that in turn holds the atomic nucleus together. This is the hardest of Nature's fundamental forces to crack, but recent theoretical advances, mean that the properties of the quark are at last being revealed.« less
Nonequilibrium flows with smooth particle applied mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kum, Oyeon

1995-07-01

Smooth particle methods are relatively new methods for simulating solid and fluid flows through they have a 20-year history of solving complex hydrodynamic problems in astrophysics, such as colliding planets and stars, for which correct answers are unknown. The results presented in this thesis evaluate the adaptability or fitness of the method for typical hydrocode production problems. For finite hydrodynamic systems, boundary conditions are important. A reflective boundary condition with image particles is a good way to prevent a density anomaly at the boundary and to keep the fluxes continuous there. Boundary values of temperature and velocity can be separatelymore » controlled. The gradient algorithm, based on differentiating the smooth particle expression for (uρ) and (Tρ), does not show numerical instabilities for the stress tensor and heat flux vector quantities which require second derivatives in space when Fourier`s heat-flow law and Newton`s viscous force law are used. Smooth particle methods show an interesting parallel linking to them to molecular dynamics. For the inviscid Euler equation, with an isentropic ideal gas equation of state, the smooth particle algorithm generates trajectories isomorphic to those generated by molecular dynamics. The shear moduli were evaluated based on molecular dynamics calculations for the three weighting functions, B spline, Lucy, and Cusp functions. The accuracy and applicability of the methods were estimated by comparing a set of smooth particle Rayleigh-Benard problems, all in the laminar regime, to corresponding highly-accurate grid-based numerical solutions of continuum equations. Both transient and stationary smooth particle solutions reproduce the grid-based data with velocity errors on the order of 5%. The smooth particle method still provides robust solutions at high Rayleigh number where grid-based methods fails.« less
A Modification and Analysis of Lagrangian Trajectory Modeling and Granular Dynamics of Lunar Dust Particles

NASA Technical Reports Server (NTRS)

Long, Jason M.; Lane, John E.; Metzger, Philip T.

2008-01-01

A previously developed mathematical model is amended to more accurately incorporate the effects of lift and drag on single dust particles in order to predict their behavior in the wake of high velocity gas flow. The model utilizes output from a CFD or DSMC simulation of exhaust from a rocket nozzle hot gas jet. An extension of the Saffman equation for lift based on the research of McLaughlin (1991) and Mei (1992) is used, while an equation for the Magnus force modeled after the work of Oesterle (1994) and Tsuji et al (1985) is applied. A relationship for drag utilizing a particle shape factor (phi = 0.8) is taken from the work of Haider and Levenspiel (1989) for application to non-spherical particle dynamics. The drag equation is further adjusted to account for rarefaction and compressibility effects in rarefied and high Mach number flows according to the work of Davies (1945) and Loth (2007) respectively. Simulations using a more accurate model with the correction factor (Epsilon = 0.8 in a 20% particle concentration gas flow) given by Richardson and Zaki (1954) and Rowe (1961) show that particles have lower ejection angles than those that were previously calculated. This is more prevalent in smaller particles, which are shown through velocity and trajectory comparison to be more influenced by the flow of the surrounding gas. It is shown that particles are more affected by minor changes to drag forces than larger adjustments to lift forces, demanding a closer analysis of the shape and behavior of lunar dust particles and the composition of the surrounding gas flow.

A Variational Formulation of Macro-Particle Algorithms for Kinetic Plasma Simulations

NASA Astrophysics Data System (ADS)

Shadwick, B. A.

