Using Static Percentiles of AE9/AP9 to Approximate Dynamic Monte Carlo Runs for Radiation Analysis of Spiral Transfer Orbits

NASA Astrophysics Data System (ADS)

Kwan, Betty P.; O'Brien, T. Paul

2015-06-01

The Aerospace Corporation performed a study to determine whether static percentiles of AE9/AP9 can be used to approximate dynamic Monte Carlo runs for radiation analysis of spiral transfer orbits. Solar panel degradation is a major concern for solar-electric propulsion because solar-electric propulsion depends on the power output of the solar panel. Different spiral trajectories have different radiation environments that could lead to solar panel degradation. Because the spiral transfer orbits only last weeks to months, an average environment does not adequately address the possible transient enhancements of the radiation environment that must be accounted for in optimizing the transfer orbit trajectory. Therefore, to optimize the trajectory, an ensemble of Monte Carlo simulations of AE9/AP9 would normally be run for every spiral trajectory to determine the 95th percentile radiation environment. To avoid performing lengthy Monte Carlo dynamic simulations for every candidate spiral trajectory in the optimization, we found a static percentile that would be an accurate representation of the full Monte Carlo simulation for a representative set of spiral trajectories. For 3 LEO to GEO and 1 LEO to MEO trajectories, a static 90th percentile AP9 is a good approximation of the 95th percentile fluence with dynamics for 4-10 MeV protons, and a static 80th percentile AE9 is a good approximation of the 95th percentile fluence with dynamics for 0.5-2 MeV electrons. While the specific percentiles chosen cannot necessarily be used in general for other orbit trade studies, the concept of determining a static percentile as a quick approximation to a full Monte Carlo ensemble of simulations can likely be applied to other orbit trade studies. We expect the static percentile to depend on the region of space traversed, the mission duration, and the radiation effect considered.

Electron capture in collisions of S4+ with atomic hydrogen

NASA Astrophysics Data System (ADS)

Stancil, P. C.; Turner, A. R.; Cooper, D. L.; Schultz, D. R.; Rakovic, M. J.; Fritsch, W.; Zygelman, B.

2001-06-01

Charge transfer processes due to collisions of ground state S4+(3s2 1S) ions with atomic hydrogen are investigated for energies between 1 meV u-1 and 10 MeV u-1 using the quantum mechanical molecular-orbital close-coupling (MOCC), atomic-orbital close-coupling, classical trajectory Monte Carlo (CTMC) and continuum distorted wave methods. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach. A number of variants of the CTMC approach were explored, including different momentum and radial distributions for the initial state, as well as effective charge and quantum-defect models to determine the corresponding quantum state after capture into final partially stripped S3+ excited classical states. Hydrogen target isotope effects are explored and rate coefficients for temperatures between 100 and 106 K are also presented.

Uncertainties in the production of p nuclides in thermonuclear supernovae determined by Monte Carlo variations

NASA Astrophysics Data System (ADS)

Nishimura, N.; Rauscher, T.; Hirschi, R.; Murphy, A. St J.; Cescutti, G.; Travaglio, C.

2018-03-01

Thermonuclear supernovae originating from the explosion of a white dwarf accreting mass from a companion star have been suggested as a site for the production of p nuclides. Such nuclei are produced during the explosion, in layers enriched with seed nuclei coming from prior strong s processing. These seeds are transformed into proton-richer isotopes mainly by photodisintegration reactions. Several thousand trajectories from a 2D explosion model were used in a Monte Carlo approach. Temperature-dependent uncertainties were assigned individually to thousands of rates varied simultaneously in post-processing in an extended nuclear reaction network. The uncertainties in the final nuclear abundances originating from uncertainties in the astrophysical reaction rates were determined. In addition to the 35 classical p nuclides, abundance uncertainties were also determined for the radioactive nuclides 92Nb, 97, 98Tc, 146Sm, and for the abundance ratios Y(92Mo)/Y(94Mo), Y(92Nb)/Y(92Mo), Y(97Tc)/Y(98Ru), Y(98Tc)/Y(98Ru), and Y(146Sm)/Y(144Sm), important for Galactic Chemical Evolution studies. Uncertainties found were generally lower than a factor of 2, although most nucleosynthesis flows mainly involve predicted rates with larger uncertainties. The main contribution to the total uncertainties comes from a group of trajectories with high peak density originating from the interior of the exploding white dwarf. The distinction between low-density and high-density trajectories allows more general conclusions to be drawn, also applicable to other simulations of white dwarf explosions.

Enhanced Sampling of an Atomic Model with Hybrid Nonequilibrium Molecular Dynamics-Monte Carlo Simulations Guided by a Coarse-Grained Model.

PubMed

Chen, Yunjie; Roux, Benoît

2015-08-11

Molecular dynamics (MD) trajectories based on a classical equation of motion provide a straightforward, albeit somewhat inefficient approach, to explore and sample the configurational space of a complex molecular system. While a broad range of techniques can be used to accelerate and enhance the sampling efficiency of classical simulations, only algorithms that are consistent with the Boltzmann equilibrium distribution yield a proper statistical mechanical computational framework. Here, a multiscale hybrid algorithm relying simultaneously on all-atom fine-grained (FG) and coarse-grained (CG) representations of a system is designed to improve sampling efficiency by combining the strength of nonequilibrium molecular dynamics (neMD) and Metropolis Monte Carlo (MC). This CG-guided hybrid neMD-MC algorithm comprises six steps: (1) a FG configuration of an atomic system is dynamically propagated for some period of time using equilibrium MD; (2) the resulting FG configuration is mapped onto a simplified CG model; (3) the CG model is propagated for a brief time interval to yield a new CG configuration; (4) the resulting CG configuration is used as a target to guide the evolution of the FG system; (5) the FG configuration (from step 1) is driven via a nonequilibrium MD (neMD) simulation toward the CG target; (6) the resulting FG configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-ends momentum reversal prescription is used for the neMD trajectories of the FG system to guarantee that the CG-guided hybrid neMD-MC algorithm obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The enhanced sampling achieved with the method is illustrated with a model system with hindered diffusion and explicit-solvent peptide simulations. Illustrative tests indicate that the method can yield a speedup of about 80 times for the model system and up to 21 times for polyalanine and (AAQAA)3 in water.

Enhanced Sampling of an Atomic Model with Hybrid Nonequilibrium Molecular Dynamics—Monte Carlo Simulations Guided by a Coarse-Grained Model

PubMed Central

2015-01-01

Molecular dynamics (MD) trajectories based on a classical equation of motion provide a straightforward, albeit somewhat inefficient approach, to explore and sample the configurational space of a complex molecular system. While a broad range of techniques can be used to accelerate and enhance the sampling efficiency of classical simulations, only algorithms that are consistent with the Boltzmann equilibrium distribution yield a proper statistical mechanical computational framework. Here, a multiscale hybrid algorithm relying simultaneously on all-atom fine-grained (FG) and coarse-grained (CG) representations of a system is designed to improve sampling efficiency by combining the strength of nonequilibrium molecular dynamics (neMD) and Metropolis Monte Carlo (MC). This CG-guided hybrid neMD-MC algorithm comprises six steps: (1) a FG configuration of an atomic system is dynamically propagated for some period of time using equilibrium MD; (2) the resulting FG configuration is mapped onto a simplified CG model; (3) the CG model is propagated for a brief time interval to yield a new CG configuration; (4) the resulting CG configuration is used as a target to guide the evolution of the FG system; (5) the FG configuration (from step 1) is driven via a nonequilibrium MD (neMD) simulation toward the CG target; (6) the resulting FG configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-ends momentum reversal prescription is used for the neMD trajectories of the FG system to guarantee that the CG-guided hybrid neMD-MC algorithm obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The enhanced sampling achieved with the method is illustrated with a model system with hindered diffusion and explicit-solvent peptide simulations. Illustrative tests indicate that the method can yield a speedup of about 80 times for the model system and up to 21 times for polyalanine and (AAQAA)3 in water. PMID:26574442

Modeling the Flow of Rarefied Gases at NASA

NASA Technical Reports Server (NTRS)

Forrest E. Lumpkin, III

2012-01-01

At modest temperatures, the thermal energy of atmospheric diatomic gases such as nitrogen is primarily distributed between only translational and rotational energy modes. Furthermore, these energy modes are fully excited such that the specific heat at constant volume is well approximated by the simple expression C(sub v) = 5/2 R. As a result, classical mechanics provides a suitable approximation at such temperatures of the true quantum mechanical behavior of the inter-molecular collisions of such molecules. Using classical mechanics, the transfer of energy between rotational and translation energy modes is studied. The approach of Lordi and Mates is adopted to compute the trajectories and time dependent rotational orientations and energies during the collision of two non-polar diatomic molecules. A Monte-Carlo analysis is performed collecting data from the results of many such simulations in order to estimate the rotational relaxation time. A Graphical Processing Unit (GPU) is employed to improve the performance of the Monte-Carlo analysis. A comparison of the performance of the GPU implementation to an implementation on traditional computer architecture is made. Effects of the assumed inter-molecular potential on the relaxation time are studied. The seminar will also present highlights of computational analyses performed at NASA Johnson Space Center of heat transfer in rarefied gases.

Trajectory description of the quantum–classical transition for wave packet interference

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2016-08-15

The quantum–classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum–classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum–classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow themore » main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum–classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightful trajectory interpretation for the quantum–classical transition of wave packet interference.« less

Large-scale atomistic calculations of clusters in intense x-ray pulses

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

Ho, Phay J.; Knight, Chris

Here, we present the methodology of our recently developed Monte-Carlo/ Molecular-Dynamics method for studying the fundamental ultrafast dynamics induced by high-fluence, high-intensity x-ray free electron laser (XFEL) pulses in clusters. The quantum nature of the initiating ionization process is accounted for by a Monte Carlo method to calculate probabilities of electronic transitions, including photo absorption, inner-shell relaxation, photon scattering, electron collision and recombination dynamics, and thus track the transient electronic configurations explicitly. The freed electrons and ions are followed by classical particle trajectories using a molecular dynamics algorithm. These calculations reveal the surprising role of electron-ion recombination processes that leadmore » to the development of nonuniform spatial charge density profiles in x-ray excited clusters over femtosecond timescales. In the high-intensity limit, it is important to include the recombination dynamics in the calculated scattering response even for a 2- fs pulse. We also demonstrate that our numerical codes and algorithms can make e!cient use of the computational power of massively parallel supercomputers to investigate the intense-field dynamics in systems with increasing complexity and size at the ultrafast timescale and in non-linear x-ray interaction regimes. In particular, picosecond trajectories of XFEL clusters with attosecond time resolution containing millions of particles can be e!ciently computed on upwards of 262,144 processes.« less

Large-scale atomistic calculations of clusters in intense x-ray pulses

DOE PAGES

Ho, Phay J.; Knight, Chris

2017-04-28

Here, we present the methodology of our recently developed Monte-Carlo/ Molecular-Dynamics method for studying the fundamental ultrafast dynamics induced by high-fluence, high-intensity x-ray free electron laser (XFEL) pulses in clusters. The quantum nature of the initiating ionization process is accounted for by a Monte Carlo method to calculate probabilities of electronic transitions, including photo absorption, inner-shell relaxation, photon scattering, electron collision and recombination dynamics, and thus track the transient electronic configurations explicitly. The freed electrons and ions are followed by classical particle trajectories using a molecular dynamics algorithm. These calculations reveal the surprising role of electron-ion recombination processes that leadmore » to the development of nonuniform spatial charge density profiles in x-ray excited clusters over femtosecond timescales. In the high-intensity limit, it is important to include the recombination dynamics in the calculated scattering response even for a 2- fs pulse. We also demonstrate that our numerical codes and algorithms can make e!cient use of the computational power of massively parallel supercomputers to investigate the intense-field dynamics in systems with increasing complexity and size at the ultrafast timescale and in non-linear x-ray interaction regimes. In particular, picosecond trajectories of XFEL clusters with attosecond time resolution containing millions of particles can be e!ciently computed on upwards of 262,144 processes.« less

Low-energy charge transfer for collisions of Si3+ with atomic hydrogen

NASA Astrophysics Data System (ADS)

Bruhns, H.; Kreckel, H.; Savin, D. W.; Seely, D. G.; Havener, C. C.

2008-06-01

Cross sections of charge transfer for Si3+ ions with atomic hydrogen at collision energies of ≈40-2500eV/u were carried out using a merged-beam technique at the Multicharged Ion Research Facility at Oak Ridge National Laboratory. The data span an energy range in which both molecular orbital close coupling (MOCC) and classical trajectory Monte Carlo (CTMC) calculations are available. The influence of quantum mechanical effects of the ionic core as predicted by MOCC is clearly seen in our results. However, discrepancies between our experiment and MOCC results toward higher collision energies are observed. At energies above 1000 eV/u good agreement is found with CTMC results.

Off-diagonal expansion quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Albash, Tameem; Wagenbreth, Gene; Hen, Itay

2017-12-01

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

Off-diagonal expansion quantum Monte Carlo.

PubMed

Albash, Tameem; Wagenbreth, Gene; Hen, Itay

2017-12-01

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

IRVE-II Post-Flight Trajectory Reconstruction

NASA Technical Reports Server (NTRS)

O'Keefe, Stephen A.; Bose, David M.

2010-01-01

NASA s Inflatable Re-entry Vehicle Experiment (IRVE) II successfully demonstrated an inflatable aerodynamic decelerator after being launched aboard a sounding rocket from Wallops Flight Facility (WFF). Preliminary day of flight data compared well with pre-flight Monte Carlo analysis, and a more complete trajectory reconstruction performed with an Extended Kalman Filter (EKF) approach followed. The reconstructed trajectory and comparisons to an attitude solution provided by NASA Sounding Rocket Operations Contract (NSROC) personnel at WFF are presented. Additional comparisons are made between the reconstructed trajectory and pre and post-flight Monte Carlo trajectory predictions. Alternative observations of the trajectory are summarized which leverage flight accelerometer measurements, the pre-flight aerodynamic database, and on-board flight video. Finally, analysis of the payload separation and aeroshell deployment events are presented. The flight trajectory is reconstructed to fidelity sufficient to assess overall project objectives related to flight dynamics and overall, IRVE-II flight dynamics are in line with expectations

Semiclassical propagation of Wigner functions.

PubMed

Dittrich, T; Gómez, E A; Pachón, L A

2010-06-07

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrodinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

Classical Trajectories and Quantum Spectra

NASA Technical Reports Server (NTRS)

Mielnik, Bogdan; Reyes, Marco A.

1996-01-01

A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but non-perturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.

Pre-conditioned backward Monte Carlo solutions to radiative transport in planetary atmospheres. Fundamentals: Sampling of propagation directions in polarising media

NASA Astrophysics Data System (ADS)

García Muñoz, A.; Mills, F. P.

2015-01-01

Context. The interpretation of polarised radiation emerging from a planetary atmosphere must rely on solutions to the vector radiative transport equation (VRTE). Monte Carlo integration of the VRTE is a valuable approach for its flexible treatment of complex viewing and/or illumination geometries, and it can intuitively incorporate elaborate physics. Aims: We present a novel pre-conditioned backward Monte Carlo (PBMC) algorithm for solving the VRTE and apply it to planetary atmospheres irradiated from above. As classical BMC methods, our PBMC algorithm builds the solution by simulating the photon trajectories from the detector towards the radiation source, i.e. in the reverse order of the actual photon displacements. Methods: We show that the neglect of polarisation in the sampling of photon propagation directions in classical BMC algorithms leads to unstable and biased solutions for conservative, optically-thick, strongly polarising media such as Rayleigh atmospheres. The numerical difficulty is avoided by pre-conditioning the scattering matrix with information from the scattering matrices of prior (in the BMC integration order) photon collisions. Pre-conditioning introduces a sense of history in the photon polarisation states through the simulated trajectories. Results: The PBMC algorithm is robust, and its accuracy is extensively demonstrated via comparisons with examples drawn from the literature for scattering in diverse media. Since the convergence rate for MC integration is independent of the integral's dimension, the scheme is a valuable option for estimating the disk-integrated signal of stellar radiation reflected from planets. Such a tool is relevant in the prospective investigation of exoplanetary phase curves. We lay out two frameworks for disk integration and, as an application, explore the impact of atmospheric stratification on planetary phase curves for large star-planet-observer phase angles. By construction, backward integration provides a better control than forward integration over the planet region contributing to the solution, and this presents a clear advantage when estimating the disk-integrated signal at moderate and large phase angles. A one-slab, plane-parallel version of the PBMC algorithm is available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/573/A72

Statistical methods for launch vehicle guidance, navigation, and control (GN&C) system design and analysis

NASA Astrophysics Data System (ADS)

Rose, Michael Benjamin

A novel trajectory and attitude control and navigation analysis tool for powered ascent is developed. The tool is capable of rapid trade-space analysis and is designed to ultimately reduce turnaround time for launch vehicle design, mission planning, and redesign work. It is streamlined to quickly determine trajectory and attitude control dispersions, propellant dispersions, orbit insertion dispersions, and navigation errors and their sensitivities to sensor errors, actuator execution uncertainties, and random disturbances. The tool is developed by applying both Monte Carlo and linear covariance analysis techniques to a closed-loop, launch vehicle guidance, navigation, and control (GN&C) system. The nonlinear dynamics and flight GN&C software models of a closed-loop, six-degree-of-freedom (6-DOF), Monte Carlo simulation are formulated and developed. The nominal reference trajectory (NRT) for the proposed lunar ascent trajectory is defined and generated. The Monte Carlo truth models and GN&C algorithms are linearized about the NRT, the linear covariance equations are formulated, and the linear covariance simulation is developed. The performance of the launch vehicle GN&C system is evaluated using both Monte Carlo and linear covariance techniques and their trajectory and attitude control dispersion, propellant dispersion, orbit insertion dispersion, and navigation error results are validated and compared. Statistical results from linear covariance analysis are generally within 10% of Monte Carlo results, and in most cases the differences are less than 5%. This is an excellent result given the many complex nonlinearities that are embedded in the ascent GN&C problem. Moreover, the real value of this tool lies in its speed, where the linear covariance simulation is 1036.62 times faster than the Monte Carlo simulation. Although the application and results presented are for a lunar, single-stage-to-orbit (SSTO), ascent vehicle, the tools, techniques, and mathematical formulations that are discussed are applicable to ascent on Earth or other planets as well as other rocket-powered systems such as sounding rockets and ballistic missiles.

Extending Bell's beables to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories

NASA Astrophysics Data System (ADS)

Lorenzen, F.; de Ponte, M. A.; Moussa, M. H. Y.

2009-09-01

In this paper, employing the Itô stochastic Schrödinger equation, we extend Bell’s beable interpretation of quantum mechanics to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories. For a particular choice of the source of stochasticity, the one leading to a dissipative Lindblad-type correction to the Hamiltonian dynamics, we find that the diffusive terms in Nelsons stochastic trajectories are naturally incorporated into Bohm’s causal dynamics, yielding a unified Bohm-Nelson theory. In particular, by analyzing the interference between quantum trajectories, we clearly identify the decoherence time, as estimated from the quantum formalism. We also observe the quantum-to-classical transition in the convergence of the infinite ensemble of quantum trajectories to their classical counterparts. Finally, we show that our extended beables circumvent the problems in Bohm’s causal dynamics regarding stationary states in quantum mechanics.

Semiclassical evaluation of quantum fidelity

NASA Astrophysics Data System (ADS)

Vanicek, Jiri

2004-03-01

We present a numerically feasible semiclassical method to evaluate quantum fidelity (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform semiclassical expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows a Monte-Carlo evaluation, this uniform expression is accurate at times where there are 10^70 semiclassical contributions. Remarkably, the method also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and thus provide a ``defense" of the linear response theory from the famous Van Kampen objection. We point out the potential use of our uniform expression in other areas because it gives a most direct link between the quantum Feynman propagator based on the path integral and the semiclassical Van Vleck propagator based on the sum over classical trajectories. Finally, we test the applicability of our method in integrable and mixed systems.

Simulation of wave packet tunneling of interacting identical particles

NASA Astrophysics Data System (ADS)

Lozovik, Yu. E.; Filinov, A. V.; Arkhipov, A. S.

2003-02-01

We demonstrate a different method of simulation of nonstationary quantum processes, considering the tunneling of two interacting identical particles, represented by wave packets. The used method of quantum molecular dynamics (WMD) is based on the Wigner representation of quantum mechanics. In the context of this method ensembles of classical trajectories are used to solve quantum Wigner-Liouville equation. These classical trajectories obey Hamiltonian-like equations, where the effective potential consists of the usual classical term and the quantum term, which depends on the Wigner function and its derivatives. The quantum term is calculated using local distribution of trajectories in phase space, therefore, classical trajectories are not independent, contrary to classical molecular dynamics. The developed WMD method takes into account the influence of exchange and interaction between particles. The role of direct and exchange interactions in tunneling is analyzed. The tunneling times for interacting particles are calculated.

Complex trajectories in a classical periodic potential

NASA Astrophysics Data System (ADS)

Anderson, Alexander G.; Bender, Carl M.

2012-11-01

This paper examines the complex trajectories of a classical particle in the potential V(x) = -cos (x). Almost all the trajectories describe a particle that hops from one well to another in an erratic fashion. However, it is shown analytically that there are two special classes of trajectories x(t) determined only by the energy of the particle and not by the initial position of the particle. The first class consists of periodic trajectories; that is, trajectories that return to their initial position x(0) after some real time T. The second class consists of trajectories for which there exists a real time T such that x(t + T) = x(t) ± 2π. These two classes of classical trajectories are analogous to valence and conduction bands in quantum mechanics, where the quantum particle either remains localized or else tunnels resonantly (conducts) through a crystal lattice. These two special types of trajectories are associated with sets of energies of measure 0. For other energies, it is shown that for long times the average velocity of the particle becomes a fractal-like function of energy.

Mission Operations and Navigation Toolkit Environment

NASA Technical Reports Server (NTRS)

Sunseri, Richard F.; Wu, Hsi-Cheng; Hanna, Robert A.; Mossey, Michael P.; Duncan, Courtney B.; Evans, Scott E.; Evans, James R.; Drain, Theodore R.; Guevara, Michelle M.; Martin Mur, Tomas J.;

Interplay between Coulomb-focusing and non-dipole effects in strong-field ionization with elliptical polarization

NASA Astrophysics Data System (ADS)

Daněk, J.; Klaiber, M.; Hatsagortsyan, K. Z.; Keitel, C. H.; Willenberg, B.; Maurer, J.; Mayer, B. W.; Phillips, C. R.; Gallmann, L.; Keller, U.

2018-06-01

We study strong-field ionization and rescattering beyond the long-wavelength limit of the dipole approximation with elliptically polarized mid-IR laser pulses. Full three-dimensional photoelectron momentum distributions (PMDs) measured with velocity map imaging and tomographic reconstruction revealed an unexpected sharp ridge structure in the polarization plane (2018 Phys. Rev. A 97 013404). This thin line-shaped ridge structure for low-energy photoelectrons is correlated with the ellipticity-dependent asymmetry of the PMD along the beam propagation direction. The peak of the projection of the PMD onto the beam propagation axis is shifted from negative to positive values when the sharp ridge fades away with increasing ellipticity. With classical trajectory Monte Carlo simulations and analytical analysis, we study the underlying physics of this feature. The underlying physics is based on the interplay between the lateral drift of the ionized electron, the laser magnetic field induced drift in the laser propagation direction, and Coulomb focusing. To apply our observations to emerging techniques relying on strong-field ionization processes, including time-resolved holography and molecular imaging, we present a detailed classical trajectory-based analysis of our observations. The analysis leads to the explanation of the fine structure of the ridge and its non-dipole behavior upon rescattering while introducing restrictions on the ellipticity. These restrictions as well as the ionization and recollision phases provide additional observables to gain information on the timing of the ionization and recollision process and non-dipole properties of the ionization process.

Proton-impact ionization cross sections of adenine measured at 0.5 and 2.0 MeV by electron spectroscopy

NASA Astrophysics Data System (ADS)

Iriki, Y.; Kikuchi, Y.; Imai, M.; Itoh, A.

2011-11-01

Double-differential ionization cross sections (DDCSs) of vapor-phase adenine molecules (C5H5N5) by 0.5- and 2.0-MeV proton impact have been measured by the electron spectroscopy method. Electrons ejected from adenine were analyzed by a 45∘ parallel-plate electrostatic spectrometer over an energy range of 1.0-1000 eV at emission angles from 15∘ to 165∘. Single-differential cross sections (SDCSs) and total ionization cross sections (TICSs) were also deduced. It was found from the Platzman plot, defined as SDCSs divided by the classical Rutherford knock-on cross sections per target electron, that the SDCSs at higher electron energies are proportional to the total number of valence electrons (50) of adenine, while those at low-energy electrons are highly enhanced due to dipole and higher-order interactions. The present results of TICS are in fairly good agreement with recent classical trajectory Monte Carlo calculations, and moreover, a simple analytical formula gives nearly equivalent cross sections in magnitude at the incident proton energies investigated.

Effects of weakly coupled and dense quantum plasmas environments on charge exchange and ionization processes in Na+ + Rb(5s) atom collisions

NASA Astrophysics Data System (ADS)

Pandey, Mukesh Kumar; Lin, Yen-Chang; Ho, Yew Kam

2017-02-01

The effects of weakly coupled or classical and dense quantum plasmas environment on charge exchange and ionization processes in Na+ + Rb(5s) atom collision at keV energy range have been investigated using classical trajectory Monte Carlo (CTMC) method. The interaction of three charged particles are described by the Debye-Hückel screen potential for weakly coupled plasma, whereas exponential cosine-screened Coulomb potential have been used for dense quantum plasma environment and the effects of both conditions on the cross sections are compared. It is found that screening effects on cross sections in high Debye length condition is quite small in both plasma environments. However, enhanced screening effects on cross sections are observed in dense quantum plasmas for low Debye length condition, which becomes more effective while decreasing the Debye length. Also, we have found that our calculated results for plasma-free case are comparable with the available theoretical results. These results are analyzed in light of available theoretical data with the choice of model potentials.

Enhanced configurational sampling with hybrid non-equilibrium molecular dynamics-Monte Carlo propagator

NASA Astrophysics Data System (ADS)

Suh, Donghyuk; Radak, Brian K.; Chipot, Christophe; Roux, Benoît

2018-01-01

Molecular dynamics (MD) trajectories based on classical equations of motion can be used to sample the configurational space of complex molecular systems. However, brute-force MD often converges slowly due to the ruggedness of the underlying potential energy surface. Several schemes have been proposed to address this problem by effectively smoothing the potential energy surface. However, in order to recover the proper Boltzmann equilibrium probability distribution, these approaches must then rely on statistical reweighting techniques or generate the simulations within a Hamiltonian tempering replica-exchange scheme. The present work puts forth a novel hybrid sampling propagator combining Metropolis-Hastings Monte Carlo (MC) with proposed moves generated by non-equilibrium MD (neMD). This hybrid neMD-MC propagator comprises three elementary elements: (i) an atomic system is dynamically propagated for some period of time using standard equilibrium MD on the correct potential energy surface; (ii) the system is then propagated for a brief period of time during what is referred to as a "boosting phase," via a time-dependent Hamiltonian that is evolved toward the perturbed potential energy surface and then back to the correct potential energy surface; (iii) the resulting configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-end momentum reversal prescription is used at the end of the neMD trajectories to guarantee that the hybrid neMD-MC sampling propagator obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The hybrid neMD-MC sampling propagator is designed and implemented to enhance the sampling by relying on the accelerated MD and solute tempering schemes. It is also combined with the adaptive biased force sampling algorithm to examine. Illustrative tests with specific biomolecular systems indicate that the method can yield a significant speedup.

Enhanced configurational sampling with hybrid non-equilibrium molecular dynamics-Monte Carlo propagator.

PubMed

Suh, Donghyuk; Radak, Brian K; Chipot, Christophe; Roux, Benoît

2018-01-07

Molecular dynamics (MD) trajectories based on classical equations of motion can be used to sample the configurational space of complex molecular systems. However, brute-force MD often converges slowly due to the ruggedness of the underlying potential energy surface. Several schemes have been proposed to address this problem by effectively smoothing the potential energy surface. However, in order to recover the proper Boltzmann equilibrium probability distribution, these approaches must then rely on statistical reweighting techniques or generate the simulations within a Hamiltonian tempering replica-exchange scheme. The present work puts forth a novel hybrid sampling propagator combining Metropolis-Hastings Monte Carlo (MC) with proposed moves generated by non-equilibrium MD (neMD). This hybrid neMD-MC propagator comprises three elementary elements: (i) an atomic system is dynamically propagated for some period of time using standard equilibrium MD on the correct potential energy surface; (ii) the system is then propagated for a brief period of time during what is referred to as a "boosting phase," via a time-dependent Hamiltonian that is evolved toward the perturbed potential energy surface and then back to the correct potential energy surface; (iii) the resulting configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-end momentum reversal prescription is used at the end of the neMD trajectories to guarantee that the hybrid neMD-MC sampling propagator obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The hybrid neMD-MC sampling propagator is designed and implemented to enhance the sampling by relying on the accelerated MD and solute tempering schemes. It is also combined with the adaptive biased force sampling algorithm to examine. Illustrative tests with specific biomolecular systems indicate that the method can yield a significant speedup.

The Biharmonic Oscillator and Asymmetric Linear Potentials: From Classical Trajectories to Momentum-Space Probability Densities in the Extreme Quantum Limit

ERIC Educational Resources Information Center

Ruckle, L. J.; Belloni, M.; Robinett, R. W.

2012-01-01

The biharmonic oscillator and the asymmetric linear well are two confining power-law-type potentials for which complete bound-state solutions are possible in both classical and quantum mechanics. We examine these problems in detail, beginning with studies of their trajectories in position and momentum space, evaluation of the classical probability…

Measurements of Classical Transport of Fast Ions in the LAPD

NASA Astrophysics Data System (ADS)

Zhao, L.; Boehmer, H.; Edrich, D.; Heidbrink, W. W.; McWilliams, R.; Zimmerman, D.; Lenenman, D.; Vincena, S.

2004-11-01

To study fast ion transport in a well controlled background plasma, a 3cm diameter RF ion gun launches a pulsed, 400 eV ribbon shape argon ion beam in the LArge Plasma Device (LAPD) at UCLA. The beam velocity distribution is calibrated by Laser Induced Fluorescence (LIF) on the Mirror of UCI and the beam energy is also measured by a two-grid energy analyzer at different axial locations (z=0.3-6.0 m) from the source on LAPD. Slowing down of the ion beam is observed when the beam is launched parallel or at 15 degrees to the 0.85 kG magnetic field. Using Langmuir probe measurements of the plasma parameters, the observed energy deceleration rate is consistent with classical Coulomb scattering theory. The radial beam profile is also measured by the energy analyzer when the beam is launched at 15 degrees to the magnetic field. The beam follows the expected helical trajectory and its contour has the shape predicted by Monte Carlo simulations. The diffusion measurements are performed at different axial locations where the ion beam has the same gyro-phase to eliminate the peristaltic effect. The spatial spreading of the beam is compared with classical scattering and neutral scattering theory.

Theoretical Studies in Chemical Kinetics - Annual Report, 1970.

DOE R&D Accomplishments Database

Karplus, Martin

1970-10-01

The research performed includes (a) Alkali-Halide, Alkali-Halide (MX, M?X?) Exchange Reactions; (b) Inversion Problem; (c) Quantum Mechanics of Scattering Processes, (d) Transition State Analysis of Classical Trajectories, (e) Differential Cross Sections from Classical Trajectories; and (f) Other Studies.

Recommender engine for continuous-time quantum Monte Carlo methods

NASA Astrophysics Data System (ADS)

Huang, Li; Yang, Yi-feng; Wang, Lei

2017-03-01

Recommender systems play an essential role in the modern business world. They recommend favorable items such as books, movies, and search queries to users based on their past preferences. Applying similar ideas and techniques to Monte Carlo simulations of physical systems boosts their efficiency without sacrificing accuracy. Exploiting the quantum to classical mapping inherent in the continuous-time quantum Monte Carlo methods, we construct a classical molecular gas model to reproduce the quantum distributions. We then utilize powerful molecular simulation techniques to propose efficient quantum Monte Carlo updates. The recommender engine approach provides a general way to speed up the quantum impurity solvers.

Charge Transfer in Collisions of S^4+ with He.

NASA Astrophysics Data System (ADS)

Wang, J. G.; Stancil, P. C.; Turner, A. R.; Cooper, D. L.; Schultz, D. R.; Rakovic, M. J.; Fritsch, W.; Zygelman, B.

2001-05-01

Charge transfer processes due to collisions of ground state S^4+ ions with atomic helium were investigated for energies between 0.1 meV/u and 10 MeV/u. Total and state-selective cross sections and rate coefficients were obtained utilizing the quantum-mechanical molecular-orbital close-coupling (MOCC), atomic-orbital close-coupling, classical trajectory Monte Carlo (CTMC), and continuum distorted wave methods. The MOCC calculations utilized ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach. A number of variants of the CTMC approach were also explored. Previous data are limited to an earlier Landau-Zener calculation of the total rate coefficient for which our results are two orders of magnitude larger. An observed multichannel interference effect in the MOCC results will also be discussed.

Radiative-emission analysis in charge-exchange collisions of O6 + with argon, water, and methane

NASA Astrophysics Data System (ADS)

Leung, Anthony C. K.; Kirchner, Tom

2017-04-01

Processes of electron capture followed by Auger and radiative decay were investigated in slow ion-atom and -molecule collisions. A quantum-mechanical analysis which utilizes the basis generator method within an independent electron model was carried out for collisions of O 6 + with Ar, H2O , and CH4 at impact energies of 1.17 and 2.33 keV/amu. At these impact energies, a closure approximation in the spectral representation of the Hamiltonian for molecules was found to be necessary to yield reliable results. Total single-, double-, and triple-electron-capture cross sections obtained show good agreement with previous measurements and calculations using the classical trajectory Monte Carlo method. The corresponding emission spectra from single capture for each collision system are in satisfactory agreement with previous calculations.

Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions. II. A simplified implementation.

PubMed

Tao, Guohua; Miller, William H

2012-09-28

An efficient time-dependent (TD) Monte Carlo (MC) importance sampling method has recently been developed [G. Tao and W. H. Miller, J. Chem. Phys. 135, 024104 (2011)] for the evaluation of time correlation functions using the semiclassical (SC) initial value representation (IVR) methodology. In this TD-SC-IVR method, the MC sampling uses information from both time-evolved phase points as well as their initial values, and only the "important" trajectories are sampled frequently. Even though the TD-SC-IVR was shown in some benchmark examples to be much more efficient than the traditional time-independent sampling method (which uses only initial conditions), the calculation of the SC prefactor-which is computationally expensive, especially for large systems-is still required for accepted trajectories. In the present work, we present an approximate implementation of the TD-SC-IVR method that is completely prefactor-free; it gives the time correlation function as a classical-like magnitude function multiplied by a phase function. Application of this approach to flux-flux correlation functions (which yield reaction rate constants) for the benchmark H + H(2) system shows very good agreement with exact quantum results. Limitations of the approximate approach are also discussed.

Monte Carlo algorithms for Brownian phylogenetic models.

PubMed

Horvilleur, Benjamin; Lartillot, Nicolas

2014-11-01

Brownian models have been introduced in phylogenetics for describing variation in substitution rates through time, with applications to molecular dating or to the comparative analysis of variation in substitution patterns among lineages. Thus far, however, the Monte Carlo implementations of these models have relied on crude approximations, in which the Brownian process is sampled only at the internal nodes of the phylogeny or at the midpoints along each branch, and the unknown trajectory between these sampled points is summarized by simple branchwise average substitution rates. A more accurate Monte Carlo approach is introduced, explicitly sampling a fine-grained discretization of the trajectory of the (potentially multivariate) Brownian process along the phylogeny. Generic Monte Carlo resampling algorithms are proposed for updating the Brownian paths along and across branches. Specific computational strategies are developed for efficient integration of the finite-time substitution probabilities across branches induced by the Brownian trajectory. The mixing properties and the computational complexity of the resulting Markov chain Monte Carlo sampler scale reasonably with the discretization level, allowing practical applications with up to a few hundred discretization points along the entire depth of the tree. The method can be generalized to other Markovian stochastic processes, making it possible to implement a wide range of time-dependent substitution models with well-controlled computational precision. The program is freely available at www.phylobayes.org. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Wigner phase space distribution via classical adiabatic switching

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

Bose, Amartya; Makri, Nancy; Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801

2015-09-21

Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if themore » perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.« less

Interpolating moving least-squares methods for fitting potential energy surfaces: using classical trajectories to explore configuration space.

PubMed

Dawes, Richard; Passalacqua, Alessio; Wagner, Albert F; Sewell, Thomas D; Minkoff, Michael; Thompson, Donald L

2009-04-14

We develop two approaches for growing a fitted potential energy surface (PES) by the interpolating moving least-squares (IMLS) technique using classical trajectories. We illustrate both approaches by calculating nitrous acid (HONO) cis-->trans isomerization trajectories under the control of ab initio forces from low-level HF/cc-pVDZ electronic structure calculations. In this illustrative example, as few as 300 ab initio energy/gradient calculations are required to converge the isomerization rate constant at a fixed energy to approximately 10%. Neither approach requires any preliminary electronic structure calculations or initial approximate representation of the PES (beyond information required for trajectory initial conditions). Hessians are not required. Both approaches rely on the fitting error estimation properties of IMLS fits. The first approach, called IMLS-accelerated direct dynamics, propagates individual trajectories directly with no preliminary exploratory trajectories. The PES is grown "on the fly" with the computation of new ab initio data only when a fitting error estimate exceeds a prescribed tight tolerance. The second approach, called dynamics-driven IMLS fitting, uses relatively inexpensive exploratory trajectories to both determine and fit the dynamically accessible configuration space. Once exploratory trajectories no longer find configurations with fitting error estimates higher than the designated accuracy, the IMLS fit is considered to be complete and usable in classical trajectory calculations or other applications.

Zero-point energy constraint in quasi-classical trajectory calculations.

PubMed

Xie, Zhen; Bowman, Joel M

2006-04-27

A method to constrain the zero-point energy in quasi-classical trajectory calculations is proposed and applied to the Henon-Heiles system. The main idea of this method is to smoothly eliminate the coupling terms in the Hamiltonian as the energy of any mode falls below a specified value.

Trajectory-Based Loads for the Ares I-X Test Flight Vehicle

NASA Technical Reports Server (NTRS)

Vause, Roland F.; Starr, Brett R.

2011-01-01

In trajectory-based loads, the structural engineer treats each point on the trajectory as a load case. Distributed aero, inertial, and propulsion forces are developed for the structural model which are equivalent to the integrated values of the trajectory model. Free-body diagrams are then used to solve for the internal forces, or loads, that keep the applied aero, inertial, and propulsion forces in dynamic equilibrium. There are several advantages to using trajectory-based loads. First, consistency is maintained between the integrated equilibrium equations of the trajectory analysis and the distributed equilibrium equations of the structural analysis. Second, the structural loads equations are tied to the uncertainty model for the trajectory systems analysis model. Atmosphere, aero, propulsion, mass property, and controls uncertainty models all feed into the dispersions that are generated for the trajectory systems analysis model. Changes in any of these input models will affect structural loads response. The trajectory systems model manages these inputs as well as the output from the structural model over thousands of dispersed cases. Large structural models with hundreds of thousands of degrees of freedom would execute too slowly to be an efficient part of several thousand system analyses. Trajectory-based loads provide a means for the structures discipline to be included in the integrated systems analysis. Successful applications of trajectory-based loads methods for the Ares I-X vehicle are covered in this paper. Preliminary design loads were based on 2000 trajectories using Monte Carlo dispersions. Range safety loads were tied to 8423 malfunction turn trajectories. In addition, active control system loads were based on 2000 preflight trajectories using Monte Carlo dispersions.

Zero-Point Energy Constraint for Unimolecular Dissociation Reactions. Giving Trajectories Multiple Chances To Dissociate Correctly.

PubMed

Paul, Amit K; Hase, William L

2016-01-28

A zero-point energy (ZPE) constraint model is proposed for classical trajectory simulations of unimolecular decomposition and applied to CH4* → H + CH3 decomposition. With this model trajectories are not allowed to dissociate unless they have ZPE in the CH3 product. If not, they are returned to the CH4* region of phase space and, if necessary, given additional opportunities to dissociate with ZPE. The lifetime for dissociation of an individual trajectory is the time it takes to dissociate with ZPE in CH3, including multiple possible returns to CH4*. With this ZPE constraint the dissociation of CH4* is exponential in time as expected for intrinsic RRKM dynamics and the resulting rate constant is in good agreement with the harmonic quantum value of RRKM theory. In contrast, a model that discards trajectories without ZPE in the reaction products gives a CH4* → H + CH3 rate constant that agrees with the classical and not quantum RRKM value. The rate constant for the purely classical simulation indicates that anharmonicity may be important and the rate constant from the ZPE constrained classical trajectory simulation may not represent the complete anharmonicity of the RRKM quantum dynamics. The ZPE constraint model proposed here is compared with previous models for restricting ZPE flow in intramolecular dynamics, and connecting product and reactant/product quantum energy levels in chemical dynamics simulations.

Backward and forward Monte Carlo method for vector radiative transfer in a two-dimensional graded index medium

NASA Astrophysics Data System (ADS)

Qian, Lin-Feng; Shi, Guo-Dong; Huang, Yong; Xing, Yu-Ming

2017-10-01

In vector radiative transfer, backward ray tracing is seldom used. We present a backward and forward Monte Carlo method to simulate vector radiative transfer in a two-dimensional graded index medium, which is new and different from the conventional Monte Carlo method. The backward and forward Monte Carlo method involves dividing the ray tracing into two processes backward tracing and forward tracing. In multidimensional graded index media, the trajectory of a ray is usually a three-dimensional curve. During the transport of a polarization ellipse, the curved ray trajectory will induce geometrical effects and cause Stokes parameters to continuously change. The solution processes for a non-scattering medium and an anisotropic scattering medium are analysed. We also analyse some parameters that influence the Stokes vector in two-dimensional graded index media. The research shows that the Q component of the Stokes vector cannot be ignored. However, the U and V components of the Stokes vector are very small.

Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects

NASA Astrophysics Data System (ADS)

Smith, Brendan; Akimov, Alexey V.

2018-04-01

A simple and robust methodology, dubbed Entangled Trajectories Hamiltonian Dynamics (ETHD), is developed to capture quantum nuclear effects such as tunneling and zero-point energy through the coupling of multiple classical trajectories. The approach reformulates the classically mapped second-order Quantized Hamiltonian Dynamics (QHD-2) in terms of coupled classical trajectories. The method partially enforces the uncertainty principle and facilitates tunneling. The applicability of the method is demonstrated by studying the dynamics in symmetric double well and cubic metastable state potentials. The methodology is validated using exact quantum simulations and is compared to QHD-2. We illustrate its relationship to the rigorous Bohmian quantum potential approach, from which ETHD can be derived. Our simulations show a remarkable agreement of the ETHD calculation with the quantum results, suggesting that ETHD may be a simple and inexpensive way of including quantum nuclear effects in molecular dynamics simulations.

Continuous quantum measurement and the quantum to classical transition

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

Bhattacharya, Tanmoy; Habib, Salman; Jacobs, Kurt

2003-04-01

While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantum mechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. 85, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes that affect all macroscopic systems are taken into account, quantum mechanics indeed predicts the emergence of classical motion. We derive inequalities thatmore » describe the parameter regime in which classical motion is obtained, and provide numerical examples. We also demonstrate two further important properties of the classical limit: first, that multiple observers all agree on the motion of an object, and second, that classical statistical inference may be used to correctly track the classical motion.« less

Vectorization of a classical trajectory code on a floating point systems, Inc. Model 164 attached processor.

PubMed

Kraus, Wayne A; Wagner, Albert F

1986-04-01

A triatomic classical trajectory code has been modified by extensive vectorization of the algorithms to achieve much improved performance on an FPS 164 attached processor. Extensive timings on both the FPS 164 and a VAX 11/780 with floating point accelerator are presented as a function of the number of trajectories simultaneously run. The timing tests involve a potential energy surface of the LEPS variety and trajectories with 1000 time steps. The results indicate that vectorization results in timing improvements on both the VAX and the FPS. For larger numbers of trajectories run simultaneously, up to a factor of 25 improvement in speed occurs between VAX and FPS vectorized code. Copyright © 1986 John Wiley & Sons, Inc.

Mission Analysis, Operations, and Navigation Toolkit Environment (Monte) Version 040

NASA Technical Reports Server (NTRS)

Sunseri, Richard F.; Wu, Hsi-Cheng; Evans, Scott E.; Evans, James R.; Drain, Theodore R.; Guevara, Michelle M.

2012-01-01

Monte is a software set designed for use in mission design and spacecraft navigation operations. The system can process measurement data, design optimal trajectories and maneuvers, and do orbit determination, all in one application. For the first time, a single software set can be used for mission design and navigation operations. This eliminates problems due to different models and fidelities used in legacy mission design and navigation software. The unique features of Monte 040 include a blowdown thruster model for GRAIL (Gravity Recovery and Interior Laboratory) with associated pressure models, as well as an updated, optimalsearch capability (COSMIC) that facilitated mission design for ARTEMIS. Existing legacy software lacked the capabilities necessary for these two missions. There is also a mean orbital element propagator and an osculating to mean element converter that allows long-term orbital stability analysis for the first time in compiled code. The optimized trajectory search tool COSMIC allows users to place constraints and controls on their searches without any restrictions. Constraints may be user-defined and depend on trajectory information either forward or backwards in time. In addition, a long-term orbit stability analysis tool (morbiter) existed previously as a set of scripts on top of Monte. Monte is becoming the primary tool for navigation operations, a core competency at JPL. The mission design capabilities in Monte are becoming mature enough for use in project proposals as well as post-phase A mission design. Monte has three distinct advantages over existing software. First, it is being developed in a modern paradigm: object- oriented C++ and Python. Second, the software has been developed as a toolkit, which allows users to customize their own applications and allows the development team to implement requirements quickly, efficiently, and with minimal bugs. Finally, the software is managed in accordance with the CMMI (Capability Maturity Model Integration), where it has been ap praised at maturity level 3.

The effect of the charge exchange source on the velocity and 'temperature' distributions and their anisotropies in the earth's exosphere

NASA Technical Reports Server (NTRS)

Hodges, R. R., Jr.; Rohrbaugh, R. P.; Tinsley, B. A.

1981-01-01

The velocity distribution of atomic hydrogen in the earth's exosphere is calculated as a function of altitude and direction taking into account both the classic exobase source and the higher-altitude plasmaspheric charge exchange source. Calculations are performed on the basis of a Monte Carlo technique in which random ballistic trajectories of individual atoms are traced through a three-dimensional grid of audit zones, at which relative concentrations and momentum or energy fluxes are obtained. In the case of the classical exobase source alone, the slope of the velocity distribution is constant only for the upward radial velocity component and increases dramatically with altitude for the incoming radial and transverse velocity components, resulting in a temperature decrease. The charge exchange source, which produces the satellite hydrogen component and the hot ballistic and escape components of the exosphere, is found to enhance the wings of the velocity distributions, however this effect is not sufficient to overcome the temperature decreases at altitudes above one earth radius. The resulting global model of the hydrogen exosphere may be used as a realistic basis for radiative transfer calculations.

Line mixing effects in isotropic Raman spectra of pure N{sub 2}: A classical trajectory study

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

Ivanov, Sergey V., E-mail: serg.vict.ivanov@gmail.com; Boulet, Christian; Buzykin, Oleg G.

2014-11-14

Line mixing effects in the Q branch of pure N{sub 2} isotropic Raman scattering are studied at room temperature using a classical trajectory method. It is the first study using an extended modified version of Gordon's classical theory of impact broadening and shift of rovibrational lines. The whole relaxation matrix is calculated using an exact 3D classical trajectory method for binary collisions of rigid N{sub 2} molecules employing the most up-to-date intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve off-diagonal cross-sections to make them obeying exactly the principle of detailed balance. The adequacy of themore » results is confirmed by the sum rule. The comparison is made with available experimental data as well as with benchmark fully quantum close coupling [F. Thibault, C. Boulet, and Q. Ma, J. Chem. Phys. 140, 044303 (2014)] and refined semi-classical Robert-Bonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semi-classical) were made using the same PES. The agreement between classical and quantum relaxation matrices is excellent, opening the way to the analysis of more complex molecular systems.« less

Determination of the absolute carrier-envelope phase by angle-resolved photoelectron spectra of Ar by intense circularly polarized few-cycle pulses

NASA Astrophysics Data System (ADS)

Fukahori, Shinichi; Ando, Toshiaki; Miura, Shun; Kanya, Reika; Yamanouchi, Kaoru; Rathje, Tim; Paulus, Gerhard G.

2017-05-01

The angle-resolved photoelectron spectra of Ar are recorded using intense circularly polarized near-infrared few-cycle laser pulses, and the effect of the depletion of Ar atoms by the ionization and the effect of the Coulombic potential are examined by the classical trajectory Monte Carlo simulations. On the basis of the comparison between the experimental and theoretical photoelectron spectra, a procedure for estimating the absolute carrier-envelope phase (CEP) of the few-cycle laser pulses interacting with atoms and molecules is proposed. It is confirmed that the absolute CEP can securely be estimated without any numerical calculations once the angular distribution of the yield of photoelectrons having the kinetic energy larger than 30 eV is measured with the peak laser intensity in the range between 1 ×1014 and 5 ×1014W /c m2 .

Energy-dependent angular shifts in the photoelectron momentum distribution for atoms in elliptically polarized laser pulses

NASA Astrophysics Data System (ADS)

Xie, Hui; Li, Min; Luo, Siqiang; Li, Yang; Zhou, Yueming; Cao, Wei; Lu, Peixiang

2017-12-01

We measure the photoelectron momentum distributions from atoms ionized by strong elliptically polarized laser fields at the wavelengths of 400 and 800 nm, respectively. The momentum distributions show distinct angular shifts, which sensitively depend on the electron energy. We find that the deflection angle with respect to the major axis of the laser ellipse decreases with the increase of the electron energy for large ellipticities. This energy-dependent angular shift is well reproduced by both numerical solutions of the time-dependent Schrödinger equation and the classical-trajectory Monte Carlo model. We show that the ionization time delays among the electrons with different energies are responsible for the energy-dependent angular shifts. On the other hand, for small ellipticities, we find the deflection angle increases with increasing the electron energy, which might be caused by electron rescattering in the elliptically polarized fields.

Aerocapture Performance Analysis for a Neptune-Triton Exploration Mission

NASA Technical Reports Server (NTRS)

Starr, Brett R.; Westhelle, Carlos H.; Masciarelli, James P.

2004-01-01

A systems analysis has been conducted for a Neptune-Triton Exploration Mission in which aerocapture is used to capture a spacecraft at Neptune. Aerocapture uses aerodynamic drag instead of propulsion to decelerate from the interplanetary approach trajectory to a captured orbit during a single pass through the atmosphere. After capture, propulsion is used to move the spacecraft from the initial captured orbit to the desired science orbit. A preliminary assessment identified that a spacecraft with a lift to drag ratio of 0.8 was required for aerocapture. Performance analyses of the 0.8 L/D vehicle were performed using a high fidelity flight simulation within a Monte Carlo executive to determine mission success statistics. The simulation was the Program to Optimize Simulated Trajectories (POST) modified to include Neptune specific atmospheric and planet models, spacecraft aerodynamic characteristics, and interplanetary trajectory models. To these were added autonomous guidance and pseudo flight controller models. The Monte Carlo analyses incorporated approach trajectory delivery errors, aerodynamic characteristics uncertainties, and atmospheric density variations. Monte Carlo analyses were performed for a reference set of uncertainties and sets of uncertainties modified to produce increased and reduced atmospheric variability. For the reference uncertainties, the 0.8 L/D flatbottom ellipsled vehicle achieves 100% successful capture and has a 99.87 probability of attaining the science orbit with a 360 m/s V budget for apoapsis and periapsis adjustment. Monte Carlo analyses were also performed for a guidance system that modulates both bank angle and angle of attack with the reference set of uncertainties. An alpha and bank modulation guidance system reduces the 99.87 percentile DELTA V 173 m/s (48%) to 187 m/s for the reference set of uncertainties.

Quantum speedup of Monte Carlo methods.

PubMed

Montanaro, Ashley

2015-09-08

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

Quantum speedup of Monte Carlo methods

PubMed Central

Montanaro, Ashley

2015-01-01

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently. PMID:26528079

Fast alternative Monte Carlo formalism for a class of problems in biophotonics

NASA Astrophysics Data System (ADS)

Miller, Steven D.

1997-12-01

A practical and effective, alternative Monte Carlo formalism is presented that rapidly finds flux solutions to the radiative transport equation for a class of problems in biophotonics; namely, wide-beam irradiance of finite, optically anisotropic homogeneous or heterogeneous biomedias, which both strongly scatter and absorb light. Such biomedias include liver, tumors, blood, or highly blood perfused tissues. As Fermat rays comprising a wide coherent (laser) beam enter the tissue, they evolve into a bundle of random optical paths or trajectories due to scattering. Overall, this can be physically interpreted as a bundle of Markov trajectories traced out by a 'gas' of Brownian-like point photons being successively scattered and absorbed. By considering the cumulative flow of a statistical bundle of trajectories through interior data planes, the effective equivalent information of the (generally unknown) analytical flux solutions of the transfer equation rapidly emerges. Unlike the standard Monte Carlo techniques, which evaluate scalar fluence, this technique is faster, more efficient, and simpler to apply for this specific class of optical situations. Other analytical or numerical techniques can either become unwieldy or lack viability or are simply more difficult to apply. Illustrative flux calculations are presented for liver, blood, and tissue-tumor-tissue systems.

An ab initio chemical reaction model for the direct simulation Monte Carlo study of non-equilibrium nitrogen flows.

PubMed

Mankodi, T K; Bhandarkar, U V; Puranik, B P

2017-08-28

A new ab initio based chemical model for a Direct Simulation Monte Carlo (DSMC) study suitable for simulating rarefied flows with a high degree of non-equilibrium is presented. To this end, Collision Induced Dissociation (CID) cross sections for N 2 +N 2 →N 2 +2N are calculated and published using a global complete active space self-consistent field-complete active space second order perturbation theory N 4 potential energy surface and quasi-classical trajectory algorithm for high energy collisions (up to 30 eV). CID cross sections are calculated for only a selected set of ro-vibrational combinations of the two nitrogen molecules, and a fitting scheme based on spectroscopic weights is presented to interpolate the CID cross section for all possible ro-vibrational combinations. The new chemical model is validated by calculating equilibrium reaction rate coefficients that can be compared well with existing shock tube and computational results. High-enthalpy hypersonic nitrogen flows around a cylinder in the transition flow regime are simulated using DSMC to compare the predictions of the current ab initio based chemical model with the prevailing phenomenological model (the total collision energy model). The differences in the predictions are discussed.

Liouville master equation for multielectron dynamics: Neutralization of highly charged ions near a LiF surface

NASA Astrophysics Data System (ADS)

Wirtz, Ludger; Reinhold, Carlos O.; Lemell, Christoph; Burgdörfer, Joachim

2003-01-01

We present a simulation of the neutralization of highly charged ions in front of a lithium fluoride surface including the close-collision regime above the surface. The present approach employs a Monte Carlo solution of the Liouville master equation for the joint probability density of the ionic motion and the electronic population of the projectile and the target surface. It includes single as well as double particle-hole (de)excitation processes and incorporates electron correlation effects through the conditional dynamics of population strings. The input in terms of elementary one- and two-electron transfer rates is determined from classical trajectory Monte Carlo calculations as well as quantum-mechanical Auger calculations. For slow projectiles and normal incidence, the ionic motion depends sensitively on the interplay between image acceleration towards the surface and repulsion by an ensemble of positive hole charges in the surface (“trampoline effect”). For Ne10+ we find that image acceleration is dominant and no collective backscattering high above the surface takes place. For grazing incidence, our simulation delineates the pathways to complete neutralization. In accordance with recent experimental observations, most ions are reflected as neutral or even as singly charged negative particles, irrespective of the charge state of the incoming ions.

Dose calculation of dynamic trajectory radiotherapy using Monte Carlo.

PubMed

Manser, P; Frauchiger, D; Frei, D; Volken, W; Terribilini, D; Fix, M K

2018-04-06

Using volumetric modulated arc therapy (VMAT) delivery technique gantry position, multi-leaf collimator (MLC) as well as dose rate change dynamically during the application. However, additional components can be dynamically altered throughout the dose delivery such as the collimator or the couch. Thus, the degrees of freedom increase allowing almost arbitrary dynamic trajectories for the beam. While the dose delivery of such dynamic trajectories for linear accelerators is technically possible, there is currently no dose calculation and validation tool available. Thus, the aim of this work is to develop a dose calculation and verification tool for dynamic trajectories using Monte Carlo (MC) methods. The dose calculation for dynamic trajectories is implemented in the previously developed Swiss Monte Carlo Plan (SMCP). SMCP interfaces the treatment planning system Eclipse with a MC dose calculation algorithm and is already able to handle dynamic MLC and gantry rotations. Hence, the additional dynamic components, namely the collimator and the couch, are described similarly to the dynamic MLC by defining data pairs of positions of the dynamic component and the corresponding MU-fractions. For validation purposes, measurements are performed with the Delta4 phantom and film measurements using the developer mode on a TrueBeam linear accelerator. These measured dose distributions are then compared with the corresponding calculations using SMCP. First, simple academic cases applying one-dimensional movements are investigated and second, more complex dynamic trajectories with several simultaneously moving components are compared considering academic cases as well as a clinically motivated prostate case. The dose calculation for dynamic trajectories is successfully implemented into SMCP. The comparisons between the measured and calculated dose distributions for the simple as well as for the more complex situations show an agreement which is generally within 3% of the maximum dose or 3mm. The required computation time for the dose calculation remains the same when the additional dynamic moving components are included. The results obtained for the dose comparisons for simple and complex situations suggest that the extended SMCP is an accurate dose calculation and efficient verification tool for dynamic trajectory radiotherapy. This work was supported by Varian Medical Systems. Copyright © 2018. Published by Elsevier GmbH.

