Particle Size Influence on the Effective Permeability of Composite Materials

NASA Astrophysics Data System (ADS)

Xiang, Tai; Zhong, Ru-Neng; Yao, Bin; Qin, Shao-Jing; Zheng, Qin-Hong

2018-05-01

The energy method, which estimates the effective permeability of composite material is proposed. We approximate the effective static magnetic permeability by energy method and Maxwell-Garnett method for spherical particles dispersing system. Considering the effect of the interface layer between the medium and the particle, we study the nanoparticles embedded in a medium exactly. The interface layer property plays a significant factor for the effective permeability of the composite material in which nano-sized particles embedded. Supported by National Natural Science Foundation of Yunnan province under Grant No. 2014FB141 and National Natural Science Foundation under Grant No. 1121403 of China

Light Scattering by Wavelength-Sized Particles "Dusted" with Subwavelength-Sized Grains

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.

2011-01-01

The numerically exact superposition T-matrix method is used to compute the scattering cross sections and the Stokes scattering matrix for polydisperse spherical particles covered with a large number of much smaller grains. We show that the optical effect of the presence of microscopic dust on the surfaces of wavelength-sized, weakly absorbing particles is much less significant than that of a major overall asphericity of the particle shape.

An exact and efficient first passage time algorithm for reaction-diffusion processes on a 2D-lattice

NASA Astrophysics Data System (ADS)

Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.

2014-01-01

We present an exact and efficient algorithm for reaction-diffusion-nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

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

Bezzola, Andri, E-mail: andri.bezzola@gmail.com; Bales, Benjamin B., E-mail: bbbales2@gmail.com; Alkire, Richard C., E-mail: r-alkire@uiuc.edu

2014-01-01

We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for largemore » ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.« less

Novel branching particle method for tracking

NASA Astrophysics Data System (ADS)

Ballantyne, David J.; Chan, Hubert Y.; Kouritzin, Michael A.

2000-07-01

Particle approximations are used to track a maneuvering signal given only a noisy, corrupted sequence of observations, as are encountered in target tracking and surveillance. The signal exhibits nonlinearities that preclude the optimal use of a Kalman filter. It obeys a stochastic differential equation (SDE) in a seven-dimensional state space, one dimension of which is a discrete maneuver type. The maneuver type switches as a Markov chain and each maneuver identifies a unique SDE for the propagation of the remaining six state parameters. Observations are constructed at discrete time intervals by projecting a polygon corresponding to the target state onto two dimensions and incorporating the noise. A new branching particle filter is introduced and compared with two existing particle filters. The filters simulate a large number of independent particles, each of which moves with the stochastic law of the target. Particles are weighted, redistributed, or branched, depending on the method of filtering, based on their accordance with the current observation from the sequence. Each filter provides an approximated probability distribution of the target state given all back observations. All three particle filters converge to the exact conditional distribution as the number of particles goes to infinity, but differ in how well they perform with a finite number of particles. Using the exactly known ground truth, the root-mean-squared (RMS) errors in target position of the estimated distributions from the three filters are compared. The relative tracking power of the filters is quantified for this target at varying sizes, particle counts, and levels of observation noise.

Coherent Backscattering by Polydisperse Discrete Random Media: Exact T-Matrix Results

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.

2011-01-01

The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.

Better Than Counting: Density Profiles from Force Sampling

NASA Astrophysics Data System (ADS)

de las Heras, Daniel; Schmidt, Matthias

2018-05-01

Calculating one-body density profiles in equilibrium via particle-based simulation methods involves counting of events of particle occurrences at (histogram-resolved) space points. Here, we investigate an alternative method based on a histogram of the local force density. Via an exact sum rule, the density profile is obtained with a simple spatial integration. The method circumvents the inherent ideal gas fluctuations. We have tested the method in Monte Carlo, Brownian dynamics, and molecular dynamics simulations. The results carry a statistical uncertainty smaller than that of the standard counting method, reducing therefore the computation time.

Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic.

PubMed

Francesco, Marco Di; Fagioli, Simone; Rosini, Massimiliano D

2017-02-01

We consider the follow-the-leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi population formulation. We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence of vacuum. The result is based on uniform BV estimates on the discrete particle velocity. We complement our result with numerical simulations of the particle method compared with some exact solutions to the Riemann problem of the ARZ system.

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.

Single scattering from nonspherical Chebyshev particles: A compendium of calculations

NASA Technical Reports Server (NTRS)

Wiscombe, W. J.; Mugnai, A.

1986-01-01

A large set of exact calculations of the scattering from a class of nonspherical particles known as Chebyshev particles' has been performed. Phase function and degree of polarization in random orientation, and parallel and perpendicular intensities in fixed orientations, are plotted for a variety of particles shapes and sizes. The intention is to furnish a data base against which both experimental data, and the predictions of approximate methods, can be tested. The calculations are performed with the widely-used Extended Boundary Condition Method. An extensive discussion of this method is given, including much material that is not easily available elsewhere (especially the analysis of its convergence properties). An extensive review is also given of all extant methods for nonspherical scattering calculations, as well as of the available pool of experimental data.

Lagrangian particle method for compressible fluid dynamics

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang

2018-06-01

A new 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) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic-elliptic systems. Numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.

Modified Hawking radiation in a BTZ black hole using Damour Ruffini method

NASA Astrophysics Data System (ADS)

He, Xiaokai; Liu, Wenbiao

2007-09-01

Considering energy conservation, angular momentum conservation, and the particles' back reaction to space-time, the scalar particles' Hawking radiation from a BTZ black hole was investigated using Damour-Ruffini method. The exact expression of the emission rate near the horizon is obtained and the result indicates that Hawking radiation spectrum is not purely thermal. The result obtained is consistent with the previous literatures. It is in agreement with an underlying unitary theory and offers a possible mechanism to explain the information loss paradox. Whereas, the method is more concise and understandable.

Excitation energies from particle-particle random phase approximation with accurate optimized effective potentials

NASA Astrophysics Data System (ADS)

Jin, Ye; Yang, Yang; Zhang, Du; Peng, Degao; Yang, Weitao

2017-10-01

The optimized effective potential (OEP) that gives accurate Kohn-Sham (KS) orbitals and orbital energies can be obtained from a given reference electron density. These OEP-KS orbitals and orbital energies are used here for calculating electronic excited states with the particle-particle random phase approximation (pp-RPA). Our calculations allow the examination of pp-RPA excitation energies with the exact KS density functional theory (DFT). Various input densities are investigated. Specifically, the excitation energies using the OEP with the electron densities from the coupled-cluster singles and doubles method display the lowest mean absolute error from the reference data for the low-lying excited states. This study probes into the theoretical limit of the pp-RPA excitation energies with the exact KS-DFT orbitals and orbital energies. We believe that higher-order correlation contributions beyond the pp-RPA bare Coulomb kernel are needed in order to achieve even higher accuracy in excitation energy calculations.

Molecular Excitation Energies from Time-Dependent Density Functional Theory Employing Random-Phase Approximation Hessians with Exact Exchange.

PubMed

Heßelmann, Andreas

2015-04-14

Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.

Exact Solutions of Burnt-Bridge Models for Molecular Motor Transport

NASA Astrophysics Data System (ADS)

Morozov, Alexander; Pronina, Ekaterina; Kolomeisky, Anatoly; Artyomov, Maxim

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called ``bridges''), is investigated theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (``burned'') with a probability p, creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For general case of p<1 a new theoretical method is developed, and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics, periodic and random distribution of bridges and different burning dynamics are analyzed and compared. Theoretical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

Dirac Particles' Hawking Radiation from a Schwarzschild Black Hole

NASA Astrophysics Data System (ADS)

He, Xiao-Kai; Liu, Wen-Biao

2007-08-01

Considering energy conservation and the backreaction of particles to spacetime, we investigate the massless/massive Dirac particles' Hawking radiation from a Schwarzschild black hole. The exact expression of the emission rate near the horizon is obtained and the result indicates that Hawking radiation spectrum is not purely thermal. The result obtained is consistent with the results obtained before. It satisfies the underlying unitary theory and offers a possible mechanism to explain the information loss paradox. Whereas the improved Damour-Ruffini method is more concise and understandable.

Particle swarm optimization - Genetic algorithm (PSOGA) on linear transportation problem

NASA Astrophysics Data System (ADS)

Rahmalia, Dinita

2017-08-01

Linear Transportation Problem (LTP) is the case of constrained optimization where we want to minimize cost subject to the balance of the number of supply and the number of demand. The exact method such as northwest corner, vogel, russel, minimal cost have been applied at approaching optimal solution. In this paper, we use heurisitic like Particle Swarm Optimization (PSO) for solving linear transportation problem at any size of decision variable. In addition, we combine mutation operator of Genetic Algorithm (GA) at PSO to improve optimal solution. This method is called Particle Swarm Optimization - Genetic Algorithm (PSOGA). The simulations show that PSOGA can improve optimal solution resulted by PSO.

The oncogenic transforming potential of the passage of single α particles through mammalian cell nuclei

PubMed Central

Miller, Richard C.; Randers-Pehrson, Gerhard; Geard, Charles R.; Hall, Eric J.; Brenner, David J.

1999-01-01

Domestic, low-level exposure to radon gas is considered a major environmental lung-cancer hazard involving DNA damage to bronchial cells by α particles from radon progeny. At domestic exposure levels, the relevant bronchial cells are very rarely traversed by more than one α particle, whereas at higher radon levels—at which epidemiological studies in uranium miners allow lung-cancer risks to be quantified with reasonable precision—these bronchial cells are frequently exposed to multiple α-particle traversals. Measuring the oncogenic transforming effects of exactly one α particle without the confounding effects of multiple traversals has hitherto been unfeasible, resulting in uncertainty in extrapolations of risk from high to domestic radon levels. A technique to assess the effects of single α particles uses a charged-particle microbeam, which irradiates individual cells or cell nuclei with predefined exact numbers of particles. Although previously too slow to assess the relevant small oncogenic risks, recent improvements in throughput now permit microbeam irradiation of large cell numbers, allowing the first oncogenic risk measurements for the traversal of exactly one α particle through a cell nucleus. Given positive controls to ensure that the dosimetry and biological controls were comparable, the measured oncogenicity from exactly one α particle was significantly lower than for a Poisson-distributed mean of one α particle, implying that cells traversed by multiple α particles contribute most of the risk. If this result applies generally, extrapolation from high-level radon risks (involving cellular traversal by multiple α particles) may overestimate low-level (involving only single α particles) radon risks. PMID:9874764

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

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.

Lagrangian particle method for compressible fluid dynamics

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

Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang

A new 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 / multi-phase 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) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremalmore » points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.« less

Lagrangian particle method for compressible fluid dynamics

DOE PAGES

Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang

2018-02-09

A new 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 / multi-phase 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) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremalmore » points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.« less

A Kernel-Free Particle-Finite Element Method for Hypervelocity Impact Simulation. Chapter 4

NASA Technical Reports Server (NTRS)

Park, Young-Keun; Fahrenthold, Eric P.

2004-01-01

An improved hybrid particle-finite element method has been developed for the simulation of hypervelocity impact problems. Unlike alternative methods, the revised formulation computes the density without reference to any kernel or interpolation functions, for either the density or the rate of dilatation. This simplifies the state space model and leads to a significant reduction in computational cost. The improved method introduces internal energy variables as generalized coordinates in a new formulation of the thermomechanical Lagrange equations. Example problems show good agreement with exact solutions in one dimension and good agreement with experimental data in a three dimensional simulation.

Exact Hybrid Particle/Population Simulation of Rule-Based Models of Biochemical Systems

PubMed Central

Stover, Lori J.; Nair, Niketh S.; Faeder, James R.

2014-01-01

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This “network-free” approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of “partial network expansion” into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility. PMID:24699269

Exact hybrid particle/population simulation of rule-based models of biochemical systems.

PubMed

Hogg, Justin S; Harris, Leonard A; Stover, Lori J; Nair, Niketh S; Faeder, James R

2014-04-01

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This "network-free" approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of "partial network expansion" into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.

Self-diffusion in a system of interacting Langevin particles

NASA Astrophysics Data System (ADS)

Dean, D. S.; Lefèvre, A.

2004-06-01

The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature β and the particle density ρ . The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small β and ρβ constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.

Tunneling method for Hawking radiation in the Nariai case

NASA Astrophysics Data System (ADS)

Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.

2017-08-01

We revisit the tunneling picture for the Hawking effect in light of the charged Nariai manifold, because this general relativistic solution, which displays two horizons, provides the bonus to allow the knowledge of exact solutions of the field equations. We first perform a revisitation of the tunneling ansatz in the framework of particle creation in external fields à la Nikishov, which corroborates the interpretation of the semiclassical emission rate Γ_{emission} as the conditional probability rate for the creation of a couple of particles from the vacuum. Then, particle creation associated with the Hawking effect on the Nariai manifold is calculated in two ways. On the one hand, we apply the Hamilton-Jacobi formalism for tunneling, in the case of a charged scalar field on the given background. On the other hand, the knowledge of the exact solutions for the Klein-Gordon equations on Nariai manifold, and their analytic properties on the extended manifold, allow us a direct computation of the flux of particles leaving the horizon, and, as a consequence, we obtain a further corroboration of the semiclassical tunneling picture from the side of S-matrix formalism.

Non-equilibrium steady-state distributions of colloids in a tilted periodic potential

NASA Astrophysics Data System (ADS)

Ma, Xiaoguang; Lai, Pik-Yin; Ackerson, Bruce; Tong, Penger

A two-layer colloidal system is constructed to study the effects of the external force F on the non-equilibrium steady-state (NESS) dynamics of the diffusing particles over a tilted periodic potential, in which detailed balance is broken due to the presence of a steady particle flux. The periodic potential is provided by the bottom layer colloidal spheres forming a fixed crystalline pattern on a glass substrate. The corrugated surface of the bottom colloidal crystal provides a gravitational potential field for the top layer diffusing particles. By tilting the sample with respect to gravity, a tangential component F is applied to the diffusing particles. The measured NESS probability density function Pss (x , y) of the particles is found to deviate from the equilibrium distribution depending on the driving or distance from equilibrium. The experimental results are compared with the exact solution of the 1D Smoluchowski equation and the numerical results of the 2D Smoluchowski equation. Moreover, from the obtained exact 1D solution, we develop an analytical method to accurately extract the 1D potential U0 (x) from the measured Pss (x) . Work supported in part by the Research Grants Council of Hong Kong SAR.

UV-VIS depolarization from Arizona Test Dust particles at exact backscattering angle

NASA Astrophysics Data System (ADS)

Miffre, Alain; Mehri, Tahar; Francis, Mirvatte; Rairoux, Patrick

2016-01-01

In this paper, a controlled laboratory experiment is performed to accurately evaluate the depolarization from mineral dust particles in the exact backward scattering direction (ϴ=180.0±0.2°). The experiment is carried out at two wavelengths simultaneously (λ=355 nm, λ=532 nm), on a determined size and shape distribution of Arizona Test Dust (ATD) particles, used as a proxy for mineral dust particles. After validating the set-up on spherical water droplets, two determined ATD-particle size distributions, representative of mineral dust after long-range transport, are generated to accurately retrieve the UV-VIS depolarization from ATD-particles at exact backscattering angle, which is new. The measured depolarization reaches at most 37.5% at λ=355 nm (35.5% at λ=532 nm), and depends on the particle size distribution. Moreover, these laboratory findings agree with T-matrix numerical simulations, at least for a determined particle size distribution and at a determined wavelength, showing the ability of the spheroidal model to reproduce mineral dust particles in the exact backward scattering direction. However, the spectral dependence of the measured depolarization could not be reproduced with the spheroidal model, even for not evenly distributed aspect ratios. Hence, these laboratory findings can be used to evaluate the applicability of the spheroidal model in the backward scattering direction and moreover, to invert UV-VIS polarization lidar returns, which is useful for radiative transfer and climatology, in which mineral dust particles are strongly involved.

Comprehensive T-Matrix Reference Database: A 2007-2009 Update

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Zakharova, Nadia T.; Videen, Gorden; Khlebtsov, Nikolai G.; Wriedt, Thomas

2010-01-01

The T-matrix method is among the most versatile, efficient, and widely used theoretical techniques for the numerically exact computation of electromagnetic scattering by homogeneous and composite particles, clusters of particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper presents an update to the comprehensive database of T-matrix publications compiled by us previously and includes the publications that appeared since 2007. It also lists several earlier publications not included in the original database.

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..

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.

Charged particle tracking through electrostatic wire meshes using the finite element method

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

Devlin, L. J.; Karamyshev, O.; Welsch, C. P., E-mail: carsten.welsch@cockcroft.ac.uk

Wire meshes are used across many disciplines to accelerate and focus charged particles, however, analytical solutions are non-exact and few codes exist which simulate the exact fields around a mesh with physical sizes. A tracking code based in Matlab-Simulink using field maps generated using finite element software has been developed which tracks electrons or ions through electrostatic wire meshes. The fields around such a geometry are presented as an analytical expression using several basic assumptions, however, it is apparent that computational calculations are required to obtain realistic values of electric potential and fields, particularly when multiple wire meshes are deployed.more » The tracking code is flexible in that any quantitatively describable particle distribution can be used for both electrons and ions as well as other benefits such as ease of export to other programs for analysis. The code is made freely available and physical examples are highlighted where this code could be beneficial for different applications.« less

Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares

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

Gurin, Péter; Varga, Szabolcs

2015-06-14

We extend the transfer matrix method of one-dimensional hard core fluids placed between confining walls for that case where the particles can pass each other and at most two layers can form. We derive an eigenvalue equation for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between σ and 3σ (σ is the side length of the square). The exact equation of state and the nearest neighbor distribution functions show three different structures: a fluid phase with one layer, a fluid phase with two layers, and a solid-like structure where the fluidmore » layers are strongly correlated. The structural transition between differently ordered fluids develops continuously with increasing density, i.e., no thermodynamic phase transition occurs. The high density structure of the system consists of clusters with two layers which are broken with particles staying in the middle of the pore.« less

Enriched reproducing kernel particle method for fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam

2018-06-01

The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

Does really Born Oppenheimer approximation break down in charge transfer processes? An exactly solvable model

NASA Astrophysics Data System (ADS)

Kuznetsov, Alexander M.; Medvedev, Igor G.

2006-05-01

Effects of deviation from the Born-Oppenheimer approximation (BOA) on the non-adiabatic transition probability for the transfer of a quantum particle in condensed media are studied within an exactly solvable model. The particle and the medium are modeled by a set of harmonic oscillators. The dynamic interaction of the particle with a single local mode is treated explicitly without the use of BOA. Two particular situations (symmetric and non-symmetric systems) are considered. It is shown that the difference between the exact solution and the true BOA is negligibly small at realistic parameters of the model. However, the exact results differ considerably from those of the crude Condon approximation (CCA) which is usually considered in the literature as a reference point for BOA (Marcus-Hush-Dogonadze formula). It is shown that the exact rate constant can be smaller (symmetric system) or larger (non-symmetric one) than that obtained in CCA. The non-Condon effects are also studied.

Optimised effective potential for ground states, excited states, and time-dependent phenomena

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

Gross, E.K.U.

1996-12-31

(1) The optimized effective potential method is a variant of the traditional Kohn-Sham scheme. In this variant, the exchange-correlation energy E{sub xc} is an explicit functional of single-particle orbitals. The exchange-correlation potential, given as usual by the functional derivative v{sub xc} = {delta}E{sub xc}/{delta}{rho}, then satisfies as integral equation involving the single-particle orbitals. This integral equation in solved semi-analytically using a scheme recently proposed by Krieger, Li and Iafrate. If the exact (Fock) exchange-energy functional is employed together with the Colle-Salvetti orbital functional for the correlation energy, the mean absolute deviation of the resulting ground-state energies from the exact nonrelativisticmore » values is CT mH for the first-row atoms, as compared to 4.5 mH in a state-of-the-art CI calculation. The proposed scheme is thus significantly more accurate than the conventional Kohn-Sham method while the numerical effort involved is about the same as for an ordinary Hanree-Fock calculation. (2) A time-dependent generalization of the optimized-potential method is presented and applied to the linear-response regime. Since time-dependent density functional theory leads to a formally exact representation of the frequency-dependent linear density response and since the latter, as a function of frequency, has poles at the excitation energies of the fully interacting system, the formalism is suitable for the calculation of excitation energies. A simple additive correction to the Kohn-Sham single-particle excitation energies will be deduced and first results for atomic and molecular singlet and triplet excitation energies will be presented. (3) Beyond the regime of linear response, the time-dependent optimized-potential method is employed to describe atoms in strong emtosecond laser pulses. Ionization yields and harmonic spectra will be presented and compared with experimental data.« less

Exact solution for spin precession in the radiationless relativistic Kepler problem

NASA Astrophysics Data System (ADS)

Mane, S. R.

2014-11-01

There is interest in circulating beams of polarized particles in all-electric storage rings to search for nonzero permanent electric dipole moments of subatomic particles. To this end, it is helpful to derive exact analytical solutions of the spin precession in idealized models, both for pedagogical reasons and to serve as benchmark tests for analysis and design of experiments. This paper derives exact solutions for the spin precession in the relativistic Kepler problem. Some counterintuitive properties of the solutions are pointed out.

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.

Geometrical-optics approximation of forward scattering by coated particles.

PubMed

Xu, Feng; Cai, Xiaoshu; Ren, Kuanfang

2004-03-20

By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 degrees-60 degrees) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10 degrees or so.

Linear Depolarization of Lidar Returns by Aged Smoke Particles

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Liu, Li

2016-01-01

We use the numerically exact (superposition) T-matrix method to analyze recent measurements of the backscattering linear depolarization ratio (LDR) for a plume of aged smoke at lidar wavelengths ranging from 355 to 1064 nm. We show that the unique spectral dependence of the measured LDRs can be modeled, but only by assuming expressly nonspherical morphologies of smoke particles containing substantial amounts of nonabsorbing (or weakly absorbing) refractory materials such as sulfates. Our results demonstrate that spectral backscattering LDR measurements can be indicative of the presence of morphologically complex smoke particles, but additional (e.g., passive polarimetric or bistatic lidar) measurements may be required for a definitive characterization of the particle morphology and composition.

Method of self-consistent evaluation of absolute emission probabilities of particles and gamma rays

NASA Astrophysics Data System (ADS)

Badikov, Sergei; Chechev, Valery

2017-09-01

In assumption of well installed decay scheme the method provides a) exact balance relationships, b) lower (compared to the traditional techniques) uncertainties of recommended absolute emission probabilities of particles and gamma rays, c) evaluation of correlations between the recommended emission probabilities (for the same and different decay modes). Application of the method for the decay data evaluation for even curium isotopes led to paradoxical results. The multidimensional confidence regions for the probabilities of the most intensive alpha transitions constructed on the basis of present and the ENDF/B-VII.1, JEFF-3.1, DDEP evaluations are inconsistent whereas the confidence intervals for the evaluated probabilities of single transitions agree with each other.

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

Garcia, Andres

Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems canmore » be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use Langevin Molecular Dynamics (MD) simulations to assess these parameters.« less

Effects of absorption on multiple scattering by random particulate media: exact results.

PubMed

Mishchenko, Michael I; Liu, Li; Hovenier, Joop W

2007-10-01

We employ the numerically exact superposition T-matrix method to perform extensive computations of elec nottromagnetic scattering by a volume of discrete random medium densely filled with increasingly absorbing as well as non-absorbing particles. Our numerical data demonstrate that increasing absorption diminishes and nearly extinguishes certain optical effects such as depolarization and coherent backscattering and increases the angular width of coherent backscattering patterns. This result corroborates the multiple-scattering origin of such effects and further demonstrates the heuristic value of the concept of multiple scattering even in application to densely packed particulate media.

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.

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

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

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra ismore » later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a rotating quadrupole field ion trap are presented. •Exact solutions for magneto-transport in variable electromagnetic fields are shown.« less

A new mathematical solution for predicting char activation reactions

USGS Publications Warehouse

Rafsanjani, H.H.; Jamshidi, E.; Rostam-Abadi, M.

2002-01-01

The differential conservation equations that describe typical gas-solid reactions, such as activation of coal chars, yield a set of coupled second-order partial differential equations. The solution of these coupled equations by exact analytical methods is impossible. In addition, an approximate or exact solution only provides predictions for either reaction- or diffusion-controlling cases. A new mathematical solution, the quantize method (QM), was applied to predict the gasification rates of coal char when both chemical reaction and diffusion through the porous char are present. Carbon conversion rates predicted by the QM were in closer agreement with the experimental data than those predicted by the random pore model and the simple particle model. ?? 2002 Elsevier Science Ltd. All rights reserved.

An Exactly Soluble Model for Hopping Particles Moving with Correlations Between States due to Exchange Sites

NASA Astrophysics Data System (ADS)

Zhao, Xian-Geng; Jia, Sue-Tang

1992-09-01

The motion of hopping particles on an infinite chain is investigated. The model is characterized by the correlations between states due to exchange sites. The analytic solutions for this system are discussed in general case. For some special cases, exact results are obtained with the help of explicit calculations of propagators and mean square displacement deviation. Both probability propagators for the creation and annihilation of two particles or for the deformation and formation of Frenkel excitons are indicated.

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2014-10-01

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen et al., 2011). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation to Maxwell's equations, which avoids radiative noise issues by ordering out the light wave. An implicit, orbit-averaged, time-space-centered finite difference scheme is employed in both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. We have developed a simple preconditioner that targets electrostatic waves and skin currents, and allows us to employ time steps O(√{mi /me } c /veT) larger than the explicit CFL. Several 1D numerical experiments demonstrate the accuracy, performance, and conservation properties of the algorithm. In particular, the scheme is shown to be second-order accurate, and CPU speedups of more than three orders of magnitude vs. an explicit Vlasov-Maxwell solver are demonstrated in the "cold" plasma regime (where kλD ≪ 1).

Studies of phosphatidylcholine vesicles by spectroturbidimetric and dynamic light scattering methods

NASA Astrophysics Data System (ADS)

Khlebtsov, B. N.; Kovler, L. A.; Bogatyrev, V. A.; Khlebtsov, N. G.; Shchyogolev, S. Yu.

2003-09-01

A spectroturbidimetric method for the determination of the average size and thickness of the shell in polydisperse suspensions of liposome particles is discussed. The method is based on measuring the wavelength exponent of a suspension (a slope of the logarithmic turbidity spectrum) and the specific turbidity (the turbidity per unit mass concentration of the dispersed substance). The inverse problem was solved using an exact calculation of characteristics of light scattering for polydisperse suspensions of spherical bilayer particles with allowance for the spectral dependence of optical constants. A practical realization of this method is illustrated by the experimental determinations of the structural parameters of liposomes prepared from egg lecithin. Comparison experiments to determine the liposome size by the dynamic (quasielastic) light scattering method were performed as an independent control.

Adhesion of Mineral and Soot Aerosols can Strongly Affect their Scattering and Absorption Properties

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Jana M.

2012-01-01

We use the numerically exact superposition T-matrix method to compute the optical cross sections and the Stokes scattering matrix for polydisperse mineral aerosols (modeled as homogeneous spheres) covered with a large number of much smaller soot particles. These results are compared with the Lorenz-Mie results for a uniform external mixture of mineral and soot aerosols. We show that the effect of soot particles adhering to large mineral particles can be to change the extinction and scattering cross sections and the asymmetry parameter quite substantially. The effect on the phase function and degree of linear polarization can be equally significant.

Towards an exact correlated orbital theory for electrons

NASA Astrophysics Data System (ADS)

Bartlett, Rodney J.

2009-12-01

The formal and computational attraction of effective one-particle theories like Hartree-Fock and density functional theory raise the question of how far such approaches can be taken to offer exact results for selected properties of electrons in atoms, molecules, and solids. Some properties can be exactly described within an effective one-particle theory, like principal ionization potentials and electron affinities. This fact can be used to develop equations for a correlated orbital theory (COT) that guarantees a correct one-particle energy spectrum. They are built upon a coupled-cluster based frequency independent self-energy operator presented here, which distinguishes the approach from Dyson theory. The COT also offers an alternative to Kohn-Sham density functional theory (DFT), whose objective is to represent the electronic density exactly as a single determinant, while paying less attention to the energy spectrum. For any estimate of two-electron terms COT offers a litmus test of its accuracy for principal Ip's and Ea's. This feature for approximating the COT equations is illustrated numerically.

Computational wave dynamics for innovative design of coastal structures

PubMed Central

GOTOH, Hitoshi; OKAYASU, Akio

2017-01-01

For innovative designs of coastal structures, Numerical Wave Flumes (NWFs), which are solvers of Navier-Stokes equation for free-surface flows, are key tools. In this article, various methods and techniques for NWFs are overviewed. In the former half, key techniques of NWFs, namely the interface capturing (MAC, VOF, C-CUP) and significance of NWFs in comparison with the conventional wave models are described. In the latter part of this article, recent improvements of the particle method are shown as one of cores of NWFs. Methods for attenuating unphysical pressure fluctuation and improving accuracy, such as CMPS method for momentum conservation, Higher-order Source of Poisson Pressure Equation (PPE), Higher-order Laplacian, Error-Compensating Source in PPE, and Gradient Correction for ensuring Taylor-series consistency, are reviewed briefly. Finally, the latest new frontier of the accurate particle method, including Dynamic Stabilization for providing minimum-required artificial repulsive force to improve stability of computation, and Space Potential Particle for describing the exact free-surface boundary condition, is described. PMID:29021506

Fast calculation of the light differential scattering cross section of optically soft and convex bodies

NASA Astrophysics Data System (ADS)

Gruy, Frédéric

2014-02-01

Depending on the range of size and the refractive index value, an optically soft particle follows Rayleigh-Debye-Gans or RDG approximation or Van de Hulst approximation. Practically the first one is valid for small particles whereas the second one works for large particles. Klett and Sutherland (Klett JD, Sutherland RA. App. Opt. 1992;31:373) proved that the Wentzel-Kramers-Brillouin or WKB approximation leads to accurate values of the differential scattering cross section of sphere and cylinder over a wide range of size. In this paper we extend the work of Klett and Sutherland by proposing a method allowing a fast calculation of the differential scattering cross section for any shape of particle with a given orientation and illuminated by unpolarized light. Our method is based on a geometrical approximation of the particle by replacing each geometrical cross section by an ellipse and then by exactly evaluating the differential scattering cross section of the newly generated body. The latter one contains only two single integrals.

A description of rotations for DEM models of particle systems

NASA Astrophysics Data System (ADS)

Campello, Eduardo M. B.

2015-06-01

In this work, we show how a vector parameterization of rotations can be adopted to describe the rotational motion of particles within the framework of the discrete element method (DEM). It is based on the use of a special rotation vector, called Rodrigues rotation vector, and accounts for finite rotations in a fully exact manner. The use of fictitious entities such as quaternions or complicated structures such as Euler angles is thereby circumvented. As an additional advantage, stick-slip friction models with inter-particle rolling motion are made possible in a consistent and elegant way. A few examples are provided to illustrate the applicability of the scheme. We believe that simple vector descriptions of rotations are very useful for DEM models of particle systems.

Scattering Properties of Heterogeneous Mineral Particles with Absorbing Inclusions

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2015-01-01

We analyze the results of numerically exact computer modeling of scattering and absorption properties of randomly oriented poly-disperse heterogeneous particles obtained by placing microscopic absorbing grains randomly on the surfaces of much larger spherical mineral hosts or by imbedding them randomly inside the hosts. These computations are paralleled by those for heterogeneous particles obtained by fully encapsulating fractal-like absorbing clusters in the mineral hosts. All computations are performed using the superposition T-matrix method. In the case of randomly distributed inclusions, the results are compared with the outcome of Lorenz-Mie computations for an external mixture of the mineral hosts and absorbing grains. We conclude that internal aggregation can affect strongly both the integral radiometric and differential scattering characteristics of the heterogeneous particle mixtures.

Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations.

PubMed

Chavanis, P-H; Sire, C

2004-08-01

We determine an exact asymptotic expression of the blow-up time t(coll) for self-gravitating Brownian particles or bacterial populations (chemotaxis) close to the critical point in d=3. We show that t(coll) = t(*) (eta- eta(c) )(-1/2) with t(*) =0.917 677 02..., where eta represents the inverse temperature (for Brownian particles) or the mass (for bacterial colonies), and eta(c) is the critical value of eta above which the system blows up. This result is in perfect agreement with the numerical solution of the Smoluchowski-Poisson system. We also determine the exact asymptotic expression of the relaxation time close to but above the critical temperature and derive a large time asymptotic expansion for the density profile exactly at the critical point.

New Quantum Diffusion Monte Carlo Method for strong field time dependent problems

NASA Astrophysics Data System (ADS)

Kalinski, Matt

2017-04-01

We have recently formulated the Quantum Diffusion Quantum Monte Carlo (QDMC) method for the solution of the time-dependent Schrödinger equation when it is equivalent to the reaction-diffusion system coupled by the highly nonlinear potentials of the type of Shay. Here we formulate a new Time Dependent QDMC method free of the nonlinearities described by the constant stochastic process of the coupled diffusion with transmutation. As before two kinds of diffusing particles (color walkers) are considered but which can further also transmute one into the other. Each of the species undergoes the hypothetical Einstein random walk progression with transmutation. The progressed particles transmute into the particles of the other kind before contributing to or annihilating the other particles density. This fully emulates the Time Dependent Schrödinger equation for any number of quantum particles. The negative sign of the real and the imaginary parts of the wave function is handled by the ``spinor'' densities carrying the sign as the degree of freedom. We apply the method for the exact time-dependent observation of our discovered two-electron Langmuir configurations in the magnetic and circularly polarized fields.

From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

NASA Astrophysics Data System (ADS)

Bodin, Jacques

2015-03-01

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

An optical flow-based method for velocity field of fluid flow estimation

NASA Astrophysics Data System (ADS)

Głomb, Grzegorz; Świrniak, Grzegorz; Mroczka, Janusz

2017-06-01

The aim of this paper is to present a method for estimating flow-velocity vector fields using the Lucas-Kanade algorithm. The optical flow measurements are based on the Particle Image Velocimetry (PIV) technique, which is commonly used in fluid mechanics laboratories in both research institutes and industry. Common approaches for an optical characterization of velocity fields base on computation of partial derivatives of the image intensity using finite differences. Nevertheless, the accuracy of velocity field computations is low due to the fact that an exact estimation of spatial derivatives is very difficult in presence of rapid intensity changes in the PIV images, caused by particles having small diameters. The method discussed in this paper solves this problem by interpolating the PIV images using Gaussian radial basis functions. This provides a significant improvement in the accuracy of the velocity estimation but, more importantly, allows for the evaluation of the derivatives in intermediate points between pixels. Numerical analysis proves that the method is able to estimate even a separate vector for each particle with a 5× 5 px2 window, whereas a classical correlation-based method needs at least 4 particle images. With the use of a specialized multi-step hybrid approach to data analysis the method improves the estimation of the particle displacement far above 1 px.

Free-Propagator Reweighting Integrator for Single-Particle Dynamics in Reaction-Diffusion Models of Heterogeneous Protein-Protein Interaction Systems

PubMed Central

Hummer, Gerhard

2015-01-01

We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green's function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles. Trajectory reweighting in our free-propagator reweighting (FPR) method recovers the exact association rates for a pair of interacting particles at all times. FPR simulations of many-body systems accurately reproduce the theoretically known dynamic behavior for a variety of different reaction types. FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone. FPR applications include the modeling of pathways and networks of protein-driven processes where reaction rates can vary widely and thousands of proteins may participate in the formation of large assemblies. With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events. Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions. PMID:26005592

An exact solution of a simplified two-phase plume model. [for solid propellant rocket

NASA Technical Reports Server (NTRS)

Wang, S.-Y.; Roberts, B. B.

1974-01-01

An exact solution of a simplified two-phase, gas-particle, rocket exhaust plume model is presented. It may be used to make the upper-bound estimation of the heat flux and pressure loads due to particle impingement on the objects existing in the rocket exhaust plume. By including the correction factors to be determined experimentally, the present technique will provide realistic data concerning the heat and aerodynamic loads on these objects for design purposes. Excellent agreement in trend between the best available computer solution and the present exact solution is shown.

Classical integrable many-body systems disconnected with semi-simple Lie algebras

NASA Astrophysics Data System (ADS)

Inozemtsev, V. I.

2017-05-01

The review of the results in the theory of integrable many-body systems disconnected with semisimple Lie algebras is done. The one-dimensional systems of light Calogero-Sutherland-Moser particles interacting with one particle of infinite mass located at the origin are described in detail. In some cases the exact solutions of the equations of motion are obtained. The general theory of integration of the equations of motion needs the methods of algebraic geometry. The Lax pairs with spectral parameter are constructed for this purpose. The theory still contains many unsolved problems.

Dynamics of test particles in thin-shell wormhole spacetimes

NASA Astrophysics Data System (ADS)

Diemer, Valeria; Smolarek, Elena

2013-09-01

Geodesic motion in traversable Schwarzschild and Kerr thin-shell wormholes constructed by the cut-and-paste method introduced by Visser (1989 Nucl. Phys. B 328 203; 1995 Wormholes: from Einstein to Hawking (Woodbury, MN: American Institute of Physics)) is studied. The orbits are calculated exactly in terms of elliptic functions and visualized with the help of embedding diagrams.

Entanglement dynamics in a non-Markovian environment: An exactly solvable model

NASA Astrophysics Data System (ADS)

Wilson, Justin H.; Fregoso, Benjamin M.; Galitski, Victor M.

2012-05-01

We study the non-Markovian effects on the dynamics of entanglement in an exactly solvable model that involves two independent oscillators, each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time correlations, we see nonmonotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of “sudden death” and “rebirth” of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

Pressure in an exactly solvable model of active fluid

NASA Astrophysics Data System (ADS)

Marini Bettolo Marconi, Umberto; Maggi, Claudio; Paoluzzi, Matteo

2017-07-01

We consider the pressure in the steady-state regime of three stochastic models characterized by self-propulsion and persistent motion and widely employed to describe the behavior of active particles, namely, the Active Brownian particle (ABP) model, the Gaussian colored noise (GCN) model, and the unified colored noise approximation (UCNA) model. Whereas in the limit of short but finite persistence time, the pressure in the UCNA model can be obtained by different methods which have an analog in equilibrium systems, in the remaining two models only the virial route is, in general, possible. According to this method, notwithstanding each model obeys its own specific microscopic law of evolution, the pressure displays a certain universal behavior. For generic interparticle and confining potentials, we derive a formula which establishes a correspondence between the GCN and the UCNA pressures. In order to provide explicit formulas and examples, we specialize the discussion to the case of an assembly of elastic dumbbells confined to a parabolic well. By employing the UCNA we find that, for this model, the pressure determined by the thermodynamic method coincides with the pressures obtained by the virial and mechanical methods. The three methods when applied to the GCN give a pressure identical to that obtained via the UCNA. Finally, we find that the ABP virial pressure exactly agrees with the UCNA and GCN results.

Exact Doppler broadening of tabulated cross sections. [SIGMA 1 kernel broadening method

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

Cullen, D.E.; Weisbin, C.R.

1976-07-01

The SIGMA1 kernel broadening method is presented to Doppler broaden to any required accuracy a cross section that is described by a table of values and linear-linear interpolation in energy-cross section between tabulated values. The method is demonstrated to have no temperature or energy limitations and to be equally applicable to neutron or charged-particle cross sections. The method is qualitatively and quantitatively compared to contemporary approximate methods of Doppler broadening with particular emphasis on the effect of each approximation introduced.

A one-dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer 3. Numerical methods and comparisons with exact solutions

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

Gelbard, F.; Fitzgerald, J.W.; Hoppel, W.A.

1998-07-01

We present the theoretical framework and computational methods that were used by {ital Fitzgerald} {ital et al.} [this issue (a), (b)] describing a one-dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer. The concepts and limitations of modeling spatially varying multicomponent aerosols are elucidated. New numerical sectional techniques are presented for simulating multicomponent aerosol growth, settling, and eddy transport, coupled to time-dependent and spatially varying condensing vapor concentrations. Comparisons are presented with new exact solutions for settling and particle growth by simultaneous dynamic condensation of one vapor and by instantaneous equilibration with a spatially varying secondmore » vapor. {copyright} 1998 American Geophysical Union« less

Exact Green's functions for a Brownian particle reversibly binding to a fixed target in a finite, two-dimensional, circular domain

NASA Astrophysics Data System (ADS)

Kalay, Ziya

2012-06-01

Despite the apparent need to study reversible reactions between molecules confined to a two-dimensional space such as the cell membrane, exact Green’s functions for this case have not been reported. Here we present exact analytical Green’s functions for a Brownian particle reversibly reacting with a fixed reaction center in a finite two-dimensional circular region with reflecting or absorbing boundaries, considering either a spherically symmetric initial distribution or a particle that is initially bound. We show that Green’s function can be used to predict the effect of measurement uncertainties on the outcome of single-particle/molecule-tracking experiments in which molecular interactions are investigated. Hence, we bridge the gap between previously known solutions in one dimension (Agmon 1984 J. Chem. Phys. 81 2811) and three dimensions (Kim and Shin 1999 Phys. Rev. Lett. 82 1578), and provide an example of how the knowledge of Green’s function can be used to predict experimentally accessible quantities.

Unthermal charged massive Hawking radiation from a Reissner-Nordström-de Sitter black hole

NASA Astrophysics Data System (ADS)

Khayrul Hasan, M.

2015-05-01

We investigate the massive charged particles' Hawking radiation from a Reissner-Nordström-de Sitter (RNdS) black hole by Damour-Ruffini's method. We get the unthermal spectrum when the back-reaction of particles' energy and charge to spacetime is considered. The information will get out from the black hole with the corrected spectrum. The radiation is not exactly thermal and because the derivation obeys conservation laws, the non thermal Hawking radiation can carry information from the black hole. In our work the method is more simple and explicit and it can be used to explain the black hole information loss paradox, and the process satisfies underlying unitary theory.

Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics.

PubMed

Lizana, L; Ambjörnsson, T

2009-11-01

We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Delta diffusing in a one-dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function rhoT(yT,t|yT,0) that a tagged particle T (T=1,...,N) is at position yT at time t given that it at time t=0 was at position yT,0. Using a Bethe ansatz we obtain the N -particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle T , we arrive at an exact expression for rhoT(yT,t|yT,0) in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large N , maintaining L finite, using a nonstandard asymptotic technique. We derive an exact expression for rhoT(yT,t|yT,0) for a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) for times much smaller than the collision time ttaucoll but times smaller than the equilibrium time ttaue , rhoT(yT,t|yT,0) approaches a polynomial-type equilibrium probability density function. Notably, only regimes (A) and (B) are found in the previously considered infinite systems.

Theory of particle detection and multiplicity counting with dead time effects

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

Pal, L.; Pazsit, I.

The subject of this paper is the investigation of the effect of the dead time on the statistics of the particle detection process. A theoretical treatment is provided with the application of the methods of renewal theory. The detector efficiency and various types of the dead time are accounted for. Exact analytical results are derived for the probability distribution functions, the expectations and the variances of the number of detected particles. Explicit solutions are given for a few representative cases. The results should serve for the evaluation of the measurements in view of the dead time correction effects for themore » higher moments of the detector counts. (authors)« less

Exact and quasi-classical density matrix and Wigner functions for a particle in the box and half space

NASA Technical Reports Server (NTRS)

Akhundova, E. A.; Dodonov, V. V.; Manko, V. I.

1993-01-01

The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).

Particle-in-a-box model of one-dimensional excitons in conjugated polymers

NASA Astrophysics Data System (ADS)

Pedersen, Thomas G.; Johansen, Per M.; Pedersen, Henrik C.

2000-04-01

A simple two-particle model of excitons in conjugated polymers is proposed as an alternative to usual highly computationally demanding quantum chemical methods. In the two-particle model, the exciton is described as an electron-hole pair interacting via Coulomb forces and confined to the polymer backbone by rigid walls. Furthermore, by integrating out the transverse part, the two-particle equation is reduced to one-dimensional form. It is demonstrated how essentially exact solutions are obtained in the cases of short and long conjugation length, respectively. From a linear combination of these cases an approximate solution for the general case is obtained. As an application of the model the influence of a static electric field on the electron-hole overlap integral and exciton energy is considered.

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

NASA Astrophysics Data System (ADS)

Pont, Federico M.; Osenda, Omar; Serra, Pablo

2018-05-01

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

NASA Astrophysics Data System (ADS)

Plante, Ianik; Devroye, Luc

2015-09-01

Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well.

Exact milestoning

PubMed Central

Bello-Rivas, Juan M.; Elber, Ron

2015-01-01

A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied. PMID:25747056

Einstein-aether theory: dynamics of relativistic particles with spin or polarization in a Gödel-type universe

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

Balakin, Alexander B.; Popov, Vladimir A., E-mail: alexander.balakin@kpfu.ru, E-mail: vladipopov@mail.ru

In the framework of the Einstein-aether theory we consider a cosmological model, which describes the evolution of the unit dynamic vector field with activated rotational degree of freedom. We discuss exact solutions of the Einstein-aether theory, for which the space-time is of the Gödel-type, the velocity four-vector of the aether motion is characterized by a non-vanishing vorticity, thus the rotational vectorial modes can be associated with the source of the universe rotation. The main goal of our paper is to study the motion of test relativistic particles with a vectorial internal degree of freedom (spin or polarization), which is coupledmore » to the unit dynamic vector field. The particles are considered as the test ones in the given space-time background of the Gödel-type; the spin (polarization) coupling to the unit dynamic vector field is modeled using exact solutions of three types. The first exact solution describes the aether with arbitrary Jacobson's coupling constants; the second one relates to the case, when the Jacobson's constant responsible for the vorticity is vanishing; the third exact solution is obtained using three constraints for the coupling constants. The analysis of the exact expressions, which are obtained for the particle momentum and for the spin (polarization) four-vector components, shows that the interaction of the spin (polarization) with the unit vector field induces a rotation, which is additional to the geodesic precession of the spin (polarization) associated with the universe rotation as a whole.« less

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.

Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere

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

Li Jinxing; Pu Zuyin; Xie Lun

Charged particle dynamics in magnetosphere has temporal and spatial multiscale; therefore, numerical accuracy over a long integration time is required. A variational symplectic integrator (VSI) [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008) and H. Qin, X. Guan, and W. M. Tang, Phys. Plasmas 16, 042510 (2009)] for the guiding-center motion of charged particles in general magnetic field is applied to study the dynamics of charged particles in magnetosphere. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing themore » dynamics. The VSI conserves exactly a discrete Lagrangian symplectic structure and has better numerical properties over a long integration time, compared with standard integrators, such as the standard and adaptive fourth order Runge-Kutta (RK4) methods. Applying the VSI method to guiding-center dynamics in the inner magnetosphere, we can accurately calculate the particles'orbits for an arbitrary long simulating time with good conservation property. When a time-independent convection and corotation electric field is considered, the VSI method can give the accurate single particle orbit, while the RK4 method gives an incorrect orbit due to its intrinsic error accumulation over a long integrating time.« less

Benchmark Results Of Active Tracer Particles In The Open Souce Code ASPECT For Modelling Convection In The Earth's Mantle

NASA Astrophysics Data System (ADS)

Jiang, J.; Kaloti, A. P.; Levinson, H. R.; Nguyen, N.; Puckett, E. G.; Lokavarapu, H. V.