2013-10-01

Macro-particle based simulations methods are in widespread use in plasma physics; their computational efficiency and intuitive nature are largely responsible for their longevity. In the main, these algorithms are formulated by approximating the continuous equations of motion. For systems governed by a variational principle (such as collisionless plasmas), approximations of the equations of motion is known to introduce anomalous behavior, especially in system invariants. We present a variational formulation of particle algorithms for plasma simulation based on a reduction of the distribution function onto a finite collection of macro-particles. As in the usual Particle-In-Cell (PIC) formulation, these macro-particles have a definite momentum and are spatially extended. The primary advantage of this approach is the preservation of the link between symmetries and conservation laws. For example, nothing in the reduction introduces explicit time dependence to the system and, therefore, the continuous-time equations of motion exactly conserve energy; thus, these models are free of grid-heating. In addition, the variational formulation allows for constructing models of arbitrary spatial and temporal order. In contrast, the overall accuracy of the usual PIC algorithm is at most second due to the nature of the force interpolation between the gridded field quantities and the (continuous) particle position. Again in contrast to the usual PIC algorithm, here the macro-particle shape is arbitrary; the spatial extent is completely decoupled from both the grid-size and the ``smoothness'' of the shape; smoother particle shapes are not necessarily larger. For simplicity, we restrict our discussion to one-dimensional, non-relativistic, un-magnetized, electrostatic plasmas. We comment on the extension to the electromagnetic case. Supported by the US DoE under contract numbers DE-FG02-08ER55000 and DE-SC0008382.
Simplified Relativistic Force Transformation Equation.

ERIC Educational Resources Information Center

Stewart, Benjamin U.

1979-01-01

A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic forces on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and relate it to Coulomb's law.…
On the acceleration of charged particles at relativistic shock fronts

NASA Technical Reports Server (NTRS)

Kirk, J. G.; Schneider, P.

1987-01-01

The diffusive acceleration of highly relativistic particles at a shock is reconsidered. Using the same physical assumptions as Blandford and Ostriker (1978), but dropping the restriction to nonrelativistic shock velocities, the authors find approximate solutions of the particle kinetic equation by generalizing the diffusion approximation to higher order terms in the anisotropy of the particle distribution. The general solution of the transport equation on either side of the shock is constructed, which involves the solution of an eigenvalue problem. By matching the two solutions at the shock, the spectral index of the resulting power law is found by taking into account a sufficiently large number of eigenfunctions. Low-order truncation corresponds to the standard diffusion approximation and to a somewhat more general method described by Peacock (1981). In addition to the energy spectrum, the method yields the angular distribution of the particles and its spatial dependence.
Large-displacement statistics of the rightmost particle of the one-dimensional branching Brownian motion.

PubMed

Derrida, Bernard; Meerson, Baruch; Sasorov, Pavel V

2016-04-01

Consider a one-dimensional branching Brownian motion and rescale the coordinate and time so that the rates of branching and diffusion are both equal to 1. If X_{1}(t) is the position of the rightmost particle of the branching Brownian motion at time t, the empirical velocity c of this rightmost particle is defined as c=X_{1}(t)/t. Using the Fisher-Kolmogorov-Petrovsky-Piscounov equation, we evaluate the probability distribution P(c,t) of this empirical velocity c in the long-time t limit for c>2. It is already known that, for a single seed particle, P(c,t)∼exp[-(c^{2}/4-1)t] up to a prefactor that can depend on c and t. Here we show how to determine this prefactor. The result can be easily generalized to the case of multiple seed particles and to branching random walks associated with other traveling-wave equations.
Creation of vector bosons by an electric field in curved spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kangal, E. Ersin; Yanar, Hilmi; Havare, Ali

2014-04-15

We investigate the creation rate of massive spin-1 bosons in the de Sitter universe by a time-dependent electric field via the Duffin–Kemmer–Petiau (DKP) equation. Complete solutions are given by the Whittaker functions and particle creation rate is computed by using the Bogoliubov transformation technique. We analyze the influence of the electric field on the particle creation rate for the strong and vanishing electric fields. We show that the electric field amplifies the creation rate of charged, massive spin-1 particles. This effect is analyzed by considering similar calculations performed for scalar and spin-1/2 particles. -- Highlights: •Duffin–Kemmer–Petiau equation is solved exactlymore » in the presence of an electrical field. •Solutions were made in (1+1)-dimensional curved spacetime. •Particle creation rate for the de Sitter model is calculated. •Pure gravitational or pure electrical field effect on the creation rate is analyzed.« less
A 2D electrostatic PIC code for the Mark III Hypercube

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferraro, R.D.; Liewer, P.C.; Decyk, V.K.