Quantum-Classical Correspondence Principle for Work Distributions

NASA Astrophysics Data System (ADS)

Jarzynski, Christopher; Quan, H. T.; Rahav, Saar

2015-07-01

For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. This definition leads to statistical distributions of work that satisfy nonequilibrium work and fluctuation relations. While this two-point measurement definition of quantum work can be justified heuristically by appeal to the first law of thermodynamics, its relationship to the classical definition of work has not been carefully examined. In this paper, we employ semiclassical methods, combined with numerical simulations of a driven quartic oscillator, to study the correspondence between classical and quantal definitions of work in systems with 1 degree of freedom. We find that a semiclassical work distribution, built from classical trajectories that connect the initial and final energies, provides an excellent approximation to the quantum work distribution when the trajectories are assigned suitable phases and are allowed to interfere. Neglecting the interferences between trajectories reduces the distribution to that of the corresponding classical process. Hence, in the semiclassical limit, the quantum work distribution converges to the classical distribution, decorated by a quantum interference pattern. We also derive the form of the quantum work distribution at the boundary between classically allowed and forbidden regions, where this distribution tunnels into the forbidden region. Our results clarify how the correspondence principle applies in the context of quantum and classical work distributions and contribute to the understanding of work and nonequilibrium work relations in the quantum regime.

Mapping quantum-classical Liouville equation: projectors and trajectories.

PubMed

Kelly, Aaron; van Zon, Ramses; Schofield, Jeremy; Kapral, Raymond

2012-02-28

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility, and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.

Superintegrability of the Fock-Darwin system

NASA Astrophysics Data System (ADS)

Drigho-Filho, E.; Kuru, Ş.; Negro, J.; Nieto, L. M.

2017-08-01

The Fock-Darwin system is analyzed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one.

Anosov C-systems and random number generators

NASA Astrophysics Data System (ADS)

Savvidy, G. K.

2016-08-01

We further develop our previous proposal to use hyperbolic Anosov C-systems to generate pseudorandom numbers and to use them for efficient Monte Carlo calculations in high energy particle physics. All trajectories of hyperbolic dynamical systems are exponentially unstable, and C-systems therefore have mixing of all orders, a countable Lebesgue spectrum, and a positive Kolmogorov entropy. These exceptional ergodic properties follow from the C-condition introduced by Anosov. This condition defines a rich class of dynamical systems forming an open set in the space of all dynamical systems. An important property of C-systems is that they have a countable set of everywhere dense periodic trajectories and their density increases exponentially with entropy. Of special interest are the C-systems defined on higher-dimensional tori. Such C-systems are excellent candidates for generating pseudorandom numbers that can be used in Monte Carlo calculations. An efficient algorithm was recently constructed that allows generating long C-system trajectories very rapidly. These trajectories have good statistical properties and can be used for calculations in quantum chromodynamics and in high energy particle physics.

The Identification of the Mediterranean cyclones main classical trajectories towards Romania by using objective methods based on mathematical algorithms

NASA Astrophysics Data System (ADS)

Oana, Catrina; Parding, Kajsa Maria; Stefan, Sabina

2017-04-01

The importance of knowledge on the trajectories that Mediterranean cyclones follows toward Romania is fundamental because most of the times the weather phenomena that accompany them determine significant economic damage and not only. In the specialized literature, the principal classic trajectories on which the Mediterranean cyclones pass toward the south-east of Europe and by default toward Romania, causing in these areas a crucial weather conditions change in all aspects at any time during the year, have been determined in subjectively mode, many years ago, by C. Sorodoc (1962) E. I. Bordei (1983). Starting from the known 9 classic trajectories determined subjectively, in this study it was aimed and subsequently carried out their identification by this date, but objectively, using the method based on mathematic algorithms developed by Rasmus E. Benestad, Abdelkader Mezghani, and Kajsa M. Parding (2006). The study was carried out between January 2003 and December 2015, taking into account the fact that the presence of the Mediterranean cyclones may be established almost every month, these representing important links of the atmosphere movement over Europe. The data used by the daily review have contained values, in grid points, of the mean pressure field at sea level (MSLP), with spatial resolution of 0.75° x 0.75° and 6 hours temporal coverage, originating from ECMWF, ERA-Interim project (2006), and the chosen field of interest was between 15°W - 40°E and 30°N - 50°N. Of the total number of Mediterranean cyclones identified objectively, that followed trajectories toward Romania, were randomly selected only a few cases, which indicates the similarity between the paths of classic subjectively determined and those determined objectively. Validation of the results consisted in the first phase in a comparison between the trajectories identified with the classic trajectories determined subjectively, then was carried out a second validation, by analysis of the MSLP field, geopotential height and potential vorticity. As a conclusion, the results obtained highlights certainly reliability but especially the usefulness of the objective method used, in particular in carrying out the complex Mediterranean climatology studies and not only.

Validity of the classical monte carlo method to model the magnetic properties of a large transition-metal cluster: Mn19.

PubMed

Lima, Nicola; Caneschi, Andrea; Gatteschi, Dante; Kritikos, Mikael; Westin, L Gunnar

2006-03-20

The susceptibility of the large transition-metal cluster [Mn19O12(MOE)14(MOEH)10].MOEH (MOE = OC2H2O-CH3) has been fitted through classical Monte Carlo simulation, and an estimation of the exchange coupling constants has been done. With these results, it has been possible to perform a full-matrix diagonalization of the cluster core, which was used to provide information on the nature of the low-lying levels.

Ultraviolet and Visible Emission Mechanisms in Astrophysics

NASA Technical Reports Server (NTRS)

Stancil, Phillip C.; Schultz, David R.

2003-01-01

The project involved the study of ultraviolet (UV) and visible emission mechanisms in astrophysical and atmospheric environments. In many situations, the emission is a direct consequence of a charge transferring collision of an ion with a neutral with capture of an electron to an excited state of the product ion. The process is also important in establishing the ionization and thermal balance of an astrophysical plasma. As little of the necessary collision data are available, the main thrust of the project was the calculation of total and state-selective charge transfer cross sections and rate coefficients for a very large number of collision systems. The data was computed using modern explicit techniques including the molecular-orbital close-coupling (MOCC), classical trajectory Monte Carlo (CTMC), and continuum distorted wave (CDW) methods. Estimates were also made in some instances using the multichannel Landau-Zener (MCLZ) and classical over-the-barrier (COB) models. Much of the data which has been computed has been formatted for inclusion in a charge transfer database on the World Wide Web (cfadc.phy.ornl.gov/astro/ps/data/). A considerable amount of data has been generated during the lifetime of the grant. Some of it has not been analyzed, but it will be as soon as possible, the data placed on our website, and papers ultimately written.

Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

NASA Astrophysics Data System (ADS)

Bernardini, A. E.; Leal, P.; Bertolami, O.

2018-02-01

A quasi-Gaussian quantum superposition of Hořava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed Wigner function and its associated Wigner currents describe the conditions for the matching between classical and quantum phase-space trajectories. The matching quantum superposition parameter is associated to the total energy of the classical trajectory which, at the same time, drives the engendered Wigner function to the classical stationary regime. Through the analysis of the Wigner flows, the quantum fluctuations that distort the classical regime can be quantified as a measure of (non)classicality. Finally, the modifications to the Wigner currents due to the inclusion of perturbative potentials are computed in the HL quantum cosmological context. In particular, the inclusion of a cosmological constant provides complementary information that allows for connecting the age of the Universe with the overall stiff matter density profile.

Monte Carlo tree search -based non-coplanar trajectory design for station parameter optimized radiation therapy (SPORT).

PubMed

Dong, Peng; Liu, Hongcheng; Xing, Lei

2018-06-04

An important yet challenging problem in LINAC-based rotational arc radiation therapy is the design of beam trajectory, which requires simultaneous consideration of delivery efficiency and final dose distribution. In this work, we propose a novel trajectory selection strategy by developing a Monte Carlo tree search (MCTS) algorithm during the beam trajectory selection process. Methods: To search through the vast number of possible trajectories, MCTS algorithm was implemented. In this approach, a candidate trajectory is explored by starting from a leaf node and sequentially examining the next level of linked nodes with consideration of geometric and physical constraints. The maximum Upper Confidence Bounds for Trees, which is a function of average objective function value and the number of times the node under testing has been visited, was employed to intelligently select the trajectory. For each candidate trajectory, we run an inverse fluence map optimization with an infinity norm regularization. The ranking of the plan as measured by the corresponding objective function value was then fed back to update the statistics of the nodes on the trajectory. The method was evaluated with a chest wall and a brain case, and the results were compared with the coplanar and noncoplanar 4pi beam configurations. Results: For both clinical cases, the MCTS method found effective and easy-to-deliver trajectories within an hour. As compared with the coplanar plans, it offers much better sparing of the OARs while maintaining the PTV coverage. The quality of the MCTS-generated plan is found to be comparable to the 4pi plans. Conclusion: AI based on MCTS is valuable to facilitate the design of beam trajectory and paves the way for future clinical use of non-coplanar treatment delivery. . © 2018 Institute of Physics and Engineering in Medicine.

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

NASA Astrophysics Data System (ADS)

Schulte, J.

1993-03-01

The thermodynamic stability of4He4-13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.

Analysis and modeling of localized heat generation by tumor-targeted nanoparticles (Monte Carlo methods)

NASA Astrophysics Data System (ADS)

Sanattalab, Ehsan; SalmanOgli, Ahmad; Piskin, Erhan

2016-04-01

We investigated the tumor-targeted nanoparticles that influence heat generation. We suppose that all nanoparticles are fully functionalized and can find the target using active targeting methods. Unlike the commonly used methods, such as chemotherapy and radiotherapy, the treatment procedure proposed in this study is purely noninvasive, which is considered to be a significant merit. It is found that the localized heat generation due to targeted nanoparticles is significantly higher than other areas. By engineering the optical properties of nanoparticles, including scattering, absorption coefficients, and asymmetry factor (cosine scattering angle), the heat generated in the tumor's area reaches to such critical state that can burn the targeted tumor. The amount of heat generated by inserting smart agents, due to the surface Plasmon resonance, will be remarkably high. The light-matter interactions and trajectory of incident photon upon targeted tissues are simulated by MIE theory and Monte Carlo method, respectively. Monte Carlo method is a statistical one by which we can accurately probe the photon trajectories into a simulation area.

A users' manual for MCPRAM (Monte Carlo PReprocessor for AMEER) and for the fuze options in AMEER (Aero Mechanical Equation Evaluation Routines)

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

LaFarge, R.A.

1990-05-01

MCPRAM (Monte Carlo PReprocessor for AMEER), a computer program that uses Monte Carlo techniques to create an input file for the AMEER trajectory code, has been developed for the Sandia National Laboratories VAX and Cray computers. Users can select the number of trajectories to compute, which AMEER variables to investigate, and the type of probability distribution for each variable. Any legal AMEER input variable can be investigated anywhere in the input run stream with either a normal, uniform, or Rayleigh distribution. Users also have the option to use covariance matrices for the investigation of certain correlated variables such as boostermore » pre-reentry errors and wind, axial force, and atmospheric models. In conjunction with MCPRAM, AMEER was modified to include the variables introduced by the covariance matrices and to include provisions for six types of fuze models. The new fuze models and the new AMEER variables are described in this report.« less

Quantum Gibbs ensemble Monte Carlo

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

Fantoni, Riccardo, E-mail: rfantoni@ts.infn.it; Moroni, Saverio, E-mail: moroni@democritos.it

We present a path integral Monte Carlo method which is the full quantum analogue of the Gibbs ensemble Monte Carlo method of Panagiotopoulos to study the gas-liquid coexistence line of a classical fluid. Unlike previous extensions of Gibbs ensemble Monte Carlo to include quantum effects, our scheme is viable even for systems with strong quantum delocalization in the degenerate regime of temperature. This is demonstrated by an illustrative application to the gas-superfluid transition of {sup 4}He in two dimensions.

Chaotic scattering in an open vase-shaped cavity: Topological, numerical, and experimental results

NASA Astrophysics Data System (ADS)

Novick, Jaison Allen

We present a study of trajectories in a two-dimensional, open, vase-shaped cavity in the absence of forces The classical trajectories freely propagate between elastic collisions. Bound trajectories, regular scattering trajectories, and chaotic scattering trajectories are present in the vase. Most importantly, we find that classical trajectories passing through the vase's mouth escape without return. In our simulations, we propagate bursts of trajectories from point sources located along the vase walls. We record the time for escaping trajectories to pass through the vase's neck. Constructing a plot of escape time versus the initial launch angle for the chaotic trajectories reveals a vastly complicated recursive structure or a fractal. This fractal structure can be understood by a suitable coordinate transform. Reducing the dynamics to two dimensions reveals that the chaotic dynamics are organized by a homoclinic tangle, which is formed by the union of infinitely long, intersecting stable and unstable manifolds. This study is broken down into three major components. We first present a topological theory that extracts the essential topological information from a finite subset of the tangle and encodes this information in a set of symbolic dynamical equations. These equations can be used to predict a topologically forced minimal subset of the recursive structure seen in numerically computed escape time plots. We present three applications of the theory and compare these predictions to our simulations. The second component is a presentation of an experiment in which the vase was constructed from Teflon walls using an ultrasound transducer as a point source. We compare the escaping signal to a classical simulation and find agreement between the two. Finally, we present an approximate solution to the time independent Schrodinger Equation for escaping waves. We choose a set of points at which to evaluate the wave function and interpolate trajectories connecting the source point to each "detector point". We then construct the wave function directly from these classical trajectories using the two-dimensional WKB approximation. The wave function is Fourier Transformed using a Fast Fourier Transform algorithm resulting in a spectrum in which each peak corresponds to an interpolated trajectory. Our predictions are based on an imagined experiment that uses microwave propagation within an electromagnetic waveguide. Such an experiment exploits the fact that under suitable conditions both Maxwell's Equations and the Schrodinger Equation can be reduced to the Helmholtz Equation. Therefore, our predictions, while compared to the electromagnetic experiment, contain information about the quantum system. Identifying peaks in the transmission spectrum with chaotic trajectories will allow for an additional experimental verification of the intermediate recursive structure. Finally, we summarize our results and discuss possible extensions of this project.

Symmetrical windowing for quantum states in quasi-classical trajectory simulations: Application to electronically non-adiabatic processes

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

Cotton, Stephen J.; Miller, William H., E-mail: millerwh@berkeley.edu

A recently described symmetrical windowing methodology [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] for quasi-classical trajectory simulations is applied here to the Meyer-Miller [H.-D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] model for the electronic degrees of freedom in electronically non-adiabatic dynamics. Results generated using this classical approach are observed to be in very good agreement with accurate quantum mechanical results for a variety of test applications, including problems where coherence effects are significant such as the challenging asymmetric spin-boson system.

Monte-Carlo Method Application for Precising Meteor Velocity from TV Observations

NASA Astrophysics Data System (ADS)

Kozak, P.

2014-12-01

Monte-Carlo method (method of statistical trials) as an application for meteor observations processing was developed in author's Ph.D. thesis in 2005 and first used in his works in 2008. The idea of using the method consists in that if we generate random values of input data - equatorial coordinates of the meteor head in a sequence of TV frames - in accordance with their statistical distributions we get a possibility to plot the probability density distributions for all its kinematical parameters, and to obtain their mean values and dispersions. At that the theoretical possibility appears to precise the most important parameter - geocentric velocity of a meteor - which has the highest influence onto precision of meteor heliocentric orbit elements calculation. In classical approach the velocity vector was calculated in two stages: first we calculate the vector direction as a vector multiplication of vectors of poles of meteor trajectory big circles, calculated from two observational points. Then we calculated the absolute value of velocity independently from each observational point selecting any of them from some reasons as a final parameter. In the given method we propose to obtain a statistical distribution of velocity absolute value as an intersection of two distributions corresponding to velocity values obtained from different points. We suppose that such an approach has to substantially increase the precision of meteor velocity calculation and remove any subjective inaccuracies.

Modeling of molecular nitrogen collisions and dissociation processes for direct simulation Monte Carlo.

PubMed

Parsons, Neal; Levin, Deborah A; van Duin, Adri C T; Zhu, Tong

2014-12-21

The Direct Simulation Monte Carlo (DSMC) method typically used for simulating hypersonic Earth re-entry flows requires accurate total collision cross sections and reaction probabilities. However, total cross sections are often determined from extrapolations of relatively low-temperature viscosity data, so their reliability is unknown for the high temperatures observed in hypersonic flows. Existing DSMC reaction models accurately reproduce experimental equilibrium reaction rates, but the applicability of these rates to the strong thermal nonequilibrium observed in hypersonic shocks is unknown. For hypersonic flows, these modeling issues are particularly relevant for nitrogen, the dominant species of air. To rectify this deficiency, the Molecular Dynamics/Quasi-Classical Trajectories (MD/QCT) method is used to accurately compute collision and reaction cross sections for the N2(Σg+1)-N2(Σg+1) collision pair for conditions expected in hypersonic shocks using a new potential energy surface developed using a ReaxFF fit to recent advanced ab initio calculations. The MD/QCT-computed reaction probabilities were found to exhibit better physical behavior and predict less dissociation than the baseline total collision energy reaction model for strong nonequilibrium conditions expected in a shock. The MD/QCT reaction model compared well with computed equilibrium reaction rates and shock-tube data. In addition, the MD/QCT-computed total cross sections were found to agree well with established variable hard sphere total cross sections.

Monte Carlo chord length sampling for d-dimensional Markov binary mixtures

NASA Astrophysics Data System (ADS)

Larmier, Coline; Lam, Adam; Brantley, Patrick; Malvagi, Fausto; Palmer, Todd; Zoia, Andrea

2018-01-01

The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating on-the-fly the material interfaces seen by the random walkers during their trajectories. This annealed disorder approach, which formally consists of solving the approximate Levermore-Pomraning equations for linear particle transport, enables a considerable speed-up with respect to transport in quenched disorder, where ensemble-averaging of the Boltzmann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced by the spatial disorder, so that the accuracy of the solutions obtained by using this algorithm must be carefully verified with respect to reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, such comparisons have been attempted so far only for one-dimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in two-dimensional (extruded) and three-dimensional geometries, by revisiting the classical set of benchmark configurations originally proposed by Adams, Larsen and Pomraning [1] and extended by Brantley [2]. In particular, we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission/reflection coefficients as a function of the material properties of the benchmark specifications and of the system dimensionality.

Monte Carlo chord length sampling for d-dimensional Markov binary mixtures

DOE PAGES

Larmier, Coline; Lam, Adam; Brantley, Patrick; ...

2017-09-27

The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating on-the-fly the material interfaces seen by the random walkers during their trajectories. This annealed disorder approach, which formally consists of solving the approximate Levermore–Pomraning equations for linear particle transport, enables a considerable speed-up with respect to transport in quenched disorder, where ensemble-averaging of the Boltzmann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced by the spatial disorder, so that the accuracy of the solutions obtained by using thismore » algorithm must be carefully verified with respect to reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, such comparisons have been attempted so far only for one-dimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in two-dimensional (extruded) and three-dimensional geometries, by revisiting the classical set of benchmark configurations originally proposed by Adams, Larsen and Pomraning and extended by Brantley. In particular, we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission/reflection coefficients as a function of the material properties of the benchmark specifications and of the system dimensionality.« less

Monte Carlo chord length sampling for d-dimensional Markov binary mixtures

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

Larmier, Coline; Lam, Adam; Brantley, Patrick

The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating on-the-fly the material interfaces seen by the random walkers during their trajectories. This annealed disorder approach, which formally consists of solving the approximate Levermore–Pomraning equations for linear particle transport, enables a considerable speed-up with respect to transport in quenched disorder, where ensemble-averaging of the Boltzmann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced by the spatial disorder, so that the accuracy of the solutions obtained by using thismore » algorithm must be carefully verified with respect to reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, such comparisons have been attempted so far only for one-dimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in two-dimensional (extruded) and three-dimensional geometries, by revisiting the classical set of benchmark configurations originally proposed by Adams, Larsen and Pomraning and extended by Brantley. In particular, we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission/reflection coefficients as a function of the material properties of the benchmark specifications and of the system dimensionality.« less

Path integral Monte Carlo ground state approach: formalism, implementation, and applications

NASA Astrophysics Data System (ADS)

Yan, Yangqian; Blume, D.

2017-11-01

Monte Carlo techniques have played an important role in understanding strongly correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum mechanical systems, the path integral Monte Carlo approach with its variants has been employed widely. Since semi-classical or classical approaches will not be discussed in this review, path integral based approaches can for our purposes be divided into two categories: approaches applicable to quantum mechanical systems at zero temperature and approaches applicable to quantum mechanical systems at finite temperature. While these two approaches are related to each other, the underlying formulation and aspects of the algorithm differ. This paper reviews the path integral Monte Carlo ground state (PIGS) approach, which solves the time-independent Schrödinger equation. Specifically, the PIGS approach allows for the determination of expectation values with respect to eigen states of the few- or many-body Schrödinger equation provided the system Hamiltonian is known. The theoretical framework behind the PIGS algorithm, implementation details, and sample applications for fermionic systems are presented.

Charge transfer and ionization in collisions of Si3+ with H from low to high energy

NASA Astrophysics Data System (ADS)

Wang, J. G.; He, B.; Ning, Y.; Liu, C. L.; Yan, J.; Stancil, P. C.; Schultz, D. R.

2006-11-01

Charge transfer processes due to collisions of ground state Si3+(3sS1) ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) and classical-trajectory Monte Carlo (CTMC) methods. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained from Herrero [J. Phys. B 29, 5583 (1996)] which were calculated with a full configuration-interaction method. Total and state-selective single-electron capture cross sections are obtained for collision energies from 0.01eV/u to 1MeV/u . Total and state-selective rate coefficients are also presented for temperatures from 2×103K to 107K . Comparison with existing data reveals that the total CTMC cross sections are in good agreement with the experimental measurements at the higher considered energies and that previous Landau-Zener calculations underestimate the total rate coefficients by a factor of up to two. The CTMC calculations of target ionization are presented for high energies.

Charge Exchange of Ne^9+ for X-ray Emission

NASA Astrophysics Data System (ADS)

Lyons, David

2016-01-01

Using the molecular-orbital close-coupling (MOCC) method, single electron capture (SEC) cross sections were computed for Ne^9+ colliding with H.Potential energies and nonadiabatic couplings were calculated and used to obtain the MOCC cross sections which are final-quantum-state-resolved including a separation of singlet and triplet states. Atomic-orbital close-coupling, classical trajectory Monte Carlo, and multichannel Landau-Zener (MCLZ) calculations are also performed. Cross sections for more complicated targets including He, H2, N2, H2O, CO, and CO2, were obtained with the MCLZ method. The SEC results are compared with experimental and other theoretical data, where available. The SEC cross sections are being used in cascade models to predict X-ray emission spectra relevant to solar systemand astrophysical environments.D. Lyons, R. S. Cumbee, P. D. Mullen, P. C. Stancil (UGA), D. R. Schultz (UNT), P. Liebermann (Wuppertal Univ.),R. Buenker (NCSU).This work was partially supported by NASA grant NNX09AC46G.

n l -> n' l' transition rates in electron and proton - Rydberg atom collision

NASA Astrophysics Data System (ADS)

Vrinceanu, Daniel

2017-04-01

Electrons and protons drive the recombination dynamics of highly excited Rydberg atoms in cold rarefied plasmas found in astrophysical conditions such as primordial recombination or star formation in H-II clouds. It has been recognized that collisions induce both energy and angular momentum transitions in Rydberg atoms, although in different proportions, depending on the initial state, temperature and the given species considered in the collision (electron or proton). Most studies focused on one collision type at a time, under the assumption that collision types are independent or their effects are not competing. The classical Monte-Carlo trajectory simulations presented in this work calculate the rates for both energy and angular momentum transfers and show their interdependence. For example, energy transfer with small angular momentum change are more efficient for target states with initial large angular momentum. The author acknowledges support received from the National Science Foundation through a Grant for the Center for Research on Complex Networks (HRD-1137732).

Non-gaussian signatures of general inflationary trajectories

NASA Astrophysics Data System (ADS)

Horner, Jonathan S.; Contaldi, Carlo R.

2014-09-01

We carry out a numerical calculation of the bispectrum in generalised trajectories of canonical, single-field inflation. The trajectories are generated in the Hamilton-Jacobi (HJ) formalism based on Hubble Slow Roll (HSR) parameters. The calculation allows generally shape and scale dependent bispectra, or dimensionless fNL, in the out-of-slow-roll regime. The distributions of fNL for various shapes and HSR proposals are shown as an example of how this procedure can be used within the context of Monte Carlo exploration of inflationary trajectories. We also show how allowing out-of-slow-roll behaviour can lead to a bispectrum that is relatively large for equilateral shapes.

Uncertainty Optimization Applied to the Monte Carlo Analysis of Planetary Entry Trajectories

NASA Technical Reports Server (NTRS)

Olds, John; Way, David

2001-01-01

Recently, strong evidence of liquid water under the surface of Mars and a meteorite that might contain ancient microbes have renewed interest in Mars exploration. With this renewed interest, NASA plans to send spacecraft to Mars approx. every 26 months. These future spacecraft will return higher-resolution images, make precision landings, engage in longer-ranging surface maneuvers, and even return Martian soil and rock samples to Earth. Future robotic missions and any human missions to Mars will require precise entries to ensure safe landings near science objective and pre-employed assets. Potential sources of water and other interesting geographic features are often located near hazards, such as within craters or along canyon walls. In order for more accurate landings to be made, spacecraft entering the Martian atmosphere need to use lift to actively control the entry. This active guidance results in much smaller landing footprints. Planning for these missions will depend heavily on Monte Carlo analysis. Monte Carlo trajectory simulations have been used with a high degree of success in recent planetary exploration missions. These analyses ascertain the impact of off-nominal conditions during a flight and account for uncertainty. Uncertainties generally stem from limitations in manufacturing tolerances, measurement capabilities, analysis accuracies, and environmental unknowns. Thousands of off-nominal trajectories are simulated by randomly dispersing uncertainty variables and collecting statistics on forecast variables. The dependability of Monte Carlo forecasts, however, is limited by the accuracy and completeness of the assumed uncertainties. This is because Monte Carlo analysis is a forward driven problem; beginning with the input uncertainties and proceeding to the forecasts outputs. It lacks a mechanism to affect or alter the uncertainties based on the forecast results. If the results are unacceptable, the current practice is to use an iterative, trial-and-error approach to reconcile discrepancies. Therefore, an improvement to the Monte Carlo analysis is needed that will allow the problem to be worked in reverse. In this way, the largest allowable dispersions that achieve the required mission objectives can be determined quantitatively.

Second-order variational equations for N-body simulations

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2016-07-01

First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first- and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first- and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.

Galileo's Trajectory with Mild Resistance

ERIC Educational Resources Information Center

Groetsch, C. W.

2012-01-01

An aspect of Galileo's classical trajectory that persists in a simple resistance model is noted. The resistive model provides a case study for the classroom analysis of limiting behaviour of an implicitly defined function. (Contains 1 note.)

On the modeling of the 2010 Gulf of Mexico Oil Spill

NASA Astrophysics Data System (ADS)

Mariano, A. J.; Kourafalou, V. H.; Srinivasan, A.; Kang, H.; Halliwell, G. R.; Ryan, E. H.; Roffer, M.

2011-09-01

Two oil particle trajectory forecasting systems were developed and applied to the 2010 Deepwater Horizon Oil Spill in the Gulf of Mexico. Both systems use ocean current fields from high-resolution numerical ocean circulation model simulations, Lagrangian stochastic models to represent unresolved sub-grid scale variability to advect oil particles, and Monte Carlo-based schemes for representing uncertain biochemical and physical processes. The first system assumes two-dimensional particle motion at the ocean surface, the oil is in one state, and the particle removal is modeled as a Monte Carlo process parameterized by a one number removal rate. Oil particles are seeded using both initial conditions based on observations and particles released at the location of the Maconda well. The initial conditions (ICs) of oil particle location for the two-dimensional surface oil trajectory forecasts are based on a fusing of all available information including satellite-based analyses. The resulting oil map is digitized into a shape file within which a polygon filling software generates longitude and latitude with variable particle density depending on the amount of oil present in the observations for the IC. The more complex system assumes three (light, medium, heavy) states for the oil, each state has a different removal rate in the Monte Carlo process, three-dimensional particle motion, and a particle size-dependent oil mixing model. Simulations from the two-dimensional forecast system produced results that qualitatively agreed with the uncertain "truth" fields. These simulations validated the use of our Monte Carlo scheme for representing oil removal by evaporation and other weathering processes. Eulerian velocity fields for predicting particle motion from data-assimilative models produced better particle trajectory distributions than a free running model with no data assimilation. Monte Carlo simulations of the three-dimensional oil particle trajectory, whose ensembles were generated by perturbing the size of the oil particles and the fraction in a given size range that are released at depth, the two largest unknowns in this problem. 36 realizations of the model were run with only subsurface oil releases. An average of these results yields that after three months, about 25% of the oil remains in the water column and that most of the oil is below 800 m.

On the transition from the quantum to the classical regime for massive scalar particles: A spatiotemporal approach

NASA Astrophysics Data System (ADS)

Lusanna, Luca; Pauri, Massimo

2014-08-01

If the classical structure of space-time is assumed to define an a priori scenario for the formulation of quantum theory (QT), the coordinate representation of the solutions of the Schroedinger equation of a quantum system containing one ( N) massive scalar particle has a preferred status. Let us consider all of the solutions admitting a multipolar expansion of the probability density function (and more generally of the Wigner function) around a space-time trajectory to be properly selected. For every normalized solution there is a privileged trajectory implying the vanishing of the dipole moment of the multipolar expansion: it is given by the expectation value of the position operator . Then, the special subset of solutions which satisfy Ehrenfest's Theorem (named thereby Ehrenfest monopole wave functions (EMWF)), have the important property that this privileged classical trajectory is determined by a closed Newtonian equation of motion where the effective force is the Newtonian force plus non-Newtonian terms (of order ħ 2 or higher) depending on the higher multipoles of the probability distribution ρ. Note that the superposition of two EMWFs is not an EMWF, a result to be strongly hoped for, given the possible unwanted implications concerning classical spatial perception. These results can be extended to N-particle systems in such a way that, when N classical trajectories with all the dipole moments vanishing and satisfying Ehrenfest theorem are associated with the normalized wave functions of the N-body system, we get a natural transition from the 3 N-dimensional configuration space to the space-time. Moreover, these results can be extended to relativistic quantum mechanics. Consequently, in suitable states of N quantum particle which are EMWF, we get the "emergence" of corresponding "classical particles" following Newton-like trajectories in space-time. Note that all this holds true in the standard framework of quantum mechanics, i.e. assuming, in particular, the validity of Born's rule and the individual system interpretation of the wave function (no ensemble interpretation). These results are valid without any approximation (like ħ → 0, big quantum numbers, etc.). Moreover, we do not commit ourselves to any specific ontological interpretation of quantum theory (such as, e.g., the Bohmian one). We will argue that, in substantial agreement with Bohr's viewpoint, the macroscopic description of the preparation, certain intermediate steps and the detection of the final outcome of experiments involving massive particles are dominated by these classical "effective" trajectories. This approach can be applied to the point of view of de-coherence in the case of a diagonal reduced density matrix ρ red (an improper mixture) depending on the position variables of a massive particle and of a pointer. When both the particle and the pointer wave functions appearing in ρ red are EMWF, the expectation value of the particle and pointer position variables becomes a statistical average on a classical ensemble. In these cases an improper quantum mixture becomes a classical statistical one, thus providing a particular answer to an open problem of de-coherence about the emergence of classicality.

Prediction of the Aerothermodynamic Environment of the Huygens Probe

NASA Technical Reports Server (NTRS)

Hollis, Brian R.; Striepe, Scott A.; Wright, Michael J.; Bose, Deepak; Sutton, Kenneth; Takashima, Naruhisa

2005-01-01

An investigation of the aerothermodynamic environment of the Huygens entry probe has been conducted. A Monte Carlo simulation of the trajectory of the probe during entry into Titan's atmosphere was performed to identify a worst-case heating rate trajectory. Flowfield and radiation transport computations were performed at points along this trajectory to obtain convective and radiative heat-transfer distributions on the probe's heat shield. This investigation identified important physical and numerical factors, including atmospheric CH4 concentration, transition to turbulence, numerical diffusion modeling, and radiation modeling, which strongly influenced the aerothermodynamic environment.

Direct observation and theory of trajectory-dependent electronic energy losses in medium-energy ion scattering.

PubMed

Hentz, A; Parkinson, G S; Quinn, P D; Muñoz-Márquez, M A; Woodruff, D P; Grande, P L; Schiwietz, G; Bailey, P; Noakes, T C Q

2009-03-06

The energy spectrum associated with scattering of 100 keV H+ ions from the outermost few atomic layers of Cu(111) in different scattering geometries provides direct evidence of trajectory-dependent electronic energy loss. Theoretical simulations, combining standard Monte Carlo calculations of the elastic scattering trajectories with coupled-channel calculations to describe inner-shell ionization and excitation as a function of impact parameter, reproduce the effects well and provide a means for far more complete analysis of medium-energy ion scattering data.

MONTE: the next generation of mission design and navigation software

NASA Astrophysics Data System (ADS)

Evans, Scott; Taber, William; Drain, Theodore; Smith, Jonathon; Wu, Hsi-Cheng; Guevara, Michelle; Sunseri, Richard; Evans, James

2018-03-01

The Mission analysis, Operations and Navigation Toolkit Environment (MONTE) (Sunseri et al. in NASA Tech Briefs 36(9), 2012) is an astrodynamic toolkit produced by the Mission Design and Navigation Software Group at the Jet Propulsion Laboratory. It provides a single integrated environment for all phases of deep space and Earth orbiting missions. Capabilities include: trajectory optimization and analysis, operational orbit determination, flight path control, and 2D/3D visualization. MONTE is presented to the user as an importable Python language module. This allows a simple but powerful user interface via CLUI or script. In addition, the Python interface allows MONTE to be used seamlessly with other canonical scientific programming tools such as SciPy, NumPy, and Matplotlib. MONTE is the prime operational orbit determination software for all JPL navigated missions.

Carrier trajectory tracking equations for Simple-band Monte Carlo simulation of avalanche multiplication processes

NASA Astrophysics Data System (ADS)

Ong, J. S. L.; Charin, C.; Leong, J. H.

2017-12-01

Avalanche photodiodes (APDs) with steep electric field gradients generally have low excess noise that arises from carrier multiplication within the internal gain of the devices, and the Monte Carlo (MC) method is among popular device simulation tools for such devices. However, there are few articles relating to carrier trajectory modeling in MC models for such devices. In this work, a set of electric-field-gradient-dependent carrier trajectory tracking equations are developed and used to update the positions of carriers along the path during Simple-band Monte Carlo (SMC) simulations of APDs with non-uniform electric fields. The mean gain and excess noise results obtained from the SMC model employing these equations show good agreement with the results reported for a series of silicon diodes, including a p+n diode with steep electric field gradients. These results confirm the validity and demonstrate the feasibility of the trajectory tracking equations applied in SMC models for simulating mean gain and excess noise in APDs with non-uniform electric fields. Also, the simulation results of mean gain, excess noise, and carrier ionization positions obtained from the SMC model of this work agree well with those of the conventional SMC model employing the concept of a uniform electric field within a carrier free-flight. These results demonstrate that the electric field variation within a carrier free-flight has an insignificant effect on the predicted mean gain and excess noise results. Therefore, both the SMC model of this work and the conventional SMC model can be used to predict the mean gain and excess noise in APDs with highly non-uniform electric fields.

A Probabilistic Framework for Constructing Temporal Relations in Replica Exchange Molecular Trajectories.

PubMed

Chattopadhyay, Aditya; Zheng, Min; Waller, Mark Paul; Priyakumar, U Deva

2018-05-23

Knowledge of the structure and dynamics of biomolecules is essential for elucidating the underlying mechanisms of biological processes. Given the stochastic nature of many biological processes, like protein unfolding, it's almost impossible that two independent simulations will generate the exact same sequence of events, which makes direct analysis of simulations difficult. Statistical models like Markov Chains, transition networks etc. help in shedding some light on the mechanistic nature of such processes by predicting long-time dynamics of these systems from short simulations. However, such methods fall short in analyzing trajectories with partial or no temporal information, for example, replica exchange molecular dynamics or Monte Carlo simulations. In this work we propose a probabilistic algorithm, borrowing concepts from graph theory and machine learning, to extract reactive pathways from molecular trajectories in the absence of temporal data. A suitable vector representation was chosen to represent each frame in the macromolecular trajectory (as a series of interaction and conformational energies) and dimensionality reduction was performed using principal component analysis (PCA). The trajectory was then clustered using a density-based clustering algorithm, where each cluster represents a metastable state on the potential energy surface (PES) of the biomolecule under study. A graph was created with these clusters as nodes with the edges learnt using an iterative expectation maximization algorithm. The most reactive path is conceived as the widest path along this graph. We have tested our method on RNA hairpin unfolding trajectory in aqueous urea solution. Our method makes the understanding of the mechanism of unfolding in RNA hairpin molecule more tractable. As this method doesn't rely on temporal data it can be used to analyze trajectories from Monte Carlo sampling techniques and replica exchange molecular dynamics (REMD).

Classical versus quantum dynamical chaos: Sensitivity to external perturbations, stability and reversibility

NASA Astrophysics Data System (ADS)

Sokolov, Valentin V.; Zhirov, Oleg V.; Kharkov, Yaroslav A.

The extraordinary complexity of classical trajectories of typical nonlinear systems that manifest stochastic behavior is intimately connected with exponential sensitivity to small variations of initial conditions and/or weak external perturbations. In rigorous terms, such classical systems are characterized by positive algorithmic complexity described by the Lyapunov exponent or, alternatively, by the Kolmogorov-Sinai entropy. The said implies that, in spite of the fact that, formally, any however complex trajectory of a perfectly isolated (closed) system is unique and differentiable for any certain initial conditions and the motion is perfectly reversible, it is impractical to treat that sort of classical systems as closed ones. Inevitably, arbitrary weak influence of an environment crucially impacts the dynamics. This influence, that can be considered as a noise, rapidly effaces the memory of initial conditions and turns the motion into an irreversible random process. In striking contrast, the quantum mechanics of the classically chaotic systems exhibit much weaker sensitivity and strong memory of the initial state. Qualitatively, this crucial difference could be expected in view of a much simpler structure of quantum states as compared to the extraordinary complexity of random and unpredictable classical trajectories. However the very notion of trajectories is absent in quantum mechanics so that the concept of exponential instability seems to be irrelevant in this case. The problem of a quantitative measure of complexity of a quantum state of motion, that is a very important and nontrivial issue of the theory of quantum dynamical chaos, is the one of our concern. With such a measure in hand, we quantitatively analyze the stability and reversibility of quantum dynamics in the presence of external noise. To solve this problem we point out that individual classical trajectories are of minor interest if the motion is chaotic. Properties of all of them are alike in this case and rather the behavior of their manifolds carries really valuable information. Therefore the phase-space methods and, correspondingly, the Liouville form of the classical mechanics become the most adequate. It is very important that, opposite to the classical trajectories, the classical phase space distribution and the Liouville equation have direct quantum analogs. Hence, the analogy and difference of classical and quantum dynamics can be traced by comparing the classical (W(c)(I,θ;t)) and quantum (Wigner function W(I,θ;t)) phase space distributions both expressed in identical phase-space variables but ruled by different(!) linear equations. The paramount property of the classical dynamical chaos is the exponentially fast structuring of the system's phase space on finer and finer scales. On the contrary, degree of structuring of the corresponding Wigner function is restricted by the quantization of the phase space. This makes Wigner function more coarse and relatively "simple" as compared to its classical counterpart. Fourier analysis affords quite suitable ground for analyzing complexity of a phase space distribution, that is equally valid in classical and quantum cases. We demonstrate that the typical number of Fourier harmonics is indeed a relevant measure of complexity of states of motion in both classical as well as quantum cases. This allowed us to investigate in detail and introduce a quantitative measure of sensitivity to an external noisy environment and formulate the conditions under which the quantum motion remains reversible. It turns out that while the mean number of harmonics of the classical phase-space distribution of a non-integrable system grows with time exponentially during the whole time of the motion, the time of exponential upgrowth of this number in the case of the corresponding quantum Wigner function is restricted only to the Ehrenfest interval 0 < t < tE - just the interval within which the Wigner function still satisfies the classical Liouville equation. We showed that the number of harmonics increases beyond this interval algebraically. This fact gains a crucial importance when the Ehrenfest time is so short that the exponential regime has no time to show up. Under this condition the quantum motion turns out to be quite stable and reversible.

Mixed quantum/classical investigation of the photodissociation of NH3(Ã) and a practical method for maintaining zero-point energy in classical trajectories

NASA Astrophysics Data System (ADS)

Bonhommeau, David; Truhlar, Donald G.

2008-07-01

The photodissociation dynamics of ammonia upon excitation of the out-of-plane bending mode (mode ν2 with n2=0,…,6 quanta of vibration) in the à electronic state is investigated by means of several mixed quantum/classical methods, and the calculated final-state properties are compared to experiments. Five mixed quantum/classical methods are tested: one mean-field approach (the coherent switching with decay of mixing method), two surface-hopping methods [the fewest switches with time uncertainty (FSTU) and FSTU with stochastic decay (FSTU/SD) methods], and two surface-hopping methods with zero-point energy (ZPE) maintenance [the FSTU /SD+trajectory projection onto ZPE orbit (TRAPZ) and FSTU /SD+minimal TRAPZ (mTRAPZ) methods]. We found a qualitative difference between final NH2 internal energy distributions obtained for n2=0 and n2>1, as observed in experiments. Distributions obtained for n2=1 present an intermediate behavior between distributions obtained for smaller and larger n2 values. The dynamics is found to be highly electronically nonadiabatic with all these methods. NH2 internal energy distributions may have a negative energy tail when the ZPE is not maintained throughout the dynamics. The original TRAPZ method was designed to maintain ZPE in classical trajectories, but we find that it leads to unphysically high internal vibrational energies. The mTRAPZ method, which is new in this work and provides a general method for maintaining ZPE in either single-surface or multisurface trajectories, does not lead to unphysical results and is much less time consuming. The effect of maintaining ZPE in mixed quantum/classical dynamics is discussed in terms of agreement with experimental findings. The dynamics for n2=0 and n2=6 are also analyzed to reveal details not available from experiment, in particular, the time required for quenching of electronic excitation and the adiabatic energy gap and geometry at the time of quenching.

Mixed quantum/classical investigation of the photodissociation of NH3(A) and a practical method for maintaining zero-point energy in classical trajectories.

PubMed

Bonhommeau, David; Truhlar, Donald G

2008-07-07

The photodissociation dynamics of ammonia upon excitation of the out-of-plane bending mode (mode nu(2) with n(2)=0,[ellipsis (horizontal)],6 quanta of vibration) in the A electronic state is investigated by means of several mixed quantum/classical methods, and the calculated final-state properties are compared to experiments. Five mixed quantum/classical methods are tested: one mean-field approach (the coherent switching with decay of mixing method), two surface-hopping methods [the fewest switches with time uncertainty (FSTU) and FSTU with stochastic decay (FSTU/SD) methods], and two surface-hopping methods with zero-point energy (ZPE) maintenance [the FSTUSD+trajectory projection onto ZPE orbit (TRAPZ) and FSTUSD+minimal TRAPZ (mTRAPZ) methods]. We found a qualitative difference between final NH(2) internal energy distributions obtained for n(2)=0 and n(2)>1, as observed in experiments. Distributions obtained for n(2)=1 present an intermediate behavior between distributions obtained for smaller and larger n(2) values. The dynamics is found to be highly electronically nonadiabatic with all these methods. NH(2) internal energy distributions may have a negative energy tail when the ZPE is not maintained throughout the dynamics. The original TRAPZ method was designed to maintain ZPE in classical trajectories, but we find that it leads to unphysically high internal vibrational energies. The mTRAPZ method, which is new in this work and provides a general method for maintaining ZPE in either single-surface or multisurface trajectories, does not lead to unphysical results and is much less time consuming. The effect of maintaining ZPE in mixed quantum/classical dynamics is discussed in terms of agreement with experimental findings. The dynamics for n(2)=0 and n(2)=6 are also analyzed to reveal details not available from experiment, in particular, the time required for quenching of electronic excitation and the adiabatic energy gap and geometry at the time of quenching.

Scout trajectory error propagation computer program

NASA Technical Reports Server (NTRS)

Myler, T. R.

1982-01-01

Since 1969, flight experience has been used as the basis for predicting Scout orbital accuracy. The data used for calculating the accuracy consists of errors in the trajectory parameters (altitude, velocity, etc.) at stage burnout as observed on Scout flights. Approximately 50 sets of errors are used in Monte Carlo analysis to generate error statistics in the trajectory parameters. A covariance matrix is formed which may be propagated in time. The mechanization of this process resulted in computer program Scout Trajectory Error Propagation (STEP) and is described herein. Computer program STEP may be used in conjunction with the Statistical Orbital Analysis Routine to generate accuracy in the orbit parameters (apogee, perigee, inclination, etc.) based upon flight experience.

Autonomous quantum to classical transitions and the generalized imaging theorem

NASA Astrophysics Data System (ADS)

Briggs, John S.; Feagin, James M.

2016-03-01

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. Here we prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Currently, the quantum to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.

Autonomous quantum to classical transitions and the generalized imaging theorem

DOE PAGES

Briggs, John S.; Feagin, James M.

2016-03-16

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. We prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Now, the quantummore » to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.« less

Electron capture and excitation processes in H+-H collisions in dense quantum plasmas

NASA Astrophysics Data System (ADS)

Jakimovski, D.; Markovska, N.; Janev, R. K.

2016-10-01

Electron capture and excitation processes in proton-hydrogen atom collisions taking place in dense quantum plasmas are studied by employing the two-centre atomic orbital close-coupling (TC-AOCC) method. The Debye-Hückel cosine (DHC) potential is used to describe the plasma screening effects on the Coulomb interaction between charged particles. The properties of a hydrogen atom with DHC potential are investigated as a function of the screening strength of the potential. It is found that the decrease in binding energy of nl levels with increasing screening strength is considerably faster than in the case of the Debye-Hückel (DH) screening potential, appropriate for description of charged particle interactions in weakly coupled classical plasmas. This results in a reduction in the number of bound states in the DHC potential with respect to that in the DH potential for the same plasma screening strength, and is reflected in the dynamics of excitation and electron capture processes for the two screened potentials. The TC-AOCC cross sections for total and state-selective electron capture and excitation cross sections with the DHC potential are calculated for a number of representative screening strengths in the 1-300 keV energy range and compared with those for the DH and pure Coulomb potential. The total capture cross sections for a selected number of screening strengths are compared with the available results from classical trajectory Monte Carlo calculations.

Comparison of effects of copropagated and precomputed atmosphere profiles on Monte Carlo trajectory simulation

NASA Technical Reports Server (NTRS)

Queen, Eric M.; Omara, Thomas M.

1990-01-01

A realization of a stochastic atmosphere model for use in simulations is presented. The model provides pressure, density, temperature, and wind velocity as a function of latitude, longitude, and altitude, and is implemented in a three degree of freedom simulation package. This implementation is used in the Monte Carlo simulation of an aeroassisted orbital transfer maneuver and results are compared to those of a more traditional approach.

TU-F-17A-05: Calculating Tumor Trajectory and Dose-Of-The-Day for Highly Mobile Tumors Using Cone-Beam CT Projections

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

Jones, B; Miften, M

2014-06-15

Purpose: Cone-beam CT (CBCT) projection images provide anatomical data in real-time over several respiratory cycles, forming a comprehensive picture of tumor movement. We developed a method using these projections to determine the trajectory and dose of highly mobile tumors during each fraction of treatment. Methods: CBCT images of a respiration phantom were acquired, where the trajectory mimicked a lung tumor with high amplitude (2.4 cm) and hysteresis. A template-matching algorithm was used to identify the location of a steel BB in each projection. A Gaussian probability density function for tumor position was calculated which best fit the observed trajectory ofmore » the BB in the imager geometry. Two methods to improve the accuracy of tumor track reconstruction were investigated: first, using respiratory phase information to refine the trajectory estimation, and second, using the Monte Carlo method to sample the estimated Gaussian tumor position distribution. 15 clinically-drawn abdominal/lung CTV volumes were used to evaluate the accuracy of the proposed methods by comparing the known and calculated BB trajectories. Results: With all methods, the mean position of the BB was determined with accuracy better than 0.1 mm, and root-mean-square (RMS) trajectory errors were lower than 5% of marker amplitude. Use of respiratory phase information decreased RMS errors by 30%, and decreased the fraction of large errors (>3 mm) by half. Mean dose to the clinical volumes was calculated with an average error of 0.1% and average absolute error of 0.3%. Dosimetric parameters D90/D95 were determined within 0.5% of maximum dose. Monte-Carlo sampling increased RMS trajectory and dosimetric errors slightly, but prevented over-estimation of dose in trajectories with high noise. Conclusions: Tumor trajectory and dose-of-the-day were accurately calculated using CBCT projections. This technique provides a widely-available method to evaluate highly-mobile tumors, and could facilitate better strategies to mitigate or compensate for motion during SBRT.« less

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.

Discrepancy-based error estimates for Quasi-Monte Carlo III. Error distributions and central limits

NASA Astrophysics Data System (ADS)

Hoogland, Jiri; Kleiss, Ronald

1997-04-01

In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-random point sets, we derive various results on the probability distribution of the integration error, which can be compared to the standard Central Limit Theorem for normal stochastic sampling. In many cases, a Gaussian error distribution is obtained.

An Overview of Importance Splitting for Rare Event Simulation

ERIC Educational Resources Information Center

Morio, Jerome; Pastel, Rudy; Le Gland, Francois

2010-01-01

Monte Carlo simulations are a classical tool to analyse physical systems. When unlikely events are to be simulated, the importance sampling technique is often used instead of Monte Carlo. Importance sampling has some drawbacks when the problem dimensionality is high or when the optimal importance sampling density is complex to obtain. In this…

Study of optical and electronic properties of nickel from reflection electron energy loss spectra

NASA Astrophysics Data System (ADS)

Xu, H.; Yang, L. H.; Da, B.; Tóth, J.; Tőkési, K.; Ding, Z. J.

2017-09-01

We use the classical Monte Carlo transport model of electrons moving near the surface and inside solids to reproduce the measured reflection electron energy-loss spectroscopy (REELS) spectra. With the combination of the classical transport model and the Markov chain Monte Carlo (MCMC) sampling of oscillator parameters the so-called reverse Monte Carlo (RMC) method was developed, and used to obtain optical constants of Ni in this work. A systematic study of the electronic and optical properties of Ni has been performed in an energy loss range of 0-200 eV from the measured REELS spectra at primary energies of 1000 eV, 2000 eV and 3000 eV. The reliability of our method was tested by comparing our results with the previous data. Moreover, the accuracy of our optical data has been confirmed by applying oscillator strength-sum rule and perfect-screening-sum rule.

Monte Carlo simulation of a noisy quantum channel with memory.

PubMed

Akhalwaya, Ismail; Moodley, Mervlyn; Petruccione, Francesco

2015-10-01

The classical capacity of quantum channels is well understood for channels with uncorrelated noise. For the case of correlated noise, however, there are still open questions. We calculate the classical capacity of a forgetful channel constructed by Markov switching between two depolarizing channels. Techniques have previously been applied to approximate the output entropy of this channel and thus its capacity. In this paper, we use a Metropolis-Hastings Monte Carlo approach to numerically calculate the entropy. The algorithm is implemented in parallel and its performance is studied and optimized. The effects of memory on the capacity are explored and previous results are confirmed to higher precision.

Mean-trajectory approximation for electronic and vibrational-electronic nonlinear spectroscopy

NASA Astrophysics Data System (ADS)

Loring, Roger F.

2017-04-01

Mean-trajectory approximations permit the calculation of nonlinear vibrational spectra from semiclassically quantized trajectories on a single electronically adiabatic potential surface. By describing electronic degrees of freedom with classical phase-space variables and subjecting these to semiclassical quantization, mean-trajectory approximations may be extended to compute both nonlinear electronic spectra and vibrational-electronic spectra. A general mean-trajectory approximation for both electronic and nuclear degrees of freedom is presented, and the results for purely electronic and for vibrational-electronic four-wave mixing experiments are quantitatively assessed for harmonic surfaces with linear electronic-nuclear coupling.

Oxygen transport properties estimation by DSMC-CT simulations

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

Bruno, Domenico; Frezzotti, Aldo; Ghiroldi, Gian Pietro

Coupling DSMC simulations with classical trajectories calculations is emerging as a powerful tool to improve predictive capabilities of computational rarefied gas dynamics. The considerable increase of computational effort outlined in the early application of the method (Koura,1997) can be compensated by running simulations on massively parallel computers. In particular, GPU acceleration has been found quite effective in reducing computing time (Ferrigni,2012; Norman et al.,2013) of DSMC-CT simulations. The aim of the present work is to study rarefied Oxygen flows by modeling binary collisions through an accurate potential energy surface, obtained by molecular beams scattering (Aquilanti, et al.,1999). The accuracy ofmore » the method is assessed by calculating molecular Oxygen shear viscosity and heat conductivity following three different DSMC-CT simulation methods. In the first one, transport properties are obtained from DSMC-CT simulations of spontaneous fluctuation of an equilibrium state (Bruno et al, Phys. Fluids, 23, 093104, 2011). In the second method, the collision trajectory calculation is incorporated in a Monte Carlo integration procedure to evaluate the Taxman’s expressions for the transport properties of polyatomic gases (Taxman,1959). In the third, non-equilibrium zero and one-dimensional rarefied gas dynamic simulations are adopted and the transport properties are computed from the non-equilibrium fluxes of momentum and energy. The three methods provide close values of the transport properties, their estimated statistical error not exceeding 3%. The experimental values are slightly underestimated, the percentage deviation being, again, few percent.« less

A model for explaining fusion suppression using classical trajectory method

NASA Astrophysics Data System (ADS)

Phookan, C. K.; Kalita, K.

2015-01-01

We adopt a semi-classical approach for explanation of projectile breakup and above barrier fusion suppression for the reactions 6Li+152Sm and 6Li+144Sm. The cut-off impact parameter for fusion is determined by employing quantum mechanical ideas. Within this cut-off impact parameter for fusion, the fraction of projectiles undergoing breakup is determined using the method of classical trajectory in two-dimensions. For obtaining the initial conditions of the equations of motion, a simplified model of the 6Li nucleus has been proposed. We introduce a simple formula for explanation of fusion suppression. We find excellent agreement between the experimental and calculated fusion cross section. A slight modification of the above formula for fusion suppression is also proposed for a three-dimensional model.

Transition of recollision trajectories from linear to elliptical polarization

DOE PAGES

Li, Yingbin; Yu, Benhai; Tang, Qingbin; ...

2016-03-15

Using a classical ensemble method, we revisit the topic of recollision and nonsequential double ionization with elliptically polarized laser fields. We focus on how the recollision mechanism transitions from short trajectories with linear polarization to long trajectories with elliptical polarization. Furthermore, we propose how this transition can be observed by measuring the carrier-envelop-phase dependence of the correlated electron momentum spectra using currently available few-cycle laser pulses.

POLYANA-A tool for the calculation of molecular radial distribution functions based on Molecular Dynamics trajectories

NASA Astrophysics Data System (ADS)

Dimitroulis, Christos; Raptis, Theophanes; Raptis, Vasilios

2015-12-01

We present an application for the calculation of radial distribution functions for molecular centres of mass, based on trajectories generated by molecular simulation methods (Molecular Dynamics, Monte Carlo). When designing this application, the emphasis was placed on ease of use as well as ease of further development. In its current version, the program can read trajectories generated by the well-known DL_POLY package, but it can be easily extended to handle other formats. It is also very easy to 'hack' the program so it can compute intermolecular radial distribution functions for groups of interaction sites rather than whole molecules.

Emulation of rocket trajectory based on a six degree of freedom model

NASA Astrophysics Data System (ADS)

Zhang, Wenpeng; Li, Fan; Wu, Zhong; Li, Rong

2008-10-01

In this paper, a 6-DOF motion mathematical model is discussed. It is consisted of body dynamics and kinematics block, aero dynamics block and atmosphere block. Based on Simulink, the whole rocket trajectory mathematical model is developed. In this model, dynamic system simulation becomes easy and visual. The method of modularization design gives more convenience to transplant. At last, relevant data is given to be validated by Monte Carlo means. Simulation results show that the flight trajectory of the rocket can be simulated preferably by means of this model, and it also supplies a necessary simulating tool for the development of control system.