2016-12-01

We present the results of three standard benchmarks for the new active tracer particle algorithm in ASPECT. The three benchmarks are SolKz, SolCx, and SolVI (also known as the 'inclusion benchmark') first proposed by Duretz, May, Gerya, and Tackley (G Cubed, 2011) and in subsequent work by Theilman, May, and Kaus (Pure and Applied Geophysics, 2014). Each of the three benchmarks compares the accuracy of the numerical solution to a steady (time-independent) solution of the incompressible Stokes equations with a known exact solution. These benchmarks are specifically designed to test the accuracy and effectiveness of the numerical method when the viscosity varies up to six orders of magnitude. ASPECT has been shown to converge to the exact solution of each of these benchmarks at the correct design rate when all of the flow variables, including the density and viscosity, are discretized on the underlying finite element grid (Krobichler, Heister, and Bangerth, GJI, 2012). In our work we discretize the density and viscosity by initially placing the true values of the density and viscosity at the intial particle positions. At each time step, including the initialization step, the density and viscosity are interpolated from the particles onto the finite element grid. The resulting Stokes system is solved for the velocity and pressure, and the particle positions are advanced in time according to this new, numerical, velocity field. Note that this procedure effectively changes a steady solution of the Stokes equaton (i.e., one that is independent of time) to a solution of the Stokes equations that is time dependent. Furthermore, the accuracy of the active tracer particle algorithm now also depends on the accuracy of the interpolation algorithm and of the numerical method one uses to advance the particle positions in time. Finally, we will present new interpolation algorithms designed to increase the overall accuracy of the active tracer algorithms in ASPECT and interpolation algotithms designed to conserve properties, such as mass density, that are being carried by the particles.

SPAMCART: a code for smoothed particle Monte Carlo radiative transfer

NASA Astrophysics Data System (ADS)

Lomax, O.; Whitworth, A. P.

2016-10-01

We present a code for generating synthetic spectral energy distributions and intensity maps from smoothed particle hydrodynamics simulation snapshots. The code is based on the Lucy Monte Carlo radiative transfer method, I.e. it follows discrete luminosity packets as they propagate through a density field, and then uses their trajectories to compute the radiative equilibrium temperature of the ambient dust. The sources can be extended and/or embedded, and discrete and/or diffuse. The density is not mapped on to a grid, and therefore the calculation is performed at exactly the same resolution as the hydrodynamics. We present two example calculations using this method. First, we demonstrate that the code strictly adheres to Kirchhoff's law of radiation. Secondly, we present synthetic intensity maps and spectra of an embedded protostellar multiple system. The algorithm uses data structures that are already constructed for other purposes in modern particle codes. It is therefore relatively simple to implement.

Large-amplitude hydromagnetic waves in collisionless relativistic plasma - Exact solution for the fast-mode magnetoacoustic wave

NASA Technical Reports Server (NTRS)

Barnes, A.

1983-01-01

An exact nonlinear solution is found to the relativistic kinetic and electrodynamic equations (in their hydromagnetic limit) that describes the large-amplitude fast-mode magnetoacoustic wave propagating normal to the magnetic field in a collisionless, previously uniform plasma. It is pointed out that a wave of this kind will be generated by transverse compression of any collisionless plasma. The solution is in essence independent of the detailed form of the particle momentum distribution functions. The solution is obtained, in part, through the method of characteristics; the wave exhibits the familiar properties of steepening and shock formation. A detailed analysis is given of the ultrarelativistic limit of this wave.

The variational method in quantum mechanics: an elementary introduction

NASA Astrophysics Data System (ADS)

Borghi, Riccardo

2018-05-01

Variational methods in quantum mechanics are customarily presented as invaluable techniques to find approximate estimates of ground state energies. In the present paper a short catalogue of different celebrated potential distributions (both 1D and 3D), for which an exact and complete (energy and wavefunction) ground state determination can be achieved in an elementary way, is illustrated. No previous knowledge of calculus of variations is required. Rather, in all presented cases the exact energy functional minimization is achieved by using only a couple of simple mathematical tricks: ‘completion of square’ and integration by parts. This makes our approach particularly suitable for undergraduates. Moreover, the key role played by particle localization is emphasized through the entire analysis. This gentle introduction to the variational method could also be potentially attractive for more expert students as a possible elementary route toward a rather advanced topic on quantum mechanics: the factorization method. Such an unexpected connection is outlined in the final part of the paper.

Stationary swarming motion of active Brownian particles in parabolic external potential

NASA Astrophysics Data System (ADS)

Zhu, Wei Qiu; Deng, Mao Lin

2005-08-01

We investigate the stationary swarming motion of active Brownian particles in parabolic external potential and coupled to its mass center. Using Monte Carlo simulation we first show that the mass center approaches to rest after a sufficient long period of time. Thus, all the particles of a swarm have identical stationary motion relative to the mass center. Then the stationary probability density obtained by using the stochastic averaging method for quasi integrable Hamiltonian systems in our previous paper for the motion in 4-dimensional phase space of single active Brownian particle with Rayleigh friction model in parabolic potential is used to describe the relative stationary motion of each particle of the swarm and to obtain more probability densities including that for the total energy of the swarm. The analytical results are confirmed by comparing with those from simulation and also shown to be consistent with the existing deterministic exact steady-state solution.

Particle acceleration at a reconnecting magnetic separator

NASA Astrophysics Data System (ADS)

Threlfall, J.; Neukirch, T.; Parnell, C. E.; Eradat Oskoui, S.

2015-02-01

Context. While the exact acceleration mechanism of energetic particles during solar flares is (as yet) unknown, magnetic reconnection plays a key role both in the release of stored magnetic energy of the solar corona and the magnetic restructuring during a flare. Recent work has shown that special field lines, called separators, are common sites of reconnection in 3D numerical experiments. To date, 3D separator reconnection sites have received little attention as particle accelerators. Aims: We investigate the effectiveness of separator reconnection as a particle acceleration mechanism for electrons and protons. Methods: We study the particle acceleration using a relativistic guiding-centre particle code in a time-dependent kinematic model of magnetic reconnection at a separator. Results: The effect upon particle behaviour of initial position, pitch angle, and initial kinetic energy are examined in detail, both for specific (single) particle examples and for large distributions of initial conditions. The separator reconnection model contains several free parameters, and we study the effect of changing these parameters upon particle acceleration, in particular in view of the final particle energy ranges that agree with observed energy spectra.

Comprehensive T-Matrix Reference Database: A 2012 - 2013 Update

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Videen, Gorden; Khlebtsov, Nikolai G.; Wriedt, Thomas

2013-01-01

The T-matrix method is one of the most versatile, efficient, and accurate theoretical techniques widely used for numerically exact computer calculations of electromagnetic scattering by single and composite particles, discrete random media, and particles imbedded in complex environments. This paper presents the fifth update to the comprehensive database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2012. It also lists several earlier publications not incorporated in the original database, including Peter Waterman's reports from the 1960s illustrating the history of the T-matrix approach and demonstrating that John Fikioris and Peter Waterman were the true pioneers of the multi-sphere method otherwise known as the generalized Lorenz - Mie theory.

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

Cai Xiaoming; Chen Shu; Wang Yupeng

The superfluid-to-Anderson-insulator transition of a strongly repulsive Bose gas is studied in a one-dimensional incommensurate optical lattice. In the hard-core limit, the Bose-Fermi mapping allows us to deal with the system using the exact numerical method. Based on the Aubry-Andre model, we exploit the phase transition of the hard-core boson system from the superfluid phase with all single-particle states extended to the Bose-glass phase with all the single-particle states being Anderson localized as the strength of the incommensurate potential increases relative to the hopping amplitude. We evaluate the superfluid fraction, one-particle density matrices, momentum distributions, the natural orbitals, and theirmore » occupations. All of these quantities show that there exists a superfluid-to-insulator phase transition in the system.« less

Numerical approach for finite volume three-body interaction

NASA Astrophysics Data System (ADS)

Guo, Peng; Gasparian, Vladimir

2018-01-01

In the present work, we study a numerical approach to one dimensional finite volume three-body interaction, the method is demonstrated by considering a toy model of three spinless particles interacting with pair-wise δ -function potentials. The numerical results are compared with the exact solutions of three spinless bosons interaction when the strength of short-range interactions are set equal for all pairs.

Direct Simulation of Extinction in a Slab of Spherical Particles

NASA Technical Reports Server (NTRS)

Mackowski, D.W.; Mishchenko, Michael I.

2013-01-01

The exact multiple sphere superposition method is used to calculate the coherent and incoherent contributions to the ensemble-averaged electric field amplitude and Poynting vector in systems of randomly positioned nonabsorbing spherical particles. The target systems consist of cylindrical volumes, with radius several times larger than length, containing spheres with positional configurations generated by a Monte Carlo sampling method. Spatially dependent values for coherent electric field amplitude, coherent energy flux, and diffuse energy flux, are calculated by averaging of exact local field and flux values over multiple configurations and over spatially independent directions for fixed target geometry, sphere properties, and sphere volume fraction. Our results reveal exponential attenuation of the coherent field and the coherent energy flux inside the particulate layer and thereby further corroborate the general methodology of the microphysical radiative transfer theory. An effective medium model based on plane wave transmission and reflection by a plane layer is used to model the dependence of the coherent electric field on particle packing density. The effective attenuation coefficient of the random medium, computed from the direct simulations, is found to agree closely with effective medium theories and with measurements. In addition, the simulation results reveal the presence of a counter-propagating component to the coherent field, which arises due to the internal reflection of the main coherent field component by the target boundary. The characteristics of the diffuse flux are compared to, and found to be consistent with, a model based on the diffusion approximation of the radiative transfer theory.

Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems

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

Xiao, Jianyuan; Qin, Hong; Liu, Jian

2015-11-01

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint arXiv: 1505.06076 (2015)], which produces fivemore » exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. (C) 2015 AIP Publishing LLC.« less

Complete particle-pair annihilation as a dynamical signature of the spectral singularity

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

Li, G.R.; Zhang, X.Z.; Song, Z., E-mail: nkquantum@gmail.com

2014-10-15

Motivated by the physical relevance of a spectral singularity of interacting many-particle system, we explore the dynamics of two bosons as well as fermions in one-dimensional system with imaginary delta interaction strength. Based on the exact solution, it shows that the two-particle collision leads to amplitude-reduction of the wave function. For fermion pair, the amplitude-reduction depends on the spin configuration of two particles. In both cases, the residual amplitude can vanish when the relative group velocity of two single-particle Gaussian wave packets with equal width reaches the magnitude of the interaction strength, exhibiting complete particle-pair annihilation at the spectral singularity.more » - Highlights: • We investigate the physical relevance of a spectral singularity. • The two-particle collision leads to amplitude-reduction of the wave function. • There is a singularity spectrum which leads to complete particle-pair annihilation. • Complete particle-pair annihilation can only occur for two distinguishable bosons and singlet fermions. • Pair annihilation provides a detection method of the spectral singularity in the experiment.« less

Microscopic derivation of particle-based coarse-grained dynamics: Exact expression for memory function

NASA Astrophysics Data System (ADS)

Izvekov, Sergei

2017-03-01

We consider the generalized Langevin equations of motion describing exactly the particle-based coarse-grained dynamics in the classical microscopic ensemble that were derived recently within the Mori-Zwanzig formalism based on new projection operators [S. Izvekov, J. Chem. Phys. 138(13), 134106 (2013)]. The fundamental difference between the new family of projection operators and the standard Zwanzig projection operator used in the past to derive the coarse-grained equations of motion is that the new operators average out the explicit irrelevant trajectories leading to the possibility of solving the projected dynamics exactly. We clarify the definition of the projection operators and revisit the formalism to compute the projected dynamics exactly for the microscopic system in equilibrium. The resulting expression for the projected force is in the form of a "generalized additive fluctuating force" describing the departure of the generalized microscopic force associated with the coarse-grained coordinate from its projection. Starting with this key expression, we formulate a new exact formula for the memory function in terms of microscopic and coarse-grained conservative forces. We conclude by studying two independent limiting cases of practical importance: the Markov limit (vanishing correlations of projected force) and the limit of weak dependence of the memory function on the particle momenta. We present computationally affordable expressions which can be efficiently evaluated from standard molecular dynamics simulations.

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.

Correlation functions in first-order phase transitions

NASA Astrophysics Data System (ADS)

Garrido, V.; Crespo, D.

1997-09-01

Most of the physical properties of systems underlying first-order phase transitions can be obtained from the spatial correlation functions. In this paper, we obtain expressions that allow us to calculate all the correlation functions from the droplet size distribution. Nucleation and growth kinetics is considered, and exact solutions are obtained for the case of isotropic growth by using self-similarity properties. The calculation is performed by using the particle size distribution obtained by a recently developed model (populational Kolmogorov-Johnson-Mehl-Avrami model). Since this model is less restrictive than that used in previously existing theories, the result is that the correlation functions can be obtained for any dependence of the kinetic parameters. The validity of the method is tested by comparison with the exact correlation functions, which had been obtained in the available cases by the time-cone method. Finally, the correlation functions corresponding to the microstructure developed in partitioning transformations are obtained.

Constant pressure and temperature discrete-time Langevin molecular dynamics

NASA Astrophysics Data System (ADS)

Grønbech-Jensen, Niels; Farago, Oded

2014-11-01

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.

On the motion of a quantum particle in the spinning cosmic string space–time

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

Hassanabadi, H., E-mail: h.hasanabadi@shahroodut.ac.ir; Afshardoost, A.; Zarrinkamar, S.

2015-05-15

We analyze the energy spectrum and the wave function of a particle subjected to magnetic field in the spinning cosmic string space–time and investigate the influence of the spinning reference frame and topological defect on the system. To do this we solve Schrödinger equation in the spinning cosmic string background. In our work, instead of using an approximation in the calculations, we use the quasi-exact ansatz approach which gives the exact solutions for some primary levels. - Highlights: • Solving the Schrödinger equation in the spinning cosmic string space time. • Proposing a quasi-exact analytical solution to the general formmore » of the corresponding equation. • Generalizing the previous works.« less

The power of exact conditions in electronic structure theory

NASA Astrophysics Data System (ADS)

Bartlett, Rodney J.; Ranasinghe, Duminda S.

2017-02-01

Once electron correlation is included in an effective one-particle operator, one has a correlated orbital theory (COT). One such theory is Kohn-Sham density functional theory (KS-DFT), but there are others. Such methods have the prospect to redefine traditional Molecular Orbital (MO) theory by building a quantitative component upon its conceptual framework. This paper asks the question what conditions should such a theory satisfy and can this be accomplished? One such condition for a COT is that the orbital eigenvalues should satisfy an ionization theorem that generalizes Koopmans' approximation to the exact principal ionization potentials for every electron in a molecule. Guided by this principle, minimal parameterizations of KS-DFT are made that provide a good approximation to a quantitative MO theory.

Unthermal Hawking Radiation from a General Stationary Black Hole

NASA Astrophysics Data System (ADS)

Zhang, Yong-Ping; Dai, Qian; Liu, Wen-Biao

2008-02-01

Using Damour Ruffini's method, Hawking radiation from a general stationary black hole is investigated again deeply. Considering the back reaction of the particle to the space-time and energy conservation, we find that the radiation is not exactly thermal and can take out information from the black hole. This can be used to explain the information loss paradox, and the result is consistent with the works finished before.

Comprehensive Thematic T-Matrix Reference Database: A 2015-2017 Update

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Zakharova, Nadezhda; Khlebtsov, Nikolai G.; Videen, Gorden; Wriedt, Thomas

2017-01-01

The T-matrix method pioneered by Peter C. Waterman is one of the most versatile and efficient numerically exact computer solvers of the time-harmonic macroscopic Maxwell equations. It is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, periodic structures (including metamaterials), and particles in the vicinity of plane or rough interfaces separating media with different refractive indices. This paper is the eighth update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated in 2004 and lists relevant publications that have appeared since 2015. It also references a small number of earlier publications overlooked previously.

Hawking radiation of charged Dirac particles from a Kerr-Newman black hole

NASA Astrophysics Data System (ADS)

Zhou, Shiwei; Liu, Wenbiao

2008-05-01

Charged Dirac particles’ Hawking radiation from a Kerr-Newman black hole is calculated using Damour-Ruffini’s method. When energy conservation and the backreaction of particles to the space-time are considered, the emission spectrum is not purely thermal anymore. The leading term is exactly the Boltzman factor, and the deviation from the purely thermal spectrum can bring some information out, which can be treated as an explanation to the information loss paradox. The result can also be treated as a quantum-corrected radiation temperature, which is dependent on the black hole background and the radiation particle’s energy, angular momentum, and charge.

Comprehensive thematic T-matrix reference database: A 2015-2017 update

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Zakharova, Nadezhda T.; Khlebtsov, Nikolai G.; Videen, Gorden; Wriedt, Thomas

2017-11-01

The T-matrix method pioneered by Peter C. Waterman is one of the most versatile and efficient numerically exact computer solvers of the time-harmonic macroscopic Maxwell equations. It is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, periodic structures (including metamaterials), and particles in the vicinity of plane or rough interfaces separating media with different refractive indices. This paper is the eighth update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated in 2004 and lists relevant publications that have appeared since 2015. It also references a small number of earlier publications overlooked previously.

Wave-function functionals

NASA Astrophysics Data System (ADS)

Pan, Xiao-Yin; Slamet, Marlina; Sahni, Viraht

2010-04-01

We extend our prior work on the construction of variational wave functions ψ that are functionals of functions χ:ψ=ψ[χ] rather than simply being functions. In this manner, the space of variations is expanded over those of traditional variational wave functions. In this article we perform the constrained search over the functions χ chosen such that the functional ψ[χ] satisfies simultaneously the constraints of normalization and the exact expectation value of an arbitrary single- or two-particle Hermitian operator, while also leading to a rigorous upper bound to the energy. As such the wave function functional is accurate not only in the region of space in which the principal contributions to the energy arise but also in the other region of the space represented by the Hermitian operator. To demonstrate the efficacy of these ideas, we apply such a constrained search to the ground state of the negative ion of atomic hydrogen H-, the helium atom He, and its positive ions Li+ and Be2+. The operators W whose expectations are obtained exactly are the sum of the single-particle operators W=∑irin,n=-2,-1,1,2, W=∑iδ(ri), W=-(1)/(2)∑i∇i2, and the two-particle operators W=∑nun,n=-2,-1,1,2, where u=|ri-rj|. Comparisons with the method of Lagrangian multipliers and of other constructions of wave-function functionals are made. Finally, we present further insights into the construction of wave-function functionals by studying a previously proposed construction of functionals ψ[χ] that lead to the exact expectation of arbitrary Hermitian operators. We discover that analogous to the solutions of the Schrödinger equation, there exist ψ[χ] that are unphysical in that they lead to singular values for the expectations. We also explain the origin of the singularity.

Analysis of 100 pharmaceuticals and their degradates in water samples by liquid chromatography/quadrupole time-of-flight mass spectrometry.

PubMed

Ferrer, Imma; Thurman, E Michael

2012-10-12

A straightforward methodology for the chromatographic separation and accurate mass identification of 100 pharmaceuticals including some of their degradation products was developed using liquid chromatography/quadrupole time-of-flight mass spectrometry (LC/Q-TOF-MS). A table compiling the protonated or deprotonated exact masses for all compounds, as well as the exact mass of several fragment ions obtained by MS-MS is included. Excellent chromatographic separation was achieved by using 3.5 μm particle size columns and a slow and generic 30-min gradient. Isobaric and isomeric compounds (same nominal mass and same exact mass, respectively) were distinguished by various methods, including chromatography separation, MS-MS fragmentation, and isotopic signal identification. Method reporting limits of detection ranged from 1 to 1000 ng/L, after solid-phase extraction of 100mL aqueous samples. The methodology was successfully applied to the analysis of surface water impacted by wastewater effluent by identifying many of the pharmaceuticals and metabolites included in the list. Examples are given for some of the most unusual findings in environmental samples. This paper is meant to serve as a guide for those doing analysis of pharmaceuticals in environmental samples, by providing exact mass measurements of several well known, as well as newly identified and environmentally relevant pharmaceuticals in water samples. Copyright © 2012 Elsevier B.V. All rights reserved.

Vibration-translation energy transfer in anharmonic diatomic molecules. 1: A critical evaluation of the semiclassical approximation

NASA Technical Reports Server (NTRS)

Mckenzie, R. L.

1974-01-01

The semiclassical approximation is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Solutions for correlations along the coexistence curve and at the critical point of a kagomé lattice gas with three-particle interactions

NASA Astrophysics Data System (ADS)

Barry, J. H.; Muttalib, K. A.; Tanaka, T.

2008-01-01

We consider a two-dimensional (d=2) kagomé lattice gas model with attractive three-particle interactions around each triangular face of the kagomé lattice. Exact solutions are obtained for multiparticle correlations along the liquid and vapor branches of the coexistence curve and at criticality. The correlation solutions are also determined along the continuation of the curvilinear diameter of the coexistence region into the disordered fluid region. The method generates a linear algebraic system of correlation identities with coefficients dependent only upon the interaction parameter. Using a priori knowledge of pertinent solutions for the density and elementary triplet correlation, one finds a closed and linearly independent set of correlation identities defined upon a spatially compact nine-site cluster of the kagomé lattice. Resulting exact solution curves of the correlations are plotted and discussed as functions of the temperature and are compared with corresponding results in a traditional kagomé lattice gas having nearest-neighbor pair interactions. An example of application for the multiparticle correlations is demonstrated in cavitation theory.

Brownian motion in non-equilibrium systems and the Ornstein-Uhlenbeck stochastic process.

PubMed

Donado, F; Moctezuma, R E; López-Flores, L; Medina-Noyola, M; Arauz-Lara, J L

2017-10-03

The Ornstein-Uhlenbeck stochastic process is an exact mathematical model providing accurate representations of many real dynamic processes in systems in a stationary state. When applied to the description of random motion of particles such as that of Brownian particles, it provides exact predictions coinciding with those of the Langevin equation but not restricted to systems in thermal equilibrium but only conditioned to be stationary. Here, we investigate experimentally single particle motion in a two-dimensional granular system in a stationary state, consisting of 1 mm stainless balls on a plane circular surface. The motion of the particles is produced by an alternating magnetic field applied perpendicular to the surface of the container. The mean square displacement of the particles is measured for a range of low concentrations and it is found that following an appropriate scaling of length and time, the short-time experimental curves conform a master curve covering the range of particle motion from ballistic to diffusive in accordance with the description of the Ornstein-Uhlenbeck model.

Effective photon mass and exact translating quantum relativistic structures

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

Haas, Fernando, E-mail: fernando.haas@ufrgs.br; Manrique, Marcos Antonio Albarracin, E-mail: sagret10@hotmail.com

2016-04-15

Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can reveal a localization in the radial direction perpendicular to the wave packet propagation, thanks to a non-vanishing scalar potential. The external electromagnetic field, the particle current density, and the charge density are determined. The stability analysis of the solutions is performed by means of numerical simulations. The results are useful for the description of a charged quantum test particle in the relativistic regime, provided spinmore » effects are not decisive.« less

Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field

NASA Astrophysics Data System (ADS)

Zhang, Ruili; Wang, Yulei; He, Yang; Xiao, Jianyuan; Liu, Jian; Qin, Hong; Tang, Yifa

2018-02-01

Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. The numerical simulation of relativistic dynamics is often multi-scale and requires accurate long-term numerical simulations. Therefore, explicit symplectic algorithms are much more preferable than non-symplectic methods and implicit symplectic algorithms. In this paper, we employ the proper time and express the Hamiltonian as the sum of exactly solvable terms and product-separable terms in space-time coordinates. Then, we give the explicit symplectic algorithms based on the generating functions of orders 2 and 3 for relativistic dynamics of a charged particle. The methodology is not new, which has been applied to non-relativistic dynamics of charged particles, but the algorithm for relativistic dynamics has much significance in practical simulations, such as the secular simulation of runaway electrons in tokamaks.

Fine structure of the entanglement entropy in the O(2) model.

PubMed

Yang, Li-Ping; Liu, Yuzhi; Zou, Haiyuan; Xie, Z Y; Meurice, Y

2016-01-01

We compare two calculations of the particle density in the superfluid phase of the O(2) model with a chemical potential μ in 1+1 dimensions. The first relies on exact blocking formulas from the Tensor Renormalization Group (TRG) formulation of the transfer matrix. The second is a worm algorithm. We show that the particle number distributions obtained with the two methods agree well. We use the TRG method to calculate the thermal entropy and the entanglement entropy. We describe the particle density, the two entropies and the topology of the world lines as we increase μ to go across the superfluid phase between the first two Mott insulating phases. For a sufficiently large temporal size, this process reveals an interesting fine structure: the average particle number and the winding number of most of the world lines in the Euclidean time direction increase by one unit at a time. At each step, the thermal entropy develops a peak and the entanglement entropy increases until we reach half-filling and then decreases in a way that approximately mirrors the ascent. This suggests an approximate fermionic picture.

Hot-stage microscopy for determination of API fragmentation: comparison with other methods.

PubMed

Šimek, Michal; Grünwaldová, Veronika; Kratochvíl, Bohumil

2016-08-01

Although the fragmentation of the active pharmaceutical ingredient (API) is a phenomenon that is mentioned in many literature sources, no well-suited analytical tools for its investigation are currently known. We used the hot-stage microscopy method, already presented in our previous work, and studied the real fragmentation of the tadalafil particles in model tablets which were prepared under different compaction pressures. The morphology, spectral imaging and evaluation of plastic and elastic energies were also analyzed to support the hot-stage method. The prepared blend of tadalafil and excipients was compacted under a several forces from 5 to 35 kN to reveal the trend of fragmentation. The exact fragmentation of tadalafil with increased compaction pressure was revealed by the hot-stage microscopic method and it was in good agreement with plastic and elastic energies. Conversely, spectral imaging, which is being used for this analysis, was considered to be inaccurate methodology as mainly agglomerates, not individual particles, were measured. The availability of the hot-stage microscopic method equips pharmaceutical scientists with an in vitro assessment technique that will more reliably determine the fragmentation of the API in finished tablets and the behavior of the particles when compacted.

An analytical particle mover for the charge- and energy-conserving, nonlinearly implicit, electrostatic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2013-08-01

We propose a 1D analytical particle mover for the recent charge- and energy-conserving electrostatic particle-in-cell (PIC) algorithm in Ref. [G. Chen, L. Chacón, D.C. Barnes, An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm, Journal of Computational Physics 230 (2011) 7018-7036]. The approach computes particle orbits exactly for a given piece-wise linear electric field. The resulting PIC algorithm maintains the exact charge and energy conservation properties of the original algorithm, but with improved performance (both in efficiency and robustness against the number of particles and timestep). We demonstrate the advantageous properties of the scheme with a challenging multiscale numerical test case, the ion acoustic wave. Using the analytical mover as a reference, we demonstrate that the choice of error estimator in the Crank-Nicolson mover has significant impact on the overall performance of the implicit PIC algorithm. The generalization of the approach to the multi-dimensional case is outlined, based on a novel and simple charge conserving interpolation scheme.

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.

Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D

NASA Astrophysics Data System (ADS)

Cadilhe, A.; Voter, Arthur F.

2018-02-01

The trajectories of two particles undergoing Langevin dynamics while sharing a common noise sequence can merge into a single (master) trajectory. Here, we present an exact solution for a particle undergoing Langevin dynamics in a harmonic, time-dependent potential, thus extending the idea of synchronization to nonequilibrium systems. We calculate the synchronization level, i.e., the mismatch between two trajectories sharing a common noise sequence, in the underdamped, critically damped, and overdamped regimes. Finally, we provide asymptotic expansions in various limiting cases and compare to the time independent case.

Momentum-space cluster dual-fermion method

NASA Astrophysics Data System (ADS)

Iskakov, Sergei; Terletska, Hanna; Gull, Emanuel

2018-03-01

Recent years have seen the development of two types of nonlocal extensions to the single-site dynamical mean field theory. On one hand, cluster approximations, such as the dynamical cluster approximation, recover short-range momentum-dependent correlations nonperturbatively. On the other hand, diagrammatic extensions, such as the dual-fermion theory, recover long-ranged corrections perturbatively. The correct treatment of both strong short-ranged and weak long-ranged correlations within the same framework is therefore expected to lead to a quick convergence of results, and offers the potential of obtaining smooth self-energies in nonperturbative regimes of phase space. In this paper, we present an exact cluster dual-fermion method based on an expansion around the dynamical cluster approximation. Unlike previous formulations, our method does not employ a coarse-graining approximation to the interaction, which we show to be the leading source of error at high temperature, and converges to the exact result independently of the size of the underlying cluster. We illustrate the power of the method with results for the second-order cluster dual-fermion approximation to the single-particle self-energies and double occupancies.

Boyd Report1

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

Crow, A J

2009-07-07

Andrew Crow arrived at Lawrence Livermore National Laboratory with the intention of continuing work on the Complex Particle Kinetic (CPK) method developed D. Larson and D. Hewett. Andrew Crow had previously worked on duplicating the results of D. Hewett in his previous work. Since arrival, A. Crow has been working with D. Larson on a slightly different project. The current method, still under development, is a Particle in Cell (PIC) code with the following features: (1) all particles begin each timestep at a gridpoint; (2) particles are then advanced in time using a standard special advancement method. The exact methodmore » has not been decided upon, but there are many reliable methods from which to choose. (3) All particles within each cell undergo a simultaneous implicit collision step. This is the current area of focus. Currently, A. Crow is not aware of any method of performing implicit collisions over a large number of charged particles. Implicit methods for charged particle movement and electron-electron collisions, have been developed. The work of L. pareschi and G. Russo on the Time Relaxed Direct Simulation Monte Carlo method, also appears to be a good basis for implicit particle collisions. (4) Each individual particle will be divided into a set of particles with a Gaussian velocity distribution. This will collect some of the thermal effects created by the collisions. This algorithm has not been created. (5) Particles will be projected on to the grid points. Currently, a linear weighting technique is intended to be used, but has not settled upon. (6) Once on the gridpoints the particle number will be reduced using a set of quadrature points based on the third order velocity moments of the particles. The method proposed by R. Fox has been programmed and shown to conserve energy, momentum and mass to machine precision. In addition to reducing the number of particles this method will work to quiet the simulation it will behave as a higher order version of the Quiet DSMC method proposed by B. Albright et al. (7) These quadrature points then become the new particles for the next timestep. the advantage of this method can be many: The self force on ions can be easily removed since all particles begin on grid points. The size of the timesteps should not be limited by collision rate, and should only be impacted by particle travel time through the cell. The particle reduction technique should keep many of the higher order features of the particle distribution while reducing the number of particles in the system. It should also quite the variance in the system. The two largest unknowns, at this time are, how large a part numerical diffusion will play in the scheme and how computationally expensive each timestep will be.« less

A new PIC noise reduction technique

NASA Astrophysics Data System (ADS)

Barnes, D. C.

2014-10-01

Numerical solution of the Vlasov equation is considered in a general situation in which there is an underlying static solution (equilibrium). There are no further assumptions about dimensionality, smallenss of orbits, or disparate time scales. The semi-characteristic (SC) method for Vlasov solution is described. The usual characteristics of the equation, which are the single particle orbits, are modified in such a way that the equilibrium phase-space flow is removed. In this way, the shot noise introduced by the usual discrete particle representation of the equilibrium is static in time and can be removed completely by subtraction. An almost exact algorithm for this is based on the observation that a (infinitesimal or) discrete time step of any equilibrium MC realization is again a realization of the equilibrium, building up strings of associated simulation particles. In this way, the only added discretization error arises from the need to extrapolate backward in time the chain end points one dt using a canonical transformation. Previously developed energy-conserving time-implicit methods are applied without modification. 1D ES examples of Landau damping and velocity-space instability are given to illustrate the method.

Exact theory of freeze-out

NASA Astrophysics Data System (ADS)

Cannoni, Mirco

2015-03-01

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature . The point , which coincides with the stationary point of the equation for the quantity , is where the maximum departure of the WIMPs abundance from the thermal value is reached. For each mass and total annihilation cross section , the temperature and the actual WIMPs abundance are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval . The matching of the two abundances at is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1-2 % in the case of -wave and -wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics.

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

Bello-Rivas, Juan M.; Elber, Ron; Department of Chemistry, University of Texas at Austin, Austin, Texas 78712

A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of themore » new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied.« less

Aerodynamic beam generator for large particles

DOEpatents

Brockmann, John E.; Torczynski, John R.; Dykhuizen, Ronald C.; Neiser, Richard A.; Smith, Mark F.

2002-01-01

A new type of aerodynamic particle beam generator is disclosed. This generator produces a tightly focused beam of large material particles at velocities ranging from a few feet per second to supersonic speeds, depending on the exact configuration and operating conditions. Such generators are of particular interest for use in additive fabrication techniques.

Symmetry restoration and quantumness reestablishment.

PubMed

Zeng, Guo-Mo; Wu, Lian-Ao; Xing, Hai-Jun

2014-09-18

A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.

Viscosity of a concentrated suspension of rigid monosized particles

NASA Astrophysics Data System (ADS)

Brouwers, H. J. H.

2010-05-01

This paper addresses the relative viscosity of concentrated suspensions loaded with unimodal hard particles. So far, exact equations have only been put forward in the dilute limit, e.g., by Einstein [A. Einstein, Ann. Phys. 19, 289 (1906) (in German); Ann. Phys. 34, 591 (1911) (in German)] for spheres. For larger concentrations, a number of phenomenological models for the relative viscosity was presented, which depend on particle concentration only. Here, an original and exact closed form expression is derived based on geometrical considerations that predicts the viscosity of a concentrated suspension of monosized particles. This master curve for the suspension viscosity is governed by the relative viscosity-concentration gradient in the dilute limit (for spheres the Einstein limit) and by random close packing of the unimodal particles in the concentrated limit. The analytical expression of the relative viscosity is thoroughly compared with experiments and simulations reported in the literature, concerning both dilute and concentrated suspensions of spheres, and good agreement is found.

Radial rescaling approach for the eigenvalue problem of a particle in an arbitrarily shaped box.

PubMed

Lijnen, Erwin; Chibotaru, Liviu F; Ceulemans, Arnout

2008-01-01

In the present work we introduce a methodology for solving a quantum billiard with Dirichlet boundary conditions. The procedure starts from the exactly known solutions for the particle in a circular disk, which are subsequently radially rescaled in such a way that they obey the new boundary conditions. In this way one constructs a complete basis set which can be used to obtain the eigenstates and eigenenergies of the corresponding quantum billiard to a high level of precision. Test calculations for several regular polygons show the efficiency of the method which often requires one or two basis functions to describe the lowest eigenstates with high accuracy.

Identifying and quantifying interactions in a laboratory swarm

NASA Astrophysics Data System (ADS)

Puckett, James; Kelley, Douglas; Ouellette, Nicholas

2013-03-01

Emergent collective behavior, such as in flocks of birds or swarms of bees, is exhibited throughout the animal kingdom. Many models have been developed to describe swarming and flocking behavior using systems of self-propelled particles obeying simple rules or interacting via various potentials. However, due to experimental difficulties and constraints, little empirical data exists for characterizing the exact form of the biological interactions. We study laboratory swarms of flying Chironomus riparius midges, using stereoimaging and particle tracking techniques to record three-dimensional trajectories for all the individuals in the swarm. We describe methods to identify and quantify interactions by examining these trajectories, and report results on interaction magnitude, frequency, and mutuality.

Dielectrophoretic immobilisation of nanoparticles as isolated singles in regular arrays

NASA Astrophysics Data System (ADS)

Knigge, Xenia; Wenger, Christian; Bier, Frank F.; Hölzel, Ralph

2018-02-01

We demonstrate the immobilisation of polystyrene nanoparticles on vertical nano-electrodes by means of dielectrophoresis. The electrodes have diameters of 500 nm or 50 nm, respectively, and are arranged in arrays of several thousand electrodes, allowing many thousands of experiments in parallel. At a frequency of 15 kHz, which is found favourable for polystyrene, several occupation patterns are observed, and both temporary and permanent immobilisation is achieved. In addition, a histogram method is applied, which allows to determine the number of particles occupying the electrodes. These results are validated with scanning electron microscopy images. Immobilising exactly one particle at each electrode tip is achieved for electrode tip diameters with half the particle size. Extension of this system down to the level of single molecules is envisaged, which will avoid ensemble averaging at still statistically large sample sizes.

Power series solution of the inhomogeneous exclusion process

NASA Astrophysics Data System (ADS)

Szavits-Nossan, Juraj; Romano, M. Carmen; Ciandrini, Luca

2018-05-01

We develop a power series method for the nonequilibrium steady state of the inhomogeneous one-dimensional totally asymmetric simple exclusion process (TASEP) in contact with two particle reservoirs and with site-dependent hopping rates in the bulk. The power series is performed in the entrance or exit rates governing particle exchange with the reservoirs, and the corresponding particle current is computed analytically up to the cubic term in the entry or exit rate, respectively. We also show how to compute higher-order terms using combinatorial objects known as Young tableaux. Our results address the long outstanding problem of finding the exact nonequilibrium steady state of the inhomogeneous TASEP. The findings are particularly relevant to the modeling of mRNA translation in which the rate of translation initiation, corresponding to the entrance rate in the TASEP, is typically small.

Two-particle correlation function and dihadron correlation approach

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

Vechernin, V. V., E-mail: v.vechernin@spbu.ru; Ivanov, K. O.; Neverov, D. I.

It is shown that, in the case of asymmetric nuclear interactions, the application of the traditional dihadron correlation approach to determining a two-particle correlation function C may lead to a form distorted in relation to the canonical pair correlation function {sub C}{sup 2}. This result was obtained both by means of exact analytic calculations of correlation functions within a simple string model for proton–nucleus and deuteron–nucleus collisions and by means of Monte Carlo simulations based on employing the HIJING event generator. It is also shown that the method based on studying multiplicity correlations in two narrow observation windows separated inmore » rapidity makes it possible to determine correctly the canonical pair correlation function C{sub 2} for all cases, including the case where the rapidity distribution of product particles is not uniform.« less

Generalized Langevin equation with a three parameter Mittag-Leffler noise

NASA Astrophysics Data System (ADS)

Sandev, Trifce; Tomovski, Živorad; Dubbeldam, Johan L. A.

2011-10-01

The relaxation functions for a given generalized Langevin equation in the presence of a three parameter Mittag-Leffler noise are studied analytically. The results are represented by three parameter Mittag-Leffler functions. Exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the Laplace transform method. The asymptotic behavior of the particle in the short and long time limits are found by using the Tauberian theorems. It is shown that for large times the particle motion is subdiffusive for β-1<αδ<β, and superdiffusive for β<αδ. Many previously obtained results are recovered. Due to the many parameters contained in the noise term, the model considered in this work may be used to improve the description of data and to model anomalous diffusive processes in complex media.

Investigation of the two-quasiparticle bands in the doubly-odd nucleus 166Ta using a particle-number conserving cranked shell model

NASA Astrophysics Data System (ADS)

Zhang, ZhenHua

2016-07-01

The high-spin rotational properties of two-quasiparticle bands in the doubly-odd 166Ta are analyzed using the cranked shell model with pairing correlations treated by a particle-number conserving method, in which the blocking effects are taken into account exactly. The experimental moments of inertia and alignments and their variations with the rotational frequency hω are reproduced very well by the particle-number conserving calculations, which provides a reliable support to the configuration assignments in previous works for these bands. The backbendings in these two-quasiparticle bands are analyzed by the calculated occupation probabilities and the contributions of each orbital to the total angular momentum alignments. The moments of inertia and alignments for the Gallagher-Moszkowski partners of these observed two-quasiparticle rotational bands are also predicted.

Multiscale modeling of particle in suspension with smoothed dissipative particle dynamics

NASA Astrophysics Data System (ADS)

Bian, Xin; Litvinov, Sergey; Qian, Rui; Ellero, Marco; Adams, Nikolaus A.

2012-01-01

We apply smoothed dissipative particle dynamics (SDPD) [Español and Revenga, Phys. Rev. E 67, 026705 (2003)] to model solid particles in suspension. SDPD is a thermodynamically consistent version of smoothed particle hydrodynamics (SPH) and can be interpreted as a multiscale particle framework linking the macroscopic SPH to the mesoscopic dissipative particle dynamics (DPD) method. Rigid structures of arbitrary shape embedded in the fluid are modeled by frozen particles on which artificial velocities are assigned in order to satisfy exactly the no-slip boundary condition on the solid-liquid interface. The dynamics of the rigid structures is decoupled from the solvent by solving extra equations for the rigid body translational/angular velocities derived from the total drag/torque exerted by the surrounding liquid. The correct scaling of the SDPD thermal fluctuations with the fluid-particle size allows us to describe the behavior of the particle suspension on spatial scales ranging continuously from the diffusion-dominated regime typical of sub-micron-sized objects towards the non-Brownian regime characterizing macro-continuum flow conditions. Extensive tests of the method are performed for the case of two/three dimensional bulk particle-system both in Brownian/ non-Brownian environment showing numerical convergence and excellent agreement with analytical theories. Finally, to illustrate the ability of the model to couple with external boundary geometries, the effect of confinement on the diffusional properties of a single sphere within a micro-channel is considered, and the dependence of the diffusion coefficient on the wall-separation distance is evaluated and compared with available analytical results.

Multidimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Chacon, Luis

2015-09-01

We discuss a new, conservative, fully implicit 2D-3V particle-in-cell algorithm for non-radiative, electromagnetic kinetic plasma simulations, based on the Vlasov-Darwin model. Unlike earlier linearly implicit PIC schemes and standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. This has been demonstrated in 1D electrostatic and electromagnetic contexts. In this study, we build on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the Darwin field and particle orbit equations for multiple species in multiple dimensions. The Vlasov-Darwin model is very attractive for PIC simulations because it avoids radiative noise issues in non-radiative electromagnetic regimes. The algorithm conserves global energy, local charge, and particle canonical-momentum exactly, even with grid packing. The nonlinear iteration is effectively accelerated with a fluid preconditioner, which allows efficient use of large timesteps, O(√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D and 2D. Support from the LANL LDRD program and the DOE-SC ASCR office.

Multi-dimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations in curvilinear geometry

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacon, Luis

2015-11-01

We discuss a new, conservative, fully implicit 2D3V Vlasov-Darwin particle-in-cell algorithm in curvilinear geometry for non-radiative, electromagnetic kinetic plasma simulations. Unlike standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. Here, we extend these algorithms to curvilinear geometry. The algorithm retains its exact conservation properties in curvilinear grids. The nonlinear iteration is effectively accelerated with a fluid preconditioner for weakly to modestly magnetized plasmas, which allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D (slow shock) and 2D (island coalescense).

GEMPIC: geometric electromagnetic particle-in-cell methods

NASA Astrophysics Data System (ADS)

Kraus, Michael; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

2017-08-01

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

Applicability of Rayleigh–Gans Scattering to Spherical Particles

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

Kerker, M.; Farone, W. A.; Matijevic, E.

1963-01-01

Exact computations of scattering functions for spheres are compared with those obtained from the Rayleigh-Gans theory of scattering of electromagnetic radiation. The range of validity for spheres as a guide for non-homogeneous particles and other geometries. This study is limited to non-absorbing particles with real indices of refraction. (C.E.S.)

Unbinding slave spins in the Anderson impurity model

NASA Astrophysics Data System (ADS)

Guerci, Daniele; Fabrizio, Michele

2017-11-01

We show that a generic single-orbital Anderson impurity model, lacking, for instance, any kind of particle-hole symmetry, can be exactly mapped without any constraint onto a resonant level model coupled to two Ising variables, which reduce to one if the hybridization is particle-hole symmetric. The mean-field solution of this model is found to be stable to unphysical spontaneous magnetization of the impurity, unlike the saddle-point solution in the standard slave-boson representation. Remarkably, the mean-field estimate of the Wilson ratio approaches the exact value RW=2 in the Kondo regime.

Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap

NASA Astrophysics Data System (ADS)

Scopa, Stefano; Unterberger, Jéremie; Karevski, Dragi

2018-05-01

We study the unitary dynamics of a 1D gas of hard-core bosons trapped into a harmonic potential which varies periodically in time with frequency . Such periodic systems can be classified into orbits of different monodromies corresponding to two different physical situations, namely the case in which the bosonic cloud remains stable during the time-evolution and the case where it turns out to be unstable. In the present work we derive in the large particle number limit exact results for the stroboscopic evolution of the energy and particle densities in both physical situations.

Quantizing the Toda lattice

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

Siddharthan, R.; Shastry, B.S.

In this work we study the quantum Toda lattice, developing the asymptotic Bethe ansatz method first used by Sutherland. Despite its known limitations we find, on comparing with Gutzwiller{close_quote}s exact method, that it works well in this particular problem and in fact becomes exact as {h_bar} grows large. We calculate ground state and excitation energies for finite-sized lattices, identify excitations as phonons and solitons on the basis of their quantum numbers, and find their dispersions. These are similar to the classical dispersions for small {h_bar}, and remain similar all the way up to {h_bar}=1, but then deviate substantially as wemore » go farther into the quantum regime. On comparing the sound velocities for various {h_bar} obtained thus with that predicted by conformal theory we conclude that the Bethe ansatz gives the energies per particle accurate to O(1/N{sup 2}). On that assumption we can find correlation functions. Thus the Bethe ansatz method can be used to yield much more than the thermodynamic properties which previous authors have calculated. {copyright} {ital 1997} {ital The American Physical Society}« less

Clustering of galaxies with f(R) gravity

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; Faizal, Mir; Hameeda, Mir; Pourhassan, Behnam; Salzano, Vincenzo; Upadhyay, Sudhaker

2018-02-01

Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newton's potential given by f(R) gravity. We compute the corrected N-particle partition function analytically. The corrected partition function leads to more exact equations of state of the system. By assuming that the system follows quasi-equilibrium, we derive the exact distribution function that exhibits the f(R) correction. Moreover, we evaluate the critical temperature and discuss the stability of the system. We observe the effects of correction of f(R) gravity on the power-law behaviour of particle-particle correlation function also. In order to check the feasibility of an f(R) gravity approach to the clustering of galaxies, we compare our results with an observational galaxy cluster catalogue.

Computer modeling of test particle acceleration at oblique shocks

NASA Technical Reports Server (NTRS)

Decker, Robert B.