We have implemented a 2D electrostastic plasma particle in cell (PIC) simulation code on the Caltech/JPL Mark IIIfp Hypercube. The code simulates plasma effects by evolving in time the trajectories of thousands to millions of charged particles subject to their self-consistent fields. Each particle`s position and velocity is advanced in time using a leap frog method for integrating Newton`s equations of motion in electric and magnetic fields. The electric field due to these moving charged particles is calculated on a spatial grid at each time by solving Poisson`s equation in Fourier space. These two tasks represent the largest part ofmore » the computation. To obtain efficient operation on a distributed memory parallel computer, we are using the General Concurrent PIC (GCPIC) algorithm previously developed for a 1D parallel PIC code.« less
The role of particle collisions in pneumatic transport

NASA Technical Reports Server (NTRS)

Mastorakos, E.; Louge, M.; Jenkins, J. T.

1989-01-01

A model of dilute gas-solid flow in vertical risers is developed in which the particle phase is treated as a granular material, the balance equations for rapid granular flow are modified to incorporate the drag force from the gas, and boundary conditions, based on collisional exchanges of momentum and energy at the wall, are employed. In this model, it is assumed that the particle fluctuations are determined by inter-particle collisions only and that the turbulence of the gas is unaffected by the presence of the particles. The model is developed in the context of, but not limited to, steady, fully developed flow. A numerical solution of the resulting governing equations provides concentration profiles generally observed in dilute pneumatic flow, velocity profiles in good agreement with the measurements of Tsuji, et al. (1984), and an explanation for the enhancement of turbulence that they observed.
LAMMPS integrated materials engine (LIME) for efficient automation of particle-based simulations: application to equation of state generation

NASA Astrophysics Data System (ADS)

Barnes, Brian C.; Leiter, Kenneth W.; Becker, Richard; Knap, Jaroslaw; Brennan, John K.

2017-07-01

We describe the development, accuracy, and efficiency of an automation package for molecular simulation, the large-scale atomic/molecular massively parallel simulator (LAMMPS) integrated materials engine (LIME). Heuristics and algorithms employed for equation of state (EOS) calculation using a particle-based model of a molecular crystal, hexahydro-1,3,5-trinitro-s-triazine (RDX), are described in detail. The simulation method for the particle-based model is energy-conserving dissipative particle dynamics, but the techniques used in LIME are generally applicable to molecular dynamics simulations with a variety of particle-based models. The newly created tool set is tested through use of its EOS data in plate impact and Taylor anvil impact continuum simulations of solid RDX. The coarse-grain model results from LIME provide an approach to bridge the scales from atomistic simulations to continuum simulations.
Semiannual Report October 1, 1999 through March 31, 2000

DTIC Science & Technology

2000-04-01

Mark Carpenter (NASA Langley). Textbook Multigrid Efficiency for the Navier-Stokes Equations Boris Diskin A typical modern Reynolds-Averaged...defined as textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work...basic elements of the barriers to be overcome in extending textbook efficiencies to the compressible RANS equations, namely entering flows, far wake
Celestial dynamics and astrometry in expanding universe