Adaptive Stress Testing of Airborne Collision Avoidance Systems

NASA Technical Reports Server (NTRS)

Lee, Ritchie; Kochenderfer, Mykel J.; Mengshoel, Ole J.; Brat, Guillaume P.; Owen, Michael P.

2015-01-01

This paper presents a scalable method to efficiently search for the most likely state trajectory leading to an event given only a simulator of a system. Our approach uses a reinforcement learning formulation and solves it using Monte Carlo Tree Search (MCTS). The approach places very few requirements on the underlying system, requiring only that the simulator provide some basic controls, the ability to evaluate certain conditions, and a mechanism to control the stochasticity in the system. Access to the system state is not required, allowing the method to support systems with hidden state. The method is applied to stress test a prototype aircraft collision avoidance system to identify trajectories that are likely to lead to near mid-air collisions. We present results for both single and multi-threat encounters and discuss their relevance. Compared with direct Monte Carlo search, this MCTS method performs significantly better both in finding events and in maximizing their likelihood.

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion

NASA Astrophysics Data System (ADS)

Olšina, Jan; Kramer, Tobias; Kreisbeck, Christoph; Mančal, Tomáš

2014-10-01

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Effect of nuclear shielding in collision of positive charged helium ions with helium atoms

NASA Astrophysics Data System (ADS)

Ghavaminia, Hoda; Ghavaminia, Shirin

2018-03-01

Differential in angle and absolute cross sections in energy of the scattered particles are obtained for single charge exchange in ^3He^+-^4He collisions by means of the four body boundary-corrected first Born approximation (CB1-4B). The quantum-mechanical post and prior transition amplitudes are derived in terms of two-dimensional real integrals in the case of the prior form and five-dimensional quadratures for the post form. The effect of the dynamic electron correlation through the complete perturbation potential and the nuclear-screening influence of the passive electrons on the electron capture process is investigated. The results obtained in the CB1-4B method are compared with the available experimental data. For differential cross sections, the present results are in better agreement with experimental data than other theoretical data at extreme forward scattering angles. The integral cross sections are in excellent agreement with the experiment. Also, total cross sections for single electron capture, has been investigated using the classical trajectory Monte Carlo method. The present calculated results are found to be in an excellent agreement with the experimental data.

Measurements of C V flows from thermal charge-exchange excitation in divertor plasmas

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

Zaniol, B.; Isler, R. C.; Brooks, N. H.

2001-10-01

Certain transitions of C IV (C{sup 3+}) from n=7 to n=6 ({approx}7226 {angstrom}) and from n=6 to n=5 ({approx}4660 {angstrom}) sometimes appear much brighter in tokamak divertors than expected for electron-impact excitation from the ground state. This situation occurs because of charge exchange between C V (C{sup 4+}) and recycling thermal deuterium atoms in the n=2 level. As a result, it is possible to extend parallel flow measurements of carbon, which have previously been performed on C II--C IV ions using Doppler shift spectroscopy, to include flows of the He-like C V ions. The work described here includes modeling ofmore » the spectral features, correlation of state populations with classical Monte Carlo trajectory (CTMC) predictions, and applications to flow measurements in the DIII-D divertor [Plasma Physics Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159; Proceedings of the 18th IEEE/NPSS Symposium on Fusion Engineering, Albuquerque (Institute of Electrical and Electronic Engineers, Piscataway, 1999), p. 515].« less

Measurements of C V flows from thermal charge-exchange excitation in divertor plasmas

NASA Astrophysics Data System (ADS)

Zaniol, B.; Isler, R. C.; Brooks, N. H.; West, W. P.; Olson, R. E.

2001-10-01

Certain transitions of C IV (C3+) from n=7 to n=6 (≈7226 Å) and from n=6 to n=5 (≈4660 Å) sometimes appear much brighter in tokamak divertors than expected for electron-impact excitation from the ground state. This situation occurs because of charge exchange between C V (C4+) and recycling thermal deuterium atoms in the n=2 level. As a result, it is possible to extend parallel flow measurements of carbon, which have previously been performed on C II-C IV ions using Doppler shift spectroscopy, to include flows of the He-like C V ions. The work described here includes modeling of the spectral features, correlation of state populations with classical Monte Carlo trajectory (CTMC) predictions, and applications to flow measurements in the DIII-D divertor [Plasma Physics Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159; Proceedings of the 18th IEEE/NPSS Symposium on Fusion Engineering, Albuquerque (Institute of Electrical and Electronic Engineers, Piscataway, 1999), p. 515].

Quantum work in the Bohmian framework

NASA Astrophysics Data System (ADS)

Sampaio, R.; Suomela, S.; Ala-Nissila, T.; Anders, J.; Philbin, T. G.

2018-01-01

At nonzero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for example, is characterized by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase-space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with an exactly solvable example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states, which is reflected in higher moments of the work. The proposed approach introduces a fundamentally different perspective on quantum thermodynamics, allowing full thermodynamic characterization of the dynamics of quantum systems, including the measurement process.

Monte Carlo Simulations of Radiative and Neutrino Transport under Astrophysical Conditions

NASA Astrophysics Data System (ADS)

Krivosheyev, Yu. M.; Bisnovatyi-Kogan, G. S.

2018-05-01

Monte Carlo simulations are utilized to model radiative and neutrino transfer in astrophysics. An algorithm that can be used to study radiative transport in astrophysical plasma based on simulations of photon trajectories in a medium is described. Formation of the hard X-ray spectrum of the Galactic microquasar SS 433 is considered in detail as an example. Specific requirements for applying such simulations to neutrino transport in a densemedium and algorithmic differences compared to its application to photon transport are discussed.

Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

NASA Astrophysics Data System (ADS)

Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan

2018-02-01

Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo Simulations

NASA Technical Reports Server (NTRS)

Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Isakov, Sergei V.; Neven, Hartmut; Mazzola, Guglielmo; Troyer, Matthias

2015-01-01

Recent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.

Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models

NASA Astrophysics Data System (ADS)

Kimura, Kenji; Higuchi, Saburo

2017-11-01

We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This movement can be regarded as a random walk in a random environment with a feedback. We investigate this random walk numerically in the case of the classical XY model in 1, 2, and 3 dimensions to find that it is superdiffusive near the critical point of the underlying spin system. It is suggested that the performance improvement of the ECMC is related to this anomalous behavior.

Automatic determination of optimal linear drilling trajectories for cochlear access accounting for drill-positioning error.

PubMed

Noble, Jack H; Majdani, Omid; Labadie, Robert F; Dawant, Benoit; Fitzpatrick, J Michael

2010-09-01

Cochlear implantation is a surgical procedure in which an electrode array is permanently implanted into the cochlea to stimulate the auditory nerve and allow deaf people to hear. Percutaneous cochlear access, a new minimally invasive implantation approach, requires drilling a single linear channel from the skull surface to the cochlea. The focus of this paper addresses a major challenge with this approach, which is the ability to determine, in a pre-operative CT, a safe and effective drilling trajectory. A measure of the safety and effectiveness of a given trajectory relative to sensitive structures is derived using a Monte Carlo approach. The drilling trajectory that maximizes this measure is found using an optimization algorithm. In tests on 13 ears, the technique was shown to find approximately twice as many acceptable trajectories as those found manually by an experienced surgeon. Using this method, safe trajectories can be automatically determined quickly and consistently. Copyright 2010 John Wiley & Sons, Ltd.

Assessing the Performance of Classical Test Theory Item Discrimination Estimators in Monte Carlo Simulations

ERIC Educational Resources Information Center

Bazaldua, Diego A. Luna; Lee, Young-Sun; Keller, Bryan; Fellers, Lauren

2017-01-01

The performance of various classical test theory (CTT) item discrimination estimators has been compared in the literature using both empirical and simulated data, resulting in mixed results regarding the preference of some discrimination estimators over others. This study analyzes the performance of various item discrimination estimators in CTT:…

Comparison of Quantum and Classical Monte Carlo on a Simple Model Phase Transition

NASA Astrophysics Data System (ADS)

Cohen, D. E.; Cohen, R. E.

2005-12-01

Most simulations of phase transitions in minerals use classical molecular dynamics or classical Monte Carlo. However, it is known that in some cases, quantum effects are quite large, even for perovskite oxides [1]. We have studied the simplest model of a phase transition where this can be tested, that of interacting of double wells with an infinite- range interaction. The energy is E = ∑i (-A xi2 + B xi4 + ξ xi) . We used the same parameters used in a study of vibrational spectra and soft- mode behavior [4], A=0.01902, B=0.14294, ξ=0.025 in Hartree atomic units. This gives Tc of about 400 K. We varied the oscillator mass from 18 to 100. Classical Monte Carlo and path integral Monte Carlo (PIMC) were performed on this model. The maximum effect was for the lightest mass, in which PIMC gave a 75K lower Tc than the classical simulation. This is similar to the reduction in Tc observed in PIMC simulations for BaTiO3 at zero pressure [1]. We will explore the effects of varying the well depths. Shallower wells would show a greater quantum effect, as was seen in the high pressure BaTiO3 simulations, since pressure reduces the double well depths [5]. [1] Iniguez, J. & Vanderbilt, D. First-principles study of the temperature-pressure phase diagram of BaTiO3. Phys. Rev. Lett. 89, 115503 (2002). [2] Gillis, N. S. & Koehler, T. R. Phase transitions in a simple model ferroelectric-- -comparison of exact and variational treatments of a molecular-field Hamiltonian. Phys. Rev. B 9, 3806 (1974). [3] Koehler, T. R. & Gillis, N. S. Phase Transitions in a Model of Interacting Anharmonic Oscillators. Phys. Rev. B 7, 4980 (1973). [4] Flocken, J. W., Guenther, R. A., Hardy, J. R. & Boyer, L. L. Dielectric response spectrum of a damped one-dimensional double-well oscillator. Phys. Rev. B 40, 11496-11501 (1989). [5] Cohen, R. E. Origin of ferroelectricity in oxide ferroelectrics and the difference in ferroelectric behavior of BaTiO3 and PbTiO3. Nature 358, 136-138 (1992).

Trajectories and traversal times in quantum tunneling

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

Huang, Zhi Hong.

1989-01-01

The classical concepts of trajectories and traversal times applied to quantum tunneling are discussed. By using the Wentzel-Kramers-Brillouin approximation, it is found that in a forbidden region of a multidimensional space the wave function can be described by two sets of trajectories, or equivalently by two sets of wave fronts. The trajectories belonging to different sets are mutually orthogonal. An extended Huygens construction is proposed to determine these wave fronts and trajectories. In contrast to the classical results in the allowed region, these trajectories couple to each other. However, if the incident wave is normal to the turning surface, themore » trajectories are found to be independent and can be determined by Newton's equations of motion with inverted potential and energy. The multidimensional tunneling theory is then applied to the scanning tunneling microscope to calculate the current density distribution and to derive the expressions for the lateral resolution and the surface corrugation amplitude. The traversal time in quantum tunneling, i.e. tunneling time, is found to depend on model calculations and simulations. Computer simulation of a wave packet tunneling through a square barrier is performed. Several approaches, including the phase method, Larmor clock, and time-dependent barrier model, are investigated. For a square barrier, two characteristic times are found: One is equal to the barrier width divided by the magnitude of the imaginary velocity; the other is equal to the decay length divided by the incident velocity. It is believed that the tunneling time can only be defined operationally.« less

Quantum-enhanced reinforcement learning for finite-episode games with discrete state spaces

NASA Astrophysics Data System (ADS)

Neukart, Florian; Von Dollen, David; Seidel, Christian; Compostella, Gabriele

2017-12-01

Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization and sampling tasks. Here, we present a way to partially embed both Monte Carlo policy iteration for finding an optimal policy on random observations, as well as how to embed n sub-optimal state-value functions for approximating an improved state-value function given a policy for finite horizon games with discrete state spaces on a D-Wave 2000Q quantum processing unit (QPU). We explain how both problems can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that quantum-enhanced Monte Carlo policy evaluation allows for finding equivalent or better state-value functions for a given policy with the same number episodes compared to a purely classical Monte Carlo algorithm. Additionally, we describe a quantum-classical policy learning algorithm. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical policy evaluation algorithm.

State-specific tunneling lifetimes from classical trajectories: H-atom dissociation in electronically excited pyrrole

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

Xie, Weiwei; Domcke, Wolfgang; Farantos, Stavros C.

A trajectory method of calculating tunneling probabilities from phase integrals along straight line tunneling paths, originally suggested by Makri and Miller [J. Chem. Phys. 91, 4026 (1989)] and recently implemented by Truhlar and co-workers [Chem. Sci. 5, 2091 (2014)], is tested for one- and two-dimensional ab initio based potentials describing hydrogen dissociation in the {sup 1}B{sub 1} excited electronic state of pyrrole. The primary observables are the tunneling rates in a progression of bending vibrational states lying below the dissociation barrier and their isotope dependences. Several initial ensembles of classical trajectories have been considered, corresponding to the quasiclassical and themore » quantum mechanical samplings of the initial conditions. It is found that the sampling based on the fixed energy Wigner density gives the best agreement with the quantum mechanical dissociation rates.« less

Moyal dynamics and trajectories

NASA Astrophysics Data System (ADS)

Braunss, G.

2010-01-01

We give first an approximation of the operator δh: f → δhf := h*planckf - f*planckh in terms of planck2n, n >= 0, where h\\equiv h(p,q), (p,q)\\in {\\mathbb R}^{2 n} , is a Hamilton function and *planck denotes the star product. The operator, which is the generator of time translations in a *planck-algebra, can be considered as a canonical extension of the Liouville operator Lh: f → Lhf := {h, f}Poisson. Using this operator we investigate the dynamics and trajectories of some examples with a scheme that extends the Hamilton-Jacobi method for classical dynamics to Moyal dynamics. The examples we have chosen are Hamiltonians with a one-dimensional quartic potential and two-dimensional radially symmetric nonrelativistic and relativistic Coulomb potentials, and the Hamiltonian for a Schwarzschild metric. We further state a conjecture concerning an extension of the Bohr-Sommerfeld formula for the calculation of the exact eigenvalues for systems with classically periodic trajectories.

Wigner flow reveals topological order in quantum phase space dynamics.

PubMed

Steuernagel, Ole; Kakofengitis, Dimitris; Ritter, Georg

2013-01-18

The behavior of classical mechanical systems is characterized by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why traditionally only the time evolution of wave functions is studied in quantum dynamics. These studies are quite insensitive to the underlying structure of quantum phase space dynamics. We identify the flow that is the quantum analog of classical particle flow along phase portrait lines. It reveals hidden features of quantum dynamics and extra complexity. Being constrained by conserved flow winding numbers, it also reveals fundamental topological order in quantum dynamics that has so far gone unnoticed.

Parameter sensitivity analysis for pesticide impacts on honeybee colonies

EPA Science Inventory

We employ Monte Carlo simulation and linear sensitivity analysis techniques to describe the dynamics of a bee exposure model, VarroaPop. Daily simulations are performed that simulate hive population trajectories, taking into account queen strength, foraging success, weather, colo...

Sobol’ sensitivity analysis for stressor impacts on honeybee colonies

EPA Science Inventory

We employ Monte Carlo simulation and nonlinear sensitivity analysis techniques to describe the dynamics of a bee exposure model, VarroaPop. Daily simulations are performed of hive population trajectories, taking into account queen strength, foraging success, mite impacts, weather...

Quantitative underwater 3D motion analysis using submerged video cameras: accuracy analysis and trajectory reconstruction.

PubMed

Silvatti, Amanda P; Cerveri, Pietro; Telles, Thiago; Dias, Fábio A S; Baroni, Guido; Barros, Ricardo M L

2013-01-01

In this study we aim at investigating the applicability of underwater 3D motion capture based on submerged video cameras in terms of 3D accuracy analysis and trajectory reconstruction. Static points with classical direct linear transform (DLT) solution, a moving wand with bundle adjustment and a moving 2D plate with Zhang's method were considered for camera calibration. As an example of the final application, we reconstructed the hand motion trajectories in different swimming styles and qualitatively compared this with Maglischo's model. Four highly trained male swimmers performed butterfly, breaststroke and freestyle tasks. The middle fingertip trajectories of both hands in the underwater phase were considered. The accuracy (mean absolute error) of the two calibration approaches (wand: 0.96 mm - 2D plate: 0.73 mm) was comparable to out of water results and highly superior to the classical DLT results (9.74 mm). Among all the swimmers, the hands' trajectories of the expert swimmer in the style were almost symmetric and in good agreement with Maglischo's model. The kinematic results highlight symmetry or asymmetry between the two hand sides, intra- and inter-subject variability in terms of the motion patterns and agreement or disagreement with the model. The two outcomes, calibration results and trajectory reconstruction, both move towards the quantitative 3D underwater motion analysis.

Multivalued classical mechanics arising from singularity loops in complex time

NASA Astrophysics Data System (ADS)

Koch, Werner; Tannor, David J.

2018-02-01

Complex-valued classical trajectories in complex time encounter singular times at which the momentum diverges. A closed time contour around such a singular time may result in final values for q and p that differ from their initial values. In this work, we develop a calculus for determining the exponent and prefactor of the asymptotic time dependence of p from the singularities of the potential as the singularity time is approached. We identify this exponent with the number of singularity loops giving distinct solutions to Hamilton's equations of motion. The theory is illustrated for the Eckart, Coulomb, Morse, and quartic potentials. Collectively, these potentials illustrate a wide variety of situations: poles and essential singularities at finite and infinite coordinate values. We demonstrate quantitative agreement between analytical and numerical exponents and prefactors, as well as the connection between the exponent and the time circuit count. This work provides the theoretical underpinnings for the choice of time contours described in the studies of Doll et al. [J. Chem. Phys. 58(4), 1343-1351 (1973)] and Petersen and Kay [J. Chem. Phys. 141(5), 054114 (2014)]. It also has implications for wavepacket reconstruction from complex classical trajectories when multiple branches of trajectories are involved.

Conflict Probability Estimation for Free Flight

NASA Technical Reports Server (NTRS)

Paielli, Russell A.; Erzberger, Heinz

1996-01-01

The safety and efficiency of free flight will benefit from automated conflict prediction and resolution advisories. Conflict prediction is based on trajectory prediction and is less certain the farther in advance the prediction, however. An estimate is therefore needed of the probability that a conflict will occur, given a pair of predicted trajectories and their levels of uncertainty. A method is developed in this paper to estimate that conflict probability. The trajectory prediction errors are modeled as normally distributed, and the two error covariances for an aircraft pair are combined into a single equivalent covariance of the relative position. A coordinate transformation is then used to derive an analytical solution. Numerical examples and Monte Carlo validation are presented.

Multiple-time-stepping generalized hybrid Monte Carlo methods

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

Escribano, Bruno, E-mail: bescribano@bcamath.org; Akhmatskaya, Elena; IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao

2015-01-01

Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2–4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC).more » The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems.« less

Fractional dynamics using an ensemble of classical trajectories

NASA Astrophysics Data System (ADS)

Sun, Zhaopeng; Dong, Hao; Zheng, Yujun

2018-01-01

A trajectory-based formulation for fractional dynamics is presented and the trajectories are generated deterministically. In this theoretical framework, we derive a new class of estimators in terms of confluent hypergeometric function (F11) to represent the Riesz fractional derivative. Using this method, the simulation of free and confined Lévy flight are in excellent agreement with the exact numerical and analytical results. In addition, the barrier crossing in a bistable potential driven by Lévy noise of index α is investigated. In phase space, the behavior of trajectories reveal the feature of Lévy flight in a better perspective.

Preserving correlations between trajectories for efficient path sampling

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

Gingrich, Todd R.; Geissler, Phillip L.; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720

2015-06-21

Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to dynamical pathways that are substantial, yet sufficiently modest to obtain reasonable acceptance rates. Satisfying this requirement becomes very challenging in the case of long trajectories, due to the characteristic divergences of chaotic dynamics. Here, we examine schemes for addressing this problem, which engineer correlation between a trial trajectory and its reference path, for instance using artificial forces. Our analysis is facilitated by a modern perspective onmore » Markov chain Monte Carlo sampling, inspired by non-equilibrium statistical mechanics, which clarifies the types of sampling strategies that can scale to long trajectories. Viewed in this light, the most promising such strategy guides a trial trajectory by manipulating the sequence of random numbers that advance its stochastic time evolution, as done in a handful of existing methods. In cases where this “noise guidance” synchronizes trajectories effectively, as the Glauber dynamics of a two-dimensional Ising model, we show that efficient path sampling can be achieved for even very long trajectories.« less

On Choosing a Rational Flight Trajectory to the Moon

NASA Astrophysics Data System (ADS)

Gordienko, E. S.; Khudorozhkov, P. A.

2017-12-01

The algorithm for choosing a trajectory of spacecraft flight to the Moon is discussed. The characteristic velocity values needed for correcting the flight trajectory and a braking maneuver are estimated using the Monte Carlo method. The profile of insertion and flight to a near-circular polar orbit with an altitude of 100 km of an artificial lunar satellite (ALS) is given. The case of two corrections applied during the flight and braking phases is considered. The flight to an ALS orbit is modeled in the geocentric geoequatorial nonrotating coordinate system with the influence of perturbations from the Earth, the Sun, and the Moon factored in. The characteristic correction costs corresponding to corrections performed at different time points are examined. Insertion phase errors, the errors of performing the needed corrections, and the errors of determining the flight trajectory parameters are taken into account.

Self-learning Monte Carlo method

DOE PAGES

Liu, Junwei; Qi, Yang; Meng, Zi Yang; ...

2017-01-04

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. Lastly, we demonstrate the efficiency of SLMC in a spin model at the phasemore » transition point, achieving a 10–20 times speedup.« less

Random Numbers and Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Scherer, Philipp O. J.

Many-body problems often involve the calculation of integrals of very high dimension which cannot be treated by standard methods. For the calculation of thermodynamic averages Monte Carlo methods are very useful which sample the integration volume at randomly chosen points. After summarizing some basic statistics, we discuss algorithms for the generation of pseudo-random numbers with given probability distribution which are essential for all Monte Carlo methods. We show how the efficiency of Monte Carlo integration can be improved by sampling preferentially the important configurations. Finally the famous Metropolis algorithm is applied to classical many-particle systems. Computer experiments visualize the central limit theorem and apply the Metropolis method to the traveling salesman problem.

Sensitivity analyses for simulating pesticide impacts on honey bee colonies

EPA Science Inventory

We employ Monte Carlo simulation and sensitivity analysis techniques to describe the population dynamics of pesticide exposure to a honey bee colony using the VarroaPop + Pesticide model. Simulations are performed of hive population trajectories with and without pesti...

Three dimensional dose distribution comparison of simple and complex acquisition trajectories in dedicated breast CT

PubMed Central

Shah, Jainil P.; Mann, Steve D.; McKinley, Randolph L.; Tornai, Martin P.

2015-01-01

Purpose: A novel breast CT system capable of arbitrary 3D trajectories has been developed to address cone beam sampling insufficiency as well as to image further into the patient’s chest wall. The purpose of this study was to characterize any trajectory-related differences in 3D x-ray dose distribution in a pendant target when imaged with different orbits. Methods: Two acquisition trajectories were evaluated: circular azimuthal (no-tilt) and sinusoidal (saddle) orbit with ±15° tilts around a pendant breast, using Monte Carlo simulations as well as physical measurements. Simulations were performed with tungsten (W) filtration of a W-anode source; the simulated source flux was normalized to the measured exposure of a W-anode source. A water-filled cylindrical phantom was divided into 1 cm3 voxels, and the cumulative energy deposited was tracked in each voxel. Energy deposited per voxel was converted to dose, yielding the 3D distributed dose volumes. Additionally, three cylindrical phantoms of different diameters (10, 12.5, and 15 cm) and an anthropomorphic breast phantom, initially filled with water (mimicking pure fibroglandular tissue) and then with a 75% methanol-25% water mixture (mimicking 50–50 fibroglandular-adipose tissues), were used to simulate the pendant breast geometry and scanned on the physical system. Ionization chamber calibrated radiochromic film was used to determine the dose delivered in a 2D plane through the center of the volume for a fully 3D CT scan using the different orbits. Results: Measured experimental results for the same exposure indicated that the mean dose measured throughout the central slice for different diameters ranged from 3.93 to 5.28 mGy, with the lowest average dose measured on the largest cylinder with water mimicking a homogeneously fibroglandular breast. These results align well with the cylinder phantom Monte Carlo studies which also showed a marginal difference in dose delivered by a saddle trajectory in the central slice. Regardless of phantom material or filled fluid density, dose delivered by the saddle scan was negligibly different than the simple circular, no-tilt scans. The average dose measured in the breast phantom was marginally higher for saddle than the circular no tilt scan at 3.82 and 3.87 mGy, respectively. Conclusions: Not only does nontraditional 3D-trajectory CT scanning yield more complete sampling of the breast volume but also has comparable dose deposition throughout the breast and anterior chest volume, as verified by Monte Carlo simulation and physical measurements. PMID:26233179

Improvement of Simulation Method in Validation of Software of the Coordinate Measuring Systems

NASA Astrophysics Data System (ADS)

Nieciąg, Halina

2015-10-01

Software is used in order to accomplish various tasks at each stage of the functioning of modern measuring systems. Before metrological confirmation of measuring equipment, the system has to be validated. This paper discusses the method for conducting validation studies of a fragment of software to calculate the values of measurands. Due to the number and nature of the variables affecting the coordinate measurement results and the complex character and multi-dimensionality of measurands, the study used the Monte Carlo method of numerical simulation. The article presents an attempt of possible improvement of results obtained by classic Monte Carlo tools. The algorithm LHS (Latin Hypercube Sampling) was implemented as alternative to the simple sampling schema of classic algorithm.

Comparing Classical Water Models Using Molecular Dynamics to Find Bulk Properties

ERIC Educational Resources Information Center

Kinnaman, Laura J.; Roller, Rachel M.; Miller, Carrie S.

2018-01-01

A computational chemistry exercise for the undergraduate physical chemistry laboratory is described. In this exercise, students use the molecular dynamics package Amber to generate trajectories of bulk liquid water for 4 different water models (TIP3P, OPC, SPC/E, and TIP4Pew). Students then process the trajectory to calculate structural (radial…

On the Trajectories of Projectiles Depicted in Early Ballistic Woodcuts

ERIC Educational Resources Information Center

Stewart, Sean M.

2012-01-01

Motivated by quaint woodcut depictions often found in many late 16th and 17th century ballistic manuals of cannonballs fired in air, a comparison of their shapes with those calculated for the classic case of a projectile moving in a linear resisting medium is made. In considering the asymmetrical nature of such trajectories, the initial launch…

Optimal solar sail planetocentric trajectories

NASA Technical Reports Server (NTRS)

Sackett, L. L.

1977-01-01

The analysis of solar sail planetocentric optimal trajectory problem is described. A computer program was produced to calculate optimal trajectories for a limited performance analysis. A square sail model is included and some consideration is given to a heliogyro sail model. Orbit to a subescape point and orbit to orbit transfer are considered. Trajectories about the four inner planets can be calculated and shadowing, oblateness, and solar motion may be included. Equinoctial orbital elements are used to avoid the classical singularities, and the method of averaging is applied to increase computational speed. Solution of the two-point boundary value problem which arises from the application of optimization theory is accomplished with a Newton procedure. Time optimal trajectories are emphasized, but a penalty function has been considered to prevent trajectories which intersect a planet's surface.

Data Analysis Techniques for Physical Scientists

NASA Astrophysics Data System (ADS)

Pruneau, Claude A.

2017-10-01

Preface; How to read this book; 1. The scientific method; Part I. Foundation in Probability and Statistics: 2. Probability; 3. Probability models; 4. Classical inference I: estimators; 5. Classical inference II: optimization; 6. Classical inference III: confidence intervals and statistical tests; 7. Bayesian inference; Part II. Measurement Techniques: 8. Basic measurements; 9. Event reconstruction; 10. Correlation functions; 11. The multiple facets of correlation functions; 12. Data correction methods; Part III. Simulation Techniques: 13. Monte Carlo methods; 14. Collision and detector modeling; List of references; Index.

Centrality measures highlight proton traps and access points to proton highways in kinetic Monte Carlo trajectories

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

Krueger, Rachel A.; Haibach, Frederick G.; Fry, Dana L.

2015-04-21

A centrality measure based on the time of first returns rather than the number of steps is developed and applied to finding proton traps and access points to proton highways in the doped perovskite oxides: AZr{sub 0.875}D{sub 0.125}O{sub 3}, where A is Ba or Sr and the dopant D is Y or Al. The high centrality region near the dopant is wider in the SrZrO{sub 3} systems than the BaZrO{sub 3} systems. In the aluminum-doped systems, a region of intermediate centrality (secondary region) is found in a plane away from the dopant. Kinetic Monte Carlo (kMC) trajectories show that thismore » secondary region is an entry to fast conduction planes in the aluminum-doped systems in contrast to the highest centrality area near the dopant trap. The yttrium-doped systems do not show this secondary region because the fast conduction routes are in the same plane as the dopant and hence already in the high centrality trapped area. This centrality measure complements kMC by highlighting key areas in trajectories. The limiting activation barriers found via kMC are in very good agreement with experiments and related to the barriers to escape dopant traps.« less

FORMAL UNCERTAINTY ANALYSIS OF A LAGRANGIAN PHOTOCHEMICAL AIR POLLUTION MODEL. (R824792)

EPA Science Inventory

This study applied Monte Carlo analysis with Latin
hypercube sampling to evaluate the effects of uncertainty
in air parcel trajectory paths, emissions, rate constants,
deposition affinities, mixing heights, and atmospheric stability
on predictions from a vertically...

The Development and Evaluation of an Operational Aerobraking Strategy for the Mars 2001 Odyssey Orbiter

NASA Technical Reports Server (NTRS)

Tartabini, Paul V.; Munk, Michelle M.; Powell, Richard W.

2002-01-01

The Mars 2001 Odyssey Orbiter successfully completed the aerobraking phase of its mission on January 11, 2002. This paper discusses the support provided by NASA's Langley Research Center to the navigation team at the Jet Propulsion Laboratory in the planning and operational support of Mars Odyssey Aerobraking. Specifically, the development of a three-degree-of-freedom aerobraking trajectory simulation and its application to pre-flight planning activities as well as operations is described. The importance of running the simulation in a Monte Carlo fashion to capture the effects of mission and atmospheric uncertainties is demonstrated, and the utility of including predictive logic within the simulation that could mimic operational maneuver decision-making is shown. A description is also provided of how the simulation was adapted to support flight operations as both a validation and risk reduction tool and as a means of obtaining a statistical basis for maneuver strategy decisions. This latter application was the first use of Monte Carlo trajectory analysis in an aerobraking mission.

James Webb Space Telescope Initial Mid-Course Correction Monte Carlo Implementation using Task Parallelism

NASA Technical Reports Server (NTRS)

Petersen, Jeremy; Tichy, Jason; Wawrzyniak, Geoffrey; Richon, Karen

2014-01-01

The James Webb Space Telescope will be launched into a highly elliptical orbit that does not possess sufficient energy to achieve a proper Sun-Earth L2 libration point orbit. Three mid-course correction (MCC) maneuvers are planned to rectify the energy deficit: MCC-1a, MCC-1b, and MCC-2. To validate the propellant budget and trajectory design methods, a set of Monte Carlo analyses that incorporate MCC maneuver modeling and execution are employed. The first analysis focuses on the effects of launch vehicle injection errors on the magnitude of MCC-1a. The second on the spread of potential V based on the performance of the propulsion system as applied to all three MCC maneuvers. The final highlights the slight, but notable, contribution of the attitude thrusters during each MCC maneuver. Given the possible variations in these three scenarios, the trajectory design methods are determined to be robust to errors in the modeling of the flight system.

James Webb Space Telescope Initial Mid-Course Correction Monte Carlo Implementation using Task Parallelism

NASA Technical Reports Server (NTRS)

Petersen, Jeremy; Tichy, Jason; Wawrzyniak, Geoffrey; Richon, Karen

2014-01-01

The James Webb Space Telescope will be launched into a highly elliptical orbit that does not possess sufficient energy to achieve a proper Sun-Earth/Moon L2 libration point orbit. Three mid-course correction (MCC) maneuvers are planned to rectify the energy deficit: MCC-1a, MCC-1b, and MCC-2. To validate the propellant budget and trajectory design methods, a set of Monte Carlo analyses that incorporate MCC maneuver modeling and execution are employed. The first analysis focuses on the effects of launch vehicle injection errors on the magnitude of MCC-1a. The second on the spread of potential V based on the performance of the propulsion system as applied to all three MCC maneuvers. The final highlights the slight, but notable, contribution of the attitude thrusters during each MCC maneuver. Given the possible variations in these three scenarios, the trajectory design methods are determined to be robust to errors in the modeling of the flight system.

Hyper-X Stage Separation Trajectory Validation Studies

NASA Technical Reports Server (NTRS)

Tartabini, Paul V.; Bose, David M.; McMinn, John D.; Martin, John G.; Strovers, Brian K.

2003-01-01

An independent twelve degree-of-freedom simulation of the X-43A separation trajectory was created with the Program to Optimize Simulated trajectories (POST II). This simulation modeled the multi-body dynamics of the X-43A and its booster and included the effect of two pyrotechnically actuated pistons used to push the vehicles apart as well as aerodynamic interaction forces and moments between the two vehicles. The simulation was developed to validate trajectory studies conducted with a 14 degree-of-freedom simulation created early in the program using the Automatic Dynamic Analysis of Mechanics Systems (ADAMS) simulation software. The POST simulation was less detailed than the official ADAMS-based simulation used by the Project, but was simpler, more concise and ran faster, while providing similar results. The increase in speed provided by the POST simulation provided the Project with an alternate analysis tool. This tool was ideal for performing separation control logic trade studies that required the running of numerous Monte Carlo trajectories.

Trajectory Simulation of Meteors Assuming Mass Loss and Fragmentation

NASA Technical Reports Server (NTRS)

Allen, Gary A., Jr.; Prabhu, Dinesh K.; Saunders, David A

2015-01-01

Program used to simulate atmospheric flight trajectories of entry capsules [1] Includes models of atmospheres of different planetary destinations - Earth, Mars, Venus, Jupiter, Saturn, Uranus, Titan, ... Solves 3-­-degrees of freedom (3DoF) equations for a single body treated as a point mass. Also supports 6-DoF trajectory simula4on and Monte Carlo analyses. Uses Fehlberg-­-Runge-­-Kuna (4th-5th order) time integraion with automaic step size control. Includes rotating spheroidal planet with gravitational field having a J2 harmonic. Includes a variety of engineering aerodynamic and heat flux models. Capable of specifying events - heatshield jettison, parachute deployment, etc. - at predefined altitudes or Mach number. Has material thermal response models of typical aerospace materials integrated.

Trajectory Control and Optimization for Responsive Spacecraft

DTIC Science & Technology

2012-03-22

Orbital Elements and Local-Vertical-Local-Horizontal Frame 10 2.3 Equinoctial Frame with respect to ECI Frame [17] . . . . . . . . . 14 3.1...position and velocity, classical orbital elements , and equinoctial elements . These methods are detailed in the following sections. 2.1.1 Inertial Position...trajectory. However, if the singularities are unavoidable equinoctial orbital elements could be used. 2.1.3 Equinoctial Elements . Equinoctial

Sensitivity analyses for simulating pesticide impacts on honey bee colonies

USDA-ARS?s Scientific Manuscript database

We employ Monte Carlo simulation and sensitivity analysis techniques to describe the population dynamics of pesticide exposure to a honey bee colony using the VarroaPop+Pesticide model. Simulations are performed of hive population trajectories with and without pesticide exposure to determine the eff...

Trajectory study of supercollision relaxation in highly vibrationally excited pyrazine and CO2.

PubMed

Li, Ziman; Sansom, Rebecca; Bonella, Sara; Coker, David F; Mullin, Amy S

2005-09-01

Classical trajectory calculations were performed to simulate state-resolved energy transfer experiments of highly vibrationally excited pyrazine (E(vib) = 37,900 cm(-1)) and CO(2), which were conducted using a high-resolution transient infrared absorption spectrometer. The goal here is to use classical trajectories to simulate the supercollision energy transfer pathway wherein large amounts of energy are transferred in single collisions in order to compare with experimental results. In the trajectory calculations, Newton's laws of motion are used for the molecular motion, isolated molecules are treated as collections of harmonic oscillators, and intermolecular potentials are formed by pairwise Lennard-Jones potentials. The calculations qualitatively reproduce the observed energy partitioning in the scattered CO(2) molecules and show that the relative partitioning between bath rotation and translation is dependent on the moment of inertia of the bath molecule. The simulations show that the low-frequency modes of the vibrationally excited pyrazine contribute most to the strong collisions. The majority of collisions lead to small DeltaE values and primarily involve single encounters between the energy donor and acceptor. The large DeltaE exchanges result from both single impulsive encounters and chattering collisions that involve multiple encounters.

Threshold collision-induced dissociation of diatomic molecules: a case study of the energetics and dynamics of O2- collisions with Ar and Xe.

PubMed

Ahu Akin, F; Ree, Jongbaik; Ervin, Kent M; Kyu Shin, Hyung

2005-08-08

The energetics and dynamics of collision-induced dissociation of O2- with Ar and Xe targets are studied experimentally using guided ion-beam tandem mass spectrometry. The cross sections and the collision dynamics are modeled theoretically by classical trajectory calculations. Experimental apparent threshold energies are 2.1 and 1.1 eV in excess of the thermochemical O2- bond dissociation energy for argon and xenon, respectively. Classical trajectory calculations confirm the observed threshold behavior and the dependence of cross sections on the relative kinetic energy. Representative trajectories reveal that the bond dissociation takes place on a short time scale of about 50 fs in strong direct collisions. Collision-induced dissociation is found to be remarkably restricted to the perpendicular approach of ArXe to the molecular axis of O2-, while collinear collisions do not result in dissociation. The higher collisional energy-transfer efficiency of xenon compared with argon is attributed to both mass and polarizability effects.

Wisdom from Conservatory Faculty: Insights on Success in Classical Music Performance

ERIC Educational Resources Information Center

Jarvin, Linda; Subotnik, Rena F.

2010-01-01

What does it take to become a successful performer of Western classical music in the United States today? What factors, beyond technical proficiency and musicality, come into play? We started exploring these questions in a study of gatekeepers' (e.g., critics, artistic directors) views on key variables that contribute to the career trajectories of…

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

NASA Astrophysics Data System (ADS)

Deng, Zhaojie; Arsenault, Sam; Caranica, Cristian; Griffith, James; Zhu, Taotao; Al-Omari, Ahmad; Schüttler, Heinz-Bernd; Arnold, Jonathan; Mao, Leidong

2016-10-01

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype.

Electron capture in collisions of S4+ with helium

NASA Astrophysics Data System (ADS)

Wang, J. G.; Turner, A. R.; Cooper, D. L.; Schultz, D. R.; Rakovic, M. J.; Fritsch, W.; Stancil, P. C.; Zygelman, B.

2002-07-01

Charge transfer due to collisions of ground-state S4+(3s2 1S) ions with helium is investigated for energies between 0.1 meV u-1 and 10 MeV u-1. Total and state-selective single electron capture (SEC) cross sections and rate coefficients are obtained utilizing the quantum mechanical molecular-orbital close-coupling (MOCC), atomic-orbital close-coupling (AOCC), classical trajectory Monte Carlo (CTMC) and continuum distorted wave methods. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach. Previous data are limited to a calculation of the total SEC rate coefficient using the Landau-Zener model that is, in comparison to the results presented here, three orders of magnitude smaller. The MOCC SEC cross sections at low energy reveal a multichannel interference effect. True double capture is also investigated with the AOCC and CTMC approaches while autoionizing double capture and transfer ionization (TI) is explored with CTMC. SEC is found to be the dominant process except for E>200 keV u-1 when TI becomes the primary capture channel. Astrophysical implications are briefly discussed.

Charge transfer between O6+ and atomic hydrogen

NASA Astrophysics Data System (ADS)

Wu, Y.; Stancil, P. C.; Liebermann, H. P.; Buenker, R. J.; Schultz, D. R.; Hui, Y.

2011-05-01

The charge exchange process has been found to play a dominant role in the production of X-rays and/or EUV photons observed in cometary and planetary atmospheres and from the heliosphere. Charge transfer cross sections, especially state-selective cross sections, are necessary parameters in simulations of X-ray emission. In the present work, charge transfer due to collisions of ground state O6+(1s2 1 S) with atomic hydrogen has been investigated theoretically using the quantum-mechanical molecular-orbital close-coupling method (QMOCC). The multi-reference single- and double-excitation configuration interaction approach (MRDCI) has been applied to compute the adiabatic potential and nonadiabatic couplings, and the atomic basis sets used have been optimized with the method proposed previously to obtain precise potential data. Total and state-selective cross sections are calculated for energies between 10 meV/u and 10 keV/u. The QMOCC results are compared to available experimental and theoretical data as well as to new atomic-orbital close-coupling (AOCC) and classical trajectory Monte Carlo (CTMC) calculations. A recommended set of cross sections, based on the MOCC, AOCC, and CTMC calculations, is deduced which should aid in X-ray modeling studies.

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

PubMed Central

Deng, Zhaojie; Arsenault, Sam; Caranica, Cristian; Griffith, James; Zhu, Taotao; Al-Omari, Ahmad; Schüttler, Heinz-Bernd; Arnold, Jonathan; Mao, Leidong

2016-01-01

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype. PMID:27786253

Charge Exchange X-Ray Emission due to Highly Charged Ion Collisions with H, He, and H2: Line Ratios for Heliospheric and Interstellar Applications

NASA Astrophysics Data System (ADS)

Cumbee, R. S.; Mullen, P. D.; Lyons, D.; Shelton, R. L.; Fogle, M.; Schultz, D. R.; Stancil, P. C.

2018-01-01

The fundamental collisional process of charge exchange (CX) has been established as a primary source of X-ray emission from the heliosphere, planetary exospheres, and supernova remnants. In this process, X-ray emission results from the capture of an electron by a highly charged ion from a neutral atom or molecule, to form a highly excited, high-charge state ion. As the captured electron cascades down to the lowest energy level, photons are emitted, including X-rays. To provide reliable CX-induced X-ray spectral models to realistically simulate these environments, line ratios and spectra are computed using theoretical CX cross sections obtained with the multi-channel Landau-Zener, atomic-orbital close-coupling, molecular-orbital close-coupling, and classical trajectory Monte Carlo methods for various collisional velocities relevant to astrophysics. X-ray spectra were computed for collisions of bare and H-like C to Al ions with H, He, and H2 with results compared to available experimental data. Using these line ratios, XSPEC models of CX emission in the northeast rim of the Cygnus Loop supernova remnant and the heliosphere are shown as examples with ion velocity dependence.

On the Monte Carlo simulation of electron transport in the sub-1 keV energy range.

PubMed

Thomson, Rowan M; Kawrakow, Iwan

2011-08-01

The validity of "classic" Monte Carlo (MC) simulations of electron and positron transport at sub-1 keV energies is investigated in the context of quantum theory. Quantum theory dictates that uncertainties on the position and energy-momentum four-vectors of radiation quanta obey Heisenberg's uncertainty relation; however, these uncertainties are neglected in "classical" MC simulations of radiation transport in which position and momentum are known precisely. Using the quantum uncertainty relation and electron mean free path, the magnitudes of uncertainties on electron position and momentum are calculated for different kinetic energies; a validity bound on the classical simulation of electron transport is derived. In order to satisfy the Heisenberg uncertainty principle, uncertainties of 5% must be assigned to position and momentum for 1 keV electrons in water; at 100 eV, these uncertainties are 17 to 20% and are even larger at lower energies. In gaseous media such as air, these uncertainties are much smaller (less than 1% for electrons with energy 20 eV or greater). The classical Monte Carlo transport treatment is questionable for sub-1 keV electrons in condensed water as uncertainties on position and momentum must be large (relative to electron momentum and mean free path) to satisfy the quantum uncertainty principle. Simulations which do not account for these uncertainties are not faithful representations of the physical processes, calling into question the results of MC track structure codes simulating sub-1 keV electron transport. Further, the large difference in the scale at which quantum effects are important in gaseous and condensed media suggests that track structure measurements in gases are not necessarily representative of track structure in condensed materials on a micrometer or a nanometer scale.

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation formore » the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.« less

Monte Carlo sampling in diffusive dynamical systems

NASA Astrophysics Data System (ADS)

Tapias, Diego; Sanders, David P.; Altmann, Eduardo G.

2018-05-01

We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements, where deviations from a diffusive process are most prominent. We search for initial conditions using a proposal that correlates states in the Markov chain constructed via a Metropolis-Hastings algorithm. We show that our method outperforms the direct sampling method and also Metropolis-Hastings methods with alternative proposals. We test our general method through numerical simulations in 1D (box-map) and 2D (Lorentz gas) systems.

Revisiting Adiabatic Switching for Initial Conditions in Quasi-Classical Trajectory Calculations: Application to CH4.

PubMed

Qu, Chen; Bowman, Joel M

2016-07-14

Semiclassical quantization of vibrational energies, using adiabatic switching (AS), is applied to CH4 using a recent ab initio potential energy surface, for which exact quantum calculations of vibrational energies are available. Details of the present calculations, which employ a harmonic normal-mode zeroth-order Hamiltonian, emphasize the importance of transforming to the Eckart frame during the propagation of the adiabatically switched Hamiltonian. The AS energies for the zero-point, and fundamental excitations of two modes are in good agreement with the quantum ones. The use of AS in the context of quasi-classical trajectory calculations is revisited, following previous work reported in 1995, which did not recommend the procedure. We come to a different conclusion here.

Classical scattering calculations for diatomic molecules: A general procedure and application to the microwave spectrum O2

NASA Technical Reports Server (NTRS)

Mingelgrin, U.

1972-01-01

Many properties of gaseous systems such as electromagnetic absorption and emission, sound dispersion and absorption, may be elucidated if the nature of collisions between the particles in the system is understood. A procedure for the calculation of the classical trajectories of two interacting diatomic molecules is described. The dynamics of the collision will be assumed to be that of two rigid rotors moving in a specified potential. The actual outcome of a representative sample of many trajectories at 298K was computed, and the use of these values at any temperature for calculations of various molecular properties will be described. Calculations performed for the O2 microwave spectrum are given to demonstrate the use of the procedure described.

Lenard-Balescu calculations and classical molecular dynamics simulations of electrical and thermal conductivities of hydrogen plasmas

DOE PAGES

Whitley, Heather D.; Scullard, Christian R.; Benedict, Lorin X.; ...

2014-12-04

Here, we present a discussion of kinetic theory treatments of linear electrical and thermal transport in hydrogen plasmas, for a regime of interest to inertial confinement fusion applications. In order to assess the accuracy of one of the more involved of these approaches, classical Lenard-Balescu theory, we perform classical molecular dynamics simulations of hydrogen plasmas using 2-body quantum statistical potentials and compute both electrical and thermal conductivity from out particle trajectories using the Kubo approach. Our classical Lenard-Balescu results employing the identical statistical potentials agree well with the simulations.

Semiclassical relation between open trajectories and periodic orbits for the Wigner time delay.

PubMed

Kuipers, Jack; Sieber, Martin

2008-04-01

The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system. We show how these two pictures are related on the semiclassical level. We start from the semiclassical formula with the scattering trajectories and derive from it all terms in the periodic orbit formula for the time delay. The main ingredient in this calculation are correlations between scattering trajectories which are due to trajectories that approach the trapped periodic orbits closely. The equivalence between the two pictures is also demonstrated by considering correlation functions of the time delay. A corresponding calculation for the conductance gives no periodic orbit contributions in leading order.

Anharmonic quantum mechanical systems do not feature phase space trajectories

NASA Astrophysics Data System (ADS)

Oliva, Maxime; Kakofengitis, Dimitris; Steuernagel, Ole

2018-07-01

Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absence of trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantum mechanical systems is responsible for the occurrence of singularities in their phase space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase space dynamics.

Non-adiabatic dynamics around a conical intersection with surface-hopping coupled coherent states

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

Humeniuk, Alexander; Mitrić, Roland, E-mail: roland.mitric@uni-wuerzburg.de

A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully’s fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronicmore » wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states.« less

Self-Learning Monte Carlo Method

NASA Astrophysics Data System (ADS)

Liu, Junwei; Qi, Yang; Meng, Zi Yang; Fu, Liang

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of general and efficient update algorithm for large size systems close to phase transition or with strong frustrations, for which local updates perform badly. In this work, we propose a new general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup. This work is supported by the DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010526.

Aerodynamic characterisation and trajectory simulations for the Ariane-5 booster recovery system

NASA Astrophysics Data System (ADS)

Meiboom, F. P.

One of the most critical aspects of the early phases of the development of the Ariane-5 booster recovery system was the determination of the behavior of the booster during its atmospheric reentry, since this behavior determines the start conditions for the parachute system elements. A combination of wind-tunnel tests (subsonic and supersonic) and analytical methods was applied to define the aerodynamic characteristics of the booster. This aerodynamic characterization in combination with information of the ascent trajectory, atmospheric properties and booster mass and inertia were used as input for the 6-DOF trajectory simulations of the vehicle. Uncertainties in aerodynamic properties and deviations in atmospheric and booster properties were incorporated to define the range of initial conditions for the parachute system, utilizing stochastic (Monte-Carlo) methods.

Fully differential cross sections for the single ionization of helium by fast ions: Classical model calculations

NASA Astrophysics Data System (ADS)

Sarkadi, L.

2018-04-01

Fully differential cross sections (FDCSs) have been calculated for the single ionization of helium by 1- and 3-MeV proton and 100-MeV/u C6 + ion impact using the classical trajectory Monte Carlo (CTMC) method in the nonrelativistic, three-body approximation. The calculations were made employing a Wigner-type model in which the quantum-mechanical position distribution of the electron is approximated by a weighted integral of the microcanonical distribution over a range of the binding energy of the electron. In the scattering plane, the model satisfactorily reproduces the observed shape of the binary peak. In the region of the peak the calculated FDCSs agree well with the results of continuum-distorted-wave calculations for all the investigated collisions. For 1-MeV proton impact the experimentally observed shift of the binary peak with respect to the first Born approximation is compared with the shifts obtained by different higher-order quantum-mechanical theories and the present CTMC method. The best result was achieved by CTMC, but still a large part of the shift remained unexplained. Furthermore, it was found that the classical theory failed to reproduce the shape of the recoil peak observed in the experiments, it predicts a much narrower peak. This indicates that the formation of the recoil peak is dominated by quantum-mechanical effects. For 100-MeV/u C6 + ion impact the present CTMC calculations confirmed the existence of the "double-peak" structure of the angular distribution of the electron in the plane perpendicular to the momentum transfer, in accordance with the observation, the prediction of an incoherent semiclassical model, and previous CTMC results. This finding together with wave-packet calculations suggests that the "C6 + puzzle" may be solved by considering the loss of the projectile coherence. Experiments to be conducted using ion beams of anisotropic coherence are proposed for a more differential investigation of the ionization dynamics.

A multi-state trajectory method for non-adiabatic dynamics simulations

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

Tao, Guohua, E-mail: taogh@pkusz.edu.cn

2016-03-07

A multi-state trajectory approach is proposed to describe nuclear-electron coupled dynamics in nonadiabatic simulations. In this approach, each electronic state is associated with an individual trajectory, among which electronic transition occurs. The set of these individual trajectories constitutes a multi-state trajectory, and nuclear dynamics is described by one of these individual trajectories as the system is on the corresponding state. The total nuclear-electron coupled dynamics is obtained from the ensemble average of the multi-state trajectories. A variety of benchmark systems such as the spin-boson system have been tested and the results generated using the quasi-classical version of the method showmore » reasonably good agreement with the exact quantum calculations. Featured in a clear multi-state picture, high efficiency, and excellent numerical stability, the proposed method may have advantages in being implemented to realistic complex molecular systems, and it could be straightforwardly applied to general nonadiabatic dynamics involving multiple states.« less

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

Shah, Jainil P., E-mail: jainil.shah@duke.edu; Mann, Steve D.; McKinley, Randolph L.

Purpose: A novel breast CT system capable of arbitrary 3D trajectories has been developed to address cone beam sampling insufficiency as well as to image further into the patient’s chest wall. The purpose of this study was to characterize any trajectory-related differences in 3D x-ray dose distribution in a pendant target when imaged with different orbits. Methods: Two acquisition trajectories were evaluated: circular azimuthal (no-tilt) and sinusoidal (saddle) orbit with ±15° tilts around a pendant breast, using Monte Carlo simulations as well as physical measurements. Simulations were performed with tungsten (W) filtration of a W-anode source; the simulated source fluxmore » was normalized to the measured exposure of a W-anode source. A water-filled cylindrical phantom was divided into 1 cm{sup 3} voxels, and the cumulative energy deposited was tracked in each voxel. Energy deposited per voxel was converted to dose, yielding the 3D distributed dose volumes. Additionally, three cylindrical phantoms of different diameters (10, 12.5, and 15 cm) and an anthropomorphic breast phantom, initially filled with water (mimicking pure fibroglandular tissue) and then with a 75% methanol-25% water mixture (mimicking 50–50 fibroglandular-adipose tissues), were used to simulate the pendant breast geometry and scanned on the physical system. Ionization chamber calibrated radiochromic film was used to determine the dose delivered in a 2D plane through the center of the volume for a fully 3D CT scan using the different orbits. Results: Measured experimental results for the same exposure indicated that the mean dose measured throughout the central slice for different diameters ranged from 3.93 to 5.28 mGy, with the lowest average dose measured on the largest cylinder with water mimicking a homogeneously fibroglandular breast. These results align well with the cylinder phantom Monte Carlo studies which also showed a marginal difference in dose delivered by a saddle trajectory in the central slice. Regardless of phantom material or filled fluid density, dose delivered by the saddle scan was negligibly different than the simple circular, no-tilt scans. The average dose measured in the breast phantom was marginally higher for saddle than the circular no tilt scan at 3.82 and 3.87 mGy, respectively. Conclusions: Not only does nontraditional 3D-trajectory CT scanning yield more complete sampling of the breast volume but also has comparable dose deposition throughout the breast and anterior chest volume, as verified by Monte Carlo simulation and physical measurements.« less

Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation.

PubMed

Liu, Jian; Miller, William H

2007-06-21

It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" [H. W. Lee and M. D. Scully, J. Chem. Phys. 77, 4604 (1982)] and the full Donoso-Martens dynamics (full DMD) and the second order DMD based on "Donoso-Martens trajectories" [A. Donoso and C. C. Martens, Phys. Rev. Lett. 8722, 223202 (2001)]--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.

Zero-point energy conservation in classical trajectory simulations: Application to H2CO

NASA Astrophysics Data System (ADS)

Lee, Kin Long Kelvin; Quinn, Mitchell S.; Kolmann, Stephen J.; Kable, Scott H.; Jordan, Meredith J. T.

2018-05-01

A new approach for preventing zero-point energy (ZPE) violation in quasi-classical trajectory (QCT) simulations is presented and applied to H2CO "roaming" reactions. Zero-point energy may be problematic in roaming reactions because they occur at or near bond dissociation thresholds and these channels may be incorrectly open or closed depending on if, or how, ZPE has been treated. Here we run QCT simulations on a "ZPE-corrected" potential energy surface defined as the sum of the molecular potential energy surface (PES) and the global harmonic ZPE surface. Five different harmonic ZPE estimates are examined with four, on average, giving values within 4 kJ/mol—chemical accuracy—for H2CO. The local harmonic ZPE, at arbitrary molecular configurations, is subsequently defined in terms of "projected" Cartesian coordinates and a global ZPE "surface" is constructed using Shepard interpolation. This, combined with a second-order modified Shepard interpolated PES, V, allows us to construct a proof-of-concept ZPE-corrected PES for H2CO, Veff, at no additional computational cost to the PES itself. Both V and Veff are used to model product state distributions from the H + HCO → H2 + CO abstraction reaction, which are shown to reproduce the literature roaming product state distributions. Our ZPE-corrected PES allows all trajectories to be analysed, whereas, in previous simulations, a significant proportion was discarded because of ZPE violation. We find ZPE has little effect on product rotational distributions, validating previous QCT simulations. Running trajectories on V, however, shifts the product kinetic energy release to higher energy than on Veff and classical simulations of kinetic energy release should therefore be viewed with caution.

Effect of polarization forces on carbon deposition on a non-spherical nanoparticle. Monte Carlo simulations [Effect of polarization forces on atom deposition on a non-spherical nanoparticle. Monte Carlo simulations

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

Nemchinsky, V.; Khrabry, A.

Trajectories of a polarizable species (atoms or molecules) in the vicinity of a negatively charged nanoparticle (at a floating potential) are considered. The atoms are pulled into regions of strong electric field by polarization forces. The polarization increases the deposition rate of the atoms and molecules at the nanoparticle. The effect of the non-spherical shape of the nanoparticle is investigated by the Monte Carlo method. The shape of the non-spherical nanoparticle is approximated by an ellipsoid. The total deposition rate and its flux density distribution along the nanoparticle surface are calculated. As a result, it is shown that the fluxmore » density is not uniform along the surface. It is maximal at the nanoparticle tips.« less

Effect of polarization forces on carbon deposition on a non-spherical nanoparticle. Monte Carlo simulations [Effect of polarization forces on atom deposition on a non-spherical nanoparticle. Monte Carlo simulations

DOE PAGES

Nemchinsky, V.; Khrabry, A.