1988-01-01

The present evaluation of the basic techniques and illustrative results of charged particle-modeling numerical codes suitable for particle acceleration at oblique, fast-mode collisionless shocks emphasizes the treatment of ions as test particles, calculating particle dynamics through numerical integration along exact phase-space orbits. Attention is given to the acceleration of particles at planar, infinitessimally thin shocks, as well as to plasma simulations in which low-energy ions are injected and accelerated at quasi-perpendicular shocks with internal structure.

Efficient Voronoi volume estimation for DEM simulations of granular materials under confined conditions

PubMed Central

Frenning, Göran

2015-01-01

When the discrete element method (DEM) is used to simulate confined compression of granular materials, the need arises to estimate the void space surrounding each particle with Voronoi polyhedra. This entails recurring Voronoi tessellation with small changes in the geometry, resulting in a considerable computational overhead. To overcome this limitation, we propose a method with the following features:•A local determination of the polyhedron volume is used, which considerably simplifies implementation of the method.•A linear approximation of the polyhedron volume is utilised, with intermittent exact volume calculations when needed.•The method allows highly accurate volume estimates to be obtained at a considerably reduced computational cost. PMID:26150975

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

Nonlinear Boltzmann equation for the homogeneous isotropic case: Minimal deterministic Matlab program

NASA Astrophysics Data System (ADS)

Asinari, Pietro

2010-10-01

The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic model for many applications in thermodynamics, econophysics and sociodynamics. Despite recent hardware improvements, the solution of the Boltzmann equation remains extremely challenging from the computational point of view, in particular by deterministic methods (free of stochastic noise). This work aims to improve a deterministic direct method recently proposed [V.V. Aristov, Kluwer Academic Publishers, 2001] for solving the HIBE with a generic collisional kernel and, in particular, for taking care of the late dynamics of the relaxation towards the equilibrium. Essentially (a) the original problem is reformulated in terms of particle kinetic energy (exact particle number and energy conservation during microscopic collisions) and (b) the computation of the relaxation rates is improved by the DVM-like correction, where DVM stands for Discrete Velocity Model (ensuring that the macroscopic conservation laws are exactly satisfied). Both these corrections make possible to derive very accurate reference solutions for this test case. Moreover this work aims to distribute an open-source program (called HOMISBOLTZ), which can be redistributed and/or modified for dealing with different applications, under the terms of the GNU General Public License. The program has been purposely designed in order to be minimal, not only with regards to the reduced number of lines (less than 1000), but also with regards to the coding style (as simple as possible). Program summaryProgram title: HOMISBOLTZ Catalogue identifier: AEGN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 23 340 No. of bytes in distributed program, including test data, etc.: 7 635 236 Distribution format: tar.gz Programming language: Tested with Matlab version ⩽6.5. However, in principle, any recent version of Matlab or Octave should work Computer: All supporting Matlab or Octave Operating system: All supporting Matlab or Octave RAM: 300 MBytes Classification: 23 Nature of problem: The problem consists in integrating the homogeneous Boltzmann equation for a generic collisional kernel in case of isotropic symmetry, by a deterministic direct method. Difficulties arise from the multi-dimensionality of the collisional operator and from satisfying the conservation of particle number and energy (momentum is trivial for this test case) as accurately as possible, in order to preserve the late dynamics. Solution method: The solution is based on the method proposed by Aristov (2001) [1], but with two substantial improvements: (a) the original problem is reformulated in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium). Both these corrections make possible to derive very accurate reference solutions for this test case. Restrictions: The nonlinear Boltzmann equation is extremely challenging from the computational point of view, in particular for deterministic methods, despite the increased computational power of recent hardware. In this work, only the homogeneous isotropic case is considered, for making possible the development of a minimal program (by a simple scripting language) and allowing the user to check the advantages of the proposed improvements beyond Aristov's (2001) method [1]. The initial conditions are supposed parameterized according to a fixed analytical expression, but this can be easily modified. Running time: From minutes to hours (depending on the adopted discretization of the kinetic energy space). For example, on a 64 bit workstation with Intel CoreTM i7-820Q Quad Core CPU at 1.73 GHz and 8 MBytes of RAM, the provided test run (with the corresponding binary data file storing the pre-computed relaxation rates) requires 154 seconds. References:V.V. Aristov, Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows, Kluwer Academic Publishers, 2001.

Exact solution for a non-Markovian dissipative quantum dynamics.

PubMed

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

Topics in Diffusion Limited Reaction Processes

NASA Astrophysics Data System (ADS)

Lin, Jian-Cheng

We study, both theoretically and numerically, the macroscopic particle concentration in a class of simple diffusion-limited reactions: one species coagulation A + A to A, reversible coagulation A + A rightleftharpoons A, A + A to A with particle input, A + A rightleftharpoons A with particle input, single species annihilation A + A to inert, and two species annihilation A + B to inert. The main interest is in the asymptotic behavior of the particle concentration. We review the standard mean-field theory, mass-reaction kinetics and the associated nonlinear rate and diffusion-reaction equations. Theoretically we study the concentration using several closure schemes for truncating the infinite hierarchy of the kinetic equations for the joint density functions. Our goal is to evaluate the quality of some nonsystematic approximations by comparison with exact solutions. It is found that these approximations are very good at capturing the asymptotic behavior of the particle concentrations in the irreversible reactions, while they fail to predict the far-from-equilibrium dynamic phase transition in the one dimensional reversible coagulation reaction predicted by exact results. Numerically we use Monte Carlo simulation to study concentrations in the single species reversible coagulation process. In one dimension the numerical results are in excellent agreement with the exact analytic results. In two dimensions, our simulation data in the transient states suggest an interesting scaling for the deviation of the concentration from its equilibrium value, delta C(t) ~ exp( -beta(C_0)t^{alpha(C_0) }), where alpha(C_0) and beta(C_0) are functions of the initial concentration C_0. However, it seems unlikely to be able to answer the question of the existence of a dynamic phase transition in two dimensions by Monte Carlo simulation within a reasonable CPU time due to the long persistence of the transient states. In an appendix we solve exactly an annihilation-related percolation problem.

Light scattering by hexagonal ice crystals with distributed inclusions

NASA Astrophysics Data System (ADS)

Panetta, R. Lee; Zhang, Jia-Ning; Bi, Lei; Yang, Ping; Tang, Guanlin

2016-07-01

Inclusions of air bubbles or soot particles have significant effects on the single-scattering properties of ice crystals, effects that in turn have significant impacts on the radiation budget of an atmosphere containing the crystals. This study investigates some of the single-scattering effects in the case of hexagonal ice crystals, including effects on the backscattering depolarization ratio, a quantity of practical importance in the interpretation of lidar observations. One distinguishing feature of the study is an investigation of scattering properties at a visible wavelength for a crystal with size parameter (x) above 100, a size regime where one expects some agreement between exact methods and geometrical optics methods. This expectation is generally borne out in a test comparison of how the sensitivity of scattering properties to the distribution of a given volume fraction of included air is represented using (i) an approximate Monte Carlo Ray Tracing (MCRT) method and (ii) a numerically exact pseudo-spectral time-domain (PSTD) method. Another distinguishing feature of the study is a close examination, using the numerically exact Invariant-Imbedding T-Matrix (II-TM) method, of how some optical properties of importance to satellite remote sensing vary as the volume fraction of inclusions and size of crystal are varied. Although such an investigation of properties in the x>100 regime faces serious computational burdens that force a large number of idealizations and simplifications in the study, the results nevertheless provide an intriguing glimpse of what is evidently a quite complex sensitivity of optical scattering properties to inclusions of air or soot as volume fraction and size parameter are varied.

X-ray analysis of aerosol samples from a therapeutic cave

NASA Astrophysics Data System (ADS)

Alföldy, B.; Török, Sz.; Kocsonya, A.; Szőkefalvi-Nagy, Z.; Balla, Md. I.

2001-04-01

Cave therapy is an efficient therapeutic method to cure asthma, the exact healing effect, however, is not clarified, yet. This study is motivated by the basic assumption that aerosols do play the key role in the cave therapy. This study is based on measurements of single aerosol particles originating from a therapeutic cave of Budapest, Hungary (Szemlőhegyi cave). Aerosol particles have been collected in the regions arranged for the therapeutic treatment. Samples were further analysed for chemical and morphological aspects, determining the particle size distribution and classifying them according to elemental composition. Three particle classes have been detected based on major element concentration: alumino-silicate, quartz and calcium carbonate. Calcium ions have well-known physiological influence: anti-spastic, anti-inflammation and excretion reducing effects. Inflammation, accompanying spasm and extreme excretion production cause the smothering stigma, the so-called asthma. Therefore it could be assumed that calcium ions present in high concentration in the cave's atmosphere is the major cause of the healing effect.

Overlaps with arbitrary two-site states in the XXZ spin chain

NASA Astrophysics Data System (ADS)

Pozsgay, B.

2018-05-01

We present a conjectured exact formula for overlaps between the Bethe states of the spin-1/2 XXZ chain and generic two-site states. The result takes the same form as in the previously known cases: it involves the same ratio of two Gaudin-like determinants, and a product of single-particle overlap functions, which can be fixed using a combination of the quench action and quantum transfer matrix methods. Our conjecture is confirmed by numerical data from exact diagonalization. For one-site states, the formula is found to be correct even in chains with odd length. It is also pointed out that the ratio of the Gaudin-like determinants plays a crucial role in the overlap sum rule: it guarantees that in the thermodynamic limit there remains no term in the quench action.

Exact Critical Exponents for the Antiferromagnetic Quantum Critical Metal in Two Dimensions

NASA Astrophysics Data System (ADS)

Schlief, Andres; Lunts, Peter; Lee, Sung-Sik

2017-04-01

Unconventional metallic states which do not support well-defined single-particle excitations can arise near quantum phase transitions as strong quantum fluctuations of incipient order parameters prevent electrons from forming coherent quasiparticles. Although antiferromagnetic phase transitions occur commonly in correlated metals, understanding the nature of the strange metal realized at the critical point in layered systems has been hampered by a lack of reliable theoretical methods that take into account strong quantum fluctuations. We present a nonperturbative solution to the low-energy theory for the antiferromagnetic quantum critical metal in two spatial dimensions. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by a new control parameter that emerges dynamically. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures.

Formally exact integral equation theory of the exchange-only potential in density functional theory: Refined closure approximation

NASA Astrophysics Data System (ADS)

March, N. H.; Nagy, Á.

A fonnally exact integral equation theory for the exchange-only potential Vx(r) in density functional theory was recently set up by Howard and March [I.A. Howard, N.H. March, J. Chem. Phys. 119 (2003) 5789]. It involved a `closure' function P(r) satisfying the exact sum rule ∫ P(r) dr = 0. The simplest choice P(r) = 0 recovers then the approximation proposed by Della Sala and Görling [F. Della Sala, A. Görling, J. Chem. Phys. 115 (2001) 5718] and by Gritsenko and Baerends [O.V. Gritsenko, E.J. Baerends, Phys. Rev. A 64 (2001) 042506]. Here, refined choices of P(r) are proposed, the most direct being based on the KLI (Krieger-Li-Iafrate) approximation. A further choice given some attention is where P(r) involves frontier orbital properties. In particular, the introduction of the LUMO (lowest unoccupied molecular) orbital, along with the energy separation between HOMO (highest occupied molecular orbital) and LUMO levels, should prove a significant step beyond current approximations to the optimized potential method, all of which involve only single-particle occupied orbitals.

Path-integral Monte Carlo method for Rényi entanglement entropies.

PubMed

Herdman, C M; Inglis, Stephen; Roy, P-N; Melko, R G; Del Maestro, A

2014-07-01

We introduce a quantum Monte Carlo algorithm to measure the Rényi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path-integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability, and interactions. We present proof-of-principle calculations and benchmark against an exactly soluble model of interacting bosons in one spatial dimension. As this algorithm retains the fundamental polynomial scaling of quantum Monte Carlo when applied to sign-problem-free models, future applications should allow for the study of entanglement entropy in large-scale many-body systems of interacting bosons.

Correcting for particle counting bias error in turbulent flow

NASA Technical Reports Server (NTRS)

Edwards, R. V.; Baratuci, W.

1985-01-01

An ideal seeding device is proposed generating particles that exactly follow the flow out are still a major source of error, i.e., with a particle counting bias wherein the probability of measuring velocity is a function of velocity. The error in the measured mean can be as much as 25%. Many schemes have been put forward to correct for this error, but there is not universal agreement as to the acceptability of any one method. In particular it is sometimes difficult to know if the assumptions required in the analysis are fulfilled by any particular flow measurement system. To check various correction mechanisms in an ideal way and to gain some insight into how to correct with the fewest initial assumptions, a computer simulation is constructed to simulate laser anemometer measurements in a turbulent flow. That simulator and the results of its use are discussed.

Solutions of burnt-bridge models for molecular motor transport.

PubMed

Morozov, Alexander Yu; Pronina, Ekaterina; Kolomeisky, Anatoly B; Artyomov, Maxim N

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called "bridges"), is investigated theoretically by analyzing discrete-state stochastic "burnt-bridge" models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed ("burned") with a probability p , creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into a one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For the general case of p<1 a theoretical method is developed and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics for periodic distribution of bridges and different burning dynamics are analyzed and compared. Analytical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

Solutions of burnt-bridge models for molecular motor transport

NASA Astrophysics Data System (ADS)

Morozov, Alexander Yu.; Pronina, Ekaterina; Kolomeisky, Anatoly B.; Artyomov, Maxim N.

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called “bridges”), is investigated theoretically by analyzing discrete-state stochastic “burnt-bridge” models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (“burned”) with a probability p , creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into a one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For the general case of p<1 a theoretical method is developed and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics for periodic distribution of bridges and different burning dynamics are analyzed and compared. Analytical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

Stability of the wobbling motion in the triaxially deformed odd-A nucleus

NASA Astrophysics Data System (ADS)

Tanabe, Kosai; Sugawara-Tanabe, Kazuko

2017-12-01

In order to analyze the content of the exact solutions for particle-rotor models with both the rigid and the hydrodynamical moments of inertia (MoI), as a theoretical probe we apply the Holstein-Primakoff (HP) boson expansion method to the total angular momentum I and the single-particle angular momentum j. We study the competition between Coriolis force and the single-particle potential by employing the different choices of the diagonal HP boson representations for the components of I and j along a common coordinate axis, and along perpendicular axes. We do not find any wobbling level sequence associated with the rotation around the principal axis with the medium MoI. The staggering in the alignments of I about the axis with the medium MoI is found in the limited range of I, while the vector R(=I-j) is confined about the axis with the largest MoI.

[Study on the surface-enhanced Raman spectrum of trimethoprim].

PubMed

Zhang, Jin-zhi; Wang, Yuan

2003-02-01

A new method is given in this paper to study the spectra of trimethoprim by using the surface-enhanced Raman spectrum (SERS) technology and the highly efficient thin layer chromatography (TLC) dissociation technology. The results of SERS indicate that the main vibrant spectral band can be obtained by TLC in the samples of about 6 micrograms. The expansion and contraction of pyrimidine ring can be obviously increased and the molecule information can be exactly presented under the action of silver particles.

Stationary phase method and delay times for relativistic and non-relativistic tunneling particles

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

Bernardini, A.E.

2009-06-15

The stationary phase method is frequently adopted for calculating tunneling phase times of analytically-continuous Gaussian or infinite-bandwidth step pulses which collide with a potential barrier. This report deals with the basic concepts on deducing transit times for quantum scattering: the stationary phase method and its relation with delay times for relativistic and non-relativistic tunneling particles. After reexamining the above-barrier diffusion problem, we notice that the applicability of this method is constrained by several subtleties in deriving the phase time that describes the localization of scattered wave packets. Using a recently developed procedure - multiple wave packet decomposition - for somemore » specifical colliding configurations, we demonstrate that the analytical difficulties arising when the stationary phase method is applied for obtaining phase (traversal) times are all overcome. In this case, we also investigate the general relation between phase times and dwell times for quantum tunneling/scattering. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, we demonstrate that these two distinct transit time definitions are explicitly connected. The traversal times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Multiple wave packet decomposition shows us that the phase time (group delay) describes the exact position of the scattered particles and, in addition to the exact relation with the dwell time, leads to correct conceptual understanding of both transit time definitions. At last, we extend the non-relativistic formalism to the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation where the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are all quantified and the problematic superluminal interpretation based on the non-relativistic tunneling dynamics is revisited. Lessons concerning the dynamics of relativistic tunneling and the mathematical structure of its solutions suggest revealing insights into mathematically analogous condensed-matter experiments using electrostatic barriers in single- and bi-layer graphene, for which the accelerated tunneling effect deserves a more careful investigation.« less

MHD Flow of Sodium Alginate-Based Casson Type Nanofluid Passing Through A Porous Medium With Newtonian Heating.

PubMed

Khan, Arshad; Khan, Dolat; Khan, Ilyas; Ali, Farhad; Karim, Faizan Ul; Imran, Muhammad

2018-06-05

Casson nanofluid, unsteady flow over an isothermal vertical plate with Newtonian heating (NH) is investigated. Sodium alginate (base fluid)is taken as counter example of Casson fluid. MHD and porosity effects are considered. Effects of thermal radiation along with heat generation are examined. Sodium alginate with Silver, Titanium oxide, Copper and Aluminum oxide are added as nano particles. Initial value problem with physical boundary condition is solved by using Laplace transform method. Exact results are obtained for temperature and velocity fields. Skin-friction and Nusselt number are calculated. The obtained results are analyzed graphically for emerging flow parameters and discussed. It is bring into being that temperature and velocity profile are decreasing with increasing nano particles volume fraction.

Hyper-Systolic Processing on APE100/QUADRICS:. n2-LOOP Computations

NASA Astrophysics Data System (ADS)

Lippert, Thomas; Ritzenhöfer, Gero; Glaessner, Uwe; Hoeber, Henning; Seyfried, Armin; Schilling, Klaus

We investigate the performance gains from hyper-systolic implementations of n2-loop problems on the massively parallel computer Quadrics, exploiting its three-dimensional interprocessor connectivity. For illustration we study the communication aspects of an exact molecular dynamics simulation of n particles with Coulomb (or gravitational) interactions. We compare the interprocessor communication costs of the standard-systolic and the hyper-systolic approaches for various granularities. We predict gain factors as large as three on the Q4 and eight on the QH4 and measure actual performances on these machine configurations. We conclude that it appears feasible to investigate the thermodynamics of a full gravitating n-body problem with O(16.000) particles using the new method on a QH4 system.

Electromagnetic Scattering by Fully Ordered and Quasi-Random Rigid Particulate Samples

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.

2016-01-01

In this paper we have analyzed circumstances under which a rigid particulate sample can behave optically as a true discrete random medium consisting of particles randomly moving relative to each other during measurement. To this end, we applied the numerically exact superposition T-matrix method to model far-field scattering characteristics of fully ordered and quasi-randomly arranged rigid multiparticle groups in fixed and random orientations. We have shown that, in and of itself, averaging optical observables over movements of a rigid sample as a whole is insufficient unless it is combined with a quasi-random arrangement of the constituent particles in the sample. Otherwise, certain scattering effects typical of discrete random media (including some manifestations of coherent backscattering) may not be accurately replicated.

Landau problem with time dependent mass in time dependent electric and harmonic background fields

NASA Astrophysics Data System (ADS)

Lawson, Latévi M.; Avossevou, Gabriel Y. H.

2018-04-01

The spectrum of a Hamiltonian describing the dynamics of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field is obtained. The configuration space wave function of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian, we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce a unitary transformation in the framework of the algebraic formalism to construct the invariant operator of the system and then to obtain the exact solution of the Hamiltonian. We recover the solutions of the ordinary Landau problem in the absence of the electric and harmonic fields for a constant particle mass.

Spin and pseudospin symmetric Dirac particles in the field of Tietz—Hua potential including Coulomb tensor interaction

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-09-01

Approximate analytical solutions of the Dirac equation for Tietz—Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin—orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin—orbit coupling terms κ(κ ± 1)r-2. Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov—Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.

Large accumulation of micro-sized synthetic polymer particles in the sea surface microlayer.

PubMed

Song, Young Kyoung; Hong, Sang Hee; Jang, Mi; Kang, Jung-Hoon; Kwon, Oh Youn; Han, Gi Myung; Shim, Won Joon

2014-08-19

Determining the exact abundance of microplastics on the sea surface can be susceptible to the sampling method used. The sea surface microlayer (SML) can accumulate light plastic particles, but this has not yet been sampled. The abundance of microplastics in the SML was evaluated off the southern coast of Korea. The SML sampling method was then compared to bulk surface water filtering, a hand net (50 μm mesh), and a Manta trawl net (330 μm mesh). The mean abundances were in the order of SML water > hand net > bulk water > Manta trawl net. Fourier transform infrared spectroscopy (FTIR) identified that alkyds and poly(acrylate/styrene) accounted for 81 and 11%, respectively, of the total polymer content of the SML samples. These polymers originated from paints and the fiber-reinforced plastic (FRP) matrix used on ships. Synthetic polymers from ship coatings should be considered to be a source of microplastics. Selecting a suitable sampling method is crucial for evaluating microplastic pollution.

Interacting particle systems in time-dependent geometries

NASA Astrophysics Data System (ADS)

Ali, A.; Ball, R. C.; Grosskinsky, S.; Somfai, E.

2013-09-01

Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be described effectively by space-time trajectories of interacting particles, such as domain boundaries in two-dimensional growth or river networks. We study trajectories embedded in time-dependent geometries, and the main focus is on uniformly expanding or decreasing domains for which we obtain an exact mapping to simple fixed domain systems while preserving the local scale invariance properties. This approach was recently introduced in Ali et al (2013 Phys. Rev. E 87 020102(R)) and here we provide a detailed discussion on its applicability for self-affine Markovian models, and how it can be adapted to self-affine models with memory or explicit time dependence. The mapping corresponds to a nonlinear time transformation which converges to a finite value for a large class of trajectories, enabling an exact analysis of asymptotic properties in expanding domains. We further provide a detailed discussion of different particle interactions and generalized geometries. All our findings are based on exact computations and are illustrated numerically for various examples, including Lévy processes and fractional Brownian motion.

Efficient numerical technique for calculating the properties of interacting dimers in the Peierls-Hubbard model

NASA Astrophysics Data System (ADS)

Sous, John; Chakraborty, Monodeep; Krems, Roman; Berciu, Mona

2017-04-01

We develop a method to compute the Green's function for two particles in an infinite chain and coupled to phonons by interactions that modulate their hopping as described by the Peierls/Su-Schrieffer-Heeger (SSH) model. The method is based on a variational approximation to the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy and is shown to agree with exact digaonalization calculations. We show that the properties of bipolarons arising in such models is qualitatively different from those of the well-studied Holstein bipolarons. In particular, we show that depending on the particle statistics, strongly bound bipolarons may or may not form. In the case of hard-core bosons, we demonstrate novel effects for dimers such as sharp transitions and self-trapping. In the case of soft-core particles/ spinfull fermions, we show that the mediated interactions lead to overscreeing of the bare Hubbard U repulsion resulting in the formation of strongly bound bipolarons. This work was supported by NSERC of Canada and the Stewart Blusson Quantum Matter Institute.

Exact solution of two interacting run-and-tumble random walkers with finite tumble duration

NASA Astrophysics Data System (ADS)

Slowman, A. B.; Evans, M. R.; Blythe, R. A.

2017-09-01

We study a model of interacting run-and-tumble random walkers operating under mutual hardcore exclusion on a one-dimensional lattice with periodic boundary conditions. We incorporate a finite, poisson-distributed, tumble duration so that a particle remains stationary whilst tumbling, thus generalising the persistent random walker model. We present the exact solution for the nonequilibrium stationary state of this system in the case of two random walkers. We find this to be characterised by two lengthscales, one arising from the jamming of approaching particles, and the other from one particle moving when the other is tumbling. The first of these lengthscales vanishes in a scaling limit where the continuous-space dynamics is recovered whilst the second remains finite. Thus the nonequilibrium stationary state reveals a rich structure of attractive, jammed and extended pieces.

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.

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

A new numerically stable implementation of the T-matrix method for electromagnetic scattering by spheroidal particles

NASA Astrophysics Data System (ADS)

Somerville, W. R. C.; Auguié, B.; Le Ru, E. C.

2013-07-01

We propose, describe, and demonstrate a new numerically stable implementation of the extended boundary-condition method (EBCM) to compute the T-matrix for electromagnetic scattering by spheroidal particles. Our approach relies on the fact that for many of the EBCM integrals in the special case of spheroids, a leading part of the integrand integrates exactly to zero, which causes catastrophic loss of precision in numerical computations. This feature was in fact first pointed out by Waterman in the context of acoustic scattering and electromagnetic scattering by infinite cylinders. We have recently studied it in detail in the case of electromagnetic scattering by particles. Based on this study, the principle of our new implementation is therefore to compute all the integrands without the problematic part to avoid the primary cause of loss of precision. Particular attention is also given to choosing the algorithms that minimise loss of precision in every step of the method, without compromising on speed. We show that the resulting implementation can efficiently compute in double precision arithmetic the T-matrix and therefore optical properties of spheroidal particles to a high precision, often down to a remarkable accuracy (10-10 relative error), over a wide range of parameters that are typically considered problematic. We discuss examples such as high-aspect ratio metallic nanorods and large size parameter (≈35) dielectric particles, which had been previously modelled only using quadruple-precision arithmetic codes.

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)

An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm in curvilinear geometry

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.; Barnes, D. C.

2012-03-01

A recent proof-of-principle study proposes an energy- and charge-conserving, fully implicit particle-in-cell algorithm in one dimension [1], which is able to use timesteps comparable to the dynamical timescale of interest. Here, we generalize the method to employ non-uniform meshes via a curvilinear map. The key enabling technology is a hybrid particle pusher [2], with particle positions updated in logical space and particle velocities updated in physical space. The self-adaptive, charge-conserving particle mover of Ref. [1] is extended to the non-uniform mesh case. The fully implicit implementation, using a Jacobian-free Newton-Krylov iterative solver, remains exactly charge- and energy-conserving. The extension of the formulation to multiple dimensions will be discussed. We present numerical experiments of 1D electrostatic, long-timescale ion-acoustic wave and ion-acoustic shock wave simulations, demonstrating that charge and energy are conserved to round-off for arbitrary mesh non-uniformity, and that the total momentum remains well conserved.[4pt] [1] Chen, Chac'on, Barnes, J. Comput. Phys. 230 (2011). [0pt] [2] Camporeale and Delzanno, Bull. Am. Phys. Soc. 56(6) (2011); Wang, et al., J. Plasma Physics, 61 (1999).

Scattering and radiative properties of complex soot and soot-containing particles

NASA Astrophysics Data System (ADS)

Liu, L.; Mishchenko, M. I.; Mackowski, D. W.; Dlugach, J.

2012-12-01

Tropospheric soot and soot containing aerosols often exhibit nonspherical overall shapes and complex morphologies. They can externally, semi-externally, and internally mix with other aerosol species. This poses a tremendous challenge in particle characterization, remote sensing, and global climate modeling studies. To address these challenges, we used the new numerically exact public-domain Fortran-90 code based on the superposition T-matrix method (STMM) and other theoretical models to analyze the potential effects of aggregation and heterogeneity on light scattering and absorption by morphologically complex soot containing particles. The parameters we computed include the whole scattering matrix elements, linear depolarization ratios, optical cross-sections, asymmetry parameters, and single scattering albedos. It is shown that the optical characteristics of soot and soot containing aerosols very much depend on particle sizes, compositions, and aerosol overall shapes. The soot particle configurations and heterogeneities can have a substantial effect that can result in a significant enhancement of extinction and absorption relative to those computed from the Lorenz-Mie theory. Meanwhile the model calculated information combined with in-situ and remote sensed data can be used to constrain soot particle shapes and sizes which are much needed in climate models.

Hybrid Particle-Element Simulation of Impact on Composite Orbital Debris Shields

NASA Technical Reports Server (NTRS)

Fahrenthold, Eric P.

2004-01-01

This report describes the development of new numerical methods and new constitutive models for the simulation of hypervelocity impact effects on spacecraft. The research has included parallel implementation of the numerical methods and material models developed under the project. Validation work has included both one dimensional simulations, for comparison with exact solutions, and three dimensional simulations of published hypervelocity impact experiments. The validated formulations have been applied to simulate impact effects in a velocity and kinetic energy regime outside the capabilities of current experimental methods. The research results presented here allow for the expanded use of numerical simulation, as a complement to experimental work, in future design of spacecraft for hypervelocity impact effects.

DNA-PCR analysis of bloodstains sampled by the polyvinyl-alcohol method.

PubMed

Schyma, C; Huckenbeck, W; Bonte, W

1999-01-01

Among the usual techniques of sampling gunshot residues (GSR), the polyvinyl-alcohol method (PVAL) includes the advantage of embedding all particles, foreign bodies and stains on the surface of the shooter's hand in exact and reproducible topographic localization. The aim of the present study on ten persons killed by firearms was to check the possibility of DNA-PCR typing of blood traces embedded in the PVAL gloves in a second step following GSR analysis. The results of these examinations verify that the PVAL technique does not include factors that inhibit successful PCR typing. Thus the PVAL method can be recommended as a combination technique to secure and preserve inorganic and biological traces at the same time.

Quantum Engineering of Dynamical Gauge Fields on Optical Lattices

DTIC Science & Technology

2016-07-08

exact blocking formulas from the TRG formulation of the transfer matrix. The second is a worm algorithm. The particle number distributions obtained...a fact that can be explained by an approximate particle- hole symmetry. We have also developed a computer code suite for simulating the Abelian

Exact diagonalization library for quantum electron models

NASA Astrophysics Data System (ADS)

Iskakov, Sergei; Danilov, Michael

2018-04-01

We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. The observables that can be computed using EDLib are single particle Green's functions and spin-spin correlation functions. This code provides three different types of Hamiltonian matrix storage that can be chosen based on the model.

Neutron Monitor Observations and Space Weather, 1. Automatically Search of Great Solar Energetic Particle Event Beginning.

NASA Astrophysics Data System (ADS)

Dorman, L. I.; Pustil'Nik, L. A.; Sternlieb, A.; Zukerman, I. G.

It is well known that in periods of great SEP fluxes of energetic particles can be so big that memory of computers and other electronics in space may be destroyed, satellites and spacecrafts became dead: according to NOAA Space Weather Scales are danger- ous Solar Radiation Storms S5-extreme (flux level of particles with energy > 10 MeV more than 10^5), S4-severe (flux more than 10^4) and S3-strong (flux more than 10^3). In these periods is necessary to switch off some part of electronics for few hours to protect computer memories. These periods are also dangerous for astronauts on space- ships, and passengers and crew in commercial jets (especially during S5 storms). The problem is how to forecast exactly these dangerous phenomena. We show that exact forecast can be made by using high-energy particles (few GeV/nucleon and higher) which transportation from the Sun is characterized by much bigger diffusion coeffi- cient than for small and middle energy particles. Therefore high energy particles came from the Sun much more early (8-20 minutes after acceleration and escaping into so- lar wind) than main part of smaller energy particles caused dangerous situation for electronics (about 30-60 minutes later). We describe here principles and experience of automatically working of program "FEP-Search". The positive result which shows the exact beginning of FEP event on the Emilio Segre' Observatory (2025 m above sea level, Rc=10.8 GV), is determined now automatically by simultaneously increas- ing on 2.5 St. Dev. in two sections of neutron supermonitor. The next 1-min data the program "FEP-Search" uses for checking that the observed increase reflects the begin- ning of real great FEP or not. If yes, automatically starts to work on line the programs "FEP-Research".

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2017-01-01

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

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.

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.

Optimized Diffusion of Run-and-Tumble Particles in Crowded Environments

NASA Astrophysics Data System (ADS)

Bertrand, Thibault; Zhao, Yongfeng; Bénichou, Olivier; Tailleur, Julien; Voituriez, Raphaël

2018-05-01

We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a d -dimensional cubic lattice in the presence of diffusing hard-core obstacles. We derive an explicit expression for the diffusivity of the RTP, which is exact in the limit of low density of fixed obstacles. To do so, we introduce a generalization of Kac's theorem on the mean return times of Markov processes, which we expect to be relevant for a large class of lattice gas problems. Our results show the diffusivity of RTPs to be nonmonotonic in the tumbling probability for low enough obstacle mobility. These results prove the potential for the optimization of the transport of RTPs in crowded and disordered environments with applications to motile artificial and biological systems.

New exact solutions of the Dirac and Klein-Gordon equations of a charged particle propagating in a strong laser field in an underdense plasma

NASA Astrophysics Data System (ADS)

Varró, Sándor

2014-03-01

Exact solutions are presented of the Dirac and Klein-Gordon equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave in a medium of index of refraction nm<1. In the Dirac case the solutions are expressed in terms of new complex polynomials, and in the Klein-Gordon case the found solutions are expressed in terms of Ince polynomials. In each case they form a doubly infinite set, labeled by two integer quantum numbers. These integer numbers represent quantized momentum components of the charged particle along the polarization vector and along the propagation direction of the electromagnetic radiation. Since this radiation may represent a plasmon wave of arbitrary high amplitude, propagating in an underdense plasma, the solutions obtained may have relevance in describing possible quantum features of novel acceleration mechanisms.

Kinetic field theory: exact free evolution of Gaussian phase-space correlations

NASA Astrophysics Data System (ADS)

Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias

2018-04-01

In recent work we developed a description of cosmic large-scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial correlations between particles sampled from random Gaussian density and velocity fields have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correlations between all phase-space coordinates exactly by adopting a diagrammatic language for the different forms of correlations, directly inspired by the Mayer cluster expansion. We will demonstrate that explicit expressions for phase-space density cumulants of arbitrary n-point order, which fully capture the non-linear coupling of free streaming kinematics due to initial correlations, can be obtained from a simple set of Feynman rules. These cumulants will be the foundation for future investigations of perturbation theory in particle interactions.

Exact solutions for mass-dependent irreversible aggregations.

PubMed

Son, Seung-Woo; Christensen, Claire; Bizhani, Golnoosh; Grassberger, Peter; Paczuski, Maya

2011-10-01

We consider the mass-dependent aggregation process (k+1)X→X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one, either with k neighbors in one dimension, or--in the well-mixed case--with k other clusters picked randomly. We find the same combinatorial exact solutions for the probability to find any given configuration of particles on a ring or line, and in the well-mixed case. The mass distribution of a single cluster exhibits scaling laws and the finite-size scaling form is given. The relation to the classical sum kernel of irreversible aggregation is discussed.

A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1 + 1 dimensions

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

Lienert, Matthias, E-mail: lienert@math.lmu.de

2015-04-15

The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time){sup N} to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to amore » relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.« less

Multi-stage approach for structural damage detection problem using basis pursuit and particle swarm optimization

NASA Astrophysics Data System (ADS)

Gerist, Saleheh; Maheri, Mahmoud R.

2016-12-01

In order to solve structural damage detection problem, a multi-stage method using particle swarm optimization is presented. First, a new spars recovery method, named Basis Pursuit (BP), is utilized to preliminarily identify structural damage locations. The BP method solves a system of equations which relates the damage parameters to the structural modal responses using the sensitivity matrix. Then, the results of this stage are subsequently enhanced to the exact damage locations and extents using the PSO search engine. Finally, the search space is reduced by elimination of some low damage variables using micro search (MS) operator embedded in the PSO algorithm. To overcome the noise present in structural responses, a method known as Basis Pursuit De-Noising (BPDN) is also used. The efficiency of the proposed method is investigated by three numerical examples: a cantilever beam, a plane truss and a portal plane frame. The frequency response is used to detect damage in the examples. The simulation results demonstrate the accuracy and efficiency of the proposed method in detecting multiple damage cases and exhibit its robustness regarding noise and its advantages compared to other reported solution algorithms.

Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory: Convergence analysis of the dual fermion technique

NASA Astrophysics Data System (ADS)

Gukelberger, Jan; Kozik, Evgeny; Hafermann, Hartmut

2017-07-01

The dual fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work, we compute the dual fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact diagrammatic determinant Monte Carlo simulations to systematically assess convergence of the dual fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT Néel transition, the dual fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered (4 ≤U /t ≤12 ), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find, however, that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.

Particle-fluid interaction corrections for flow measurements with a laser Doppler flowmeter

NASA Technical Reports Server (NTRS)

Berman, N. S.

1972-01-01

A discussion is given of particle lags in mean flows, acoustic oscillations at single frequencies and in turbulent flows. Some simplified cases lead to exact solutions. For turbulent flows linearization of the equation of motion after assuming the fluid and particle streamlines coincide also leads to a solution. The results show that particle lags are a function of particle size and frequency of oscillation. Additional studies are necessary to evaluate the effect of turbulence when a major portion of the energy is concentrated in small eddies.

Treatment of pairing correlations based on the equations of motion for zero-coupled pair operators

NASA Astrophysics Data System (ADS)

Andreozzi, F.; Covello, A.; Gargano, A.; Ye, Liu Jian; Porrino, A.

1985-07-01

The pairing problem is treated by means of the equations of motion for zero-coupled pair operators. Exact equations for the seniority-v states of N particles are derived. These equations can be solved by a step-by-step procedure which consists of progressively adding pairs of particles to a core. The theory can be applied at several levels of approximation depending on the number of core states which are taken into account. Some numerical applications to the treatment of v=0, v=1, and v=2 states in the Ni isotopes are performed. The accuracy of various approximations is tested by comparison with exact results. For the seniority-one and seniority-two problems it turns out that the results obtained from the first-order theory are very accurate, while those of higher order calculations are practically exact. Concerning the seniority-zero problem, a fifth-order calculation reproduces quite well the three lowest states.

Localization in finite vibroimpact chains: Discrete breathers and multibreathers.

PubMed

Grinberg, Itay; Gendelman, Oleg V

2016-09-01

We explore the dynamics of strongly localized periodic solutions (discrete solitons or discrete breathers) in a finite one-dimensional chain of oscillators. Localization patterns with both single and multiple localization sites (breathers and multibreathers) are considered. The model involves parabolic on-site potential with rigid constraints (the displacement domain of each particle is finite) and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an inelastic impact according to Newton's impact model. The rigid nonideal impact constraints are the only source of nonlinearity and damping in the system. We demonstrate that this vibro-impact model allows derivation of exact analytic solutions for the breathers and multibreathers with an arbitrary set of localization sites, both in conservative and in forced-damped settings. Periodic boundary conditions are considered; exact solutions for other types of boundary conditions are also available. Local character of the nonlinearity permits explicit derivation of a monodromy matrix for the breather solutions. Consequently, the stability of the derived breather and multibreather solutions can be efficiently studied in the framework of simple methods of linear algebra, and with rather moderate computational efforts. One reveals that that the finiteness of the chain fragment and possible proximity of the localization sites strongly affect both the existence and the stability patterns of these localized solutions.

Path integral Monte Carlo and the electron gas

NASA Astrophysics Data System (ADS)

Brown, Ethan W.

Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finite-temperature. By stochastically sampling Feynman's path integral representation of the quantum many-body density matrix, path integral Monte Carlo includes non-perturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, high-pressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finite-temperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixed-node constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warm-dense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finite-temperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixed-node approximation. As a first step, we utilize the variational principle inherent in the path integral Monte Carlo method to optimize the nodal surface. By using a ansatz resembling a free particle density matrix, we make a unique connection between a nodal effective mass and the traditional effective mass of many-body quantum theory. We then propose and test several alternate nodal ansatzes and apply them to single atomic systems. Finally, we propose a method to tackle the sign problem head on, by leveraging the relatively simple structure of permutation space. Using this method, we find we can perform exact simulations this of the electron gas and 3He that were previously impossible.

Exact solutions to model surface and volume charge distributions

NASA Astrophysics Data System (ADS)

Mukhopadhyay, S.; Majumdar, N.; Bhattacharya, P.; Jash, A.; Bhattacharya, D. S.

2016-10-01

Many important problems in several branches of science and technology deal with charges distributed along a line, over a surface and within a volume. Recently, we have made use of new exact analytic solutions of surface charge distributions to develop the nearly exact Boundary Element Method (neBEM) toolkit. This 3D solver has been successful in removing some of the major drawbacks of the otherwise elegant Green's function approach and has been found to be very accurate throughout the computational domain, including near- and far-field regions. Use of truly distributed singularities (in contrast to nodally concentrated ones) on rectangular and right-triangular elements used for discretizing any three-dimensional geometry has essentially removed many of the numerical and physical singularities associated with the conventional BEM. In this work, we will present this toolkit and the development of several numerical models of space charge based on exact closed-form expressions. In one of the models, Particles on Surface (ParSur), the space charge inside a small elemental volume of any arbitrary shape is represented as being smeared on several surfaces representing the volume. From the studies, it can be concluded that the ParSur model is successful in getting the estimates close to those obtained using the first-principles, especially close to and within the cell. In the paper, we will show initial applications of ParSur and other models in problems related to high energy physics.

Tensor spherical harmonics theories on the exact nature of the elastic fields of a spherically anisotropic multi-inhomogeneous inclusion

NASA Astrophysics Data System (ADS)

Shodja, H. M.; Khorshidi, A.

2013-04-01

Eshelby's theories on the nature of the disturbance strains due to polynomial eigenstrains inside an isotropic ellipsoidal inclusion, and the form of homogenizing eigenstrains corresponding to remote polynomial loadings in the equivalent inclusion method (EIM) are not valid for spherically anisotropic inclusions and inhomogeneities. Materials with spherically anisotropic behavior are frequently encountered in nature, for example, some graphite particles or polyethylene spherulites. Moreover, multi-inclusions/inhomogeneities/inhomogeneous inclusions have abundant engineering and scientific applications and their exact theoretical treatment would be of great value. The present work is devoted to the development of a mathematical framework for the exact treatment of a spherical multi-inhomogeneous inclusion with spherically anisotropic constituents embedded in an unbounded isotropic matrix. The formulations herein are based on tensor spherical harmonics having orthogonality and completeness properties. For polynomial eigenstrain field and remote applied loading, several theorems on the exact closed-form expressions of the elastic fields associated with the matrix and all the phases of the inhomogeneous inclusion are stated and proved. Several classes of impotent eigenstrain fields associated to a generally anisotropic inclusion as well as isotropic and spherically anisotropic multi-inclusions are also introduced. The presented theories are useful for obtaining highly accurate solutions of desired accuracy when the constituent phases of the multi-inhomogeneous inclusion are made of functionally graded materials (FGMs).

Exact Analytical Solution of the Peristaltic Nanofluids Flow in an Asymmetric Channel with Flexible Walls and Slip Condition: Application to the Cancer Treatment

PubMed Central

Ebaid, Abdelhalim; Aly, Emad H.

2013-01-01

In the cancer treatment, magnetic nanoparticles are injected into the blood vessel nearest to the cancer's tissues. The dynamic of these nanoparticles occurs under the action of the peristaltic waves generated on the flexible walls of the blood vessel. Studying such nanofluid flow under this action is therefore useful in treating tissues of the cancer. In this paper, the mathematical model describing the slip peristaltic flow of nanofluid was analytically investigated. Exact expressions were deduced for the temperature distribution and nano-particle concentration. In addition, the effects of the slip, thermophoresis, and Brownian motion parameters on the temperature and nano-particle concentration profiles were discussed and further compared with other approximate results in the literatures. In particular, these results have been obtained at the same values of the physical examined parameters that was considered in Akbar et al., “Peristaltic flow of a nanofluid with slip effects,” 2012. The results reveal that remarkable differences are detected between the exact current results and those approximately obtained in the literatures for behaviour of the temperature profile and nano-particles concentration. Accordingly, the current analysis and results are considered as optimal and therefore may be taken as a base for any future comparisons. PMID:24151526

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.

Laser-Induced Linear-Field Particle Acceleration in Free Space.

PubMed

Wong, Liang Jie; Hong, Kyung-Han; Carbajo, Sergio; Fallahi, Arya; Piot, Philippe; Soljačić, Marin; Joannopoulos, John D; Kärtner, Franz X; Kaminer, Ido

2017-09-11

Linear-field particle acceleration in free space (which is distinct from geometries like the linac that requires components in the vicinity of the particle) has been studied for over 20 years, and its ability to eventually produce high-quality, high energy multi-particle bunches has remained a subject of great interest. Arguments can certainly be made that linear-field particle acceleration in free space is very doubtful given that first-order electron-photon interactions are forbidden in free space. Nevertheless, we chose to develop an accurate and truly predictive theoretical formalism to explore this remote possibility when intense, few-cycle electromagnetic pulses are used in a computational experiment. The formalism includes exact treatment of Maxwell's equations and exact treatment of the interaction among the multiple individual particles at near and far field. Several surprising results emerge. We find that electrons interacting with intense laser pulses in free space are capable of gaining substantial amounts of energy that scale linearly with the field amplitude. For example, 30 keV electrons (2.5% energy spread) are accelerated to 61 MeV (0.5% spread) and to 205 MeV (0.25% spread) using 250 mJ and 2.5 J lasers respectively. These findings carry important implications for our understanding of ultrafast electron-photon interactions in strong fields.

Coupled electrostatic and material surface stresses yield anomalous particle interactions and deformation

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

Kemp, B. A., E-mail: bkemp@astate.edu; Nikolayev, I.; Sheppard, C. J.

2016-04-14

Like-charges repel, and opposite charges attract. This fundamental tenet is a result of Coulomb's law. However, the electrostatic interactions between dielectric particles remain topical due to observations of like-charged particle attraction and the self-assembly of colloidal systems. Here, we show, using both an approximate description and an exact solution of Maxwell's equations, that nonlinear charged particle forces result even for linear material systems and can be responsible for anomalous electrostatic interactions such as like-charged particle attraction and oppositely charged particle repulsion. Furthermore, these electrostatic interactions and the deformation of such particles have fundamental implications for our understanding of macroscopic electrodynamics.

Fine structure of spectrum of twist-three operators in QCD

NASA Astrophysics Data System (ADS)

Belitsky, A. V.

1999-04-01

We unravel the structure of the spectrum of the anomalous dimensions of the quark-gluon twist-3 operators which are responsible for the multiparton correlations in hadrons and enter as a leading contribution to several physical cross sections. The method of analysis is based on the recent finding of a non-trivial integral of motion for the corresponding Hamiltonian problem in multicolour limit which results into exact integrability of the three-particle system. Quasiclassical expansion is used for solving the problem. We address the chiral-odd sector as a case of study.

Fluid moments of the nonlinear Landau collision operator

DOE PAGES

Hirvijoki, E.; Lingam, M.; Pfefferle, D.; ...

2016-08-09

An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. In conclusion, the proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality and flow.