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei

2012-08-01

Post - Newtonian theory of motion of celestial bodies and propagation of light was instrumental in conducting the critical experimental tests of general relativity and in building the astronomical ephemerides of celestial bodies in the solar system with an unparalleled precision. The cornerstone of the theory is the postulate that the solar system is gravitationally isolated from the rest of the universe and the background spacetime is asymptotically flat. The present talk abolishes this postulate and lays down the principles of celestial dynamics of particles and light moving in gravitational field of a localized astronomical system embedded to the expanding universe. We formulate the precise mathematical concept of the Newtonian limit of Einstein ’s field equations in the conformally - flat spacetime and analyse the geodesic equations of motion o f particles and light in this limit. We demonstrate that the equations of motion of particles and light can be reduced to their Newtonian counterparts by doing conformal transformations of time and space coordinates. However, the Newtonian equations for particles and light differ by terms of the first order in the Hubble constant. This leads to the important conclusion that the equations of motion used currently by Space Navigation Centres and Astronomical Observatories for calculating orbits of celestial bodies, are incomplete and missing some terms of cosmological origin. We explicitly identify the missing terms and demonstrate that they bring about a noticeable discrepancy between the observed and calculated astronomical ephemerides. We argue that a number of observed celestial anomalies in the solar system can be explained as caused by the Hubble expansion of the universe.
Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

NASA Astrophysics Data System (ADS)

Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2018-05-01

The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.
Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

PubMed

Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O

2014-11-01

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.
Charged particle periodicity in the Saturnian magnetosphere

NASA Technical Reports Server (NTRS)

Carbary, J. F.; Krimigis, S. M.

1982-01-01

The present investigation is concerned with the first definitive evidence for charged particle modulations near the magnetic rotation period at Saturn. This periodicity is apparent in the ratios (and spectra) of low energy charged particles in the Saturnian magnetosphere. Most of the data presented were taken during the Voyager 2 outbound portion of the Saturn encounter. During this time the spacecraft was at high latitudes (approximately 30 deg) in the southern hemisphere of the Saturnian magnetosphere. The probe's trajectory was approximately along the dawn meridian at an essentially constant local time. The observation that the charged particle modulation is consistent with the Saturn Kilometric Radiation (SKR) period provides a basic input for the resolution of a puzzle which has existed ever since the discovery of the SKR modulation. The charged particle periodicity identified suggests that a basic asymmetry must exist in the Saturnian magnetosphere.
Computation techniques and computer programs to analyze Stirling cycle engines using characteristic dynamic energy equations

NASA Technical Reports Server (NTRS)

Larson, V. H.

1982-01-01

The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.
Brownian motion of a particle with arbitrary shape.

PubMed

Cichocki, Bogdan; Ekiel-Jeżewska, Maria L; Wajnryb, Eligiusz

2015-06-07

Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the Smoluchowski equation. The role of the particle mobility center is determined and discussed.
Charged particle capturing in air flow by linear Paul trap

NASA Astrophysics Data System (ADS)

Lapitsky, D. S.; Filinov, V. S.; Vladimirov, V. I.; Syrovatka, R. A.; Vasilyak, L. M.; Pecherkin, V. Ya; Deputatova, L. V.

2018-01-01

The paper presents the simulation results of micro- and nanoparticle capturing in an air flows by linear Paul traps in assumption that particles gain their charges in corona discharge, its electric field strength is restricted by Paschen equation and spherical shape of particles.
A new method to calculate unsteady particle kinematics and drag coefficient in a subsonic post-shock flow

NASA Astrophysics Data System (ADS)

Bordoloi, Ankur D.; Ding, Liuyang; Martinez, Adam A.; Prestridge, Katherine; Adrian, Ronald J.

2018-07-01

We introduce a new method (piecewise integrated dynamics equation fit, PIDEF) that uses the particle dynamics equation to determine unsteady kinematics and drag coefficient (C D) for a particle in subsonic post-shock flow. The uncertainty of this method is assessed based on simulated trajectories for both quasi-steady and unsteady flow conditions. Traditional piecewise polynomial fitting (PPF) shows high sensitivity to measurement error and the function used to describe C D, creating high levels of relative error (1) when applied to unsteady shock-accelerated flows. The PIDEF method provides reduced uncertainty in calculations of unsteady acceleration and drag coefficient for both quasi-steady and unsteady flows. This makes PIDEF a preferable method over PPF for complex flows where the temporal response of C D is unknown. We apply PIDEF to experimental measurements of particle trajectories from 8-pulse particle tracking and determine the effect of incident Mach number on relaxation kinematics and drag coefficient of micron-sized particles.
Study of discrete-particle effects in a one-dimensional plasma simulation with the Krook type collision model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lai, Po-Yen; Chen, Liu; Institute for Fusion Theory and Simulation, Zhejiang University, 310027 Hangzhou