2018-02-01

Trajectories of a polarizable species (atoms or molecules) in the vicinity of a negatively charged nanoparticle (at a floating potential) are considered. The atoms are pulled into regions of strong electric field by polarization forces. The polarization increases the deposition rate of the atoms and molecules at the nanoparticle. The effect of the non-spherical shape of the nanoparticle is investigated by the Monte Carlo method. The shape of the non-spherical nanoparticle is approximated by an ellipsoid. The total deposition rate and its flux density distribution along the nanoparticle surface are calculated. As a result, it is shown that the fluxmore » density is not uniform along the surface. It is maximal at the nanoparticle tips.« less

The envelope of ballistic trajectories and elliptic orbits

NASA Astrophysics Data System (ADS)

Butikov, Eugene I.

2015-11-01

Simple geometric derivations are given for the shape of the "safety domain" boundary for the family of Keplerian orbits of equal energy in a central gravitational field and for projectile trajectories in a uniform field. Examples of practical uses of the envelope of the family of orbits are discussed and illustrated by computer simulations. This material is appropriate for physics teachers and undergraduate students studying classical mechanics and orbital motions.

KmL3D: a non-parametric algorithm for clustering joint trajectories.

PubMed

Genolini, C; Pingault, J B; Driss, T; Côté, S; Tremblay, R E; Vitaro, F; Arnaud, C; Falissard, B

2013-01-01

In cohort studies, variables are measured repeatedly and can be considered as trajectories. A classic way to work with trajectories is to cluster them in order to detect the existence of homogeneous patterns of evolution. Since cohort studies usually measure a large number of variables, it might be interesting to study the joint evolution of several variables (also called joint-variable trajectories). To date, the only way to cluster joint-trajectories is to cluster each trajectory independently, then to cross the partitions obtained. This approach is unsatisfactory because it does not take into account a possible co-evolution of variable-trajectories. KmL3D is an R package that implements a version of k-means dedicated to clustering joint-trajectories. It provides facilities for the management of missing values, offers several quality criteria and its graphic interface helps the user to select the best partition. KmL3D can work with any number of joint-variable trajectories. In the restricted case of two joint trajectories, it proposes 3D tools to visualize the partitioning and then export 3D dynamic rotating-graphs to PDF format. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Effects of reactant rotational excitation on H + O2--> OH + O reaction rate constant: quantum wave packet, quasi-classical trajectory and phase space theory calculations.

PubMed

Lin, Shi Ying; Guo, Hua; Lendvay, György; Xie, Daiqian

2009-06-21

We examine the impact of initial rotational excitation on the reactivity of the H + O(2)--> OH + O reaction. Accurate Chebyshev wave packet calculations have been carried out for the upsilon(i) = 0, j(i) = 9 initial state of O(2) and the J = 50 partial wave. In addition, we present Gaussian-weighted quasi-classical trajectory and phase space theory calculations of the integral cross section and thermal rate constant for the title reaction. These theoretical results suggest that the initial rotational excitation significantly enhances reactivity with an amount comparable to the effect of initial vibrational state excitation. The inclusion of internally excited reactants is shown to improve the agreement with experimental rate constant.

Gaussian-based techniques for quantum propagation from the time-dependent variational principle: Formulation in terms of trajectories of coupled classical and quantum variables

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

Shalashilin, Dmitrii V.; Burghardt, Irene

2008-08-28

In this article, two coherent-state based methods of quantum propagation, namely, coupled coherent states (CCS) and Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH), are put on the same formal footing, using a derivation from a variational principle in Lagrangian form. By this approach, oscillations of the classical-like Gaussian parameters and oscillations of the quantum amplitudes are formally treated in an identical fashion. We also suggest a new approach denoted here as coupled coherent states trajectories (CCST), which completes the family of Gaussian-based methods. Using the same formalism for all related techniques allows their systematization and a straightforward comparison of their mathematical structuremore » and cost.« less

Fluctuating observation time ensembles in the thermodynamics of trajectories

NASA Astrophysics Data System (ADS)

Budini, Adrián A.; Turner, Robert M.; Garrahan, Juan P.

2014-03-01

The dynamics of stochastic systems, both classical and quantum, can be studied by analysing the statistical properties of dynamical trajectories. The properties of ensembles of such trajectories for long, but fixed, times are described by large-deviation (LD) rate functions. These LD functions play the role of dynamical free energies: they are cumulant generating functions for time-integrated observables, and their analytic structure encodes dynamical phase behaviour. This ‘thermodynamics of trajectories’ approach is to trajectories and dynamics what the equilibrium ensemble method of statistical mechanics is to configurations and statics. Here we show that, just like in the static case, there are a variety of alternative ensembles of trajectories, each defined by their global constraints, with that of trajectories of fixed total time being just one of these. We show how the LD functions that describe an ensemble of trajectories where some time-extensive quantity is constant (and large) but where total observation time fluctuates can be mapped to those of the fixed-time ensemble. We discuss how the correspondence between generalized ensembles can be exploited in path sampling schemes for generating rare dynamical trajectories.

Importance sampling large deviations in nonequilibrium steady states. I.

PubMed

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T

2018-03-28

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

Importance sampling large deviations in nonequilibrium steady states. I

NASA Astrophysics Data System (ADS)

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.

2018-03-01

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

Exploring cluster Monte Carlo updates with Boltzmann machines

NASA Astrophysics Data System (ADS)

Wang, Lei

2017-11-01

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

Ground-state candidate for the classical dipolar kagome Ising antiferromagnet

NASA Astrophysics Data System (ADS)

Chioar, I. A.; Rougemaille, N.; Canals, B.

2016-06-01

We have investigated the low-temperature thermodynamic properties of the classical dipolar kagome Ising antiferromagnet using Monte Carlo simulations, in the quest for the ground-state manifold. In spite of the limitations of a single-spin-flip approach, we managed to identify certain ordering patterns in the low-temperature regime and we propose a candidate for this unknown state. This configuration presents some intriguing features and is fully compatible with the extrapolations of the at-equilibrium thermodynamic behavior sampled so far, making it a very likely choice for the dipolar long-range ordered state of the classical kagome Ising antiferromagnet.

Quantum annealing of the traveling-salesman problem.

PubMed

Martonák, Roman; Santoro, Giuseppe E; Tosatti, Erio

2004-11-01

We propose a path-integral Monte Carlo quantum annealing scheme for the symmetric traveling-salesman problem, based on a highly constrained Ising-like representation, and we compare its performance against standard thermal simulated annealing. The Monte Carlo moves implemented are standard, and consist in restructuring a tour by exchanging two links (two-opt moves). The quantum annealing scheme, even with a drastically simple form of kinetic energy, appears definitely superior to the classical one, when tested on a 1002-city instance of the standard TSPLIB.

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.}

State-to-state models of vibrational relaxation in Direct Simulation Monte Carlo (DSMC)

NASA Astrophysics Data System (ADS)

Oblapenko, G. P.; Kashkovsky, A. V.; Bondar, Ye A.

2017-02-01

In the present work, the application of state-to-state models of vibrational energy exchanges to the Direct Simulation Monte Carlo (DSMC) is considered. A state-to-state model for VT transitions of vibrational energy in nitrogen and oxygen, based on the application of the inverse Laplace transform to results of quasiclassical trajectory calculations (QCT) of vibrational energy transitions, along with the Forced Harmonic Oscillator (FHO) state-to-state model is implemented in DSMC code and applied to flows around blunt bodies. Comparisons are made with the widely used Larsen-Borgnakke model and the in uence of multi-quantum VT transitions is assessed.

Calculated rate constants for the reaction ClO + O yields Cl + O2 between 220 and 1000 deg K. [molecular trajectories and stratospheric ozone

NASA Technical Reports Server (NTRS)

Jaffee, R. L.

1978-01-01

Classical trajectory calculations are presented for the reaction ClO + O yields Cl + O2, a reaction which is an important step in the chlorine-catalyzed destruction of ozone which is thought to occur in the 220 and 1000 K. The calculated rate constant is 4.36 x 10 to the minus 11th power exp (-191/T)cu cm molecule (-1)s(-1) and its value at 300 K is 2.3 plus or minus 10 to the 11th power cu cm molecule (-1)s(-1), about a factor of 2 lower than recent experimental data. The empirical potential energy surface used in the calculations was constructed to fit experimental data for ClO, O2 and ClOO molecules. Other important features of this potential surface, such as the barrier to reaction, were varied systematically and calculations were performed for a range of conditions to determine the best theoretical rate constants. Results demonstrate the utility of classical trajectory methods for determining activation energies and other kinetic data for important atmospheric reactions.

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

NASA Astrophysics Data System (ADS)

Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido

2016-06-01

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

NASA Astrophysics Data System (ADS)

Beck, Joakim; Dia, Ben Mansour; Espath, Luis F. R.; Long, Quan; Tempone, Raúl

2018-06-01

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

Gutzwiller Monte Carlo approach for a critical dissipative spin model

NASA Astrophysics Data System (ADS)

Casteels, Wim; Wilson, Ryan M.; Wouters, Michiel

2018-06-01

We use the Gutzwiller Monte Carlo approach to simulate the dissipative X Y Z model in the vicinity of a dissipative phase transition. This approach captures classical spatial correlations together with the full on-site quantum behavior while neglecting nonlocal quantum effects. By considering finite two-dimensional lattices of various sizes, we identify a ferromagnetic and two paramagnetic phases, in agreement with earlier studies. The greatly reduced numerical complexity of the Gutzwiller Monte Carlo approach facilitates efficient simulation of relatively large lattice sizes. The inclusion of the spatial correlations allows to capture parts of the phase diagram that are completely missed by the widely applied Gutzwiller decoupling of the density matrix.

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

Rodríguez-Cantano, Rocío; Pérez de Tudela, Ricardo; Bartolomei, Massimiliano

Coronene-doped helium clusters have been studied by means of classical and quantum mechanical (QM) methods using a recently developed He–C{sub 24}H{sub 12} global potential based on the use of optimized atom-bond improved Lennard-Jones functions. Equilibrium energies and geometries at global and local minima for systems with up to 69 He atoms were calculated by means of an evolutive algorithm and a basin-hopping approach and compared with results from path integral Monte Carlo (PIMC) calculations at 2 K. A detailed analysis performed for the smallest sizes shows that the precise localization of the He atoms forming the first solvation layer overmore » the molecular substrate is affected by differences between relative potential minima. The comparison of the PIMC results with the predictions from the classical approaches and with diffusion Monte Carlo results allows to examine the importance of both the QM and thermal effects.« less

Statistical Analysis of the Uncertainty in Pre-Flight Aerodynamic Database of a Hypersonic Vehicle

NASA Astrophysics Data System (ADS)

Huh, Lynn

The objective of the present research was to develop a new method to derive the aerodynamic coefficients and the associated uncertainties for flight vehicles via post- flight inertial navigation analysis using data from the inertial measurement unit. Statistical estimates of vehicle state and aerodynamic coefficients are derived using Monte Carlo simulation. Trajectory reconstruction using the inertial navigation system (INS) is a simple and well used method. However, deriving realistic uncertainties in the reconstructed state and any associated parameters is not so straight forward. Extended Kalman filters, batch minimum variance estimation and other approaches have been used. However, these methods generally depend on assumed physical models, assumed statistical distributions (usually Gaussian) or have convergence issues for non-linear problems. The approach here assumes no physical models, is applicable to any statistical distribution, and does not have any convergence issues. The new approach obtains the statistics directly from a sufficient number of Monte Carlo samples using only the generally well known gyro and accelerometer specifications and could be applied to the systems of non-linear form and non-Gaussian distribution. When redundant data are available, the set of Monte Carlo simulations are constrained to satisfy the redundant data within the uncertainties specified for the additional data. The proposed method was applied to validate the uncertainty in the pre-flight aerodynamic database of the X-43A Hyper-X research vehicle. In addition to gyro and acceleration data, the actual flight data include redundant measurements of position and velocity from the global positioning system (GPS). The criteria derived from the blend of the GPS and INS accuracy was used to select valid trajectories for statistical analysis. The aerodynamic coefficients were derived from the selected trajectories by either direct extraction method based on the equations in dynamics, or by the inquiry of the pre-flight aerodynamic database. After the application of the proposed method to the case of the X-43A Hyper-X research vehicle, it was found that 1) there were consistent differences in the aerodynamic coefficients from the pre-flight aerodynamic database and post-flight analysis, 2) the pre-flight estimation of the pitching moment coefficients was significantly different from the post-flight analysis, 3) the type of distribution of the states from the Monte Carlo simulation were affected by that of the perturbation parameters, 4) the uncertainties in the pre-flight model were overestimated, 5) the range where the aerodynamic coefficients from the pre-flight aerodynamic database and post-flight analysis are in closest agreement is between Mach *.* and *.* and more data points may be needed between Mach * and ** in the pre-flight aerodynamic database, 6) selection criterion for valid trajectories from the Monte Carlo simulations was mostly driven by the horizontal velocity error, 7) the selection criterion must be based on reasonable model to ensure the validity of the statistics from the proposed method, and 8) the results from the proposed method applied to the two different flights with the identical geometry and similar flight profile were consistent.

Transfer Trajectory Design for the Mars Atmosphere and Volatile Evolution (MAVEN) Mission

NASA Technical Reports Server (NTRS)

Folta, David; Demcak, Stuart; Young, Brian; Berry, Kevin

2013-01-01

The Mars Atmosphere and Volatile Evolution (MAVEN) mission will determine the history of the loss of volatiles from the Martian atmosphere from a highly inclined elliptical orbit. MAVEN will launch from Cape Canaveral Air Force Station on an Atlas-V 401 during an extended 36-day launch period opening November 18, 2013. The MAVEN Navigation and Mission Design team performed a Monte Carlo analysis of the Type-II transfer to characterize; dispersions of the arrival B-Plane, trajectory correction maneuvers (TCMs), and the probability of Mars impact. This paper presents detailed analysis of critical MOI event coverage, maneuver constraints, deltaV-99 budgets, and Planetary Protection requirements.

Real-time dynamics of matrix quantum mechanics beyond the classical approximation

NASA Astrophysics Data System (ADS)

Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas

2018-03-01

We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.

Simulation of radiation damping in rings, using stepwise ray-tracing methods

DOE PAGES

Meot, F.

2015-06-26

The ray-tracing code Zgoubi computes particle trajectories in arbitrary magnetic and/or electric field maps or analytical field models. It includes a built-in fitting procedure, spin tracking many Monte Carlo processes. The accuracy of the integration method makes it an efficient tool for multi-turn tracking in periodic machines. Energy loss by synchrotron radiation, based on Monte Carlo techniques, had been introduced in Zgoubi in the early 2000s for studies regarding the linear collider beam delivery system. However, only recently has this Monte Carlo tool been used for systematic beam dynamics and spin diffusion studies in rings, including eRHIC electron-ion collider projectmore » at the Brookhaven National Laboratory. Some beam dynamics aspects of this recent use of Zgoubi capabilities, including considerations of accuracy as well as further benchmarking in the presence of synchrotron radiation in rings, are reported here.« less

Trajectory Optimization for Missions to Small Bodies with a Focus on Scientific Merit.

PubMed

Englander, Jacob A; Vavrina, Matthew A; Lim, Lucy F; McFadden, Lucy A; Rhoden, Alyssa R; Noll, Keith S

2017-01-01

Trajectory design for missions to small bodies is tightly coupled both with the selection of targets for a mission and with the choice of spacecraft power, propulsion, and other hardware. Traditional methods of trajectory optimization have focused on finding the optimal trajectory for an a priori selection of destinations and spacecraft parameters. Recent research has expanded the field of trajectory optimization to multidisciplinary systems optimization that includes spacecraft parameters. The logical next step is to extend the optimization process to include target selection based not only on engineering figures of merit but also scientific value. This paper presents a new technique to solve the multidisciplinary mission optimization problem for small-bodies missions, including classical trajectory design, the choice of spacecraft power and propulsion systems, and also the scientific value of the targets. This technique, when combined with modern parallel computers, enables a holistic view of the small body mission design process that previously required iteration among several different design processes.

Ehrenfest dynamics is purity non-preserving: A necessary ingredient for decoherence

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

Alonso, J. L.; Instituto de Biocomputacion y Fisica de Sistemas Complejos; Unidad Asociada IQFR-BIFI, Universidad de Zaragoza, Mariano Esquillor s/n, E-50018 Zaragoza

2012-08-07

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamicsmore » makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.« less

Power-law distributions for a trapped ion interacting with a classical buffer gas.

PubMed

DeVoe, Ralph G

2009-02-13

Classical collisions with an ideal gas generate non-Maxwellian distribution functions for a single ion in a radio frequency ion trap. The distributions have power-law tails whose exponent depends on the ratio of buffer gas to ion mass. This provides a statistical explanation for the previously observed transition from cooling to heating. Monte Carlo results approximate a Tsallis distribution over a wide range of parameters and have ab initio agreement with experiment.

Representing and selecting vibrational angular momentum states for quasiclassical trajectory chemical dynamics simulations.

PubMed

Lourderaj, Upakarasamy; Martínez-Núñez, Emilio; Hase, William L

2007-10-18

Linear molecules with degenerate bending modes have states, which may be represented by the quantum numbers N and L. The former gives the total energy for these modes and the latter identifies their vibrational angular momentum jz. In this work, the classical mechanical analog of the N,L-quantum states is reviewed, and an algorithm is presented for selecting initial conditions for these states in quasiclassical trajectory chemical dynamics simulations. The algorithm is illustrated by choosing initial conditions for the N = 3 and L = 3 and 1 states of CO2. Applications of this algorithm are considered for initial conditions without and with zero-point energy (zpe) included in the vibrational angular momentum states and the C-O stretching modes. The O-atom motions in the x,y-plane are determined for these states from classical trajectories in Cartesian coordinates and are compared with the motion predicted by the normal-mode model. They are only in agreement for the N = L = 3 state without vibrational angular momentum zpe. For the remaining states, the Cartesian O-atom motions are considerably different from the elliptical motion predicted by the normal-mode model. This arises from bend-stretch coupling, including centrifugal distortion, in the Cartesian trajectories, which results in tubular instead of elliptical motion. Including zpe in the C-O stretch modes introduces considerable complexity into the O-atom motions for the vibrational angular momentum states. The short-time O-atom motions for these trajectories are highly irregular and do not appear to have any identifiable characteristics. However, the O-atom motions for trajectories integrated for substantially longer period of times acquire unique properties. With C-O stretch zpe included, the long-time O-atom motion becomes tubular for trajectories integrated to approximately 14 ps for the L = 3 states and to approximately 44 ps for the L = 1 states.

Analysis of self-overlap reveals trade-offs in plankton swimming trajectories

PubMed Central

Bianco, Giuseppe; Mariani, Patrizio; Visser, Andre W.; Mazzocchi, Maria Grazia; Pigolotti, Simone

2014-01-01

Movement is a fundamental behaviour of organisms that not only brings about beneficial encounters with resources and mates, but also at the same time exposes the organism to dangerous encounters with predators. The movement patterns adopted by organisms should reflect a balance between these contrasting processes. This trade-off can be hypothesized as being evident in the behaviour of plankton, which inhabit a dilute three-dimensional environment with few refuges or orienting landmarks. We present an analysis of the swimming path geometries based on a volumetric Monte Carlo sampling approach, which is particularly adept at revealing such trade-offs by measuring the self-overlap of the trajectories. Application of this method to experimentally measured trajectories reveals that swimming patterns in copepods are shaped to efficiently explore volumes at small scales, while achieving a large overlap at larger scales. Regularities in the observed trajectories make the transition between these two regimes always sharper than in randomized trajectories or as predicted by random walk theory. Thus, real trajectories present a stronger separation between exploration for food and exposure to predators. The specific scale and features of this transition depend on species, gender and local environmental conditions, pointing at adaptation to state and stage-dependent evolutionary trade-offs. PMID:24789560

Classical trajectory studies of gas phase reaction dynamics and kinetics using ab initio potential energy surfaces

NASA Technical Reports Server (NTRS)

Jaffe, Richard L.; Pattengill, Merle D.; Schwenke, David W.

1989-01-01

Strategies for constructing global potential energy surfaces from a limited number of accurate ab initio electronic energy calculations are discussed. Generally, these data are concentrated in small regions of configuration space (e.g., in the vicinity of saddle points and energy minima) and difficulties arise in generating a potential function that is globally well-behaved. Efficient computer codes for carrying out classical trajectory calculations on vector and parallel processors are also described. Illustrations are given from recent work on the following chemical systems: Ca + HF yields CaF + H, H + H + H2 yields H2 + H2, N + O2 yields NO + O and O + N2 yields NO + N. The dynamics and kinetics of metathesis, dissociation, recombination, energy transfer and complex formation processes will be discussed.

Incidents Prediction in Road Junctions Using Artificial Neural Networks

NASA Astrophysics Data System (ADS)

Hajji, Tarik; Alami Hassani, Aicha; Ouazzani Jamil, Mohammed

2018-05-01

The implementation of an incident detection system (IDS) is an indispensable operation in the analysis of the road traffics. However the IDS may, in no case, represent an alternative to the classical monitoring system controlled by the human eye. The aim of this work is to increase detection and prediction probability of incidents in camera-monitored areas. Knowing that, these areas are monitored by multiple cameras and few supervisors. Our solution is to use Artificial Neural Networks (ANN) to analyze moving objects trajectories on captured images. We first propose a modelling of the trajectories and their characteristics, after we develop a learning database for valid and invalid trajectories, and then we carry out a comparative study to find the artificial neural network architecture that maximizes the rate of valid and invalid trajectories recognition.

Predicting absorption and dispersion in acoustics by direct simulation Monte Carlo: Quantum and classical models for molecular relaxation.

PubMed

Hanford, Amanda D; O'Connor, Patrick D; Anderson, James B; Long, Lyle N

2008-06-01

In the current study, real gas effects in the propagation of sound waves are simulated using the direct simulation Monte Carlo method for a wide range of frequencies. This particle method allows for treatment of acoustic phenomena at high Knudsen numbers, corresponding to low densities and a high ratio of the molecular mean free path to wavelength. Different methods to model the internal degrees of freedom of diatomic molecules and the exchange of translational, rotational and vibrational energies in collisions are employed in the current simulations of a diatomic gas. One of these methods is the fully classical rigid-rotor/harmonic-oscillator model for rotation and vibration. A second method takes into account the discrete quantum energy levels for vibration with the closely spaced rotational levels classically treated. This method gives a more realistic representation of the internal structure of diatomic and polyatomic molecules. Applications of these methods are investigated in diatomic nitrogen gas in order to study the propagation of sound and its attenuation and dispersion along with their dependence on temperature. With the direct simulation method, significant deviations from continuum predictions are also observed for high Knudsen number flows.

Poincaré resonances and the limits of trajectory dynamics.

PubMed Central

Petrosky, T; Prigogine, I

1993-01-01

In previous papers we have shown that the elimination of the resonance divergences in large Poincare systems leads to complex irreducible spectral representations for the Liouville-von Neumann operator. Complex means that time symmetry is broken and irreducibility means that this representation is implementable only by statistical ensembles and not by trajectories. We consider in this paper classical potential scattering. Our theory applies to persistent scattering. Numerical simulations show quantitative agreement with our predictions. PMID:11607428

Formaldehyde roaming dynamics: Comparison of quasi-classical trajectory calculations and experiments.

PubMed

Houston, Paul L; Wang, Xiaohong; Ghosh, Aryya; Bowman, Joel M; Quinn, Mitchell S; Kable, Scott H

2017-07-07

The photodissociation dynamics of roaming in formaldehyde are studied by comparing quasi-classical trajectory calculations performed on a new potential energy surface (PES) to new and detailed experimental results detailing the CO + H 2 product state distributions and their correlations. The new PES proves to be a significant improvement over the past one, now more than a decade old. The new experiments probe both the CO and H 2 products of the formaldehyde dissociation. The experimental and trajectory data offer unprecedented detail about the correlations between internal states of the CO and H 2 dissociation products as well as information on how these distributions are different for the roaming and transition-state pathways. The data investigated include, for dissociation on the formaldehyde 2 1 4 3 band, (a) the speed distributions for individual vibrational/rotational states of the CO products, providing information about the correlated internal energy distributions of the H 2 product, and (b) the rotational and vibrational distributions for the CO and H 2 products as well as the contributions to each from both the transition state and roaming channels. The agreement between the trajectory and experimental data is quite satisfactory, although minor differences are noted. The general agreement provides support for future use of the experimental techniques and the new PES in understanding the dynamics of photodissociative processes.

A novel Kinetic Monte Carlo algorithm for Non-Equilibrium Simulations

NASA Astrophysics Data System (ADS)

Jha, Prateek; Kuzovkov, Vladimir; Grzybowski, Bartosz; Olvera de La Cruz, Monica

2012-02-01

We have developed an off-lattice kinetic Monte Carlo simulation scheme for reaction-diffusion problems in soft matter systems. The definition of transition probabilities in the Monte Carlo scheme are taken identical to the transition rates in a renormalized master equation of the diffusion process and match that of the Glauber dynamics of Ising model. Our scheme provides several advantages over the Brownian dynamics technique for non-equilibrium simulations. Since particle displacements are accepted/rejected in a Monte Carlo fashion as opposed to moving particles following a stochastic equation of motion, nonphysical movements (e.g., violation of a hard core assumption) are not possible (these moves have zero acceptance). Further, the absence of a stochastic ``noise'' term resolves the computational difficulties associated with generating statistically independent trajectories with definitive mean properties. Finally, since the timestep is independent of the magnitude of the interaction forces, much longer time-steps can be employed than Brownian dynamics. We discuss the applications of this scheme for dynamic self-assembly of photo-switchable nanoparticles and dynamical problems in polymeric systems.

The Development and Comparison of Molecular Dynamics Simulation and Monte Carlo Simulation

NASA Astrophysics Data System (ADS)

Chen, Jundong

2018-03-01

Molecular dynamics is an integrated technology that combines physics, mathematics and chemistry. Molecular dynamics method is a computer simulation experimental method, which is a powerful tool for studying condensed matter system. This technique not only can get the trajectory of the atom, but can also observe the microscopic details of the atomic motion. By studying the numerical integration algorithm in molecular dynamics simulation, we can not only analyze the microstructure, the motion of particles and the image of macroscopic relationship between them and the material, but can also study the relationship between the interaction and the macroscopic properties more conveniently. The Monte Carlo Simulation, similar to the molecular dynamics, is a tool for studying the micro-molecular and particle nature. In this paper, the theoretical background of computer numerical simulation is introduced, and the specific methods of numerical integration are summarized, including Verlet method, Leap-frog method and Velocity Verlet method. At the same time, the method and principle of Monte Carlo Simulation are introduced. Finally, similarities and differences of Monte Carlo Simulation and the molecular dynamics simulation are discussed.

Control of asteroid retrieval trajectories to libration point orbits

NASA Astrophysics Data System (ADS)

Ceriotti, Matteo; Sanchez, Joan Pau

2016-09-01

The fascinating idea of shepherding asteroids for science and resource utilization is being considered as a credible concept in a not too distant future. Past studies identified asteroids which could be efficiently injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system. However, the trajectories are unstable, and errors in the capture maneuver would lead to complete mission failure, with potential danger of collision with the Earth, if uncontrolled. This paper investigates the controllability of some asteroids along the transfers and the periodic orbits, assuming the use of a solar-electric low-thrust system shepherding the asteroid. Firstly, an analytical approach is introduced to estimate the stability of the trajectories from a dynamical point of view; then, a numerical control scheme based on a linear quadratic regulator is proposed, where the gains are optimized for each trajectory through a genetic algorithm. A stochastic simulation with a Monte Carlo approach is used to account for different perturbed initial conditions and the epistemic uncertainty on the asteroid mass. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets.

Signatures of the electron saddle swaps mechanism in the photon spectra following charge-exchange collisions

NASA Astrophysics Data System (ADS)

Otranto, Sebastian

2014-10-01

During the last few years, several experimental and theoretical studies have focused on state selective charge exchange processes between charged ions and alkali metals. These data are of particular importance for the tokamak nuclear fusion reactor program, since diagnostics on the plasma usually rely on charge-exchange spectroscopy. In this sense, alkali metals, have been proposed as potential alternatives to excited hydrogen/deuterium for which laboratory experiments are not feasible at present. In this talk, we present our recent work involving ion collisions with alkali metals. Oscillatory structures in the angular differential charge-exchange cross sections obtained using the MOTRIMS technique are correctly described by classical trajectory Monte Carlo simulations. These oscillations are found to originate from the number of swaps the electron undergoes around the projectile-target potential saddle before capture takes place and are very prominent at impact energies below 10 keV/amu. Moreover, cross sections of higher order of differentiability also indicate that the swaps leave distinctive signatures in the (n,l)-state selective cross sections and in the photon line emission cross sections. Oscillatory structures for the x-ray hardness ratio parameter are also predicted. In collaboration with Ronnie Hoekstra, Zernike Institute for Advanced Materials, University of Groningen and Ronald Olson, Department of Physics, Missouri University of Science and Technology.

A study of internal energy relaxation in shocks using molecular dynamics based models

NASA Astrophysics Data System (ADS)

Li, Zheng; Parsons, Neal; Levin, Deborah A.

2015-10-01

Recent potential energy surfaces (PESs) for the N2 + N and N2 + N2 systems are used in molecular dynamics (MD) to simulate rates of vibrational and rotational relaxations for conditions that occur in hypersonic flows. For both chemical systems, it is found that the rotational relaxation number increases with the translational temperature and decreases as the rotational temperature approaches the translational temperature. The vibrational relaxation number is observed to decrease with translational temperature and approaches the rotational relaxation number in the high temperature region. The rotational and vibrational relaxation numbers are generally larger in the N2 + N2 system. MD-quasi-classical trajectory (QCT) with the PESs is also used to calculate the V-T transition cross sections, the collision cross section, and the dissociation cross section for each collision pair. Direct simulation Monte Carlo (DSMC) results for hypersonic flow over a blunt body with the total collision cross section from MD/QCT simulations, Larsen-Borgnakke with new relaxation numbers, and the N2 dissociation rate from MD/QCT show a profile with a decreased translational temperature and a rotational temperature close to vibrational temperature. The results demonstrate that many of the physical models employed in DSMC should be revised as fundamental potential energy surfaces suitable for high temperature conditions become available.

Equivalence principle for quantum systems: dephasing and phase shift of free-falling particles

NASA Astrophysics Data System (ADS)

Anastopoulos, C.; Hu, B. L.

2018-02-01

We ask the question of how the (weak) equivalence principle established in classical gravitational physics should be reformulated and interpreted for massive quantum objects that may also have internal degrees of freedom (dof). This inquiry is necessary because even elementary concepts like a classical trajectory are not well defined in quantum physics—trajectories originating from quantum histories become viable entities only under stringent decoherence conditions. From this investigation we posit two logically and operationally distinct statements of the equivalence principle for quantum systems. Version A: the probability distribution of position for a free-falling particle is the same as the probability distribution of a free particle, modulo a mass-independent shift of its mean. Version B: any two particles with the same velocity wave-function behave identically in free fall, irrespective of their masses. Both statements apply to all quantum states, including those without a classical correspondence, and also for composite particles with quantum internal dof. We also investigate the consequences of the interaction between internal and external dof induced by free fall. For a class of initial states, we find dephasing occurs for the translational dof, namely, the suppression of the off-diagonal terms of the density matrix, in the position basis. We also find a gravitational phase shift in the reduced density matrix of the internal dof that does not depend on the particle’s mass. For classical states, the phase shift has a natural classical interpretation in terms of gravitational red-shift and special relativistic time-dilation.

Mars Exploration Rover Six-Degree-Of-Freedom Entry Trajectory Analysis

NASA Technical Reports Server (NTRS)

Desai, Prasun N.; Schoenenberger, Mark; Cheatwood, F. M.

2003-01-01

The Mars Exploration Rover mission will be the next opportunity for surface exploration of Mars in January 2004. Two rovers will be delivered to the surface of Mars using the same entry, descent, and landing scenario that was developed and successfully implemented by Mars Pathfinder. This investigation describes the trajectory analysis that was performed for the hypersonic portion of the MER entry. In this analysis, a six-degree-of-freedom trajectory simulation of the entry is performed to determine the entry characteristics of the capsules. In addition, a Monte Carlo analysis is also performed to statistically assess the robustness of the entry design to off-nominal conditions to assure that all entry requirements are satisfied. The results show that the attitude at peak heating and parachute deployment are well within entry limits. In addition, the parachute deployment dynamics pressure and Mach number are also well within the design requirements.

Semiclassical propagator of the Wigner function.

PubMed

Dittrich, Thomas; Viviescas, Carlos; Sandoval, Luis

2006-02-24

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.

Computer program for prediction of fuel consumption statistical data for an upper stage three-axes stabilized on-off control system

NASA Technical Reports Server (NTRS)

1982-01-01

A FORTRAN coded computer program and method to predict the reaction control fuel consumption statistics for a three axis stabilized rocket vehicle upper stage is described. A Monte Carlo approach is used which is more efficient by using closed form estimates of impulses. The effects of rocket motor thrust misalignment, static unbalance, aerodynamic disturbances, and deviations in trajectory, mass properties and control system characteristics are included. This routine can be applied to many types of on-off reaction controlled vehicles. The pseudorandom number generation and statistical analyses subroutines including the output histograms can be used for other Monte Carlo analyses problems.

Direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation.

PubMed

Garcia, Alejandro L; Wagner, Wolfgang

2003-11-01

In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.

Absolute Helmholtz free energy of highly anharmonic crystals: theory vs Monte Carlo.

PubMed

Yakub, Lydia; Yakub, Eugene

2012-04-14

We discuss the problem of the quantitative theoretical prediction of the absolute free energy for classical highly anharmonic solids. Helmholtz free energy of the Lennard-Jones (LJ) crystal is calculated accurately while accounting for both the anharmonicity of atomic vibrations and the pair and triple correlations in displacements of the atoms from their lattice sites. The comparison with most precise computer simulation data on sublimation and melting lines revealed that theoretical predictions are in excellent agreement with Monte Carlo simulation data in the whole range of temperatures and densities studied.

Cell-model prediction of the melting of a Lennard-Jones solid

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

Holian, B.L.

The classical free energy of the Lennard-Jones 6-12 solid is computed from a single-particle anharmonic cell model with a correction to the entropy given by the classical correlational entropy of quasiharmonic lattice dynamics. The free energy of the fluid is obtained from the Hansen-Ree analytic fit to Monte Carlo equation-of-state calculations. The resulting predictions of the solid-fluid coexistence curves by this corrected cell model of the solid are in excellent agreement with the computer experiments.

Tracking of Ball and Players in Beach Volleyball Videos

PubMed Central

Gomez, Gabriel; Herrera López, Patricia; Link, Daniel; Eskofier, Bjoern

2014-01-01

This paper presents methods for the determination of players' positions and contact time points by tracking the players and the ball in beach volleyball videos. Two player tracking methods are compared, a classical particle filter and a rigid grid integral histogram tracker. Due to mutual occlusion of the players and the camera perspective, results are best for the front players, with 74,6% and 82,6% of correctly tracked frames for the particle method and the integral histogram method, respectively. Results suggest an improved robustness against player confusion between different particle sets when tracking with a rigid grid approach. Faster processing and less player confusions make this method superior to the classical particle filter. Two different ball tracking methods are used that detect ball candidates from movement difference images using a background subtraction algorithm. Ball trajectories are estimated and interpolated from parabolic flight equations. The tracking accuracy of the ball is 54,2% for the trajectory growth method and 42,1% for the Hough line detection method. Tracking results of over 90% from the literature could not be confirmed. Ball contact frames were estimated from parabolic trajectory intersection, resulting in 48,9% of correctly estimated ball contact points. PMID:25426936

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

Potomkin, Mykhailo; Kaiser, Andreas; Berlyand, Leonid

We consider active particles swimming in a convergent fluid flow in a trapezoid nozzle with no-slip walls. We use mathematical modeling to analyze trajectories of these particles inside the nozzle. By extensive Monte Carlo simulations, we show that trajectories are strongly affected by the background fluid flow and geometry of the nozzle leading to wall accumulation and upstream motion (rheotaxis). In particular, we describe the non-trivial focusing of active rods depending on physical and geometrical parameters. It is also established that the convergent component of the background flow leads to stability of both downstream and upstream swimming at the centerline.more » The stability of downstream swimming enhances focusing, and the stability of upstream swimming enables rheotaxis in the bulk.« less

TEMPEST: Twin Electric Magnetospheric Probes Exploring on Spiral Trajectories--A Proposal to the Medium Class Explorer Program

NASA Technical Reports Server (NTRS)

1995-01-01

The objective of the Twin Electric Magnetospheric Probes Exploring on Spiral Trajectories (TEMPEST) mission is to understand the nature and causes of magnetic storm conditions in the magnetosphere whether they be manifested classically in the buildup of the ring current, or (as recently discovered) by storms of relativistic electrons that cause the deep dielectric charging responsible for disabling satellites in synchronous orbit, or by the release of energy into the auroral ionosphere and the plasma sheet during substorms.

Comparison of cross sections from the quasi-classical trajectory method and the j(z)-conserving centrifugal sudden approximation with accurate quantum results for an atom-rigid nonlinear polyatomic collision

NASA Technical Reports Server (NTRS)

Schwenke, David W.

1993-01-01

We report the results of a series of calculations of state-to-state integral cross sections for collisions between O and nonvibrating H2O in the gas phase on a model nonreactive potential energy surface. The dynamical methods used include converged quantum mechanical scattering calculations, the j(z) conserving centrifugal sudden (j(z)-CCS) approximation, and quasi-classical trajectory (QCT) calculations. We consider three total energies 0.001, 0.002, and 0.005 E(h) and the nine initial states with rotational angular momentum less than or equal to 2 (h/2 pi). The j(z)-CCS approximation gives good results, while the QCT method can be quite unreliable for transitions to specific rotational sublevels. However, the QCT cross sections summed over final sublevels and averaged over initial sublevels are in better agreement with the quantum results.

On classical mechanical systems with non-linear constraints

NASA Astrophysics Data System (ADS)

Terra, Gláucio; Kobayashi, Marcelo H.

2004-03-01

In the present work, we analyze classical mechanical systems with non-linear constraints in the velocities. We prove that the d'Alembert-Chetaev trajectories of a constrained mechanical system satisfy both Gauss' principle of least constraint and Hölder's principle. In the case of a free mechanics, they also satisfy Hertz's principle of least curvature if the constraint manifold is a cone. We show that the Gibbs-Maggi-Appell (GMA) vector field (i.e. the second-order vector field which defines the d'Alembert-Chetaev trajectories) conserves energy for any potential energy if, and only if, the constraint is homogeneous (i.e. if the Liouville vector field is tangent to the constraint manifold). We introduce the Jacobi-Carathéodory metric tensor and prove Jacobi-Carathéodory's theorem assuming that the constraint manifold is a cone. Finally, we present a version of Liouville's theorem on the conservation of volume for the flow of the GMA vector field.

Optimal trajectories for aeroassisted orbital transfer

NASA Technical Reports Server (NTRS)

Miele, A.; Venkataraman, P.

1983-01-01

Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.

Covariance Analysis Tool (G-CAT) for Computing Ascent, Descent, and Landing Errors

NASA Technical Reports Server (NTRS)

Boussalis, Dhemetrios; Bayard, David S.

2013-01-01

G-CAT is a covariance analysis tool that enables fast and accurate computation of error ellipses for descent, landing, ascent, and rendezvous scenarios, and quantifies knowledge error contributions needed for error budgeting purposes. Because GCAT supports hardware/system trade studies in spacecraft and mission design, it is useful in both early and late mission/ proposal phases where Monte Carlo simulation capability is not mature, Monte Carlo simulation takes too long to run, and/or there is a need to perform multiple parametric system design trades that would require an unwieldy number of Monte Carlo runs. G-CAT is formulated as a variable-order square-root linearized Kalman filter (LKF), typically using over 120 filter states. An important property of G-CAT is that it is based on a 6-DOF (degrees of freedom) formulation that completely captures the combined effects of both attitude and translation errors on the propagated trajectories. This ensures its accuracy for guidance, navigation, and control (GN&C) analysis. G-CAT provides the desired fast turnaround analysis needed for error budgeting in support of mission concept formulations, design trade studies, and proposal development efforts. The main usefulness of a covariance analysis tool such as G-CAT is its ability to calculate the performance envelope directly from a single run. This is in sharp contrast to running thousands of simulations to obtain similar information using Monte Carlo methods. It does this by propagating the "statistics" of the overall design, rather than simulating individual trajectories. G-CAT supports applications to lunar, planetary, and small body missions. It characterizes onboard knowledge propagation errors associated with inertial measurement unit (IMU) errors (gyro and accelerometer), gravity errors/dispersions (spherical harmonics, masscons), and radar errors (multiple altimeter beams, multiple Doppler velocimeter beams). G-CAT is a standalone MATLAB- based tool intended to run on any engineer's desktop computer.

Open Quantum Systems and Classical Trajectories

NASA Astrophysics Data System (ADS)

Rebolledo, Rolando

2004-09-01

A Quantum Markov Semigroup consists of a family { T} = ({ T}t)_{t ∈ B R+} of normal ω*- continuous completely positive maps on a von Neumann algebra 𝔐 which preserve the unit and satisfy the semigroup property. This class of semigroups has been extensively used to represent open quantum systems. This article is aimed at studying the existence of a { T} -invariant abelian subalgebra 𝔄 of 𝔐. When this happens, the restriction of { T}t to 𝔄 defines a classical Markov semigroup T = (Tt)t ∈ ∝ + say, associated to a classical Markov process X = (Xt)t ∈ ∝ +. The structure (𝔄, T, X) unravels the quantum Markov semigroup { T} , providing a bridge between open quantum systems and classical stochastic processes.

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

Zhang, Ying-Jie, E-mail: yingjiezhang@qfnu.edu.cn; Han, Wei; Xia, Yun-Jie, E-mail: yjxia@qfnu.edu.cn

We propose a scheme of controlling entanglement dynamics of a quantum system by applying the external classical driving field for two atoms separately located in a single-mode photon cavity. It is shown that, with a judicious choice of the classical-driving strength and the atom–photon detuning, the effective atom–photon interaction Hamiltonian can be switched from Jaynes–Cummings model to anti-Jaynes–Cummings model. By tuning the controllable atom–photon interaction induced by the classical field, we illustrate that the evolution trajectory of the Bell-like entanglement states can be manipulated from entanglement-sudden-death to no-entanglement-sudden-death, from no-entanglement-invariant to entanglement-invariant. Furthermore, the robustness of the initial Bell-like entanglementmore » can be improved by the classical driving field in the leaky cavities. This classical-driving-assisted architecture can be easily extensible to multi-atom quantum system for scalability.« less

Generalized Gaussian wave packet dynamics: Integrable and chaotic systems.

PubMed

Pal, Harinder; Vyas, Manan; Tomsovic, Steven

2016-01-01

The ultimate semiclassical wave packet propagation technique is a complex, time-dependent Wentzel-Kramers-Brillouin method known as generalized Gaussian wave packet dynamics (GGWPD). It requires overcoming many technical difficulties in order to be carried out fully in practice. In its place roughly twenty years ago, linearized wave packet dynamics was generalized to methods that include sets of off-center, real trajectories for both classically integrable and chaotic dynamical systems that completely capture the dynamical transport. The connections between those methods and GGWPD are developed in a way that enables a far more practical implementation of GGWPD. The generally complex saddle-point trajectories at its foundation are found using a multidimensional Newton-Raphson root search method that begins with the set of off-center, real trajectories. This is possible because there is a one-to-one correspondence. The neighboring trajectories associated with each off-center, real trajectory form a path that crosses a unique saddle; there are exceptions that are straightforward to identify. The method is applied to the kicked rotor to demonstrate the accuracy improvement as a function of ℏ that comes with using the saddle-point trajectories.

Tsien's method for generating non-Keplerian trajectories. Part 2: The question of thrust to orbit a sphere and the restricted three-body problem

NASA Technical Reports Server (NTRS)

Murad, P. A.

1993-01-01

Tsien's method is extended to treat the orbital motion of a body undergoing accelerations and decelerations. A generalized solution is discussed for the generalized case where a body undergoes azimuthal and radial thrust and the problem is further simplified for azimuthal thrust alone. Judicious selection of thrust could generate either an elliptic or hyperbolic trajectory. This is unexpected especially when the body has only enough energy for a lower state trajectory. The methodology is extended treating the problem of vehicle thrust for orbiting a sphere and vehicle thrust within the classical restricted three-body problem. Results for the latter situation can produce hyperbolic trajectories through eigen value decomposition. Since eigen values for no-thrust can be imaginary, thrust can generate real eigen values to describe hyperbolic trajectories. Keplerian dynamics appears to represent but a small subset of a much larger non-Keplerian domain especially when thrust effects are considered. The need for high thrust long duration space-based propulsion systems for changing a trajectory's canonical form is clearly demonstrated.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.

PubMed

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-10-17

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

PubMed Central

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-01-01

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law. PMID:27748418

Quantum trajectory analysis of multimode subsystem-bath dynamics.

PubMed

Wyatt, Robert E; Na, Kyungsun

2002-01-01

The dynamics of a swarm of quantum trajectories is investigated for systems involving the interaction of an active mode (the subsystem) with an M-mode harmonic reservoir (the bath). Equations of motion for the position, velocity, and action function for elements of the probability fluid are integrated in the Lagrangian (moving with the fluid) picture of quantum hydrodynamics. These fluid elements are coupled through the Bohm quantum potential and as a result evolve as a correlated ensemble. Wave function synthesis along the trajectories permits an exact description of the quantum dynamics for the evolving probability fluid. The approach is fully quantum mechanical and does not involve classical or semiclassical approximations. Computational results are presented for three systems involving the interaction on an active mode with M=1, 10, and 15 bath modes. These results include configuration space trajectory evolution, flux analysis of the evolving ensemble, wave function synthesis along trajectories, and energy partitioning along specific trajectories. These results demonstrate the feasibility of using a small number of quantum trajectories to obtain accurate quantum results on some types of open quantum systems that are not amenable to standard quantum approaches involving basis set expansions or Eulerian space-fixed grids.

A Monte Carlo–Based Bayesian Approach for Measuring Agreement in a Qualitative Scale

PubMed Central

Pérez Sánchez, Carlos Javier

2014-01-01

Agreement analysis has been an active research area whose techniques have been widely applied in psychology and other fields. However, statistical agreement among raters has been mainly considered from a classical statistics point of view. Bayesian methodology is a viable alternative that allows the inclusion of subjective initial information coming from expert opinions, personal judgments, or historical data. A Bayesian approach is proposed by providing a unified Monte Carlo–based framework to estimate all types of measures of agreement in a qualitative scale of response. The approach is conceptually simple and it has a low computational cost. Both informative and non-informative scenarios are considered. In case no initial information is available, the results are in line with the classical methodology, but providing more information on the measures of agreement. For the informative case, some guidelines are presented to elicitate the prior distribution. The approach has been applied to two applications related to schizophrenia diagnosis and sensory analysis. PMID:29881002

The OH + D2 --> HOD + D angle-velocity distribution: quasi-classical trajectory calculations on the YZCL2 and WSLFH potential energy surfaces and comparison with experiments at ET = 0.28 eV.

PubMed

Sierra, José Daniel; Martínez, Rodrigo; Hernando, Jordi; González, Miguel

2009-12-28

The angle-velocity distribution (HOD) of the OH + D(2) reaction at a relative translational energy of 0.28 eV has been calculated using the quasi-classical trajectory (QCT) method on the two most recent potential energy surfaces available (YZCL2 and WSLFH PESs), widely extending a previous investigation of our group. Comparison with the high resolution experiments of Davis and co-workers (Science, 2000, 290, 958) shows that the structures (peaks) found in the relative translational energy distributions of products could not be satisfactorily reproduced in the calculations, probably due to the classical nature of the QCT method and the importance of quantum effects. The calculations, however, worked quite well for other properties. Overall, both surfaces led to similar results, although the YZCL2 surface is more accurate to describe the H(3)O PES, as derived from comparison with high level ab initio results. The differences observed in the QCT calculations were interpreted considering the somewhat larger anisotropy of the YZCL2 PES when compared with the WSLFH PES.

Efficient hybrid non-equilibrium molecular dynamics--Monte Carlo simulations with symmetric momentum reversal.

PubMed

Chen, Yunjie; Roux, Benoît

2014-09-21

Hybrid schemes combining the strength of molecular dynamics (MD) and Metropolis Monte Carlo (MC) offer a promising avenue to improve the sampling efficiency of computer simulations of complex systems. A number of recently proposed hybrid methods consider new configurations generated by driving the system via a non-equilibrium MD (neMD) trajectory, which are subsequently treated as putative candidates for Metropolis MC acceptance or rejection. To obey microscopic detailed balance, it is necessary to alter the momentum of the system at the beginning and/or the end of the neMD trajectory. This strict rule then guarantees that the random walk in configurational space generated by such hybrid neMD-MC algorithm will yield the proper equilibrium Boltzmann distribution. While a number of different constructs are possible, the most commonly used prescription has been to simply reverse the momenta of all the particles at the end of the neMD trajectory ("one-end momentum reversal"). Surprisingly, it is shown here that the choice of momentum reversal prescription can have a considerable effect on the rate of convergence of the hybrid neMD-MC algorithm, with the simple one-end momentum reversal encountering particularly acute problems. In these neMD-MC simulations, different regions of configurational space end up being essentially isolated from one another due to a very small transition rate between regions. In the worst-case scenario, it is almost as if the configurational space does not constitute a single communicating class that can be sampled efficiently by the algorithm, and extremely long neMD-MC simulations are needed to obtain proper equilibrium probability distributions. To address this issue, a novel momentum reversal prescription, symmetrized with respect to both the beginning and the end of the neMD trajectory ("symmetric two-ends momentum reversal"), is introduced. Illustrative simulations demonstrate that the hybrid neMD-MC algorithm robustly yields a correct equilibrium probability distribution with this prescription.

Efficient hybrid non-equilibrium molecular dynamics - Monte Carlo simulations with symmetric momentum reversal

NASA Astrophysics Data System (ADS)

Chen, Yunjie; Roux, Benoît

2014-09-01

Hybrid schemes combining the strength of molecular dynamics (MD) and Metropolis Monte Carlo (MC) offer a promising avenue to improve the sampling efficiency of computer simulations of complex systems. A number of recently proposed hybrid methods consider new configurations generated by driving the system via a non-equilibrium MD (neMD) trajectory, which are subsequently treated as putative candidates for Metropolis MC acceptance or rejection. To obey microscopic detailed balance, it is necessary to alter the momentum of the system at the beginning and/or the end of the neMD trajectory. This strict rule then guarantees that the random walk in configurational space generated by such hybrid neMD-MC algorithm will yield the proper equilibrium Boltzmann distribution. While a number of different constructs are possible, the most commonly used prescription has been to simply reverse the momenta of all the particles at the end of the neMD trajectory ("one-end momentum reversal"). Surprisingly, it is shown here that the choice of momentum reversal prescription can have a considerable effect on the rate of convergence of the hybrid neMD-MC algorithm, with the simple one-end momentum reversal encountering particularly acute problems. In these neMD-MC simulations, different regions of configurational space end up being essentially isolated from one another due to a very small transition rate between regions. In the worst-case scenario, it is almost as if the configurational space does not constitute a single communicating class that can be sampled efficiently by the algorithm, and extremely long neMD-MC simulations are needed to obtain proper equilibrium probability distributions. To address this issue, a novel momentum reversal prescription, symmetrized with respect to both the beginning and the end of the neMD trajectory ("symmetric two-ends momentum reversal"), is introduced. Illustrative simulations demonstrate that the hybrid neMD-MC algorithm robustly yields a correct equilibrium probability distribution with this prescription.

A model of curved saccade trajectories: spike rate adaptation in the brainstem as the cause of deviation away.

PubMed

Kruijne, Wouter; Van der Stigchel, Stefan; Meeter, Martijn

2014-03-01

The trajectory of saccades to a target is often affected whenever there is a distractor in the visual field. Distractors can cause a saccade to deviate towards their location or away from it. The oculomotor mechanisms that produce deviation towards distractors have been thoroughly explored in behavioral, neurophysiological and computational studies. The mechanisms underlying deviation away, on the other hand, remain unclear. Behavioral findings suggest a mechanism of spatially focused, top-down inhibition in a saccade map, and deviation away has become a tool to investigate such inhibition. However, this inhibition hypothesis has little neuroanatomical or neurophysiological support, and recent findings go against it. Here, we propose that deviation away results from an unbalanced saccade drive from the brainstem, caused by spike rate adaptation in brainstem long-lead burst neurons. Adaptation to stimulation in the direction of the distractor results in an unbalanced drive away from it. An existing model of the saccade system was extended with this theory. The resulting model simulates a wide range of findings on saccade trajectories, including findings that have classically been interpreted to support inhibition views. Furthermore, the model replicated the effect of saccade latency on deviation away, but predicted this effect would be absent with large (400 ms) distractor-target onset asynchrony. This prediction was confirmed in an experiment, which demonstrates that the theory both explains classical findings on saccade trajectories and predicts new findings. Copyright © 2014 Elsevier Inc. All rights reserved.

Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.

PubMed

Saller, Maximilian A C; Habershon, Scott

2017-07-11

Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation.

Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems

NASA Astrophysics Data System (ADS)

Harada, Hiromitsu; Mouchet, Amaury; Shudo, Akira

2017-10-01

The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann surface provides complete information on the topology of complex paths, which allows us to enumerate all the possible candidates contributing to the semiclassical sum formula for tunnelling splittings. This naturally leads to action relations among classically disjoined regions, revealing entirely non-local nature in the quantization condition. The importance of the proper treatment of Stokes phenomena is also discussed in Hamiltonians in the normal form.

Symmetrical Windowing for Quantum States in Quasi-Classical Trajectory Simulations

NASA Astrophysics Data System (ADS)

Cotton, Stephen Joshua

An approach has been developed for extracting approximate quantum state-to-state information from classical trajectory simulations which "quantizes" symmetrically both the initial and final classical actions associated with the degrees of freedom of interest using quantum number bins (or "window functions") which are significantly narrower than unit-width. This approach thus imposes a more stringent quantization condition on classical trajectory simulations than has been traditionally employed, while doing so in a manner that is time-symmetric and microscopically reversible. To demonstrate this "symmetric quasi-classical" (SQC) approach for a simple real system, collinear H + H2 reactive scattering calculations were performed [S.J. Cotton and W.H. Miller, J. Phys. Chem. A 117, 7190 (2013)] with SQC-quantization applied to the H 2 vibrational degree of freedom (DOF). It was seen that the use of window functions of approximately 1/2-unit width led to calculated reaction probabilities in very good agreement with quantum mechanical results over the threshold energy region, representing a significant improvement over what is obtained using the traditional quasi-classical procedure. The SQC approach was then applied [S.J. Cotton and W.H. Miller, J. Chem. Phys. 139, 234112 (2013)] to the much more interesting and challenging problem of incorporating non-adiabatic effects into what would otherwise be standard classical trajectory simulations. To do this, the classical Meyer-Miller (MM) Hamiltonian was used to model the electronic DOFs, with SQC-quantization applied to the classical "electronic" actions of the MM model---representing the occupations of the electronic states---in order to extract the electronic state population dynamics. It was demonstrated that if one ties the zero-point energy (ZPE) of the electronic DOFs to the SQC windowing function's width parameter this very simple SQC/MM approach is capable of quantitatively reproducing quantum mechanical results for a range of standard benchmark models of electronically non-adiabatic processes, including applications where "quantum" coherence effects are significant. Notably, among these benchmarks was the well-studied "spin-boson" model of condensed phase non-adiabatic dynamics, in both its symmetric and asymmetric forms---the latter of which many classical approaches fail to treat successfully. The SQC/MM approach to the treatment of non-adiabatic dynamics was next applied [S.J. Cotton, K. Igumenshchev, and W.H. Miller, J. Chem. Phys., 141, 084104 (2014)] to several recently proposed models of condensed phase electron transfer (ET) processes. For these problems, a flux-side correlation function framework modified for consistency with the SQC approach was developed for the calculation of thermal ET rate constants, and excellent accuracy was seen over wide ranges of non-adiabatic coupling strength and energetic bias/exothermicity. Significantly, the "inverted regime" in thermal rate constants (with increasing bias) known from Marcus Theory was reproduced quantitatively for these models---representing the successful treatment of another regime that classical approaches generally have difficulty in correctly describing. Relatedly, a model of photoinduced proton coupled electron transfer (PCET) was also addressed, and it was shown that the SQC/MM approach could reasonably model the explicit population dynamics of the photoexcited electron donor and acceptor states over the four parameter regimes considered. The potential utility of the SQC/MM technique lies in its stunning simplicity and the ease by which it may readily be incorporated into "ordinary" molecular dynamics (MD) simulations. In short, a typical MD simulation may be augmented to take non-adiabatic effects into account simply by introducing an auxiliary pair of classical "electronic" action-angle variables for each energetically viable Born-Oppenheimer surface, and time-evolving these auxiliary variables via Hamilton's equations (using the MM electronic Hamiltonian) in the same manner that the other classical variables---i.e., the coordinates of all the nuclei---are evolved forward in time. In a complex molecular system involving many hundreds or thousands of nuclear DOFs, the propagation of these extra "electronic" variables represents a modest increase in computational effort, and yet, the examples presented herein suggest that in many instances the SQC/MM approach will describe the true non-adiabatic quantum dynamics to a reasonable and useful degree of quantitative accuracy.