Hamilton's principle and normal mode coupling in an aspherical planet with a fluid core

NASA Astrophysics Data System (ADS)

Al-Attar, David; Crawford, Ophelia; Valentine, Andrew P.; Trampert, Jeannot

2018-04-01

We apply Hamilton's principle to obtain the exact equations of motion for an elastic planet that is rotating, self-gravitating, and comprises both fluid and solid regions. This variational problem is complicated by the occurrence of tangential slip at fluid-solid boundaries, but we show how this can be accommodated both directly and using the method of Lagrange multipliers. A novelty of our approach is that the planet's motion is described relative to an arbitrary reference configuration, with this generality offering advantages for numerical calculations. In particular, aspherical topography on the free surface or internal boundaries of the planet's equilibrium configuration can be converted exactly into effective volumetric heterogeneities within a geometrically spherical reference body by applying a suitable particle relabelling transformation. The theory is then specialised to consider the linearised motion of a planet about a steadily rotating equilibrium configuration, with these results having applications to normal mode coupling calculations used within studies of long period seismology, tidal deformation, and related fields. In particular, we explain how our new theory will, for the first time, allow aspherical boundary topography to be incorporated exactly within such coupling calculations.

A Keplerian-based Hamiltonian splitting for gravitational N-body simulations

NASA Astrophysics Data System (ADS)

Gonçalves Ferrari, G.; Boekholt, T.; Portegies Zwart, S. F.

2014-05-01

We developed a Keplerian-based Hamiltonian splitting for solving the gravitational N-body problem. This splitting allows us to approximate the solution of a general N-body problem by a composition of multiple, independently evolved two-body problems. While the Hamiltonian splitting is exact, we show that the composition of independent two-body problems results in a non-symplectic non-time-symmetric first-order map. A time-symmetric second-order map is then constructed by composing this basic first-order map with its self-adjoint. The resulting method is precise for each individual two-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with primordial binaries. The superposition of Kepler solutions for each pair of particles makes the method excellently suited for parallel computing; we achieve ≳64 per cent efficiency for only eight particles per core, but close to perfect scaling for 16 384 particles on a 128 core distributed-memory computer. We present several implementations in SAKURA, one of which is publicly available via the AMUSE framework.

Mechanochemical mechanism for reaction of aluminium nano- and micrometre-scale particles.

PubMed

Levitas, Valery I

2013-11-28

A recently suggested melt-dispersion mechanism (MDM) for fast reaction of aluminium (Al) nano- and a few micrometre-scale particles during fast heating is reviewed. Volume expansion of 6% during Al melting produces pressure of several GPa in a core and tensile hoop stresses of 10 GPa in an oxide shell. Such stresses cause dynamic fracture and spallation of the shell. After spallation, an unloading wave propagates to the centre of the particle and creates a tensile pressure of 3-8 GPa. Such a tensile pressure exceeds the cavitation strength of liquid Al and disperses the melt into small, bare clusters (fragments) that fly at a high velocity. Reaction of the clusters is not limited by diffusion through a pre-existing oxide shell. Some theoretical and experimental results related to the MDM are presented. Various theoretical predictions based on the MDM are in good qualitative and quantitative agreement with experiments, which resolves some basic puzzles in combustion of Al particles. Methods to control and improve reactivity of Al particles are formulated, which are exactly opposite to the current trends based on diffusion mechanism. Some of these suggestions have experimental confirmation.

Energy Distributions in Small Populations: Pascal versus Boltzmann

ERIC Educational Resources Information Center

Kugel, Roger W.; Weiner, Paul A.

2010-01-01

The theoretical distributions of a limited amount of energy among small numbers of particles with discrete, evenly-spaced quantum levels are examined systematically. The average populations of energy states reveal the pattern of Pascal's triangle. An exact formula for the probability that a particle will be in any given energy state is derived.…

Interaction of axions with relativistic spinning particles

NASA Astrophysics Data System (ADS)

Popov, V. A.; Balakin, A. B.

2016-05-01

We consider a covariant phenomenological model, which describes an interaction between a pseudoscalar (axion) field and massive spinning particles. The model extends the Bagrmann-Michel-Telegdy approach in application to the axion electrodynamics. We present some exact solutions and discuss them in the context of experimental tests of the model and axion detection.

A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon

DOE PAGES

Drummond, J. M.; Papathanasiou, G.; Spradlin, M.

2015-03-16

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4, 7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the 7 ll 6 collinear limit. This unique symbol ismore » both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the threeloop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n > 6.« less

Multiple Scattering in Planetary Regoliths Using Incoherent Interactions

NASA Astrophysics Data System (ADS)

Muinonen, K.; Markkanen, J.; Vaisanen, T.; Penttilä, A.

2017-12-01

We consider scattering of light by a planetary regolith using novel numerical methods for discrete random media of particles. Understanding the scattering process is of key importance for spectroscopic, photometric, and polarimetric modeling of airless planetary objects, including radar studies. In our modeling, the size of the spherical random medium can range from microscopic to macroscopic sizes, whereas the particles are assumed to be of the order of the wavelength in size. We extend the radiative transfer and coherent backscattering method (RT-CB) to the case of dense packing of particles by adopting the ensemble-averaged first-order incoherent extinction, scattering, and absorption characteristics of a volume element of particles as input. In the radiative transfer part, at each absorption and scattering process, we account for absorption with the help of the single-scattering albedo and peel off the Stokes parameters of radiation emerging from the medium in predefined scattering angles. We then generate a new scattering direction using the joint probability density for the local polar and azimuthal scattering angles. In the coherent backscattering part, we utilize amplitude scattering matrices along the radiative-transfer path and the reciprocal path. Furthermore, we replace the far-field interactions of the RT-CB method with rigorous interactions facilitated by the Superposition T-matrix method (STMM). This gives rise to a new RT-RT method, radiative transfer with reciprocal interactions. For microscopic random media, we then compare the new results to asymptotically exact results computed using the STMM, succeeding in the numerical validation of the new methods.Acknowledgments. Research supported by European Research Council with Advanced Grant No. 320773 SAEMPL, Scattering and Absorption of ElectroMagnetic waves in ParticuLate media. Computational resources provided by CSC - IT Centre for Science Ltd, Finland.

Hybrid-DFT  +  V w method for band structure calculation of semiconducting transition metal compounds: the case of cerium dioxide.

PubMed

Ivády, Viktor; Gali, Adam; Abrikosov, Igor A

2017-11-15

Hybrid functionals' non-local exchange-correlation potential contains a derivative discontinuity that improves on standard semi-local density functional theory (DFT) band gaps. Moreover, by careful parameterization, hybrid functionals can provide self-interaction reduced description of selected states. On the other hand, the uniform description of all the electronic states of a given system is a known drawback of these functionals that causes varying accuracy in the description of states with different degrees of localization. This limitation can be remedied by the orbital dependent exact exchange extension of hybrid functionals; the hybrid-DFT  +  V w method (Ivády et al 2014 Phys. Rev. B 90 035146). Based on the analogy of quasi-particle equations and hybrid-DFT single particle equations, here we demonstrate that parameters of hybrid-DFT  +  V w functional can be determined from approximate theoretical quasi-particle spectra without any fitting to experiment. The proposed method is illustrated on the charge self-consistent electronic structure calculation for cerium dioxide where itinerant valence states interact with well-localized 4f atomic like states, making this system challenging for conventional methods, either hybrid-DFT or LDA  +  U, and therefore allowing for a demonstration of the advantages of the proposed scheme.

Charged Dirac Particles' Hawking Radiation via Tunneling of Both Horizons and Thermodynamics Properties of Kerr-Newman-Kasuya-Taub-NUT-AdS Black Holes

NASA Astrophysics Data System (ADS)

Ali, M. Hossain; Sultana, Kausari

2013-12-01

We investigate Hawking radiation of electrically and magnetically charged Dirac particles from a dyonic Kerr-Newman-Kasuya-Taub-NUT-Anti-de Sitter (KNKTN-AdS) black hole by considering thermal characters of both the outer and inner horizons. We apply Damour-Ruffini method and membrane method to calculate the temperature and the entropy of the inner horizon of the KNKTN-AdS black hole. The inner horizon admits thermal character with positive temperature and entropy proportional to its area. The inner horizon entropy contributes to the total entropy of the black hole in the context of Nernst theorem. Considering conservation of energy, charges, angular momentum, and the back-reaction of emitting particles to the spacetime, we obtain the emission spectra for both the inner and outer horizons. The total emission rate is obtained as the product of the emission rates of the inner and outer horizons. It deviates from the purely thermal spectrum with the leading term exactly the Boltzman factor and can bring some information out. The result thus can be treated as an explanation to the information loss paradox.

Forwardscattering corrections for optical extinction measurements in aerosol media. II - Polydispersions

NASA Technical Reports Server (NTRS)

Deepak, A.; Box, M. A.

1978-01-01

The paper presents a parametric study of the forwardscattering corrections for experimentally measured optical extinction coefficients in polydisperse particulate media, since some forward scattered light invariably enters, along with the direct beam, into the finite aperture of the detector. Forwardscattering corrections are computed by two methods: (1) using the exact Mie theory, and (2) the approximate Rayleigh diffraction formula for spherical particles. A parametric study of the dependence of the corrections on mode radii, real and imaginary parts of the complex refractive index, and half-angle of the detector's view cone has been carried out for three different size distribution functions of the modified gamma type. In addition, a study has been carried out to investigate the range of these parameters in which the approximate formulation is valid. The agreement is especially good for small-view cone angles and large particles, which improves significantly for slightly absorbing aerosol particles. Also discussed is the dependence of these corrections on the experimental design of the transmissometer systems.

Core-softened potentials, multiple liquid-liquid critical points, and density anomaly regions: An exact solution

NASA Astrophysics Data System (ADS)

Rizzatti, Eduardo O.; Barbosa, Marco Aurélio A.; Barbosa, Marcia C.

2018-02-01

The pressure versus temperature phase diagram of a system of particles interacting through a multiscale shoulder-like potential is exactly computed in one dimension. The N-shoulder potential exhibits N density anomaly regions in the phase diagram if the length scales can be connected by a convex curve. The result is analyzed in terms of the convexity of the Gibbs free energy.

On Babinet's principle and diffraction associated with an arbitrary particle.

PubMed

Sun, Bingqiang; Yang, Ping; Kattawar, George W; Mishchenko, Michael I

2017-12-01

Babinet's principle is widely used to compute the diffraction by a particle. However, the diffraction by a 3-D object is not totally the same as that simulated with Babinet's principle. This Letter uses a surface integral equation to exactly formulate the diffraction by an arbitrary particle and illustrate the condition for the applicability of Babinet's principle. The present results may serve to close the debate on the diffraction formalism.

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

Vieira, H.S., E-mail: horacio.santana.vieira@hotmail.com; Bezerra, V.B., E-mail: valdir@fisica.ufpb.br; Muniz, C.R., E-mail: celiomuniz@yahoo.com

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein–Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles. - Highlights: • The covariant Klein–Gordon equation for a charged massive scalar field in the Kerr–Newman black hole is solved.more » • Both angular and radial parts are transformed to a Heun-type equation. • The resulting Hawking radiation spectrum of scalar particles has a thermal character.« less

Fully adaptive propagation of the quantum-classical Liouville equation

NASA Astrophysics Data System (ADS)

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-01

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Fully adaptive propagation of the quantum-classical Liouville equation.

PubMed

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-15

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Inertial floaters in stratified turbulence

NASA Astrophysics Data System (ADS)

Sozza, A.; De Lillo, F.; Boffetta, G.

2018-01-01

We investigate numerically the dynamics and statistics of inertial particles transported by stratified turbulence, in the case of particle density intermediate in the average density profile of the fluid. Under these conditions, particles tend to form a thin layer around the corresponding fluid isopycnal. The thickness of the resulting layer is determined by a balance between buoyancy (which attracts the particle to the isopycnal) and inertia (which prevents them from following it exactly). By means of extensive numerical simulations, we explore the parameter space of the system and we find that in a range of parameters particles form fractal clusters within the layer.

Coulomb interactions in charged fluids.

PubMed

Vernizzi, Graziano; Guerrero-García, Guillermo Iván; de la Cruz, Monica Olvera

2011-07-01

The use of Ewald summation schemes for calculating long-range Coulomb interactions, originally applied to ionic crystalline solids, is a very common practice in molecular simulations of charged fluids at present. Such a choice imposes an artificial periodicity which is generally absent in the liquid state. In this paper we propose a simple analytical O(N(2)) method which is based on Gauss's law for computing exactly the Coulomb interaction between charged particles in a simulation box, when it is averaged over all possible orientations of a surrounding infinite lattice. This method mitigates the periodicity typical of crystalline systems and it is suitable for numerical studies of ionic liquids, charged molecular fluids, and colloidal systems with Monte Carlo and molecular dynamics simulations.

Relativistic symmetries in the Rosen—Morse potential and tensor interaction using the Nikiforov—Uvarov method

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-04-01

Approximate analytical bound-state solutions of the Dirac particle in the fields of attractive and repulsive Rosen—Morse (RM) potentials including the Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number κ. The Pekeris approximation is used to deal with the spin-orbit coupling terms κ (κ± 1)r-2. In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov—Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between the spin and p-spin state doublets.

Nonlinear Boltzmann equation for the homogeneous isotropic case: Some improvements to deterministic methods and applications to relaxation towards local equilibrium

NASA Astrophysics Data System (ADS)

Asinari, P.

2011-03-01

Boltzmann equation is one the most powerful paradigms for explaining transport phenomena in fluids. Since early fifties, it received a lot of attention due to aerodynamic requirements for high altitude vehicles, vacuum technology requirements and nowadays, micro-electro-mechanical systems (MEMs). Because of the intrinsic mathematical complexity of the problem, Boltzmann himself started his work by considering first the case when the distribution function does not depend on space (homogeneous case), but only on time and the magnitude of the molecular velocity (isotropic collisional integral). The interest with regards to the homogeneous isotropic Boltzmann equation goes beyond simple dilute gases. In the so-called econophysics, a Boltzmann type model is sometimes introduced for studying the distribution of wealth in a simple market. Another recent application of the homogeneous isotropic Boltzmann equation is given by opinion formation modeling in quantitative sociology, also called socio-dynamics or sociophysics. The present work [1] aims to improve the deterministic method for solving homogenous isotropic Boltzmann equation proposed by Aristov [2] by two ideas: (a) the homogeneous isotropic problem is reformulated first in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium).

On the velocity space discretization for the Vlasov-Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

NASA Astrophysics Data System (ADS)

Camporeale, E.; Delzanno, G. L.; Bergen, B. K.; Moulton, J. D.

2016-01-01

We describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier-Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC.

26 CFR 1.669(a)-3 - Tax computed by the exact throwback method.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 26 Internal Revenue 8 2010-04-01 2010-04-01 false Tax computed by the exact throwback method. 1... Taxable Years Beginning Before January 1, 1969 § 1.669(a)-3 Tax computed by the exact throwback method. (a... compute the tax, on amounts deemed distributed under section 666, by the exact throwback method provided...

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.

Light scattering and absorption by space weathered planetary bodies: Novel numerical solution

NASA Astrophysics Data System (ADS)

Markkanen, Johannes; Väisänen, Timo; Penttilä, Antti; Muinonen, Karri

2017-10-01

Airless planetary bodies are exposed to space weathering, i.e., energetic electromagnetic and particle radiation, implantation and sputtering from solar wind particles, and micrometeorite bombardment.Space weathering is known to alter the physical and chemical composition of the surface of an airless body (C. Pieters et al., J. Geophys. Res. Planets, 121, 2016). From the light scattering perspective, one of the key effects is the production of nanophase iron (npFe0) near the exposed surfaces (B. Hapke, J. Geophys. Res., 106, E5, 2001). At visible and ultraviolet wavelengths these particles have a strong electromagnetic response which has a major impact on scattering and absorption features. Thus, to interpret the spectroscopic observations of space-weathered asteroids, the model should treat the contributions of the npFe0 particles rigorously.Our numerical approach is based on the hierarchical geometric optics (GO) and radiative transfer (RT). The modelled asteroid is assumed to consist of densely packed silicate grains with npFe0 inclusions. We employ our recently developed RT method for dense random media (K. Muinonen, et al., Radio Science, submitted, 2017) to compute the contributions of the npFe0 particles embedded in silicate grains. The dense media RT method requires computing interactions of the npFe0 particles in the volume element for which we use the exact fast superposition T-matrix method (J. Markkanen, and A.J. Yuffa, JQSRT 189, 2017). Reflections and refractions on the grain surface and propagation in the grain are addressed by the GO. Finally, the standard RT is applied to compute scattering by the entire asteroid.Our numerical method allows for a quantitative interpretation of the spectroscopic observations of space-weathered asteroids. In addition, it may be an important step towards more rigorous a thermophysical model of asteroids when coupled with the radiative and conductive heat transfer techniques.Acknowledgments. Research supported by European Research Council with Advanced Grant No. 320773 SAEMPL. Computational resources provided by CSC- IT Centre for Science Ltd, Finland.

EXACT S-MATRICES FOR AdS3/CFT2

NASA Astrophysics Data System (ADS)

Ahn, Changrim; Bombardelli, Diego

2013-12-01

We propose exact S-matrices for the AdS3/CFT2 duality between type IIB strings on AdS3×S3×M4 with M4 = S3×S1 or T4 and the corresponding two-dimensional conformal field theories. We fix the two-particle S-matrices on the basis of the symmetries su(1|1) and su(1|1)×su(1|1). A crucial justification comes from the derivation of the all-loop Bethe ansatz matching exactly the recent conjecture proposed by Babichenko et al. [J. High Energy Phys.1003, 058 (2010), arXiv:0912.1723 [hep-th

Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory

NASA Astrophysics Data System (ADS)

Sciarappa, Antonio

2017-10-01

We provide a proposal, motivated by Separation of Variables and gauge theory arguments, for constructing exact solutions to the quantum Baxter equation associated to the N-particle relativistic Toda chain and test our proposal against numerical results. Quantum Mechanical non-perturbative corrections, essential in order to obtain a sensible solution, are taken into account in our gauge theory approach by considering codimension two defects on curved backgrounds (squashed S 5 and degenerate limits) rather than flat space; this setting also naturally incorporates exact quantization conditions and energy spectrum of the relativistic Toda chain as well as its modular dual structure.

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)

Ultrarelativistic boost of a black hole in the magnetic universe of Levi-Civita-Bertotti-Robinson

NASA Astrophysics Data System (ADS)

Ortaggio, Marcello; Astorino, Marco

2018-05-01

We consider an exact Einstein-Maxwell solution constructed by Alekseev and Garcia, which describes a Schwarzschild black hole immersed in the magnetic universe of Levi-Civita, Bertotti, and Robinson (LCBR). After reviewing the basic properties of this spacetime, we study the ultrarelativistic limit in which the black hole is boosted to the speed of light, while sending its mass to 0. This results in a nonexpanding impulsive wave traveling in the LCBR universe. The wave front is a 2-sphere carrying two null point particles at its poles—a remnant of the structure of the original static spacetime. It is also shown that the obtained line element belongs to the Kundt class of spacetimes, and the relation with the known family of exact gravitational waves of finite duration propagating in the LCBR background is clarified. In the limit of a vanishing electromagnetic field, one point particle is pushed away to infinity and the single-particle Aichelburg-Sexl p p -wave propagating in Minkowski space is recovered.

Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles

NASA Astrophysics Data System (ADS)

Baule, Adrian

2017-07-01

Random sequential adsorption (RSA) of particles of a particular shape is used in a large variety of contexts to model particle aggregation and jamming. A key feature of these models is the observed algebraic time dependence of the asymptotic jamming coverage ˜t-ν as t →∞ . However, the exact value of the exponent ν is not known apart from the simplest case of the RSA of monodisperse spheres adsorbed on a line (Renyi's seminal "car parking problem"), where ν =1 can be derived analytically. Empirical simulation studies have conjectured on a case-by-case basis that for general nonspherical particles, ν =1 /(d +d ˜ ), where d denotes the dimension of the domain, and d ˜ the number of orientational degrees of freedom of a particle. Here, we solve this long-standing problem analytically for the d =1 case—the "Paris car parking problem." We prove, in particular, that the scaling exponent depends on the particle shape, contrary to the original conjecture and, remarkably, falls into two universality classes: (i) ν =1 /(1 +d ˜ /2 ) for shapes with a smooth contact distance, e.g., ellipsoids, and (ii) ν =1 /(1 +d ˜ ) for shapes with a singular contact distance, e.g., spherocylinders and polyhedra. The exact solution explains, in particular, why many empirically observed scalings fall in between these two limits.

Laser-Induced Linear-Field Particle Acceleration in Free Space

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

Wong, Liang Jie; Hong, Kyung -Han; Carbajo, Sergio

Linear-field particle acceleration in free space (which is distinct from geometries like the linac that requires components in the vicinity of the particle) has been studied for over 20 years, and its ability to eventually produce high-quality, high energy multi-particle bunches has remained a subject of great interest. Arguments can certainly be made that linear-field particle acceleration in free space is very doubtful given that first-order electron-photon interactions are forbidden in free space. Nevertheless, we chose to develop an accurate and truly predictive theoretical formalism to explore this remote possibility when intense, few-cycle electromagnetic pulses are used in a computationalmore » experiment. The formalism includes exact treatment of Maxwell’s equations and exact treatment of the interaction among the multiple individual particles at near and far field. Several surprising results emerge. We find that electrons interacting with intense laser pulses in free space are capable of gaining substantial amounts of energy that scale linearly with the feld amplitude. For example, 30keV electrons (2.5% energy spread) are accelerated to 61MeV (0.5% spread) and to 205MeV (0.25% spread) using 250 mJ and 2.5J lasers respectively. Furthermore, these findings carry important implications for our understanding of ultrafast electron-photon interactions in strong fields.« less

Laser-Induced Linear-Field Particle Acceleration in Free Space

DOE PAGES

Wong, Liang Jie; Hong, Kyung -Han; Carbajo, Sergio; ...

2017-09-11

Linear-field particle acceleration in free space (which is distinct from geometries like the linac that requires components in the vicinity of the particle) has been studied for over 20 years, and its ability to eventually produce high-quality, high energy multi-particle bunches has remained a subject of great interest. Arguments can certainly be made that linear-field particle acceleration in free space is very doubtful given that first-order electron-photon interactions are forbidden in free space. Nevertheless, we chose to develop an accurate and truly predictive theoretical formalism to explore this remote possibility when intense, few-cycle electromagnetic pulses are used in a computationalmore » experiment. The formalism includes exact treatment of Maxwell’s equations and exact treatment of the interaction among the multiple individual particles at near and far field. Several surprising results emerge. We find that electrons interacting with intense laser pulses in free space are capable of gaining substantial amounts of energy that scale linearly with the feld amplitude. For example, 30keV electrons (2.5% energy spread) are accelerated to 61MeV (0.5% spread) and to 205MeV (0.25% spread) using 250 mJ and 2.5J lasers respectively. Furthermore, these findings carry important implications for our understanding of ultrafast electron-photon interactions in strong fields.« less

Coherent pulses in the diffusive transport of charged particles`

NASA Technical Reports Server (NTRS)

Kota, J.

1994-01-01

We present exact solutions to the diffusive transport of charged particles following impulsive injection for a simple model of scattering. A modified, two-parameter relaxation-time model is considered that simulates the low rate of scattering through perpendicular pitch-angle. Scattering is taken to be isotropic within each of the foward- and backward-pointing hemispheres, respectively, but, at the same time, a reduced rate of sccattering is assumed from one hemisphere to the other one. By applying a technique of Fourier- and Laplace-transform, the inverse transformation can be performed and exact solutions can be reached. By contrast with the first, and so far only exact solutions of Federov and Shakov, this wider class of solutions gives rise to coherent pulses to appear. The present work addresses omnidirectional densities for isotropic injection from an instantaneous and localized source. The dispersion relations are briefly discussed. We find, for this particular model, two diffusive models to exist up to a certain limiting wavenumber. The corresponding eigenvalues are real at the lowest wavenumbers. Complex eigenvalues, which are responsible for coherent pulses, appear at higher wavenumbers.

Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries

NASA Astrophysics Data System (ADS)

Savickas, David

2015-04-01

General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).

Mutagenic effects of a single and an exact number of alpha particles in mammalian cells

NASA Technical Reports Server (NTRS)

Hei, T. K.; Wu, L. J.; Liu, S. X.; Vannais, D.; Waldren, C. A.; Randers-Pehrson, G.

1997-01-01

One of the main uncertainties in risk estimation for environmental radon exposure using lung cancer data from underground miners is the extrapolation from high- to low-dose exposure where multiple traversal is extremely rare. The biological effects of a single alpha particle are currently unknown. Using the recently available microbeam source at the Radiological Research Accelerator Facility at Columbia University, we examined the frequencies and molecular spectrum of S1- mutants induced in human-hamster hybrid (A(L)) cells by either a single or an exact number of alpha particles. Exponentially growing cells were stained briefly with a nontoxic concentration of Hoechst dye for image analysis, and the location of individual cells was computer-monitored. The nucleus of each cell was irradiated with either 1,2,4, or 8 alpha particles at a linear energy transfer of 90 keV/microm consistent with the energy spectrum of domestic radon exposure. Although single-particle traversal was only slightly cytotoxic to A(L) cells (survival fraction approximately 0.82), it was highly mutagenic, and the induced mutant fraction averaged 110 mutants per 10(5) survivors. In addition, both toxicity and mutant induction were dose-dependent. Multiplex PCR analysis of mutant DNA showed that the proportion of mutants with multilocus deletions increased with the number of particle traversals. These data provide direct evidence that a single a particle traversing a nucleus will have a high probability of resulting in a mutation and highlight the need for radiation protection at low doses.

Mutagenic effects of a single and an exact number of alpha particles in mammalian cells.

PubMed

Hei, T K; Wu, L J; Liu, S X; Vannais, D; Waldren, C A; Randers-Pehrson, G

1997-04-15

One of the main uncertainties in risk estimation for environmental radon exposure using lung cancer data from underground miners is the extrapolation from high- to low-dose exposure where multiple traversal is extremely rare. The biological effects of a single alpha particle are currently unknown. Using the recently available microbeam source at the Radiological Research Accelerator Facility at Columbia University, we examined the frequencies and molecular spectrum of S1- mutants induced in human-hamster hybrid (A(L)) cells by either a single or an exact number of alpha particles. Exponentially growing cells were stained briefly with a nontoxic concentration of Hoechst dye for image analysis, and the location of individual cells was computer-monitored. The nucleus of each cell was irradiated with either 1,2,4, or 8 alpha particles at a linear energy transfer of 90 keV/microm consistent with the energy spectrum of domestic radon exposure. Although single-particle traversal was only slightly cytotoxic to A(L) cells (survival fraction approximately 0.82), it was highly mutagenic, and the induced mutant fraction averaged 110 mutants per 10(5) survivors. In addition, both toxicity and mutant induction were dose-dependent. Multiplex PCR analysis of mutant DNA showed that the proportion of mutants with multilocus deletions increased with the number of particle traversals. These data provide direct evidence that a single a particle traversing a nucleus will have a high probability of resulting in a mutation and highlight the need for radiation protection at low doses.

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.

Model parameter learning using Kullback-Leibler divergence

NASA Astrophysics Data System (ADS)

Lin, Chungwei; Marks, Tim K.; Pajovic, Milutin; Watanabe, Shinji; Tung, Chih-kuan

2018-02-01

In this paper, we address the following problem: For a given set of spin configurations whose probability distribution is of the Boltzmann type, how do we determine the model coupling parameters? We demonstrate that directly minimizing the Kullback-Leibler divergence is an efficient method. We test this method against the Ising and XY models on the one-dimensional (1D) and two-dimensional (2D) lattices, and provide two estimators to quantify the model quality. We apply this method to two types of problems. First, we apply it to the real-space renormalization group (RG). We find that the obtained RG flow is sufficiently good for determining the phase boundary (within 1% of the exact result) and the critical point, but not accurate enough for critical exponents. The proposed method provides a simple way to numerically estimate amplitudes of the interactions typically truncated in the real-space RG procedure. Second, we apply this method to the dynamical system composed of self-propelled particles, where we extract the parameter of a statistical model (a generalized XY model) from a dynamical system described by the Viscek model. We are able to obtain reasonable coupling values corresponding to different noise strengths of the Viscek model. Our method is thus able to provide quantitative analysis of dynamical systems composed of self-propelled particles.

A Gaussian theory for fluctuations in simple liquids.

PubMed

Krüger, Matthias; Dean, David S

2017-04-07

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

Electron localisation in static and time-dependent one-dimensional model systems

NASA Astrophysics Data System (ADS)

Durrant, T. R.; Hodgson, M. J. P.; Ramsden, J. D.; Godby, R. W.

2018-02-01

The most direct signature of electron localisation is the tendency of an electron in a many-body system to exclude other same-spin electrons from its vicinity. By applying this concept directly to the exact many-body wavefunction, we find that localisation can vary considerably between different ground-state systems, and can also be strongly disrupted, as a function of time, when a system is driven by an applied electric field. We use this measure to assess the well-known electron localisation function (ELF), both in its approximate single-particle form (often applied within density-functional theory) and its full many-particle form. The full ELF always gives an excellent description of localisation, but the approximate ELF fails in time-dependent situations, even when the exact Kohn-Sham orbitals are employed.

A Gaussian theory for fluctuations in simple liquids

NASA Astrophysics Data System (ADS)

Krüger, Matthias; Dean, David S.

2017-04-01

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

Nonthermal Hawking radiation from NUT-Taub-like black hole

NASA Astrophysics Data System (ADS)

Zhao, GuoMing; Li, PengZhang

2012-04-01

Using Damour-Ruffini method, we investigate Hawking radiation from NUT-Taub-like (NT-like) black hole. Considering the total energy conservation and the back reaction of the particle to the spacetime, we get the radiation spectrum on the black hole event horizon, which is related to the change of Bekenstein-Hawking entropy. Meanwhile, we find that the radiation is not exactly thermal, and can take out information from the black hole, which can be used to explain the information loss paradox. The result that we get satisfies the unitary theory of quantum mechanics and is consistent with the work finished before.

Mean-force-field and mean-spherical approximations for the electric microfield distribution at a charged point in the charged-hard-particles fluid

NASA Astrophysics Data System (ADS)

Rosenfeld, Yaakov

1989-01-01

The linearized mean-force-field approximation, leading to a Gaussian distribution, provides an exact formal solution to the mean-spherical integral equation model for the electric microfield distribution at a charged point in the general charged-hard-particles fluid. Lado's explicit solution for plasmas immediately follows this general observation.

Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface

ERIC Educational Resources Information Center

Fernandez, Francisco M.

2010-01-01

We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…

Analytical and exact solutions of the spherical and cylindrical diodes of Langmuir-Blodgett law

NASA Astrophysics Data System (ADS)

Torres-Cordoba, Rafael; Martinez-Garcia, Edgar

2017-10-01

This paper discloses the exact solutions of a mathematical model that describes the cylindrical and spherical electron current emissions within the context of a physics approximation method. The solution involves analyzing the 1D nonlinear Poisson equation, for the radial component. Although an asymptotic solution has been previously obtained, we present a theoretical solution that satisfies arbitrary boundary conditions. The solution is found in its parametric form (i.e., φ(r )=φ(r (τ)) ) and is valid when the electric field at the cathode surface is non-zero. Furthermore, the non-stationary spatial solution of the electric potential between the anode and the cathode is also presented. In this work, the particle-beam interface is considered to be at the end of the plasma sheath as described by Sutherland et al. [Phys. Plasmas 12, 033103 2005]. Three regimes of space charge effects—no space charge saturation, space charge limited, and space charge saturation—are also considered.

FRW and domain walls in higher spin gravity

NASA Astrophysics Data System (ADS)

Aros, R.; Iazeolla, C.; Noreña, J.; Sezgin, E.; Sundell, P.; Yin, Y.

2018-03-01

We present exact solutions to Vasiliev's bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are infinite dimensional higher-spin extensions of spacetime isometries generated by six Killing vectors. The solutions presented are obtained by using a method of holomorphic factorization in noncommutative twistor space and gauge functions. In interpreting the solutions in terms of Fronsdal-type fields in space-time, a field-dependent higher spin transformation is required, which is implemented at leading order. To this order, the scalar field solves Klein-Gordon equation with conformal mass in ( A) dS 4 . We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description. We observe that the factorization method provides a convenient framework for setting up a perturbation theory around the exact solutions, and we propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Gravitoelectromagnetic analogy based on tidal tensors

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

Costa, L. Filipe O.; Herdeiro, Carlos A. R.

2008-07-15

We propose a new approach to a physical analogy between general relativity and electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations, which makes transparent both the similarities and key differences between the two interactions. The following realizations of the analogy are given. The first one matches linearized gravitational tidal tensors to exact electromagnetic tidal tensors in Minkowski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultrastationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third wemore » show that our approach leads to a two-step exact derivation of Papapetrou's equation describing the force exerted on a spinning test particle. Analogous scalar invariants built from tidal tensors of both theories are also discussed.« less

Correlated scattering states of N-body Coulomb systems

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

Berakdar, J.

1997-03-01

For N charged particles of equal masses moving in the field of a heavy residual charge, an approximate analytical solution of the many-body time-independent Schr{umlt o}dinger equation is derived at a total energy above the complete fragmentation threshold. All continuum particles are treated on equal footing. The proposed correlated wave function represents, to leading order, an exact solution of the many-body Schr{umlt o}dinger equation in the asymptotic region defined by large interparticle separations. Thus, in this asymptotic region the N-body Coulomb modifications to the plane-wave motion of free particles are rigorously estimated. It is shown that the Kato cusp conditionsmore » are satisfied by the derived wave function at all two-body coalescence points. An expression of the normalization of this wave function is also given. To render possible the calculations of scattering amplitudes for transitions leading to a four-body scattering state, an effective-charge method is suggested in which the correlations between the continuum particles are completely subsumed into effective interactions with the residual charge. Analytical expressions for these effective interactions are derived and discussed for physical situations. {copyright} {ital 1997} {ital The American Physical Society}« less

Nonlinear Field Equations and Solitons as Particles

NASA Astrophysics Data System (ADS)

Maccari, Attilio

2006-05-01

Profound advances have recently interested nonlinear field theories and their exact or approximate solutions. We review the last results and point out some important unresolved questions. It is well known that quantum field theories are based upon Fourier series and the identification of plane waves with free particles. On the contrary, nonlinear field theories admit the existence of coherent solutions (dromions, solitons and so on). Moreover, one can construct lower dimensional chaotic patterns, periodic-chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution. We discuss in some detail a nonlinear Dirac field and a spontaneous symmetry breaking model that are reduced by means of the asymptotic perturbation method to a system of nonlinear evolution equations integrable via an appropriate change of variables. Their coherent, chaotic and fractal solutions are examined in some detail. Finally, we consider the possible identification of some types of coherent solutions with extended particles along the de Broglie-Bohm theory. However, the last findings suggest an inadequacy of the particle concept that appears only as a particular case of nonlinear field theories excitations.

Chemical association in simple models of molecular and ionic fluids. III. The cavity function

NASA Astrophysics Data System (ADS)

Zhou, Yaoqi; Stell, George

1992-01-01

Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ``linear'' approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier's principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data.

Pair and triple correlations in the A+B-->B diffusion-controlled reaction

NASA Astrophysics Data System (ADS)

Kuzovkov, Vladimir; Kotomin, Eugene

1994-03-01

An exact solution for the one-dimensional kinetics of the diffusion-controlled reaction A+B-->B is obtained by means of the three-particle correlation functions. Because of a lattice discreteness each site could be occupied by a single particle only which leads to the so-called ``bus effect'': Recombination of any particle A is defined by a spatial configuration of two nearest particles B only surrounding A from its left and right. This results in the unusual algebraic decay law, n(t)~t-1, which asymptotically (as t-->∞) does not depend on the trap B concentration.

A Radiation Chemistry Code Based on the Greens Functions of the Diffusion Equation

NASA Technical Reports Server (NTRS)

Plante, Ianik; Wu, Honglu

2014-01-01

Ionizing radiation produces several radiolytic species such as.OH, e-aq, and H. when interacting with biological matter. Following their creation, radiolytic species diffuse and chemically react with biological molecules such as DNA. Despite years of research, many questions on the DNA damage by ionizing radiation remains, notably on the indirect effect, i.e. the damage resulting from the reactions of the radiolytic species with DNA. To simulate DNA damage by ionizing radiation, we are developing a step-by-step radiation chemistry code that is based on the Green's functions of the diffusion equation (GFDE), which is able to follow the trajectories of all particles and their reactions with time. In the recent years, simulations based on the GFDE have been used extensively in biochemistry, notably to simulate biochemical networks in time and space and are often used as the "gold standard" to validate diffusion-reaction theories. The exact GFDE for partially diffusion-controlled reactions is difficult to use because of its complex form. Therefore, the radial Green's function, which is much simpler, is often used. Hence, much effort has been devoted to the sampling of the radial Green's functions, for which we have developed a sampling algorithm This algorithm only yields the inter-particle distance vector length after a time step; the sampling of the deviation angle of the inter-particle vector is not taken into consideration. In this work, we show that the radial distribution is predicted by the exact radial Green's function. We also use a technique developed by Clifford et al. to generate the inter-particle vector deviation angles, knowing the inter-particle vector length before and after a time step. The results are compared with those predicted by the exact GFDE and by the analytical angular functions for free diffusion. This first step in the creation of the radiation chemistry code should help the understanding of the contribution of the indirect effect in the formation of DNA damage and double-strand breaks.

An Exact Model-Based Method for Near-Field Sources Localization with Bistatic MIMO System.

PubMed

Singh, Parth Raj; Wang, Yide; Chargé, Pascal

2017-03-30

In this paper, we propose an exact model-based method for near-field sources localization with a bistatic multiple input, multiple output (MIMO) radar system, and compare it with an approximated model-based method. The aim of this paper is to propose an efficient way to use the exact model of the received signals of near-field sources in order to eliminate the systematic error introduced by the use of approximated model in most existing near-field sources localization techniques. The proposed method uses parallel factor (PARAFAC) decomposition to deal with the exact model. Thanks to the exact model, the proposed method has better precision and resolution than the compared approximated model-based method. The simulation results show the performance of the proposed method.

Constrained variation in Jastrow method at high density

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

Owen, J.C.; Bishop, R.F.; Irvine, J.M.

1976-11-01

A method is derived for constraining the correlation function in a Jastrow variational calculation which permits the truncation of the cluster expansion after two-body terms, and which permits exact minimization of the two-body cluster by functional variation. This method is compared with one previously proposed by Pandharipande and is found to be superior both theoretically and practically. The method is tested both on liquid /sup 3/He, by using the Lennard--Jones potential, and on the model system of neutrons treated as Boltzmann particles (''homework'' problem). Good agreement is found both with experiment and with other calculations involving the explicit evaluation ofmore » higher-order terms in the cluster expansion. The method is then applied to a more realistic model of a neutron gas up to a density of 4 neutrons per F/sup 3/, and is found to give ground-state energies considerably lower than those of Pandharipande. (AIP)« less

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

PubMed Central

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

Particle contamination effects in EUVL: enhanced theory for the analytical determination of critical particle sizes

NASA Astrophysics Data System (ADS)

Brandstetter, Gerd; Govindjee, Sanjay

2012-03-01

Existing analytical and numerical methodologies are discussed and then extended in order to calculate critical contamination-particle sizes, which will result in deleterious effects during EUVL E-chucking in the face of an error budget on the image-placement-error (IPE). The enhanced analytical models include a gap dependant clamping pressure formulation, the consideration of a general material law for realistic particle crushing and the influence of frictional contact. We present a discussion of the defects of the classical de-coupled modeling approach where particle crushing and mask/chuck indentation are separated from the global computation of mask bending. To repair this defect we present a new analytic approach based on an exact Hankel transform method which allows a fully coupled solution. This will capture the contribution of the mask indentation to the image-placement-error (estimated IPE increase of 20%). A fully coupled finite element model is used to validate the analytical models and to further investigate the impact of a mask back-side CrN-layer. The models are applied to existing experimental data with good agreement. For a standard material combination, a given IPE tolerance of 1 nm and a 15 kPa closing pressure, we derive bounds for single particles of cylindrical shape (radius × height < 44 μm) and spherical shape (diameter < 12 μm).

[Polyethylene disease].

PubMed

Sosna, A; Radonský, T; Pokorný, D; Veigl, D; Horák, Z; Jahoda, D

2003-01-01

The experience obtained during revision surgery and findings of polyethylene granulomas in surrounding tissues of replacement as well as marked differences in the viability of implants resulted in the study of polyethylene disease and its basic mechanisms producing the development of osteoaggressive granulomas. We investigated the morphology of particles and their number in tissues surrounding the implant. The aim of our study was to develop a method for the detection of polyethylene particles in tissues, to identify different types of wear and to assess factors that may influence the viability of joint arthroplasty in general. Every revizion of joint arthroplasty performed during the last five years was evaluated in terms of the presence of polyethylene granules and the viability state of articular polyethylene inserts. A total of 55 samples were taken from tissues around loosened endoprostheses. The location of each sample was exactly determined. A technique was developed to identify wear particles and to visualize them after all organic structures of a polyethylene granuloma were dissolved with nitrogenic acid. The viability of articular polyethylene implants showed extreme differences in relation to different periods of manufacture and probably also to different methods of sterilization. Articular inserts sterilized with formaldehyde (the method used at the beginning of arthroplasty in our country) showed the highest viability and the lowest wear. The polyethylene particles present in tissues surrounding the implant were characterized in terms of morphology and size. The comparison of literature data and our results has revealed that there are many unknown facts about the quality and structure of polyethylene. The method of sterilization also appears to play a role. Because the issue is complex, we were not able to identify all factors leading, in some cases, to an early and unexpected failure of the implant and we consider further investigation to be necessary. Polyethylene disease is an important factor limiting the viability of joint arthroplasty. It results from a complex interaction of polyethylene particles arising by wear with surrounding tissues. The particles, less than 0.5 micron in size, are phagocytized by macrophages and, by complex mechanism of expression of inflammation mediators, they result in the inhibition of osteogenesis and activation of osteoclastic processes. The previous methods of sterilization with formaldehyde vapors apparently reduced wear influenced the resistance of polyethylene to wear to a lesser degree. A method was developed to detect these particles and to characterize their morphology in the tissues of a polyethylene granuloma.

Combined Parameter and State Estimation Problem in a Complex Domain: RF Hyperthermia Treatment Using Nanoparticles

NASA Astrophysics Data System (ADS)

Bermeo Varon, L. A.; Orlande, H. R. B.; Eliçabe, G. E.

2016-09-01

The particle filter methods have been widely used to solve inverse problems with sequential Bayesian inference in dynamic models, simultaneously estimating sequential state variables and fixed model parameters. This methods are an approximation of sequences of probability distributions of interest, that using a large set of random samples, with presence uncertainties in the model, measurements and parameters. In this paper the main focus is the solution combined parameters and state estimation in the radiofrequency hyperthermia with nanoparticles in a complex domain. This domain contains different tissues like muscle, pancreas, lungs, small intestine and a tumor which is loaded iron oxide nanoparticles. The results indicated that excellent agreements between estimated and exact value are obtained.

Three-body unitarity in the finite volume

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

Mai, M.; Döring, M.

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativisticmore » $$3\\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.« less

Three-body unitarity in the finite volume

DOE PAGES

Mai, M.; Döring, M.

2017-12-18

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativisticmore » $$3\\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.« less

A hybrid artificial bee colony algorithm and pattern search method for inversion of particle size distribution from spectral extinction data

NASA Astrophysics Data System (ADS)

Wang, Li; Li, Feng; Xing, Jian

2017-10-01

In this paper, a hybrid artificial bee colony (ABC) algorithm and pattern search (PS) method is proposed and applied for recovery of particle size distribution (PSD) from spectral extinction data. To be more useful and practical, size distribution function is modelled as the general Johnson's ? function that can overcome the difficulty of not knowing the exact type beforehand encountered in many real circumstances. The proposed hybrid algorithm is evaluated through simulated examples involving unimodal, bimodal and trimodal PSDs with different widths and mean particle diameters. For comparison, all examples are additionally validated by the single ABC algorithm. In addition, the performance of the proposed algorithm is further tested by actual extinction measurements with real standard polystyrene samples immersed in water. Simulation and experimental results illustrate that the hybrid algorithm can be used as an effective technique to retrieve the PSDs with high reliability and accuracy. Compared with the single ABC algorithm, our proposed algorithm can produce more accurate and robust inversion results while taking almost comparative CPU time over ABC algorithm alone. The superiority of ABC and PS hybridization strategy in terms of reaching a better balance of estimation accuracy and computation effort increases its potentials as an excellent inversion technique for reliable and efficient actual measurement of PSD.

TIME-DOMAIN METHODS FOR DIFFUSIVE TRANSPORT IN SOFT MATTER

PubMed Central

Fricks, John; Yao, Lingxing; Elston, Timothy C.; Gregory Forest, And M.

2015-01-01

Passive microrheology [12] utilizes measurements of noisy, entropic fluctuations (i.e., diffusive properties) of micron-scale spheres in soft matter to infer bulk frequency-dependent loss and storage moduli. Here, we are concerned exclusively with diffusion of Brownian particles in viscoelastic media, for which the Mason-Weitz theoretical-experimental protocol is ideal, and the more challenging inference of bulk viscoelastic moduli is decoupled. The diffusive theory begins with a generalized Langevin equation (GLE) with a memory drag law specified by a kernel [7, 16, 22, 23]. We start with a discrete formulation of the GLE as an autoregressive stochastic process governing microbead paths measured by particle tracking. For the inverse problem (recovery of the memory kernel from experimental data) we apply time series analysis (maximum likelihood estimators via the Kalman filter) directly to bead position data, an alternative to formulas based on mean-squared displacement statistics in frequency space. For direct modeling, we present statistically exact GLE algorithms for individual particle paths as well as statistical correlations for displacement and velocity. Our time-domain methods rest upon a generalization of well-known results for a single-mode exponential kernel [1, 7, 22, 23] to an arbitrary M-mode exponential series, for which the GLE is transformed to a vector Ornstein-Uhlenbeck process. PMID:26412904

Diffraction of a Gaussian Beam by a Spherical Obstacle

NASA Technical Reports Server (NTRS)

Lock, James A.; Hovenac, Edward A.

1993-01-01

The Kirchhoff integral for diffraction in the near-forward direction is derived from the exact solution of the electromagnetic boundary value problem of a focused Gaussian laser beam incident on a spherical particle. The diffracted intensity in the vicinity of the particle is computed and the way in which the features of the diffraction pattern depend on the width of the Gaussian beam is commented on.

Monte Carlo study of exact {ital S}-matrix duality in nonsimply laced affine Toda theories

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

Beccaria, M.

The ({ital g}{sub 2}{sup (1)},{ital d}{sub 4}{sup (3)}) pair of nonsimply laced affine Toda theories is studied from the point of view of nonperturbative duality. The classical spectrum of each member is composed of two massive scalar particles. The exact {ital S}-matrix prediction for the dual behavior of the coupling-dependent mass ratio is found to be in strong agreement with Monte Carlo data. {copyright} {ital 1996 The American Physical Society.}

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.