2015-09-15

The thermal relaxation time of a one-dimensional plasma has been demonstrated to scale with N{sub D}{sup 2} due to discrete particle effects by collisionless particle-in-cell (PIC) simulations, where N{sub D} is the particle number in a Debye length. The N{sub D}{sup 2} scaling is consistent with the theoretical analysis based on the Balescu-Lenard-Landau kinetic equation. However, it was found that the thermal relaxation time is anomalously shortened to scale with N{sub D} while externally introducing the Krook type collision model in the one-dimensional electrostatic PIC simulation. In order to understand the discrete particle effects enhanced by the Krook type collisionmore » model, the superposition principle of dressed test particles was applied to derive the modified Balescu-Lenard-Landau kinetic equation. The theoretical results are shown to be in good agreement with the simulation results when the collisional effects dominate the plasma system.« less
Numerical simulation of hemorrhage in human injury

NASA Astrophysics Data System (ADS)

Chong, Kwitae; Jiang, Chenfanfu; Santhanam, Anand; Benharash, Peyman; Teran, Joseph; Eldredge, Jeff

2015-11-01

Smoothed Particle Hydrodynamics (SPH) is adapted to simulate hemorrhage in the injured human body. As a Lagrangian fluid simulation, SPH uses fluid particles as computational elements and thus mass conservation is trivially satisfied. In order to ensure anatomical fidelity, a three-dimensional reconstruction of a portion of the human body -here, demonstrated on the lower leg- is sampled as skin, bone and internal tissue particles from the CT scan image of an actual patient. The injured geometry is then generated by simulation of ballistic projectiles passing through the anatomical model with the Material Point Method (MPM) and injured vessel segments are identified. From each such injured segment, SPH is used to simulate bleeding, with inflow boundary condition obtained from a coupled 1-d vascular tree model. Blood particles interact with impermeable bone and skin particles through the Navier-Stokes equations and with permeable internal tissue particles through the Brinkman equations. The SPH results are rendered in post-processing for improved visual fidelity. The overall simulation strategy is demonstrated on several injury scenarios in the lower leg.
Transport of reacting solutes in porous media: Relation between mathematical nature of problem formulation and chemical nature of reactions

USGS Publications Warehouse

Rubin, Jacob

1983-01-01

Examples involving six broad reaction classes show that the nature of transport-affecting chemistry may have a profound effect on the mathematical character of solute transport problem formulation. Substantive mathematical diversity among such formulations is brought about principally by reaction properties that determine whether (1) the reaction can be regarded as being controlled by local chemical equilibria or whether it must be considered as being controlled by kinetics, (2) the reaction is homogeneous or heterogeneous, (3) the reaction is a surface reaction (adsorption, ion exchange) or one of the reactions of classical chemistry (e.g., precipitation, dissolution, oxidation, reduction, complex formation). These properties, as well as the choice of means to describe them, stipulate, for instance, (1) the type of chemical entities for which a formulation's basic, mass-balance equations should be written; (2) the nature of mathematical transformations needed to change the problem's basic equations into operational ones. These and other influences determine such mathematical features of problem formulations as the nature of the operational transport-equation system (e.g., whether it involves algebraic, partial-differential, or integro-partial-differential simultaneous equations), the type of nonlinearities of such a system, and the character of the boundaries (e.g., whether they are stationary or moving). Exploration of the reasons for the dependence of transport mathematics on transport chemistry suggests that many results of this dependence stem from the basic properties of the reactions' chemical-relation (i.e., equilibrium or rate) equations.

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