Spin flip statistics and spin wave interference patterns in Ising ferromagnetic films: A Monte Carlo study.

PubMed

Acharyya, Muktish

2017-07-01

The spin wave interference is studied in two dimensional Ising ferromagnet driven by two coherent spherical magnetic field waves by Monte Carlo simulation. The spin waves are found to propagate and interfere according to the classic rule of interference pattern generated by two point sources. The interference pattern of spin wave is observed in one boundary of the lattice. The interference pattern is detected and studied by spin flip statistics at high and low temperatures. The destructive interference is manifested as the large number of spin flips and vice versa.

Replica-exchange Wang Landau sampling: pushing the limits of Monte Carlo simulations in materials sciences

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

Perera, Meewanage Dilina N; Li, Ying Wai; Eisenbach, Markus

We describe the study of thermodynamics of materials using replica-exchange Wang Landau (REWL) sampling, a generic framework for massively parallel implementations of the Wang Landau Monte Carlo method. To evaluate the performance and scalability of the method, we investigate the magnetic phase transition in body-centered cubic (bcc) iron using the classical Heisenberg model parameterized with first principles calculations. We demonstrate that our framework leads to a significant speedup without compromising the accuracy and precision and facilitates the study of much larger systems than is possible with its serial counterpart.

Data decomposition of Monte Carlo particle transport simulations via tally servers

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

Romano, Paul K.; Siegel, Andrew R.; Forget, Benoit

An algorithm for decomposing large tally data in Monte Carlo particle transport simulations is developed, analyzed, and implemented in a continuous-energy Monte Carlo code, OpenMC. The algorithm is based on a non-overlapping decomposition of compute nodes into tracking processors and tally servers. The former are used to simulate the movement of particles through the domain while the latter continuously receive and update tally data. A performance model for this approach is developed, suggesting that, for a range of parameters relevant to LWR analysis, the tally server algorithm should perform with minimal overhead on contemporary supercomputers. An implementation of the algorithmmore » in OpenMC is then tested on the Intrepid and Titan supercomputers, supporting the key predictions of the model over a wide range of parameters. We thus conclude that the tally server algorithm is a successful approach to circumventing classical on-node memory constraints en route to unprecedentedly detailed Monte Carlo reactor simulations.« less

A quantum–quantum Metropolis algorithm

PubMed Central

Yung, Man-Hong; Aspuru-Guzik, Alán

2012-01-01

The classical Metropolis sampling method is a cornerstone of many statistical modeling applications that range from physics, chemistry, and biology to economics. This method is particularly suitable for sampling the thermal distributions of classical systems. The challenge of extending this method to the simulation of arbitrary quantum systems is that, in general, eigenstates of quantum Hamiltonians cannot be obtained efficiently with a classical computer. However, this challenge can be overcome by quantum computers. Here, we present a quantum algorithm which fully generalizes the classical Metropolis algorithm to the quantum domain. The meaning of quantum generalization is twofold: The proposed algorithm is not only applicable to both classical and quantum systems, but also offers a quantum speedup relative to the classical counterpart. Furthermore, unlike the classical method of quantum Monte Carlo, this quantum algorithm does not suffer from the negative-sign problem associated with fermionic systems. Applications of this algorithm include the study of low-temperature properties of quantum systems, such as the Hubbard model, and preparing the thermal states of sizable molecules to simulate, for example, chemical reactions at an arbitrary temperature. PMID:22215584

Evaluation of Jacobian determinants by Monte Carlo methods: Application to the quasiclassical approximation in molecular scattering

NASA Technical Reports Server (NTRS)

Labudde, R. A.

1971-01-01

A technique is described which can be used to evaluate Jacobian determinants which occur in classical mechanical and quasiclassical approximation descriptions of molecular scattering. The method may be valuable in the study of reactive scattering using the quasiclassical approximation.

A strategy for quantum algorithm design assisted by machine learning

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Ryu, Junghee; Yoo, Seokwon; Pawłowski, Marcin; Lee, Jinhyoung

2014-07-01

We propose a method for quantum algorithm design assisted by machine learning. The method uses a quantum-classical hybrid simulator, where a ‘quantum student’ is being taught by a ‘classical teacher’. In other words, in our method, the learning system is supposed to evolve into a quantum algorithm for a given problem, assisted by a classical main-feedback system. Our method is applicable for designing quantum oracle-based algorithms. We chose, as a case study, an oracle decision problem, called a Deutsch-Jozsa problem. We showed by using Monte Carlo simulations that our simulator can faithfully learn a quantum algorithm for solving the problem for a given oracle. Remarkably, the learning time is proportional to the square root of the total number of parameters, rather than showing the exponential dependence found in the classical machine learning-based method.

Critical properties of the classical XY and classical Heisenberg models: A renormalization group study

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; de Albuquerque, Douglas F.

1997-02-01

By using two approaches of renormalization group (RG), mean field RG (MFRG) and effective field RG (EFRG), we study the critical properties of the simple cubic lattice classical XY and classical Heisenberg models. The methods are illustrated by employing its simplest approximation version in which small clusters with one ( N‧ = 1) and two ( N = 2) spins are used. The thermal and magnetic critical exponents, Yt and Yh, and the critical parameter Kc are numerically obtained and are compared with more accurate methods (Monte Carlo, series expansion and ε-expansion). The results presented in this work are in excellent agreement with these sophisticated methods. We have also shown that the exponent Yh does not depend on the symmetry n of the Hamiltonian, hence the criteria of universality for this exponent is only a function of the dimension d.

Calculating tumor trajectory and dose-of-the-day using cone-beam CT projections

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

Jones, Bernard L., E-mail: bernard.jones@ucdenver.edu; Westerly, David; Miften, Moyed

2015-02-15

Purpose: Cone-beam CT (CBCT) projection images provide anatomical data in real-time over several respiratory cycles, forming a comprehensive picture of tumor movement. The authors developed and validated a method which uses these projections to determine the trajectory of and dose to highly mobile tumors during each fraction of treatment. Methods: CBCT images of a respiration phantom were acquired, the trajectory of which mimicked a lung tumor with high amplitude (up to 2.5 cm) and hysteresis. A template-matching algorithm was used to identify the location of a steel BB in each CBCT projection, and a Gaussian probability density function for themore » absolute BB position was calculated which best fit the observed trajectory of the BB in the imager geometry. Two modifications of the trajectory reconstruction were investigated: first, using respiratory phase information to refine the trajectory estimation (Phase), and second, using the Monte Carlo (MC) method to sample the estimated Gaussian tumor position distribution. The accuracies of the proposed methods were evaluated by comparing the known and calculated BB trajectories in phantom-simulated clinical scenarios using abdominal tumor volumes. Results: With all methods, the mean position of the BB was determined with accuracy better than 0.1 mm, and root-mean-square trajectory errors averaged 3.8% ± 1.1% of the marker amplitude. Dosimetric calculations using Phase methods were more accurate, with mean absolute error less than 0.5%, and with error less than 1% in the highest-noise trajectory. MC-based trajectories prevent the overestimation of dose, but when viewed in an absolute sense, add a small amount of dosimetric error (<0.1%). Conclusions: Marker trajectory and target dose-of-the-day were accurately calculated using CBCT projections. This technique provides a method to evaluate highly mobile tumors using ordinary CBCT data, and could facilitate better strategies to mitigate or compensate for motion during stereotactic body radiotherapy.« less

Bayesian Exploratory Factor Analysis

PubMed Central

Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.; Piatek, Rémi

2014-01-01

This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates from a high dimensional set of psychological measurements. PMID:25431517

Supersonic Flight Dynamics Test 1 - Post-Flight Assessment of Simulation Performance

NASA Technical Reports Server (NTRS)

Dutta, Soumyo; Bowes, Angela L.; Striepe, Scott A.; Davis, Jody L.; Queen, Eric M.; Blood, Eric M.; Ivanov, Mark C.

2015-01-01

NASA's Low Density Supersonic Decelerator (LDSD) project conducted its first Supersonic Flight Dynamics Test (SFDT-1) on June 28, 2014. Program to Optimize Simulated Trajectories II (POST2) was one of the flight dynamics codes used to simulate and predict the flight performance and Monte Carlo analysis was used to characterize the potential flight conditions experienced by the test vehicle. This paper compares the simulation predictions with the reconstructed trajectory of SFDT-1. Additionally, off-nominal conditions seen during flight are modeled in post-flight simulations to find the primary contributors that reconcile the simulation with flight data. The results of these analyses are beneficial for the pre-flight simulation and targeting of the follow-on SFDT flights currently scheduled for summer 2015.

Focusing of active particles in a converging flow

DOE PAGES

Potomkin, Mykhailo; Kaiser, Andreas; Berlyand, Leonid; ...

2017-10-20

We consider active particles swimming in a convergent fluid flow in a trapezoid nozzle with no-slip walls. We use mathematical modeling to analyze trajectories of these particles inside the nozzle. By extensive Monte Carlo simulations, we show that trajectories are strongly affected by the background fluid flow and geometry of the nozzle leading to wall accumulation and upstream motion (rheotaxis). In particular, we describe the non-trivial focusing of active rods depending on physical and geometrical parameters. It is also established that the convergent component of the background flow leads to stability of both downstream and upstream swimming at the centerline.more » The stability of downstream swimming enhances focusing, and the stability of upstream swimming enables rheotaxis in the bulk.« less

Entry, Descent, and Landing Operations Analysis for the Mars Phoenix Lander

NASA Technical Reports Server (NTRS)

Prince, Jill L.; Desai, Prasun N.; Queen, Eric M.; Grover, Myron R.

2008-01-01

The Mars Phoenix lander was launched August 4, 2007 and remained in cruise for ten months before landing in the northern plains of Mars in May 2008. The one-month Entry, Descent, and Landing (EDL) operations phase prior to entry consisted of daily analyses, meetings, and decisions necessary to determine if trajectory correction maneuvers and environmental parameter updates to the spacecraft were required. An overview of the Phoenix EDL trajectory simulation and analysis that was performed during the EDL approach and operations phase is described in detail. The evolution of the Monte Carlo statistics and footprint ellipse during the final approach phase is also provided. The EDL operations effort accurately delivered the Phoenix lander to the desired landing region on May 25, 2008.

The suppression effect of external magnetic field on the high-power microwave window multipactor phenomenon

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

Zhang, Xue, E-mail: zhangxue.iecas@yahoo.com; Wang, Yong; Fan, Junjie

2015-02-15

To suppress the surface multipactor phenomenon and improve the transmitting power of the high-power microwave window, the application of external magnetic fields is theoretically analyzed and simulated. A Monte Carlo algorithm is used to track the secondary electron trajectories and study the multipactor scenario on the surface of a cylinder window. It is confirmed that over-resonant magnetic fields (an external magnetic field whose magnitude is slightly greater than that of a resonant magnetic field) will generate a compensating trajectory and collision, which can suppress the secondary electron avalanche. The optimal value of this external magnetic field that will avoid themore » multipactor phenomenon on cylinder windows is discussed.« less

Disturbance observer based model predictive control for accurate atmospheric entry of spacecraft

NASA Astrophysics Data System (ADS)

Wu, Chao; Yang, Jun; Li, Shihua; Li, Qi; Guo, Lei

2018-05-01

Facing the complex aerodynamic environment of Mars atmosphere, a composite atmospheric entry trajectory tracking strategy is investigated in this paper. External disturbances, initial states uncertainties and aerodynamic parameters uncertainties are the main problems. The composite strategy is designed to solve these problems and improve the accuracy of Mars atmospheric entry. This strategy includes a model predictive control for optimized trajectory tracking performance, as well as a disturbance observer based feedforward compensation for external disturbances and uncertainties attenuation. 500-run Monte Carlo simulations show that the proposed composite control scheme achieves more precise Mars atmospheric entry (3.8 km parachute deployment point distribution error) than the baseline control scheme (8.4 km) and integral control scheme (5.8 km).

OSIRIS-REx Touch-And-Go (TAG) Mission Design and Analysis

NASA Technical Reports Server (NTRS)

Berry, Kevin; Sutter, Brian; May, Alex; Williams, Ken; Barbee, Brent W.; Beckman, Mark; Williams, Bobby

2013-01-01

The Origins Spectral Interpretation Resource Identification Security Regolith Explorer (OSIRIS-REx) mission is a NASA New Frontiers mission launching in 2016 to rendezvous with the near-Earth asteroid (101955) 1999 RQ36 in late 2018. After several months in formation with and orbit about the asteroid, OSIRIS-REx will fly a Touch-And-Go (TAG) trajectory to the asteroid s surface to obtain a regolith sample. This paper describes the mission design of the TAG sequence and the propulsive maneuvers required to achieve the trajectory. This paper also shows preliminary results of orbit covariance analysis and Monte-Carlo analysis that demonstrate the ability to arrive at a targeted location on the surface of RQ36 within a 25 meter radius with 98.3% confidence.

Characterizing quantum channels with non-separable states of classical light

NASA Astrophysics Data System (ADS)

Ndagano, Bienvenu; Perez-Garcia, Benjamin; Roux, Filippus S.; McLaren, Melanie; Rosales-Guzman, Carmelo; Zhang, Yingwen; Mouane, Othmane; Hernandez-Aranda, Raul I.; Konrad, Thomas; Forbes, Andrew

2017-04-01

High-dimensional entanglement with spatial modes of light promises increased security and information capacity over quantum channels. Unfortunately, entanglement decays due to perturbations, corrupting quantum links that cannot be repaired without performing quantum tomography on the channel. Paradoxically, the channel tomography itself is not possible without a working link. Here we overcome this problem with a robust approach to characterize quantum channels by means of classical light. Using free-space communication in a turbulent atmosphere as an example, we show that the state evolution of classically entangled degrees of freedom is equivalent to that of quantum entangled photons, thus providing new physical insights into the notion of classical entanglement. The analysis of quantum channels by means of classical light in real time unravels stochastic dynamics in terms of pure state trajectories, and thus enables precise quantum error correction in short- and long-haul optical communication, in both free space and fibre.

LORAKS Makes Better SENSE: Phase-Constrained Partial Fourier SENSE Reconstruction without Phase Calibration

PubMed Central

Kim, Tae Hyung; Setsompop, Kawin; Haldar, Justin P.

2016-01-01

Purpose Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information. Theory and Methods The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly-accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely-used calibrationless uniformly-undersampled trajectories. Results Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches. Conclusion The SENSE-LORAKS framework provides promising new opportunities for highly-accelerated MRI. PMID:27037836

Reliability of Test Scores in Nonparametric Item Response Theory.

ERIC Educational Resources Information Center

Sijtsma, Klaas; Molenaar, Ivo W.

1987-01-01

Three methods for estimating reliability are studied within the context of nonparametric item response theory. Two were proposed originally by Mokken and a third is developed in this paper. Using a Monte Carlo strategy, these three estimation methods are compared with four "classical" lower bounds to reliability. (Author/JAZ)

Inferential Procedures for Correlation Coefficients Corrected for Attenuation.

ERIC Educational Resources Information Center

Hakstian, A. Ralph; And Others

1988-01-01

A model and computation procedure based on classical test score theory are presented for determination of a correlation coefficient corrected for attenuation due to unreliability. Delta and Monte Carlo method applications are discussed. A power analysis revealed no serious loss in efficiency resulting from correction for attentuation. (TJH)

Teaching Classical Statistical Mechanics: A Simulation Approach.

ERIC Educational Resources Information Center

Sauer, G.

1981-01-01

Describes a one-dimensional model for an ideal gas to study development of disordered motion in Newtonian mechanics. A Monte Carlo procedure for simulation of the statistical ensemble of an ideal gas with fixed total energy is developed. Compares both approaches for a pseudoexperimental foundation of statistical mechanics. (Author/JN)

Unbiased Rare Event Sampling in Spatial Stochastic Systems Biology Models Using a Weighted Ensemble of Trajectories

PubMed Central

Donovan, Rory M.; Tapia, Jose-Juan; Sullivan, Devin P.; Faeder, James R.; Murphy, Robert F.; Dittrich, Markus; Zuckerman, Daniel M.

2016-01-01

The long-term goal of connecting scales in biological simulation can be facilitated by scale-agnostic methods. We demonstrate that the weighted ensemble (WE) strategy, initially developed for molecular simulations, applies effectively to spatially resolved cell-scale simulations. The WE approach runs an ensemble of parallel trajectories with assigned weights and uses a statistical resampling strategy of replicating and pruning trajectories to focus computational effort on difficult-to-sample regions. The method can also generate unbiased estimates of non-equilibrium and equilibrium observables, sometimes with significantly less aggregate computing time than would be possible using standard parallelization. Here, we use WE to orchestrate particle-based kinetic Monte Carlo simulations, which include spatial geometry (e.g., of organelles, plasma membrane) and biochemical interactions among mobile molecular species. We study a series of models exhibiting spatial, temporal and biochemical complexity and show that although WE has important limitations, it can achieve performance significantly exceeding standard parallel simulation—by orders of magnitude for some observables. PMID:26845334

Statistical properties of the anomalous scaling exponent estimator based on time-averaged mean-square displacement

NASA Astrophysics Data System (ADS)

Sikora, Grzegorz; Teuerle, Marek; Wyłomańska, Agnieszka; Grebenkov, Denis

2017-08-01

The most common way of estimating the anomalous scaling exponent from single-particle trajectories consists of a linear fit of the dependence of the time-averaged mean-square displacement on the lag time at the log-log scale. We investigate the statistical properties of this estimator in the case of fractional Brownian motion (FBM). We determine the mean value, the variance, and the distribution of the estimator. Our theoretical results are confirmed by Monte Carlo simulations. In the limit of long trajectories, the estimator is shown to be asymptotically unbiased, consistent, and with vanishing variance. These properties ensure an accurate estimation of the scaling exponent even from a single (long enough) trajectory. As a consequence, we prove that the usual way to estimate the diffusion exponent of FBM is correct from the statistical point of view. Moreover, the knowledge of the estimator distribution is the first step toward new statistical tests of FBM and toward a more reliable interpretation of the experimental histograms of scaling exponents in microbiology.

Mars Exploration Rover Terminal Descent Mission Modeling and Simulation

NASA Technical Reports Server (NTRS)

Raiszadeh, Behzad; Queen, Eric M.

2004-01-01

Because of NASA's added reliance on simulation for successful interplanetary missions, the MER mission has developed a detailed EDL trajectory modeling and simulation. This paper summarizes how the MER EDL sequence of events are modeled, verification of the methods used, and the inputs. This simulation is built upon a multibody parachute trajectory simulation tool that has been developed in POST I1 that accurately simulates the trajectory of multiple vehicles in flight with interacting forces. In this model the parachute and the suspended bodies are treated as 6 Degree-of-Freedom (6 DOF) bodies. The terminal descent phase of the mission consists of several Entry, Descent, Landing (EDL) events, such as parachute deployment, heatshield separation, deployment of the lander from the backshell, deployment of the airbags, RAD firings, TIRS firings, etc. For an accurate, reliable simulation these events need to be modeled seamlessly and robustly so that the simulations will remain numerically stable during Monte-Carlo simulations. This paper also summarizes how the events have been modeled, the numerical issues, and modeling challenges.

Statistics of Delta v magnitude for a trajectory correction maneuver containing deterministic and random components

NASA Technical Reports Server (NTRS)

Bollman, W. E.; Chadwick, C.

1982-01-01

A number of interplanetary missions now being planned involve placing deterministic maneuvers along the flight path to alter the trajectory. Lee and Boain (1973) examined the statistics of trajectory correction maneuver (TCM) magnitude with no deterministic ('bias') component. The Delta v vector magnitude statistics were generated for several values of random Delta v standard deviations using expansions in terms of infinite hypergeometric series. The present investigation uses a different technique (Monte Carlo simulation) to generate Delta v magnitude statistics for a wider selection of random Delta v standard deviations and also extends the analysis to the case of nonzero deterministic Delta v's. These Delta v magnitude statistics are plotted parametrically. The plots are useful in assisting the analyst in quickly answering questions about the statistics of Delta v magnitude for single TCM's consisting of both a deterministic and a random component. The plots provide quick insight into the nature of the Delta v magnitude distribution for the TCM.

Terminal altitude maximization for Mars entry considering uncertainties

NASA Astrophysics Data System (ADS)

Cui, Pingyuan; Zhao, Zeduan; Yu, Zhengshi; Dai, Juan

2018-04-01

Uncertainties present in the Mars atmospheric entry process may cause state deviations from the nominal designed values, which will lead to unexpected performance degradation if the trajectory is designed merely based on the deterministic dynamic model. In this paper, a linear covariance based entry trajectory optimization method is proposed considering the uncertainties presenting in the initial states and parameters. By extending the elements of the state covariance matrix as augmented states, the statistical behavior of the trajectory is captured to reformulate the performance metrics and path constraints. The optimization problem is solved by the GPOPS-II toolbox in MATLAB environment. Monte Carlo simulations are also conducted to demonstrate the capability of the proposed method. Primary trading performances between the nominal deployment altitude and its dispersion can be observed by modulating the weights on the dispersion penalty, and a compromised result referring to maximizing the 3σ lower bound of the terminal altitude is achieved. The resulting path constraints also show better satisfaction in a disturbed environment compared with the nominal situation.

Effective dynamics of a classical point charge

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

Polonyi, Janos, E-mail: polonyi@iphc.cnrs.fr

2014-03-15

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-polemore » of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out. -- Highlights: •Extension of the classical action principle for dissipative systems. •New derivation of the Abraham–Lorentz force for a point charge. •Absence of a runaway solution of the Abraham–Lorentz force. •Acausality in classical electrodynamics. •Renormalization of classical electrodynamics of point charges.« less

Application of Vehicle Dynamic Modeling in Uavs for Precise Determination of Exterior Orientation

NASA Astrophysics Data System (ADS)

Khaghani, M.; Skaloud, J.

2016-06-01

Advances in unmanned aerial vehicles (UAV) and especially micro aerial vehicle (MAV) technology together with increasing quality and decreasing price of imaging devices have resulted in growing use of MAVs in photogrammetry. The practicality of MAV mapping is seriously enhanced with the ability to determine parameters of exterior orientation (EO) with sufficient accuracy, in both absolute and relative senses (change of attitude between successive images). While differential carrier phase GNSS satisfies cm-level positioning accuracy, precise attitude determination is essential for both direct sensor orientation (DiSO) and integrated sensor orientation (ISO) in corridor mapping or in block configuration imaging over surfaces with low texture. Limited cost, size, and weight of MAVs represent limitations on quality of onboard navigation sensors and puts emphasis on exploiting full capacity of available resources. Typically short flying times (10-30 minutes) also limit the possibility of estimating and/or correcting factors such as sensor misalignment and poor attitude initialization of inertial navigation system (INS). This research aims at increasing the accuracy of attitude determination in both absolute and relative senses with no extra sensors onboard. In comparison to classical INS/GNSS setup, novel approach is presented here to integrated state estimation, in which vehicle dynamic model (VDM) is used as the main process model. Such system benefits from available information from autopilot and physical properties of the platform in enhancing performance of determination of trajectory and parameters of exterior orientation consequently. The navigation system employs a differential carrier phase GNSS receiver and a micro electro-mechanical system (MEMS) grade inertial measurement unit (IMU), together with MAV control input from autopilot. Monte-Carlo simulation has been performed on trajectories for typical corridor mapping and block imaging. Results reveal considerable reduction in attitude errors with respect to conventional INS/GNSS system, in both absolute and relative senses. This eventually translates into higher redundancy and accuracy for photogrammetry applications.

Reliability-based trajectory optimization using nonintrusive polynomial chaos for Mars entry mission

NASA Astrophysics Data System (ADS)

Huang, Yuechen; Li, Haiyang

2018-06-01

This paper presents the reliability-based sequential optimization (RBSO) method to settle the trajectory optimization problem with parametric uncertainties in entry dynamics for Mars entry mission. First, the deterministic entry trajectory optimization model is reviewed, and then the reliability-based optimization model is formulated. In addition, the modified sequential optimization method, in which the nonintrusive polynomial chaos expansion (PCE) method and the most probable point (MPP) searching method are employed, is proposed to solve the reliability-based optimization problem efficiently. The nonintrusive PCE method contributes to the transformation between the stochastic optimization (SO) and the deterministic optimization (DO) and to the approximation of trajectory solution efficiently. The MPP method, which is used for assessing the reliability of constraints satisfaction only up to the necessary level, is employed to further improve the computational efficiency. The cycle including SO, reliability assessment and constraints update is repeated in the RBSO until the reliability requirements of constraints satisfaction are satisfied. Finally, the RBSO is compared with the traditional DO and the traditional sequential optimization based on Monte Carlo (MC) simulation in a specific Mars entry mission to demonstrate the effectiveness and the efficiency of the proposed method.

Generalized correlation integral vectors: A distance concept for chaotic dynamical systems

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

Haario, Heikki, E-mail: heikki.haario@lut.fi; Kalachev, Leonid, E-mail: KalachevL@mso.umt.edu; Hakkarainen, Janne

2015-06-15

Several concepts of fractal dimension have been developed to characterise properties of attractors of chaotic dynamical systems. Numerical approximations of them must be calculated by finite samples of simulated trajectories. In principle, the quantities should not depend on the choice of the trajectory, as long as it provides properly distributed samples of the underlying attractor. In practice, however, the trajectories are sensitive with respect to varying initial values, small changes of the model parameters, to the choice of a solver, numeric tolerances, etc. The purpose of this paper is to present a statistically sound approach to quantify this variability. Wemore » modify the concept of correlation integral to produce a vector that summarises the variability at all selected scales. The distribution of this stochastic vector can be estimated, and it provides a statistical distance concept between trajectories. Here, we demonstrate the use of the distance for the purpose of estimating model parameters of a chaotic dynamic model. The methodology is illustrated using computational examples for the Lorenz 63 and Lorenz 95 systems, together with a framework for Markov chain Monte Carlo sampling to produce posterior distributions of model parameters.« less

Effects of convection electric field on upwelling and escape of ionospheric O(+)

NASA Technical Reports Server (NTRS)

Cladis, J. B.; Chiu, Yam T.; Peterson, William K.

1992-01-01

A Monte Carlo code is used to explore the full effects of the convection electric field on distributions of upflowing O(+) ions from the cusp/cleft ionosphere. Trajectories of individual ions/neutrals are computed as they undergo multiple charge-exchange collisions. In the ion state, the trajectories are computed in realistic models of the magnetic field and the convection, corotation, and ambipolar electric fields. The effects of ion-ion collisions are included, and the trajectories are computed with and without simultaneous stochastic heating perpendicular to the magnetic field by a realistic model of broadband, low frequency waves. In the neutral state, ballistic trajectories in the gravitational field are computed. The initial conditions of the ions, in addition to ambipolar electric field and the number densities and temperatures of O(+), H(+), and electrons as a function of height in the cusp/cleft region were obtained from the results of Gombosi and Killeen (1987), who used a hydrodynamic code to simulate the time-dependent frictional-heating effects in a magnetic tube during its motion though the convection throat. The distribution of the ion fluxes as a function of height are constructed from the case histories.

Student Support for Research in Hierarchical Control and Trajectory Planning

NASA Technical Reports Server (NTRS)

Martin, Clyde F.

1999-01-01

Generally, classical polynomial splines tend to exhibit unwanted undulations. In this work, we discuss a technique, based on control principles, for eliminating these undulations and increasing the smoothness properties of the spline interpolants. We give a generalization of the classical polynomial splines and show that this generalization is, in fact, a family of splines that covers the broad spectrum of polynomial, trigonometric and exponential splines. A particular element in this family is determined by the appropriate control data. It is shown that this technique is easy to implement. Several numerical and curve-fitting examples are given to illustrate the advantages of this technique over the classical approach. Finally, we discuss the convergence properties of the interpolant.

Study of geometric phase using classical coupled oscillators

NASA Astrophysics Data System (ADS)

Bhattacharjee, Sharba; Dey, Biprateep; Mohapatra, Ashok K.

2018-05-01

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the evolution of the oscillator on an equivalent Hilbert space, which may be represented as a trajectory on the surface of a sphere. The cyclic evolution of the system leads to a change in phase, which consists of a dynamic phase along with an additional phase shift dependent on the geometry of the evolution. A simple experiment suitable for advanced undergraduate students is designed to study the geometric phase incurred during cyclic evolution of a coupled oscillator.

RNA folding kinetics using Monte Carlo and Gillespie algorithms.

PubMed

Clote, Peter; Bayegan, Amir H

2018-04-01

RNA secondary structure folding kinetics is known to be important for the biological function of certain processes, such as the hok/sok system in E. coli. Although linear algebra provides an exact computational solution of secondary structure folding kinetics with respect to the Turner energy model for tiny ([Formula: see text]20 nt) RNA sequences, the folding kinetics for larger sequences can only be approximated by binning structures into macrostates in a coarse-grained model, or by repeatedly simulating secondary structure folding with either the Monte Carlo algorithm or the Gillespie algorithm. Here we investigate the relation between the Monte Carlo algorithm and the Gillespie algorithm. We prove that asymptotically, the expected time for a K-step trajectory of the Monte Carlo algorithm is equal to [Formula: see text] times that of the Gillespie algorithm, where [Formula: see text] denotes the Boltzmann expected network degree. If the network is regular (i.e. every node has the same degree), then the mean first passage time (MFPT) computed by the Monte Carlo algorithm is equal to MFPT computed by the Gillespie algorithm multiplied by [Formula: see text]; however, this is not true for non-regular networks. In particular, RNA secondary structure folding kinetics, as computed by the Monte Carlo algorithm, is not equal to the folding kinetics, as computed by the Gillespie algorithm, although the mean first passage times are roughly correlated. Simulation software for RNA secondary structure folding according to the Monte Carlo and Gillespie algorithms is publicly available, as is our software to compute the expected degree of the network of secondary structures of a given RNA sequence-see http://bioinformatics.bc.edu/clote/RNAexpNumNbors .

Electron capture in collisions of ? with H and ? with C

NASA Astrophysics Data System (ADS)

Stancil, P. C.; Gu, J.-P.; Havener, C. C.; Krstic, P. S.; Schultz, D. R.; Kimura, M.; Zygelman, B.; Hirsch, G.; Buenker, R. J.; Bannister, M. E.

1998-08-01

A comprehensive theoretical and experimental study of electron capture in collisions of 0953-4075/31/16/017/img15 with H and 0953-4075/31/16/017/img16 with C extending over the energy range 0953-4075/31/16/017/img17 to 0953-4075/31/16/017/img18 is presented. A variety of theoretical approaches were used including those based on quantal molecular-orbital close-coupling (MOCC), multielectron hidden crossings (MEHC), quantal decay and classical trajectory Monte Carlo techniques. Radiative charge transfer cross sections were computed using the optical potential/distorted wave (OPDW) and fully quantal (FQ) approaches. The MOCC, OPDW and FQ calculations incorporated ab initio potentials, nonadiabatic coupling matrix elements and transition moments computed at the configuration-interaction level. Ab initio potential surfaces in the plane of complex internuclear distance were obtained for the MEHC calculations. Merged-beam measurements were performed between 0953-4075/31/16/017/img19 and 0953-4075/31/16/017/img20 for the 0953-4075/31/16/017/img21 collision system. Diagnostics of the 0953-4075/31/16/017/img15 beam with a crossed electron beam could find no presence of a 0953-4075/31/16/017/img15 metastable component. The current results, in conjunction with previous measurements, are used to deduce a set of recommended cross sections.

Development of a two-dimensional binning model for N{sub 2}–N relaxation in hypersonic shock conditions

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

Zhu, Tong, E-mail: tongzhu2@illinois.edu; Levin, Deborah A., E-mail: deblevin@illinois.edu; Li, Zheng, E-mail: zul107@psu.edu

2016-08-14

A high fidelity internal energy relaxation model for N{sub 2}–N suitable for use in direct simulation Monte Carlo (DSMC) modeling of chemically reacting flows is proposed. A novel two-dimensional binning approach with variable bin energy resolutions in the rotational and vibrational modes is developed for treating the internal mode of N{sub 2}. Both bin-to-bin and state-specific relaxation cross sections are obtained using the molecular dynamics/quasi-classical trajectory (MD/QCT) method with two potential energy surfaces as well as the state-specific database of Jaffe et al. The MD/QCT simulations of inelastic energy exchange between N{sub 2} and N show that there is amore » strong forward-preferential scattering behavior at high collision velocities. The 99 bin model is used in homogeneous DSMC relaxation simulations and is found to be able to recover the state-specific master equation results of Panesi et al. when the Jaffe state-specific cross sections are used. Rotational relaxation energy profiles and relaxation times obtained using the ReaxFF and Jaffe potential energy surfaces (PESs) are in general agreement but there are larger differences between the vibrational relaxation times. These differences become smaller as the translational temperature increases because the difference in the PES energy barrier becomes less important.« less

Simulation of bipolar charge transport in nanocomposite polymer films

NASA Astrophysics Data System (ADS)

Lean, Meng H.; Chu, Wei-Ping L.

2015-03-01

This paper describes 3D particle-in-cell simulation of bipolar charge injection and transport through nanocomposite film comprised of ferroelectric ceramic nanofillers in an amorphous polymer matrix. The classical electrical double layer (EDL) model for a monopolar core is extended (eEDL) to represent the nanofiller by replacing it with a dipolar core. Charge injection at the electrodes assumes metal-polymer Schottky emission at low to moderate fields and Fowler-Nordheim tunneling at high fields. Injected particles migrate via field-dependent Poole-Frenkel mobility and recombine with Monte Carlo selection. The simulation algorithm uses a boundary integral equation method for solution of the Poisson equation coupled with a second-order predictor-corrector scheme for robust time integration of the equations of motion. The stability criterion of the explicit algorithm conforms to the Courant-Friedrichs-Levy limit assuring robust and rapid convergence. The model is capable of simulating a wide dynamic range spanning leakage current to pre-breakdown. Simulation results for BaTiO3 nanofiller in amorphous polymer matrix indicate that charge transport behavior depend on nanoparticle polarization with anti-parallel orientation showing the highest leakage conduction and therefore lowest level of charge trapping in the interaction zone. Charge recombination is also highest, at the cost of reduced leakage conduction charge. The eEDL model predicts the meandering pathways of charge particle trajectories.

A Lorentz model for weak magnetic field bioeffects: part I--thermal noise is an essential component of AC/DC effects on bound ion trajectory.

PubMed

Muehsam, David J; Pilla, Arthur A

2009-09-01

We have previously employed the Lorentz-Langevin model to describe the effects of weak exogenous magnetic fields via the classical Lorentz force on a charged ion bound in a harmonic oscillator potential, in the presence of thermal noise forces. Previous analyses predicted that microT-range fields give rise to a rotation of the oscillator orientation at the Larmor frequency and bioeffects were based upon the assumption that the classical trajectory of the bound charge itself could modulate a biochemical process. Here, it is shown that the thermal component of the motion follows the Larmor trajectory. The results show that the Larmor frequency is independent of the thermal noise strength, and the motion retains the form of a coherent oscillator throughout the binding lifetime, rather than devolving into a random walk. Thermal equilibration results in a continual increase in the vibrational amplitude of the rotating oscillator towards the steady-state amplitude, but does not affect the Larmor orbit. Thus, thermal noise contributes to, rather than inhibits, the effect of the magnetic field upon reactivity. Expressions are derived for the ensemble average of position and the velocity of the thermal component of the oscillator motion. The projection of position and velocity onto a Cartesian axis measures the nonuniformity of the Larmor trajectory and is illustrated for AC and combined AC/DC magnetic fields, suggesting a means of interpreting resonance phenomena. It is noted that the specific location and height of resonances are dependent upon binding lifetime and initial AC phase.

Classical and quantum filaments in the ground state of trapped dipolar Bose gases

NASA Astrophysics Data System (ADS)

Cinti, Fabio; Boninsegni, Massimo

2017-07-01

We study, by quantum Monte Carlo simulations, the ground state of a harmonically confined dipolar Bose gas with aligned dipole moments and with the inclusion of a repulsive two-body potential of varying range. Two different limits can clearly be identified, namely, a classical one in which the attractive part of the dipolar interaction dominates and the system forms an ordered array of parallel filaments and a quantum-mechanical one, wherein filaments are destabilized by zero-point motion, and eventually the ground state becomes a uniform cloud. The physical character of the system smoothly evolves from classical to quantum mechanical as the range of the repulsive two-body potential increases. An intermediate regime is observed in which ordered filaments are still present, albeit forming different structures from the ones predicted classically; quantum-mechanical exchanges of indistinguishable particles across different filaments allow phase coherence to be established, underlying a global superfluid response.

Quantum and classical ripples in graphene

NASA Astrophysics Data System (ADS)

Hašík, Juraj; Tosatti, Erio; MartoÅák, Roman

2018-04-01

Thermal ripples of graphene are well understood at room temperature, but their quantum counterparts at low temperatures are in need of a realistic quantitative description. Here we present atomistic path-integral Monte Carlo simulations of freestanding graphene, which show upon cooling a striking classical-quantum evolution of height and angular fluctuations. The crossover takes place at ever-decreasing temperatures for ever-increasing wavelengths so that a completely quantum regime is never attained. Zero-temperature quantum graphene is flatter and smoother than classical graphene at large scales yet rougher at short scales. The angular fluctuation distribution of the normals can be quantitatively described by coexistence of two Gaussians, one classical strongly T -dependent and one quantum about 2° wide, of zero-point character. The quantum evolution of ripple-induced height and angular spread should be observable in electron diffraction in graphene and other two-dimensional materials, such as MoS2, bilayer graphene, boron nitride, etc.

Stratification, School-Work Linkages and Vocational Education

ERIC Educational Resources Information Center

Ainsworth, James W.; Roscigno, Vincent J.

2005-01-01

Building on more classical status attainment and reproduction perspectives, this article examines the extent of class, race and gender inequality in high school vocational education, and the consequences for students' later educational and occupational trajectories. Analyses demonstrate significant class, race and gender disparities in vocational…

Weak-field few-femtosecond VUV photodissociation dynamics of water isotopologues

NASA Astrophysics Data System (ADS)

Baumann, Arne; Bazzi, Sophia; Rompotis, Dimitrios; Schepp, Oliver; Azima, Armin; Wieland, Marek; Popova-Gorelova, Daria; Vendrell, Oriol; Santra, Robin; Drescher, Markus

2017-07-01

We present a joint experimental and theoretical study of the VUV-induced dynamics of H2O and its deuterated isotopologues in the first excited state (A ˜1B1 ) utilizing a VUV-pump VUV-probe scheme combined with a b initio classical trajectory calculations. 16-fs VUV pulses centered at 161 nm created by fifth-order harmonic generation are employed for single-shot pump-probe measurements. Combined with a precise determination of the VUV pulses' temporal profile, they provide the necessary temporal resolution to elucidate sub-10-fs dissociation dynamics in the 1+1 photon ionization time window. Ionization with a single VUV photon complements established strong-field ionization schemes by disclosing the molecular dynamics under perturbative conditions. Kinetic isotope effects derived from the pump-probe experiment are found to be in agreement with our by ab initio classical trajectory calculations, taking into account photoionization cross sections for the ground and first excited state of the water cation.

Monte Carlo simulation of energy deposition by low-energy electrons in molecular hydrogen

NASA Technical Reports Server (NTRS)

Heaps, M. G.; Furman, D. R.; Green, A. E. S.

1975-01-01

A set of detailed atomic cross sections has been used to obtain the spatial deposition of energy by 1-20-eV electrons in molecular hydrogen by a Monte Carlo simulation of the actual trajectories. The energy deposition curve (energy per distance traversed) is quite peaked in the forward direction about the entry point for electrons with energies above the threshold of the electronic states, but the peak decreases and broadens noticeably as the electron energy decreases below 10 eV (threshold for the lowest excitable electronic state of H2). The curve also assumes a very symmetrical shape for energies below 10 eV, indicating the increasing importance of elastic collisions in determining the shape of the curve, although not the mode of energy deposition.

Mars Microprobe Entry Analysis

NASA Technical Reports Server (NTRS)

Braun, Robert D.; Mitcheltree, Robert A.; Cheatwood, F. McNeil

1998-01-01

The Mars Microprobe mission will provide the first opportunity for subsurface measurements, including water detection, near the south pole of Mars. In this paper, performance of the Microprobe aeroshell design is evaluated through development of a six-degree-of-freedom (6-DOF) aerodynamic database and flight dynamics simulation. Numerous mission uncertainties are quantified and a Monte-Carlo analysis is performed to statistically assess mission performance. Results from this 6-DOF Monte-Carlo simulation demonstrate that, in a majority of the cases (approximately 2-sigma), the penetrator impact conditions are within current design tolerances. Several trajectories are identified in which the current set of impact requirements are not satisfied. From these cases, critical design parameters are highlighted and additional system requirements are suggested. In particular, a relatively large angle-of-attack range near peak heating is identified.

Uncertainty in predictions of oil spill trajectories in a coastal zone

NASA Astrophysics Data System (ADS)

Sebastião, P.; Guedes Soares, C.

2006-12-01

A method is introduced to determine the uncertainties in the predictions of oil spill trajectories using a classic oil spill model. The method considers the output of the oil spill model as a function of random variables, which are the input parameters, and calculates the standard deviation of the output results which provides a measure of the uncertainty of the model as a result of the uncertainties of the input parameters. In addition to a single trajectory that is calculated by the oil spill model using the mean values of the parameters, a band of trajectories can be defined when various simulations are done taking into account the uncertainties of the input parameters. This band of trajectories defines envelopes of the trajectories that are likely to be followed by the spill given the uncertainties of the input. The method was applied to an oil spill that occurred in 1989 near Sines in the southwestern coast of Portugal. This model represented well the distinction between a wind driven part that remained offshore, and a tide driven part that went ashore. For both parts, the method defined two trajectory envelopes, one calculated exclusively with the wind fields, and the other using wind and tidal currents. In both cases reasonable approximation to the observed results was obtained. The envelope of likely trajectories that is obtained with the uncertainty modelling proved to give a better interpretation of the trajectories that were simulated by the oil spill model.

Ups and downs of the expatriate experience? Understanding work adjustment trajectories and career outcomes.

PubMed

Zhu, Jing; Wanberg, Connie R; Harrison, David A; Diehn, Erica W

2016-04-01

We examine changes in work adjustment among 179 expatriates from 3 multinational organizations from predeparture through the first 9 months of a new international assignment. Our 10-wave results challenge classic U-shaped theories of expatriate adjustment (e.g., Torbiorn, 1982). Consistent with uncertainty reduction theory, our results instead suggest that expatriates typically experience a gradual increase in work adjustment over time. Two resources that expatriates bring to their assignments (previous culture-specific work experience and core self-evaluations) moderate the trajectory of work adjustment. Trajectory of adjustment predicts Month 9 career instrumentality and turnover intention, as well as career advancement (job promotion) 1.5 years further. Implications for theory, as well as for changes in expatriate management practices, are discussed. (c) 2016 APA, all rights reserved).

Electronic excitation and quenching of atoms at insulator surfaces

NASA Technical Reports Server (NTRS)

Swaminathan, P. K.; Garrett, Bruce C.; Murthy, C. S.

1988-01-01

A trajectory-based semiclassical method is used to study electronically inelastic collisions of gas atoms with insulator surfaces. The method provides for quantum-mechanical treatment of the internal electronic dynamics of a localized region involving the gas/surface collision, and a classical treatment of all the nuclear degrees of freedom (self-consistently and in terms of stochastic trajectories), and includes accurate simulation of the bath-temperature effects. The method is easy to implement and has a generality that holds promise for many practical applications. The problem of electronically inelastic dynamics is solved by computing a set of stochastic trajectories that on thermal averaging directly provide electronic transition probabilities at a given temperature. The theory is illustrated by a simple model of a two-state gas/surface interaction.

Hierarchical Control and Trajectory Planning

NASA Technical Reports Server (NTRS)

Martin, Clyde F.; Horn, P. W.

1994-01-01

Most of the time on this project was spent on the trajectory planning problem. The construction is equivalent to the classical spline construction in the case that the system matrix is nilpotent. If the dimension of the system is n then the spline of degree 2n-1 is constructed. This gives a new approach to the construction of splines that is more efficient than the usual construction and at the same time allows the construction of a much larger class of splines. All known classes of splines are reconstructed using the approach of linear control theory. As a numerical analysis tool control theory gives a very good tool for constructing splines. However, for the purposes of trajectory planning it is quite another story. Enclosed in this document are four reports done under this grant.

Superconformal Baryon-Meson Symmetry and Light-Front Holographic QCD

DOE PAGES

Dosch, Hans Guenter; de Teramond, Guy F.; Brodsky, Stanley J.

2015-04-10

We construct an effective QCD light-front Hamiltonian for both mesons and baryons in the chiral limit based on the generalized supercharges of a superconformal graded algebra. The superconformal construction is shown to be equivalent to a semi-classical approximation to light-front QCD and its embedding in AdS space. The specific breaking of conformal invariance inside the graded algebra uniquely determines the effective confinement potential. The generalized supercharges connect the baryon and meson spectra to each other in a remarkable manner. In particular, the π/b 1 Regge trajectory is identified as the superpartner of the nucleon trajectory. However, the lowest-lying state onmore » this trajectory, the π-meson is massless in the chiral limit and has no supersymmetric partner.« less

Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Alexander, Steven; Coldwell, R. L.

2015-03-01

The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this poster I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.

Communication: Note on detailed balance in symmetrical quasi-classical models for electronically non-adiabatic dynamics

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

Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com

2015-04-07

It is noted that the recently developed symmetrical quasi-classical (SQC) treatment of the Meyer-Miller (MM) model for the simulation of electronically non-adiabatic dynamics provides a good description of detailed balance, even though the dynamics which results from the classical MM Hamiltonian is “Ehrenfest dynamics” (i.e., the force on the nuclei is an instantaneous coherent average over all electronic states). This is seen to be a consequence of the SQC windowing methodology for “processing” the results of the trajectory calculation. For a particularly simple model discussed here, this is shown to be true regardless of the choice of windowing function employedmore » in the SQC model, and for a more realistic full classical molecular dynamics simulation, it is seen to be maintained correctly for very long time.« less

On understanding the relationship between structure in the potential surface and observables in classical dynamics: A functional sensitivity analysis approach

NASA Astrophysics Data System (ADS)

Judson, Richard S.; Rabitz, Herschel

1987-04-01

The relationship between structure in the potential surface and classical mechanical observables is examined by means of functional sensitivity analysis. Functional sensitivities provide maps of the potential surface, highlighting those regions that play the greatest role in determining the behavior of observables. A set of differential equations for the sensitivities of the trajectory components are derived. These are then solved using a Green's function method. It is found that the sensitivities become singular at the trajectory turning points with the singularities going as η-3/2, with η being the distance from the nearest turning point. The sensitivities are zero outside of the energetically and dynamically allowed region of phase space. A second set of equations is derived from which the sensitivities of observables can be directly calculated. An adjoint Green's function technique is employed, providing an efficient method for numerically calculating these quantities. Sensitivity maps are presented for a simple collinear atom-diatom inelastic scattering problem and for two Henon-Heiles type Hamiltonians modeling intramolecular processes. It is found that the positions of the trajectory caustics in the bound state problem determine regions of the highest potential surface sensitivities. In the scattering problem (which is impulsive, so that ``sticky'' collisions did not occur), the positions of the turning points of the individual trajectory components determine the regions of high sensitivity. In both cases, these lines of singularities are superimposed on a rich background structure. Most interesting is the appearance of classical interference effects. The interference features in the sensitivity maps occur most noticeably where two or more lines of turning points cross. The important practical motivation for calculating the sensitivities derives from the fact that the potential is a function, implying that any direct attempt to understand how local potential regions affect the behavior of the observables by repeatedly and systematically altering the potential will be prohibitively expensive. The functional sensitivity method enables one to perform this analysis at a fraction of the computational labor required for the direct method.

Behavior of light polarization in photon-scalar interaction

NASA Astrophysics Data System (ADS)

Azizi, Azizollah; Nasirimoghadam, Soudabe

2017-11-01

Quantum theories of gravity help us to improve our insight into the gravitational interactions. Motivated by the interesting effect of gravity on the photon trajectory, we treat a quantum recipe concluding a classical interaction of light and a massive object such as the sun. We use the linear quantum gravity to compute the classical potential of a photon interacting with a massive scalar. The leading terms have a traditional 1/r subordinate and demonstrate a polarization-dependent behavior. This result challenges the equivalence principle; attractive and/or repulsive interactions are admissible.

Above-Threshold Ionization by an Elliptically Polarized Field: Quantum Tunneling Interferences and Classical Dodging

NASA Astrophysics Data System (ADS)

Paulus, G. G.; Zacher, F.; Walther, H.; Lohr, A.; Becker, W.; Kleber, M.

1998-01-01

Measurements of above-threshold ionization electron spectra in an elliptically polarized field as a function of the ellipticity are presented. In the rescattering regime, electron yields quickly drop with increasing ellipticity. The yields of lower-energy electrons rise again when circular polarization is approached. A classical explanation for these effects is provided. Additional local maxima in the yields of lower-energy electrons can be interpreted as being due to interferences of electron trajectories that tunnel out at different times within one cycle of the field.

Molecular simulation of the thermodynamic, structural, and vapor-liquid equilibrium properties of neon

NASA Astrophysics Data System (ADS)

Vlasiuk, Maryna; Frascoli, Federico; Sadus, Richard J.

2016-09-01

The thermodynamic, structural, and vapor-liquid equilibrium properties of neon are comprehensively studied using ab initio, empirical, and semi-classical intermolecular potentials and classical Monte Carlo simulations. Path integral Monte Carlo simulations for isochoric heat capacity and structural properties are also reported for two empirical potentials and one ab initio potential. The isobaric and isochoric heat capacities, thermal expansion coefficient, thermal pressure coefficient, isothermal and adiabatic compressibilities, Joule-Thomson coefficient, and the speed of sound are reported and compared with experimental data for the entire range of liquid densities from the triple point to the critical point. Lustig's thermodynamic approach is formally extended for temperature-dependent intermolecular potentials. Quantum effects are incorporated using the Feynman-Hibbs quantum correction, which results in significant improvement in the accuracy of predicted thermodynamic properties. The new Feynman-Hibbs version of the Hellmann-Bich-Vogel potential predicts the isochoric heat capacity to an accuracy of 1.4% over the entire range of liquid densities. It also predicts other thermodynamic properties more accurately than alternative intermolecular potentials.

Ion-Stockmayer clusters: Minima, classical thermodynamics, and variational ground state estimates of Li+(CH3NO2)n (n = 1-20)

NASA Astrophysics Data System (ADS)

Curotto, E.

2015-12-01

Structural optimizations, classical NVT ensemble, and variational Monte Carlo simulations of ion Stockmayer clusters parameterized to approximate the Li+(CH3NO2)n (n = 1-20) systems are performed. The Metropolis algorithm enhanced by the parallel tempering strategy is used to measure internal energies and heat capacities, and a parallel version of the genetic algorithm is employed to obtain the most important minima. The first solvation sheath is octahedral and this feature remains the dominant theme in the structure of clusters with n ≥ 6. The first "magic number" is identified using the adiabatic solvent dissociation energy, and it marks the completion of the second solvation layer for the lithium ion-nitromethane clusters. It corresponds to the n = 18 system, a solvated ion with the first sheath having octahedral symmetry, weakly bound to an eight-membered and a four-membered ring crowning a vertex of the octahedron. Variational Monte Carlo estimates of the adiabatic solvent dissociation energy reveal that quantum effects further enhance the stability of the n = 18 system relative to its neighbors.

Non-Arrhenius temperature dependence of the island density of one-dimensional Al chains on Si(100): A kinetic Monte Carlo study

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

Albia, Jason R.; Albao, Marvin A., E-mail: maalbao@uplb.edu.ph

Classical nucleation theory predicts that the evolution of mean island density with temperature during growth in one-dimensional systems obeys the Arrhenius relation. In this study, kinetic Monte Carlo simulations of a suitable atomistic lattice-gas model were performed to investigate the experimentally observed non-Arrhenius scaling behavior of island density in the case of one-dimensional Al islands grown on Si(100). Previously, it was proposed that adatom desorption resulted in a transition temperature signaling the departure from classical predictions. Here, the authors demonstrate that desorption above the transition temperature is not possible. Instead, the authors posit that the existence of a transition temperaturemore » is due to a combination of factors such as reversibility of island growth, presence of C-defects, adatom diffusion rates, as well as detachment rates at island ends. In addition, the authors show that the anomalous non-Arrhenius behavior vanishes when adatom binds irreversibly with C-defects as observed in In on Si(100) studies.« less

Spin-Ice Thin Films: Large-N Theory and Monte Carlo Simulations

NASA Astrophysics Data System (ADS)

Lantagne-Hurtubise, Étienne; Rau, Jeffrey G.; Gingras, Michel J. P.

2018-04-01

We explore the physics of highly frustrated magnets in confined geometries, focusing on the Coulomb phase of pyrochlore spin ices. As a specific example, we investigate thin films of nearest-neighbor spin ice, using a combination of analytic large-N techniques and Monte Carlo simulations. In the simplest film geometry, with surfaces perpendicular to the [001] crystallographic direction, we observe pinch points in the spin-spin correlations characteristic of a two-dimensional Coulomb phase. We then consider the consequences of crystal symmetry breaking on the surfaces of the film through the inclusion of orphan bonds. We find that when these bonds are ferromagnetic, the Coulomb phase is destroyed by the presence of fluctuating surface magnetic charges, leading to a classical Z2 spin liquid. Building on this understanding, we discuss other film geometries with surfaces perpendicular to the [110] or the [111] direction. We generically predict the appearance of surface magnetic charges and discuss their implications for the physics of such films, including the possibility of an unusual Z3 classical spin liquid. Finally, we comment on open questions and promising avenues for future research.

Probabilistic Tracking and Trajectory Planning for Autonomous Ground Vehicles in Urban Environments

DTIC Science & Technology

2016-03-05

SECURITY CLASSIFICATION OF: The aim of this research is to develop a unified theory for perception and planning in autonomous ground vehicles, with a...Report Title The aim of this research is to develop a unified theory for perception and planning in autonomous ground vehicles, with a specific focus on...a combination of experimentally collected vision data and Monte- Carlo simulations. Smoothing for improved perception and robustness in planning

Stochastic solution to quantum dynamics

NASA Technical Reports Server (NTRS)

John, Sarah; Wilson, John W.

1994-01-01

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

On simulations of rarefied vapor flows with condensation

NASA Astrophysics Data System (ADS)

Bykov, Nikolay; Gorbachev, Yuriy; Fyodorov, Stanislav

2018-05-01

Results of the direct simulation Monte Carlo of 1D spherical and 2D axisymmetric expansions into vacuum of condens-ing water vapor are presented. Two models based on the kinetic approach and the size-corrected classical nucleation theory are employed for simulations. The difference in obtained results is discussed and advantages of the kinetic approach in comparison with the modified classical theory are demonstrated. The impact of clusterization on flow parameters is observed when volume fraction of clusters in the expansion region exceeds 5%. Comparison of the simulation data with the experimental results demonstrates good agreement.

Ca + HF - The anatomy of a chemical insertion reaction

NASA Technical Reports Server (NTRS)

Jaffe, R. L.; Pattengill, M. D.; Mascarello, F. G.; Zare, R. N.

1987-01-01

A comprehensive first-principles theoretical investigation of the gas phase reaction Ca + HF - CaF + H is reported. Ab initio potential energy calculations are first discussed, along with characteristics of the computed potential energy surface. Next, the fitting of the computed potential energy points to a suitable analytical functional form is described, and maps of the fitted potential surface are displayed. The methodology and results of a classical trajectory calculation utilizing the fitted potential surface are presented. Finally, the significance of the trajectory study results is discussed, and generalizations concerning dynamical aspects of Ca + HF scattering are drawn.

Rule-based navigation control design for autonomous flight

NASA Astrophysics Data System (ADS)

Contreras, Hugo; Bassi, Danilo

2008-04-01

This article depicts a navigation control system design that is based on a set of rules in order to follow a desired trajectory. The full control of the aircraft considered here comprises: a low level stability control loop, based on classic PID controller and the higher level navigation whose main job is to exercise lateral control (course) and altitude control, trying to follow a desired trajectory. The rules and PID gains were adjusted systematically according to the result of flight simulation. In spite of its simplicity, the rule-based navigation control proved to be robust, even with big perturbation, like crossing winds.

Quantum trajectories in elastic atom-surface scattering: threshold and selective adsorption resonances.

PubMed

Sanz, A S; Miret-Artés, S

2005-01-01

The elastic resonant scattering of He atoms off the Cu(117) surface is fully described with the formalism of quantum trajectories provided by Bohmian mechanics. Within this theory of quantum motion, the concept of trapping is widely studied and discussed. Classically, atoms undergo impulsive collisions with the surface, and then the trapped motion takes place covering at least two consecutive unit cells. However, from a Bohmian viewpoint, atom trajectories can smoothly adjust to the equipotential energy surface profile in a sort of sliding motion; thus the trapping process could eventually occur within one single unit cell. In particular, both threshold and selective adsorption resonances are explained by means of this quantum trapping considering different space and time scales. Furthermore, a mapping between each region of the (initial) incoming plane wave and the different parts of the diffraction and resonance patterns can be easily established, an important issue only provided by a quantum trajectory formalism. (c) 2005 American Institute of Physics.