Constraints on Particle Sizes in Saturn's G Ring from Ring Plane Crossing Observations

NASA Astrophysics Data System (ADS)

Throop, H. B.; Esposito, L. W.

1996-09-01

The ring plane crossings in 1995--96 allowed earth-based observations of Saturn's diffuse rings (Nicholson et al., Nature 272, 1996; De Pater et al. Icarus 121, 1996) at a phase angle of alpha ~ 5 deg . We calculate the G ring reflectance for steady state distributions of dust to km-sized bodies from a range of physical models which track the evolution of the G ring from its initial formation following the disruption of a progenitor satellite (Canup & Esposito 1996, \\ Icarus,\\ in press). We model scattering from the ring's small particles using an exact T-matrix method for nonspherical, absorptive particles (Mishchenko et al. 1996, \\ JGR Atmo., in press), large particles using the phase function and spectrum of Europa, and intermediate particles using a linear combination of the small and large limits. Two distinct particle size distributions from the CE96 model fit the observed spectrum. The first is that of a dusty ring, with the majority of ring reflectance in dust particles of relatedly shallow power law size distribution exponent q ~ 2.5. The second has equal reflectances from a) dust in the range q ~ 3.5 -- 6.5 and b) macroscopic bodies > 1 mm. In this second case, the respective slightly blue and red components combine to form the observed relatively flat spectrum. Although light scattering in backscatter is not sufficient to completely constrain the G ring size distribution, the distributions predicted by the CE96 model can explain the earth-based observations.

Hydrodynamics of soap films probed by two-particle microrheology

NASA Astrophysics Data System (ADS)

Prasad, Vikram; Weeks, Eric R.

2007-11-01

A soap film consists of a thin water layer that is separated from two bulk air phases above and below it by surfactant monolayers. The flow fields in the soap film created in response to a perturbation depend on coupling between these different phases, the exact nature of which is unknown. In order to determine this coupling, we use polystyrene spheres as tracer particles and track their diffusive motions in the soap film. The correlated Brownian motion of pairs of particles (two-particle microrheology) maps out the flow field, and provides a measure of the surface viscosity of the soap film as well. This measured surface viscosity agrees well with the value obtained from self diffusion of single particles (one-particle microrheology) in the film.

Symplectic orbit and spin tracking code for all-electric storage rings

NASA Astrophysics Data System (ADS)

Talman, Richard M.; Talman, John D.

2015-07-01

Proposed methods for measuring the electric dipole moment (EDM) of the proton use an intense, polarized proton beam stored in an all-electric storage ring "trap." At the "magic" kinetic energy of 232.792 MeV, proton spins are "frozen," for example always parallel to the instantaneous particle momentum. Energy deviation from the magic value causes in-plane precession of the spin relative to the momentum. Any nonzero EDM value will cause out-of-plane precession—measuring this precession is the basis for the EDM determination. A proposed implementation of this measurement shows that a proton EDM value of 10-29e -cm or greater will produce a statistically significant, measurable precession after multiply repeated runs, assuming small beam depolarization during 1000 s runs, with high enough precision to test models of the early universe developed to account for the present day particle/antiparticle population imbalance. This paper describes an accelerator simulation code, eteapot, a new component of the Unified Accelerator Libraries (ual), to be used for long term tracking of particle orbits and spins in electric bend accelerators, in order to simulate EDM storage ring experiments. Though qualitatively much like magnetic rings, the nonconstant particle velocity in electric rings gives them significantly different properties, especially in weak focusing rings. Like the earlier code teapot (for magnetic ring simulation) this code performs exact tracking in an idealized (approximate) lattice rather than the more conventional approach, which is approximate tracking in a more nearly exact lattice. The Bargmann-Michel-Telegdi (BMT) equation describing the evolution of spin vectors through idealized bend elements is also solved exactly—original to this paper. Furthermore the idealization permits the code to be exactly symplectic (with no artificial "symplectification"). Any residual spurious damping or antidamping is sufficiently small to permit reliable tracking for the long times, such as the 1000 s assumed in estimating the achievable EDM precision. This paper documents in detail the theoretical formulation implemented in eteapot. An accompanying paper describes the practical application of the eteapot code in the Universal Accelerator Libraries (ual) environment to "resurrect," or reverse engineer, the "AGS-analog" all-electric ring built at Brookhaven National Laboratory in 1954. Of the (very few) all-electric rings ever commissioned, the AGS-analog ring is the only relativistic one and is the closest to what is needed for measuring proton (or, even more so, electron) EDM's. The companion paper also describes preliminary lattice studies for the planned proton EDM storage rings as well as testing the code for long time orbit and spin tracking.

Demonstration of Numerical Equivalence of Ensemble and Spectral Averaging in Electromagnetic Scattering by Random Particulate Media

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Zakharova, Nadezhda T.

2016-01-01

The numerically exact superposition T-matrix method is used to model far-field electromagnetic scattering by two types of particulate object. Object 1 is a fixed configuration which consists of N identical spherical particles (with N 200 or 400) quasi-randomly populating a spherical volume V having a median size parameter of 50. Object 2 is a true discrete random medium (DRM) comprising the same number N of particles randomly moving throughout V. The median particle size parameter is fixed at 4. We show that if Object 1 is illuminated by a quasi-monochromatic parallel beam then it generates a typical speckle pattern having no resemblance to the scattering pattern generated by Object 2. However, if Object 1 is illuminated by a parallel polychromatic beam with a 10 bandwidth then it generates a scattering pattern that is largely devoid of speckles and closely reproduces the quasi-monochromatic pattern generated by Object 2. This result serves to illustrate the capacity of the concept of electromagnetic scattering by a DRM to encompass fixed quasi-random particulate samples provided that they are illuminated by polychromatic light.

Quantum and classical dissipation of charged particles

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

Ibarra-Sierra, V.G.; Anzaldo-Meneses, A.; Cardoso, J.L.

2013-08-15

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail. -- Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle.more » •Classical and quantum dynamics of a damped electric charge.« less

Phase dilemma in natural orbital functional theory from the N-representability perspective

NASA Astrophysics Data System (ADS)

Mitxelena, Ion; Rodriguez-Mayorga, Mauricio; Piris, Mario

2018-06-01

Any rigorous approach to first-order reduced density matrix ( Γ) functional theory faces the phase dilemma, that is, having to deal with a large number of possible combinations of signs in terms of the electron-electron interaction energy. This problem was discovered by reducing a ground-state energy generated from an approximate N-particle wavefunction into a functional of Γ, known as the top-down method. Here, we show that the phase dilemma also appears in the bottom-up method, in which the functional E[ Γ] is generated by progressive inclusion of N-representability conditions on the reconstructed two-particle reduced density matrix. It is shown that an adequate choice of signs is essential to accurately describe model systems with strong non-dynamic (static) electron correlation, specifically, the one-dimensional Hubbard model with periodic boundary conditions and hydrogen rings. For the latter, the Piris natural orbital functional 7 (PNOF7), with phases equal to -1 for the inter-pair energy terms containing the exchange-time-inversion integrals, agrees with exact diagonalization results.

Quantum Weak Values and Logic: An Uneasy Couple

NASA Astrophysics Data System (ADS)

Svensson, Bengt E. Y.

2017-03-01

Quantum mechanical weak values of projection operators have been used to answer which-way questions, e. g. to trace which arms in a multiple Mach-Zehnder setup a particle may have traversed from a given initial to a prescribed final state. I show that this procedure might lead to logical inconsistencies in the sense that different methods used to answer composite questions, like "Has the particle traversed the way X or the way Y?", may result in different answers depending on which methods are used to find the answer. I illustrate the problem by considering some examples: the "quantum pigeonhole" framework of Aharonov et al., the three-box problem, and Hardy's paradox. To prepare the ground for my main conclusion on the incompatibility in certain cases of weak values and logic, I study the corresponding situation for strong/projective measurements. In this case, no logical inconsistencies occur provided one is always careful in specifying exactly to which ensemble or sample space one refers. My results cast doubts on the utility of quantum weak values in treating cases like the examples mentioned.

Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory.

PubMed

Krüger, Matthias; Solon, Alexandre; Démery, Vincent; Rohwer, Christian M; Dean, David S

2018-02-28

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.

Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory

NASA Astrophysics Data System (ADS)

Krüger, Matthias; Solon, Alexandre; Démery, Vincent; Rohwer, Christian M.; Dean, David S.

2018-02-01

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.

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.

Meshfree truncated hierarchical refinement for isogeometric analysis

NASA Astrophysics Data System (ADS)

Atri, H. R.; Shojaee, S.

2018-05-01

In this paper truncated hierarchical B-spline (THB-spline) is coupled with reproducing kernel particle method (RKPM) to blend advantages of the isogeometric analysis and meshfree methods. Since under certain conditions, the isogeometric B-spline and NURBS basis functions are exactly represented by reproducing kernel meshfree shape functions, recursive process of producing isogeometric bases can be omitted. More importantly, a seamless link between meshfree methods and isogeometric analysis can be easily defined which provide an authentic meshfree approach to refine the model locally in isogeometric analysis. This procedure can be accomplished using truncated hierarchical B-splines to construct new bases and adaptively refine them. It is also shown that the THB-RKPM method can provide efficient approximation schemes for numerical simulations and represent a promising performance in adaptive refinement of partial differential equations via isogeometric analysis. The proposed approach for adaptive locally refinement is presented in detail and its effectiveness is investigated through well-known benchmark examples.

Resumming the large-N approximation for time evolving quantum systems

NASA Astrophysics Data System (ADS)

Mihaila, Bogdan; Dawson, John F.; Cooper, Fred

2001-05-01

In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation values of operators in our numerical simulations. These approximations can be understood either in terms of a truncation to the infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a particular two-particle irreducible vacuum energy graph in the effective action of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the case of quantum mechanics where the Lagrangian is L(x,ẋ)=(12)∑Ni=1x˙2i-(g/8N)[∑Ni=1x2i- r20]2. The key to these approximations is to treat both the x propagator and the x2 propagator on similar footing which leads to a theory whose graphs have the same topology as QED with the x2 propagator playing the role of the photon. The bare vertex approximation is obtained by replacing the exact vertex function by the bare one in the exact Schwinger-Dyson equations for the one and two point functions. The second approximation, which we call the dynamic Debye screening approximation, makes the further approximation of replacing the exact x2 propagator by its value at leading order in the 1/N expansion. These two approximations are compared with exact numerical simulations for the quantum roll problem. The bare vertex approximation captures the physics at large and modest N better than the dynamic Debye screening approximation.

Comparing exact energy solutions of quartic eigenvalue polynomials in commutative, non-commutative and non-commutative phase frameworks for boson π‑

NASA Astrophysics Data System (ADS)

Derakhshani, Z.; Ghominejad, M.

2018-04-01

In this paper, the behavior of a Duffin-Kemmer-Petiau (DKP) boson particle in the presence of a harmonic energy-dependent interaction, under the influence of an external magnetic field is precisely studied. In order to exactly solve all equations in commutative (C), non-commutative (NC) and non-commutative phase (NCP) frameworks, the Nikiforov-Uvarov (NU) powerful exact approach is employed. All these attempts end up with solving their quartic equations, trying to find and discuss on their discriminant function Δ, in a unique way which has never been discussed for any boson in any other research, especially for the boson π‑ on which, we have been exclusively concerned. We finally succeeded to obtain the exact energy spectrums and wave functions under the effects of NC and NCP parameters and energy-dependent interaction on energy eigenvalues. In this step, we analyze the behaviors of their quartic energy eigenvalue polynomials in three sections and accurately compare all achieved physical-admissible roots one by one. This comparison surprisingly shows that the NC and NCP effects on the other hand, and the assumed harmonic energy-dependent interaction on the other hand, have almost the same order of perturbation effects for limited amounts of the magnetic field in a system of DKP bosons. Furthermore, through some calculations within this paper, we came up with a very crucial point about the NU method which was mistakenly being used in many papers by several researchers and improved it to be used safely.

Path-integral representation for the relativistic particle propagators and BFV quantization

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

Fradkin, E.S.; Gitman, D.M.

1991-11-15

The path-integral representations for the propagators of scalar and spinor fields in an external electromagnetic field are derived. The Hamiltonian form of such expressions can be interpreted in the sense of Batalin-Fradkin-Vilkovisky quantization of one-particle theory. The Lagrangian representation as derived allows one to extract in a natural way the expressions for the corresponding gauge-invariant (reparametrization- and supergauge-invariant) actions for pointlike scalar and spinning particles. At the same time, the measure and ranges of integrations, admissible gauge conditions, and boundary conditions can be exactly established.

A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Ghanbari, Behzad; Inc, Mustafa

2018-04-01

The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.

Hawking radiation As tunneling

PubMed

Parikh; Wilczek

2000-12-11

We present a short and direct derivation of Hawking radiation as a tunneling process, based on particles in a dynamical geometry. The imaginary part of the action for the classically forbidden process is related to the Boltzmann factor for emission at the Hawking temperature. Because the derivation respects conservation laws, the exact spectrum is not precisely thermal. We compare and contrast the problem of spontaneous emission of charged particles from a charged conductor.

Quantum Engineering of Dynamical Gauge Fields on Optical Lattices

DTIC Science & Technology

2016-07-08

opens the door for exciting new research directions, such as quantum simulation of the Schwinger model and of non-Abelian models. (a) Papers...exact blocking formulas from the TRG formulation of the transfer matrix. The second is a worm algorithm. The particle number distributions obtained...a fact that can be explained by an approximate particle- hole symmetry. We have also developed a computer code suite for simulating the Abelian

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium.

PubMed

Netz, Roland R

2018-05-14

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium

NASA Astrophysics Data System (ADS)

Netz, Roland R.

2018-05-01

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

LETTER TO THE EDITOR: Single-species reactions on a random catalytic chain

NASA Astrophysics Data System (ADS)

Oshanin, G.; Burlatsky, S. F.

2002-11-01

We present an exact solution for a catalytically activated annihilation A + A → 0 reaction taking place on a one-dimensional chain in which some segments (placed at random, with mean concentration p) possess special, catalytic properties. An annihilation reaction takes place as soon as any two A particles land from the reservoir onto two vacant sites at the extremities of the catalytic segment, or when any A particle lands onto a vacant site on a catalytic segment while the site at the other extremity of this segment is already occupied by another A particle. We find that the disorder-average pressure P(quen) per site of such a chain is given by P(quen) = P(Lan) + β-1F, where P(Lan) = β-1 ln(1 + z) is the Langmuir adsorption pressure, (z being the activity and β-1 the temperature), while β-1F is the reaction-induced contribution, which can be expressed, under appropriate change of notation, as the Lyapunov exponent for the product of 2 × 2 random matrices, obtained exactly by Derrida and Hilhorst (1983 J. Phys. A: Math. Gen. 16 2641). Explicit asymptotic formulae for the particle mean density and the compressibility are also presented.

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.

Nonexistence of exact solutions agreeing with the Gaussian beam on the beam axis or in the focal plane

NASA Astrophysics Data System (ADS)

Lekner, John; Andrejic, Petar

2018-01-01

Solutions of the Helmholtz equation which describe electromagnetic beams (and also acoustic or particle beams) are discussed. We show that an exact solution which reproduces the Gaussian beam waveform on the beam axis does not exist. This is surprising, since the Gaussian beam is a solution of the paraxial equation, and thus supposedly accurate on and near the beam axis. Likewise, a solution of the Helmholtz equation which exactly reproduces the Gaussian beam in the focal plane does not exist. We show that the last statement also holds for Bessel-Gauss beams. However, solutions of the Helmholtz equation (one of which is discussed in detail) can approximate the Gaussian waveform within the central focal region.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method

NASA Astrophysics Data System (ADS)

Volokitin, V.; Liniov, A.; Meyerov, I.; Hartmann, M.; Ivanchenko, M.; Hänggi, P.; Denisov, S.

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dim H =N ≲300 , while the direct long-time numerical integration of the master equation becomes increasingly problematic for N ≳400 , especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η1,η2,...,ηn} , one could propagate a quantum trajectory (with ηi's as norm thresholds) in a numerically exact way. By using a scalable N -particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N =2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method.

PubMed

Volokitin, V; Liniov, A; Meyerov, I; Hartmann, M; Ivanchenko, M; Hänggi, P; Denisov, S

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dimH=N≲300, while the direct long-time numerical integration of the master equation becomes increasingly problematic for N≳400, especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η_{1},η_{2},...,η_{n}}, one could propagate a quantum trajectory (with η_{i}'s as norm thresholds) in a numerically exact way. By using a scalable N-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N=2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Force Evaluation in the Lattice Boltzmann Method Involving Curved Geometry

NASA Technical Reports Server (NTRS)

Mei, Renwei; Yu, Dazhi; Shyy, Wei; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum- exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second order accuracy based on our recent works. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.

Heating and Acceleration of Charged Particles by Weakly Compressible Magnetohydrodynamic Turbulence

NASA Astrophysics Data System (ADS)

Lynn, Jacob William

We investigate the interaction between low-frequency magnetohydrodynamic (MHD) turbulence and a distribution of charged particles. Understanding this physics is central to understanding the heating of the solar wind, as well as the heating and acceleration of other collisionless plasmas. Our central method is to simulate weakly compressible MHD turbulence using the Athena code, along with a distribution of test particles which feel the electromagnetic fields of the turbulence. We also construct analytic models of transit-time damping (TTD), which results from the mirror force caused by compressible (fast or slow) MHD waves. Standard linear-theory models in the literature require an exact resonance between particle and wave velocities to accelerate particles. The models developed in this thesis go beyond standard linear theory to account for the fact that wave-particle interactions decorrelate over a short time, which allows particles with velocities off resonance to undergo acceleration and velocity diffusion. We use the test particle simulation results to calibrate and distinguish between different models for this velocity diffusion. Test particle heating is larger than the linear theory prediction, due to continued acceleration of particles with velocities off-resonance. We also include an artificial pitch-angle scattering to the test particle motion, representing the effect of high-frequency waves or velocity-space instabilities. For low scattering rates, we find that the scattering enforces isotropy and enhances heating by a modest factor. For much higher scattering rates, the acceleration is instead due to a non-resonant effect, as particles "frozen" into the fluid adiabatically gain and lose energy as eddies expand and contract. Lastly, we generalize our calculations to allow for relativistic test particles. Linear theory predicts that relativistic particles with velocities much higher than the speed of waves comprising the turbulence would undergo no acceleration; resonance-broadening modifies this conclusion and allows for a continued Fermi-like acceleration process. This may affect the observed spectra of black hole accretion disks by accelerating relativistic particles into a quasi-powerlaw tail.

A multi-dimensional nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell (PIC) algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; CoCoMans Team

2014-10-01

For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.

Condensate statistics and thermodynamics of weakly interacting Bose gas: Recursion relation approach

NASA Astrophysics Data System (ADS)

Dorfman, K. E.; Kim, M.; Svidzinsky, A. A.

2011-03-01

We study condensate statistics and thermodynamics of weakly interacting Bose gas with a fixed total number N of particles in a cubic box. We find the exact recursion relation for the canonical ensemble partition function. Using this relation, we calculate the distribution function of condensate particles for N=200. We also calculate the distribution function based on multinomial expansion of the characteristic function. Similar to the ideal gas, both approaches give exact statistical moments for all temperatures in the framework of Bogoliubov model. We compare them with the results of unconstraint canonical ensemble quasiparticle formalism and the hybrid master equation approach. The present recursion relation can be used for any external potential and boundary conditions. We investigate the temperature dependence of the first few statistical moments of condensate fluctuations as well as thermodynamic potentials and heat capacity analytically and numerically in the whole temperature range.

Re-examining the effect of particle phase functions on the remote-sensing reflectance.

PubMed

Xiong, Yuanheng; Zhang, Xiaodong; He, Shuangyan; Gray, Deric J

2017-08-20

Even though it is well known that both the magnitude and detailed angular shape of scattering (phase function, PF), particularly in the backward angles, affect the color of the ocean, the current remote-sensing reflectance (R rs ) models typically account for the effect of its magnitude only through the backscattering coefficient (b b ). Using 116 volume scattering function (VSF) measurements previously collected in three coastal waters around the U.S. and in the water of the North Atlantic Ocean, we re-examined the effect of particle PF on R rs in four scenarios. In each scenario, the magnitude of particle backscattering (i.e., b bp ) is known, but the knowledge on the angular shape of particle backscattering is assumed to increase from knowing nothing about the shape of particle PFs to partially knowing the particle backscattering ratio (B p ), the exact backscattering shape as defined by β˜ p (γ≥90°) (particle VSF normalized by the particle total scattering coefficient), and the exact backscattering shape as defined by the χ p factor (particle VSF normalized by the particle backscattering coefficient). At sun zenith angle=30°, the nadir-viewed R rs would vary up to 65%, 35%, 20%, and 10%, respectively, as the constraints on the shape of particle backscattering become increasingly stringent from scenarios 1 to 4. In all four scenarios, the R rs variations increase with both viewing and sun angles and are most prominent in the direction opposite the sun. Our results show a greater impact of the measured particle PFs on R rs than previously found, mainly because our VSF data show a much greater variability in B p , β˜ p (γ≥90°), and χ p than previously known. Among the uncertainties in R rs due to the particle PFs, about 97% can be explained by χ p , 90% by β˜ p (γ≥90°), and 27% by B p . The results indicate that the uncertainty in ocean color remote sensing can be significantly constrained by accounting for χ p of the VSFs.

Efficient particle acceleration in shocks

NASA Astrophysics Data System (ADS)

Heavens, A. F.

1984-10-01

A self-consistent non-linear theory of acceleration of particles by shock waves is developed, using an extension of the two-fluid hydrodynamical model by Drury and Völk. The transport of the accelerated particles is governed by a diffusion coefficient which is initially assumed to be independent of particle momentum, to obtain exact solutions for the spectrum. It is found that steady-state shock structures with high acceleration efficiency are only possible for shocks with Mach numbers less than about 12. A more realistic diffusion coefficient is then considered, and this maximum Mach number is reduced to about 6. The efficiency of the acceleration process determines the relative importance of the non-relativistic and relativistic particles in the distribution of accelerated particles, and this determines the effective specific heat ratio.

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.

Contour-time approach to the Bose-Hubbard model in the strong coupling regime: Studying two-point spatio-temporal correlations at the Hartree-Fock-Bogoliubov level

NASA Astrophysics Data System (ADS)

Fitzpatrick, Matthew R. C.; Kennett, Malcolm P.

2018-05-01

We develop a formalism that allows the study of correlations in space and time in both the superfluid and Mott insulating phases of the Bose-Hubbard Model. Specifically, we obtain a two particle irreducible effective action within the contour-time formalism that allows for both equilibrium and out of equilibrium phenomena. We derive equations of motion for both the superfluid order parameter and two-point correlation functions. To assess the accuracy of this formalism, we study the equilibrium solution of the equations of motion and compare our results to existing strong coupling methods as well as exact methods where possible. We discuss applications of this formalism to out of equilibrium situations.

Closed form solutions of two time fractional nonlinear wave equations

NASA Astrophysics Data System (ADS)

Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

2018-06-01

In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

Crossover between few and many fermions in a harmonic trap

NASA Astrophysics Data System (ADS)

Grining, Tomasz; Tomza, Michał; Lesiuk, Michał; Przybytek, Michał; Musiał, Monika; Moszynski, Robert; Lewenstein, Maciej; Massignan, Pietro

2015-12-01

The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled-cluster method. For few fermions we recover the results of exact diagonalization, yet with this method we are able to study much larger systems. We compute the energy, the chemical potential, the pairing gap, and the density profile of the trapped clouds, smoothly mapping the crossover between the few-body and many-body limits. The energy is found to converge surprisingly rapidly to the many-body result for every value of the interaction strength. Many more particles are instead needed to give rise to the nonanalytic behavior of the pairing gap, and to smoothen the pronounced even-odd oscillations of the chemical potential induced by the shell structure of the trap.

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles

DOE PAGES

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.

2017-04-18

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicitymore » $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $$\\textbf 2 \\to \\textbf 2$$, $$\\textbf 2 \\to \\textbf 3$$ and $$\\textbf 3 \\to \\textbf 3$$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K-matrix has no singularities below the three-particle threshold. Finally, the quantization condition is exact up to corrections of the order $$\\mathcal{O}(e^{-mL})$$ and holds for any choice of total momenta satisfying the boundary conditions.« less

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles

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

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicitymore » $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $$\\textbf 2 \\to \\textbf 2$$, $$\\textbf 2 \\to \\textbf 3$$ and $$\\textbf 3 \\to \\textbf 3$$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K-matrix has no singularities below the three-particle threshold. Finally, the quantization condition is exact up to corrections of the order $$\\mathcal{O}(e^{-mL})$$ and holds for any choice of total momenta satisfying the boundary conditions.« less

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.

Coupling Fluid and Kineitc Effects in Space Weather: an interdisciplinary task

NASA Astrophysics Data System (ADS)

Lapenta, Giovanni; González-Herrero, Diego; Boella, Elisabetta; Siddi, Lorenzo; Cazzola, Emanuele

2017-04-01

Two agents are key to space weather: electromagentic fields and energetic particles. Magnetic fields carried by plasmas in the solar wind interact with the Earth magnetosphere and solar energetic particles produced by solar events or in cosmic rays affect the space environment. Describing both is challenging. Magnetized plasmas are most effectively described by magneto-hydrodynamics, MHD, a fluid theory based on describing some fields defined in space: electromagnetic fields, density, velocity and temperature of the plasma. High energy particles, instead need a more detailed approach , kinetic theory, where statistical distributions of particles are governed by the Boltzmann equation. While fluid models are based on the ordinary space and time, kinetic models require a six dimensional space, called phase space, besides time. The two methods are not separated, the processes leading to the production of energetic particles are the same that involve space plasamas and fields. Arriving at a single self-consistent model has been the goal of the Swiff project funded by the EC in FP7 and it is now a key goal of the ongoing DEEP-ER project. We present a new approach developed with the goal of extending the reach of kinetic models to the fluid scales. Kinetic models are a higher order description and all fluid effects are included in them. However, the cost in terms of computing power is much higher and it has been so far prohibitively expensive to treat space weather events fully kinetically. We have now designed a new method capable of reducing that cost by several orders of magnitude making it possible for kinetic models to study space weather events [1,2]. We will report the new methodology and show its application to space weather mdeling. [1] Giovanni Lapenta,Exactly Energy Conserving Semi-Implicit Particle in Cell Formulation, to appear, JCP, arXiv:1602.06326 [2] Giovanni Lapenta, Diego Gonzalez-Herrero, Elisabetta Boella, Multiple scale kinetic simulations with the energy conserving semi implicit particle in cell (PIC) method, submitted JPP, arXiv:1612.08289

Diffusion in Deterministic Interacting Lattice Systems

NASA Astrophysics Data System (ADS)

Medenjak, Marko; Klobas, Katja; Prosen, Tomaž

2017-09-01

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.

An exact solution for a thick domain wall in general relativity

NASA Technical Reports Server (NTRS)

Goetz, Guenter; Noetzold, Dirk

1989-01-01

An exact solution of the Einstein equations for a static, planar domain wall with finite thickness is presented. At infinity, density and pressure vanish and the space-time tends to the Minkowski vacuum on one side of the wall and to the Taub vacuum on the other side. A surprising feature of this solution is that the density and pressure distribution are symmetric about the central plane of the wall whereas the space-time metric and therefore also the gravitational field experienced by a test particle is asymmetric.

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

DOE PAGES

Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C.; ...

2016-09-01

We present a numerical solution of the quantum Lenard-Balescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and kinetic energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous one-component plasma with various initial conditions. Unlike the more usual Landau/Fokker-Planck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the non-logarithmic order-unity terms. The spectral method can also be used to solve the Landau equation andmore » a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full Lenard-Balescu solution in the weak-coupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.« less

Theoretical study of the dependence of single impurity Anderson model on various parameters within distributional exact diagonalization method

NASA Astrophysics Data System (ADS)

Syaina, L. P.; Majidi, M. A.

2018-04-01

Single impurity Anderson model describes a system consisting of non-interacting conduction electrons coupled with a localized orbital having strongly interacting electrons at a particular site. This model has been proven successful to explain the phenomenon of metal-insulator transition through Anderson localization. Despite the well-understood behaviors of the model, little has been explored theoretically on how the model properties gradually evolve as functions of hybridization parameter, interaction energy, impurity concentration, and temperature. Here, we propose to do a theoretical study on those aspects of a single impurity Anderson model using the distributional exact diagonalization method. We solve the model Hamiltonian by randomly generating sampling distribution of some conducting electron energy levels with various number of occupying electrons. The resulting eigenvalues and eigenstates are then used to define the local single-particle Green function for each sampled electron energy distribution using Lehmann representation. Later, we extract the corresponding self-energy of each distribution, then average over all the distributions and construct the local Green function of the system to calculate the density of states. We repeat this procedure for various values of those controllable parameters, and discuss our results in connection with the criteria of the occurrence of metal-insulator transition in this system.

Toward Higher-Order Mass Detection: Influence of an Adsorbate's Rotational Inertia and Eccentricity on the Resonant Response of a Bernoulli-Euler Cantilever Beam.

PubMed

Heinrich, Stephen M; Dufour, Isabelle

2015-11-19

In this paper a new theoretical model is derived, the results of which permit a detailed examination of how the resonant characteristics of a cantilever are influenced by a particle (adsorbate) attached at an arbitrary position along the beam's length. Unlike most previous work, the particle need not be small in mass or dimension relative to the beam, and the adsorbate's geometric characteristics are incorporated into the model via its rotational inertia and eccentricity relative to the beam axis. For the special case in which the adsorbate's (translational) mass is indeed small, an analytical solution is obtained for the particle-induced resonant frequency shift of an arbitrary flexural mode, including the effects of rotational inertia and eccentricity. This solution is shown to possess the exact first-order behavior in the normalized particle mass and represents a generalization of analytical solutions derived by others in earlier studies. The results suggest the potential for "higher-order" nanobeam-based mass detection methods by which the multi-mode frequency response reflects not only the adsorbate's mass but also important geometric data related to its size, shape, or orientation (i.e., the mass distribution), thus resulting in more highly discriminatory techniques for discrete-mass sensing.

A gyrokinetic collision operator for magnetized Lorentz plasmas

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

Liu Chang; Ma Chenhao; Yu Xiongjie

2011-03-15

A gyrocenter collision operator for magnetized Lorentz plasmas is derived using the Fokker-Plank method. The gyrocenter collision operator consists of drift and diffusion terms in the gyrocenter coordinates, including the diffusion of the gyrocenter, which does not exist for the collision operator in the particle phase space coordinates. The gyrocenter collision operator also depends on the transverse electric field explicitly, which is crucial for the correct treatment of collisional effects and transport in the gyrocenter coordinates. The gyrocenter collision operator derived is applied to calculate the particle and heat transport fluxes in a magnetized Lorentz plasma with an electric field.more » The particle and heat transport fluxes calculated from our gyrocenter collision operator agree exactly with the classical Braginskii's result [S. I. Braginskii, Reviews of Plasma Physics (Consultants Bureau, New York, 1965), Vol. 1, p. 205: P. Helander and D. J. Sigmar, Collisional Transport in Magnetized Plasmas (Cambridge University, Cambridge, 2002), p. 65], which validates the correctness of our collision operator. To calculate the transport fluxes correctly, it is necessary to apply the pullback transformation associated with gyrocenter coordinate transformation in the presence of collisions, which also serves as a practical algorithm for evaluating collisional particle and heat transport fluxes in the gyrocenter coordinates.« less

Acoustic radiation force of a Bessel beam on a porous sphere.

PubMed

Azarpeyvand, Mahdi

2012-06-01

The possibility of using acoustic Bessel beams to produce an axial pulling force on porous particles is examined in an exact manner. The mathematical model utilizes the appropriate partial-wave expansion method in spherical coordinates, while Biot's model is used to describe the wave motion within the poroelastic medium. Of particular interest here is to examine the feasibility of using Bessel beams for (a) acoustic manipulation of fine porous particles and (b) suppression of particle resonances. To verify the viability of the technique, the radiation force and scattering form-function are calculated for aluminum and silica foams at various porosities. Inspection of the results has shown that acoustic manipulation of low porosity (<0.3) spheres is similar to that of solid elastic spheres, but this behavior significantly changes at higher porosities. Results have also shown a strong correlation between the backscattered form-function and the regions of negative radiation force. It has also been observed that the high-order resonances of the particle can be effectively suppressed by choosing the beam conical angle such that the acoustic contribution from that particular mode vanishes. This investigation may be helpful in the development of acoustic tweezers for manipulation of micro-porous drug delivery carrier and contrast agents.

Toward Higher-Order Mass Detection: Influence of an Adsorbate’s Rotational Inertia and Eccentricity on the Resonant Response of a Bernoulli-Euler Cantilever Beam

PubMed Central

Heinrich, Stephen M.; Dufour, Isabelle

2015-01-01

In this paper a new theoretical model is derived, the results of which permit a detailed examination of how the resonant characteristics of a cantilever are influenced by a particle (adsorbate) attached at an arbitrary position along the beam’s length. Unlike most previous work, the particle need not be small in mass or dimension relative to the beam, and the adsorbate’s geometric characteristics are incorporated into the model via its rotational inertia and eccentricity relative to the beam axis. For the special case in which the adsorbate’s (translational) mass is indeed small, an analytical solution is obtained for the particle-induced resonant frequency shift of an arbitrary flexural mode, including the effects of rotational inertia and eccentricity. This solution is shown to possess the exact first-order behavior in the normalized particle mass and represents a generalization of analytical solutions derived by others in earlier studies. The results suggest the potential for “higher-order” nanobeam-based mass detection methods by which the multi-mode frequency response reflects not only the adsorbate’s mass but also important geometric data related to its size, shape, or orientation (i.e., the mass distribution), thus resulting in more highly discriminatory techniques for discrete-mass sensing. PMID:26610493

Fluctuation theorem for entropy production during effusion of an ideal gas with momentum transfer.

PubMed

Wood, Kevin; Van den Broeck, C; Kawai, R; Lindenberg, Katja

2007-06-01

We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Cleuren [Phys. Rev. E 74, 021117 (2006)], we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.

[Air pollution and cardiovascular toxicity: known risks].

PubMed

Kostrzewa, A; Filleul, L; Eilstein, D; Harrabi, I; Tessier, J F

2004-03-01

Review of studies about epidemiological and physiopathological knowledge of ambient air particles short-term cardio-vascular effects. CURRENTS AND STRONG POINTS: Many studies, in contrasted countries for pollution's sources, meteorological conditions or socio-demographical characteristics, have shown health effects due to ambient air particles. After having studied mainly the respiratory effects of particulate air pollution, epidemiologists are now interested in the cardio-vascular effects of ambient air particles. In fact, serious effects seem to exist in fragile people which can get to emergency department visits, hospitalisation and even death. In addition, studies have shown less serious effects, but likely to be frequent (cardiac symptoms, and stoppages for cardio-vascular causes, notably). The exact mechanism by which particles have cardio-vascular adverse health effects is unknown, but experimental and epidemiological studies have led to several hypotheses: local pulmonary effects seem to be followed by systemic effects, which would be responsible for effects on the electrical activity of the heart through cardiac autonomic dysfunction and effects on the blood supply to the heart. The objective of this work is to summarise epidemiological and physiopathological knowledge about the cardio-vascular effects of ambient air particles. To evaluate the real importance of cardio-vascular effects due to particulate air pollution and to identify their exact mechanism, a more precise knowledge of detailed causes of deaths and hospitalisations and a better knowledge of less serious effects, but likely to be frequent, is necessary. Equally, a detailed identification of fragile people is essential for developing preventive actions.

Exact charge and energy conservation in implicit PIC with mapped computational meshes

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

Chen, Guangye; Barnes, D. C.

This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov Poisson formulation), ours is based on a nonlinearly converged Vlasov Amp re (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant Friedrichs Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicitmore » time steps (unlike the earlier energy-conserving explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.« less

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.

Investigation of the Influence of Microgravity on Transport Mechanism in a Virtual Spaceflight Chamber: A Flight Definition Program

NASA Technical Reports Server (NTRS)

Trolinger, James D.; Rangel, Roger; Witherow, William; Rogers, Jan; Lal, Ravindra B.

1999-01-01

A need exists for understanding precisely how particles move and interact in a fluid in the absence of gravity. Such understanding is required, for example, for modeling and predicting crystal growth in space where crystals grow from solution around nucleation sites as well as for any study of particles or bubbles in liquids or in experiments where particles are used as tracers for mapping microconvection. We have produced an exact solution to the general equation of motion of particles at extremely low Reynolds number in microgravity that covers a wide range of interesting conditions. We have also developed diagnostic tools and experimental techniques to test the validity of the general equation . This program, which started in May, 1998, will produce the flight definition for an experiment in a microgravity environment of space to validate the theoretical model. We will design an experiment with the help of the theoretical model that is optimized for testing the model, measuring g, g-jitter, and other microgravity phenomena. This paper describes the goals, rational, and approach for the flight definition program. The first objective of this research is to understand the physics of particle interactions with fluids and other particles in low Reynolds number flows in microgravity. Secondary objectives are to (1) observe and quantify g-jitter effects and microconvection on particles in fluids, (2) validate an exact solution to the general equation of motion of a particle in a fluid, and (3) to characterize the ability of isolation tables to isolate experiments containing particle in liquids. The objectives will be achieved by recording a large number of holograms of particle fields in microgravity under controlled conditions, extracting the precise three-dimensional position of all of the particles as a function of time and examining the effects of all parameters on the motion of the particles. The feasibility for achieving these results has already been established in the ongoing ground-based NRA, which led to the "virtual spaceflight chamber" concept.

Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of nonlinear PDEs.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd; Mohyud-Din, Syed Tauseef

2013-01-01

The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.

Theory of elastic interaction between arbitrary colloidal particles in confined nematic liquid crystals.

PubMed

Tovkach, O M; Chernyshuk, S B; Lev, B I

2012-12-01

We develop the method proposed by Chernyshuk and Lev [Phys. Rev. E 81, 041701 (2010)] for theoretical investigation of elastic interactions between colloidal particles of arbitrary shape and chirality (polar as well as azimuthal anchoring) in the confined nematic liquid crystal (NLC). General expressions for six different types of multipole elastic interactions are obtained in the confined NLC: monopole-monopole (Coulomb type), monopole-dipole, monopole-quadrupole, dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions. The obtained formulas remain valid in the presence of the external electric or magnetic fields. The exact equations are found for all multipole coefficients for the weak anchoring case. For the strong anchoring coupling, the connection between the symmetry of the shape or director and multipole coefficients is obtained, which enables us to predict which multipole coefficients vanish and which remain nonzero. The particles with azimuthal helicoid anchoring are considered as an example. Dipole-dipole interactions between helicoid cylinders and cones are found in the confined NLC. In addition, the banana-shaped particles in homeotropic and planar nematic cells are considered. It is found that the dipole-dipole interaction between banana-shaped particles differs greatly from the dipole-dipole interaction between the axially symmetrical particles in the nematic cell. There is a crossover from attraction to repulsion between banana particles along some directions in nematic cells. It is shown that monopoles do not "feel" the type of nematic cell: monopole-monopole interaction turns out to be the same in homeotropic and planar nematic cells and converges to the Coulomb law as thickness increases, L→∞.

Classical Control System Design: A non-Graphical Method for Finding the Exact System Parameters

NASA Astrophysics Data System (ADS)

Hussein, Mohammed Tawfik

2008-06-01

The Root Locus method of control system design was developed in the 1940's. It is a set of rules that helps in sketching the path traced by the roots of the closed loop characteristic equation of the system, as a parameter such as a controller gain, k, is varied. The procedure provides approximate sketching guidelines. Designs on control systems using the method are therefore not exact. This paper aims at a non-graphical method for finding the exact system parameters to place a pair of complex conjugate poles on a specified damping ratio line. The overall procedure is based on the exact solution of complex equations on the PC using numerical methods.

MEASURING PROJECTOR

DOEpatents

Franck, J.V.; Broadhead, P.S.; Skiff, E.W.

1959-07-14

A semiautomatic measuring projector particularly adapted for measurement of the coordinates of photographic images of particle tracks as prcduced in a bubble or cloud chamber is presented. A viewing screen aids the operator in selecting a particle track for measurement. After approximate manual alignment, an image scanning system coupled to a servo control provides automatic exact alignment of a track image with a reference point. The apparatus can follow along a track with a continuous motion while recording coordinate data at various selected points along the track. The coordinate data is recorded on punched cards for subsequent computer calculation of particle trajectory, momentum, etc.

The role of charged particles in the positive corona-generated photon count in a rod to plane air gap

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

Bian, X. M.; Wang, Y. J.; MacAlpine, J. M. K.

The relationship between the calculated charged-particle densities in positive corona, the rate of streamer production, and the photon count from the corona were investigated and found to be closely related. Both the densities of electrons and positive ions peaked at 11.8 kV, near the corona inception voltage; they then fell rapidly before slowly rising again. This behavior was exactly matched by the measured photon count. The calculation of the charged-particle density in a positive corona was achieved by means of a fluid model.

Solving large scale structure in ten easy steps with COLA

NASA Astrophysics Data System (ADS)

Tassev, Svetlin; Zaldarriaga, Matias; Eisenstein, Daniel J.

2013-06-01

We present the COmoving Lagrangian Acceleration (COLA) method: an N-body method for solving for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory (LPT). Unlike standard N-body methods, the COLA method can straightforwardly trade accuracy at small-scales in order to gain computational speed without sacrificing accuracy at large scales. This is especially useful for cheaply generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing, as those catalogs are essential for performing detailed error analysis for ongoing and future surveys of LSS. As an illustration, we ran a COLA-based N-body code on a box of size 100 Mpc/h with particles of mass ≈ 5 × 109Msolar/h. Running the code with only 10 timesteps was sufficient to obtain an accurate description of halo statistics down to halo masses of at least 1011Msolar/h. This is only at a modest speed penalty when compared to mocks obtained with LPT. A standard detailed N-body run is orders of magnitude slower than our COLA-based code. The speed-up we obtain with COLA is due to the fact that we calculate the large-scale dynamics exactly using LPT, while letting the N-body code solve for the small scales, without requiring it to capture exactly the internal dynamics of halos. Achieving a similar level of accuracy in halo statistics without the COLA method requires at least 3 times more timesteps than when COLA is employed.

Interaction of evaporating and condensing particles in the free-molecular regime

NASA Astrophysics Data System (ADS)

Kogan, M. N.; Bobrov, I. N.; Cercignani, C.; Frezzotti, A.

1995-07-01

In a previous paper it was shown that repulsive/attractive forces arise between evaporating/ condensing particles in the free-molecular regime. Here we obtain explicit expressions for these forces in the case of spherical particles with equal temperatures. The temperature of the surrounding vapor is, generally speaking, different from that of the particles. Numerical results are obtained for different values of the ratios between particle and vapor temperatures and pressures, of the particles radii and of the evaporation coefficients. In the case when the evaporation coefficient equals unity, an exact expression is obtained for the force between particles of different radii. A simple model describing coagulation processes and taking the above-mentioned forces into account is proposed. It is shown that for large values of the vapor supersaturation, the influence of these forces on the coagulation rate may be very pronounced.

Statistical mechanics of few-particle systems: exact results for two useful models

NASA Astrophysics Data System (ADS)

Miranda, Enrique N.

2017-11-01

The statistical mechanics of small clusters (n ˜ 10-50 elements) of harmonic oscillators and two-level systems is studied exactly, following the microcanonical, canonical and grand canonical formalisms. For clusters with several hundred particles, the results from the three formalisms coincide with those found in the thermodynamic limit. However, for clusters formed by a few tens of elements, the three ensembles yield different results. For a cluster with a few tens of harmonic oscillators, when the heat capacity per oscillator is evaluated within the canonical formalism, it reaches a limit value equal to k B , as in the thermodynamic case, while within the microcanonical formalism the limit value is k B (1-1/n). This difference could be measured experimentally. For a cluster with a few tens of two-level systems, the heat capacity evaluated within the canonical and microcanonical ensembles also presents differences that could be detected experimentally. Both the microcanonical and grand canonical formalism show that the entropy is non-additive for systems this small, while the canonical ensemble reaches the opposite conclusion. These results suggest that the microcanonical ensemble is the most appropriate for dealing with systems with tens of particles.

Recent advances in nonlinear implicit, electrostatic particle-in-cell (PIC) algorithms

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; Barnes, Daniel

2012-10-01

An implicit 1D electrostatic PIC algorithmfootnotetextChen, Chac'on, Barnes, J. Comput. Phys. 230 (2011) has been developed that satisfies exact energy and charge conservation. The algorithm employs a kinetic-enslaved Jacobian-free Newton-Krylov methodfootnotetextIbid. that ensures nonlinear convergence while taking timesteps comparable to the dynamical timescale of interest. Here we present two main improvements of the algorithm. The first is the formulation of a preconditioner based on linearized fluid equations, which are closed using available particle information. The computational benefit is that solving the fluid system is much cheaper than the kinetic one. The effectiveness of the preconditioner in accelerating nonlinear iterations on challenging problems will be demonstrated. A second improvement is the generalization of Ref. 1 to curvilinear meshes,footnotetextChac'on, Chen, Barnes, J. Comput. Phys. submitted (2012) with a hybrid particle update of positions and velocities in logical and physical space respectively.footnotetextSwift, J. Comp. Phys., 126 (1996) The curvilinear algorithm remains exactly charge and energy-conserving, and can be extended to multiple dimensions. We demonstrate the accuracy and efficiency of the algorithm with a 1D ion-acoustic shock wave simulation.

Considerations for the independent reaction times and step-by-step methods for radiation chemistry simulations

NASA Astrophysics Data System (ADS)

Plante, Ianik; Devroye, Luc

2017-10-01

Ionizing radiation interacts with the water molecules of the tissues mostly by ionizations and excitations, which result in the formation of the radiation track structure and the creation of radiolytic species such as H.,.OH, H2, H2O2, and e-aq. After their creation, these species diffuse and may chemically react with the neighboring species and with the molecules of the medium. Therefore radiation chemistry is of great importance in radiation biology. As the chemical species are not distributed homogeneously, the use of conventional models of homogeneous reactions cannot completely describe the reaction kinetics of the particles. Actually, many simulations of radiation chemistry are done using the Independent Reaction Time (IRT) method, which is a very fast technique to calculate radiochemical yields but which do not calculate the positions of the radiolytic species as a function of time. Step-by-step (SBS) methods, which are able to provide such information, have been used only sparsely because these are time-consuming in terms of calculation. Recent improvements in computer performance now allow the regular use of the SBS method in radiation chemistry. The SBS and IRT methods are both based on the Green's functions of the diffusion equation (GFDE). In this paper, several sampling algorithms of the GFDE and for the IRT method are presented. We show that the IRT and SBS methods are exactly equivalent for 2-particles systems for diffusion and partially diffusion-controlled reactions between non-interacting particles. We also show that the results obtained with the SBS simulation method with periodic boundary conditions are in agreement with the predictions by classical reaction kinetics theory, which is an important step towards using this method for modelling of biochemical networks and metabolic pathways involved in oxidative stress. Finally, the first simulation results obtained with the code RITRACKS (Relativistic Ion Tracks) are presented.

A model study of aggregates composed of spherical soot monomers with an acentric carbon shell

NASA Astrophysics Data System (ADS)

Luo, Jie; Zhang, Yongming; Zhang, Qixing

2018-01-01

Influences of morphology on the optical properties of soot particles have gained increasing attentions. However, studies on the effect of the way primary particles are coated on the optical properties is few. Aimed to understand how the primary particles are coated affect the optical properties of soot particles, the coated soot particle was simulated using the acentric core-shell monomers model (ACM), which was generated by randomly moving the cores of concentric core-shell monomers (CCM) model. Single scattering properties of the CCM model with identical fractal parameters were calculated 50 times at first to evaluate the optical diversities of different realizations of fractal aggregates with identical parameters. The results show that optical diversities of different realizations for fractal aggregates with identical parameters cannot be eliminated by averaging over ten random realizations. To preserve the fractal characteristics, 10 realizations of each model were generated based on the identical 10 parent fractal aggregates, and then the results were averaged over each 10 realizations, respectively. The single scattering properties of all models were calculated using the numerically exact multiple-sphere T-matrix (MSTM) method. It is found that the single scattering properties of randomly coated soot particles calculated using the ACM model are extremely close to those using CCM model and homogeneous aggregate (HA) model using Maxwell-Garnett effective medium theory. Our results are different from previous studies. The reason may be that the differences in previous studies were caused by fractal characteristics but not models. Our findings indicate that how the individual primary particles are coated has little effect on the single scattering properties of soot particles with acentric core-shell monomers. This work provides a suggestion for scattering model simplification and model selection.

Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Abuasad, Salah; Hashim, Ishak

2018-04-01

In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

Light dark matter and galaxy formation

NASA Astrophysics Data System (ADS)

Ascasibar, Yago

2006-11-01

What if dark matter particles were as light as a few MeV? Well, they would ``just'' need to decay or annihilate in exactly the right amount to explain the observed dark matter density... However, such a process would yield a detectable imprint on both particle and cosmological scales. Some of the signatures would be difficult to measure; some others would determine whether a galaxy can form stars or not. Does any (actually all) of these weird things happen?

Numerically Exact Computer Simulations of Light Scattering by Densely Packed, Random Particulate Media

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2011-01-01

Direct computer simulations of electromagnetic scattering by discrete random media have become an active area of research. In this progress review, we summarize and analyze our main results obtained by means of numerically exact computer solutions of the macroscopic Maxwell equations. We consider finite scattering volumes with size parameters in the range, composed of varying numbers of randomly distributed particles with different refractive indices. The main objective of our analysis is to examine whether all backscattering effects predicted by the low-density theory of coherent backscattering (CB) also take place in the case of densely packed media. Based on our extensive numerical data we arrive at the following conclusions: (i) all backscattering effects predicted by the asymptotic theory of CB can also take place in the case of densely packed media; (ii) in the case of very large particle packing density, scattering characteristics of discrete random media can exhibit behavior not predicted by the low-density theories of CB and radiative transfer; (iii) increasing the absorptivity of the constituent particles can either enhance or suppress typical manifestations of CB depending on the particle packing density and the real part of the refractive index. Our numerical data strongly suggest that spectacular backscattering effects identified in laboratory experiments and observed for a class of high-albedo Solar System objects are caused by CB.

Electromagnetic fields and potentials generated by massless charged particles

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

Azzurli, Francesco, E-mail: francesco.azzurli@gmail.com; Lechner, Kurt, E-mail: lechner@pd.infn.it; INFN, Sezione di Padova, Via F. Marzolo, 8, 35131 Padova

2014-10-15

We provide for the first time the exact solution of Maxwell’s equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard–Wiechert field the electromagnetic field acquires singular δ-like contributions whose support and dimensionality depend crucially on whether the motion is (a) linear, (b) accelerated unbounded, (c) accelerated bounded. In the first two cases the particle generates amore » planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string. - Highlights: • First exact solution of Maxwell’s equations for massless charges in arbitrary motion. • Explicit expressions of electromagnetic fields and potentials. • Derivations are rigorous and based on distribution theory. • The form of the field depends heavily on whether the motion is bounded or unbounded. • The electromagnetic field contains unexpected Dirac-delta-function contributions.« less

Collisional evolution of rotating, non-identical particles. [in Saturn rings

NASA Technical Reports Server (NTRS)

Salo, H.

1987-01-01

Hameen-Anttila's (1984) theory of self-gravitating collisional particle disks is extended to include the effects of particle spin. Equations are derived for the coupled evolution of random velocities and spins, showing that friction and surface irregularity both reduce the local velocity dispersion and transfer significant amounts of random kinetic energy to rotational energy. Results for the equilibrium ratio of rotational energy to random kinetic energy are exact not only for identical nongravitating mass points, but also if finite size, self-gravitating forces, or size distribution are included. The model is applied to the dynamics of Saturn's rings, showing that the inclusion of rotation reduces the geometrical thickness of the layer of cm-sized particles to, at most, about one-half, with large particles being less affected.

Particle-hole symmetry, many-body localization, and topological edge modes

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Friedman, Aaron J.; Parameswaran, S. A.; Potter, Andrew C.

We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders. Supported by the Gordon and Betty Moore Foundation's EPiQS Initiative (Grant GBMF4307 (ACP), the Quantum Materials Program at LBNL (RV), NSF Grant DMR-1455366 and UCOP Research Catalyst Award No. CA-15-327861 (SAP).

On the theory and simulation of multiple Coulomb scattering of heavy-charged particles.

PubMed

Striganov, S I

2005-01-01

The Moliere theory of multiple Coulomb scattering is modified to take into account the difference between processes of scattering off atomic nuclei and electrons. A simple analytical expression for angular distribution of charged particles passing through a thick absorber is found. It does not assume any special form for a differential scattering cross section and has a wider range of applicability than a gaussian approximation. A well-known method to simulate multiple Coulomb scatterings is based on treating 'soft' and 'hard' collisions differently. An angular deflection in a large number of 'soft' collisions is sampled using the proposed distribution function, a small number of 'hard' collision are simulated directly. A boundary between 'hard' and 'soft' collisions is defined, providing a precise sampling of a scattering angle (1% level) and a small number of 'hard' collisions. A corresponding simulating module takes into account projectile and nucleus charged distributions and exact kinematics of a projectile-electron interaction.

Three-dimensional structural dynamics of DNA origami Bennett linkages using individual-particle electron tomography

DOE PAGES

Lei, Dongsheng; Marras, Alexander E.; Liu, Jianfang; ...

2018-02-09

Scaffolded DNA origami has proven to be a powerful and efficient technique to fabricate functional nanomachines by programming the folding of a single-stranded DNA template strand into three-dimensional (3D) nanostructures, designed to be precisely motion-controlled. Although two-dimensional (2D) imaging of DNA nanomachines using transmission electron microscopy and atomic force microscopy suggested these nanomachines are dynamic in 3D, geometric analysis based on 2D imaging was insufficient to uncover the exact motion in 3D. In this paper, we use the individual-particle electron tomography method and reconstruct 129 density maps from 129 individual DNA origami Bennett linkage mechanisms at ~6-14 nm resolution. The statisticalmore » analyses of these conformations lead to understanding the 3D structural dynamics of Bennett linkage mechanisms. Moreover, our effort provides experimental verification of a theoretical kinematics model of DNA origami, which can be used as feedback to improve the design and control of motion via optimized DNA sequences and routing.« less

Three-dimensional structural dynamics of DNA origami Bennett linkages using individual-particle electron tomography

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

Lei, Dongsheng; Marras, Alexander E.; Liu, Jianfang

Scaffolded DNA origami has proven to be a powerful and efficient technique to fabricate functional nanomachines by programming the folding of a single-stranded DNA template strand into three-dimensional (3D) nanostructures, designed to be precisely motion-controlled. Although two-dimensional (2D) imaging of DNA nanomachines using transmission electron microscopy and atomic force microscopy suggested these nanomachines are dynamic in 3D, geometric analysis based on 2D imaging was insufficient to uncover the exact motion in 3D. In this paper, we use the individual-particle electron tomography method and reconstruct 129 density maps from 129 individual DNA origami Bennett linkage mechanisms at ~6-14 nm resolution. The statisticalmore » analyses of these conformations lead to understanding the 3D structural dynamics of Bennett linkage mechanisms. Moreover, our effort provides experimental verification of a theoretical kinematics model of DNA origami, which can be used as feedback to improve the design and control of motion via optimized DNA sequences and routing.« less

Hidden algebra method (quasi-exact-solvability in quantum mechanics)

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

Turbiner, Alexander; Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F.

1996-02-20

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.

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

Talman, Richard M.; Talman, John D.

Proposed methods for measuring the electric dipole moment (EDM) of the proton use an intense, polarized proton beam stored in an all-electric storage ring “trap.” At the “magic” kinetic energy of 232.792 MeV, proton spins are “frozen,” for example always parallel to the instantaneous particle momentum. Energy deviation from the magic value causes in-plane precession of the spin relative to the momentum. Any nonzero EDM value will cause out-of-plane precession—measuring this precession is the basis for the EDM determination. A proposed implementation of this measurement shows that a proton EDM value of 10 –29e–cm or greater will produce a statisticallymore » significant, measurable precession after multiply repeated runs, assuming small beam depolarization during 1000 s runs, with high enough precision to test models of the early universe developed to account for the present day particle/antiparticle population imbalance. This paper describes an accelerator simulation code, eteapot, a new component of the Unified Accelerator Libraries (ual), to be used for long term tracking of particle orbits and spins in electric bend accelerators, in order to simulate EDM storage ring experiments. Though qualitatively much like magnetic rings, the nonconstant particle velocity in electric rings gives them significantly different properties, especially in weak focusing rings. Like the earlier code teapot (for magnetic ring simulation) this code performs exact tracking in an idealized (approximate) lattice rather than the more conventional approach, which is approximate tracking in a more nearly exact lattice. The Bargmann-Michel-Telegdi (BMT) equation describing the evolution of spin vectors through idealized bend elements is also solved exactly—original to this paper. Furthermore the idealization permits the code to be exactly symplectic (with no artificial “symplectification”). Any residual spurious damping or antidamping is sufficiently small to permit reliable tracking for the long times, such as the 1000 s assumed in estimating the achievable EDM precision. This paper documents in detail the theoretical formulation implemented in eteapot. An accompanying paper describes the practical application of the eteapot code in the Universal Accelerator Libraries (ual) environment to “resurrect,” or reverse engineer, the “AGS-analog” all-electric ring built at Brookhaven National Laboratory in 1954. Of the (very few) all-electric rings ever commissioned, the AGS-analog ring is the only relativistic one and is the closest to what is needed for measuring proton (or, even more so, electron) EDM’s. As a result, the companion paper also describes preliminary lattice studies for the planned proton EDM storage rings as well as testing the code for long time orbit and spin tracking.« less

Symplectic orbit and spin tracking code for all-electric storage rings

DOE PAGES

Talman, Richard M.; Talman, John D.

2015-07-22

Proposed methods for measuring the electric dipole moment (EDM) of the proton use an intense, polarized proton beam stored in an all-electric storage ring “trap.” At the “magic” kinetic energy of 232.792 MeV, proton spins are “frozen,” for example always parallel to the instantaneous particle momentum. Energy deviation from the magic value causes in-plane precession of the spin relative to the momentum. Any nonzero EDM value will cause out-of-plane precession—measuring this precession is the basis for the EDM determination. A proposed implementation of this measurement shows that a proton EDM value of 10 –29e–cm or greater will produce a statisticallymore » significant, measurable precession after multiply repeated runs, assuming small beam depolarization during 1000 s runs, with high enough precision to test models of the early universe developed to account for the present day particle/antiparticle population imbalance. This paper describes an accelerator simulation code, eteapot, a new component of the Unified Accelerator Libraries (ual), to be used for long term tracking of particle orbits and spins in electric bend accelerators, in order to simulate EDM storage ring experiments. Though qualitatively much like magnetic rings, the nonconstant particle velocity in electric rings gives them significantly different properties, especially in weak focusing rings. Like the earlier code teapot (for magnetic ring simulation) this code performs exact tracking in an idealized (approximate) lattice rather than the more conventional approach, which is approximate tracking in a more nearly exact lattice. The Bargmann-Michel-Telegdi (BMT) equation describing the evolution of spin vectors through idealized bend elements is also solved exactly—original to this paper. Furthermore the idealization permits the code to be exactly symplectic (with no artificial “symplectification”). Any residual spurious damping or antidamping is sufficiently small to permit reliable tracking for the long times, such as the 1000 s assumed in estimating the achievable EDM precision. This paper documents in detail the theoretical formulation implemented in eteapot. An accompanying paper describes the practical application of the eteapot code in the Universal Accelerator Libraries (ual) environment to “resurrect,” or reverse engineer, the “AGS-analog” all-electric ring built at Brookhaven National Laboratory in 1954. Of the (very few) all-electric rings ever commissioned, the AGS-analog ring is the only relativistic one and is the closest to what is needed for measuring proton (or, even more so, electron) EDM’s. As a result, the companion paper also describes preliminary lattice studies for the planned proton EDM storage rings as well as testing the code for long time orbit and spin tracking.« less

A Monte Carlo (N,V,T) study of the stability of charged interfaces: A simulation on a hypersphere

NASA Astrophysics Data System (ADS)

Delville, A.; Pellenq, R. J.-M.; Caillol, J. M.

1997-05-01

We have used an exact expression of the Coulombic interactions derived on a hypersphere of an Euclidian space of dimension four to determine the swelling behavior of two infinite charged plates neutralized by exchangeable counterions. Monte Carlo simulations in the (N,V,T) ensemble allows for a derivation of short-ranged hard core repulsions and long-ranged electrostatic forces, which are the two components of the interionic forces in the context of the primitive model. Comparison with numerical results obtained by a classical Euclidian method illustrates the efficiency of the hyperspherical approach, especially at strong coupling between the charged particles, i.e., for divalent counterions and small plate separation.

Current transport properties and phase diagram of a Kitaev chain with long-range pairing

NASA Astrophysics Data System (ADS)

Giuliano, Domenico; Paganelli, Simone; Lepori, Luca

2018-04-01

We describe a method to probe the quantum phase transition between the short-range topological phase and the long-range topological phase in the superconducting Kitaev chain with long-range pairing, both exhibiting subgap modes localized at the edges. The method relies on the effects of the finite mass of the subgap edge modes in the long-range regime (which survives in the thermodynamic limit) on the single-particle scattering coefficients through the chain connected to two normal leads. Specifically, we show that, when the leads are biased at a voltage V with respect to the superconducting chain, the Fano factor is either zero (in the short-range correlated phase) or 2 e (in the long-range correlated phase). As a result, we find that the Fano factor works as a directly measurable quantity to probe the quantum phase transition between the two phases. In addition, we note a remarkable "critical fractionalization effect" in the Fano factor, which is exactly equal to e along the quantum critical line. Finally, we note that a dual implementation of our proposed device makes it suitable as a generator of large-distance entangled two-particle states.

Distribution of velocities and acceleration for a particle in Brownian correlated disorder: Inertial case

NASA Astrophysics Data System (ADS)

Le Doussal, Pierre; Petković, Aleksandra; Wiese, Kay Jörg

2012-06-01

We study the motion of an elastic object driven in a disordered environment in presence of both dissipation and inertia. We consider random forces with the statistics of random walks and reduce the problem to a single degree of freedom. It is the extension of the mean-field Alessandro-Beatrice- Bertotti-Montorsi (ABBM) model in presence of an inertial mass m. While the ABBM model can be solved exactly, its extension to inertia exhibits complicated history dependence due to oscillations and backward motion. The characteristic scales for avalanche motion are studied from numerics and qualitative arguments. To make analytical progress, we consider two variants which coincide with the original model whenever the particle moves only forward. Using a combination of analytical and numerical methods together with simulations, we characterize the distributions of instantaneous acceleration and velocity, and compare them in these three models. We show that for large driving velocity, all three models share the same large-deviation function for positive velocities, which is obtained analytically for small and large m, as well as for m=6/25. The effect of small additional thermal and quantum fluctuations can be treated within an approximate method.

Bottom-up preparation and structural study of monodispersed lipid particles with internal structure

NASA Astrophysics Data System (ADS)

Kim, Hojun; Alfeche, Alana; Leal, Cecilia

Lipid based nanoparticles having internal bicontinuous cubic phases, also known as cubosomes, are becoming increasingly interesting drug delivery platforms. Compared to the liposomes, they offer an augmented surface area for drug encapsulation. However, this simple argument is insufficient to explain the cellular delivery performance of cubosomes compared to other lipid-based nanoparticles. One could argue that their topology facilitates membrane fusion and endosomal escape but at the moment the exact mechanism of cubosome cellular internalization and endosomal escape is still unknown. This is partially because the practical use of cubosomes has been limited due to hurdles of uncontrollable size and shape distributions. The conventional top-down preparation methods (sonication/homogenization) yield large and polydisperse particles. In this presentation we introduce a new system based on microfluidic devices to prepare small (200 nm) and monodisperse cubosomes with a quality not possible using conventional methods. With this approach, we successfully prepared spherical and monodisperse cubosomes (PDI: 0.01) with and without drug loading. To characterize the cubosomes and the formation mechanisms, we utilize Small Angle X-ray Scattering (SAXS) and Cryogenic TEM. We acknowledge the funding source as a NIH.

SLDAssay: A software package and web tool for analyzing limiting dilution assays.

PubMed

Trumble, Ilana M; Allmon, Andrew G; Archin, Nancie M; Rigdon, Joseph; Francis, Owen; Baldoni, Pedro L; Hudgens, Michael G

2017-11-01

Serial limiting dilution (SLD) assays are used in many areas of infectious disease related research. This paper presents SLDAssay, a free and publicly available R software package and web tool for analyzing data from SLD assays. SLDAssay computes the maximum likelihood estimate (MLE) for the concentration of target cells, with corresponding exact and asymptotic confidence intervals. Exact and asymptotic goodness of fit p-values, and a bias-corrected (BC) MLE are also provided. No other publicly available software currently implements the BC MLE or the exact methods. For validation of SLDAssay, results from Myers et al. (1994) are replicated. Simulations demonstrate the BC MLE is less biased than the MLE. Additionally, simulations demonstrate that exact methods tend to give better confidence interval coverage and goodness-of-fit tests with lower type I error than the asymptotic methods. Additional advantages of using exact methods are also discussed. Copyright © 2017 Elsevier B.V. All rights reserved.

Cobalt adatoms on graphene: Effects of anisotropies on the correlated electronic structure

NASA Astrophysics Data System (ADS)

Mozara, R.; Valentyuk, M.; Krivenko, I.; Şaşıoǧlu, E.; Kolorenč, J.; Lichtenstein, A. I.

2018-02-01

Impurities on surfaces experience a geometric symmetry breaking induced not only by the on-site crystal-field splitting and the orbital-dependent hybridization, but also by different screening of the Coulomb interaction in different directions. We present a many-body study of the Anderson impurity model representing a Co adatom on graphene, taking into account all anisotropies of the effective Coulomb interaction, which we obtained by the constrained random-phase approximation. The most pronounced differences are naturally displayed by the many-body self-energy projected onto the single-particle states. For the solution of the Anderson impurity model and analytical continuation of the Matsubara data, we employed new implementations of the continuous-time hybridization expansion quantum Monte Carlo and the stochastic optimization method, and we verified the results in parallel with the exact diagonalization method.

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

Costa, Liborio I., E-mail: liborio78@gmail.com

A new Markov Chain Monte Carlo method for simulating the dynamics of particle systems characterized by hard-core interactions is introduced. In contrast to traditional Kinetic Monte Carlo approaches, where the state of the system is associated with minima in the energy landscape, in the proposed method, the state of the system is associated with the set of paths traveled by the atoms and the transition probabilities for an atom to be displaced are proportional to the corresponding velocities. In this way, the number of possible state-to-state transitions is reduced to a discrete set, and a direct link between the Montemore » Carlo time step and true physical time is naturally established. The resulting rejection-free algorithm is validated against event-driven molecular dynamics: the equilibrium and non-equilibrium dynamics of hard disks converge to the exact results with decreasing displacement size.« less

Radiation of quantum black holes and modified uncertainty relation

NASA Astrophysics Data System (ADS)

Kamali, A. D.; Pedram, P.

In this paper, using a deformed algebra [X,P] = iℏ/(1 ‑ λ2P2) which is originated from various theories of gravity, we study thermodynamical properties of quantum black holes (BHs) in canonical ensembles. We exactly calculate the modified internal energy, entropy and heat capacity. Moreover, we investigate a tunneling mechanism of massless particle in phase space. In this regard, the tunneling radiation of BH receives new corrections and the exact radiant spectrum is no longer precisely thermal. In addition, we show that our results are compatible with other quantum gravity (QG) approaches.

Exact solutions and phenomenological constraints from massive scalars in a gravity's rainbow spacetime

NASA Astrophysics Data System (ADS)

Bezerra, V. B.; Christiansen, H. R.; Cunha, M. S.; Muniz, C. R.

2017-07-01

We obtain the exact (confluent Heun) solutions to the massive scalar field in a gravity's rainbow Schwarzschild metric. With these solutions at hand, we study the Hawking radiation resulting from the tunneling rate through the event horizon. We show that the emission spectrum obeys nonextensive statistics and is halted when a certain mass remnant is reached. Next, we infer constraints on the rainbow parameters from recent LHC particle physics experiments and Hubble STIS astrophysics measurements. Finally, we study the low frequency limit in order to find the modified energy spectrum around the source.

The exact analysis of contingency tables in medical research.

PubMed

Mehta, C R

1994-01-01

A unified view of exact nonparametric inference, with special emphasis on data in the form of contingency tables, is presented. While the concept of exact tests has been in existence since the early work of RA Fisher, the computational complexity involved in actually executing such tests precluded their use until fairly recently. Modern algorithmic advances, combined with the easy availability of inexpensive computing power, has renewed interest in exact methods of inference, especially because they remain valid in the face of small, sparse, imbalanced, or heavily tied data. After defining exact p-values in terms of the permutation principle, we reference algorithms for computing them. Several data sets are then analysed by both exact and asymptotic methods. We end with a discussion of the available software.

Iterative and variational homogenization methods for filled elastomers

NASA Astrophysics Data System (ADS)

Goudarzi, Taha

Elastomeric composites have increasingly proved invaluable in commercial technological applications due to their unique mechanical properties, especially their ability to undergo large reversible deformation in response to a variety of stimuli (e.g., mechanical forces, electric and magnetic fields, changes in temperature). Modern advances in organic materials science have revealed that elastomeric composites hold also tremendous potential to enable new high-end technologies, especially as the next generation of sensors and actuators featured by their low cost together with their biocompatibility, and processability into arbitrary shapes. This potential calls for an in-depth investigation of the macroscopic mechanical/physical behavior of elastomeric composites directly in terms of their microscopic behavior with the objective of creating the knowledge base needed to guide their bottom-up design. The purpose of this thesis is to generate a mathematical framework to describe, explain, and predict the macroscopic nonlinear elastic behavior of filled elastomers, arguably the most prominent class of elastomeric composites, directly in terms of the behavior of their constituents --- i.e., the elastomeric matrix and the filler particles --- and their microstructure --- i.e., the content, size, shape, and spatial distribution of the filler particles. This will be accomplished via a combination of novel iterative and variational homogenization techniques capable of accounting for interphasial phenomena and finite deformations. Exact and approximate analytical solutions for the fundamental nonlinear elastic response of dilute suspensions of rigid spherical particles (either firmly bonded or bonded through finite size interphases) in Gaussian rubber are first generated. These results are in turn utilized to construct approximate solutions for the nonlinear elastic response of non-Gaussian elastomers filled with a random distribution of rigid particles (again, either firmly bonded or bonded through finite size interphases) at finite concentrations. Three-dimensional finite element simulations are also carried out to gain further insight into the proposed theoretical solutions. Inter alia, we make use of these solutions to examine the effects of particle concentration, mono- and poly-dispersity of the filler particle size, and the presence of finite size interphases on the macroscopic response of filled elastomers. The solutions are found able to explain and describe experimental results that to date have been understood only in part. More generally, the solutions provide a robust tool to efficiently guide the design of filled elastomers with desired macroscopic properties. The homogenization techniques developed in this work are not limited to nonlinear elasticity, but can be readily utilized to study multi-functional properties as well. For demonstration purposes, we work out a novel exact solution for the macroscopic dielectric response of filled elastomers with interphasial space charges.

Quantum tunneling and scattering of a composite object

NASA Astrophysics Data System (ADS)

Ahsan, Naureen

Reaction physics involving composite objects with internal degrees of freedom is an important subject since it is encountered in the context of nuclear processes like fusion, fission, particle decay, as well as many other branches of science. Quantum tunneling and scattering of a composite object are explored in this work. A few model Hamiltonians are chosen as examples where a two-particle system interacts, in one dimension, with a target that poses a delta-potential or an infinite wall potential. It is assumed that only one of the two components interacts with the target. The study includes the harmonic oscillator and the infinite square well as examples of intrinsic Hamiltonians that do not allow the projectile to break up, and a finite square well and a delta-well as examples of Hamiltonians that do. The Projection Method and the Variable Phase Method are applied with the aim of an exact solution to the relevant scattering problems. These methods are discussed in the context of the pertinent convergence issues related thereto, and of their applicability. Virtual excitations of the projectile into the classically forbidden energy-domain are found to play a dominant and non-perturbative role in shaping reaction observables, giving rise to enhanced or reduced tunneling in various situations. Cusps and discontinuities are found to appear in observables as manifestations of unitarity and redistribution of flux at the thresholds. The intrinsic structure gives rise to resonancelike behavior in tunneling probabilities. It is also shown that there is charge asymmetry in the scattering of a composite object, unlike in the case of a structureless particle.

Exact Solutions for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota System by the Analytical Methods.

PubMed

Manafian Heris, Jalil; Lakestani, Mehrdad

2014-01-01

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

A charge- and energy-conserving implicit, electrostatic particle-in-cell algorithm on mapped computational meshes

NASA Astrophysics Data System (ADS)

Chacón, L.; Chen, G.; Barnes, D. C.

2013-01-01

We describe the extension of the recent charge- and energy-conserving one-dimensional electrostatic particle-in-cell algorithm in Ref. [G. Chen, L. Chacón, D.C. Barnes, An energy- and charge-conserving, implicit electrostatic particle-in-cell algorithm, Journal of Computational Physics 230 (2011) 7018-7036] to mapped (body-fitted) computational meshes. The approach maintains exact charge and energy conservation properties. Key to the algorithm is a hybrid push, where particle positions are updated in logical space, while velocities are updated in physical space. The effectiveness of the approach is demonstrated with a challenging numerical test case, the ion acoustic shock wave. The generalization of the approach to multiple dimensions is outlined.

Differential memory in the trilinear model magnetotail

NASA Technical Reports Server (NTRS)

Chen, James; Mitchell, Horage G.; Palmadesso, Peter J.

1990-01-01

The previously proposed concept of 'differential memory' is quantitatively demonstrated using an idealized analytical model of particle dynamics in the magnetotail geometry. In this model (the 'trilinear' tail model) the magnetotail is divided into three regions. The particle orbits are solved exactly in each region, thus reducing the orbit integration to an analytical mapping. It is shown that the trilinear model reproduces the essential phase space features of the earlier model (Chen and Palmadesso, 1986), possessing well-defined entry and exit regions, and stochastic, integrable (regular), and transient orbits, occupying disjoint phase space regions. Different regions have widely separated characteristic time scales corresponding to different types of particle motion. Using the analytical model, the evolution of single-particle distribution functions is calculated.

Particle Sizer

NASA Technical Reports Server (NTRS)

1987-01-01

Microspheres are tiny plastic beads that represent the first commercial products manufactured in orbit. An example of how they are used is a new aerodynamic particle sizer designated APS 33B produced by TSI Incorporated. TSI purchased the microspheres from the National Bureau of Standards which certified their exact size and the company uses them in calibration of the APS 33B* instrument, latest in a line of TSI systems for generating counting and weighing minute particles of submicron size. Instruments are used for evaluating air pollution control devices, quantifying environments, meteorological research, testing filters, inhalation, toxicology and other areas where generation or analysis of small airborne particles is required. * The APS 33B is no longer being manufactured. An improved version, APS 3320, is now being manufactured. 2/28/97

Rubber particle proteins, HbREF and HbSRPP, show different interactions with model membranes.

PubMed

Berthelot, Karine; Lecomte, Sophie; Estevez, Yannick; Zhendre, Vanessa; Henry, Sarah; Thévenot, Julie; Dufourc, Erick J; Alves, Isabel D; Peruch, Frédéric

2014-01-01

The biomembrane surrounding rubber particles from the hevea latex is well known for its content of numerous allergen proteins. HbREF (Hevb1) and HbSRPP (Hevb3) are major components, linked on rubber particles, and they have been shown to be involved in rubber synthesis or quality (mass regulation), but their exact function is still to be determined. In this study we highlighted the different modes of interactions of both recombinant proteins with various membrane models (lipid monolayers, liposomes or supported bilayers, and multilamellar vesicles) to mimic the latex particle membrane. We combined various biophysical methods (polarization-modulation-infrared reflection-adsorption spectroscopy (PM-IRRAS)/ellipsometry, attenuated-total reflectance Fourier-transform infrared (ATR-FTIR), solid-state nuclear magnetic resonance (NMR), plasmon waveguide resonance (PWR), fluorescence spectroscopy) to elucidate their interactions. Small rubber particle protein (SRPP) shows less affinity than rubber elongation factor (REF) for the membranes but displays a kind of "covering" effect on the lipid headgroups without disturbing the membrane integrity. Its structure is conserved in the presence of lipids. Contrarily, REF demonstrates higher membrane affinity with changes in its aggregation properties, the amyloid nature of REF, which we previously reported, is not favored in the presence of lipids. REF binds and inserts into membranes. The membrane integrity is highly perturbed, and we suspect that REF is even able to remove lipids from the membrane leading to the formation of mixed micelles. These two homologous proteins show affinity to all membrane models tested but neatly differ in their interacting features. This could imply differential roles on the surface of rubber particles. © 2013.

Signatures of fractional exclusion statistics in the spectroscopy of quantum Hall droplets.

PubMed

Cooper, Nigel R; Simon, Steven H

2015-03-13

We show how spectroscopic experiments on a small Laughlin droplet of rotating bosons can directly demonstrate Haldane fractional exclusion statistics of quasihole excitations. The characteristic signatures appear in the single-particle excitation spectrum. We show that the transitions are governed by a "many-body selection rule" which allows one to relate the number of allowed transitions to the number of quasihole states on a finite geometry. We illustrate the theory with numerically exact simulations of small numbers of particles.

Toward a Greater Understanding of the Reduction of Drift Coefficients in the Presence of Turbulence

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

Engelbrecht, N. E.; Strauss, R. D.; Burger, R. A.

2017-06-01

Drift effects play a significant role in the transport of charged particles in the heliosphere. A turbulent magnetic field is also known to reduce the effects of particle drifts. The exact nature of this reduction, however, is not clear. This study aims to provide some insight into this reduction and proposes a relatively simple, tractable means of modeling it that provides results in reasonable agreement with numerical simulations of the drift coefficient in a turbulent magnetic field.

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.

Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces

NASA Astrophysics Data System (ADS)

Cammarota, V.; Orsingher, E.

2008-12-01

A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincaré half-plane and Poincaré disk) is examined. Each particle can split into two particles only once at Poisson spaced times and deviates orthogonally when splitted. At time t, after N( t) Poisson events, there are N( t)+1 particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as t increases and for different values of the parameters c (hyperbolic velocity of motion) and λ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented.

Continuum theory for cluster morphologies of soft colloids.

PubMed

Kosmrlj, A; Pauschenwein, G J; Kahl, G; Ziherl, P

2011-06-09

We introduce a continuum description of the thermodynamics of colloids with a core-corona architecture. In the case of thick coronas, their overlap can be treated approximately by replacing the exact one-particle density distribution by a suitably shaped step profile, which provides a convenient way of modeling the spherical, columnar, lamellar, and inverted cluster morphologies predicted by numerical simulations and the more involved theories. We use the model to study monodisperse particles with the hard-core/square-shoulder pair interaction as the simplest representatives of the core-corona class. We derive approximate analytical expressions for the enthalpies of the cluster morphologies which offer a clear insight into the mechanisms at work, and we calculate the lattice spacing and the cluster size for all morphologies of the phase sequence as well as the phase-transition pressures. By comparing the results with the exact crystalline minimum-enthalpy configurations, we show that the accuracy of the theory increases with shoulder width. We discuss possible extensions of the theory that could account for the finite-temperature effects.

Kinetic Description of Ionospheric Outflows Based on the Exact Form of Fokker-Planck Collision Operator: Electrons

NASA Technical Reports Server (NTRS)

Khazanov, George V.; Khabibrakhmanov, Ildar K.; Glocer, Alex

2012-01-01

We present the results of a finite difference implementation of the kinetic Fokker-Planck model with an exact form of the nonlinear collisional operator, The model is time dependent and three-dimensional; one spatial dimension and two in velocity space. The spatial dimension is aligned with the local magnetic field, and the velocity space is defined by the magnitude of the velocity and the cosine of pitch angle. An important new feature of model, the concept of integration along the particle trajectories, is discussed in detail. Integration along the trajectories combined with the operator time splitting technique results in a solution scheme which accurately accounts for both the fast convection of the particles along the magnetic field lines and relatively slow collisional process. We present several tests of the model's performance and also discuss simulation results of the evolution of the plasma distribution for realistic conditions in Earth's plasmasphere under different scenarios.

General relativity exactly described in terms of Newton's laws within curved geometries

NASA Astrophysics Data System (ADS)

Savickas, D.

2014-07-01

Many years ago Milne and McCrea showed in their well-known paper that the Hubble expansion occurring in general relativity could be exactly described by the use of Newtonian mechanics. It will be shown that a similar method can be extended to, and used within, curved geometries when Newton's second law is expressed within a four-dimensional curved spacetime. The second law will be shown to yield an equation that is exactly identical to the geodesic equation of motion of general relativity. This in itself yields no new information concerning relativity since the equation is mathematically identical to the relativistic equation. However, when the time in the second law is defined to have a constant direction as effectively occurs in Newtonian mechanics, and no longer acts as a fourth dimension as exists in relativity theory, it separates into a vector equation in a curved three-dimensional space and an additional second scalar equation that describes conservation of energy. It is shown that the curved Newtonian equations of motion define the metric coefficients which occur in the Schwarzschild solution and that they also define its equations of motion. Also, because the curved Newtonian equations developed here use masses as gravitational sources, as occurs in Newtonian mechanics, they make it possible to derive the solution for other kinds of mass distributions and are used here to find the metric equation for a thin mass-rod and the equation of motion for a mass particle orbiting it in its relativistic gravitational field.

Third Bose fugacity coefficient in one dimension, as a function of asymptotic quantities

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

Amaya-Tapia, A., E-mail: jano@fis.unam.mx; Larsen, S.Y.; Lassaut, M.

2011-02-15

In one of the very few exact quantum mechanical calculations of fugacity coefficients, [L.R. Dodd, A.M. Gibbs. J. Math. Phys. 15 (1974) 41] obtained b{sub 2} and b{sub 3} for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For b{sub 2}, we have shown [A. Amaya-Tapia, S.Y. Larsen, M. Lassaut. Mol. Phys. 103 (2005) 1301-1306. < (arXiv:physics/0405150)>] that Dodd and Gibbs' result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in one dimension. Now, we develop an exact expressionmore » for b{sub 3}-b{sub 3}{sup 0} (where b{sub 3}{sup 0} is the free particle fugacity coefficient) in terms of sums and differences of three-body eigenphase shifts. Further, we show that if we obtain these eigenphase shifts in a Distorted-Born approximation, then, to first order, we reproduce the leading low temperature behaviour, obtained from an expansion of the twofold integral of Dodd and Gibbs. The contributions of the oscillating terms cancel. The formalism that we propose is not limited to one dimension, but seeks to provide a general method to obtain virial coefficients, fugacity coefficients, in terms of asymptotic quantities. The exact one dimensional results allow us to confirm the validity of our approach in this domain.« less

Hidden algebra method (quasi-exact-solvability in quantum mechanics)

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

Turbiner, A.

1996-02-01

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}

Role of quantum statistics in multi-particle decay dynamics

NASA Astrophysics Data System (ADS)

Marchewka, Avi; Granot, Er'el

2015-04-01

The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.

Considering the reversibility of passive and reactive transport problems: Are forward-in-time and backward-in-time models ever equivalent?

NASA Astrophysics Data System (ADS)

Engdahl, N.

2017-12-01

Backward in time (BIT) simulations of passive tracers are often used for capture zone analysis, source area identification, and generation of travel time and age distributions. The BIT approach has the potential to become an immensely powerful tool for direct inverse modeling but the necessary relationships between the processes modeled in the forward and backward models have yet to be formally established. This study explores the time reversibility of passive and reactive transport models in a variety of 2D heterogeneous domains using particle-based random walk methods for the transport and nonlinear reaction steps. Distributed forward models are used to generate synthetic observations that form the initial conditions for the backward in time models and we consider both linear-flood and point injections. The results for passive travel time distributions show that forward and backward models are not exactly equivalent but that the linear-flood BIT models are reasonable approximations. Point based BIT models fall within the travel time range of the forward models, though their distributions can be distinctive in some cases. The BIT approximation is not as robust when nonlinear reactive transport is considered and we find that this reaction system is only exactly reversible under uniform flow conditions. We use a series of simplified, longitudinally symmetric, but heterogeneous, domains to illustrate the causes of these discrepancies between the two model types. Many of the discrepancies arise because diffusion is a "self-adjoint" operator, which causes mass to spread in the forward and backward models. This allows particles to enter low velocity regions in the both models, which has opposite effects in the forward and reverse models. It may be possible to circumvent some of these limitations using an anti-diffusion model to undo mixing when time is reversed, but this is beyond the capabilities of the existing Lagrangian methods.

Using sorted invariant mass variables to evade combinatorial ambiguities in cascade decays

DOE PAGES

Kim, Doojin; Matchev, Konstantin T.; Park, Myeonghun

2016-02-19

The classic method for mass determination in a SUSY-like cascade decay chain relies on measurements of the kinematic endpoints in the invariant mass distributions of suitable collections of visible decay products. However, the procedure is complicated by combinatorial ambiguities: e.g., the visible final state particles may be indistinguishable (as in the case of QCD jets), or one may not know the exact order in which they are emitted along the decay chain. In order to avoid such combinatorial ambiguities, we propose to treat the nal state particles fully democratically and consider the sorted set of the invariant masses of allmore » possible partitions of the visible particles in the decay chain. In particular, for a decay to N visible particles, one considers the sorted sets of all possible n-body invariant mass combinations (2≤ n≤ N) and determines the kinematic endpoint m (n,r) max of the distribution of the r-th largest n-body invariant mass m (n,r) for each possible value of n and r. For the classic example of a squark decay in supersymmetry, we provide analytical formulas for the interpretation of these endpoints in terms of the underlying physical masses. We point out that these measurements can be used to determine the structure of the decay topology, e.g., the number and position of intermediate on-shell resonances.« less

Using sorted invariant mass variables to evade combinatorial ambiguities in cascade decays

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

Kim, Doojin; Matchev, Konstantin T.; Park, Myeonghun

The classic method for mass determination in a SUSY-like cascade decay chain relies on measurements of the kinematic endpoints in the invariant mass distributions of suitable collections of visible decay products. However, the procedure is complicated by combinatorial ambiguities: e.g., the visible final state particles may be indistinguishable (as in the case of QCD jets), or one may not know the exact order in which they are emitted along the decay chain. In order to avoid such combinatorial ambiguities, we propose to treat the nal state particles fully democratically and consider the sorted set of the invariant masses of allmore » possible partitions of the visible particles in the decay chain. In particular, for a decay to N visible particles, one considers the sorted sets of all possible n-body invariant mass combinations (2≤ n≤ N) and determines the kinematic endpoint m (n,r) max of the distribution of the r-th largest n-body invariant mass m (n,r) for each possible value of n and r. For the classic example of a squark decay in supersymmetry, we provide analytical formulas for the interpretation of these endpoints in terms of the underlying physical masses. We point out that these measurements can be used to determine the structure of the decay topology, e.g., the number and position of intermediate on-shell resonances.« less

Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice

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

Ellery, Adam J.; Simpson, Matthew J.; Baker, Ruth E.

2016-05-07

The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motionmore » of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.« less

Exact solutions of a hierarchy of mixing speeds models

NASA Astrophysics Data System (ADS)

Cornille, H.; Platkowski, T.

1992-07-01

This paper presents several new aspects of discrete kinetic theory (DKT). First a hierarchy of d-dimensional (d=1,2,3) models is proposed with (2d+3) velocities and three moduli speeds: 0, 2, and a third one that can be arbitrary. It is assumed that the particles at rest have an internal energy which, for microscopic collisions, supplies for the loss of the kinetic energy. In a more general way than usual, collisions are allowed that mix particles with different speeds. Second, for the (1+1)-dimensional restriction of the systems of PDE for these models which have two independent quadratic collision terms we construct different exact solutions. The usual types of exact solutions are studied: periodic solutions and shock wave solutions obtained from the standard linearization of the scalar Riccati equations called Riccatian shock waves. Then other types of solutions of the coupled Riccati equations are found called non-Riccatian shock waves and they are compared with the previous ones. The main new result is that, between the upstream and downstream states, these new solutions are not necessarily monotonous. Further, for the shock problem, a two-dimensional dynamical system of ODE is solved numerically with limit values corresponding to the upstream and downstream states. As a by-product of this study two new linearizations for the Riccati coupled equations with two functions are proposed.

Solving large scale structure in ten easy steps with COLA

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

Tassev, Svetlin; Zaldarriaga, Matias; Eisenstein, Daniel J., E-mail: stassev@cfa.harvard.edu, E-mail: matiasz@ias.edu, E-mail: deisenstein@cfa.harvard.edu

2013-06-01

We present the COmoving Lagrangian Acceleration (COLA) method: an N-body method for solving for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory (LPT). Unlike standard N-body methods, the COLA method can straightforwardly trade accuracy at small-scales in order to gain computational speed without sacrificing accuracy at large scales. This is especially useful for cheaply generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing, as those catalogs are essential for performing detailed error analysis for ongoing and future surveys of LSS. As anmore » illustration, we ran a COLA-based N-body code on a box of size 100 Mpc/h with particles of mass ≈ 5 × 10{sup 9}M{sub s}un/h. Running the code with only 10 timesteps was sufficient to obtain an accurate description of halo statistics down to halo masses of at least 10{sup 11}M{sub s}un/h. This is only at a modest speed penalty when compared to mocks obtained with LPT. A standard detailed N-body run is orders of magnitude slower than our COLA-based code. The speed-up we obtain with COLA is due to the fact that we calculate the large-scale dynamics exactly using LPT, while letting the N-body code solve for the small scales, without requiring it to capture exactly the internal dynamics of halos. Achieving a similar level of accuracy in halo statistics without the COLA method requires at least 3 times more timesteps than when COLA is employed.« less

Exact special twist method for quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Dagrada, Mario; Karakuzu, Seher; Vildosola, Verónica Laura; Casula, Michele; Sorella, Sandro

2016-12-01

We present a systematic investigation of the special twist method introduced by Rajagopal et al. [Phys. Rev. B 51, 10591 (1995), 10.1103/PhysRevB.51.10591] for reducing finite-size effects in correlated calculations of periodic extended systems with Coulomb interactions and Fermi statistics. We propose a procedure for finding special twist values which, at variance with previous applications of this method, reproduce the energy of the mean-field infinite-size limit solution within an adjustable (arbitrarily small) numerical error. This choice of the special twist is shown to be the most accurate single-twist solution for curing one-body finite-size effects in correlated calculations. For these reasons we dubbed our procedure "exact special twist" (EST). EST only needs a fully converged independent-particles or mean-field calculation within the primitive cell and a simple fit to find the special twist along a specific direction in the Brillouin zone. We first assess the performances of EST in a simple correlated model such as the three-dimensional electron gas. Afterwards, we test its efficiency within ab initio quantum Monte Carlo simulations of metallic elements of increasing complexity. We show that EST displays an overall good performance in reducing finite-size errors comparable to the widely used twist average technique but at a much lower computational cost since it involves the evaluation of just one wave function. We also demonstrate that the EST method shows similar performances in the calculation of correlation functions, such as the ionic forces for structural relaxation and the pair radial distribution function in liquid hydrogen. Our conclusions point to the usefulness of EST for correlated supercell calculations; our method will be particularly relevant when the physical problem under consideration requires large periodic cells.

Topics in High-Energy Astrophysics: X-ray Time Lags and Gamma-ray Flares

NASA Astrophysics Data System (ADS)

Kroon, John J.

2016-03-01

The Universe is host to a wide variety of high-energy processes that convert gravitational potential energy or rest-mass energy into non-thermal radiation such as bremsstrahlung and synchrotron. Prevailing models of X-ray emission from accreting Black Hole Binaries (BHBs) struggle to simultaneously fit the quiescent X-ray spectrum and the transients which result in the phenomenon known as X-ray time lags. And similarly, classical models of diffusive shock acceleration in pulsar wind nebulae fail to explain the extreme particle acceleration in very short timescales as is inferred from recent gamma-ray flares from the Crab nebula. In this dissertation, I develop new exact analytic models to shed light on these intriguing processes. I take a fresh look at the formation of X-ray time lags in compact sources using a new mathematical approach in which I obtain the exact Green's function solution. The resulting Green's function allows one to explore a variety of injection scenarios, including both monochromatic and broadband (bremsstrahlung) seed photon injection. I obtain the exact solution for the dependence of the time lags on the Fourier frequency, for both homogeneous and inhomogeneous clouds. The model can successfully reproduce both the observed time lags and the quiescent X-ray spectrum using a single set of coronal parameters. I show that the implied coronal radii in the new model are significantly smaller than those obtained in the Monte Carlo simulations, hence greatly reducing the coronal heating problem. Recent bright gamma-ray flares from the Crab nebula observed by AGILE and Fermi reaching GeV energies and lasting several days challenge the contemporary model for particle acceleration in pulsar wind nebulae, specifically the diffusive shock acceleration model. Simulations indicate electron/positron pairs in the Crab nebula pulsar wind must be accelerated up to PeV energies in the presence of ambient magnetic fields with strength B ~100 microG. No comprehensive model has been presented that simultaneously and self-consistently explains the energetic and temporal properties of the observed flares. In this component of my dissertation research, I revisit the problem based on an analytical approach using a transport equation that includes terms describing electrostatic acceleration, stochastic wave-particle acceleration, synchrotron losses, and particle escape. I obtain an exact solution and use it to compute the resulting gamma-ray synchrotron spectrum. I find that the spectra of all the Fermi-LAT flares from the Crab nebula can be reproduced with this model using magnetic fields that are in agreement with multi-wavelength observations.