On-the-Fly ab Initio Semiclassical Calculation of Glycine Vibrational Spectrum

PubMed Central

2017-01-01

We present an on-the-fly ab initio semiclassical study of vibrational energy levels of glycine, calculated by Fourier transform of the wavepacket correlation function. It is based on a multiple coherent states approach integrated with monodromy matrix regularization for chaotic dynamics. All four lowest-energy glycine conformers are investigated by means of single-trajectory semiclassical spectra obtained upon classical evolution of on-the-fly trajectories with harmonic zero-point energy. For the most stable conformer I, direct dynamics trajectories are also run for each vibrational mode with energy equal to the first harmonic excitation. An analysis of trajectories evolved up to 50 000 atomic time units demonstrates that, in this time span, conformers II and III can be considered as isolated species, while conformers I and IV show a pretty facile interconversion. Therefore, previous perturbative studies based on the assumption of isolated conformers are often reliable but might be not completely appropriate in the case of conformer IV and conformer I for which interconversion occurs promptly. PMID:28489368

A Monte Carlo simulation code for calculating damage and particle transport in solids: The case for electron-bombarded solids for electron energies up to 900 MeV

NASA Astrophysics Data System (ADS)

Yan, Qiang; Shao, Lin

2017-03-01

Current popular Monte Carlo simulation codes for simulating electron bombardment in solids focus primarily on electron trajectories, instead of electron-induced displacements. Here we report a Monte Carol simulation code, DEEPER (damage creation and particle transport in matter), developed for calculating 3-D distributions of displacements produced by electrons of incident energies up to 900 MeV. Electron elastic scattering is calculated by using full-Mott cross sections for high accuracy, and primary-knock-on-atoms (PKAs)-induced damage cascades are modeled using ZBL potential. We compare and show large differences in 3-D distributions of displacements and electrons in electron-irradiated Fe. The distributions of total displacements are similar to that of PKAs at low electron energies. But they are substantially different for higher energy electrons due to the shifting of PKA energy spectra towards higher energies. The study is important to evaluate electron-induced radiation damage, for the applications using high flux electron beams to intentionally introduce defects and using an electron analysis beam for microstructural characterization of nuclear materials.

Quantum Dynamics and a Semiclassical Description of the Photon.

ERIC Educational Resources Information Center

Henderson, Giles

1980-01-01

Uses computer graphics and nonstationary, superposition wave functions to reveal the dynamic quantum trajectories of several molecular and electronic transitions. These methods are then coupled with classical electromagnetic theory to provide a conceptually clear picture of the emission process and emitted radiation localized in time and space.…

Re-Imagining a Christian University in a Secular Age

ERIC Educational Resources Information Center

Warner, Rob

2013-01-01

The contours of a secular age, as delineated by classical and contemporary sociologists of religion, have tended to result in secularising trajectories for church-founded institutions of Higher Education, some of which have migrated towards secular normativity. This article explores these trends and then proposes five characteristics of an…

Generalized quantum theory of recollapsing homogeneous cosmologies

NASA Astrophysics Data System (ADS)

Craig, David; Hartle, James B.

2004-06-01

A sum-over-histories generalized quantum theory is developed for homogeneous minisuperspace type A Bianchi cosmological models, focusing on the particular example of the classically recollapsing Bianchi type-IX universe. The decoherence functional for such universes is exhibited. We show how the probabilities of decoherent sets of alternative, coarse-grained histories of these model universes can be calculated. We consider in particular the probabilities for classical evolution defined by a suitable coarse graining. For a restricted class of initial conditions and coarse grainings we exhibit the approximate decoherence of alternative histories in which the universe behaves classically and those in which it does not. For these situations we show that the probability is near unity for the universe to recontract classically if it expands classically. We also determine the relative probabilities of quasiclassical trajectories for initial states of WKB form, recovering for such states a precise form of the familiar heuristic “JṡdΣ” rule of quantum cosmology, as well as a generalization of this rule to generic initial states.

Smoothed quantum-classical states in time-irreversible hybrid dynamics

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2017-09-01

We consider a quantum system continuously monitored in time which in turn is coupled to an arbitrary dissipative classical system (diagonal reduced density matrix). The quantum and classical dynamics can modify each other, being described by an arbitrary time-irreversible hybrid Lindblad equation. Given a measurement trajectory, a conditional bipartite stochastic state can be inferred by taking into account all previous recording information (filtering). Here, we demonstrate that the joint quantum-classical state can also be inferred by taking into account both past and future measurement results (smoothing). The smoothed hybrid state is estimated without involving information from unobserved measurement channels. Its average over recording realizations recovers the joint time-irreversible behavior. As an application we consider a fluorescent system monitored by an inefficient photon detector. This feature is taken into account through a fictitious classical two-level system. The average purity of the smoothed quantum state increases over that of the (mixed) state obtained from the standard quantum jump approach.

LORAKS makes better SENSE: Phase-constrained partial fourier SENSE reconstruction without phase calibration.

PubMed

Kim, Tae Hyung; Setsompop, Kawin; Haldar, Justin P

2017-03-01

Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information. The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely used calibrationless uniformly undersampled trajectories. Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches. The SENSE-LORAKS framework provides promising new opportunities for highly accelerated MRI. Magn Reson Med 77:1021-1035, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Quantum dynamics in phase space: Moyal trajectories 2

NASA Astrophysics Data System (ADS)

Braunss, G.

2013-01-01

Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010), 10.1088/1751-8113/43/2/025302] where we had calculated ℏ2-approximations of quantum phase space viz. Moyal trajectories of examples with one and two degrees of freedom, we present in this paper the calculation of ℏ2-approximations for four examples: a two-dimensional Toda chain, the radially symmetric Schwarzschild field, and two examples with three degrees of freedom, the latter being the nonrelativistic spherically Coulomb potential and the relativistic cylinder symmetrical Coulomb potential with a magnetic field H. We show in particular that an ℏ2-approximation of the nonrelativistic Coulomb field has no singularity at the origin (r = 0) whereas the classical trajectories are singular at r = 0. In the third example, we show in particular that for an arbitrary function γ(H, z) the expression β ≡ pz + γ(H, z) is classically (ℏ = 0) a constant of motion, whereas for ℏ ≠ 0 this holds only if γ(H, z) is an arbitrary polynomial of second order in z. This statement is shown to extend correspondingly to a cylinder symmetrical Schwarzschild field with a magnetic field. We exhibit in detail a number of properties of the radially symmetric Schwarzschild field. We exhibit finally the problems of the nonintegrable Hénon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.

Classical density functional theory and Monte Carlo simulation study of electric double layer in the vicinity of a cylindrical electrode

NASA Astrophysics Data System (ADS)

Zhou, Shiqi; Lamperski, Stanisław; Sokołowska, Marta

2017-07-01

We have performed extensive Monte-Carlo simulations and classical density functional theory (DFT) calculations of the electrical double layer (EDL) near a cylindrical electrode in a primitive model (PM) modified by incorporating interionic dispersion interactions. It is concluded that (i) in general, an unsophisticated use of the mean field (MF) approximation for the interionic dispersion interactions does not distinctly worsen the classical DFT performance, even if the salt ions considered are highly asymmetrical in size (3:1) and charge (5:1), the bulk molar concentration considered is high up to a total bulk ion packing fraction of 0.314, and the surface charge density of up to 0.5 C m-2. (ii) More specifically, considering the possible noises in the simulation, the local volume charge density profiles are the most accurately predicted by the classical DFT in all situations, and the co- and counter-ion singlet distributions are also rather accurately predicted; whereas the mean electrostatic potential profile is relatively less accurately predicted due to an integral amplification of minor inaccuracy of the singlet distributions. (iii) It is found that the layered structure of the co-ion distribution is abnormally possible only if the surface charge density is high enough (for example 0.5 C m-2) moreover, the co-ion valence abnormally influences the peak height of the first counter-ion layer, which decreases with the former. (iv) Even if both the simulation and DFT indicate an insignificant contribution of the interionic dispersion interaction to the above three ‘local’ quantities, it is clearly shown by the classical DFT that the interionic dispersion interaction does significantly influence a ‘global’ quantity like the cylinder surface-aqueous electrolyte interfacial tension, and this may imply the role of the interionic dispersion interaction in explaining the specific Hofmeister effects. We elucidate all of the above observations based on the arguments from the liquid state theory and at the molecular scale.

Fluctuation theorems in feedback-controlled open quantum systems: Quantum coherence and absolute irreversibility

NASA Astrophysics Data System (ADS)

Murashita, Yûto; Gong, Zongping; Ashida, Yuto; Ueda, Masahito

2017-10-01

The thermodynamics of quantum coherence has attracted growing attention recently, where the thermodynamic advantage of quantum superposition is characterized in terms of quantum thermodynamics. We investigate the thermodynamic effects of quantum coherent driving in the context of the fluctuation theorem. We adopt a quantum-trajectory approach to investigate open quantum systems under feedback control. In these systems, the measurement backaction in the forward process plays a key role, and therefore the corresponding time-reversed quantum measurement and postselection must be considered in the backward process, in sharp contrast to the classical case. The state reduction associated with quantum measurement, in general, creates a zero-probability region in the space of quantum trajectories of the forward process, which causes singularly strong irreversibility with divergent entropy production (i.e., absolute irreversibility) and hence makes the ordinary fluctuation theorem break down. In the classical case, the error-free measurement ordinarily leads to absolute irreversibility, because the measurement restricts classical paths to the region compatible with the measurement outcome. In contrast, in open quantum systems, absolute irreversibility is suppressed even in the presence of the projective measurement due to those quantum rare events that go through the classically forbidden region with the aid of quantum coherent driving. This suppression of absolute irreversibility exemplifies the thermodynamic advantage of quantum coherent driving. Absolute irreversibility is shown to emerge in the absence of coherent driving after the measurement, especially in systems under time-delayed feedback control. We show that absolute irreversibility is mitigated by increasing the duration of quantum coherent driving or decreasing the delay time of feedback control.

Exploring the importance of quantum effects in nucleation: The archetypical Nen case

NASA Astrophysics Data System (ADS)

Unn-Toc, Wesley; Halberstadt, Nadine; Meier, Christoph; Mella, Massimo

2012-07-01

The effect of quantum mechanics (QM) on the details of the nucleation process is explored employing Ne clusters as test cases due to their semi-quantal nature. In particular, we investigate the impact of quantum mechanics on both condensation and dissociation rates in the framework of the microcanonical ensemble. Using both classical trajectories and two semi-quantal approaches (zero point averaged dynamics, ZPAD, and Gaussian-based time dependent Hartree, G-TDH) to model cluster and collision dynamics, we simulate the dissociation and monomer capture for Ne8 as a function of the cluster internal energy, impact parameter and collision speed. The results for the capture probability Ps(b) as a function of the impact parameter suggest that classical trajectories always underestimate capture probabilities with respect to ZPAD, albeit at most by 15%-20% in the cases we studied. They also do so in some important situations when using G-TDH. More interestingly, dissociation rates kdiss are grossly overestimated by classical mechanics, at least by one order of magnitude. We interpret both behaviours as mainly due to the reduced amount of kinetic energy available to a quantum cluster for a chosen total internal energy. We also find that the decrease in monomer dissociation energy due to zero point energy effects plays a key role in defining dissociation rates. In fact, semi-quantal and classical results for kdiss seem to follow a common "corresponding states" behaviour when the proper definition of internal and dissociation energies are used in a transition state model estimation of the evaporation rate constants.

Poster — Thur Eve — 46: Monte Carlo model of the Novalis Classic 6MV stereotactic linear accelerator using the GATE simulation platform

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

Wiebe, J; Department of Physics and Astronomy, University of Calgary, Calgary, AB; Ploquin, N

2014-08-15

Monte Carlo (MC) simulation is accepted as the most accurate method to predict dose deposition when compared to other methods in radiation treatment planning. Current dose calculation algorithms used for treatment planning can become inaccurate when small radiation fields and tissue inhomogeneities are present. At our centre the Novalis Classic linear accelerator (linac) is used for Stereotactic Radiosurgery (SRS). The first MC model to date of the Novalis Classic linac was developed at our centre using the Geant4 Application for Tomographic Emission (GATE) simulation platform. GATE is relatively new, open source MC software built from CERN's Geometry and Tracking 4more » (Geant4) toolkit. The linac geometry was modeled using manufacturer specifications, as well as in-house measurements of the micro MLC's. Among multiple model parameters, the initial electron beam was adjusted so that calculated depth dose curves agreed with measured values. Simulations were run on the European Grid Infrastructure through GateLab. Simulation time is approximately 8 hours on GateLab for a complete head model simulation to acquire a phase space file. Current results have a majority of points within 3% of the measured dose values for square field sizes ranging from 6×6 mm{sup 2} to 98×98 mm{sup 2} (maximum field size on the Novalis Classic linac) at 100 cm SSD. The x-ray spectrum was determined from the MC data as well. The model provides an investigation into GATE'S capabilities and has the potential to be used as a research tool and an independent dose calculation engine for clinical treatment plans.« less

Quantum Bohmian model for financial market

NASA Astrophysics Data System (ADS)

Choustova, Olga Al.

2007-01-01

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. The Hamiltonian formalism on the price/price-change phase space describes the classical-like evolution of prices. This classical dynamics of prices is determined by “hard” conditions (natural resources, industrial production, services and so on). These conditions are mathematically described by the classical financial potential V(q), where q=(q1,…,qn) is the vector of prices of various shares. But the information exchange and market psychology play important (and sometimes determining) role in price dynamics. We propose to describe such behavioral financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial behavioral waves takes into account the market psychology. The real trajectories of prices are determined (through the financial analogue of the second Newton law) by two financial potentials: classical-like V(q) (“hard” market conditions) and quantum-like U(q) (behavioral market conditions).

Mixed quantum-classical simulations of the vibrational relaxation of photolyzed carbon monoxide in a hemoprotein

NASA Astrophysics Data System (ADS)

Schubert, Alexander; Falvo, Cyril; Meier, Christoph

2016-08-01

We present mixed quantum-classical simulations on relaxation and dephasing of vibrationally excited carbon monoxide within a protein environment. The methodology is based on a vibrational surface hopping approach treating the vibrational states of CO quantum mechanically, while all remaining degrees of freedom are described by means of classical molecular dynamics. The CO vibrational states form the "surfaces" for the classical trajectories of protein and solvent atoms. In return, environmentally induced non-adiabatic couplings between these states cause transitions describing the vibrational relaxation from first principles. The molecular dynamics simulation yields a detailed atomistic picture of the energy relaxation pathways, taking the molecular structure and dynamics of the protein and its solvent fully into account. Using the ultrafast photolysis of CO in the hemoprotein FixL as an example, we study the relaxation of vibrationally excited CO and evaluate the role of each of the FixL residues forming the heme pocket.

Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm

NASA Astrophysics Data System (ADS)

Gubernatis, James

2014-03-01

A common computational task is solving a set of ordinary differential equations (o.d.e.'s). A little known theorem says that the solution of any set of o.d.e.'s is exactly solved by the expectation value over a set of arbitary Poisson processes of a particular function of the elements of the matrix that defines the o.d.e.'s. The theorem thus provides a new starting point to develop real and imaginary-time continous-time solvers for quantum Monte Carlo algorithms, and several simple observations enable various quantum Monte Carlo techniques and variance reduction methods to transfer to a new context. I will state the theorem, note a transformation to a very simple computational scheme, and illustrate the use of some techniques from the directed-loop algorithm in context of the wavefunction Monte Carlo method that is used to solve the Lindblad master equation for the dynamics of open quantum systems. I will end by noting that as the theorem does not depend on the source of the o.d.e.'s coming from quantum mechanics, it also enables the transfer of continuous-time methods from quantum Monte Carlo to the simulation of various classical equations of motion heretofore only solved deterministically.

Discrete Fractional Component Monte Carlo Simulation Study of Dilute Nonionic Surfactants at the Air-Water Interface.

PubMed

Yoo, Brian; Marin-Rimoldi, Eliseo; Mullen, Ryan Gotchy; Jusufi, Arben; Maginn, Edward J

2017-09-26

We present a newly developed Monte Carlo scheme to predict bulk surfactant concentrations and surface tensions at the air-water interface for various surfactant interfacial coverages. Since the concentration regimes of these systems of interest are typically very dilute (≪10 -5 mol. frac.), Monte Carlo simulations with the use of insertion/deletion moves can provide the ability to overcome finite system size limitations that often prohibit the use of modern molecular simulation techniques. In performing these simulations, we use the discrete fractional component Monte Carlo (DFCMC) method in the Gibbs ensemble framework, which allows us to separate the bulk and air-water interface into two separate boxes and efficiently swap tetraethylene glycol surfactants C 10 E 4 between boxes. Combining this move with preferential translations, volume biased insertions, and Wang-Landau biasing vastly enhances sampling and helps overcome the classical "insertion problem", often encountered in non-lattice Monte Carlo simulations. We demonstrate that this methodology is both consistent with the original molecular thermodynamic theory (MTT) of Blankschtein and co-workers, as well as their recently modified theory (MD/MTT), which incorporates the results of surfactant infinite dilution transfer free energies and surface tension calculations obtained from molecular dynamics simulations.

A stereoscopic imaging system for laser back scatter based trajectory measurement in ballistics: part 2

NASA Astrophysics Data System (ADS)

Chalupka, Uwe; Rothe, Hendrik

2012-03-01

The progress on a laser- and stereo-camera-based trajectory measurement system that we already proposed and described in recent publications is given. The system design was extended from one to two more powerful, DSP-controllable LASER systems. Experimental results of the extended system using different projectile-/weapon combinations will be shown and discussed. Automatic processing of acquired images using common 3DIP techniques was realized. Processing steps to extract trajectory segments from images as representative for the current application will be presented. Used algorithms for backward-calculation of the projectile trajectory will be shown. Verification of produced results is done against simulated trajectories, once in terms of detection robustness and once in terms of detection accuracy. Fields of use for the current system are within the ballistic domain. The first purpose is for trajectory measurement of small and middle caliber projectiles on a shooting range. Extension to big caliber projectiles as well as an application for sniper detection is imaginable, but would require further work. Beside classical RADAR, acoustic and optical projectile detection methods, the current system represents a further projectile location method under the new class of electro-optical methods that have been evolved in recent decades and that uses 3D imaging acquisition and processing techniques.

Extended hamiltonian formalism and Lorentz-violating lagrangians

NASA Astrophysics Data System (ADS)

Colladay, Don

2017-09-01

A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

Quantum trajectories for high-order-harmonic generation from multiple rescattering events in the long-wavelength regime

NASA Astrophysics Data System (ADS)

He, Lixin; Li, Yang; Wang, Zhe; Zhang, Qingbin; Lan, Pengfei; Lu, Peixiang

2014-05-01

We have performed the quantum trajectory analysis for high-order-harmonic generation (HHG) with different driving laser wavelengths. By defining the ratio of HHG yields of the Nth and first rescattering events (YN/Y1), we quantitatively evaluate the HHG contributions from multiple rescatterings. The results show that the HHG yield ratio increases gradually with the increase of the laser wavelength, which demonstrates that high-order rescatterings provide ascendent contributions to HHG at longer wavelength. By calculating the classical electron trajectories, we find significant differences exist in the electron behaviors between the first and high-order rescatterings. Further investigations have demonstrated that the increasing HHG yield ratio is mainly attributed to the relatively smaller contributions from the short path of the first electron rescattering at longer laser wavelength.

LiquidLib: A comprehensive toolbox for analyzing classical and ab initio molecular dynamics simulations of liquids and liquid-like matter with applications to neutron scattering experiments

NASA Astrophysics Data System (ADS)

Walter, Nathan P.; Jaiswal, Abhishek; Cai, Zhikun; Zhang, Yang

2018-07-01

Neutron scattering is a powerful experimental technique for characterizing the structure and dynamics of materials on the atomic or molecular scale. However, the interpretation of experimental data from neutron scattering is oftentimes not trivial, partly because scattering methods probe ensemble-averaged information in the reciprocal space. Therefore, computer simulations, such as classical and ab initio molecular dynamics, are frequently used to unravel the time-dependent atomistic configurations that can reproduce the scattering patterns and thus assist in the understanding of the microscopic origin of certain properties of materials. LiquidLib is a post-processing package for analyzing the trajectory of atomistic simulations of liquids and liquid-like matter with application to neutron scattering experiments. From an atomistic simulation, LiquidLib provides the computation of various statistical quantities including the pair distribution function, the weighted and unweighted structure factors, the mean squared displacement, the non-Gaussian parameter, the four-point correlation function, the velocity auto correlation function, the self and collective van Hove correlation functions, the self and collective intermediate scattering functions, and the bond orientational order parameter. LiquidLib analyzes atomistic trajectories generated from packages such as LAMMPS, GROMACS, and VASP. It also offers an extendable platform to conveniently integrate new quantities into the library and integrate simulation trajectories of other file formats for analysis. Weighting the quantities by element-specific neutron-scattering lengths provides results directly comparable to neutron scattering measurements. Lastly, LiquidLib is independent of dimensionality, which allows analysis of trajectories in two, three, and higher dimensions. The code is beginning to find worldwide use.

Monte Carlo wave-function description of losses in a one-dimensional Bose gas and cooling to the ground state by quantum feedback

NASA Astrophysics Data System (ADS)

Schemmer, M.; Johnson, A.; Photopoulos, R.; Bouchoule, I.

2017-04-01

The effect of atom losses on a homogeneous one-dimensional Bose gas lying within the quasicondensate regime is investigated using a Monte Carlo wave-function approach. The evolution of the system is calculated, conditioned by the loss sequence, namely, the times of individual losses and the position of the removed atoms. We describe the gas within the linearized Bogoliubov approach. For each mode, we find that, for a given quantum trajectory, the state of the system converges towards a coherent state, i.e., the ground state, displaced in phase space. We show that, provided losses are recorded with a temporal and spatially resolved detector, quantum feedback can be implemented and cooling to the ground state of one or several modes can be realized.

Command and Control of Guerrilla Groups in the Philippines, 1941-1945

DTIC Science & Technology

2017-05-25

However, the phasing concept in this case seems ex post facto , rather than descriptive of any initial design. Especially in its early days, the trajectory... post -independence era. They apply a framework that examines the environment, organization, tactics, doctrine, and technology of each phase of history...defenses on Mindanao and destroyed the bulk of Sharp’s force, though the command post at Del Monte remained intact.33 On May 9, Sharp met with a

Testing algorithms for critical slowing down

NASA Astrophysics Data System (ADS)

Cossu, Guido; Boyle, Peter; Christ, Norman; Jung, Chulwoo; Jüttner, Andreas; Sanfilippo, Francesco

2018-03-01

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge.

Computational studies of thermal and quantum phase transitions approached through non-equilibrium quenching

NASA Astrophysics Data System (ADS)

Liu, Cheng-Wei

Phase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions. The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process. I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling. For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system. To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the NEQ approach I verify the universality class of the 3D Ising spin-glasses. I also investigate the random 3-regular graphs in terms of both classical and quantum phase transitions. I demonstrate that under this simulation scheme, one can extract information associated with the classical and quantum spin-glass transitions without any knowledge prior to the simulation.

A Kalman Filter Implementation for Precision Improvement in Low-Cost GPS Positioning of Tractors

PubMed Central

Gomez-Gil, Jaime; Ruiz-Gonzalez, Ruben; Alonso-Garcia, Sergio; Gomez-Gil, Francisco Javier

2013-01-01

Low-cost GPS receivers provide geodetic positioning information using the NMEA protocol, usually with eight digits for latitude and nine digits for longitude. When these geodetic coordinates are converted into Cartesian coordinates, the positions fit in a quantization grid of some decimeters in size, the dimensions of which vary depending on the point of the terrestrial surface. The aim of this study is to reduce the quantization errors of some low-cost GPS receivers by using a Kalman filter. Kinematic tractor model equations were employed to particularize the filter, which was tuned by applying Monte Carlo techniques to eighteen straight trajectories, to select the covariance matrices that produced the lowest Root Mean Square Error in these trajectories. Filter performance was tested by using straight tractor paths, which were either simulated or real trajectories acquired by a GPS receiver. The results show that the filter can reduce the quantization error in distance by around 43%. Moreover, it reduces the standard deviation of the heading by 75%. Data suggest that the proposed filter can satisfactorily preprocess the low-cost GPS receiver data when used in an assistance guidance GPS system for tractors. It could also be useful to smooth tractor GPS trajectories that are sharpened when the tractor moves over rough terrain. PMID:24217355

MARS Science Laboratory Post-Landing Location Estimation Using Post2 Trajectory Simulation

NASA Technical Reports Server (NTRS)

Davis, J. L.; Shidner, Jeremy D.; Way, David W.

2013-01-01

The Mars Science Laboratory (MSL) Curiosity rover landed safely on Mars August 5th, 2012 at 10:32 PDT, Earth Received Time. Immediately following touchdown confirmation, best estimates of position were calculated to assist in determining official MSL locations during entry, descent and landing (EDL). Additionally, estimated balance mass impact locations were provided and used to assess how predicted locations compared to actual locations. For MSL, the Program to Optimize Simulated Trajectories II (POST2) was the primary trajectory simulation tool used to predict and assess EDL performance from cruise stage separation through rover touchdown and descent stage impact. This POST2 simulation was used during MSL operations for EDL trajectory analyses in support of maneuver decisions and imaging MSL during EDL. This paper presents the simulation methodology used and results of pre/post-landing MSL location estimates and associated imagery from Mars Reconnaissance Orbiter s (MRO) High Resolution Imaging Science Experiment (HiRISE) camera. To generate these estimates, the MSL POST2 simulation nominal and Monte Carlo data, flight telemetry from onboard navigation, relay orbiter positions from MRO and Mars Odyssey and HiRISE generated digital elevation models (DEM) were utilized. A comparison of predicted rover and balance mass location estimations against actual locations are also presented.

Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins

NASA Astrophysics Data System (ADS)

Kulagin, S. A.; Prokof'ev, N.; Starykh, O. A.; Svistunov, B.; Varney, C. N.

2013-02-01

We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo sampling of skeleton Feynman diagrams within the fermionization framework offers a universal first-principles tool for strongly correlated lattice quantum systems. We observe the fermionic sign blessing—cancellation of higher order diagrams leading to a finite convergence radius of the series. We calculate the magnetic susceptibility of the triangular-lattice quantum antiferromagnet in the correlated paramagnet regime and reveal a surprisingly accurate microscopic correspondence with its classical counterpart at all accessible temperatures. The extrapolation of the observed relation to zero temperature suggests the absence of the magnetic order in the ground state. We critically examine the implications of this unusual scenario.

bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport

DOE PAGES

Ryan, Benjamin R; Dolence, Joshua C.; Gammie, Charles F.

2015-06-25

We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of our implementation, and a suite of test and convergence results. We also describe example applications to radiative Bondi accretion and tomore » a slowly accreting Kerr black hole in axisymmetry.« 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.

(Re)evaluating the Implications of the Autoregressive Latent Trajectory Model Through Likelihood Ratio Tests of Its Initial Conditions.

PubMed

Ou, Lu; Chow, Sy-Miin; Ji, Linying; Molenaar, Peter C M

2017-01-01

The autoregressive latent trajectory (ALT) model synthesizes the autoregressive model and the latent growth curve model. The ALT model is flexible enough to produce a variety of discrepant model-implied change trajectories. While some researchers consider this a virtue, others have cautioned that this may confound interpretations of the model's parameters. In this article, we show that some-but not all-of these interpretational difficulties may be clarified mathematically and tested explicitly via likelihood ratio tests (LRTs) imposed on the initial conditions of the model. We show analytically the nested relations among three variants of the ALT model and the constraints needed to establish equivalences. A Monte Carlo simulation study indicated that LRTs, particularly when used in combination with information criterion measures, can allow researchers to test targeted hypotheses about the functional forms of the change process under study. We further demonstrate when and how such tests may justifiably be used to facilitate our understanding of the underlying process of change using a subsample (N = 3,995) of longitudinal family income data from the National Longitudinal Survey of Youth.

Multiscale statistics of trajectories with applications to fluid particles in turbulence and football players

NASA Astrophysics Data System (ADS)

Schneider, Kai; Kadoch, Benjamin; Bos, Wouter

2017-11-01

The angle between two subsequent particle displacement increments is evaluated as a function of the time lag. The directional change of particles can thus be quantified at different scales and multiscale statistics can be performed. Flow dependent and geometry dependent features can be distinguished. The mean angle satisfies scaling behaviors for short time lags based on the smoothness of the trajectories. For intermediate time lags a power law behavior can be observed for some turbulent flows, which can be related to Kolmogorov scaling. The long time behavior depends on the confinement geometry of the flow. We show that the shape of the probability distribution function of the directional change can be well described by a Fischer distribution. Results for two-dimensional (direct and inverse cascade) and three-dimensional turbulence with and without confinement, illustrate the properties of the proposed multiscale statistics. The presented Monte-Carlo simulations allow disentangling geometry dependent and flow independent features. Finally, we also analyze trajectories of football players, which are, in general, not randomly spaced on a field.

A Smoluchowski model of crystallization dynamics of small colloidal clusters

NASA Astrophysics Data System (ADS)

Beltran-Villegas, Daniel J.; Sehgal, Ray M.; Maroudas, Dimitrios; Ford, David M.; Bevan, Michael A.

2011-10-01

We investigate the dynamics of colloidal crystallization in a 32-particle system at a fixed value of interparticle depletion attraction that produces coexisting fluid and solid phases. Free energy landscapes (FELs) and diffusivity landscapes (DLs) are obtained as coefficients of 1D Smoluchowski equations using as order parameters either the radius of gyration or the average crystallinity. FELs and DLs are estimated by fitting the Smoluchowski equations to Brownian dynamics (BD) simulations using either linear fits to locally initiated trajectories or global fits to unbiased trajectories using Bayesian inference. The resulting FELs are compared to Monte Carlo Umbrella Sampling results. The accuracy of the FELs and DLs for modeling colloidal crystallization dynamics is evaluated by comparing mean first-passage times from BD simulations with analytical predictions using the FEL and DL models. While the 1D models accurately capture dynamics near the free energy minimum fluid and crystal configurations, predictions near the transition region are not quantitatively accurate. A preliminary investigation of ensemble averaged 2D order parameter trajectories suggests that 2D models are required to capture crystallization dynamics in the transition region.

Finite element model updating using the shadow hybrid Monte Carlo technique

NASA Astrophysics Data System (ADS)

Boulkaibet, I.; Mthembu, L.; Marwala, T.; Friswell, M. I.; Adhikari, S.

2015-02-01

Recent research in the field of finite element model updating (FEM) advocates the adoption of Bayesian analysis techniques to dealing with the uncertainties associated with these models. However, Bayesian formulations require the evaluation of the Posterior Distribution Function which may not be available in analytical form. This is the case in FEM updating. In such cases sampling methods can provide good approximations of the Posterior distribution when implemented in the Bayesian context. Markov Chain Monte Carlo (MCMC) algorithms are the most popular sampling tools used to sample probability distributions. However, the efficiency of these algorithms is affected by the complexity of the systems (the size of the parameter space). The Hybrid Monte Carlo (HMC) offers a very important MCMC approach to dealing with higher-dimensional complex problems. The HMC uses the molecular dynamics (MD) steps as the global Monte Carlo (MC) moves to reach areas of high probability where the gradient of the log-density of the Posterior acts as a guide during the search process. However, the acceptance rate of HMC is sensitive to the system size as well as the time step used to evaluate the MD trajectory. To overcome this limitation we propose the use of the Shadow Hybrid Monte Carlo (SHMC) algorithm. The SHMC algorithm is a modified version of the Hybrid Monte Carlo (HMC) and designed to improve sampling for large-system sizes and time steps. This is done by sampling from a modified Hamiltonian function instead of the normal Hamiltonian function. In this paper, the efficiency and accuracy of the SHMC method is tested on the updating of two real structures; an unsymmetrical H-shaped beam structure and a GARTEUR SM-AG19 structure and is compared to the application of the HMC algorithm on the same structures.

CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models

NASA Astrophysics Data System (ADS)

Komura, Yukihiro; Okabe, Yutaka

2014-03-01

We present sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the q-state Potts model, and the classical XY model. As for the lattice, both the 2D (square) lattice and the 3D (simple cubic) lattice are treated. We already reported the idea of the GPU implementation for 2D models (Komura and Okabe, 2012). We here explain the details of sample programs, and discuss the performance of the present GPU implementation for the 3D Ising and XY models. We also show the calculated results of the moment ratio for these models, and discuss phase transitions. Catalogue identifier: AERM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5632 No. of bytes in distributed program, including test data, etc.: 14688 Distribution format: tar.gz Programming language: C, CUDA. Computer: System with an NVIDIA CUDA enabled GPU. Operating system: System with an NVIDIA CUDA enabled GPU. Classification: 23. External routines: NVIDIA CUDA Toolkit 3.0 or newer Nature of problem: Monte Carlo simulation of classical spin systems. Ising, q-state Potts model, and the classical XY model are treated for both two-dimensional and three-dimensional lattices. Solution method: GPU-based Swendsen-Wang multi-cluster spin flip Monte Carlo method. The CUDA implementation for the cluster-labeling is based on the work by Hawick et al. [1] and that by Kalentev et al. [2]. Restrictions: The system size is limited depending on the memory of a GPU. Running time: For the parameters used in the sample programs, it takes about a minute for each program. Of course, it depends on the system size, the number of Monte Carlo steps, etc. References: [1] K.A. Hawick, A. Leist, and D. P. Playne, Parallel Computing 36 (2010) 655-678 [2] O. Kalentev, A. Rai, S. Kemnitzb, and R. Schneider, J. Parallel Distrib. Comput. 71 (2011) 615-620

Force-field functor theory: classical force-fields which reproduce equilibrium quantum distributions

PubMed Central

Babbush, Ryan; Parkhill, John; Aspuru-Guzik, Alán

2013-01-01

Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory. PMID:24790954

Transport studies in high-performance field reversed configuration plasmas

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

Gupta, S., E-mail: sgupta@trialphaenergy.com; Barnes, D. C.; Dettrick, S. A.

2016-05-15

A significant improvement of field reversed configuration (FRC) lifetime and plasma confinement times in the C-2 plasma, called High Performance FRC regime, has been observed with neutral beam injection (NBI), improved edge stability, and better wall conditioning [Binderbauer et al., Phys. Plasmas 22, 056110 (2015)]. A Quasi-1D (Q1D) fluid transport code has been developed and employed to carry out transport analysis of such C-2 plasma conditions. The Q1D code is coupled to a Monte-Carlo code to incorporate the effect of fast ions, due to NBI, on the background FRC plasma. Numerically, the Q1D transport behavior with enhanced transport coefficients (butmore » with otherwise classical parametric dependencies) such as 5 times classical resistive diffusion, classical thermal ion conductivity, 20 times classical electron thermal conductivity, and classical fast ion behavior fit with the experimentally measured time evolution of the excluded flux radius, line-integrated density, and electron/ion temperature. The numerical study shows near sustainment of poloidal flux for nearly 1 ms in the presence of NBI.« less

Trajectory dynamics study of the Ar + CH4 dissociation reaction at high temperatures: the importance of zero-point-energy effects.

PubMed

Marques, J M C; Martínez-Núñez, E; Fernandez-Ramos, A; Vazquez, S A

2005-06-23

Large-scale classical trajectory calculations have been performed to study the reaction Ar + CH4--> CH3 +H + Ar in the temperature range 2500 < or = T/K < or = 4500. The potential energy surface used for ArCH4 is the sum of the nonbonding pairwise potentials of Hase and collaborators (J. Chem. Phys. 2001, 114, 535) that models the intermolecular interaction and the CH4 intramolecular potential of Duchovic et al. (J. Phys. Chem. 1984, 88, 1339), which has been modified to account for the H-H repulsion at small bending angles. The thermal rate coefficient has been calculated, and the zero-point energy (ZPE) of the CH3 product molecule has been taken into account in the analysis of the results; also, two approaches have been applied for discarding predissociative trajectories. In both cases, good agreement is observed between the experimental and trajectory results after imposing the ZPE of CH3. The energy-transfer parameters have also been obtained from trajectory calculations and compared with available values estimated from experiment using the master equation formalism; in general, the agreement is good.

Voyager 2 Neptune targeting strategy

NASA Technical Reports Server (NTRS)

Potts, C. L.; Francis, K.; Matousek, S. E.; Cesarone, R. J.; Gray, D. L.

1989-01-01

The success of the Voyager 2 flybys of Neptune and Triton depends upon the ability to correct the spacecraft's trajectory. Accurate spacecraft delivery to the desired encounter conditions will promote the maximum science return. However, Neptune's great distance causes large a priori uncertainties in Neptune and Triton ephemerides and planetary system parameters. Consequently, the 'ideal' trajectory is unknown beforehand. The targeting challenge is to utilize the gradually improving knowledge as the spacecraft approaches Neptune to meet the science objectives, but with an overriding concern for spacecraft safety and a desire to limit propellant expenditure. A unique targeting strategy has been developed in response to this challenge. Through the use of a Monte Carlo simulation, candidate strategies are evaluated by the degree to which they meet these objectives and are compared against each other in determining the targeting strategy to be adopted.

A Computationally Inexpensive Optimal Guidance via Radial-Basis-Function Neural Network for Autonomous Soft Landing on Asteroids

PubMed Central

Zhang, Peng; Liu, Keping; Zhao, Bo; Li, Yuanchun

2015-01-01

Optimal guidance is essential for the soft landing task. However, due to its high computational complexities, it is hardly applied to the autonomous guidance. In this paper, a computationally inexpensive optimal guidance algorithm based on the radial basis function neural network (RBFNN) is proposed. The optimization problem of the trajectory for soft landing on asteroids is formulated and transformed into a two-point boundary value problem (TPBVP). Combining the database of initial states with the relative initial co-states, an RBFNN is trained offline. The optimal trajectory of the soft landing is determined rapidly by applying the trained network in the online guidance. The Monte Carlo simulations of soft landing on the Eros433 are performed to demonstrate the effectiveness of the proposed guidance algorithm. PMID:26367382

An analytical derivation of MC-SCF vibrational wave functions for the quantum dynamical simulation of multiple proton transfer reactions: Initial application to protonated water chains

NASA Astrophysics Data System (ADS)

Drukker, Karen; Hammes-Schiffer, Sharon

1997-07-01

This paper presents an analytical derivation of a multiconfigurational self-consistent-field (MC-SCF) solution of the time-independent Schrödinger equation for nuclear motion (i.e. vibrational modes). This variational MC-SCF method is designed for the mixed quantum/classical molecular dynamics simulation of multiple proton transfer reactions, where the transferring protons are treated quantum mechanically while the remaining degrees of freedom are treated classically. This paper presents a proof that the Hellmann-Feynman forces on the classical degrees of freedom are identical to the exact forces (i.e. the Pulay corrections vanish) when this MC-SCF method is used with an appropriate choice of basis functions. This new MC-SCF method is applied to multiple proton transfer in a protonated chain of three hydrogen-bonded water molecules. The ground state and the first three excited state energies and the ground state forces agree well with full configuration interaction calculations. Sample trajectories are obtained using adiabatic molecular dynamics methods, and nonadiabatic effects are found to be insignificant for these sample trajectories. The accuracy of the excited states will enable this MC-SCF method to be used in conjunction with nonadiabatic molecular dynamics methods. This application differs from previous work in that it is a real-time quantum dynamical nonequilibrium simulation of multiple proton transfer in a chain of water molecules.

Mission Design, Guidance, and Navigation of a Callisto-Io-Ganymede Triple Flyby Jovian Capture

NASA Astrophysics Data System (ADS)

Didion, Alan M.

Use of a triple-satellite-aided capture maneuver to enter Jovian orbit reduces insertion DeltaV and provides close flyby science opportunities at three of Jupiter's four large Galilean moons. This capture can be performed while maintaining appropriate Jupiter standoff distance and setting up a suitable apojove for plotting an extended tour. This paper has three main chapters, the first of which discusses the design and optimization of a triple-flyby capture trajectory. A novel triple-satellite-aided capture uses sequential flybys of Callisto, Io, and Ganymede to reduce the DeltaV required to capture into orbit about Jupiter. An optimal broken-plane maneuver is added between Earth and Jupiter to form a complete chemical/impulsive interplanetary trajectory from Earth to Jupiter. Such a trajectory can yield significant fuel savings over single and double-flyby capture schemes while maintaining a brief and simple interplanetary transfer phase. The second chapter focuses on the guidance and navigation of such trajectories in the presence of spacecraft navigation errors, ephemeris errors, and maneuver execution errors. A powered-flyby trajectory correction maneuver (TCM) is added to the nominal trajectory at Callisto and the nominal Jupiter orbit insertion (JOI) maneuver is modified to both complete the capture and target the Ganymede flyby. A third TCM is employed after all the flybys to act as a JOI cleanup maneuver. A Monte Carlo simulation shows that the statistical DeltaV required to correct the trajectory is quite manageable and the flyby characteristics are very consistent. The developed methods maintain flexibility for adaptation to similar launch, cruise, and capture conditions. The third chapter details the methodology and results behind a completely separate project to design and optimize an Earth-orbiting three satellite constellation to perform very long baseline interferometry (VLBI) as part of the 8th annual Global Trajectory Optimisation Competition (GTOC8). A script is designed to simulate the prescribed constellation and record its observations; the observations made are scored according to a provided performance index.

Uncertainty and dispersion in air parcel trajectories near the tropical tropopause

NASA Astrophysics Data System (ADS)

Bergman, John; Jensen, Eric; Pfister, Leonhard; Bui, Thoapaul

2016-04-01

The Tropical Tropopause Layer (TTL) is important as the gateway to the stratosphere for chemical constituents produced at the Earth's surface. As such, understanding the processes that transport air through the upper tropical troposphere is important for a number of current scientific issues such as the impact of stratospheric water vapor on the global radiative budget and the depletion of ozone by both anthropogenically- and naturally-produced halocarbons. Compared to the lower troposphere, transport in the TTL is relatively unaffected by turbulent motion. Consequently, Lagrangian particle models are thought to provide reasonable estimates of parcel pathways through the TTL. However, there are complications that make trajectory analyses difficult to interpret; uncertainty in the wind data used to drive these calculations and trajectory dispersion being among the most important. These issues are examined using ensembles of backward air parcel trajectories that are initially tightly grouped near the tropical tropopause using three approaches: A Monte Carlo ensemble, in which different members use identical resolved wind fluctuations but different realizations of stochastic, multi-fractal simulations of unresolved winds, perturbed initial location ensembles, in which members use identical resolved wind fields but initial locations are displaced 2° in latitude and longitude, and a multi-model ensemble that uses identical initial conditions but different resolved wind fields and/or trajectory formulations. Comparisons among the approaches distinguish, to some degree, physical dispersion from that due to data uncertainty and the impact of unresolved wind fluctuations from that of resolved variability.

Emergent quantum mechanics without wavefunctions

NASA Astrophysics Data System (ADS)

Mesa Pascasio, J.; Fussy, S.; Schwabl, H.; Grössing, G.

2016-03-01

We present our model of an Emergent Quantum Mechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques.

Emergence of Global Shape Processing Continues through Adolescence

ERIC Educational Resources Information Center

Scherf, K. Suzanne; Behrmann, Marlene; Kimchi, Ruth; Luna, Beatriz

2009-01-01

The developmental trajectory of perceptual organization in humans is unclear. This study investigated perceptual grouping abilities across a wide age range (8-30 years) using a classic compound letter global/local (GL) task and a more fine-grained microgenetic prime paradigm (MPP) with both few- and many-element hierarchical displays. In the GL…

Classical Trajectory Study of Collision Energy Transfer between Ne and C2H2 on a Full Dimensional Accurate Potential Energy Surface.

PubMed

Liu, Yang; Huang, Yin; Ma, Jianyi; Li, Jun

2018-02-15

Collision energy transfer plays an important role in gas phase reaction kinetics and relaxation of excited molecules. However, empirical treatments are generally adopted for the collisional energy transfer in the master equation based approach. In this work, classical trajectory approach is employed to investigate the collision energy transfer dynamics in the C 2 H 2 -Ne system. The entire potential energy surface is described as the sum of the C 2 H 2 potential and interaction potential between C 2 H 2 and Ne. It is highlighted that both parts of the entire potential are highly accurate. In particular, the interaction potential is fit to ∼41 300 configurations determined at the level of CCSD(T)-F12a/cc-pCVTZ-F12 with the counterpoise correction. Collision energy transfer dynamics are then carried out on this benchmark potential and the widely used Lennard-Jones and Buckingham interaction potentials. Energy transfers and related probability densities at different collisional energies are reported and discussed.

Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling

NASA Astrophysics Data System (ADS)

Katsiolides, Grigoris; Müller, Eike H.; Scheichl, Robert; Shardlow, Tony; Giles, Michael B.; Thomson, David J.

2018-02-01

A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations (SDEs). The computational bottleneck is the Monte Carlo algorithm, which simulates the motion of a large number of model particles in a turbulent velocity field; for each particle, a trajectory is calculated with a numerical timestepping method. Choosing an efficient numerical method is particularly important in operational emergency-response applications, such as tracking radioactive clouds from nuclear accidents or predicting the impact of volcanic ash clouds on international aviation, where accurate and timely predictions are essential. In this paper, we investigate the application of the Multilevel Monte Carlo (MLMC) method to simulate the propagation of particles in a representative one-dimensional dispersion scenario in the atmospheric boundary layer. MLMC can be shown to result in asymptotically superior computational complexity and reduced computational cost when compared to the Standard Monte Carlo (StMC) method, which is currently used in atmospheric dispersion modelling. To reduce the absolute cost of the method also in the non-asymptotic regime, it is equally important to choose the best possible numerical timestepping method on each level. To investigate this, we also compare the standard symplectic Euler method, which is used in many operational models, with two improved timestepping algorithms based on SDE splitting methods.

Examples of Complete Solvability of 2D Classical Superintegrable Systems

NASA Astrophysics Data System (ADS)

Chen, Yuxuan; Kalnins, Ernie G.; Li, Qiushi; Miller, Willard, Jr.

2015-11-01

Classical (maximal) superintegrable systems in n dimensions are Hamiltonian systems with 2n-1 independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved algebraically. In this paper we show explicitly, mostly through examples of 2nd order superintegrable systems in 2 dimensions, how the trajectories can be determined in detail using rather elementary algebraic, geometric and analytic methods applied to the closed quadratic algebra of symmetries of the system, without resorting to separation of variables techniques or trying to integrate Hamilton's equations. We treat a family of 2nd order degenerate systems: oscillator analogies on Darboux, nonzero constant curvature, and flat spaces, related to one another via contractions, and obeying Kepler's laws. Then we treat two 2nd order nondegenerate systems, an analogy of a caged Coulomb problem on the 2-sphere and its contraction to a Euclidean space caged Coulomb problem. In all cases the symmetry algebra structure provides detailed information about the trajectories, some of which are rather complicated. An interesting example is the occurrence of ''metronome orbits'', trajectories confined to an arc rather than a loop, which are indicated clearly from the structure equations but might be overlooked using more traditional methods. We also treat the Post-Winternitz system, an example of a classical 4th order superintegrable system that cannot be solved using separation of variables. Finally we treat a superintegrable system, related to the addition theorem for elliptic functions, whose constants of the motion are only rational in the momenta. It is a system of special interest because its constants of the motion generate a closed polynomial algebra. This paper contains many new results but we have tried to present most of the materials in a fashion that is easily accessible to nonexperts, in order to provide entrée to superintegrablity theory.

Anomalous Diffusion of Single Particles in Cytoplasm

PubMed Central

Regner, Benjamin M.; Vučinić, Dejan; Domnisoru, Cristina; Bartol, Thomas M.; Hetzer, Martin W.; Tartakovsky, Daniel M.; Sejnowski, Terrence J.

2013-01-01

The crowded intracellular environment poses a formidable challenge to experimental and theoretical analyses of intracellular transport mechanisms. Our measurements of single-particle trajectories in cytoplasm and their random-walk interpretations elucidate two of these mechanisms: molecular diffusion in crowded environments and cytoskeletal transport along microtubules. We employed acousto-optic deflector microscopy to map out the three-dimensional trajectories of microspheres migrating in the cytosolic fraction of a cellular extract. Classical Brownian motion (BM), continuous time random walk, and fractional BM were alternatively used to represent these trajectories. The comparison of the experimental and numerical data demonstrates that cytoskeletal transport along microtubules and diffusion in the cytosolic fraction exhibit anomalous (nonFickian) behavior and posses statistically distinct signatures. Among the three random-walk models used, continuous time random walk provides the best representation of diffusion, whereas microtubular transport is accurately modeled with fractional BM. PMID:23601312

Sequential Geoacoustic Filtering and Geoacoustic Inversion

DTIC Science & Technology

2015-09-30

and online algorithms. We show here that CS obtains higher resolution than MVDR, even in scenarios, which favor classical high-resolution methods...windows actually performs better than conventional beamforming and MVDR/ MUSIC (see Figs. 1-2). Compressive geoacoustic inversion Geoacoustic...histograms based on 100 Monte Carlo simulations, and c)(CS, exhaustive-search, CBF, MVDR, and MUSIC performance versus SNR. The true source positions

Ion-Stockmayer clusters: Minima, classical thermodynamics, and variational ground state estimates of Li{sup +}(CH{sub 3}NO{sub 2}){sub n} (n = 1–20)

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

Curotto, E., E-mail: curotto@arcadia.edu

2015-12-07

Structural optimizations, classical NVT ensemble, and variational Monte Carlo simulations of ion Stockmayer clusters parameterized to approximate the Li{sup +}(CH{sub 3}NO{sub 2}){sub n} (n = 1–20) systems are performed. The Metropolis algorithm enhanced by the parallel tempering strategy is used to measure internal energies and heat capacities, and a parallel version of the genetic algorithm is employed to obtain the most important minima. The first solvation sheath is octahedral and this feature remains the dominant theme in the structure of clusters with n ≥ 6. The first “magic number” is identified using the adiabatic solvent dissociation energy, and it marksmore » the completion of the second solvation layer for the lithium ion-nitromethane clusters. It corresponds to the n = 18 system, a solvated ion with the first sheath having octahedral symmetry, weakly bound to an eight-membered and a four-membered ring crowning a vertex of the octahedron. Variational Monte Carlo estimates of the adiabatic solvent dissociation energy reveal that quantum effects further enhance the stability of the n = 18 system relative to its neighbors.« less

Dynamically biased statistical model for the ortho/para conversion in the H2 + H3+ → H3+ + H2 reaction.

PubMed

Gómez-Carrasco, Susana; González-Sánchez, Lola; Aguado, Alfredo; Sanz-Sanz, Cristina; Zanchet, Alexandre; Roncero, Octavio

2012-09-07

In this work we present a dynamically biased statistical model to describe the evolution of the title reaction from statistical to a more direct mechanism, using quasi-classical trajectories (QCT). The method is based on the one previously proposed by Park and Light [J. Chem. Phys. 126, 044305 (2007)]. A recent global potential energy surface is used here to calculate the capture probabilities, instead of the long-range ion-induced dipole interactions. The dynamical constraints are introduced by considering a scrambling matrix which depends on energy and determine the probability of the identity/hop/exchange mechanisms. These probabilities are calculated using QCT. It is found that the high zero-point energy of the fragments is transferred to the rest of the degrees of freedom, what shortens the lifetime of H(5)(+) complexes and, as a consequence, the exchange mechanism is produced with lower proportion. The zero-point energy (ZPE) is not properly described in quasi-classical trajectory calculations and an approximation is done in which the initial ZPE of the reactants is reduced in QCT calculations to obtain a new ZPE-biased scrambling matrix. This reduction of the ZPE is explained by the need of correcting the pure classical level number of the H(5)(+) complex, as done in classical simulations of unimolecular processes and to get equivalent quantum and classical rate constants using Rice-Ramsperger-Kassel-Marcus theory. This matrix allows to obtain a ratio of hop/exchange mechanisms, α(T), in rather good agreement with recent experimental results by Crabtree et al. [J. Chem. Phys. 134, 194311 (2011)] at room temperature. At lower temperatures, however, the present simulations predict too high ratios because the biased scrambling matrix is not statistical enough. This demonstrates the importance of applying quantum methods to simulate this reaction at the low temperatures of astrophysical interest.

Dynamically biased statistical model for the ortho/para conversion in the H2+H3+ --> H3++ H2 reaction

NASA Astrophysics Data System (ADS)

Gómez-Carrasco, Susana; González-Sánchez, Lola; Aguado, Alfredo; Sanz-Sanz, Cristina; Zanchet, Alexandre; Roncero, Octavio

2012-09-01

In this work we present a dynamically biased statistical model to describe the evolution of the title reaction from statistical to a more direct mechanism, using quasi-classical trajectories (QCT). The method is based on the one previously proposed by Park and Light [J. Chem. Phys. 126, 044305 (2007), 10.1063/1.2430711]. A recent global potential energy surface is used here to calculate the capture probabilities, instead of the long-range ion-induced dipole interactions. The dynamical constraints are introduced by considering a scrambling matrix which depends on energy and determine the probability of the identity/hop/exchange mechanisms. These probabilities are calculated using QCT. It is found that the high zero-point energy of the fragments is transferred to the rest of the degrees of freedom, what shortens the lifetime of H_5^+ complexes and, as a consequence, the exchange mechanism is produced with lower proportion. The zero-point energy (ZPE) is not properly described in quasi-classical trajectory calculations and an approximation is done in which the initial ZPE of the reactants is reduced in QCT calculations to obtain a new ZPE-biased scrambling matrix. This reduction of the ZPE is explained by the need of correcting the pure classical level number of the H_5^+ complex, as done in classical simulations of unimolecular processes and to get equivalent quantum and classical rate constants using Rice-Ramsperger-Kassel-Marcus theory. This matrix allows to obtain a ratio of hop/exchange mechanisms, α(T), in rather good agreement with recent experimental results by Crabtree et al. [J. Chem. Phys. 134, 194311 (2011), 10.1063/1.3587246] at room temperature. At lower temperatures, however, the present simulations predict too high ratios because the biased scrambling matrix is not statistical enough. This demonstrates the importance of applying quantum methods to simulate this reaction at the low temperatures of astrophysical interest.

When the lowest energy does not induce native structures: parallel minimization of multi-energy values by hybridizing searching intelligences.

PubMed

Lü, Qiang; Xia, Xiao-Yan; Chen, Rong; Miao, Da-Jun; Chen, Sha-Sha; Quan, Li-Jun; Li, Hai-Ou

2012-01-01

Protein structure prediction (PSP), which is usually modeled as a computational optimization problem, remains one of the biggest challenges in computational biology. PSP encounters two difficult obstacles: the inaccurate energy function problem and the searching problem. Even if the lowest energy has been luckily found by the searching procedure, the correct protein structures are not guaranteed to obtain. A general parallel metaheuristic approach is presented to tackle the above two problems. Multi-energy functions are employed to simultaneously guide the parallel searching threads. Searching trajectories are in fact controlled by the parameters of heuristic algorithms. The parallel approach allows the parameters to be perturbed during the searching threads are running in parallel, while each thread is searching the lowest energy value determined by an individual energy function. By hybridizing the intelligences of parallel ant colonies and Monte Carlo Metropolis search, this paper demonstrates an implementation of our parallel approach for PSP. 16 classical instances were tested to show that the parallel approach is competitive for solving PSP problem. This parallel approach combines various sources of both searching intelligences and energy functions, and thus predicts protein conformations with good quality jointly determined by all the parallel searching threads and energy functions. It provides a framework to combine different searching intelligence embedded in heuristic algorithms. It also constructs a container to hybridize different not-so-accurate objective functions which are usually derived from the domain expertise.

When the Lowest Energy Does Not Induce Native Structures: Parallel Minimization of Multi-Energy Values by Hybridizing Searching Intelligences

PubMed Central

Lü, Qiang; Xia, Xiao-Yan; Chen, Rong; Miao, Da-Jun; Chen, Sha-Sha; Quan, Li-Jun; Li, Hai-Ou

2012-01-01

Background Protein structure prediction (PSP), which is usually modeled as a computational optimization problem, remains one of the biggest challenges in computational biology. PSP encounters two difficult obstacles: the inaccurate energy function problem and the searching problem. Even if the lowest energy has been luckily found by the searching procedure, the correct protein structures are not guaranteed to obtain. Results A general parallel metaheuristic approach is presented to tackle the above two problems. Multi-energy functions are employed to simultaneously guide the parallel searching threads. Searching trajectories are in fact controlled by the parameters of heuristic algorithms. The parallel approach allows the parameters to be perturbed during the searching threads are running in parallel, while each thread is searching the lowest energy value determined by an individual energy function. By hybridizing the intelligences of parallel ant colonies and Monte Carlo Metropolis search, this paper demonstrates an implementation of our parallel approach for PSP. 16 classical instances were tested to show that the parallel approach is competitive for solving PSP problem. Conclusions This parallel approach combines various sources of both searching intelligences and energy functions, and thus predicts protein conformations with good quality jointly determined by all the parallel searching threads and energy functions. It provides a framework to combine different searching intelligence embedded in heuristic algorithms. It also constructs a container to hybridize different not-so-accurate objective functions which are usually derived from the domain expertise. PMID:23028708

Dual levitated coils for antihydrogen production

NASA Astrophysics Data System (ADS)

Wofford, J. D.; Ordonez, C. A.

2013-04-01

Two coaxial superconducting magnetic coils that carry currents in the same direction and that are simultaneously levitated may serve for antihydrogen plasma confinement. The configuration may be suitable for use by a collaboration at the CERN Antiproton Decelerator facility to test fundamental symmetries between the properties of hydrogen and antihydrogen. Nested Penning traps are currently used to confine recombining antihydrogen plasma. Symmetry studies require the production of sufficiently cold antihydrogen. However, plasma drifts within nested Penning traps can increase the kinetic energy of antiprotons that form antihydrogen atoms. Dual levitated coils may serve to confine relatively large, cold, dense non-drifting recombining antihydrogen plasmas. A minimum-B magnetic field that is produced by the coils could provide for atom trapping. A toroidal plasma is confined between the coils. High density plasmas may be possible, by allowing plasma pressure to balance mechanical pressure to keep the coils apart. Progress is reported on theoretical and experimental efforts. The theoretical effort includes the development of a classical trajectory Monte Carlo simulation of confinement. The experimental effort includes levitation of a NdFeB permanent ring magnet, which produces a magnetic field that is qualitatively similar to the field that would be produced by the two coaxial superconducting magnetic coils. Liquid-nitrogen-cooled Bi-2223 high-temperature-superconducting components, with a critical temperature of 108 K, were used to levitate the ring magnet. An issue concerning keeping the plane of the levitated ring horizontal is discussed.

Subtle Monte Carlo Updates in Dense Molecular Systems.

PubMed

Bottaro, Sandro; Boomsma, Wouter; E Johansson, Kristoffer; Andreetta, Christian; Hamelryck, Thomas; Ferkinghoff-Borg, Jesper

2012-02-14

Although Markov chain Monte Carlo (MC) simulation is a potentially powerful approach for exploring conformational space, it has been unable to compete with molecular dynamics (MD) in the analysis of high density structural states, such as the native state of globular proteins. Here, we introduce a kinetic algorithm, CRISP, that greatly enhances the sampling efficiency in all-atom MC simulations of dense systems. The algorithm is based on an exact analytical solution to the classic chain-closure problem, making it possible to express the interdependencies among degrees of freedom in the molecule as correlations in a multivariate Gaussian distribution. We demonstrate that our method reproduces structural variation in proteins with greater efficiency than current state-of-the-art Monte Carlo methods and has real-time simulation performance on par with molecular dynamics simulations. The presented results suggest our method as a valuable tool in the study of molecules in atomic detail, offering a potential alternative to molecular dynamics for probing long time-scale conformational transitions.

OWL: A scalable Monte Carlo simulation suite for finite-temperature study of materials

NASA Astrophysics Data System (ADS)

Li, Ying Wai; Yuk, Simuck F.; Cooper, Valentino R.; Eisenbach, Markus; Odbadrakh, Khorgolkhuu

The OWL suite is a simulation package for performing large-scale Monte Carlo simulations. Its object-oriented, modular design enables it to interface with various external packages for energy evaluations. It is therefore applicable to study the finite-temperature properties for a wide range of systems: from simple classical spin models to materials where the energy is evaluated by ab initio methods. This scheme not only allows for the study of thermodynamic properties based on first-principles statistical mechanics, it also provides a means for massive, multi-level parallelism to fully exploit the capacity of modern heterogeneous computer architectures. We will demonstrate how improved strong and weak scaling is achieved by employing novel, parallel and scalable Monte Carlo algorithms, as well as the applications of OWL to a few selected frontier materials research problems. This research was supported by the Office of Science of the Department of Energy under contract DE-AC05-00OR22725.

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.

A walk through the approximations of ab initio multiple spawning

NASA Astrophysics Data System (ADS)

Mignolet, Benoit; Curchod, Basile F. E.

2018-04-01

Full multiple spawning offers an in principle exact framework for excited-state dynamics, where nuclear wavefunctions in different electronic states are represented by a set of coupled trajectory basis functions that follow classical trajectories. The couplings between trajectory basis functions can be approximated to treat molecular systems, leading to the ab initio multiple spawning method which has been successfully employed to study the photochemistry and photophysics of several molecules. However, a detailed investigation of its approximations and their consequences is currently missing in the literature. In this work, we simulate the explicit photoexcitation and subsequent excited-state dynamics of a simple system, LiH, and we analyze (i) the effect of the ab initio multiple spawning approximations on different observables and (ii) the convergence of the ab initio multiple spawning results towards numerically exact quantum dynamics upon a progressive relaxation of these approximations. We show that, despite the crude character of the approximations underlying ab initio multiple spawning for this low-dimensional system, the qualitative excited-state dynamics is adequately captured, and affordable corrections can further be applied to ameliorate the coupling between trajectory basis functions.

The control of electron quantum trajectories on the high-order harmonic generation of CO and N2 molecules in the presence of a low frequency field.

PubMed

Koushki, A M; Sadighi-Bonabi, R; Mohsen-Nia, M; Irani, E

2018-04-14

In the present work, an efficient method is theoretically investigated for extending high-order harmonics and ultrashort attosecond pulse generation in N 2 and CO molecules by using the time-dependent density functional theory approach. Our results show that by utilizing chirped laser field in the presence of a low frequency field, not only is the harmonic cutoff extended remarkably but also the single short quantum trajectory is selected to contribute to the harmonic spectra. When a low frequency field is added to the two-color chirped laser field, the long quantum trajectories are suppressed and only the short quantum trajectories contribute to the higher harmonic emission mechanism. As a result, the spectral modulation is significantly decreased and an intense ultrashort pulse can be generated from the supercontinuum region of high harmonics. With such a scheme, the isolated ultrashort attosecond pulses can be generated in length, velocity, and acceleration gauges. Furthermore, these results are explained by using the classical and quantum time-frequency analyses.

The control of electron quantum trajectories on the high-order harmonic generation of CO and N2 molecules in the presence of a low frequency field

NASA Astrophysics Data System (ADS)

Koushki, A. M.; Sadighi-Bonabi, R.; Mohsen-Nia, M.; Irani, E.

2018-04-01

In the present work, an efficient method is theoretically investigated for extending high-order harmonics and ultrashort attosecond pulse generation in N2 and CO molecules by using the time-dependent density functional theory approach. Our results show that by utilizing chirped laser field in the presence of a low frequency field, not only is the harmonic cutoff extended remarkably but also the single short quantum trajectory is selected to contribute to the harmonic spectra. When a low frequency field is added to the two-color chirped laser field, the long quantum trajectories are suppressed and only the short quantum trajectories contribute to the higher harmonic emission mechanism. As a result, the spectral modulation is significantly decreased and an intense ultrashort pulse can be generated from the supercontinuum region of high harmonics. With such a scheme, the isolated ultrashort attosecond pulses can be generated in length, velocity, and acceleration gauges. Furthermore, these results are explained by using the classical and quantum time-frequency analyses.

Non-statistical effects in bond fission reactions of 1,2-difluoroethane

NASA Astrophysics Data System (ADS)

Schranz, Harold W.; Raff, Lionel M.; Thompson, Donald L.

1991-08-01

A microcanonical, classical variational transition-state theory based on the use of the efficient microcanonical sampling (EMS) procedure is applied to simple bond fission in 1,2-difluoroethane. Comparison is made with results of trajectory calculations performed on the same global potential-energy surface. Agreement between the statistical theory and trajectory results for CC CF and CH bond fissions is poor with differences as large as a factor of 125. Most importantly, at the lower energy studied, 6.0 eV, the statistical calculations predict considerably slower rates than those computed from trajectories. We conclude from these results that the statistical assumptions inherent in the transition-state theory method are not valid for 1,2-difluoroethane in spite of the fact that the total intramolecular energy transfer rate out of CH and CC normal and local modes is large relative to the bond fission rates. The IVR rate is not globally rapid and the trajectories do not access all of the energetically available phase space uniformly on the timescale of the reactions.

A walk through the approximations of ab initio multiple spawning.

PubMed

Mignolet, Benoit; Curchod, Basile F E

2018-04-07

Full multiple spawning offers an in principle exact framework for excited-state dynamics, where nuclear wavefunctions in different electronic states are represented by a set of coupled trajectory basis functions that follow classical trajectories. The couplings between trajectory basis functions can be approximated to treat molecular systems, leading to the ab initio multiple spawning method which has been successfully employed to study the photochemistry and photophysics of several molecules. However, a detailed investigation of its approximations and their consequences is currently missing in the literature. In this work, we simulate the explicit photoexcitation and subsequent excited-state dynamics of a simple system, LiH, and we analyze (i) the effect of the ab initio multiple spawning approximations on different observables and (ii) the convergence of the ab initio multiple spawning results towards numerically exact quantum dynamics upon a progressive relaxation of these approximations. We show that, despite the crude character of the approximations underlying ab initio multiple spawning for this low-dimensional system, the qualitative excited-state dynamics is adequately captured, and affordable corrections can further be applied to ameliorate the coupling between trajectory basis functions.

Improving multivariate Horner schemes with Monte Carlo tree search

NASA Astrophysics Data System (ADS)

Kuipers, J.; Plaat, A.; Vermaseren, J. A. M.; van den Herik, H. J.

2013-11-01

Optimizing the cost of evaluating a polynomial is a classic problem in computer science. For polynomials in one variable, Horner's method provides a scheme for producing a computationally efficient form. For multivariate polynomials it is possible to generalize Horner's method, but this leaves freedom in the order of the variables. Traditionally, greedy schemes like most-occurring variable first are used. This simple textbook algorithm has given remarkably efficient results. Finding better algorithms has proved difficult. In trying to improve upon the greedy scheme we have implemented Monte Carlo tree search, a recent search method from the field of artificial intelligence. This results in better Horner schemes and reduces the cost of evaluating polynomials, sometimes by factors up to two.

A GPU-based large-scale Monte Carlo simulation method for systems with long-range interactions

NASA Astrophysics Data System (ADS)

Liang, Yihao; Xing, Xiangjun; Li, Yaohang

2017-06-01

In this work we present an efficient implementation of Canonical Monte Carlo simulation for Coulomb many body systems on graphics processing units (GPU). Our method takes advantage of the GPU Single Instruction, Multiple Data (SIMD) architectures, and adopts the sequential updating scheme of Metropolis algorithm. It makes no approximation in the computation of energy, and reaches a remarkable 440-fold speedup, compared with the serial implementation on CPU. We further use this method to simulate primitive model electrolytes, and measure very precisely all ion-ion pair correlation functions at high concentrations. From these data, we extract the renormalized Debye length, renormalized valences of constituent ions, and renormalized dielectric constants. These results demonstrate unequivocally physics beyond the classical Poisson-Boltzmann theory.

"Roll of Thunder, Hear My Cry": A Culturally Specific, Subversive Concept of Child Agency.

ERIC Educational Resources Information Center

McDowell, Kelly

2002-01-01

Presents a critique of Mildred D. Taylor's "Roll of Thunder, Hear My Cry" with regard to its positioning of the child subject. Proposes that the novel contrasts classic works of children's fiction by following a trajectory of child agency, which is enabled through the novel's racial specificity. Discusses the role of historical…

Effect Sizes for Growth-Modeling Analysis for Controlled Clinical Trials in the Same Metric as for Classical Analysis

ERIC Educational Resources Information Center

Feingold, Alan

2009-01-01

The use of growth-modeling analysis (GMA)--including hierarchical linear models, latent growth models, and general estimating equations--to evaluate interventions in psychology, psychiatry, and prevention science has grown rapidly over the last decade. However, an effect size associated with the difference between the trajectories of the…

4D BADA-based Trajectory Generator and 3D Guidance Algorithm

NASA Technical Reports Server (NTRS)

Palacios, Eduardo Sepulveda; Johnson, Marcus A.

2013-01-01

This paper presents a hybrid integration between aerodynamic, airline procedures and other BADA-based (Base of Aircraft Data) coefficients with a classical aircraft dynamic model. This paper also describes a three-dimensional guidance algorithm implemented in order to produce commands for the aircraft to follow a flight plan. The software chosen for this work is MATLAB.

A Classical Trajectory Study of the Dissociation and Isomerization of C2H5

DTIC Science & Technology

2013-01-01

modifications are possible but would be sensible only in the context of systematic ab initio calculations to provide the basis for such changes. As the... Ciudad , T.; Ramírez, R.; Schulte, J.; Böhm, M. C. Anharmonic Effects on the Structural and Vibrational Properties of the Ethyl Radical: A Path Integral

Functional Nonlinear Mixed Effects Models For Longitudinal Image Data

PubMed Central

Luo, Xinchao; Zhu, Lixing; Kong, Linglong; Zhu, Hongtu

2015-01-01

Motivated by studying large-scale longitudinal image data, we propose a novel functional nonlinear mixed effects modeling (FN-MEM) framework to model the nonlinear spatial-temporal growth patterns of brain structure and function and their association with covariates of interest (e.g., time or diagnostic status). Our FNMEM explicitly quantifies a random nonlinear association map of individual trajectories. We develop an efficient estimation method to estimate the nonlinear growth function and the covariance operator of the spatial-temporal process. We propose a global test and a simultaneous confidence band for some specific growth patterns. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We apply FNMEM to investigate the spatial-temporal dynamics of white-matter fiber skeletons in a national database for autism research. Our FNMEM may provide a valuable tool for charting the developmental trajectories of various neuropsychiatric and neurodegenerative disorders. PMID:26213453

Crew Exploration Vehicle Launch Abort Controller Performance Analysis

NASA Technical Reports Server (NTRS)

Sparks, Dean W., Jr.; Raney, David L.

2007-01-01

This paper covers the simulation and evaluation of a controller design for the Crew Module (CM) Launch Abort System (LAS), to measure its ability to meet the abort performance requirements. The controller used in this study is a hybrid design, including features developed by the Government and the Contractor. Testing is done using two separate 6-degree-of-freedom (DOF) computer simulation implementations of the LAS/CM throughout the ascent trajectory: 1) executing a series of abort simulations along a nominal trajectory for the nominal LAS/CM system; and 2) using a series of Monte Carlo runs with perturbed initial flight conditions and perturbed system parameters. The performance of the controller is evaluated against a set of criteria, which is based upon the current functional requirements of the LAS. Preliminary analysis indicates that the performance of the present controller meets (with the exception of a few cases) the evaluation criteria mentioned above.

Uniform quantized electron gas

NASA Astrophysics Data System (ADS)

Høye, Johan S.; Lomba, Enrique

2016-10-01

In this work we study the correlation energy of the quantized electron gas of uniform density at temperature T  =  0. To do so we utilize methods from classical statistical mechanics. The basis for this is the Feynman path integral for the partition function of quantized systems. With this representation the quantum mechanical problem can be interpreted as, and is equivalent to, a classical polymer problem in four dimensions where the fourth dimension is imaginary time. Thus methods, results, and properties obtained in the statistical mechanics of classical fluids can be utilized. From this viewpoint we recover the well known RPA (random phase approximation). Then to improve it we modify the RPA by requiring the corresponding correlation function to be such that electrons with equal spins can not be on the same position. Numerical evaluations are compared with well known results of a standard parameterization of Monte Carlo correlation energies.

Routing the asteroid surface vehicle with detailed mechanics

NASA Astrophysics Data System (ADS)

Yu, Yang; Baoyin, He-Xi

2014-06-01

The motion of a surface vehicle on/above an irregular object is investigated for a potential interest in the insitu explorations to asteroids of the solar system. A global valid numeric method, including detailed gravity and geomorphology, is developed to mimic the behaviors of the test particles governed by the orbital equations and surface coupling effects. A general discussion on the surface mechanical environment of a specified asteroid, 1620 Geographos, is presented to make a global evaluation of the surface vehicle's working conditions. We show the connections between the natural trajectories near the ground and differential features of the asteroid surface, which describes both the good and bad of typical terrains from the viewpoint of vehicles' dynamic performances. Monte Carlo simulations are performed to take a further look at the trajectories of particles initializing near the surface. The simulations reveal consistent conclusions with the analysis, i.e., the open-field flat ground and slightly concave basins/valleys are the best choices for the vehicles' dynamical security. The dependence of decending trajectories on the releasing height is studied as an application; the results show that the pole direction (where the centrifugal force is zero) is the most stable direction in which the shift of a natural trajectory will be well limited after landing. We present this work as an example for pre-analysis that provides guidance to engineering design of the exploration site and routing the surface vehicles.

Minimized state complexity of quantum-encoded cryptic processes

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Mahoney, John R.; Aghamohammadi, Cina; Crutchfield, James P.

2016-05-01

The predictive information required for proper trajectory sampling of a stochastic process can be more efficiently transmitted via a quantum channel than a classical one. This recent discovery allows quantum information processing to drastically reduce the memory necessary to simulate complex classical stochastic processes. It also points to a new perspective on the intrinsic complexity that nature must employ in generating the processes we observe. The quantum advantage increases with codeword length: the length of process sequences used in constructing the quantum communication scheme. In analogy with the classical complexity measure, statistical complexity, we use this reduced communication cost as an entropic measure of state complexity in the quantum representation. Previously difficult to compute, the quantum advantage is expressed here in closed form using spectral decomposition. This allows for efficient numerical computation of the quantum-reduced state complexity at all encoding lengths, including infinite. Additionally, it makes clear how finite-codeword reduction in state complexity is controlled by the classical process's cryptic order, and it allows asymptotic analysis of infinite-cryptic-order processes.

Mixed quantum-classical simulations of the vibrational relaxation of photolyzed carbon monoxide in a hemoprotein

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

Schubert, Alexander, E-mail: schubert@irsamc.ups-tlse.fr; Meier, Christoph; Falvo, Cyril

2016-08-07

We present mixed quantum-classical simulations on relaxation and dephasing of vibrationally excited carbon monoxide within a protein environment. The methodology is based on a vibrational surface hopping approach treating the vibrational states of CO quantum mechanically, while all remaining degrees of freedom are described by means of classical molecular dynamics. The CO vibrational states form the “surfaces” for the classical trajectories of protein and solvent atoms. In return, environmentally induced non-adiabatic couplings between these states cause transitions describing the vibrational relaxation from first principles. The molecular dynamics simulation yields a detailed atomistic picture of the energy relaxation pathways, taking themore » molecular structure and dynamics of the protein and its solvent fully into account. Using the ultrafast photolysis of CO in the hemoprotein FixL as an example, we study the relaxation of vibrationally excited CO and evaluate the role of each of the FixL residues forming the heme pocket.« less

The development, validation and application of a multi-detector CT (MDCT) scanner model for assessing organ doses to the pregnant patient and the fetus using Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Gu, J.; Bednarz, B.; Caracappa, P. F.; Xu, X. G.

2009-05-01

The latest multiple-detector technologies have further increased the popularity of x-ray CT as a diagnostic imaging modality. There is a continuing need to assess the potential radiation risk associated with such rapidly evolving multi-detector CT (MDCT) modalities and scanning protocols. This need can be met by the use of CT source models that are integrated with patient computational phantoms for organ dose calculations. Based on this purpose, this work developed and validated an MDCT scanner using the Monte Carlo method, and meanwhile the pregnant patient phantoms were integrated into the MDCT scanner model for assessment of the dose to the fetus as well as doses to the organs or tissues of the pregnant patient phantom. A Monte Carlo code, MCNPX, was used to simulate the x-ray source including the energy spectrum, filter and scan trajectory. Detailed CT scanner components were specified using an iterative trial-and-error procedure for a GE LightSpeed CT scanner. The scanner model was validated by comparing simulated results against measured CTDI values and dose profiles reported in the literature. The source movement along the helical trajectory was simulated using the pitch of 0.9375 and 1.375, respectively. The validated scanner model was then integrated with phantoms of a pregnant patient in three different gestational periods to calculate organ doses. It was found that the dose to the fetus of the 3 month pregnant patient phantom was 0.13 mGy/100 mAs and 0.57 mGy/100 mAs from the chest and kidney scan, respectively. For the chest scan of the 6 month patient phantom and the 9 month patient phantom, the fetal doses were 0.21 mGy/100 mAs and 0.26 mGy/100 mAs, respectively. The paper also discusses how these fetal dose values can be used to evaluate imaging procedures and to assess risk using recommendations of the report from AAPM Task Group 36. This work demonstrates the ability of modeling and validating an MDCT scanner by the Monte Carlo method, as well as assessing fetal and organ doses by combining the MDCT scanner model and the pregnant patient phantom.

Performance of quantum annealing on random Ising problems implemented using the D-Wave Two

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Job, Joshua; Rønnow, Troels F.; Troyer, Matthias; Lidar, Daniel A.; USC Collaboration; ETH Collaboration

2014-03-01

Detecting a possible speedup of quantum annealing compared to classical algorithms is a pressing task in experimental adiabatic quantum computing. In this talk, we discuss the performance of the D-Wave Two quantum annealing device on Ising spin glass problems. The expected time to solution for the device to solve random instances with up to 503 spins and with specified coupling ranges is evaluated while carefully addressing the issue of statistical errors. We perform a systematic comparison of the expected time to solution between the D-Wave Two and classical stochastic solvers, specifically simulated annealing, and simulated quantum annealing based on quantum Monte Carlo, and discuss the question of speedup.

The uniform quantized electron gas revisited

NASA Astrophysics Data System (ADS)

Lomba, Enrique; Høye, Johan S.

2017-11-01

In this article we continue and extend our recent work on the correlation energy of the quantized electron gas of uniform density at temperature T=0 . As before, we utilize the methods, properties, and results obtained by means of classical statistical mechanics. These were extended to quantized systems via the Feynman path integral formalism. The latter translates the quantum problem into a classical polymer problem in four dimensions. Again, the well known RPA (random phase approximation) is recovered as a basic result which we then modify and improve upon. Here we analyze the condition of thermodynamic self-consistency. Our numerical calculations exhibit a remarkable agreement with well known results of a standard parameterization of Monte Carlo correlation energies.

Communication: Classical threshold law for ion-neutral-neutral three-body recombination

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

Pérez-Ríos, Jesús; Greene, Chris H.

2015-07-28

A very recently method for classical trajectory calculations for three-body collision [Pérez-Ríos et al., J. Chem. Phys. 140, 044307 (2014)] has been applied to describe ion-neutral-neutral ternary processes for low energy collisions: 0.1 mK–10 mK. As a result, a threshold law for the three-body recombination cross section is obtained and corroborated numerically. The derived threshold law predicts the formation of weakly bound dimers, with binding energies comparable to the collision energy of the collisional partners. In this low energy range, this analysis predicts that molecular ions should dominate over molecular neutrals as the most products formed.

Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential

NASA Astrophysics Data System (ADS)

Hussin, Véronique; Marquette, Ian

2011-03-01

We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In particular, we apply these results to the infinite well and Morse potentials. We discuss how the degeneracies of the permutation symmetry of quantum two-dimensional systems can be explained using products of ladder operators. These products satisfy interesting commutation relations. The two-dimensional Morse quantum system is also related to a generalized two-dimensional Morse supersymmetric model. Arithmetical or accidental degeneracies of such system are shown to be associated to additional supersymmetry.

Cherry-picking functionally relevant substates from long md trajectories using a stratified sampling approach.

PubMed

Chandramouli, Balasubramanian; Mancini, Giordano

2016-01-01

Classical Molecular Dynamics (MD) simulations can provide insights at the nanoscopic scale into protein dynamics. Currently, simulations of large proteins and complexes can be routinely carried out in the ns-μs time regime. Clustering of MD trajectories is often performed to identify selective conformations and to compare simulation and experimental data coming from different sources on closely related systems. However, clustering techniques are usually applied without a careful validation of results and benchmark studies involving the application of different algorithms to MD data often deal with relatively small peptides instead of average or large proteins; finally clustering is often applied as a means to analyze refined data and also as a way to simplify further analysis of trajectories. Herein, we propose a strategy to classify MD data while carefully benchmarking the performance of clustering algorithms and internal validation criteria for such methods. We demonstrate the method on two showcase systems with different features, and compare the classification of trajectories in real and PCA space. We posit that the prototype procedure adopted here could be highly fruitful in clustering large trajectories of multiple systems or that resulting especially from enhanced sampling techniques like replica exchange simulations. Copyright: © 2016 by Fabrizio Serra editore, Pisa · Roma.

The Wigner distribution and 2D classical maps

NASA Astrophysics Data System (ADS)

Sakhr, Jamal

2017-07-01

The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a novel connection between the Wigner distribution and 2D classical mechanics is introduced. Based on a well-known correspondence between the Wigner distribution and the 2D Poisson point process, the hypothesis that typical pseudo-trajectories of a 2D ergodic map have a Wignerian nearest-neighbor spacing distribution (NNSD) is put forward and numerically tested. The standard Euclidean metric is used to compute the interpoint spacings. In all test cases, the hypothesis is upheld, and the range of validity of the hypothesis appears to be robust in the sense that it is not affected by the presence or absence of: (i) mixing; (ii) time-reversal symmetry; and/or (iii) dissipation.

Atomic Scale Imaging of Nucleation and Growth Trajectories of an Interfacial Bismuth Nanodroplet.

PubMed

Li, Yingxuan; Bunes, Benjamin R; Zang, Ling; Zhao, Jie; Li, Yan; Zhu, Yunqing; Wang, Chuanyi

2016-02-23

Because of the lack of experimental evidence, much confusion still exists on the nucleation and growth dynamics of a nanostructure, particularly of metal. The situation is even worse for nanodroplets because it is more difficult to induce the formation of a nanodroplet while imaging the dynamic process with atomic resolution. Here, taking advantage of an electron beam to induce the growth of Bi nanodroplets on a SrBi2Ta2O9 platelet under a high resolution transmission electron microscope (HRTEM), we directly observed the detailed growth pathways of Bi nanodroplets from the earliest stage of nucleation that were previously inaccessible. Atomic scale imaging reveals that the dynamics of nucleation involves a much more complex trajectory than previously predicted based on classical nucleation theory (CNT). The monatomic Bi layer was first formed in the nucleation process, which induced the formation of the prenucleated clusters. Following that, critical nuclei for the nanodroplets formed both directly from the addition of atoms to the prenucleated clusters by the classical growth process and indirectly through transformation of an intermediate liquid film based on the Stranski-Krastanov growth mode, in which the liquid film was induced by the self-assembly of the prenucleated clusters. Finally, the growth of the Bi nanodroplets advanced through the classical pathway and sudden droplet coalescence. This study allows us to visualize the critical steps in the nucleation process of an interfacial nanodroplet, which suggests a revision of the perspective of CNT.

Characteristic coupling time between axial and transverse energy modes for anti-hydrogen in magnetostatic traps

NASA Astrophysics Data System (ADS)

Zhong, Mike; Fajans, Joel

2016-10-01

For upcoming ALPHA collaboration laser spectroscopy and gravity experiments, the nature of the chaotic trajectories of individual antihydrogen atoms trapped in the octupole Ioffe magnetic trap is of importance. Of particular interest for experimental design is the coupling time between the axial and transverse modes of energy for the antihydrogen atoms. Using Monte Carlo simulations of semiclassical dynamics of antihydrogen trajectories, we quantify this characteristic coupling time between axial and transverse modes of energy. There appear to be two classes of trajectories: for orbits whose axial energy is higher than 10% of the total energy, the axial energy varies chaotically on the order of 1-10 seconds, whereas for orbits whose axial energy is around 10% of the total energy, the axial energy remains nearly constant on the order of 1000 seconds or longer. Furthermore, we search through parameter -space to find parameters of the magnetic trap that minimize and maximize this characteristic coupling time. This work was supported by the UC Berkeley Summer Undergraduate Research Fellowship, the Berkeley Research Computing program, the Department of Energy contract DE-FG02-06ER54904, and the National Science Foundation Grant 1500538-PHY.

Fluid-driven fracture propagation in heterogeneous media: Probability distributions of fracture trajectories

NASA Astrophysics Data System (ADS)

Santillán, David; Mosquera, Juan-Carlos; Cueto-Felgueroso, Luis

2017-11-01

Hydraulic fracture trajectories in rocks and other materials are highly affected by spatial heterogeneity in their mechanical properties. Understanding the complexity and structure of fluid-driven fractures and their deviation from the predictions of homogenized theories is a practical problem in engineering and geoscience. We conduct a Monte Carlo simulation study to characterize the influence of heterogeneous mechanical properties on the trajectories of hydraulic fractures propagating in elastic media. We generate a large number of random fields of mechanical properties and simulate pressure-driven fracture propagation using a phase-field model. We model the mechanical response of the material as that of an elastic isotropic material with heterogeneous Young modulus and Griffith energy release rate, assuming that fractures propagate in the toughness-dominated regime. Our study shows that the variance and the spatial covariance of the mechanical properties are controlling factors in the tortuousness of the fracture paths. We characterize the deviation of fracture paths from the homogenous case statistically, and conclude that the maximum deviation grows linearly with the distance from the injection point. Additionally, fracture path deviations seem to be normally distributed, suggesting that fracture propagation in the toughness-dominated regime may be described as a random walk.

Extracting Lane Geometry and Topology Information from Vehicle Fleet Trajectories in Complex Urban Scenarios Using a Reversible Jump Mcmc Method

NASA Astrophysics Data System (ADS)

Roeth, O.; Zaum, D.; Brenner, C.

2017-05-01

Highly automated driving (HAD) requires maps not only of high spatial precision but also of yet unprecedented actuality. Traditionally small highly specialized fleets of measurement vehicles are used to generate such maps. Nevertheless, for achieving city-wide or even nation-wide coverage, automated map update mechanisms based on very large vehicle fleet data gain importance since highly frequent measurements are only to be obtained using such an approach. Furthermore, the processing of imprecise mass data in contrast to few dedicated highly accurate measurements calls for a high degree of automation. We present a method for the generation of lane-accurate road network maps from vehicle trajectory data (GPS or better). Our approach therefore allows for exploiting today's connected vehicle fleets for the generation of HAD maps. The presented algorithm is based on elementary building blocks which guarantees useful lane models and uses a Reversible Jump Markov chain Monte Carlo method to explore the models parameters in order to reconstruct the one most likely emitting the input data. The approach is applied to a challenging urban real-world scenario of different trajectory accuracy levels and is evaluated against a LIDAR-based ground truth map.

Ares I-X Separation and Reentry Trajectory Analyses

NASA Technical Reports Server (NTRS)

Tartabini, Paul V.; Starr, Brett R.

2011-01-01

The Ares I-X Flight Test Vehicle was launched on October 28, 2009 and was the first and only test flight of NASA s two-stage Ares I launch vehicle design. The launch was successful and the flight test met all of its primary and secondary objectives. This paper discusses the stage separation and reentry trajectory analysis that was performed in support of the Ares I-X test flight. Pre-flight analyses were conducted to assess the risk of stage recontact during separation, to evaluate the first stage flight dynamics during reentry, and to define the range safety impact ellipses of both stages. The results of these pre-flight analyses were compared with available flight data. On-board video taken during flight showed that the flight test vehicle successfully separated without any recontact. Reconstructed trajectory data also showed that first stage flight dynamics were well characterized by pre-flight Monte Carlo results. In addition, comparisons with flight data indicated that the complex interference aerodynamic models employed in the reentry simulation were effective in capturing the flight dynamics during separation. Finally, the splash-down locations of both stages were well within predicted impact ellipses.

Fluid-driven fracture propagation in heterogeneous media: Probability distributions of fracture trajectories.

PubMed

Santillán, David; Mosquera, Juan-Carlos; Cueto-Felgueroso, Luis

2017-11-01

Hydraulic fracture trajectories in rocks and other materials are highly affected by spatial heterogeneity in their mechanical properties. Understanding the complexity and structure of fluid-driven fractures and their deviation from the predictions of homogenized theories is a practical problem in engineering and geoscience. We conduct a Monte Carlo simulation study to characterize the influence of heterogeneous mechanical properties on the trajectories of hydraulic fractures propagating in elastic media. We generate a large number of random fields of mechanical properties and simulate pressure-driven fracture propagation using a phase-field model. We model the mechanical response of the material as that of an elastic isotropic material with heterogeneous Young modulus and Griffith energy release rate, assuming that fractures propagate in the toughness-dominated regime. Our study shows that the variance and the spatial covariance of the mechanical properties are controlling factors in the tortuousness of the fracture paths. We characterize the deviation of fracture paths from the homogenous case statistically, and conclude that the maximum deviation grows linearly with the distance from the injection point. Additionally, fracture path deviations seem to be normally distributed, suggesting that fracture propagation in the toughness-dominated regime may be described as a random walk.

Automatic variance reduction for Monte Carlo simulations via the local importance function transform

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

Turner, S.A.

1996-02-01

The author derives a transformed transport problem that can be solved theoretically by analog Monte Carlo with zero variance. However, the Monte Carlo simulation of this transformed problem cannot be implemented in practice, so he develops a method for approximating it. The approximation to the zero variance method consists of replacing the continuous adjoint transport solution in the transformed transport problem by a piecewise continuous approximation containing local biasing parameters obtained from a deterministic calculation. He uses the transport and collision processes of the transformed problem to bias distance-to-collision and selection of post-collision energy groups and trajectories in a traditionalmore » Monte Carlo simulation of ``real`` particles. He refers to the resulting variance reduction method as the Local Importance Function Transform (LIFI) method. He demonstrates the efficiency of the LIFT method for several 3-D, linearly anisotropic scattering, one-group, and multigroup problems. In these problems the LIFT method is shown to be more efficient than the AVATAR scheme, which is one of the best variance reduction techniques currently available in a state-of-the-art Monte Carlo code. For most of the problems considered, the LIFT method produces higher figures of merit than AVATAR, even when the LIFT method is used as a ``black box``. There are some problems that cause trouble for most variance reduction techniques, and the LIFT method is no exception. For example, the author demonstrates that problems with voids, or low density regions, can cause a reduction in the efficiency of the LIFT method. However, the LIFT method still performs better than survival biasing and AVATAR in these difficult cases.« less

Historic disturbance regimes promote tree diversity only under low browsing regimes in eastern deciduous forest

Treesearch

Tim Nuttle; Alejandro A. Royo; Mary Beth Adams; Walter P. Carson

2013-01-01

Eastern deciduous forests are changing in species composition and diversity outside of classical successional trajectories. Three disturbance mechanisms appear central to this phenomenon: fire frequency is reduced, canopy gaps are smaller, and browsers are more abundant. Which factor is most responsible is a matter of great debate and remains unclear, at least partly...

Comparison of 3D Classical Trajectory and Transition-State Theory Reaction Cross Sections

DOE R&D Accomplishments Database

Koeppl, G. W.; Karplus, Martin

1970-10-01

Although there is excellent agreement for a system such as H+H{sub 2} --> H{sub 2}+H, in which both the potential and the particle masses are symmetric, significant deviations occur for more asymmetric reactions. A detailed analysis show that the calculated differences are from the violation of two assumptions of transition-state theory.

Lie-algebraic Approach to Dynamics of Closed Quantum Systems and Quantum-to-Classical Correspondence

NASA Astrophysics Data System (ADS)

Galitski, Victor

2012-02-01

I will briefly review our recent work on a Lie-algebraic approach to various non-equilibrium quantum-mechanical problems, which has been motivated by continuous experimental advances in the field of cold atoms. First, I will discuss non-equilibrium driven dynamics of a generic closed quantum system. It will be emphasized that mathematically a non-equilibrium Hamiltonian represents a trajectory in a Lie algebra, while the evolution operator is a trajectory in a Lie group generated by the underlying algebra via exponentiation. This turns out to be a constructive statement that establishes, in particular, the fact that classical and quantum unitary evolutions are two sides of the same coin determined uniquely by the same dynamic generators in the group. An equation for these generators - dubbed dual Schr"odinger-Bloch equation - will be derived and analyzed for a few of specific examples. This non-linear equation allows one to construct new exact non-linear solutions to quantum-dynamical systems. An experimentally-relevant example of a family of exact solutions to the many-body Landau-Zener problem will be presented. One practical application of the latter result includes dynamical means to optimize molecular production rate following a quench across the Feshbach resonance.

Effects of Solute Concentrations on Kinetic Pathways in Ni-Al-Cr Alloys

NASA Technical Reports Server (NTRS)

Booth-Morrison, Christopher; Weninger, Jessica; Sudbrack, Chantal K.; Mao, Zugang; Seidman, David N.; Noebe, Ronald D.

2008-01-01

The kinetic pathways resulting from the formation of coherent gamma'-precipitates from the gamma-matrix are studied for two Ni-Al-Cr alloys with similar gamma'-precipitate volume fractions at 873 K. The details of the phase decompositions of Ni-7.5Al-8.5Cr at.% and Ni-5.2Al-14.2Cr at.% for aging times from 1/6 to 1024 h are investigated by atom-probe tomography, and are found to differ significantly from a mean-field description of coarsening. The morphologies of the gamma'-precipitates of the alloys are similar, though the degrees of gamma'-precipitate coagulation and coalescence differ. Quantification within the framework of classical nucleation theory reveals that differences in the chemical driving forces for phase decomposition result in differences in the nucleation behavior of the two alloys. The temporal evolution of the gamma'-precipitate average radii and the gamma-matrix supersaturations follow the predictions of classical coarsening models. The compositional trajectories of the gamma-matrix phases of the alloys are found to follow approximately the equilibrium tie-lines, while the trajectories of the gamma'-precipitates do not, resulting in significant differences in the partitioning ratios of the solute elements.

Classical trajectory studies on the dynamics of one-photon double photionization of H2O

NASA Astrophysics Data System (ADS)

Streeter, Zachary; Yip, Frank; Reedy, Dylan P.; Landers, Allen; McCurdy, C. William

2017-04-01

Recent momentum imaging experiments at the Advanced Light Source have opened the possibility of measuring the complete triple differential cross section (TDCS) for one-photon double ionization of H2O in the molecular frame. The measurements depend on the complete breakup process, H2O + hν -> 2e-+ H+ + H+ +O. At the 57 eV photon energy of the experiment this process could proceed via any of the nine energetically accessible electronic states of H2O++. To discover which ionization channels contribute to the observed TDCS for the electrons measured in coincidence with different kinetic energy releases, we have carried out classical trajectory studies for breakup of the water dication on all nine potential surfaces, sampling from a Wigner phase space distribution for the vibrational ground state of H2O. The final momentum distributions of the protons and branching ratios between two- and three-body breakup are then analyzed and the results are compared with experiment to identify which ionization channels contribute to the TDCS observed in coincidence measurements of the ejected electrons. Office of Basic Energy Sciences, U.S. DOE.

ms2: A molecular simulation tool for thermodynamic properties

NASA Astrophysics Data System (ADS)

Deublein, Stephan; Eckl, Bernhard; Stoll, Jürgen; Lishchuk, Sergey V.; Guevara-Carrion, Gabriela; Glass, Colin W.; Merker, Thorsten; Bernreuther, Martin; Hasse, Hans; Vrabec, Jadran

2011-11-01

This work presents the molecular simulation program ms2 that is designed for the calculation of thermodynamic properties of bulk fluids in equilibrium consisting of small electro-neutral molecules. ms2 features the two main molecular simulation techniques, molecular dynamics (MD) and Monte-Carlo. It supports the calculation of vapor-liquid equilibria of pure fluids and multi-component mixtures described by rigid molecular models on the basis of the grand equilibrium method. Furthermore, it is capable of sampling various classical ensembles and yields numerous thermodynamic properties. To evaluate the chemical potential, Widom's test molecule method and gradual insertion are implemented. Transport properties are determined by equilibrium MD simulations following the Green-Kubo formalism. ms2 is designed to meet the requirements of academia and industry, particularly achieving short response times and straightforward handling. It is written in Fortran90 and optimized for a fast execution on a broad range of computer architectures, spanning from single processor PCs over PC-clusters and vector computers to high-end parallel machines. The standard Message Passing Interface (MPI) is used for parallelization and ms2 is therefore easily portable to different computing platforms. Feature tools facilitate the interaction with the code and the interpretation of input and output files. The accuracy and reliability of ms2 has been shown for a large variety of fluids in preceding work. Program summaryProgram title:ms2 Catalogue identifier: AEJF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Special Licence supplied by the authors No. of lines in distributed program, including test data, etc.: 82 794 No. of bytes in distributed program, including test data, etc.: 793 705 Distribution format: tar.gz Programming language: Fortran90 Computer: The simulation tool ms2 is usable on a wide variety of platforms, from single processor machines over PC-clusters and vector computers to vector-parallel architectures. (Tested with Fortran compilers: gfortran, Intel, PathScale, Portland Group and Sun Studio.) Operating system: Unix/Linux, Windows Has the code been vectorized or parallelized?: Yes. Message Passing Interface (MPI) protocol Scalability. Excellent scalability up to 16 processors for molecular dynamics and >512 processors for Monte-Carlo simulations. RAM:ms2 runs on single processors with 512 MB RAM. The memory demand rises with increasing number of processors used per node and increasing number of molecules. Classification: 7.7, 7.9, 12 External routines: Message Passing Interface (MPI) Nature of problem: Calculation of application oriented thermodynamic properties for rigid electro-neutral molecules: vapor-liquid equilibria, thermal and caloric data as well as transport properties of pure fluids and multi-component mixtures. Solution method: Molecular dynamics, Monte-Carlo, various classical ensembles, grand equilibrium method, Green-Kubo formalism. Restrictions: No. The system size is user-defined. Typical problems addressed by ms2 can be solved by simulating systems containing typically 2000 molecules or less. Unusual features: Feature tools are available for creating input files, analyzing simulation results and visualizing molecular trajectories. Additional comments: Sample makefiles for multiple operation platforms are provided. Documentation is provided with the installation package and is available at http://www.ms-2.de. Running time: The running time of ms2 depends on the problem set, the system size and the number of processes used in the simulation. Running four processes on a "Nehalem" processor, simulations calculating VLE data take between two and twelve hours, calculating transport properties between six and 24 hours.

Importance biasing scheme implemented in the PRIZMA code

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

Kandiev, I.Z.; Malyshkin, G.N.

1997-12-31

PRIZMA code is intended for Monte Carlo calculations of linear radiation transport problems. The code has wide capabilities to describe geometry, sources, material composition, and to obtain parameters specified by user. There is a capability to calculate path of particle cascade (including neutrons, photons, electrons, positrons and heavy charged particles) taking into account possible transmutations. Importance biasing scheme was implemented to solve the problems which require calculation of functionals related to small probabilities (for example, problems of protection against radiation, problems of detection, etc.). The scheme enables to adapt trajectory building algorithm to problem peculiarities.

Simulation of the Simbol-X telescope: imaging performance of a deformable x-ray telescope

NASA Astrophysics Data System (ADS)

Chauvin, Maxime; Roques, Jean-Pierre

2009-08-01

We have developed a simulation tool for a Wolter I telescope subject to deformations. The aim is to understand and predict the behavior of Simbol-X and other future missions (NuSTAR, Astro-H, IXO, ...). Our code, based on Monte-Carlo ray-tracing, computes the full photon trajectories up to the detector plane, along with the deformations. The degradation of the imaging system is corrected using metrology. This tool allows to perform many analyzes in order to optimize the configuration of any of these telescopes.

Analysis of hydrogen H-alpha observations of the coma of Comet P/Halley

NASA Technical Reports Server (NTRS)

Smyth, William H.; Marconi, M. L.; Scherb, Frank; Roesler, Fred L.

1993-01-01

The Monte Carlo Particle Trajectory Model of Combi and Smyth (1988) is used here to analyze observations of the H-alpha coma of Comet Halley. The solar excitation mechanism for the H-alpha emissions line is described. The H2O production rates derived for the H-alpha brightness measurements are shown to be very consistent with the H2O production rates determined from other Comet Halley observations of the H, O, and OH comae. Revised H2O production rates determined from 6300 A brightness measurements are presented.

A Monte Carlo method using octree structure in photon and electron transport

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

Ogawa, K.; Maeda, S.

Most of the early Monte Carlo calculations in medical physics were used to calculate absorbed dose distributions, and detector responses and efficiencies. Recently, data acquisition in Single Photon Emission CT (SPECT) has been simulated by a Monte Carlo method to evaluate scatter photons generated in a human body and a collimator. Monte Carlo simulations in SPECT data acquisition are generally based on the transport of photons only because the photons being simulated are low energy, and therefore the bremsstrahlung productions by the electrons generated are negligible. Since the transport calculation of photons without electrons is much simpler than that withmore » electrons, it is possible to accomplish the high-speed simulation in a simple object with one medium. Here, object description is important in performing the photon and/or electron transport using a Monte Carlo method efficiently. The authors propose a new description method using an octree representation of an object. Thus even if the boundaries of each medium are represented accurately, high-speed calculation of photon transport can be accomplished because the number of voxels is much fewer than that of the voxel-based approach which represents an object by a union of the voxels of the same size. This Monte Carlo code using the octree representation of an object first establishes the simulation geometry by reading octree string, which is produced by forming an octree structure from a set of serial sections for the object before the simulation; then it transports photons in the geometry. Using the code, if the user just prepares a set of serial sections for the object in which he or she wants to simulate photon trajectories, he or she can perform the simulation automatically using the suboptimal geometry simplified by the octree representation without forming the optimal geometry by handwriting.« less

Quantum dynamics in phase space: Moyal trajectories 2

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

Braunss, G.

Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010)] where we had calculated Planck-Constant-Over-Two-Pi {sup 2}-approximations of quantum phase space viz. Moyal trajectories of examples with one and two degrees of freedom, we present in this paper the calculation of Planck-Constant-Over-Two-Pi {sup 2}-approximations for four examples: a two-dimensional Toda chain, the radially symmetric Schwarzschild field, and two examples with three degrees of freedom, the latter being the nonrelativistic spherically Coulomb potential and the relativistic cylinder symmetrical Coulomb potential with a magnetic field H. We show in particular that an Planck-Constant-Over-Two-Pi {sup 2}-approximation of the nonrelativisticmore » Coulomb field has no singularity at the origin (r= 0) whereas the classical trajectories are singular at r= 0. In the third example, we show in particular that for an arbitrary function {gamma}(H, z) the expression {beta}{identical_to}p{sub z}+{gamma}(H, z) is classically ( Planck-Constant-Over-Two-Pi = 0) a constant of motion, whereas for Planck-Constant-Over-Two-Pi {ne} 0 this holds only if {gamma}(H, z) is an arbitrary polynomial of second order in z. This statement is shown to extend correspondingly to a cylinder symmetrical Schwarzschild field with a magnetic field. We exhibit in detail a number of properties of the radially symmetric Schwarzschild field. We exhibit finally the problems of the nonintegrable Henon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.« less

Biostratigraphy and biochronology of the Monte Hermoso Formation (early Pliocene) at its type locality, Buenos Aires Province, Argentina

NASA Astrophysics Data System (ADS)

Tomassini, Rodrigo L.; Montalvo, Claudia I.; Deschamps, Cecilia M.; Manera, Teresa

2013-12-01

The Monte Hermoso Formation, cropping out at its type locality of Farola Monte Hermoso (Buenos Aires Province), is a classical fossiliferous unit of the South American Neogene, highlighted by the abundance and diversity of its vertebrate remains. However, its biostratigraphy and age have been largely debated, and numerous discrepancies and controversies have been stated. In this regard, the result of the analysis of new materials recovered from the different levels of this formation, following a strict control of stratigraphic provenance, is here reported. As well, the provenance of specimens of previous collections has been evaluated. The studied assemblage consists of Osteichthyes, Amphibia, Reptilia, Aves and Mammalia. These latter are the most numerous and belong to the Didelphimorphia, Polydolopimorphia, Rodentia, Notoungulata, Litopterna and Xenarthra. The recorded taxa suggest no important faunistic variations among the different levels of the Monte Hermoso Formation that would imply significant chronological differences, and hence, justify the recognition of two biostratigraphic units. The analysis of the first and last records as well as the taxa considered as exclusive, does not support the validity of the biozones of Trigodon gaudryi and Neocavia depressidens previously proposed. On this basis, a new scheme for the Monte Hermoso Formation at its type locality is proposed, including a new single biostratigraphic unit. This unit is the Eumysops laeviplicatus Range Zone, which represents the biostratigraphic base for the Montehermosan Stage/Age of the early Pliocene.

Reliability of a Measure of Institutional Discrimination against Minorities

DTIC Science & Technology

1979-12-01

samples are presented. The first is based upon classical statistical theory and the second derives from a series of computer-generated Monte Carlo...Institutional racism and sexism . Englewood Cliffs, N. J.: Prentice-Hall, Inc., 1978. Hays, W. L. and Winkler, R. L. Statistics : probability, inference... statistical measure of the e of institutional discrimination are discussed. Two methods of dealing with the problem of reliability of the measure in small

Tests of Fit for Asymmetric Laplace Distributions with Applications on Financial Data

NASA Astrophysics Data System (ADS)

Fragiadakis, Kostas; Meintanis, Simos G.

2008-11-01

New goodness-of-fit tests for the family of asymmetric Laplace distributions are constructed. The proposed tests are based on a weighted integral incorporating the empirical characteristic function of suitably standardized data, and can be written in a closed form appropriate for computer implementation. Monte Carlo results show that the new procedure are competitive with classical goodness-of-fit methods. Applications with financial data are also included.

Spin Glass Patch Planting

NASA Technical Reports Server (NTRS)

Wang, Wenlong; Mandra, Salvatore; Katzgraber, Helmut G.

2016-01-01

In this paper, we propose a patch planting method for creating arbitrarily large spin glass instances with known ground states. The scaling of the computational complexity of these instances with various block numbers and sizes is investigated and compared with random instances using population annealing Monte Carlo and the quantum annealing DW2X machine. The method can be useful for benchmarking tests for future generation quantum annealing machines, classical and quantum mechanical optimization algorithms.

Uncertainty assessment in geodetic network adjustment by combining GUM and Monte-Carlo-simulations

NASA Astrophysics Data System (ADS)

Niemeier, Wolfgang; Tengen, Dieter

2017-06-01

In this article first ideas are presented to extend the classical concept of geodetic network adjustment by introducing a new method for uncertainty assessment as two-step analysis. In the first step the raw data and possible influencing factors are analyzed using uncertainty modeling according to GUM (Guidelines to the Expression of Uncertainty in Measurements). This approach is well established in metrology, but rarely adapted within Geodesy. The second step consists of Monte-Carlo-Simulations (MC-simulations) for the complete processing chain from raw input data and pre-processing to adjustment computations and quality assessment. To perform these simulations, possible realizations of raw data and the influencing factors are generated, using probability distributions for all variables and the established concept of pseudo-random number generators. Final result is a point cloud which represents the uncertainty of the estimated coordinates; a confidence region can be assigned to these point clouds, as well. This concept may replace the common concept of variance propagation and the quality assessment of adjustment parameters by using their covariance matrix. It allows a new way for uncertainty assessment in accordance with the GUM concept for uncertainty modelling and propagation. As practical example the local tie network in "Metsähovi Fundamental Station", Finland is used, where classical geodetic observations are combined with GNSS data.

Classical force field for hydrofluorocarbon molecular simulations. Application to the study of gas solubility in poly(vinylidene fluoride).

PubMed

Lachet, V; Teuler, J-M; Rousseau, B

2015-01-08

A classical all-atoms force field for molecular simulations of hydrofluorocarbons (HFCs) has been developed. Lennard-Jones force centers plus point charges are used to represent dispersion-repulsion and electrostatic interactions. Parametrization of this force field has been performed iteratively using three target properties of pentafluorobutane: the quantum energy of an isolated molecule, the dielectric constant in the liquid phase, and the compressed liquid density. The accuracy and transferability of this new force field has been demonstrated through the simulation of different thermophysical properties of several fluorinated compounds, showing significant improvements compared to existing models. This new force field has been applied to study solubilities of several gases in poly(vinylidene fluoride) (PVDF) above the melting temperature of this polymer. The solubility of CH4, CO2, H2S, H2, N2, O2, and H2O at infinite dilution has been computed using test particle insertions in the course of a NpT hybrid Monte Carlo simulation. For CH4, CO2, and their mixtures, some calculations beyond the Henry regime have also been performed using hybrid Monte Carlo simulations in the osmotic ensemble, allowing both swelling and solubility determination. An ideal mixing behavior is observed, with identical solubility coefficients in the mixtures and in pure gas systems.

Toward understanding the roaming mechanism in H + MgH → Mg + HH reaction

DOE PAGES

Mauguiere, Frederic A. L.; Collins, Peter; Stamatiadis, Stamatis; ...

2016-02-26

The roaming mechanism in the reaction H + MgH →Mg + HH is investigated by classical and quantum dynamics employing an accurate ab initio threedimensional ground electronic state potential energy surface. The reaction dynamics are explored by running trajectories initialized on a four-dimensional dividing surface anchored on three-dimensional normally hyperbolic invariant manifold associated with a family of unstable orbiting periodic orbits in the entrance channel of the reaction (H + MgH). By locating periodic orbits localized in the HMgH well or involving H orbiting around the MgH diatom, and following their continuation with the total energy, regions in phase spacemore » where reactive or nonreactive trajectories may be trapped are found. In this way roaming reaction pathways are deduced in phase space. Patterns similar to periodic orbits projected into configuration space are found for the quantum bound and resonance eigenstates. Roaming is attributed to the capture of the trajectories in the neighborhood of certain periodic orbits. As a result, the complex forming trajectories in the HMgH well can either return to the radical channel or “roam” to the MgHH minimum from where the molecule may react.« less

A New Computational Technique for the Generation of Optimised Aircraft Trajectories

NASA Astrophysics Data System (ADS)

Chircop, Kenneth; Gardi, Alessandro; Zammit-Mangion, David; Sabatini, Roberto

2017-12-01

A new computational technique based on Pseudospectral Discretisation (PSD) and adaptive bisection ɛ-constraint methods is proposed to solve multi-objective aircraft trajectory optimisation problems formulated as nonlinear optimal control problems. This technique is applicable to a variety of next-generation avionics and Air Traffic Management (ATM) Decision Support Systems (DSS) for strategic and tactical replanning operations. These include the future Flight Management Systems (FMS) and the 4-Dimensional Trajectory (4DT) planning and intent negotiation/validation tools envisaged by SESAR and NextGen for a global implementation. In particular, after describing the PSD method, the adaptive bisection ɛ-constraint method is presented to allow an efficient solution of problems in which two or multiple performance indices are to be minimized simultaneously. Initial simulation case studies were performed adopting suitable aircraft dynamics models and addressing a classical vertical trajectory optimisation problem with two objectives simultaneously. Subsequently, a more advanced 4DT simulation case study is presented with a focus on representative ATM optimisation objectives in the Terminal Manoeuvring Area (TMA). The simulation results are analysed in-depth and corroborated by flight performance analysis, supporting the validity of the proposed computational techniques.

Semiclassical analysis of angular differential cross sections for single-electron capture in 250-eV H++H collisions

NASA Astrophysics Data System (ADS)

Frémont, F.

2015-05-01

A classical model based on the resolution of Hamilton equations of motion is used to determine the angular distribution of H projectiles following single-electron capture in H++H collisions at an incident projectile energy of 250 eV. At such low energies, the experimental charge-exchange probability and angular differential cross sections exhibit oscillatory structures that are classically related to the number of swaps the electron experiences between the target and the projectile during the collision. These oscillations are well reproduced by models based on quantum mechanics. In the present paper, the angular distribution of H projectiles is determined classically, at angles varying from 0.1° up to 7°. The variation in intensity due to interferences caused by the indiscernibility between different trajectories is calculated, and the role of these interferences is discussed.

Reproducing Quantum Probability Distributions at the Speed of Classical Dynamics: A New Approach for Developing Force-Field Functors.

PubMed

Sundar, Vikram; Gelbwaser-Klimovsky, David; Aspuru-Guzik, Alán

2018-04-05

Modeling nuclear quantum effects is required for accurate molecular dynamics (MD) simulations of molecules. The community has paid special attention to water and other biomolecules that show hydrogen bonding. Standard methods of modeling nuclear quantum effects like Ring Polymer Molecular Dynamics (RPMD) are computationally costlier than running classical trajectories. A force-field functor (FFF) is an alternative method that computes an effective force field that replicates quantum properties of the original force field. In this work, we propose an efficient method of computing FFF using the Wigner-Kirkwood expansion. As a test case, we calculate a range of thermodynamic properties of Neon, obtaining the same level of accuracy as RPMD, but with the shorter runtime of classical simulations. By modifying existing MD programs, the proposed method could be used in the future to increase the efficiency and accuracy of MD simulations involving water and proteins.

Quantum-classical correspondence for the inverted oscillator

NASA Astrophysics Data System (ADS)

Maamache, Mustapha; Ryeol Choi, Jeong

2017-11-01

While quantum-classical correspondence for a system is a very fundamental problem in modern physics, the understanding of its mechanism is often elusive, so the methods used and the results of detailed theoretical analysis have been accompanied by active debate. In this study, the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave solution. The inverted oscillator model plays an important role in several branches of cosmology and particle physics. The quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between them. It is shown from illustrations of the probability density that, although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one, the difference becomes relatively small when the classical excitation is sufficiently high. We have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical wave. From these main interpretations and others in the text, we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system, which is a crucial concept in quantum mechanics. Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1A09919503)

Reactive collisions for NO(2Π) + N(4S) at temperatures relevant to the hypersonic flight regime.

PubMed

Denis-Alpizar, Otoniel; Bemish, Raymond J; Meuwly, Markus

2017-01-18

The NO(X 2 Π) + N( 4 S) reaction which occurs entirely in the triplet manifold of N 2 O is investigated using quasiclassical trajectories and quantum simulations. Fully-dimensional potential energy surfaces for the 3 A' and 3 A'' states are computed at the MRCI+Q level of theory and are represented using a reproducing kernel Hilbert space. The N-exchange and N 2 -formation channels are followed by using the multi-state adiabatic reactive molecular dynamics method. Up to 5000 K these reactions occur predominantly on the N 2 O 3 A'' surface. However, for higher temperatures the contributions of the 3 A' and 3 A'' states are comparable and the final state distributions are far from thermal equilibrium. From the trajectory simulations a new set of thermal rate coefficients of up to 20 000 K is determined. Comparison of the quasiclassical trajectory and quantum simulations shows that a classical description is a good approximation as determined from the final state analysis.

Seagrass ecosystem trajectory depends on the relative timescales of resistance, recovery and disturbance.

PubMed

O'Brien, Katherine R; Waycott, Michelle; Maxwell, Paul; Kendrick, Gary A; Udy, James W; Ferguson, Angus J P; Kilminster, Kieryn; Scanes, Peter; McKenzie, Len J; McMahon, Kathryn; Adams, Matthew P; Samper-Villarreal, Jimena; Collier, Catherine; Lyons, Mitchell; Mumby, Peter J; Radke, Lynda; Christianen, Marjolijn J A; Dennison, William C

2017-09-18

Seagrass ecosystems are inherently dynamic, responding to environmental change across a range of scales. Habitat requirements of seagrass are well defined, but less is known about their ability to resist disturbance. Specific means of recovery after loss are particularly difficult to quantify. Here we assess the resistance and recovery capacity of 12 seagrass genera. We document four classic trajectories of degradation and recovery for seagrass ecosystems, illustrated with examples from around the world. Recovery can be rapid once conditions improve, but seagrass absence at landscape scales may persist for many decades, perpetuated by feedbacks and/or lack of seed or plant propagules to initiate recovery. It can be difficult to distinguish between slow recovery, recalcitrant degradation, and the need for a window of opportunity to trigger recovery. We propose a framework synthesizing how the spatial and temporal scales of both disturbance and seagrass response affect ecosystem trajectory and hence resilience. Copyright © 2017 Elsevier Ltd. All rights reserved.

Detailed classification of swimming paths in the Morris Water Maze: multiple strategies within one trial

PubMed Central

Gehring, Tiago V.; Luksys, Gediminas; Sandi, Carmen; Vasilaki, Eleni

2015-01-01

The Morris Water Maze is a widely used task in studies of spatial learning with rodents. Classical performance measures of animals in the Morris Water Maze include the escape latency, and the cumulative distance to the platform. Other methods focus on classifying trajectory patterns to stereotypical classes representing different animal strategies. However, these approaches typically consider trajectories as a whole, and as a consequence they assign one full trajectory to one class, whereas animals often switch between these strategies, and their corresponding classes, within a single trial. To this end, we take a different approach: we look for segments of diverse animal behaviour within one trial and employ a semi-automated classification method for identifying the various strategies exhibited by the animals within a trial. Our method allows us to reveal significant and systematic differences in the exploration strategies of two animal groups (stressed, non-stressed), that would be unobserved by earlier methods. PMID:26423140

Multilevel Monte Carlo simulation of Coulomb collisions

DOE PAGES

Rosin, M. S.; Ricketson, L. F.; Dimits, A. M.; ...

2014-05-29

We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau–Fokker–Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy ε , the computational cost of the method is O(ε –2) or (ε –2(lnε) 2), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε –3) for direct simulation Monte Carlomore » or binary collision methods. We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ε=10 –5. Lastly, we discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.« less

Monte Carlo simulation of dynamic phase transitions and frequency dispersions of hysteresis curves in core/shell ferrimagnetic cubic nanoparticle

NASA Astrophysics Data System (ADS)

Vatansever, Erol

2017-05-01

By means of Monte Carlo simulation method with Metropolis algorithm, we elucidate the thermal and magnetic phase transition behaviors of a ferrimagnetic core/shell nanocubic system driven by a time dependent magnetic field. The particle core is composed of ferromagnetic spins, and it is surrounded by an antiferromagnetic shell. At the interface of the core/shell particle, we use antiferromagnetic spin-spin coupling. We simulate the nanoparticle using classical Heisenberg spins. After a detailed analysis, our Monte Carlo simulation results suggest that present system exhibits unusual and interesting magnetic behaviors. For example, at the relatively lower temperature regions, an increment in the amplitude of the external field destroys the antiferromagnetism in the shell part of the nanoparticle, leading to a ground state with ferromagnetic character. Moreover, particular attention has been dedicated to the hysteresis behaviors of the system. For the first time, we show that frequency dispersions can be categorized into three groups for a fixed temperature for finite core/shell systems, as in the case of the conventional bulk systems under the influence of an oscillating magnetic field.

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors

NASA Astrophysics Data System (ADS)

Pandey, Akhilesh; Kumar, Avanish; Puri, Sanjay

2017-11-01

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α , the appropriate FRCG model has the effective range d =b2/N =α2/N , for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors.

PubMed

Pandey, Akhilesh; Kumar, Avanish; Puri, Sanjay

2017-11-01

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has the effective range d=b^{2}/N=α^{2}/N, for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics

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

Albert, Julian; Kaiser, Dustin; Engel, Volker

2016-05-07

Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion ismore » treated on the same footing.« less

Quantization of the Szekeres system

NASA Astrophysics Data System (ADS)

Paliathanasis, A.; Zampeli, Adamantia; Christodoulakis, T.; Mustafa, M. T.

2018-06-01

We study the quantum corrections on the Szekeres system in the context of canonical quantization in the presence of symmetries. We start from an effective point-like Lagrangian with two integrals of motion, one corresponding to the Hamiltonian and the other to a second rank killing tensor. Imposing their quantum version on the wave function results to a solution which is then interpreted in the context of Bohmian mechanics. In this semiclassical approach, it is shown that there is no quantum corrections, thus the classical trajectories of the Szekeres system are not affected at this level. Finally, we define a probability function which shows that a stationary surface of the probability corresponds to a classical exact solution.

Developmental trajectories of offenders convicted of fraud: A follow-up to age 50 in a Dutch conviction cohort

PubMed Central

van der Geest, Victor R.; Weisburd, David; Blokland, Arjan A. J.

2016-01-01

This study describes the criminal careers of offenders convicted of fraud, distinguishing different career dimensions such as intermittency, versatility and specialization. Results indicate that most fraud offenders are versatile in the sense that they also have significant criminal records for other serious offending (that is, not fraud). At the same time they are also specialized in fraud. When we examine developmental trajectories of serious offending and next explore patterns of fraud for the groups identified, we find that offenders in our sample represent a heterogeneous group and that the classic divide between typical financial (for example, white-collar) offenders and common criminals does not apply to the majority of our sample. PMID:28989326

A multicolour graph as a complete topological invariant for \\Omega-stable flows without periodic trajectories on surfaces

NASA Astrophysics Data System (ADS)

Kruglov, V. E.; Malyshev, D. S.; Pochinka, O. V.

2018-01-01

Studying the dynamics of a flow on surfaces by partitioning the phase space into cells with the same limit behaviour of trajectories within a cell goes back to the classical papers of Andronov, Pontryagin, Leontovich and Maier. The types of cells (the number of which is finite) and how the cells adjoin one another completely determine the topological equivalence class of a flow with finitely many special trajectories. If one trajectory is chosen in every cell of a rough flow without periodic orbits, then the cells are partitioned into so-called triangular regions of the same type. A combinatorial description of such a partition gives rise to the three-colour Oshemkov-Sharko graph, the vertices of which correspond to the triangular regions, and the edges to separatrices connecting them. Oshemkov and Sharko proved that such flows are topologically equivalent if and only if the three-colour graphs of the flows are isomorphic, and described an algorithm of distinguishing three-colour graphs. But their algorithm is not efficient with respect to graph theory. In the present paper, we describe the dynamics of Ω-stable flows without periodic trajectories on surfaces in the language of four-colour graphs, present an efficient algorithm for distinguishing such graphs, and develop a realization of a flow from some abstract graph. Bibliography: 17 titles.

A scrutiny of the premise of the Rice-Ramsperger-Kassel-Marcus theory in isomerization reaction of an Ar7-type molecule

NASA Astrophysics Data System (ADS)

Takatsuka, Kazuo; Seko, Chihiro

1996-12-01

The validity of the physical premise of the Rice-Ramsperger-Kassel-Marcus (RRKM) theory is investigated in terms of the classical dynamics of isomerization reaction in Ar7-like molecules (clusters). The passage times of classical trajectories through the potential basins of isomers in the structural transitions are examined. In the high energy region corresponding to the so-called liquidlike phase, remarkable uniformity of the average passage times has been found. That is, the average passage time is characterized only by a basin through which a trajectory is currently passing and, hence, does not depend on the next visiting basins. This behavior is out of accord with the ordinary chemical law in that the ``reaction rates'' do not seem to depend on the height of the individual potential barriers. We ascribe this seemingly strange uniformity to the strong mixing (chaos) lying behind the rate process. That is, as soon as a classical path enters a basin, it gets involved into a chaotic zone in which many paths having different channels are entangled among each other, and effectively (in the statistical sense) loses its memory about which basin it came from and where it should visit next time. This model is verified by confirming that the populations of the lifetime of transition from one basin to others are expressed in exponential functions, which should have very similar exponents to each other in each passing-through basin. The inverse of the exponent is essentially proportional to the average passage time, and consequently brings about the uniformity. These populations set a foundation for the multichannel generalization of the RRKM theory. Two cases of the non-RRKM behaviors have been studied. One is a nonstatistical behavior in the low energy region such as the so-called coexistence phase. The other is the short-time behavior. It is well established [M. Berblinger and C. Schlier, J. Chem. Phys. 101, 4750 (1994)] that in a relatively simple and small system such as H+3, the so-called direct paths, which lead to dissociation before the phase-space mixing is completed, increase the probability of short-time passage. In contrast, we have found in our Ar7-like molecules that trajectories of short passage time are fewer than expected by the statistical theory. It is conceived that somewhat a long time in the initial stage of the isomerization is spent by a trajectory to find its ways out to the next basins.

Monte-Carlo Orbit/Full Wave Simulation of Fast Alfvén Wave (FW) Damping on Resonant Ions in Tokamaks

NASA Astrophysics Data System (ADS)

Choi, M.; Chan, V. S.; Tang, V.; Bonoli, P.; Pinsker, R. I.; Wright, J.

2005-09-01

To simulate the resonant interaction of fast Alfvén wave (FW) heating and Coulomb collisions on energetic ions, including finite orbit effects, a Monte-Carlo code ORBIT-RF has been coupled with a 2D full wave code TORIC4. ORBIT-RF solves Hamiltonian guiding center drift equations to follow trajectories of test ions in 2D axisymmetric numerical magnetic equilibrium under Coulomb collisions and ion cyclotron radio frequency quasi-linear heating. Monte-Carlo operators for pitch-angle scattering and drag calculate the changes of test ions in velocity and pitch angle due to Coulomb collisions. A rf-induced random walk model describing fast ion stochastic interaction with FW reproduces quasi-linear diffusion in velocity space. FW fields and its wave numbers from TORIC are passed on to ORBIT-RF to calculate perpendicular rf kicks of resonant ions valid for arbitrary cyclotron harmonics. ORBIT-RF coupled with TORIC using a single dominant toroidal and poloidal wave number has demonstrated consistency of simulations with recent DIII-D FW experimental results for interaction between injected neutral-beam ions and FW, including measured neutron enhancement and enhanced high energy tail. Comparison with C-Mod fundamental heating discharges also yielded reasonable agreement.

An operational search and rescue model for the Norwegian Sea and the North Sea

NASA Astrophysics Data System (ADS)

Breivik, Øyvind; Allen, Arthur A.

A new operational, ensemble-based search and rescue model for the Norwegian Sea and the North Sea is presented. The stochastic trajectory model computes the net motion of a range of search and rescue objects. A new, robust formulation for the relation between the wind and the motion of the drifting object (termed the leeway of the object) is employed. Empirically derived coefficients for 63 categories of search objects compiled by the US Coast Guard are ingested to estimate the leeway of the drifting objects. A Monte Carlo technique is employed to generate an ensemble that accounts for the uncertainties in forcing fields (wind and current), leeway drift properties, and the initial position of the search object. The ensemble yields an estimate of the time-evolving probability density function of the location of the search object, and its envelope defines the search area. Forcing fields from the operational oceanic and atmospheric forecast system of The Norwegian Meteorological Institute are used as input to the trajectory model. This allows for the first time high-resolution wind and current fields to be used to forecast search areas up to 60 h into the future. A limited set of field exercises show good agreement between model trajectories, search areas, and observed trajectories for life rafts and other search objects. Comparison with older methods shows that search areas expand much more slowly using the new ensemble method with high resolution forcing fields and the new leeway formulation. It is found that going to higher-order stochastic trajectory models will not significantly improve the forecast skill and the rate of expansion of search areas.

A model calculation of coherence effects in the elastic backscattering of very low energy electrons (1-20 eV) from amorphous ice.

PubMed

Liljequist, David

2012-01-01

Backscattering of very low energy electrons in thin layers of amorphous ice is known to provide experimental data for the elastic and inelastic cross sections and indicates values to be expected in liquid water. The extraction of cross sections was based on a transport analysis consistent with Monte Carlo simulation of electron trajectories. However, at electron energies below 20 eV, quantum coherence effects may be important and trajectory-based methods may be in significant error. This possibility is here investigated by calculating quantum multiple elastic scattering of electrons in a simple model of a very small, thin foil of amorphous ice. The average quantum multiple elastic scattering of electrons is calculated for a large number of simulated foils, using a point-scatterer model for the water molecule and taking inelastic absorption into account. The calculation is compared with a corresponding trajectory simulation. The difference between average quantum scattering and trajectory simulation at energies below about 20 eV is large, in particular in the forward scattering direction, and is found to be almost entirely due to coherence effects associated with the short-range order in the amorphous ice. For electrons backscattered at the experimental detection angle (45° relative to the surface normal) the difference is however small except at electron energies below about 10 eV. Although coherence effects are in general found to be strong, the mean free path values derived by trajectory-based analysis may actually be in fair agreement with the result of an analysis based on quantum scattering, at least for electron energies larger than about 10 eV.

Reactive Collisions and Final State Analysis in Hypersonic Flight Regime

DTIC Science & Technology

2016-09-13

Kelvin.[7] The gas-phase, surface reactions and energy transfer at these tempera- tures are essentially uncharacterized and the experimental methodologies...high temperatures (1000 to 20000 K) and compared with results from experimentally derived thermodynamics quantities from the NASA CEA (NASA Chemical...with a reproducing kernel Hilbert space (RKHS) method[13] combined with Legendre polynomials; (2) quasi classical trajectory (QCT) calculations to study

Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

NASA Technical Reports Server (NTRS)

Gunderson, R. W.

1975-01-01

A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

Tracing the Transition from Study to a Contemporary Creative Working Life: The Trajectories of Professional Musicians

ERIC Educational Resources Information Center

Juuti, Sini; Littleton, Karen

2012-01-01

The classical music academy is a site dominated by traditional meanings of creative practice and an image of the professional creative career as solo performer that is fully available to only a very few students after graduating. The purpose of the study reported in this paper is to explore career-young professional pianists' talk about the…

Collapse of the soap-film bridge - Quasistatic description

NASA Astrophysics Data System (ADS)

Cryer, Steven A.; Steen, Paul H.

1992-11-01

Observations of the collapse of a soap-film bridge from a connected to a disconnected state are recorded. The equilibrium framework for this nonequilibrium event is classical. Experiments confirm predictions of stable and unstable equilibria. A quasistatic description is introduced for the dynamic states to extend the static theory. It is found to adequately describe the collapse trajectory while the bridge is still connected.

Collapse of the soap-film bridge - Quasistatic description

NASA Technical Reports Server (NTRS)

Cryer, Steven A.; Steen, Paul H.

1992-01-01

Observations of the collapse of a soap-film bridge from a connected to a disconnected state are recorded. The equilibrium framework for this nonequilibrium event is classical. Experiments confirm predictions of stable and unstable equilibria. A quasistatic description is introduced for the dynamic states to extend the static theory. It is found to adequately describe the collapse trajectory while the bridge is still connected.

Removing the barrier to the calculation of activation energies

DOE PAGES

Mesele, Oluwaseun O.; Thompson, Ward H.

2016-10-06

Approaches for directly calculating the activation energy for a chemical reaction from a simulation at a single temperature are explored with applications to both classical and quantum systems. The activation energy is obtained from a time correlation function that can be evaluated from the same molecular dynamics trajectories or quantum dynamics used to evaluate the rate constant itself and thus requires essentially no extra computational work.

The probability of false positives in zero-dimensional analyses of one-dimensional kinematic, force and EMG trajectories.

PubMed

Pataky, Todd C; Vanrenterghem, Jos; Robinson, Mark A

2016-06-14

A false positive is the mistake of inferring an effect when none exists, and although α controls the false positive (Type I error) rate in classical hypothesis testing, a given α value is accurate only if the underlying model of randomness appropriately reflects experimentally observed variance. Hypotheses pertaining to one-dimensional (1D) (e.g. time-varying) biomechanical trajectories are most often tested using a traditional zero-dimensional (0D) Gaussian model of randomness, but variance in these datasets is clearly 1D. The purpose of this study was to determine the likelihood that analyzing smooth 1D data with a 0D model of variance will produce false positives. We first used random field theory (RFT) to predict the probability of false positives in 0D analyses. We then validated RFT predictions via numerical simulations of smooth Gaussian 1D trajectories. Results showed that, across a range of public kinematic, force/moment and EMG datasets, the median false positive rate was 0.382 and not the assumed α=0.05, even for a simple two-sample t test involving N=10 trajectories per group. The median false positive rate for experiments involving three-component vector trajectories was p=0.764. This rate increased to p=0.945 for two three-component vector trajectories, and to p=0.999 for six three-component vectors. This implies that experiments involving vector trajectories have a high probability of yielding 0D statistical significance when there is, in fact, no 1D effect. Either (a) explicit a priori identification of 0D variables or (b) adoption of 1D methods can more tightly control α. Copyright © 2016 Elsevier Ltd. All rights reserved.

Latent tracks and associated strain in Al2O3 irradiated with swift heavy ions

NASA Astrophysics Data System (ADS)

O'Connell, J. H.; Rymzhanov, R. A.; Skuratov, V. A.; Volkov, A. E.; Kirilkin, N. S.

2016-05-01

The morphology of latent ion tracks induced by high energy heavy ions in Al2O3 was investigated using a combination of high resolution transmission electron microscopy (HRTEM), exit wave reconstruction, geometric phase analysis and numerical simulations. Single crystal α-Al2O3 crystals were irradiated with 167 MeV Xe ions along the c-axis to fluences between 1 × 1010 and 1 × 1013 cm-2. Planar TEM lamella were prepared by focused ion beam (FIB) and geometrical phase analysis was performed on the phase image of the reconstructed complex electron wave at the specimen exit surface in order to estimate the latent strain around individual track cores. In addition to the experimental data, the material excitation in a SHI track was numerically simulated by combining Monte-Carlo code, describing the excitation of the electronic subsystem, with classical molecular dynamics of the lattice atoms. Experimental and simulation data both showed that the relaxation of the excess lattice energy results in the formation of a cylinder-like disordered region of about 4 nm in diameter consisting of an underdense core surrounded by an overdense shell. Modeling of the passage of a second ion in the vicinity of this disordered region revealed that this damaged area can be restored to a near damage free state. The estimation of a maximal effective distance of recrystallization between the ion trajectories yields values of about 6-6.5 nm which are of the same order of magnitude as those estimated from the saturation density of latent ion tracks detected by TEM.

On non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2015-04-01

In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass.

Constant-pH Hybrid Nonequilibrium Molecular Dynamics–Monte Carlo Simulation Method

PubMed Central

2016-01-01

A computational method is developed to carry out explicit solvent simulations of complex molecular systems under conditions of constant pH. In constant-pH simulations, preidentified ionizable sites are allowed to spontaneously protonate and deprotonate as a function of time in response to the environment and the imposed pH. The method, based on a hybrid scheme originally proposed by H. A. Stern (J. Chem. Phys.2007, 126, 164112), consists of carrying out short nonequilibrium molecular dynamics (neMD) switching trajectories to generate physically plausible configurations with changed protonation states that are subsequently accepted or rejected according to a Metropolis Monte Carlo (MC) criterion. To ensure microscopic detailed balance arising from such nonequilibrium switches, the atomic momenta are altered according to the symmetric two-ends momentum reversal prescription. To achieve higher efficiency, the original neMD–MC scheme is separated into two steps, reducing the need for generating a large number of unproductive and costly nonequilibrium trajectories. In the first step, the protonation state of a site is randomly attributed via a Metropolis MC process on the basis of an intrinsic pKa; an attempted nonequilibrium switch is generated only if this change in protonation state is accepted. This hybrid two-step inherent pKa neMD–MC simulation method is tested with single amino acids in solution (Asp, Glu, and His) and then applied to turkey ovomucoid third domain and hen egg-white lysozyme. Because of the simple linear increase in the computational cost relative to the number of titratable sites, the present method is naturally able to treat extremely large systems. PMID:26300709

3D Monte Carlo model with direct photon flux recording for optimal optogenetic light delivery

NASA Astrophysics Data System (ADS)

Shin, Younghoon; Kim, Dongmok; Lee, Jihoon; Kwon, Hyuk-Sang

2017-02-01

Configuring the light power emitted from the optical fiber is an essential first step in planning in-vivo optogenetic experiments. However, diffusion theory, which was adopted for optogenetic research, precluded accurate estimates of light intensity in the semi-diffusive region where the primary locus of the stimulation is located. We present a 3D Monte Carlo model that provides an accurate and direct solution for light distribution in this region. Our method directly records the photon trajectory in the separate volumetric grid planes for the near-source recording efficiency gain, and it incorporates a 3D brain mesh to support both homogeneous and heterogeneous brain tissue. We investigated the light emitted from optical fibers in brain tissue in 3D, and we applied the results to design optimal light delivery parameters for precise optogenetic manipulation by considering the fiber output power, wavelength, fiber-to-target distance, and the area of neural tissue activation.

STS-1 operational flight profile. Volume 5: Descent cycle 3. Appendix D: GRTLS six degree of freedom Monte Carlo dispersion analysis

NASA Technical Reports Server (NTRS)

Montez, M. N.

1980-01-01

The results of a six degree of freedom (6-DOF) nonlinear Monte Carlo dispersion analysis for the latest glide return to landing site (GRTLS) abort trajectory for the Space Transportation System 1 Flight are presented. For this GRTLS, the number two main engine fails at 262.5 seconds ground elapsed time. Fifty randomly selected simulations, initialized at external tank separation, are analyzed. The initial covariance matrix is a 20 x 20 matrix and includes navigation errors and dispersions in position and velocity, time, accelerometer bias, and inertial platform misalinements. In all 50 samples, speedbrake, rudder, elevon, and body flap hinge moments are acceptable. Transitions to autoland begin before 9,000 feet and there are no tailscrapes. Navigation derived dynamic pressure accuracies exceed the flight control system constraints above Mach 2.5. Three out of 50 landings exceeded tire specification limit speed of 222 knots. Pilot manual landings are expected to reduce landing speed by landing farther downrange.

New approach for absolute fluence distribution calculations in Monte Carlo simulations of light propagation in turbid media

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

Böcklin, Christoph, E-mail: boecklic@ethz.ch; Baumann, Dirk; Fröhlich, Jürg

A novel way to attain three dimensional fluence rate maps from Monte-Carlo simulations of photon propagation is presented in this work. The propagation of light in a turbid medium is described by the radiative transfer equation and formulated in terms of radiance. For many applications, particularly in biomedical optics, the fluence rate is a more useful quantity and directly derived from the radiance by integrating over all directions. Contrary to the usual way which calculates the fluence rate from absorbed photon power, the fluence rate in this work is directly calculated from the photon packet trajectory. The voxel based algorithmmore » works in arbitrary geometries and material distributions. It is shown that the new algorithm is more efficient and also works in materials with a low or even zero absorption coefficient. The capabilities of the new algorithm are demonstrated on a curved layered structure, where a non-scattering, non-absorbing layer is sandwiched between two highly scattering layers.« less

Dynamical traps in Wang-Landau sampling of continuous systems: Mechanism and solution

NASA Astrophysics Data System (ADS)

Koh, Yang Wei; Sim, Adelene Y. L.; Lee, Hwee Kuan

2015-08-01

We study the mechanism behind dynamical trappings experienced during Wang-Landau sampling of continuous systems reported by several authors. Trapping is caused by the random walker coming close to a local energy extremum, although the mechanism is different from that of the critical slowing-down encountered in conventional molecular dynamics or Monte Carlo simulations. When trapped, the random walker misses the entire or even several stages of Wang-Landau modification factor reduction, leading to inadequate sampling of the configuration space and a rough density of states, even though the modification factor has been reduced to very small values. Trapping is dependent on specific systems, the choice of energy bins, and the Monte Carlo step size, making it highly unpredictable. A general, simple, and effective solution is proposed where the configurations of multiple parallel Wang-Landau trajectories are interswapped to prevent trapping. We also explain why swapping frees the random walker from such traps. The efficacy of the proposed algorithm is demonstrated.

Monte Carlo Calculations of Suprathermal Alpha Particles Trajectories in the Rippled Field of TFTR

NASA Astrophysics Data System (ADS)

Punjabi, Alkesh; Lam, Maria; Boozer, Allen

1996-11-01

We study the transport of suprathermal alpha particles and their energy deposition into electrons, deuterons, tritons and carbon-12 impurity in the rippled field of TFTR. The Monte Carlo code (Punjabi A., Boozer A., Lam M., Kim M., and Burke K., J. Plasma Phys.), 44, 405 (1990) developed by Punjabi and Boozer for the transport of plasma particles due to MHD modes in toroidal plasmas is used in conjunction with the SHAF code (White R. B., and Boozer A., PPPL -3094) (1995) of White. we integrate drift Hamiltonian equation of motion in non-canonical, rectangular, Boozer coordinates. The deposition of alpha energy into electrons, deuterons, tritons and C-12 particles is calculated and recorded. The effects of energy and pitch angle scattering are included. The result of this study will be presented. This work is supported by the US DOE. The assistance provided by Professors R. B. White and S. Zweben of PPPL is gratefully acknowledged.

Failure Bounding And Sensitivity Analysis Applied To Monte Carlo Entry, Descent, And Landing Simulations

NASA Technical Reports Server (NTRS)

Gaebler, John A.; Tolson, Robert H.

2010-01-01

In the study of entry, descent, and landing, Monte Carlo sampling methods are often employed to study the uncertainty in the designed trajectory. The large number of uncertain inputs and outputs, coupled with complicated non-linear models, can make interpretation of the results difficult. Three methods that provide statistical insights are applied to an entry, descent, and landing simulation. The advantages and disadvantages of each method are discussed in terms of the insights gained versus the computational cost. The first method investigated was failure domain bounding which aims to reduce the computational cost of assessing the failure probability. Next a variance-based sensitivity analysis was studied for the ability to identify which input variable uncertainty has the greatest impact on the uncertainty of an output. Finally, probabilistic sensitivity analysis is used to calculate certain sensitivities at a reduced computational cost. These methods produce valuable information that identifies critical mission parameters and needs for new technology, but generally at a significant computational cost.

Path integral Monte Carlo simulations of H2 adsorbed to lithium-doped benzene: A model for hydrogen storage materials

NASA Astrophysics Data System (ADS)

Lindoy, Lachlan P.; Kolmann, Stephen J.; D'Arcy, Jordan H.; Crittenden, Deborah L.; Jordan, Meredith J. T.

2015-11-01

Finite temperature quantum and anharmonic effects are studied in H2-Li+-benzene, a model hydrogen storage material, using path integral Monte Carlo (PIMC) simulations on an interpolated potential energy surface refined over the eight intermolecular degrees of freedom based upon M05-2X/6-311+G(2df,p) density functional theory calculations. Rigid-body PIMC simulations are performed at temperatures ranging from 77 K to 150 K, producing both quantum and classical probability density histograms describing the adsorbed H2. Quantum effects broaden the histograms with respect to their classical analogues and increase the expectation values of the radial and angular polar coordinates describing the location of the center-of-mass of the H2 molecule. The rigid-body PIMC simulations also provide estimates of the change in internal energy, ΔUads, and enthalpy, ΔHads, for H2 adsorption onto Li+-benzene, as a function of temperature. These estimates indicate that quantum effects are important even at room temperature and classical results should be interpreted with caution. Our results also show that anharmonicity is more important in the calculation of U and H than coupling—coupling between the intermolecular degrees of freedom becomes less important as temperature increases whereas anharmonicity becomes more important. The most anharmonic motions in H2-Li+-benzene are the "helicopter" and "ferris wheel" H2 rotations. Treating these motions as one-dimensional free and hindered rotors, respectively, provides simple corrections to standard harmonic oscillator, rigid rotor thermochemical expressions for internal energy and enthalpy that encapsulate the majority of the anharmonicity. At 150 K, our best rigid-body PIMC estimates for ΔUads and ΔHads are -13.3 ± 0.1 and -14.5 ± 0.1 kJ mol-1, respectively.

Managing Contextual Complexity in an Experiential Learning Course: A Dynamic Systems Approach through the Identification of Turning Points in Students' Emotional Trajectories

PubMed Central

Nogueiras, Gloria; Kunnen, E. Saskia; Iborra, Alejandro

2017-01-01

This study adopts a dynamic systems approach to investigate how individuals successfully manage contextual complexity. To that end, we tracked individuals' emotional trajectories during a challenging training course, seeking qualitative changes–turning points—and we tested their relationship with the perceived complexity of the training. The research context was a 5-day higher education course based on process-oriented experiential learning, and the sample consisted of 17 students. The students used a five-point Likert scale to rate the intensity of 16 emotions and the complexity of the training on 8 measurement points. Monte Carlo permutation tests enabled to identify 30 turning points in the 272 emotional trajectories analyzed (17 students * 16 emotions each). 83% of the turning points indicated a change of pattern in the emotional trajectories that consisted of: (a) increasingly intense positive emotions or (b) decreasingly intense negative emotions. These turning points also coincided with particularly complex periods in the training as perceived by the participants (p = 0.003, and p = 0.001 respectively). The relationship between positively-trended turning points in the students' emotional trajectories and the complexity of the training may be interpreted as evidence of a successful management of the cognitive conflict arising from the clash between the students' prior ways of meaning-making and the challenging demands of the training. One of the strengths of this study is that it provides a relatively simple procedure for identifying turning points in developmental trajectories, which can be applied to various longitudinal experiences that are very common in educational and developmental contexts. Additionally, the findings contribute to sustaining that the assumption that complex contextual demands lead unfailingly to individuals' learning is incomplete. Instead, it is how individuals manage complexity which may or may not lead to learning. Finally, this study can also be considered a first step in research on the developmental potential of process-oriented experiential learning training. PMID:28515703

The next GUM and its proposals: a comparison study

NASA Astrophysics Data System (ADS)

Damasceno, J. C.; Couto, P. R. G.

2018-03-01

The Guide to the Expression of Uncertainty in Measurement (GUM) is currently under revision. New proposals for its implementation were circulated in the form of a draft document. Two of the main changes are explored in this work using a Brinell hardness model example. Changes in the evaluation of uncertainty for repeated indications and in the construction of coverage intervals are compared with the classic GUM and with Monte Carlo simulation method.

Monte Carlo Calculations of the Properties of Solid Nitromethane

DTIC Science & Technology

1991-09-01

a pressure of 6.0 GPa (Cromer, Ryan, and Schiferl 1985). The neutron spectroscopy was instrumental in allowing an accurate mathematical description...rotation of the methyl group is only slightly hindered (Cromer, Ryan, and Schiferl 1985). At 3.5 GPa, the x-ray diffraction data inferred that the... Schiferl (1985). We found that below 3.5 GPa, the classical barrier height for rotation was approximately room temperature, consi.tent with a weakly

Monte Carlo and Ab-initio calculation of TM (Ti, V, Cr, Mn, Fe, Co, Ni) doped MgH2 hydride: GGA and SIC approximation

NASA Astrophysics Data System (ADS)

Salmani, E.; Laghrissi, A.; Laamouri, R.; Benchafia, E.; Ez-Zahraouy, H.; Benyoussef, A.

2017-02-01

MgH2: TM (TM: V, Cr, Mn, Fe, Co, Ni) based dilute magnetic semiconductors (DMS) are investigated using first principle calculations. Our results show that the ferromagnetic state is stable when TM introduces magnetic moments as well as intrinsic carriers in TM: Co, V, Cr, Ti; Mg0.95TM0.05H2. Some of the DMS Ferro magnets under study exhibit a half-metallic behavior, which make them suitable for spintronic applications. The double exchange is shown to be the underlying mechanism responsible for the magnetism of such materials. The exchange interactions obtained from first principle calculations and used in a classical Ising model by a Monte Carlo approach resulted in ferromagnetic states with Curie temperatures within the ambient conditions.

Aerocapture Guidance and Performance at Mars for High-Mass Systems

NASA Technical Reports Server (NTRS)

Zumwalt, Carlie H.; Sostaric, Ronald r.; Westhelle, Carlos H.; Cianciolo, Alicia Dwyer

2010-01-01

The objective of this study is to understand the performance associated with using the aerocapture maneuver to slow high-mass systems from an Earth-approach trajectory into orbit around Mars. This work is done in conjunction with the Mars Entry Descent and Landing Systems Analysis (EDL-SA) task to explore candidate technologies necessary for development in order to land large-scale payloads on the surface of Mars. Among the technologies considered include hypersonic inflatable aerodynamic decelerators (HIADs) and rigid mid-lift to drag (L/D) aeroshells. Nominal aerocapture trajectories were developed for the mid-L/D aeroshell and two sizes of HIADs, and Monte Carlo analysis was completed to understand sensitivities to dispersions. Additionally, a study was completed in order to determine the size of the larger of the two HIADs which would maintain design constraints on peak heat rate and diameter. Results show that each of the three aeroshell designs studied is a viable option for landing high-mass payloads as none of the three exceed performance requirements.

Computing approximate random Delta v magnitude probability densities. [for spacecraft trajectory correction

NASA Technical Reports Server (NTRS)

Chadwick, C.

1984-01-01

This paper describes the development and use of an algorithm to compute approximate statistics of the magnitude of a single random trajectory correction maneuver (TCM) Delta v vector. The TCM Delta v vector is modeled as a three component Cartesian vector each of whose components is a random variable having a normal (Gaussian) distribution with zero mean and possibly unequal standard deviations. The algorithm uses these standard deviations as input to produce approximations to (1) the mean and standard deviation of the magnitude of Delta v, (2) points of the probability density function of the magnitude of Delta v, and (3) points of the cumulative and inverse cumulative distribution functions of Delta v. The approximates are based on Monte Carlo techniques developed in a previous paper by the author and extended here. The algorithm described is expected to be useful in both pre-flight planning and in-flight analysis of maneuver propellant requirements for space missions.

OSIRIS-REx Touch-And-Go (TAG) Navigation Performance

NASA Technical Reports Server (NTRS)

Berry, Kevin; Antreasian, Peter; Moreau, Michael C.; May, Alex; Sutter, Brian

2015-01-01

The Origins Spectral Interpretation Resource identification Security Regolith Explorer (OSIRIS-REx) mission is a NASA New Frontiers mission launching in 2016 to rendezvous with the near-Earth asteroid (101955) Bennu in late 2018. Following an extensive campaign of proximity operations activities to characterize the properties of Bennu and select a suitable sample site, OSIRIES-REx will fly a Touch-And-Go (TAG) trajectory to the asteroid's surface to obtain a regolith sample. The paper summarizes the mission design of the TAG sequence, the propulsive required to achieve the trajectory, and the sequence of events leading up to the TAG event. The paper will summarize the Monte-Carlo simulation of the TAG sequence and present analysis results that demonstrate the ability to conduct the TAG within 25 meters of the selected sample site and +-2 cms of the targeted contact velocity. The paper will describe some of the challenges associated with conducting precision navigation operations and ultimately contacting a very small asteroid.

OSIRI-REx Touch and Go (TAG) Navigation Performance

NASA Technical Reports Server (NTRS)

Berry, Kevin; Antreasian, Peter; Moreau, Michael C.; May, Alex; Sutter, Brian

2015-01-01

The Origins Spectral Interpretation Resource Identification Security Regolith Explorer (OSIRIS-REx) mission is a NASA New Frontiers mission launching in 2016 to rendezvous with the near-Earth asteroid (101955) Bennu in late 2018. Following an extensive campaign of proximity operations activities to characterize the properties of Bennu and select a suitable sample site, OSIRIS-REx will fly a Touch-And-Go (TAG) trajectory to the asteroid's surface to obtain a regolith sample. The paper summarizes the mission design of the TAG sequence, the propulsive maneuvers required to achieve the trajectory, and the sequence of events leading up to the TAG event. The paper also summarizes the Monte-Carlo simulation of the TAG sequence and presents analysis results that demonstrate the ability to conduct the TAG within 25 meters of the selected sample site and 2 cm/s of the targeted contact velocity. The paper describes some of the challenges associated with conducting precision navigation operations and ultimately contacting a very small asteroid.

Statistical analysis of particle trajectories in living cells

NASA Astrophysics Data System (ADS)

Briane, Vincent; Kervrann, Charles; Vimond, Myriam

2018-06-01

Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of molecules in living cells. Such inference allows us to understand and determine the organization and function of the cell. The trajectories of particles (e.g., biomolecules) in living cells, computed with the help of object tracking methods, can be modeled with diffusion processes. Three types of diffusion are considered: (i) free diffusion, (ii) subdiffusion, and (iii) superdiffusion. The mean-square displacement (MSD) is generally used to discriminate the three types of particle dynamics. We propose here a nonparametric three-decision test as an alternative to the MSD method. The rejection of the null hypothesis, i.e., free diffusion, is accompanied by claims of the direction of the alternative (subdiffusion or superdiffusion). We study the asymptotic behavior of the test statistic under the null hypothesis and under parametric alternatives which are currently considered in the biophysics literature. In addition, we adapt the multiple-testing procedure of Benjamini and Hochberg to fit with the three-decision-test setting, in order to apply the test procedure to a collection of independent trajectories. The performance of our procedure is much better than the MSD method as confirmed by Monte Carlo experiments. The method is demonstrated on real data sets corresponding to protein dynamics observed in fluorescence microscopy.

Development of an analytical guidance algorithm for lunar descent

NASA Astrophysics Data System (ADS)

Chomel, Christina Tvrdik

In recent years, NASA has indicated a desire to return humans to the moon. With NASA planning manned missions within the next couple of decades, the concept development for these lunar vehicles has begun. The guidance, navigation, and control (GN&C) computer programs that will perform the function of safely landing a spacecraft on the moon are part of that development. The lunar descent guidance algorithm takes the horizontally oriented spacecraft from orbital speeds hundreds of kilometers from the desired landing point to the landing point at an almost vertical orientation and very low speed. Existing lunar descent GN&C algorithms date back to the Apollo era with little work available for implementation since then. Though these algorithms met the criteria of the 1960's, they are cumbersome today. At the basis of the lunar descent phase are two elements: the targeting, which generates a reference trajectory, and the real-time guidance, which forces the spacecraft to fly that trajectory. The Apollo algorithm utilizes a complex, iterative, numerical optimization scheme for developing the reference trajectory. The real-time guidance utilizes this reference trajectory in the form of a quartic rather than a more general format to force the real-time trajectory errors to converge to zero; however, there exist no guarantees under any conditions for this convergence. The proposed algorithm implements a purely analytical targeting algorithm used to generate two-dimensional trajectories "on-the-fly"' or to retarget the spacecraft to another landing site altogether. It is based on the analytical solutions to the equations for speed, downrange, and altitude as a function of flight path angle and assumes two constant thrust acceleration curves. The proposed real-time guidance algorithm has at its basis the three-dimensional non-linear equations of motion and a control law that is proven to converge under certain conditions through Lyapunov analysis to a reference trajectory formatted as a function of downrange, altitude, speed, and flight path angle. The two elements of the guidance algorithm are joined in Monte Carlo analysis to prove their robustness to initial state dispersions and mass and thrust errors. The robustness of the retargeting algorithm is also demonstrated.

Entry Abort Determination Using Non-Adaptive Neural Networks for Mars Precision Landers

NASA Technical Reports Server (NTRS)

Graybeal, Sarah R.; Kranzusch, Kara M.

2005-01-01

The 2009 Mars Science Laboratory (MSL) will attempt the first precision landing on Mars using a modified version of the Apollo Earth entry guidance program. The guidance routine, Entry Terminal Point Controller (ETPC), commands the deployment of a supersonic parachute after converging the range to the landing target. For very dispersed cases, ETPC may not converge the range to the target and safely command parachute deployment within Mach number and dynamic pressure constraints. A full-lift up abort can save 85% of these failed trajectories while abandoning the precision landing objective. Though current MSL requirements do not call for an abort capability, an autonomous abort capability may be desired, for this mission or future Mars precision landers, to make the vehicle more robust. The application of artificial neural networks (NNs) as an abort determination technique was evaluated by personnel at the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC). In order to implement an abort, a failed trajectory needs to be recognized in real time. Abort determination is dependent upon several trajectory parameters whose relationships to vehicle survival are not well understood, and yet the lander must be trained to recognize unsafe situations. Artificial neural networks (NNs) provide a way to model these parameters and can provide MSL with the artificial intelligence necessary to independently declare an abort. Using the 2009 Mars Science Laboratory (MSL) mission as a case study, a non-adaptive NN was designed, trained and tested using Monte Carlo simulations of MSL descent and incorporated into ETPC. Neural network theory, the development history of the MSL NN, and initial testing with severe dust storm entry trajectory cases are discussed in Reference 1 and will not be repeated here. That analysis demonstrated that NNs are capable of recognizing failed descent trajectories and can significantly increase the survivability of MSL for very dispersed cases. NN testing was then broadened to evaluate fully dispersed entry trajectories. The NN correctly classified 99.7% of descent trajectories as abort or nonabort and reduced the probability of an unsafe parachute deployment by 83%. This second, broader testing phase is discussed in this paper.

Evidence of Vertical and Horizontal Motions on Venus: Maxwell Montes

NASA Astrophysics Data System (ADS)

Ansan, V.; Vergely, P.

1995-01-01

Based on full-resolution Magellan radar images, the detailed structural analysis of central Ishtar Terra (Venus) provides new insight to the understanding of the Venusian tectonics. Ishtar Terra, centered on 65° N latitude and 0° E longitude includes a high plateau. Lakshmi Planum, surrounded by highlands, the most important being Maxwell Montes to the East. Structural analysis has been performed with classical remote-sensing methods. Folds and faults identified on radar images were reported on structural map. Their type and distribution allowed to define the style of the crustal deformation and the context in which these structures formed. This analysis shows that Lakshmi Planum formed under a crustal stretching associated with a volcanic activity. This area then became a relatively steady platform, throughout the formation of Maxwell Montes mountain belt. Maxwell Montes is characterized by a series of NNW-SSE trending thrust faults dipping to the East, formed during a WSW-ESE horizontal shortening. In its NW quarter, the mountain belt shows a disturbed deformation controlled by pre-existing grabens and old vertical crustal fault zone. The deformation of this area is characterized by a shortening of cover above a flat detachment zone, with a progressive accommodation to the southwest. All these tectonic structures show evidence of horizontal and vertical crustal movements on Venus, with subsidence, mountain belt raise, West regional overthrusting of this mountain belt, and regional shear zone.

Potentials of Mean Force With Ab Initio Mixed Hamiltonian Models of Solvation

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

Dupuis, Michel; Schenter, Gregory K.; Garrett, Bruce C.

2003-08-01

We give an account of a computationally tractable and efficient procedure for the calculation of potentials of mean force using mixed Hamiltonian models of electronic structure where quantum subsystems are described with computationally intensive ab initio wavefunctions. The mixed Hamiltonian is mapped into an all-classical Hamiltonian that is amenable to a thermodynamic perturbation treatment for the calculation of free energies. A small number of statistically uncorrelated (solute-solvent) configurations are selected from the Monte Carlo random walk generated with the all-classical Hamiltonian approximation. Those are used in the averaging of the free energy using the mixed quantum/classical Hamiltonian. The methodology ismore » illustrated for the micro-solvated SN2 substitution reaction of methyl chloride by hydroxide. We also compare the potential of mean force calculated with the above protocol with an approximate formalism, one in which the potential of mean force calculated with the all-classical Hamiltonian is simply added to the energy of the isolated (non-solvated) solute along the reaction path. Interestingly the latter approach is found to be in semi-quantitative agreement with the full mixed Hamiltonian approximation.« less

Thermal properties of spin-S Kitaev-Heisenberg model on a honeycomb lattice

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi; Yamaji, Youhei

2018-05-01

Temperature (T) dependence of heat capacity C (T) in the S = 1 / 2 Kitaev honeycomb model shows a double-peak structure resulting from fractionalization of spins into two kinds of Majorana fermions. Recently it has been discussed that the double-peak structure in C (T) is also observed in magnetic ordered phases of the S = 1 / 2 Kitaev-Heisenberg (KH) model on a honeycomb lattice when the system is located in the vicinity of the Kitaev's spin liquid phase. In addition to the S = 1 / 2 spin case, similar double-peak structure has been confirmed in the KH honeycomb model for classical Heisenberg spins, where spin S is regarded as S → ∞ . We investigate spin-S dependence of C (T) for the KH honeycomb models by using thermal pure quantum state. We also perform classical Monte Carlo calculations to obtain C (T) for the classical KH model. From obtained results, we find that the origin of the high-temperature peak is different between the quantum spin case with small Ss and the classical Heisenberg spin case. Furthermore, the high-temperature peak in the quantum spin case, which is one of the clues for fractionalization of spins, disappears for S > 1 .

A Deterministic Transport Code for Space Environment Electrons

NASA Technical Reports Server (NTRS)

Nealy, John E.; Chang, C. K.; Norman, Ryan B.; Blattnig, Steve R.; Badavi, Francis F.; Adamczyk, Anne M.

2010-01-01

A deterministic computational procedure has been developed to describe transport of space environment electrons in various shield media. This code is an upgrade and extension of an earlier electron code. Whereas the former code was formulated on the basis of parametric functions derived from limited laboratory data, the present code utilizes well established theoretical representations to describe the relevant interactions and transport processes. The shield material specification has been made more general, as have the pertinent cross sections. A combined mean free path and average trajectory approach has been used in the transport formalism. Comparisons with Monte Carlo calculations are presented.

Analysis of SRB reentry acoustic environments. [aeroacoustic spectra determined from wind tunnel tests

NASA Technical Reports Server (NTRS)

Coffin, T.; Dandridge, R. E.; Haddock, U. W.

1979-01-01

Space shuttle solid rocket booster reentry aeroacoustic environments were estimated. Particular emphasis was given to the aft skirt/exit plane region for the Mach number regime 0.6 = or greater than M infinity = or less than 3.5. The analysis is based on the evaluation of wind tunnel model results in conjunction with Monte Carlo simulation of trajectory parameters. The experimental approach is described as well as the evaluation process utilized. Predicted environments are presented in terms of one-third octave band spectra representing space averaged values for critical regions on the solid rocket booster.

Pair Interaction of Dislocations in Two-Dimensional Crystals

NASA Astrophysics Data System (ADS)

Eisenmann, C.; Gasser, U.; Keim, P.; Maret, G.; von Grünberg, H. H.

2005-10-01

The pair interaction between crystal dislocations is systematically explored by analyzing particle trajectories of two-dimensional colloidal crystals measured by video microscopy. The resulting pair energies are compared to Monte Carlo data and to predictions derived from the standard Hamiltonian of the elastic theory of dislocations. Good agreement is found with respect to the distance and temperature dependence of the interaction potential, but not regarding the angle dependence where discrete lattice effects become important. Our results on the whole confirm that the dislocation Hamiltonian allows a quantitative understanding of the formation and interaction energies of dislocations in two-dimensional crystals.

Nothing to lose: why early career scientists make ideal entrepreneurs.

PubMed

Thon, Jonathan N

2014-12-01

An entrepreneurial movement within science strives to invert the classical trajectory of academic research careers by positioning trainees at the apex of burgeoning industries. Young scientists today have nothing to lose and everything to gain by pursuing this 'third road', and academic institutes and established companies only stand to benefit from supporting this emerging movement of discovery research with economic purpose. Copyright © 2014 Elsevier Ltd. All rights reserved.

Nonadiabatic nuclear dynamics of the ammonia cation studied by surface hopping classical trajectory calculations

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

Belyaev, Andrey K., E-mail: belyaev@herzen.spb.ru; Domcke, Wolfgang, E-mail: wolfgang.domcke@ch.tum.de; Lasser, Caroline, E-mail: classer@ma.tum.de

The Landau–Zener (LZ) type classical-trajectory surface-hopping algorithm is applied to the nonadiabatic nuclear dynamics of the ammonia cation after photoionization of the ground-state neutral molecule to the excited states of the cation. The algorithm employs a recently proposed formula for nonadiabatic LZ transition probabilities derived from the adiabatic potential energy surfaces. The evolution of the populations of the ground state and the two lowest excited adiabatic states is calculated up to 200 fs. The results agree well with quantum simulations available for the first 100 fs based on the same potential energy surfaces. Three different time scales are detected formore » the nuclear dynamics: Ultrafast Jahn–Teller dynamics between the excited states on a 5 fs time scale; fast transitions between the excited state and the ground state within a time scale of 20 fs; and relatively slow partial conversion of a first-excited-state population to the ground state within a time scale of 100 fs. Beyond 100 fs, the adiabatic electronic populations are nearly constant due to a dynamic equilibrium between the three states. The ultrafast nonradiative decay of the excited-state populations provides a qualitative explanation of the experimental evidence that the ammonia cation is nonfluorescent.« less

Temperature-dependent kinetic measurements and quasi-classical trajectory studies for the OH(+) + H2/D2 → H2O(+)/HDO(+) + H/D reactions.

PubMed

Martinez, Oscar; Ard, Shaun G; Li, Anyang; Shuman, Nicholas S; Guo, Hua; Viggiano, Albert A

2015-09-21

We have measured the temperature-dependent kinetics for the reactions of OH(+) with H2 and D2 using a selected ion flow tube apparatus. Reaction occurs via atom abstraction to result in H2O(+)/HDO(+) + H/D. Room temperature rate coefficients are in agreement with prior measurements and resulting temperature dependences are T(0.11) for the hydrogen and T(0.25) for the deuterated reactions. This work is prompted in part by recent theoretical work that mapped a full-dimensional global potential energy surface of H3O(+) for the OH(+) + H2 → H + H2O(+) reaction [A. Li and H. Guo, J. Phys. Chem. A 118, 11168 (2014)], and reported results of quasi-classical trajectory calculations, which are extended to a wider temperature range and initial rotational state specification here. Our experimental results are in excellent agreement with these calculations which accurately predict the isotope effect in addition to an enhancement of the reaction rate constant due to the molecular rotation of OH(+). The title reaction is of high importance to astrophysical models, and the temperature dependence of the rate coefficients determined here should now allow for better understanding of this reaction at temperatures more relevant to the interstellar medium.

A quasi-classical study of energy transfer in collisions of hyperthermal H atoms with SO2 molecules.

PubMed

da Silva, Ramon S; Garrido, Juan D; Ballester, Maikel Y

2017-08-28

A deep understanding of energy transfer processes in molecular collisions is at central attention in physical chemistry. Particularly vibrational excitation of small molecules colliding with hot light atoms, via a metastable complex formation, has shown to be an efficient manner of enhancing reactivity. A quasi-classical trajectory study of translation-to-vibration energy transfer (T-V ET) in collisions of hyperthermal H( 2 S) atoms with SO 2 (X̃ 1 A ' ) molecules is presented here. For such a study, a double many-body expansion potential energy surface previously reported for HSO 2 ( 2 A) is used. This work was motivated by recent experiments by Ma et al. studying collisions of H + SO 2 at the translational energy of 59 kcal/mol [J. Ma et al., Phys. Rev. A 93, 040702 (2016)]. Calculations reproduce the experimental evidence that during majority of inelastic non-reactive collision processes, there is a metastable intermediate formation (HOSO or HSO 2 ). Nevertheless, the analysis of the trajectories shows that there are two distinct mechanisms in the T-V ET process: direct and indirect. Direct T-V processes are responsible for the high population of SO 2 with relatively low vibrational excitation energy, while indirect ones dominate the conversion from translational energy to high values of the vibrational counterpart.

Atomic photoionization processes under magnification

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

Lepine, F.; Bordas, Ch.; Nicole, C.

2004-09-01

Recently, classical simulations of threshold photoionization in the presence of an electric field have shown that a clear distinction between direct and indirect trajectories followed by the outgoing electron can be observed in the patterns of electron impacts on a two-dimensional detector. Subsequently, slow photoelectron imaging experiments have been reported where this distinction could be observed in atomic xenon. Furthermore, using a magnifying electrostatic lens to improve the velocity-map imaging technique, oscillatory patterns were observed modulating the classical envelope that was measured in the experiments of Nicole et al. [Phys. Rev. Lett. 88, 133001 (2002)]. This extension of slow photoelectronmore » imaging, called photoionization microscopy, relies on the existence of interferences between various trajectories by which the electron moves from the atom to the plane of observation. In this article we present the main experimental results obtained both in slow photoelectron imaging and in photoionization microscopy. The formation of the interference pattern is discussed in the framework of a semiclassical model that is described in detail elsewhere. The qualitative information that can be drawn from the experiments is discussed, and the potential applications of photoionization microscopy are considered. Particular attention is paid to the role of continuum Stark resonances that appear between the saddle point in the Coulomb+dc field potential and the field-free ionization limit.« less

Impact of finite receiver-aperture size in a non-line-of-sight single-scatter propagation model.

PubMed

Elshimy, Mohamed A; Hranilovic, Steve

2011-12-01

In this paper, a single-scatter propagation model is developed that expands the classical model by considering a finite receiver-aperture size for non-line-of-sight communication. The expanded model overcomes some of the difficulties with the classical model, most notably, inaccuracies in scenarios with short range and low elevation angle where significant scattering takes place near the receiver. The developed model does not approximate the receiver aperture as a point, but uses its dimensions for both field-of-view and solid-angle computations. To verify the model, a Monte Carlo simulation of photon transport in a turbid medium is applied. Simulation results for temporal responses and path losses are presented at a wavelength of 260 nm that lies in the solar-blind ultraviolet region.

Cluster-Glass Phase in Pyrochlore X Y Antiferromagnets with Quenched Disorder

NASA Astrophysics Data System (ADS)

Andrade, Eric C.; Hoyos, José A.; Rachel, Stephan; Vojta, Matthias

2018-03-01

We study the impact of quenched disorder (random exchange couplings or site dilution) on easy-plane pyrochlore antiferromagnets. In the clean system, order by disorder selects a magnetically ordered state from a classically degenerate manifold. In the presence of randomness, however, different orders can be chosen locally depending on details of the disorder configuration. Using a combination of analytical considerations and classical Monte Carlo simulations, we argue that any long-range-ordered magnetic state is destroyed beyond a critical level of randomness where the system breaks into magnetic domains due to random exchange anisotropies, becoming, therefore, a glass of spin clusters, in accordance with the available experimental data. These random anisotropies originate from off-diagonal exchange couplings in the microscopic Hamiltonian, establishing their relevance to other magnets with strong spin-orbit coupling.

Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms

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

Pederson, Mark R., E-mail: mark.pederson@science.doe.gov

2015-02-14

A recent modification of the Perdew-Zunger self-interaction-correction to the density-functional formalism has provided a framework for explicitly restoring unitary invariance to the expression for the total energy. The formalism depends upon construction of Löwdin orthonormalized Fermi-orbitals which parametrically depend on variational quasi-classical electronic positions. Derivatives of these quasi-classical electronic positions, required for efficient minimization of the self-interaction corrected energy, are derived and tested, here, on atoms. Total energies and ionization energies in closed-shell singlet atoms, where correlation is less important, using the Perdew-Wang 1992 Local Density Approximation (PW92) functional, are in good agreement with experiment and non-relativistic quantum-Monte-Carlo results albeitmore » slightly too low.« less

Evaluation of Adherence to Nutritional Intervention Through Trajectory Analysis.

PubMed

Sevilla-Villanueva, B; Gibert, K; Sanchez-Marre, M; Fito, M; Covas, M I

2017-05-01

Classical pre-post intervention studies are often analyzed using traditional statistics. Nevertheless, the nutritional interventions have small effects on the metabolism and traditional statistics are not enough to detect these subtle nutrient effects. Generally, this kind of studies assumes that the participants are adhered to the assigned dietary intervention and directly analyzes its effects over the target parameters. Thus, the evaluation of adherence is generally omitted. Although, sometimes, participants do not effectively adhere to the assigned dietary guidelines. For this reason, the trajectory map is proposed as a visual tool where dietary patterns of individuals can be followed during the intervention and can also be related with nutritional prescriptions. The trajectory analysis is also proposed allowing both analysis: 1) adherence to the intervention and 2) intervention effects. The analysis is made by projecting the differences of the target parameters over the resulting trajectories between states of different time-stamps which might be considered either individually or by groups. The proposal has been applied over a real nutritional study showing that some individuals adhere better than others and some individuals of the control group modify their habits during the intervention. In addition, the intervention effects are different depending on the type of individuals, even some subgroups have opposite response to the same intervention.

Monte Carlo Analysis of Quantum Transport and Fluctuations in Semiconductor 2

DTIC Science & Technology

1988-02-01

predicted by quantum transport theory is less than that predicted by classical transport for t < 0.1ps as shown in Fig.2.19. 29 2.2.5 Semiclassical Limit...terms containing any number of OUT scattering events between two given IN scattering can be summed up analitically . Let us consider, for example, the...fields), where analitical techniques cannot be succesfully applied without introducing severe approximations. Furthermore, a direct simulafion of the