Exact p-values for pairwise comparison of Friedman rank sums, with application to comparing classifiers.

PubMed

Eisinga, Rob; Heskes, Tom; Pelzer, Ben; Te Grotenhuis, Manfred

2017-01-25

The Friedman rank sum test is a widely-used nonparametric method in computational biology. In addition to examining the overall null hypothesis of no significant difference among any of the rank sums, it is typically of interest to conduct pairwise comparison tests. Current approaches to such tests rely on large-sample approximations, due to the numerical complexity of computing the exact distribution. These approximate methods lead to inaccurate estimates in the tail of the distribution, which is most relevant for p-value calculation. We propose an efficient, combinatorial exact approach for calculating the probability mass distribution of the rank sum difference statistic for pairwise comparison of Friedman rank sums, and compare exact results with recommended asymptotic approximations. Whereas the chi-squared approximation performs inferiorly to exact computation overall, others, particularly the normal, perform well, except for the extreme tail. Hence exact calculation offers an improvement when small p-values occur following multiple testing correction. Exact inference also enhances the identification of significant differences whenever the observed values are close to the approximate critical value. We illustrate the proposed method in the context of biological machine learning, were Friedman rank sum difference tests are commonly used for the comparison of classifiers over multiple datasets. We provide a computationally fast method to determine the exact p-value of the absolute rank sum difference of a pair of Friedman rank sums, making asymptotic tests obsolete. Calculation of exact p-values is easy to implement in statistical software and the implementation in R is provided in one of the Additional files and is also available at http://www.ru.nl/publish/pages/726696/friedmanrsd.zip .

Performance comparison of a new hybrid conjugate gradient method under exact and inexact line searches

NASA Astrophysics Data System (ADS)

Ghani, N. H. A.; Mohamed, N. S.; Zull, N.; Shoid, S.; Rivaie, M.; Mamat, M.

2017-09-01

Conjugate gradient (CG) method is one of iterative techniques prominently used in solving unconstrained optimization problems due to its simplicity, low memory storage, and good convergence analysis. This paper presents a new hybrid conjugate gradient method, named NRM1 method. The method is analyzed under the exact and inexact line searches in given conditions. Theoretically, proofs show that the NRM1 method satisfies the sufficient descent condition with both line searches. The computational result indicates that NRM1 method is capable in solving the standard unconstrained optimization problems used. On the other hand, the NRM1 method performs better under inexact line search compared with exact line search.

Given a one-step numerical scheme, on which ordinary differential equations is it exact?

NASA Astrophysics Data System (ADS)

Villatoro, Francisco R.

2009-01-01

A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

Fermionic entanglement in superconducting systems

NASA Astrophysics Data System (ADS)

Di Tullio, M.; Gigena, N.; Rossignoli, R.

2018-06-01

We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states k of positive quasimomenta and their time-reversed partners k ¯. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes k ,k ¯ , k',k¯' , which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states k ,k' close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.

Collaborative emitter tracking using Rao-Blackwellized random exchange diffusion particle filtering

NASA Astrophysics Data System (ADS)

Bruno, Marcelo G. S.; Dias, Stiven S.

2014-12-01

We introduce in this paper the fully distributed, random exchange diffusion particle filter (ReDif-PF) to track a moving emitter using multiple received signal strength (RSS) sensors. We consider scenarios with both known and unknown sensor model parameters. In the unknown parameter case, a Rao-Blackwellized (RB) version of the random exchange diffusion particle filter, referred to as the RB ReDif-PF, is introduced. In a simulated scenario with a partially connected network, the proposed ReDif-PF outperformed a PF tracker that assimilates local neighboring measurements only and also outperformed a linearized random exchange distributed extended Kalman filter (ReDif-EKF). Furthermore, the novel ReDif-PF matched the tracking error performance of alternative suboptimal distributed PFs based respectively on iterative Markov chain move steps and selective average gossiping with an inter-node communication cost that is roughly two orders of magnitude lower than the corresponding cost for the Markov chain and selective gossip filters. Compared to a broadcast-based filter which exactly mimics the optimal centralized tracker or its equivalent (exact) consensus-based implementations, ReDif-PF showed a degradation in steady-state error performance. However, compared to the optimal consensus-based trackers, ReDif-PF is better suited for real-time applications since it does not require iterative inter-node communication between measurement arrivals.

Exact solution for the quench dynamics of a nested integrable system

NASA Astrophysics Data System (ADS)

Mestyán, Márton; Bertini, Bruno; Piroli, Lorenzo; Calabrese, Pasquale

2017-08-01

Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has focussed on models with an elementary (i.e. not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the quench action approach. Specifically, we consider the spin-1 Lai-Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.

Counter-ions at single charged wall: Sum rules.

PubMed

Samaj, Ladislav

2013-09-01

For inhomogeneous classical Coulomb fluids in thermal equilibrium, like the jellium or the two-component Coulomb gas, there exists a variety of exact sum rules which relate the particle one-body and two-body densities. The necessary condition for these sum rules is that the Coulomb fluid possesses good screening properties, i.e. the particle correlation functions or the averaged charge inhomogeneity, say close to a wall, exhibit a short-range (usually exponential) decay. In this work, we study equilibrium statistical mechanics of an electric double layer with counter-ions only, i.e. a globally neutral system of equally charged point-like particles in the vicinity of a plain hard wall carrying a fixed uniform surface charge density of opposite sign. At large distances from the wall, the one-body and two-body counter-ion densities go to zero slowly according to the inverse-power law. In spite of the absence of screening, all known sum rules are shown to hold for two exactly solvable cases of the present system: in the weak-coupling Poisson-Boltzmann limit (in any spatial dimension larger than one) and at a special free-fermion coupling constant in two dimensions. This fact indicates an extended validity of the sum rules and provides a consistency check for reasonable theoretical approaches.

Simulation of irradiation exposure of electronic devices due to heavy ion therapy with Monte Carlo Code MCNP6

NASA Astrophysics Data System (ADS)

Lapins, Janis; Guilliard, Nicole; Bernnat, Wolfgang; Buck, Arnulf

2017-09-01

During heavy ion irradiation therapy the patient has to be located exactly at the right position to make sure that the Bragg peak occurs in the tumour. The patient has to be moved in the range of millimetres to scan the ill tissue. For that reason a special table was developed which allows exact positioning. The electronic control can be located outside the surgery. But that has some disadvantage for the construction. To keep the system compact it would be much more comfortable to put the electronic control inside the surgery. As a lot of high energetic secondary particles are produced during the therapy causing a high dose in the room it is important to find positions with low dose rates. Therefore, investigations are needed where the electronic devices should be located to obtain a minimum of radiation, help to prevent the failure of sensitive devices. The dose rate was calculated for carbon ions with different initial energy and protons over the entire therapy room with Monte Carlo particle tracking using MCNP6. The types of secondary particles were identified and the dose rate for a thin silicon layer and an electronic mixture material was determined. In addition, the shielding effect of several selected material layers was calculated using MCNP6.

Effect of finite particle number sampling on baryon number fluctuations

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

Steinheimer, Jan; Koch, Volker

The effects of finite particle number sampling on the net baryon number cumulants, extracted from fluid dynamical simulations, are studied. The commonly used finite particle number sampling procedure introduces an additional Poissonian (or multinomial if global baryon number conservation is enforced) contribution which increases the extracted moments of the baryon number distribution. If this procedure is applied to a fluctuating fluid dynamics framework, one severely overestimates the actual cumulants. We show that the sampling of so-called test particles suppresses the additional contribution to the moments by at least one power of the number of test particles. We demonstrate this methodmore » in a numerical fluid dynamics simulation that includes the effects of spinodal decomposition due to a first-order phase transition. Furthermore, in the limit where antibaryons can be ignored, we derive analytic formulas which capture exactly the effect of particle sampling on the baryon number cumulants. These formulas may be used to test the various numerical particle sampling algorithms.« less

Effect of finite particle number sampling on baryon number fluctuations

DOE PAGES

Steinheimer, Jan; Koch, Volker

2017-09-28

The effects of finite particle number sampling on the net baryon number cumulants, extracted from fluid dynamical simulations, are studied. The commonly used finite particle number sampling procedure introduces an additional Poissonian (or multinomial if global baryon number conservation is enforced) contribution which increases the extracted moments of the baryon number distribution. If this procedure is applied to a fluctuating fluid dynamics framework, one severely overestimates the actual cumulants. We show that the sampling of so-called test particles suppresses the additional contribution to the moments by at least one power of the number of test particles. We demonstrate this methodmore » in a numerical fluid dynamics simulation that includes the effects of spinodal decomposition due to a first-order phase transition. Furthermore, in the limit where antibaryons can be ignored, we derive analytic formulas which capture exactly the effect of particle sampling on the baryon number cumulants. These formulas may be used to test the various numerical particle sampling algorithms.« less

Nonequilibrium Statistical Mechanics in One Dimension

NASA Astrophysics Data System (ADS)

Privman, Vladimir

2005-08-01

Part I. Reaction-Diffusion Systems and Models of Catalysis; 1. Scaling theories of diffusion-controlled and ballistically-controlled bimolecular reactions S. Redner; 2. The coalescence process, A+A->A, and the method of interparticle distribution functions D. ben-Avraham; 3. Critical phenomena at absorbing states R. Dickman; Part II. Kinetic Ising Models; 4. Kinetic ising models with competing dynamics: mappings, correlations, steady states, and phase transitions Z. Racz; 5. Glauber dynamics of the ising model N. Ito; 6. 1D Kinetic ising models at low temperatures - critical dynamics, domain growth, and freezing S. Cornell; Part III. Ordering, Coagulation, Phase Separation; 7. Phase-ordering dynamics in one dimension A. J. Bray; 8. Phase separation, cluster growth, and reaction kinetics in models with synchronous dynamics V. Privman; 9. Stochastic models of aggregation with injection H. Takayasu and M. Takayasu; Part IV. Random Sequential Adsorption and Relaxation Processes; 10. Random and cooperative sequential adsorption: exactly solvable problems on 1D lattices, continuum limits, and 2D extensions J. W. Evans; 11. Lattice models of irreversible adsorption and diffusion P. Nielaba; 12. Deposition-evaporation dynamics: jamming, conservation laws and dynamical diversity M. Barma; Part V. Fluctuations In Particle and Surface Systems; 13. Microscopic models of macroscopic shocks S. A. Janowsky and J. L. Lebowitz; 14. The asymmetric exclusion model: exact results through a matrix approach B. Derrida and M. R. Evans; 15. Nonequilibrium surface dynamics with volume conservation J. Krug; 16. Directed walks models of polymers and wetting J. Yeomans; Part VI. Diffusion and Transport In One Dimension; 17. Some recent exact solutions of the Fokker-Planck equation H. L. Frisch; 18. Random walks, resonance, and ratchets C. R. Doering and T. C. Elston; 19. One-dimensional random walks in random environment K. Ziegler; Part VII. Experimental Results; 20. Diffusion-limited exciton kinetics in one-dimensional systems R. Kroon and R. Sprik; 21. Experimental investigations of molecular and excitonic elementary reaction kinetics in one-dimensional systems R. Kopelman and A. L. Lin; 22. Luminescence quenching as a probe of particle distribution S. H. Bossmann and L. S. Schulman; Index.

Computational method for exact frequency-dependent rays on the basis of the solution of the Helmholtz equation

NASA Astrophysics Data System (ADS)

Protasov, M.; Gadylshin, K.

2017-07-01

A numerical method is proposed for the calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known. The properties of frequency-dependent rays are analysed and compared with classical ray theory and with the method of finite-difference modelling for the first time. In this paper, we study the dependence of these rays on the frequency of signals and show the convergence of the exact rays to the classical rays with increasing frequency. A number of numerical experiments demonstrate the distinctive features of exact frequency-dependent rays, in particular, their ability to penetrate into shadow zones that are impenetrable for classical rays.

An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1994-01-01

The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.

Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians

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

Longhi, Stefano, E-mail: stefano.longhi@fisi.polimi.it

Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H{sup -hat} (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H{sup -hat} (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for themore » Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization.« less

Nanoparticle generation and interactions with surfaces in vacuum systems

NASA Astrophysics Data System (ADS)

Khopkar, Yashdeep

Extreme ultraviolet lithography (EUVL) is the most likely candidate as the next generation technology beyond immersion lithography to be used in high volume manufacturing in the semiconductor industry. One of the most problematic areas in the development process is the fabrication of mask blanks used in EUVL. As the masks are reflective, there is a chance that any surface aberrations in the form of bumps or pits could be printed on the silicon wafers. There is a strict tolerance to the number density of such defects on the mask that can be used in the final printing process. Bumps on the surface could be formed when particles land on the mask blank surface during the deposition of multiple bi-layers of molybdenum and silicon. To identify, and possibly mitigate the source of particles during mask fabrication, SEMATECH investigated particle generation in the VEECO Nexus deposition tool. They found several sources of particles inside the tool such as valves. To quantify the particle generation from vacuum components, a test bench suitable for evaluating particle generation in the sub-100 nm particle size range was needed. The Nanoparticle test bench at SUNY Polytechnic Institute was developed as a sub-set of the overall SEMATECH suite of metrology tools used to identify and quantify sources of particles inside process tools that utilize these components in the semiconductor industry. Vacuum valves were tested using the test bench to investigate the number, size and possible sources of particles inside the valves. Ideal parameters of valve operation were also investigated using a 300-mm slit valve with the end goal of finding optimized parameters for minimum particle generation. SEMATECH also pursued the development of theoretical models of particle transport replicating the expected conditions in an ion beam deposition chamber assuming that the particles were generated. In the case of the ion beam deposition tool used in the mask blank fabrication process, the ion beam in the tool could significantly accelerate particles. Assuming that these particles are transported to various surfaces inside the deposition tool, the next challenge is to enhance the adhesion of the particles on surfaces that are located in the non-critical areas inside the tool. However, for particles in the sub-100 nm size range, suitable methods do not exist that can compare the adhesion probability of particles upon impact for a wide range of impact velocities, surfaces and particle types. Traditional methods, which rely on optical measurement of particle velocities in the micron-size regime, cannot be used for sub-100 nm particles as the particles do not scatter sufficient light for the detectors to function. All the current methods rely on electrical measurements taken from impacting particles onto a surface. However, for sub-100 nm particles, the impact velocity varies in different regions of the same impaction spot. Therefore, electrical measurements are inadequate to quantify the exact adhesion characteristics at different impact velocities to enable a comparison of multiple particle-surface systems. Therefore, we propose a new method based on the use of scanning electron microscopy (SEM) imaging to study the adhesion of particles upon impact on surfaces. The use of SEM imaging allows for single particle detection across a single impaction spot and, therefore, enables the comparison of different regions with different impact velocities in a single impaction spot. The proposed method will provide comprehensive correlation between the adhesion probability of sub-100 nm particles and a wide range of impact velocities and angles. The location of each particle is compared with impact velocity predicted by using computational fluid dynamics methods to generate a comprehensive adhesion map involving the impact of 70 nm particles on a polished surface across a large impact velocity range. The final adhesion probability map shows higher adhesion at oblique impact angles compared to normal incidence impacts. Theoretical and experiments with micron-sized particles have shown that the contact area between the particle and the surface decreases at lower incidence angles which results in a decrease in the adhesion probability of the particle. The most likely cause of this result was the role of plastic deformation of particles and its effect on adhesion. Therefore, 70 nm sucrose particles were also impacted under similar impaction conditions to compare the role of plastic deformation on the adhesion characteristics of a particle. Sucrose particles have approximately 10 times more modulus of elasticity than Polystyrene Latex (PSL) particles and were found to have almost no adhesion on the surface at the same impact velocities where the highest adhesion of PSL particles was measured. Besides the role of plastic deformation, the influence of other possible errors in this process was investigated but not found to be significant. (Abstract shortened by UMI.).

Effects of Hyperfine Particles on Reflectance Spectra from 0.3 to 25 μm

NASA Astrophysics Data System (ADS)

Mustard, John F.; Hays, John E.

1997-01-01

Fine grained particles <50 μm in size dominate particle size distributions of many planetary surfaces. Despite the predominance of fine particles in planetary regoliths, there have been few investigations of the systematic effects of the finest particles on reflectance spectra, and on the ability of quantitative models to extract compositional and/or textural information from remote observations. The effects of fine particles that are approximately the same size as the wavelength of light on reflectance spectra were investigated using narrow particle size separates of the minerals olivine and quartz across the wavelength range 0.3 to 25 μm. The minerals were ground with a mortar and pestle and sieved into five particle size separates of 5-μm intervals from <5 μm to 20-25 μm. The exact particle size distributions were determined with a particle size analyzer and are shown to be Gaussian about a mean within the range of each sieve separate. The reflectance spectra, obtained using a combination of a bidirectional reflectance spectrometer and an FTIR, exhibited a number of systematic changes as the particle size decreased to become approximately the same size and smaller than the wavelength. In the region of volume scattering, the spectra exhibited a sharp drop in reflectance with the finest particle size separates. Christiansen features became saturated when the imaginary part of the index of refraction was non-negligible, while the restrahlen bands showed continuous decrease in spectral contrast and some change in the shape of the bands with decreasing particle size, though the principal features diagnostic of composition were relatively unaffected. The transparency features showed several important changes with decreasing particle size: the spectral contrast increased then decreased, the position of the maximum reflectance of the transparency features shifted systematically to shorter wavelengths, and the symmetry of the features changed. Mie theory predicts that the extinction and scattering efficiencies should decline rapidly when particle size and wavelength are approximately equal. Using these relationships, a critical diameter where this change is predicted to occur was calculated as a function of wavelength and shown to be effective for explaining qualitatively the observed changes. Each of the mineral particle size series were then modeled quantitatively using Mie calculations to determine single-scattering albedo and a Hapke model to calculate reflectance. The models include the complex indices of refraction for olivine and quartz and the exact particle size distributions. The olivine particle size series was well modeled by these calculations, and correctly reproduced the systematic changes in the volume scattering region, the Christiansen feature, restrahlen bands, and transparency features. The quartz particle size series were less well modeled, with the greatest discrepancies in the restrahlen bands and the overall spectral contrast.

Tunneling of Charged and Magnetized Fermions from a Rotating Dyonic Taub-NUT Black Hole

NASA Astrophysics Data System (ADS)

Sultana, Kausari

2017-12-01

We investigate tunneling of charged and magnetized Dirac particles from a rotating dyonic Taub-NUT (TN) black hole (BH) called the Kerr-Newman-KasuyaTub-NUT (KNKTN) BH endowed with electric as well as magnetic charges. We derive the tunneling probability of outgoing charged particles by using the semiclassical WKB approximation to the covariant Dirac equation and obtain the corresponding Hawking temperature. The emission spectrum deviates from the purely thermal spectrum with the leading term exactly the Boltzman factor, if energy conservation and the backreaction of particles to the spacetime are considered. The results provides a quantumcorrected radiation temperature depending on the BH background and the radiation particles energy, angular momentum, and charges. The results are consistent with those already available in literature.

Reaction-diffusion on the fully-connected lattice: A+A\\rightarrow A

NASA Astrophysics Data System (ADS)

Turban, Loïc; Fortin, Jean-Yves

2018-04-01

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular, we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.

Exact quantization of Einstein-Rosen waves coupled to massless scalar matter.

PubMed

Barbero G, J Fernando; Garay, Iñaki; Villaseñor, Eduardo J S

2005-07-29

We show in this Letter that gravity coupled to a massless scalar field with full cylindrical symmetry can be exactly quantized by an extension of the techniques used in the quantization of Einstein-Rosen waves. This system provides a useful test bed to discuss a number of issues in quantum general relativity, such as the emergence of the classical metric, microcausality, and large quantum gravity effects. It may also provide an appropriate framework to study gravitational critical phenomena from a quantum point of view, issues related to black hole evaporation, and the consistent definition of test fields and particles in quantum gravity.

The memory effect for plane gravitational waves

NASA Astrophysics Data System (ADS)

Zhang, P.-M.; Duval, C.; Gibbons, G. W.; Horvathy, P. A.

2017-09-01

We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einstein's vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zel'dovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the "velocity memory effect", considered by Braginsky, Thorne, Grishchuk, and Polnarev.

Investigating the settling dynamics of cohesive silt particles with particle-resolving simulations

NASA Astrophysics Data System (ADS)

Sun, Rui; Xiao, Heng; Sun, Honglei

2018-01-01

The settling of cohesive sediment is ubiquitous in aquatic environments, and the study of the settling process is important for both engineering and environmental reasons. In the settling process, the silt particles show behaviors that are different from non-cohesive particles due to the influence of inter-particle cohesive force. For instance, the flocs formed in the settling process of cohesive silt can loosen the packing, and thus the structural densities of cohesive silt beds are much smaller than that of non-cohesive sand beds. While there is a consensus that cohesive behaviors depend on the characteristics of sediment particles (e.g., Bond number, particle size distribution), little is known about the exact influence of these characteristics on the cohesive behaviors. In addition, since the cohesive behaviors of the silt are caused by the inter-particle cohesive forces, the motions of and the contacts among silt particles should be resolved to study these cohesive behaviors in the settling process. However, studies of the cohesive behaviors of silt particles in the settling process based on particle-resolving approach are still lacking. In the present work, three-dimensional settling process is investigated numerically by using CFD-DEM (Computational Fluid Dynamics-Discrete Element Method). The inter-particle collision force, the van der Waals force, and the fluid-particle interaction forces are considered. The numerical model is used to simulate the hindered settling process of silt based on the experimental setup in the literature. The results obtained in the simulations, including the structural densities of the beds, the characteristic lines, and the particle terminal velocity, are in good agreement with the experimental observations in the literature. To the authors' knowledge, this is the first time that the influences of non-dimensional Bond number and particle polydispersity on the structural densities of silt beds have been investigated separately. The results demonstrate that the cohesive behavior of silt in the settling process is attributed to both the cohesion among silt particles themselves and the particle polydispersity. To guide to the macro-scale modeling of cohesive silt sedimentation, the collision frequency functions obtained in the numerical simulations are also presented based on the micromechanics of particles. The results obtained by using CFD-DEM indicate that the binary collision theory over-estimated the particle collision frequency in the flocculation process at high solid volume fraction.

New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

NASA Astrophysics Data System (ADS)

S Saha, Ray

2016-04-01

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

Reflection and Non-Reflection of Particle Wavepackets

ERIC Educational Resources Information Center

Cox, Timothy; Lekner, John

2008-01-01

Exact closed-form solutions of the time-dependent Schrodinger equation are obtained, describing the propagation of wavepackets in the neighbourhood of a potential. Examples given include zero reflection, total reflection and partial reflection of the wavepacket, for the sech[superscript 2]x/a, 1/x[superscript 2] and delta(x) potentials,…

Where There’s Smoke, There’s Science

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

Aiken, Allison; Dubey, Manvendra

Cloaking urban areas and wildfire zones, tiny smoke particles suspended in the atmosphere have a sizeable effect on our climate. But the exact effect of many of these aerosols-such as how much sunlight they absorb, thus warming Earth, or reflecting back to space and so cooling Earth-is very uncertain.

Origami rules for the construction of localized eigenstates of the Hubbard model in decorated lattices

NASA Astrophysics Data System (ADS)

Dias, R. G.; Gouveia, J. D.

2015-11-01

We present a method of construction of exact localized many-body eigenstates of the Hubbard model in decorated lattices, both for U = 0 and U → ∞. These states are localized in what concerns both hole and particle movement. The starting point of the method is the construction of a plaquette or a set of plaquettes with a higher symmetry than that of the whole lattice. Using a simple set of rules, the tight-binding localized state in such a plaquette can be divided, folded and unfolded to new plaquette geometries. This set of rules is also valid for the construction of a localized state for one hole in the U → ∞ limit of the same plaquette, assuming a spin configuration which is a uniform linear combination of all possible permutations of the set of spins in the plaquette.

Flexible scheme to truncate the hierarchy of pure states.

PubMed

Zhang, P-P; Bentley, C D B; Eisfeld, A

2018-04-07

The hierarchy of pure states (HOPS) is a wavefunction-based method that can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a "good" truncation method, where by "good" we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work, we demonstrate the application of the "n-particle approximation" to HOPS. We also introduce a new approximation, which we call the "n-mode approximation." We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy in two exemplary problems: absorption and energy transfer of molecular aggregates.

On Born approximation in black hole scattering

NASA Astrophysics Data System (ADS)

Batic, D.; Kelkar, N. G.; Nowakowski, M.

2011-12-01

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordström and Reissner-Nordström-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.

Flexible scheme to truncate the hierarchy of pure states

NASA Astrophysics Data System (ADS)

Zhang, P.-P.; Bentley, C. D. B.; Eisfeld, A.

2018-04-01

The hierarchy of pure states (HOPS) is a wavefunction-based method that can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a "good" truncation method, where by "good" we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work, we demonstrate the application of the "n-particle approximation" to HOPS. We also introduce a new approximation, which we call the "n-mode approximation." We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy in two exemplary problems: absorption and energy transfer of molecular aggregates.

General upper bound on single-event upset rate. [due to ionizing radiation in orbiting vehicle avionics

NASA Technical Reports Server (NTRS)

Chlouber, Dean; O'Neill, Pat; Pollock, Jim

1990-01-01

A technique of predicting an upper bound on the rate at which single-event upsets due to ionizing radiation occur in semiconducting memory cells is described. The upper bound on the upset rate, which depends on the high-energy particle environment in earth orbit and accelerator cross-section data, is given by the product of an upper-bound linear energy-transfer spectrum and the mean cross section of the memory cell. Plots of the spectrum are given for low-inclination and polar orbits. An alternative expression for the exact upset rate is also presented. Both methods rely only on experimentally obtained cross-section data and are valid for sensitive bit regions having arbitrary shape.

Dynamics of polymers: A mean-field theory

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

Fredrickson, Glenn H.; Materials Research Laboratory, University of California, Santa Barbara, California 93106; Department of Materials, University of California, Santa Barbara, California 93106

2014-02-28

We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ρ and a conjugate MSR response field ϕ, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamicsmore » involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.« less

The self-consistent multiparticle-multihole configuration mixing. Motivations, state of the art and perspectives

NASA Astrophysics Data System (ADS)

Pillet, N.; Robin, C.; Dupuis, M.; Hupin, G.; Berger, J.-F.

2017-03-01

The main objective of this paper is to review the state of the art of the multiparticle-multihole configuration mixing approach which was proposed and implemented using the Gogny interaction ˜ 10 years ago. Various theoretical aspects are re-analyzed when a Hamiltonian description is chosen: the link with exact many-body theories, the impact of truncations in the multiconfigurational space, the importance of defining single-particle orbitals which are consistent with the correlations introduced in the many-body wave function, the role of the self-consistency, and more practically the numerical convergence algorithm. Several applications done with the phenomenological effective Gogny interaction are discussed. Finally, future directions to extend and generalize the method are discussed.

Study of analytical method to seek for exact solutions of variant Boussinesq equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali

2014-01-01

In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. Primarily, we have used the enhanced (G'/G)-expansion method to find exact solutions of Variant Boussinesq equations. Then, we attain some exact solutions including soliton solutions, hyperbolic and trigonometric function solutions of this equation. 35 K99; 35P05; 35P99.

Constructing exact symmetric informationally complete measurements from numerical solutions

NASA Astrophysics Data System (ADS)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

Jamming and Localization of Interacting Run-and-Tumble Particles

NASA Astrophysics Data System (ADS)

Blythe, Richard; Evans, Martin; Slowman, Alexander

Certain species of bacteria, notably Escherichia coli, exhibit a characteristic run-and-tumble motion comprising a sequence of straight-line runs at constant velocity interspersed with tumble events that randomize the direction of motion. In a many-body setting, this nonequilibrium dynamics can generate the phenomenon of motility-induced phase separation, which is also seen for a wide variety of self-propelled particles more generally. Whilst the propensity of self-propelled particles to phase separate is understood at a mesoscopic level, the origin of this behaviour in the inelastic collisions between particles implied by the microscopic dynamics is not. Here we present exact results for run-and-tumble particles in one dimension that reveal a richly-structured stationary state that comprises a superposition of three distinct physical states whose relative weights vary with the run and tumble rates, namely a jammed state, a localized state and a delocalized state.

Modeling of particle interactions in magnetorheological elastomers

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

Biller, A. M., E-mail: kam@icmm.ru; Stolbov, O. V., E-mail: oleg100@gmail.com; Raikher, Yu. L., E-mail: raikher@icmm.ru

2014-09-21

The interaction between two particles made of an isotropic linearly polarizable magnetic material and embedded in an elastomer matrix is studied. In this case, when an external field is imposed, the magnetic attraction of the particles, contrary to point dipoles, is almost wraparound. The exact solution of the magnetic problem in the linear polarization case, although existing, is not practical; to circumvent its use, an interpolation formula is proposed. One more interpolation expression is developed for the resistance of the elastic matrix to the field-induced particle displacements. Minimization of the total energy of the pair reveals its configurational bistability inmore » a certain field range. One of the possible equilibrium states corresponds to the particles dwelling at a distance, the other—to their collapse in a tight dimer. This mesoscopic bistability causes magnetomechanical hysteresis which has important implications for the macroscopic behavior of magnetorheological elastomers.« less

Kinetic energy and angular momentum of free particles in the gyratonic pp-waves space-times

NASA Astrophysics Data System (ADS)

Maluf, J. W.; da Rocha-Neto, J. F.; Ulhoa, S. C.; Carneiro, F. L.

2018-06-01

Gyratonic pp-waves are exact solutions of Einstein’s equations that represent non-linear gravitational waves endowed with angular momentum. We consider gyratonic pp-waves that travel in the z direction and whose time dependence on the variable is given by Gaussians, so that the waves represent short bursts of gravitational radiation propagating in the z direction. We evaluate numerically the geodesics and velocities of free particles in the space-time of these waves, and find that after the passage of the waves both the kinetic energy and the angular momentum per unit mass of the particles are changed. Therefore there is a transfer of energy and angular momentum between the gravitational field and the free particles, so that the final values of the energy and angular momentum of the free particles may be smaller or larger in magnitude than the initial values.

Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

NASA Astrophysics Data System (ADS)

Malakar, Kanaya; Jemseena, V.; Kundu, Anupam; Vijay Kumar, K.; Sabhapandit, Sanjib; Majumdar, Satya N.; Redner, S.; Dhar, Abhishek

2018-04-01

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady-state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady-state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain with an absorbing boundary condition at the origin. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verification of our analytical results.

Entropy of the Bose-Einstein-condensate ground state: Correlation versus ground-state entropy

NASA Astrophysics Data System (ADS)

Kim, Moochan B.; Svidzinsky, Anatoly; Agarwal, Girish S.; Scully, Marlan O.

2018-01-01

Calculation of the entropy of an ideal Bose-Einstein condensate (BEC) in a three-dimensional trap reveals unusual, previously unrecognized, features of the canonical ensemble. It is found that, for any temperature, the entropy of the Bose gas is equal to the entropy of the excited particles although the entropy of the particles in the ground state is nonzero. We explain this by considering the correlations between the ground-state particles and particles in the excited states. These correlations lead to a correlation entropy which is exactly equal to the contribution from the ground state. The correlations themselves arise from the fact that we have a fixed number of particles obeying quantum statistics. We present results for correlation functions between the ground and excited states in a Bose gas, so as to clarify the role of fluctuations in the system. We also report the sub-Poissonian nature of the ground-state fluctuations.

Modeling of ion acceleration through drift and diffusion at interplanetary shocks

NASA Technical Reports Server (NTRS)

Decker, R. B.; Vlahos, L.

1986-01-01

A test particle simulation designed to model ion acceleration through drift and diffusion at interplanetary shocks is described. The technique consists of integrating along exact particle orbits in a system where the angle between the shock normal and mean upstream magnetic field, the level of magnetic fluctuations, and the energy of injected particles can assume a range of values. The technique makes it possible to study time-dependent shock acceleration under conditions not amenable to analytical techniques. To illustrate the capability of the numerical model, proton acceleration was considered under conditions appropriate for interplanetary shocks at 1 AU, including large-amplitude transverse magnetic fluctuations derived from power spectra of both ambient and shock-associated MHD waves.

New Perspectives on Tooth Wear

PubMed Central

Lucas, Peter W.; Omar, Ridwaan

2012-01-01

Some of the efforts that have been made to document tooth wear are reviewed here with an emphasis on nonhuman mammals, literature with which dentists may not be very familiar. We project a change in research strategy from the description of wear at various scales of measurement towards investigation of the mechanical mechanisms that actually create the texture of a worn surface. These studies should reveal exactly how tooth tissue is lost and what aspects of the structure of dental tissues affect this. The most important aspects of the interaction between the tooth surface and wear particles would appear to be particle size, particle shape, their mechanical properties with respect to those of tooth tissues, and the influence of saliva. PMID:22536239

Radiation of charged particle bunches in corrugated waveguides with small period

NASA Astrophysics Data System (ADS)

Tyukhtin, A. V.; Vorobev, V. V.; Akhmatova, E. R.; Antipov, S.

2018-04-01

Bunch radiation in periodical waveguides was mainly analyzed for situations when wavelengths are comparable to the structure period (Smith-Purcell emission). However, it is also interesting to study long wave radiation with wavelengths which are much greater than the structure period. In this paper, the electromagnetic field is analyzed using the method of equivalent boundary conditions. According to this approach, the exact boundary conditions on the complex periodic surface are replaced with certain equivalent conditions which must be fulfilled on the smooth surface. We consider a vacuum circular waveguide with a corrugated conductive wall (corrugation has rectangular form). The charge moves along the waveguide axis. The period and the depth of corrugation are much less than the waveguide radius and wavelengths under consideration. Expressions for the full field components and the wave field components are obtained. It is established that radiation consists of the only one TM waveguide mode which is excited if the charge velocity is more than certain limit value. Dependencies of the frequency and amplitude of the mode on the charge velocity and parameters of corrugation are analyzed. It is demonstrated that typical amplitude of waveguide mode from the ultra relativistic bunch has the same order as one in the ordinary regular waveguides with dielectric filling. In order to verify the method applied in this work we have simulated the electromagnetic field using the CST Particle Studio. For this purpose, we have considered the charged particle bunch with negligible thickness and Gaussian longitudinal distribution. It has been shown that the coincidence between theoretical and simulated results is good. This fact confirms that the theory based on the equivalent boundary conditions adequately describe the radiation process in the situation under consideration. The obtained results can be useful for development of methods of the electromagnetic radiation generation and technique of the wakefield acceleration of charged particles.

Multiple scattering in planetary regoliths using first-order incoherent interactions

NASA Astrophysics Data System (ADS)

Muinonen, Karri; Markkanen, Johannes; Väisänen, Timo; Penttilä, Antti

2017-10-01

We consider scattering of light by a planetary regolith modeled using discrete random media of spherical particles. The size of the random medium can range from microscopic sizes of a few wavelengths to macroscopic sizes approaching infinity. The size of the particles is assumed to be of the order of the wavelength. We extend the numerical Monte Carlo method of radiative transfer and coherent backscattering (RT-CB) to the case of dense packing of particles. We adopt the ensemble-averaged first-order incoherent extinction, scattering, and absorption characteristics of a volume element of particles as input for the RT-CB. The volume element must be larger than the wavelength but smaller than the mean free path length of incoherent extinction. In the radiative transfer part, at each absorption and scattering process, we account for absorption with the help of the single-scattering albedo and peel off the Stokes parameters of radiation emerging from the medium in predefined scattering angles. We then generate a new scattering direction using the joint probability density for the local polar and azimuthal scattering angles. In the coherent backscattering part, we utilize amplitude scattering matrices along the radiative-transfer path and the reciprocal path, and utilize the reciprocity of electromagnetic waves to verify the computation. We illustrate the incoherent volume-element scattering characteristics and compare the dense-medium RT-CB to asymptotically exact results computed using the Superposition T-matrix method (STMM). We show that the dense-medium RT-CB compares favorably to the STMM results for the current cases of sparse and dense discrete random media studied. The novel method can be applied in modeling light scattering by the surfaces of asteroids and other airless solar system objects, including UV-Vis-NIR spectroscopy, photometry, polarimetry, and radar scattering problems.Acknowledgments. Research supported by European Research Council with Advanced Grant No. 320773 SAEMPL, Scattering and Absorption of ElectroMagnetic waves in ParticuLate media. Computational resources provided by CSC - IT Centre for Science Ltd, Finland.

A new class of accurate, mesh-free hydrodynamic simulation methods

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2015-06-01

We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both SPH and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume `overlap'. We implement and test a parallel, second-order version of the method with self-gravity and cosmological integration, in the code GIZMO:1 this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require `artificial diffusion' terms; and allows the fluid elements to move with the flow, so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages versus SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced `particle noise' and numerical viscosity, more accurate sub-sonic flow evolution, and sharp shock-capturing. Advantages versus non-moving meshes include: automatic adaptivity, dramatically reduced advection errors and numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of `grid alignment' effects. We can, for example, follow hundreds of orbits of gaseous discs, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize `grid noise'. These differences are important for a range of astrophysical problems.

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2002-01-01

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Standard map in magnetized relativistic systems: fixed points and regular acceleration.

PubMed

de Sousa, M C; Steffens, F M; Pakter, R; Rizzato, F B

2010-08-01

We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves and particles interact impulsively, and allows for a series of analytical result to be exactly obtained. Unlike the traditional form of the standard map, the present map is nonlinear in the wave amplitude and displays a series of peculiar properties. Among these properties we discuss the relation involving fixed points of the maps and accelerator regimes.

Some new traveling wave exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli equations.

PubMed

Qi, Jian-ming; Zhang, Fu; Yuan, Wen-jun; Huang, Zi-feng

2014-01-01

We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions ur,2 (z) and simply periodic solutions us,2-6(z) which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.

The method of generating functions in exact scalar field inflationary cosmology

NASA Astrophysics Data System (ADS)

Chervon, Sergey V.; Fomin, Igor V.; Beesham, Aroonkumar

2018-04-01

The construction of exact solutions in scalar field inflationary cosmology is of growing interest. In this work, we review the results which have been obtained with the help of one of the most effective methods, viz., the method of generating functions for the construction of exact solutions in scalar field cosmology. We also include in the debate the superpotential method, which may be considered as the bridge to the slow roll approximation equations. Based on the review, we suggest a classification for the generating functions, and find a connection for all of them with the superpotential.

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

Calero, C.; Knorowski, C.; Travesset, A.

We investigate a general method to calculate the free energy of crystalline solids by considering the harmonic approximation and quasistatically switching the anharmonic contribution. The advantage of this method is that the harmonic approximation provides an already very accurate estimate of the free energy, and therefore the anharmonic term is numerically very small and can be determined to high accuracy. We further show that the anharmonic contribution to the free energy satisfies a number of exact inequalities that place constraints on its magnitude and allows approximate but fast and accurate estimates. The method is implemented into a readily available generalmore » software by combining the code HOODLT (Highly Optimized Object Oriented Dynamic Lattice Theory) for the harmonic part and the molecular dynamics (MD) simulation package HOOMD-blue for the anharmonic part. We use the method to calculate the low temperature phase diagram for Lennard-Jones particles. We demonstrate that hcp is the equilibrium phase at low temperature and pressure and obtain the coexistence curve with the fcc phase, which exhibits reentrant behavior. Furthermore, several implications of the method are discussed.« less

Determination of anharmonic free energy contributions: Low temperature phases of the Lennard-Jones system

DOE PAGES

Calero, C.; Knorowski, C.; Travesset, A.

2016-03-22

We investigate a general method to calculate the free energy of crystalline solids by considering the harmonic approximation and quasistatically switching the anharmonic contribution. The advantage of this method is that the harmonic approximation provides an already very accurate estimate of the free energy, and therefore the anharmonic term is numerically very small and can be determined to high accuracy. We further show that the anharmonic contribution to the free energy satisfies a number of exact inequalities that place constraints on its magnitude and allows approximate but fast and accurate estimates. The method is implemented into a readily available generalmore » software by combining the code HOODLT (Highly Optimized Object Oriented Dynamic Lattice Theory) for the harmonic part and the molecular dynamics (MD) simulation package HOOMD-blue for the anharmonic part. We use the method to calculate the low temperature phase diagram for Lennard-Jones particles. We demonstrate that hcp is the equilibrium phase at low temperature and pressure and obtain the coexistence curve with the fcc phase, which exhibits reentrant behavior. Furthermore, several implications of the method are discussed.« less

Optimal design of structures for earthquake loads by a hybrid RBF-BPSO method

NASA Astrophysics Data System (ADS)

Salajegheh, Eysa; Gholizadeh, Saeed; Khatibinia, Mohsen

2008-03-01

The optimal seismic design of structures requires that time history analyses (THA) be carried out repeatedly. This makes the optimal design process inefficient, in particular, if an evolutionary algorithm is used. To reduce the overall time required for structural optimization, two artificial intelligence strategies are employed. In the first strategy, radial basis function (RBF) neural networks are used to predict the time history responses of structures in the optimization flow. In the second strategy, a binary particle swarm optimization (BPSO) is used to find the optimum design. Combining the RBF and BPSO, a hybrid RBF-BPSO optimization method is proposed in this paper, which achieves fast optimization with high computational performance. Two examples are presented and compared to determine the optimal weight of structures under earthquake loadings using both exact and approximate analyses. The numerical results demonstrate the computational advantages and effectiveness of the proposed hybrid RBF-BPSO optimization method for the seismic design of structures.

Numerically Modeling the Erosion of Lunar Soil by Rocket Exhaust Plumes

NASA Technical Reports Server (NTRS)

2008-01-01

In preparation for the Apollo program, Leonard Roberts of the NASA Langley Research Center developed a remarkable analytical theory that predicts the blowing of lunar soil and dust beneath a rocket exhaust plume. Roberts assumed that the erosion rate was determined by the excess shear stress in the gas (the amount of shear stress greater than what causes grains to roll). The acceleration of particles to their final velocity in the gas consumes a portion of the shear stress. The erosion rate continues to increase until the excess shear stress is exactly consumed, thus determining the erosion rate. Roberts calculated the largest and smallest particles that could be eroded based on forces at the particle scale, but the erosion rate equation assumed that only one particle size existed in the soil. He assumed that particle ejection angles were determined entirely by the shape of the terrain, which acts like a ballistic ramp, with the particle aerodynamics being negligible. The predicted erosion rate and the upper limit of particle size appeared to be within an order of magnitude of small-scale terrestrial experiments but could not be tested more quantitatively at the time. The lower limit of particle size and the predictions of ejection angle were not tested. We observed in the Apollo landing videos that the ejection angles of particles streaming out from individual craters were time-varying and correlated to the Lunar Module thrust, thus implying that particle aerodynamics dominate. We modified Roberts theory in two ways. First, we used ad hoc the ejection angles measured in the Apollo landing videos, in lieu of developing a more sophisticated method. Second, we integrated Roberts equations over the lunar-particle size distribution and obtained a compact expression that could be implemented in a numerical code. We also added a material damage model that predicts the number and size of divots which the impinging particles will cause in hardware surrounding the landing rocket. Then, we performed a long-range ballistics analysis for the ejected particulates.

Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry

NASA Astrophysics Data System (ADS)

Oates, T. W. H.; Wormeester, H.; Arwin, H.

2011-12-01

In this article, spectroscopic ellipsometry studies of plasmon resonances at metal-dielectric interfaces of thin films are reviewed. We show how ellipsometry provides valuable non-invasive amplitude and phase information from which one can determine the effective dielectric functions, and how these relate to the material nanostructure and define exactly the plasmonic characteristics of the system. There are three related plasmons that are observable using spectroscopic ellipsometry; volume plasmon resonances, surface plasmon polaritons and particle plasmon resonances. We demonstrate that the established method of exploiting surface plasmon polaritons for chemical and biological sensing may be enhanced using the ellipsometric phase information and provide a comprehensive theoretical basis for the technique. We show how the particle and volume plasmon resonances in the ellipsometric spectra of nanoparticle films are directly related to size, surface coverage and constituent dielectric functions of the nanoparticles. The regularly observed splitting of the particle plasmon resonance is theoretically described using modified effective medium theories within the framework of ellipsometry. We demonstrate the wealth of information available from real-time in situ spectroscopic ellipsometry measurements of metal film deposition, including the evolution of the plasmon resonances and percolation events. Finally, we discuss how generalized and Mueller matrix ellipsometry hold great potential for characterizing plasmonic metamaterials and sub-wavelength hole arrays.

Optimising in situ gamma measurements to identify the presence of radioactive particles in land areas.

PubMed

Rostron, Peter D; Heathcote, John A; Ramsey, Michael H

2014-12-01

High-coverage in situ surveys with gamma detectors are the best means of identifying small hotspots of activity, such as radioactive particles, in land areas. Scanning surveys can produce rapid results, but the probabilities of obtaining false positive or false negative errors are often unknown, and they may not satisfy other criteria such as estimation of mass activity concentrations. An alternative is to use portable gamma-detectors that are set up at a series of locations in a systematic sampling pattern, where any positive measurements are subsequently followed up in order to determine the exact location, extent and nature of the target source. The preliminary survey is typically designed using settings of detector height, measurement spacing and counting time that are based on convenience, rather than using settings that have been calculated to meet requirements. This paper introduces the basis of a repeatable method of setting these parameters at the outset of a survey, for pre-defined probabilities of false positive and false negative errors in locating spatially small radioactive particles in land areas. It is shown that an un-collimated detector is more effective than a collimated detector that might typically be used in the field. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

Hybrid x-space: a new approach for MPI reconstruction.

PubMed

Tateo, A; Iurino, A; Settanni, G; Andrisani, A; Stifanelli, P F; Larizza, P; Mazzia, F; Mininni, R M; Tangaro, S; Bellotti, R

2016-06-07

Magnetic particle imaging (MPI) is a new medical imaging technique capable of recovering the distribution of superparamagnetic particles from their measured induced signals. In literature there are two main MPI reconstruction techniques: measurement-based (MB) and x-space (XS). The MB method is expensive because it requires a long calibration procedure as well as a reconstruction phase that can be numerically costly. On the other side, the XS method is simpler than MB but the exact knowledge of the field free point (FFP) motion is essential for its implementation. Our simulation work focuses on the implementation of a new approach for MPI reconstruction: it is called hybrid x-space (HXS), representing a combination of the previous methods. Specifically, our approach is based on XS reconstruction because it requires the knowledge of the FFP position and velocity at each time instant. The difference with respect to the original XS formulation is how the FFP velocity is computed: we estimate it from the experimental measurements of the calibration scans, typical of the MB approach. Moreover, a compressive sensing technique is applied in order to reduce the calibration time, setting a fewer number of sampling positions. Simulations highlight that HXS and XS methods give similar results. Furthermore, an appropriate use of compressive sensing is crucial for obtaining a good balance between time reduction and reconstructed image quality. Our proposal is suitable for open geometry configurations of human size devices, where incidental factors could make the currents, the fields and the FFP trajectory irregular.

Revisiting the use of the immersed-boundary lattice-Boltzmann method for simulations of suspended particles

NASA Astrophysics Data System (ADS)

Mountrakis, L.; Lorenz, E.; Hoekstra, A. G.

2017-07-01

The immersed-boundary lattice-Boltzmann method (IB-LBM) is increasingly being used in simulations of dense suspensions. These systems are computationally very expensive and can strongly benefit from lower resolutions that still maintain the desired accuracy for the quantities of interest. IB-LBM has a number of free parameters that have to be defined, often without exact knowledge of the tradeoffs, since their behavior in low resolutions is not well understood. Such parameters are the lattice constant Δ x , the number of vertices Nv, the interpolation kernel ϕ , and the LBM relaxation time τ . We investigate the effect of these IB-LBM parameters on a number of straightforward but challenging benchmarks. The systems considered are (a) the flow of a single sphere in shear flow, (b) the collision of two spheres in shear flow, and (c) the lubrication interaction of two spheres. All benchmarks are performed in three dimensions. The first two systems are used for determining two effective radii: the hydrodynamic radius rhyd and the particle interaction radius rinter. The last system is used to establish the numerical robustness of the lubrication forces, used to probe the hydrodynamic interactions in the limit of small gaps. Our results show that lower spatial resolutions result in larger hydrodynamic and interaction radii, while surface densities should be chosen above two vertices per LU2 result to prevent fluid penetration in underresolved meshes. Underresolved meshes also failed to produce the migration of particles toward the center of the domain due to lift forces in Couette flow, mostly noticeable for IBM-kernel ϕ2. Kernel ϕ4, despite being more robust toward mesh resolution, produces a notable membrane thickness, leading to the breakdown of the lubrication forces in larger gaps, and its use in dense suspensions where the mean particle distances are small can result in undesired behavior. rhyd is measured to be different from rinter, suggesting that there is no consistent measure to recalibrate the radius of the suspended particle.

Multiple-labelling immunoEM using different sizes of colloidal gold: alternative approaches to test for differential distribution and colocalization in subcellular structures.

PubMed

Mayhew, Terry M; Lucocq, John M

2011-03-01

Various methods for quantifying cellular immunogold labelling on transmission electron microscope thin sections are currently available. All rely on sound random sampling principles and are applicable to single immunolabelling across compartments within a given cell type or between different experimental groups of cells. Although methods are also available to test for colocalization in double/triple immunogold labelling studies, so far, these have relied on making multiple measurements of gold particle densities in defined areas or of inter-particle nearest neighbour distances. Here, we present alternative two-step approaches to codistribution and colocalization assessment that merely require raw counts of gold particles in distinct cellular compartments. For assessing codistribution over aggregate compartments, initial statistical evaluation involves combining contingency table and chi-squared analyses to provide predicted gold particle distributions. The observed and predicted distributions allow testing of the appropriate null hypothesis, namely, that there is no difference in the distribution patterns of proteins labelled by different sizes of gold particle. In short, the null hypothesis is that of colocalization. The approach for assessing colabelling recognises that, on thin sections, a compartment is made up of a set of sectional images (profiles) of cognate structures. The approach involves identifying two groups of compartmental profiles that are unlabelled and labelled for one gold marker size. The proportions in each group that are also labelled for the second gold marker size are then compared. Statistical analysis now uses a 2 × 2 contingency table combined with the Fisher exact probability test. Having identified double labelling, the profiles can be analysed further in order to identify characteristic features that might account for the double labelling. In each case, the approach is illustrated using synthetic and/or experimental datasets and can be refined to correct observed labelling patterns to specific labelling patterns. These simple and efficient approaches should be of more immediate utility to those interested in codistribution and colocalization in multiple immunogold labelling investigations.

Numerical simulations of electromagnetic scattering by Solar system objects

NASA Astrophysics Data System (ADS)

Dlugach, Janna M.

2016-11-01

Having been profoundly stimulated by the seminal work of Viktor V. Sobolev, I have been involved in multi-decadal research in the fields of radiative transfer, electromagnetic scattering by morphologically complex particles and particulate media, and planetary remote sensing. Much of this research has been done in close collaboration with other "descendants" of Academician Sobolev. This tutorial paper gives a representative overview of the results of extensive numerical simulations (in the vast majority carried out in collaboration with Michael Mishchenko) used to analyze remote-sensing observations of Solar system objects and based on highly accurate methods of the radiative transfer theory and direct computer solvers of the Maxwell equations. Using the atmosphere of Jupiter as a proving ground and performing T-matrix and radiative-transfer calculations helps demonstrate the strong effect of aerosol-particle shapes on the accuracy of remote-sensing retrievals. I then discuss the application of the T-matrix method, a numerically exact solution of the vector radiative transfer equation, and the theory of coherent backscattering to an analysis of polarimetric radar observations of Saturn's rings. Numerical modeling performed by using the superposition T-matrix method in application to cometary dust in the form of aggregates serves to reproduce the results of polarimetric observations of the distant comet C/2010 S1. On the basis of direct computer solutions of the Maxwell equations, it is demonstrated that all backscattering effects predicted by the low-density theories of radiative transfer and coherent backscattering can also be identified for media with volume packing densities typically encountered in natural and artificial environments. This result implies that spectacular opposition effects observed for some high-albedo atmoshereless Solar system bodies can be attributed to coherent backscattering of sunlight by regolith layers composed of microscopic particles.

Local lung deposition of ultrafine particles in healthy adults: experimental results and theoretical predictions

PubMed Central

2016-01-01

Background Ultrafine particles (UFP) of biogenic and anthropogenic origin occur in high numbers in the ambient atmosphere. In addition, aerosols containing ultrafine powders are used for the inhalation therapy of various diseases. All these facts make it necessary to obtain comprehensive knowledge regarding the exact behavior of UFP in the respiratory tract. Methods Theoretical simulations of local UFP deposition are based on previously conducted inhalation experiments, where particles with various sizes (0.04, 0.06, 0.08, and 0.10 µm) were administered to the respiratory tract by application of the aerosol bolus technique. By the sequential change of the lung penetration depth of the inspired bolus, different volumetric lung regions could be generated and particle deposition in these regions could be evaluated. The model presented in this contribution adopted all parameters used in the experiments. Besides the obligatory comparison between practical and theoretical data, also advanced modeling predictions including the effect of varying functional residual capacity (FRC) and respiratory flow rate were conducted. Results Validation of the UFP deposition model shows that highest deposition fractions occur in those volumetric lung regions corresponding to the small and partly alveolated airways of the tracheobronchial tree. Particle deposition proximal to the trachea is increased in female probands with respect to male subjects. Decrease of both the FRC and the respiratory flow rate results in an enhancement of UFP deposition. Conclusions The study comes to the conclusion that deposition of UFP taken up via bolus inhalation is influenced by a multitude of factors, among which lung morphometry and breathing conditions play a superior role. PMID:27942511

Improved method for implicit Monte Carlo

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

Brown, F. B.; Martin, W. R.

2001-01-01

The Implicit Monte Carlo (IMC) method has been used for over 30 years to analyze radiative transfer problems, such as those encountered in stellar atmospheres or inertial confinement fusion. Reference [2] provided an exact error analysis of IMC for 0-D problems and demonstrated that IMC can exhibit substantial errors when timesteps are large. These temporal errors are inherent in the method and are in addition to spatial discretization errors and approximations that address nonlinearities (due to variation of physical constants). In Reference [3], IMC and four other methods were analyzed in detail and compared on both theoretical grounds and themore » accuracy of numerical tests. As discussed in, two alternative schemes for solving the radiative transfer equations, the Carter-Forest (C-F) method and the Ahrens-Larsen (A-L) method, do not exhibit the errors found in IMC; for 0-D, both of these methods are exact for all time, while for 3-D, A-L is exact for all time and C-F is exact within a timestep. These methods can yield substantially superior results to IMC.« less

Rate Change Graph Technology: Absolute Value Point Methodology

NASA Astrophysics Data System (ADS)

Strickland, Ken; Duvernois, Michael

2011-10-01

Absolute Value Point Methodology (AVPM) is a new theoretical tool for science research centered on Rate Change Graph Technology (RCGT). The modeling techniques of AVPM surpass conventional methods by extending the geometrical rules of mathematics. Exact geometrical structures of matter and energy become clearer revealing new ways to compile advanced data. RCGT mechanics is realized from geometrical intersections that are the result of plotting changing value vs. changing geometry. RCGT methods ignore size and value to perform an objective analysis in geometry. Value and size are then re-introduced back into the analytical system for a clear and concise solution. Available AVPM applications reveal that a massive amount of data from the Big Bang to vast super-clusters is untouched by human thought. Once scientists learn to design tools from RCGT Mechanics, new and formidable approaches to experimentation and theory may lead to new discoveries. In the creation of AVPM, it has become apparent there is a particle-world that exists between strings and our familiar universe. These unrealized particles in their own nature exhibit inflation like properties and may be the progenitor of the implements of our universe. Thus space, time, energy, motion, space-time and gravity are born from its existence and decay. This announcement will be the beginning of many new ideas from the study of RCGT mechanics.

Lithium-ions diffusion kinetic in LiFePO4/carbon nanoparticles synthesized by microwave plasma chemical vapor deposition for lithium-ion batteries

NASA Astrophysics Data System (ADS)

Gao, Chao; Zhou, Jian; Liu, Guizhen; Wang, Lin

2018-03-01

Olivine structure LiFePO4/carbon nanoparticles are synthesized successfully using a microwave plasma chemical vapor deposition (MPCVD) method. Microwave is an effective method to synthesize nanomaterials, the LiFePO4/carbon nanoparticles with high crystallinity can shorten diffusion routes for ionic transfer and electron tunneling. Meanwhile, a high quality, complete and homogenous carbon layer with appropriate thickness coating on the surface of LiFePO4 particles during in situ chemical vapor deposition process, which can ensure that electrons are able to transfer fast enough from all sides. Electrochemical impedance spectroscopy (EIS) is carried out to collect information about the kinetic behavior of lithium diffusion in LiFePO4/carbon nanoparticles during the charging and discharging processes. The chemical diffusion coefficients of lithium ions, DLi, are calculated in the range of 10-15-10-9 cm2s-1. Nanoscale LiFePO4/carbon particles show the longer regions of the faster solid-solution diffusion, and corresponding to the narrower region of the slower two-phase diffusion during the insertion/exaction of lithium ions. The CV and galvanostatic charge-discharge measurements show that the LiFePO4/carbon nanoparticles perform an excellent electrochemical performance, especially the high rate capacity and cycle life.

Health effects of atmospheric particulates: a medical geology perspective.

PubMed

Duzgoren-Aydin, Nurdan S

2008-01-01

In this review, atmospheric particulates as composite airborne earth materials often containing both natural and anthropogenic components were examined in the context of medical geology. Despite a vast number of both experimental and epidemiological studies confirming the direct and indirect links between atmospheric particulates and human health, the exact nature of mechanisms affecting the particulate-induced pathogenesis largely remains unexplored. Future in depth research on these areas would be most successful if potential mechanisms are examined with reference to the physical (e.g., size, shape and surface), chemical, mineralogical and source characteristics of particulate matters. The underlying goal of this review was to present the relevant terminology and processes proposed in the literature to explain the interfaces and interactions between atmospheric particles and human body within the framework of "atmospheric particle cycles." The complexities of the interactions were demonstrated through case studies focusing on particulate matter air pollution and malignant mesothelioma occurrences due to environmental exposure to erionite-a fibrous zeolite mineral. There is an urgent need for a standard protocol or speciation methods applicable to earth-materials to guide and streamline studies on etiology of mineral-induced diseases. This protocol or speciation methods should provide relevant procedures to determine the level and extent of physical, chemical and mineralogical heterogeneity of particulate matters as well as quantitative in-situ particulate characteristics.

Breathing is different in the quantum world

NASA Astrophysics Data System (ADS)

Bonitz, Michael; Bauch, Sebastian; Balzer, Karsten; Henning, Christian; Hochstuhl, David

2009-11-01

Interacting classicle particles in a harmonic trap are known to possess a radial collective oscillation -- the breathing mode (BM). In case of Coulomb interaction its frequency is universal -- it is independent of the particle number and system dimensionality [1]. Here we study strongly correlated quantum systems. We report a qualitatively different breathing behavior: a quantum system has two BMs one of which is universal whereas the frequency of the other varies with system dimensionality, the particle spin and the strength of the pair interaction. The results are based on exact solutions of the time-dependent Schr"odinger equation for two particles and on time-dependent many-body results for larger particle numbers. Finally, we discuss experimental ways to excite and measure the breathing frequencies which should give direct access to key properties of trapped particles, including their many-body effects [2]. [4pt] [1] C. Henning et al., Phys. Rev. Lett. 101, 045002 (2008) [0pt] [2] S. Bauch, K. Balzer, C. Henning, and M. Bonitz, submitted to Phys. Rev. Lett., arXiv:0903.1993

Tight-binding tunneling amplitude of an optical lattice

NASA Astrophysics Data System (ADS)

Arzamasovs, Maksims; Liu, Bo

2017-11-01

The particle in a periodic potential is an important topic in an undergraduate quantum mechanics curriculum and a stepping stone on the way to more advanced topics, such as courses on interacting electrons in crystalline solids, and graduate-level research in solid-state and condensed matter physics. The interacting many-body phenomena are usually described in terms of the second quantized lattice Hamiltonians which treat single-particle physics on the level of tight-binding approximation and add interactions on top of it. The aim of this paper is to show how the tight-binding tunneling amplitude can be related to the strength of the periodic potential for the case of a cosine potential used in the burgeoning field of ultracold atoms. We show how to approach the problem of computing the tunneling amplitude of a deep lattice using the JWKB (Jeffreys-Wentzel-Kramers-Brillouin, also known as semiclassical) approximation. We also point out that care should be taken when applying the method of the linear combination of atomic orbitals (LCAO) in an optical lattice context. A summary of the exact solution in terms of Mathieu functions is also given.

Electron transfer statistics and thermal fluctuations in molecular junctions

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

Goswami, Himangshu Prabal; Harbola, Upendra

2015-02-28

We derive analytical expressions for probability distribution function (PDF) for electron transport in a simple model of quantum junction in presence of thermal fluctuations. Our approach is based on the large deviation theory combined with the generating function method. For large number of electrons transferred, the PDF is found to decay exponentially in the tails with different rates due to applied bias. This asymmetry in the PDF is related to the fluctuation theorem. Statistics of fluctuations are analyzed in terms of the Fano factor. Thermal fluctuations play a quantitative role in determining the statistics of electron transfer; they tend tomore » suppress the average current while enhancing the fluctuations in particle transfer. This gives rise to both bunching and antibunching phenomena as determined by the Fano factor. The thermal fluctuations and shot noise compete with each other and determine the net (effective) statistics of particle transfer. Exact analytical expression is obtained for delay time distribution. The optimal values of the delay time between successive electron transfers can be lowered below the corresponding shot noise values by tuning the thermal effects.« less

Smoldyn: particle-based simulation with rule-based modeling, improved molecular interaction and a library interface.

PubMed

Andrews, Steven S

2017-03-01

Smoldyn is a spatial and stochastic biochemical simulator. It treats each molecule of interest as an individual particle in continuous space, simulating molecular diffusion, molecule-membrane interactions and chemical reactions, all with good accuracy. This article presents several new features. Smoldyn now supports two types of rule-based modeling. These are a wildcard method, which is very convenient, and the BioNetGen package with extensions for spatial simulation, which is better for complicated models. Smoldyn also includes new algorithms for simulating the diffusion of surface-bound molecules and molecules with excluded volume. Both are exact in the limit of short time steps and reasonably good with longer steps. In addition, Smoldyn supports single-molecule tracking simulations. Finally, the Smoldyn source code can be accessed through a C/C ++ language library interface. Smoldyn software, documentation, code, and examples are at http://www.smoldyn.org . steven.s.andrews@gmail.com. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability

NASA Astrophysics Data System (ADS)

Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.

2018-02-01

As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi-exactly solvable problems. The extension to the case of non-equal masses is straightforward and is briefly discussed.

MODFLOW-2000 : the U.S. Geological Survey modular ground-water model--documentation of the Advective-Transport Observation (ADV2) Package

USGS Publications Warehouse

Anderman, Evan R.; Hill, Mary Catherine

2001-01-01

Observations of the advective component of contaminant transport in steady-state flow fields can provide important information for the calibration of ground-water flow models. This report documents the Advective-Transport Observation (ADV2) Package, version 2, which allows advective-transport observations to be used in the three-dimensional ground-water flow parameter-estimation model MODFLOW-2000. The ADV2 Package is compatible with some of the features in the Layer-Property Flow and Hydrogeologic-Unit Flow Packages, but is not compatible with the Block-Centered Flow or Generalized Finite-Difference Packages. The particle-tracking routine used in the ADV2 Package duplicates the semi-analytical method of MODPATH, as shown in a sample problem. Particles can be tracked in a forward or backward direction, and effects such as retardation can be simulated through manipulation of the effective-porosity value used to calculate velocity. Particles can be discharged at cells that are considered to be weak sinks, in which the sink applied does not capture all the water flowing into the cell, using one of two criteria: (1) if there is any outflow to a boundary condition such as a well or surface-water feature, or (2) if the outflow exceeds a user specified fraction of the cell budget. Although effective porosity could be included as a parameter in the regression, this capability is not included in this package. The weighted sum-of-squares objective function, which is minimized in the Parameter-Estimation Process, was augmented to include the square of the weighted x-, y-, and z-components of the differences between the simulated and observed advective-front locations at defined times, thereby including the direction of travel as well as the overall travel distance in the calibration process. The sensitivities of the particle movement to the parameters needed to minimize the objective function are calculated for any particle location using the exact sensitivity-equation approach; the equations are derived by taking the partial derivatives of the semi-analytical particle-tracking equation with respect to the parameters. The ADV2 Package is verified by showing that parameter estimation using advective-transport observations produces the true parameter values in a small but complicated test case when exact observations are used. To demonstrate how the ADV2 Package can be used in practice, a field application is presented. In this application, the ADV2 Package is used first in the Sensitivity-Analysis mode of MODFLOW-2000 to calculate measures of the importance of advective-transport observations relative to head-dependent flow observations when either or both are used in conjunction with hydraulic-head observations in a simulation of the sewage-discharge plume at Cape Cod, Massachusetts. The ADV2 Package is then used in the Parameter-Estimation mode of MODFLOW-2000 to determine best-fit parameter values. It is concluded that, for this problem, advective-transport observations improved the calibration of the model and the estimation of ground-water flow parameters, and the use of formal parameter-estimation methods and related techniques produced significant insight into the physical system.

Neutrinos as Probes of Lorentz Invariance

DOE PAGES

Díaz, Jorge S.

2014-01-01

Neutrinos can be used to search for deviations from exact Lorentz invariance. The worldwide experimental program in neutrino physics makes these particles a remarkable tool to search for a variety of signals that could reveal minute relativity violations. This paper reviews the generic experimental signatures of the breakdown of Lorentz symmetry in the neutrino sector.

New Potentials for Old: The Darboux Transformation in Quantum Mechanics

ERIC Educational Resources Information Center

Williams, Brian Wesley; Celius, Tevye C.

2008-01-01

The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics…

Worldsheet instantons and the amplitude for string pair production in an external field as a WKB exact functional integral

NASA Astrophysics Data System (ADS)

Gordon, James; Semenoff, Gordon W.

2018-05-01

We revisit the problem of charged string pair creation in a constant external electric field. The string states are massive and creation of pairs from the vacuum is a tunnelling process, analogous to the Schwinger process where charged particle-anti-particle pairs are created by an electric field. We find the instantons in the worldsheet sigma model which are responsible for the tunnelling events. We evaluate the sigma model partition function in the multi-instanton sector in the WKB approximation which keeps the classical action and integrates the quadratic fluctuations about the solution. We find that the summation of the result over all multi-instanton sectors reproduces the known amplitude. This suggests that corrections to the WKB limit must cancel. To show that they indeed cancel, we identify a fermionic symmetry of the sigma model which occurs in the instanton sectors and which is associated with collective coordinates. We demonstrate that the action is symmetric and that the interaction action is an exact form. These conditions are sufficient for localization of the worldsheet functional integral onto its WKB limit.

Dirac Equation in (1 +1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model

NASA Astrophysics Data System (ADS)

Pedernales, J. S.; Beau, M.; Pittman, S. M.; Egusquiza, I. L.; Lamata, L.; Solano, E.; del Campo, A.

2018-04-01

We introduce an exact mapping between the Dirac equation in (1 +1 )-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1 +1 )-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1 +1 )-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.

Expansion Potentials for Exact Far-from-Equilibrium Spreading of Particles and Energy

DOE PAGES

Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2015-12-01

We report that the rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in an isolated quantum system have an emergent thermodynamical description whenever energy or particle current commutes with the Hamiltonian. Concrete examples include the energy current in the 1D spinless fermion model with nearest-neighbor interactions (XXZ spin chain), energy current in Lorentz-invariant theories or particle current in interacting Bose gases in arbitrary dimension. Even far from equilibrium, these rates are controlled by state functions, which we call "expansion potentials", expressed as integrals of equilibrium Drude weights. This relation between nonequilibriummore » quantities and linear response implies non-equilibrium Maxwell relations for the Drude weights. Lastly, we verify our results via DMRG calculations for the XXZ chain.« less

Thermodynamics with pressure and volume under charged particle absorption

NASA Astrophysics Data System (ADS)

Gwak, Bogeun

2017-11-01

We investigate the variation of the charged anti-de Sitter black hole under charged particle absorption by considering thermodynamic volume. When the energy of the particle is considered to contribute to the internal energy of the black hole, the variation exactly corresponds to the prediction of the first law of thermodynamics. Nevertheless, we find the decrease of the Bekenstein-Hawking entropy for extremal and near-extremal black holes under the absorption, which is an irreversible process. This violation of the second law of thermodynamics is only found when considering thermodynamic volume. We test the weak cosmic censorship conjecture affected by the violation. Fortunately, the conjecture is still valid, but extremal and near-extremal black holes do not change their configurations when any particle enters the black hole. This result is quite different from the case in which thermodynamic volume is not considered.

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

PubMed

Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K

2007-07-07

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

PubMed

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

PubMed Central

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. PMID:25973605

General method of solving the Schroedinger equation of atoms and molecules

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

Nakatsuji, Hiroshi

2005-12-15

We propose a general method of solving the Schroedinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schroedinger equation and related principles, we can avoid the singularity problem of atoms and molecules and formulate a general method of calculating the exact wave functions in an analytical expansion form. We choose initial function {psi}{sub 0} and scaling g function, and then the ICI method automatically generates the wave function that hasmore » the exact structure by using the Hamiltonian of the system. The Hamiltonian contains all the information of the system. The free ICI method provides a flexible and variationally favorable procedure of constructing the exact wave function. We explain the computational procedure of the analytical ICI method routinely performed in our laboratory. Simple examples are given using hydrogen atom for the nuclear singularity case, the Hooke's atom for the electron singularity case, and the helium atom for both cases.« less

Citation Matching in Sanskrit Corpora Using Local Alignment

NASA Astrophysics Data System (ADS)

Prasad, Abhinandan S.; Rao, Shrisha

Citation matching is the problem of finding which citation occurs in a given textual corpus. Most existing citation matching work is done on scientific literature. The goal of this paper is to present methods for performing citation matching on Sanskrit texts. Exact matching and approximate matching are the two methods for performing citation matching. The exact matching method checks for exact occurrence of the citation with respect to the textual corpus. Approximate matching is a fuzzy string-matching method which computes a similarity score between an individual line of the textual corpus and the citation. The Smith-Waterman-Gotoh algorithm for local alignment, which is generally used in bioinformatics, is used here for calculating the similarity score. This similarity score is a measure of the closeness between the text and the citation. The exact- and approximate-matching methods are evaluated and compared. The methods presented can be easily applied to corpora in other Indic languages like Kannada, Tamil, etc. The approximate-matching method can in particular be used in the compilation of critical editions and plagiarism detection in a literary work.

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

Apel, V.M.; Curilef, S.; Plastino, A.R., E-mail: arplastino@unnoba.edu.ar

We explore the entanglement-related features exhibited by the dynamics of a composite quantum system consisting of a particle and an apparatus (here referred to as the “pointer”) that measures the position of the particle. We consider measurements of finite duration, and also the limit case of instantaneous measurements. We investigate the time evolution of the quantum entanglement between the particle and the pointer, with special emphasis on the final entanglement associated with the limit case of an impulsive interaction. We consider entanglement indicators based on the expectation values of an appropriate family of observables, and also an entanglement measure computedmore » on particular exact analytical solutions of the particle–pointer Schrödinger equation. The general behavior exhibited by the entanglement indicators is consistent with that shown by the entanglement measure evaluated on particular analytical solutions of the Schrödinger equation. In the limit of instantaneous measurements the system’s entanglement dynamics corresponds to that of an ideal quantum measurement process. On the contrary, we show that the entanglement evolution corresponding to measurements of finite duration departs in important ways from the behavior associated with ideal measurements. In particular, highly localized initial states of the particle lead to highly entangled final states of the particle–pointer system. This indicates that the above mentioned initial states, in spite of having an arbitrarily small position uncertainty, are not left unchanged by a finite-duration position measurement process. - Highlights: • We explore entanglement features of a quantum position measurement. • We consider instantaneous and finite-duration measurements. • We evaluate the entanglement of exact time-dependent particle–pointer states.« less

A new exact method for line radiative transfer

NASA Astrophysics Data System (ADS)

Elitzur, Moshe; Asensio Ramos, Andrés

2006-01-01

We present a new method, the coupled escape probability (CEP), for exact calculation of line emission from multi-level systems, solving only algebraic equations for the level populations. The CEP formulation of the classical two-level problem is a set of linear equations, and we uncover an exact analytic expression for the emission from two-level optically thick sources that holds as long as they are in the `effectively thin' regime. In a comparative study of a number of standard problems, the CEP method outperformed the leading line transfer methods by substantial margins. The algebraic equations employed by our new method are already incorporated in numerous codes based on the escape probability approximation. All that is required for an exact solution with these existing codes is to augment the expression for the escape probability with simple zone-coupling terms. As an application, we find that standard escape probability calculations generally produce the correct cooling emission by the CII 158-μm line but not by the 3P lines of OI.

Exact Local Correlations and Full Counting Statistics for Arbitrary States of the One-Dimensional Interacting Bose Gas

NASA Astrophysics Data System (ADS)

Bastianello, Alvise; Piroli, Lorenzo; Calabrese, Pasquale

2018-05-01

We derive exact analytic expressions for the n -body local correlations in the one-dimensional Bose gas with contact repulsive interactions (Lieb-Liniger model) in the thermodynamic limit. Our results are valid for arbitrary states of the model, including ground and thermal states, stationary states after a quantum quench, and nonequilibrium steady states arising in transport settings. Calculations for these states are explicitly presented and physical consequences are critically discussed. We also show that the n -body local correlations are directly related to the full counting statistics for the particle-number fluctuations in a short interval, for which we provide an explicit analytic result.

Exact differential equation for the density and ionization energy of a many-particle system

NASA Technical Reports Server (NTRS)

Levy, M.; Perdew, J. P.; Sahni, V.

1984-01-01

The present investigation is concerned with relations studied by Hohenberg and Kohn (1964) and Kohn and Sham (1965). The properties of a ground-state many-electron system are determined by the electron density. The correct differential equation for the density, as dictated by density-functional theory, is presented. It is found that the ground-state density n of a many-electron system obeys a Schroedinger-like differential equation which may be solved by standard Kohn-Sham programs. Results are connected to the traditional exact Kohn-Sham theory. It is pointed out that the results of the current investigations are readily extended to spin-density functional theory.

Antiparallel spin does not always contain more information

NASA Astrophysics Data System (ADS)

Ghosh, Sibasish; Roy, Anirban; Sen, Ujjwal

2001-01-01

We show that the Bloch vectors lying on any great circle comprise the largest set SL for which the parallel states \\|n-->,n-->> can always be exactly transformed into the antiparallel states \\|n-->,-n-->>. Thus more information about n--> is not extractable from \\|n-->,-n-->> than from \\|n-->,n-->> by any measuring strategy, for n-->∈SL. Surprisingly this most general transformation reduces to just a flip operation on the second particle. We also show here that a probabilistic exact parallel to antiparallel transformation is not possible if the corresponding antiparallel states span the whole Hilbert space of the two qubits. These considerations allow us to generalize a conjecture of Gisin and Popescu [Phys. Rev. Lett. 83, 432 (1999)].

Monogamy equalities for qubit entanglement from Lorentz invariance.

PubMed

Eltschka, Christopher; Siewert, Jens

2015-04-10

A striking result from nonrelativistic quantum mechanics is the monogamy of entanglement, which states that a particle can be maximally entangled only with one other party, not with several ones. While there is the exact quantitative relation for three qubits and also several inequalities describing monogamy properties, it is not clear to what extent exact monogamy relations are a general feature of quantum mechanics. We prove that in all many-qubit systems there exist strict monogamy laws for quantum correlations. They come about through the curious relationship between the nonrelativistic quantum mechanics of qubits and Minkowski space. We elucidate the origin of entanglement monogamy from this symmetry perspective and provide recipes to construct new families of such equalities.

Observation of Spin-Polarons in a strongly interacting Fermi liquid

NASA Astrophysics Data System (ADS)

Zwierlein, Martin

2009-03-01

We have observed spin-polarons in a highly imbalanced mixture of fermionic atoms using tomographic RF spectroscopy. Feshbach resonances allow to freely tune the interactions between the two spin states involved. A single spin down atom immersed in a Fermi sea of spin up atoms can do one of two things: For strong attraction, it can form a molecule with exactly one spin up partner, but for weaker interaction it will spread its attraction and surround itself with a collection of majority atoms. This spin down atom ``dressed'' with a spin up cloud constitutes the spin-polaron. We have observed a striking spectroscopic signature of this quasi-particle for various interaction strengths, a narrow peak in the spin down spectrum that emerges above a broad background. The narrow width signals a long lifetime of the spin-polaron, much longer than the collision rate with spin up atoms, as it must be for a proper quasi-particle. The peak position allows to directly measure the polaron energy. The broad pedestal at high energies reveals physics at short distances and is thus ``molecule-like'': It is exactly matched by the spin up spectra. The comparison with the area under the polaron peak allows to directly obtain the quasi-particle weight Z. We observe a smooth transition from polarons to molecules. At a critical interaction strength of 1/kFa = 0.7, the polaron peak vanishes and spin up and spin down spectra exactly match, signalling the formation of molecules. This is the same critical interaction strength found earlier to separate a normal Fermi mixture from a superfluid molecular Bose-Einstein condensate. The spin-polarons determine the low-temperature phase diagram of imbalanced Fermi mixtures. In principle, polarons can interact with each other and should, at low enough temperatures, form a superfluid of p-wave pairs. We will present a first indication for interactions between polarons.

Spectral functions of strongly correlated extended systems via an exact quantum embedding

NASA Astrophysics Data System (ADS)

Booth, George H.; Chan, Garnet Kin-Lic

2015-04-01

Density matrix embedding theory (DMET) [Phys. Rev. Lett. 109, 186404 (2012), 10.1103/PhysRevLett.109.186404], introduced an approach to quantum cluster embedding methods whereby the mapping of strongly correlated bulk problems to an impurity with finite set of bath states was rigorously formulated to exactly reproduce the entanglement of the ground state. The formalism provided similar physics to dynamical mean-field theory at a tiny fraction of the cost but was inherently limited by the construction of a bath designed to reproduce ground-state, static properties. Here, we generalize the concept of quantum embedding to dynamic properties and demonstrate accurate bulk spectral functions at similarly small computational cost. The proposed spectral DMET utilizes the Schmidt decomposition of a response vector, mapping the bulk dynamic correlation functions to that of a quantum impurity cluster coupled to a set of frequency-dependent bath states. The resultant spectral functions are obtained on the real-frequency axis, without bath discretization error, and allows for the construction of arbitrary dynamic correlation functions. We demonstrate the method on the one- (1D) and two-dimensional (2D) Hubbard model, where we obtain zero temperature and thermodynamic limit spectral functions, and show the trivial extension to two-particle Green's functions. This advance therefore extends the scope and applicability of DMET in condensed-matter problems as a computationally tractable route to correlated spectral functions of extended systems and provides a competitive alternative to dynamical mean-field theory for dynamic quantities.

Classical and quantum dynamics of a kicked relativistic particle in a box

NASA Astrophysics Data System (ADS)

Yusupov, J. R.; Otajanov, D. M.; Eshniyazov, V. E.; Matrasulov, D. U.

2018-03-01

We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion.

Development of a 3D-Printed Collimated 90Sr Beta Source

NASA Astrophysics Data System (ADS)

Daniel, Byron; NuDot Collaboration

2017-09-01

Collimated beta particle sources based on 90Sr are common calibration sources for atomic decay detector research and development. Due to the short attenuation length of beta particles in matter, the exact geometry of a collimator can drastically change the rate and energy of beta particles exiting the source. 3D printing allows for the quick and easy prototyping of collimators with custom geometries. I will describe the development of a collimator that interfaces directly to a quartz cuvette for the characterization of liquid scintillator cocktails. Future work will include developing a source for the NuDot detector which aims to reconstruct MeV electrons using the separation of Cherenkov and scintillation light. MIT Summer Research Program.

Interaction-induced effects on Bose-Hubbard parameters

NASA Astrophysics Data System (ADS)

Kremer, Mark; Sachdeva, Rashi; Benseny, Albert; Busch, Thomas

2017-12-01

We study the effects of repulsive on-site interactions on the broadening of the localized Wannier functions used for calculating the parameters to describe ultracold atoms in optical lattices. For this, we replace the common single-particle Wannier functions, which do not contain any information about the interactions, by two-particle Wannier functions obtained from an exact solution which takes the interactions into account. We then use these interaction-dependent basis functions to calculate the Bose-Hubbard model parameters, showing that they are substantially different both at low and high lattice depths from the ones calculated using single-particle Wannier functions. Our results suggest that density effects are not negligible for many parameter ranges and need to be taken into account in metrology experiments.

Pushing, pulling and electromagnetic radiation force cloaking by a pair of conducting cylindrical particles

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2018-02-01

The present analysis shows that two conducting cylindrical particles illuminated by an axially-polarized electric field of plane progressive waves at arbitrary incidence will attract, repel or become totally cloaked (i.e., invisible to the transfer of linear momentum carried by the incident waves), depending on their sizes, the interparticle distance as well as the angle of incidence of the incident field. Based on the rigorous multipole expansion method and the translational addition theorem of cylindrical wave functions, the electromagnetic (EM) radiation forces arising from multiple scattering effects between a pair of perfectly conducting cylindrical particles of circular cross-sections are derived and computed. An effective incident field on a particular particle is determined first, and used subsequently with its corresponding scattered field to derive the closed-form analytical expressions for the radiation force vector components. The mathematical expressions for the EM radiation force components (i.e. longitudinal and transverse) are exact, and have been formulated in partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the interparticle distance and the expansion coefficients. Numerical examples illustrate the analysis for two perfectly conducting circular cylinders in a homogeneous nonmagnetic medium of wave propagation. The computations for the dimensionless radiation force functions are performed with particular emphasis on varying the angle of incidence, the interparticle distance, and the sizes of the particles. Depending on the interparticle distance and angle of incidence, the cylinders yield total neutrality (or invisibility); they experience no force and become unresponsive to the transfer of the EM linear momentum due to multiple scattering cancellation effects. Moreover, pushing or pulling EM forces between the two cylinders arise depending on the interparticle distance, the angle of incidence and their size parameters. This study provides a complete analytical method and computations for the longitudinal and transverse radiation force components in the multiple scattering of EM plane progressive waves with potential applications in particle manipulation, optically-engineered metamaterials with reconfigurable periodicities and cloaking devices to name a few examples.

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Dynamic pattern matcher using incomplete data

NASA Technical Reports Server (NTRS)

Johnson, Gordon G. (Inventor); Wang, Lui (Inventor)

1993-01-01

This invention relates generally to pattern matching systems, and more particularly to a method for dynamically adapting the system to enhance the effectiveness of a pattern match. Apparatus and methods for calculating the similarity between patterns are known. There is considerable interest, however, in the storage and retrieval of data, particularly, when the search is called or initiated by incomplete information. For many search algorithms, a query initiating a data search requires exact information, and the data file is searched for an exact match. Inability to find an exact match thus results in a failure of the system or method.

Single file diffusion into a semi-infinite tube.

PubMed

Farrell, Spencer G; Brown, Aidan I; Rutenberg, Andrew D

2015-11-23

We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.

Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

NASA Astrophysics Data System (ADS)

Rao, T. R. Ramesh

2018-04-01

In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.

Methodological study of computational approaches to address the problem of strong correlations

NASA Astrophysics Data System (ADS)

Lee, Juho

The main focus of this thesis is the detailed investigation of computational methods to tackle strongly correlated materials in which a rich variety of exotic phenomena are found. A many-body problem with sizable electronic correlations can no longer be explained by independent-particle approximations such as density functional theory (DFT) or tight-binding approaches. The influence of an electron to the others is too strong for each electron to be treated as an independent quasiparticle and consequently those standard band-structure methods fail even at a qualitative level. One of the most powerful approaches for strong correlations is the dynamical mean-field theory (DMFT), which has enlightened the understanding of the Mott transition based on the Hubbard model. For realistic applications, the dynamical mean-field theory is combined with various independent-particles approaches. The most widely used one is the DMFT combined with the DFT in the local density approximation (LDA), so-called LDA+DMFT. In this approach, the electrons in the weakly correlated orbitals are calculated by LDA while others in the strongly correlated orbitals are treated by DMFT. Recently, the method combining DMFT with Hedin's GW approximation was also developed, in which the momentum-dependent self-energy is also added. In this thesis, we discuss the application of those methodologies based on DMFT. First, we apply the dynamical mean-field theory to solve the 3-dimensional Hubbard model in Chap. 3. In this application, we model the interface between the thermodynamically coexisting metal and Mott insulator. We show how to model the required slab geometry and extract the electronic spectra. We construct an effective Landau free energy and compute the variation of its parameters across the phase diagram. Finally, using a linear mixture of the density and double-occupancy, we identify a natural Ising order parameter which unifies the treatment of the bandwidth and filling controlled Mott transitions. Secondly, we study the double-counting problem, a subtle issue that arises in LDA+DMFT. We propose a highly precise double-counting functional, in which the intersection of LDA and DMFT is calculated exactly, and implement a parameter-free version of the LDA+DMFT that is tested on one of the simplest strongly correlated systems, the H2 molecule. We show that the exact double-counting treatment along with a good DMFT projector leads to very accurate and total energy and excitation spectrum of H2 molecule. Finally, we implement various versions of GW+DMFT, in its fully self-consistent way, one shot GW approximation, and quasiparticle self-consistent scheme, and studied how well these combined methods perform on H2 molecule as compared to more established methods such as LDA+DMFT. We found that most flavors of GW+DMFT break down in strongly correlated regime due to causality violation. Among GW+DMFT methods, only the self-consistent quasiparticle GW+DMFT with static double-counting, and a new method with causal double-counting, correctly recover the atomic limit at large H-atom separation. While some flavors of GW+DMFT improve the single-electron spectra of LDA+DMFT, the total energy is best predicted by LDA+DMFT, for which the exact double-counting is known, and is static.

A 128-channel picoammeter system and its application on charged particle beam current distribution measurements.

PubMed

Yu, Deyang; Liu, Junliang; Xue, Yingli; Zhang, Mingwu; Cai, Xiaohong; Hu, Jianjun; Dong, Jinmei; Li, Xin

2015-11-01

A 128-channel picoammeter system is constructed based on instrumentation amplifiers. Taking advantage of a high electric potential and narrow bandwidth in DC energetic charged beam measurements, a current resolution better than 5 fA can be achieved. Two sets of 128-channel strip electrodes are implemented on printed circuit boards and are employed for ion and electron beam current distribution measurements. Tests with 60 keV O(3+) ions and 2 keV electrons show that it can provide exact boundaries when a positive charged particle beam current distribution is measured.

Particle paths and phase plane for time-dependent similarity solutions of the one-dimensional Vlasov-Maxwell equations

NASA Technical Reports Server (NTRS)

Roberts, Dana Aaron; Abraham-Shrauner, Barbara

1987-01-01

The phase trajectories of particles in a plasma described by the one-dimensional Vlasov-Maxwell equations are determined qualitatively, analyzing exact general similarity solutions for the cases of temporally damped and growing (sinusoidal or localized) electric fields. The results of numerical integration in both untransformed and Lie-group point-transformed coordinates are presented in extensive graphs and characterized in detail. The implications of the present analysis for the stability of BGK equilibria are explored, and the existence of nonlinear solutions arbitrarily close to and significantly different from the BGK solutions is demonstrated.

Initial Stage of Aerosol Formation from Oversaturated Vapors

NASA Astrophysics Data System (ADS)

Lushnikov, A. A.; Zagainov, V. A.; Lyubovtseva, Yu. S.

2018-03-01

The formation of aerosol particles from oversaturated vapor was considered assuming that the stable nuclei of the new phase contain two (dimers) or three (trimers) condensing vapor molecules. Exact expressions were derived and analyzed for the partition functions of the dimer and trimer suspended in a carrier gas for the rectangular well and repulsive core intermolecular potentials. The equilibrium properties of these clusters and the nucleation rate of aerosol particles were discussed. The bound states of clusters were introduced using a limitation on their total energy: molecular clusters with a negative total energy were considered to exclude configurations with noninteracting fragments.

Ferromagnetic effects for nanofluid venture through composite permeable stenosed arteries with different nanosize particles

NASA Astrophysics Data System (ADS)

Akbar, Noreen Sher; Mustafa, M. T.

2015-07-01

In the present article ferromagnetic field effects for copper nanoparticles for blood flow through composite permeable stenosed arteries is discussed. The copper nanoparticles for the blood flow with water as base fluid with different nanosize particles is not explored upto yet. The equations for the Cu-water nanofluid are developed first time in literature and simplified using long wavelength and low Reynolds number assumptions. Exact solutions have been evaluated for velocity, pressure gradient, the solid volume fraction of the nanoparticles and temperature profile. Effect of various flow parameters on the flow and heat transfer characteristics are utilized.

Quantum work statistics of charged Dirac particles in time-dependent fields

DOE PAGES

Deffner, Sebastian; Saxena, Avadh

2015-09-28

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Thus, special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.

Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole

NASA Astrophysics Data System (ADS)

He, Guan-Sheng; Lin, Wen-Bin

2014-02-01

The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.

Design of exchange-correlation functionals through the correlation factor approach

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

Pavlíková Přecechtělová, Jana, E-mail: j.precechtelova@gmail.com, E-mail: Matthias.Ernzerhof@UMontreal.ca; Institut für Chemie, Theoretische Chemie / Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin; Bahmann, Hilke

The correlation factor model is developed in which the spherically averaged exchange-correlation hole of Kohn-Sham theory is factorized into an exchange hole model and a correlation factor. The exchange hole model reproduces the exact exchange energy per particle. The correlation factor is constructed in such a manner that the exchange-correlation energy correctly reduces to exact exchange in the high density and rapidly varying limits. Four different correlation factor models are presented which satisfy varying sets of physical constraints. Three models are free from empirical adjustments to experimental data, while one correlation factor model draws on one empirical parameter. The correlationmore » factor models are derived in detail and the resulting exchange-correlation holes are analyzed. Furthermore, the exchange-correlation energies obtained from the correlation factor models are employed to calculate total energies, atomization energies, and barrier heights. It is shown that accurate, non-empirical functionals can be constructed building on exact exchange. Avenues for further improvements are outlined as well.« less

Exact evaluation of the depletion force between nanospheres in a polydisperse polymer fluid under Θ conditions.

PubMed

Wang, Haiqiang; Woodward, Clifford E; Forsman, Jan

2014-05-21

We analyze a system consisting of two spherical particles immersed in a polydispersed polymer solution under theta conditions. An exact theory is developed to describe the potential of mean force between the spheres for the case where the polymer molecular weight dispersity is described by the Schulz-Flory distribution. Exact results can be derived for the protein regime, where the sphere radius (R(s)) is small compared to the average radius of gyration of the polymer (R(g)). Numerical results are relatively easily obtained in the cases where the sphere radius is increased. We find that even when q = R(g)/R(s) ⪆ 10, then the use of a monopole expansion for the polymer end-point distribution about the spheres is sufficient. For even larger spheres q ≈ 1, accuracy is maintained by including a dipolar correction. The implications of these findings on generating a full many-body effective interaction for a collection of N spheres imbedded in the polymer solution are discussed.

Exact mapping between different dynamics of isotropically trapped quantum gases

NASA Astrophysics Data System (ADS)

Wamba, Etienne; Pelster, Axel; Anglin, James R.

2016-05-01

Experiments on trapped quantum gases can probe challenging regimes of quantum many-body dynamics, where strong interactions or non-equilibrium states prevent exact theoretical treatment. In this talk, we present a class of exact mappings between all the observables of different experiments, under the experimentally attainable conditions that the gas particles interact via a homogeneously scaling two-body potential which is in general time-dependent, and are confined in an isotropic harmonic trap. We express our result through an identity relating second-quantized field operators in the Heisenberg picture of quantum mechanics which makes it general. It applies to arbitrary measurements on possibly multi-component Bose or Fermi gases in arbitrary initial quantum states, no matter how highly excited or far from equilibrium. We use an example to show how the results of two different and currently feasible experiments can be mapped onto each other by our spacetime transformation. DAMOP sorting category: 6.11 Nonlinear dynamics and out-of-equilibrium trapped gases EW acknowledge the financial support from the Alexander von Humboldt foundation.

Numerical treatment for solving two-dimensional space-fractional advection-dispersion equation using meshless method

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Sun, Fengxin; Wei, Qi; Wang, Jufeng

2018-02-01

Space-fractional advection-dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann-Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Mahak, Nadia

2018-06-01

The nonlinear Schrödinger equation (NLSE) with the aid of three order dispersion terms is investigated to find the exact solutions via the extended (G'/G2)-expansion method and the first integral method. Many exact traveling wave solutions, such as trigonometric, hyperbolic, rational, soliton and complex function solutions, are characterized with some free parameters of the problem studied. It is corroborated that the proposed techniques are manageable, straightforward and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Some figures are plotted to describe the propagation of traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions.