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.

Direct Simulation Monte Carlo Application of the Three Dimensional Forced Harmonic Oscillator Model

DTIC Science & Technology

2017-12-07

quasi -classical scattering theory [3,4] or trajectory [5] calculations, semiclassical, as well as close-coupled [6,7] or full [8] quantum mechanical...the quasi -classical trajectory (QCT) calculations approach for ab initio modeling of collision processes. The DMS method builds on an earlier work...nu ar y 30 , 2 01 8 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .T 52 28 to directly use quasi -classical or quantum mechanic

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.

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.

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.

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…

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

Classical-trajectory simulation of accelerating neutral atoms with polarized intense laser pulses

NASA Astrophysics Data System (ADS)

Xia, Q. Z.; Fu, L. B.; Liu, J.

2013-03-01

In the present paper, we perform the classical trajectory Monte Carlo simulation of the complex dynamics of accelerating neutral atoms with linearly or circularly polarized intense laser pulses. Our simulations involve the ion motion as well as the tunneling ionization and the scattering dynamics of valence electron in the combined Coulomb and electromagnetic fields, for both helium (He) and magnesium (Mg). We show that for He atoms, only linearly polarized lasers can effectively accelerate the atoms, while for Mg atoms, we find that both linearly and circularly polarized lasers can successively accelerate the atoms. The underlying mechanism is discussed and the subcycle dynamics of accelerating trajectories is investigated. We have compared our theoretical results with a recent experiment [Eichmann Nature (London)NATUAS0028-083610.1038/nature08481 461, 1261 (2009)].

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.

Investigation of Kp- and Kd-atom formation and their collisional processes with hydrogen and deuterium targets by the classical-trajectory Monte Carlo method

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

Raeisi, G. M.; Department of Physics, Shahrekord University, Shahrekord 115; Kalantari, S. Z.

The classical-trajectory Monte Carlo method has been used to study the capture of negative kaons by hydrogen and deuterium atoms; subsequently, the elastic scattering, Stark mixing, and Coulomb deexcitation cross sections of Kp and Kd atoms have been determined. The results for kaonic atom formation confirm the initial conditions that have been parametrically applied by most atomic cascade models. Our results show that Coulomb deexcitation in Kp and Kd atoms with {Delta}n>1 is important in addition to n=1. We have shown that the contribution of molecular structure effects to the cross sections of the collisional processes is larger than themore » isotopic effects of the targets. We have also compared our results with the semiclassical approaches.« less

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.

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.

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

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.

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.

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.

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.

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.

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

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.

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

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.

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.

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.

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.

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.

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.

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…

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.

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

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.

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.

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.

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

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…

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

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

Stoichiometric network analysis and associated dimensionless kinetic equations. Application to a model of the Bray-Liebhafsky reaction.

PubMed

Schmitz, Guy; Kolar-Anić, Ljiljana Z; Anić, Slobodan R; Cupić, Zeljko D

2008-12-25

The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.

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.

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.

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.

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

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

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.

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.

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.

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

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

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.

Hyperbolic geometrical optics: Hyperbolic glass

NASA Astrophysics Data System (ADS)

De Micheli, Enrico; Scorza, Irene; Viano, Giovanni Alberto

2006-02-01

We study the geometrical optics generated by a refractive index of the form n (x,y)=1/y (y>0), where y is the coordinate of the vertical axis in an orthogonal reference frame in R2. We thus obtain what we call "hyperbolic geometrical optics" since the ray trajectories are geodesics in the Poincaré-Lobachevsky half-plane H2. Then we prove that the constant phase surface are horocycles and obtain the horocyclic waves, which are closely related to the classical Poisson kernel and are the analogs of the Euclidean plane waves. By studying the transport equation in the Beltrami pseudosphere, we prove (i) the conservation of the flow in the entire strip 0

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.

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.

A Reliability Comparison of Classical and Stochastic Thickness Margin Approaches to Address Material Property Uncertainties for the Orion Heat Shield

NASA Technical Reports Server (NTRS)

Sepka, Steve; Vander Kam, Jeremy; McGuire, Kathy

2018-01-01

The Orion Thermal Protection System (TPS) margin process uses a root-sum-square approach with branches addressing trajectory, aerothermodynamics, and material response uncertainties in ablator thickness design. The material response branch applies a bond line temperature reduction between the Avcoat ablator and EA9394 adhesive by 60 C (108 F) from its peak allowed value of 260 C (500 F). This process is known as the Bond Line Temperature Material Margin (BTMM) and is intended to cover material property and performance uncertainties. The value of 60 C (108 F) is a constant, applied at any spacecraft body location and for any trajectory. By varying only material properties in a random (monte carlo) manner, the perl-based script mcCHAR is used to investigate the confidence interval provided by the BTMM. In particular, this study will look at various locations on the Orion heat shield forebody for a guided and an abort (ballistic) trajectory.

A Reliability Comparison of Classical and Stochastic Thickness Margin Approaches to Address Material Property Uncertainties for the Orion Heat Shield

NASA Technical Reports Server (NTRS)

Sepka, Steven A.; McGuire, Mary Kathleen; Vander Kam, Jeremy C.

2018-01-01

The Orion Thermal Protection System (TPS) margin process uses a root-sum-square approach with branches addressing trajectory, aerothermodynamics, and material response uncertainties in ablator thickness design. The material response branch applies a bondline temperature reduction between the Avcoat ablator and EA9394 adhesive by 60 C (108 F) from its peak allowed value of 260 C (500 F). This process is known as the Bond Line Temperature Material Margin (BTMM) and is intended to cover material property and performance uncertainties. The value of 60 C (108 F) is a constant, applied at any spacecraft body location and for any trajectory. By varying only material properties in a random (monte carlo) manner, the perl-based script mcCHAR is used to investigate the confidence interval provided by the BTMM. In particular, this study will look at various locations on the Orion heat shield forebody for a guided and an abort (ballistic) trajectory.

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

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.

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.

SU-E-T-489: Quantum versus Classical Trajectory Monte Carlo Simulations of Low Energy Electron Transport.

PubMed

Thomson, R; Kawrakow, I

2012-06-01

Widely-used classical trajectory Monte Carlo simulations of low energy electron transport neglect the quantum nature of electrons; however, at sub-1 keV energies quantum effects have the potential to become significant. This work compares quantum and classical simulations within a simplified model of electron transport in water. Electron transport is modeled in water droplets using quantum mechanical (QM) and classical trajectory Monte Carlo (MC) methods. Water droplets are modeled as collections of point scatterers representing water molecules from which electrons may be isotropically scattered. The role of inelastic scattering is investigated by introducing absorption. QM calculations involve numerically solving a system of coupled equations for the electron wavefield incident on each scatterer. A minimum distance between scatterers is introduced to approximate structured water. The average QM water droplet incoherent cross section is compared with the MC cross section; a relative error (RE) on the MC results is computed. RE varies with electron energy, average and minimum distances between scatterers, and scattering amplitude. The mean free path is generally the relevant length scale for estimating RE. The introduction of a minimum distance between scatterers increases RE substantially (factors of 5 to 10), suggesting that the structure of water must be modeled for accurate simulations. Inelastic scattering does not improve agreement between QM and MC simulations: for the same magnitude of elastic scattering, the introduction of inelastic scattering increases RE. Droplet cross sections are sensitive to droplet size and shape; considerable variations in RE are observed with changing droplet size and shape. At sub-1 keV energies, quantum effects may become non-negligible for electron transport in condensed media. Electron transport is strongly affected by the structure of the medium. Inelastic scatter does not improve agreement between QM and MC simulations of low energy electron transport in condensed media. © 2012 American Association of Physicists in Medicine.

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.

Study for elevator cage position during the braking period

NASA Astrophysics Data System (ADS)

Ungureanu, M.; Crăciun, I.; Bănică, M.; Dăscălescu, A.

2016-08-01

An important problem in order to study an elevator cage position for its braking period is to establish a correlation between the studies in the fields of mechanics and electric. The classical approaches to establish the elevator kinematic parameters are position, velocity and acceleration, but the last studies performed in order to determine the positioning performed by introducing supplementary another parameter - the jerk- which is derived with respect to time of acceleration. Thus we get a precise method for cage motion control for third-order trajectory planning.

The dissociative chemisorption of methane on Ni(100) and Ni(111): Classical and quantum studies based on the reaction path Hamiltonian

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

Mastromatteo, Michael; Jackson, Bret, E-mail: jackson@chem.umass.edu

Electronic structure methods based on density functional theory are used to construct a reaction path Hamiltonian for CH{sub 4} dissociation on the Ni(100) and Ni(111) surfaces. Both quantum and quasi-classical trajectory approaches are used to compute dissociative sticking probabilities, including all molecular degrees of freedom and the effects of lattice motion. Both approaches show a large enhancement in sticking when the incident molecule is vibrationally excited, and both can reproduce the mode specificity observed in experiments. However, the quasi-classical calculations significantly overestimate the ground state dissociative sticking at all energies, and the magnitude of the enhancement in sticking with vibrationalmore » excitation is much smaller than that computed using the quantum approach or observed in the experiments. The origin of this behavior is an unphysical flow of zero point energy from the nine normal vibrational modes into the reaction coordinate, giving large values for reaction at energies below the activation energy. Perturbative assumptions made in the quantum studies are shown to be accurate at all energies studied.« less

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)

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.

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

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

Classic and Golli Myelin Basic Protein have distinct developmental trajectories in human visual cortex.

PubMed

Siu, Caitlin R; Balsor, Justin L; Jones, David G; Murphy, Kathryn M

2015-01-01

Traditionally, myelin is viewed as insulation around axons, however, more recent studies have shown it also plays an important role in plasticity, axonal metabolism, and neuroimmune signaling. Myelin is a complex multi-protein structure composed of hundreds of proteins, with Myelin Basic Protein (MBP) being the most studied. MBP has two families: Classic-MBP that is necessary for activity driven compaction of myelin around axons, and Golli-MBP that is found in neurons, oligodendrocytes, and T-cells. Furthermore, Golli-MBP has been called a "molecular link" between the nervous and immune systems. In visual cortex specifically, myelin proteins interact with immune processes to affect experience-dependent plasticity. We studied myelin in human visual cortex using Western blotting to quantify Classic- and Golli-MBP expression in post-mortem tissue samples ranging in age from 20 days to 80 years. We found that Classic- and Golli-MBP have different patterns of change across the lifespan. Classic-MBP gradually increases to 42 years and then declines into aging. Golli-MBP has early developmental changes that are coincident with milestones in visual system sensitive period, and gradually increases into aging. There are three stages in the balance between Classic- and Golli-MBP expression, with Golli-MBP dominating early, then shifting to Classic-MBP, and back to Golli-MBP in aging. Also Golli-MBP has a wave of high inter-individual variability during childhood. These results about cortical MBP expression are timely because they compliment recent advances in MRI techniques that produce high resolution maps of cortical myelin in normal and diseased brain. In addition, the unique pattern of Golli-MBP expression across the lifespan suggests that it supports high levels of neuroimmune interaction in cortical development and in aging.

Effect of suspension kinematic on 14 DOF vehicle model

NASA Astrophysics Data System (ADS)

Wongpattananukul, T.; Chantharasenawong, C.

2017-12-01

Computer simulations play a major role in shaping modern science and engineering. They reduce time and resource consumption in new studies and designs. Vehicle simulations have been studied extensively to achieve a vehicle model used in minimum lap time solution. Simulation result accuracy depends on the abilities of these models to represent real phenomenon. Vehicles models with 7 degrees of freedom (DOF), 10 DOF and 14 DOF are normally used in optimal control to solve for minimum lap time. However, suspension kinematics are always neglected on these models. Suspension kinematics are defined as wheel movements with respect to the vehicle body. Tire forces are expressed as a function of wheel slip and wheel position. Therefore, the suspension kinematic relation is appended to the 14 DOF vehicle model to investigate its effects on the accuracy of simulate trajectory. Classical 14 DOF vehicle model is chosen as baseline model. Experiment data is collected from formula student style car test runs as baseline data for simulation and comparison between baseline model and model with suspension kinematic. Results show that in a single long turn there is an accumulated trajectory error in baseline model compared to model with suspension kinematic. While in short alternate turns, the trajectory error is much smaller. These results show that suspension kinematic had an effect on the trajectory simulation of vehicle. Which optimal control that use baseline model will result in inaccuracy control scheme.

Fully adaptive propagation of the quantum-classical Liouville equation

NASA Astrophysics Data System (ADS)

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

2004-05-01

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

Fully adaptive propagation of the quantum-classical Liouville equation.

PubMed

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

2004-05-15

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

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.

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.

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.

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…

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.

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).

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

3D hand motion trajectory prediction from EEG mu and beta bandpower.

PubMed

Korik, A; Sosnik, R; Siddique, N; Coyle, D

2016-01-01

A motion trajectory prediction (MTP) - based brain-computer interface (BCI) aims to reconstruct the three-dimensional (3D) trajectory of upper limb movement using electroencephalography (EEG). The most common MTP BCI employs a time series of bandpass-filtered EEG potentials (referred to here as the potential time-series, PTS, model) for reconstructing the trajectory of a 3D limb movement using multiple linear regression. These studies report the best accuracy when a 0.5-2Hz bandpass filter is applied to the EEG. In the present study, we show that spatiotemporal power distribution of theta (4-8Hz), mu (8-12Hz), and beta (12-28Hz) bands are more robust for movement trajectory decoding when the standard PTS approach is replaced with time-varying bandpower values of a specified EEG band, ie, with a bandpower time-series (BTS) model. A comprehensive analysis comprising of three subjects performing pointing movements with the dominant right arm toward six targets is presented. Our results show that the BTS model produces significantly higher MTP accuracy (R~0.45) compared to the standard PTS model (R~0.2). In the case of the BTS model, the highest accuracy was achieved across the three subjects typically in the mu (8-12Hz) and low-beta (12-18Hz) bands. Additionally, we highlight a limitation of the commonly used PTS model and illustrate how this model may be suboptimal for decoding motion trajectory relevant information. Although our results, showing that the mu and beta bands are prominent for MTP, are not in line with other MTP studies, they are consistent with the extensive literature on classical multiclass sensorimotor rhythm-based BCI studies (classification of limbs as opposed to motion trajectory prediction), which report the best accuracy of imagined limb movement classification using power values of mu and beta frequency bands. The methods proposed here provide a positive step toward noninvasive decoding of imagined 3D hand movements for movement-free BCIs. © 2016 Elsevier B.V. All rights reserved.

Optimum Climb to Cruise Noise Trajectories for the High Speed Civil Transport

NASA Technical Reports Server (NTRS)

Berton, Jeffrey J.

2003-01-01

By entraining large quantities of ambient air into advanced ejector nozzles, the jet noise of the proposed High Speed Civil Transport (HSCT) is expected to be reduced to levels acceptable for airport-vicinity noise certification. Away from the airport, however, this entrained air is shut off and the engines are powered up from their cutback levels to provide better thrust for the climb to cruise altitude. Unsuppressed jet noise levels propagating to the ground far from the airport are expected to be high. Complicating this problem is the HSCT's relative noise level with respect to the subsonic commercial fleet of 2010, which is expected to be much quieter than it is today after the retirement of older, louder, domestic stage II aircraft by the year 2000. In this study, the classic energy state approximation theory is extended to calculate trajectories that minimize the climb to cruise noise of the HSCT. The optimizer dynamically chooses the optimal altitude velocity trajectory, the engine power setting, and whether the ejector should be stowed or deployed with respect to practical aircraft climb constraints and noise limits.

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

Rotational dynamics of a diatomic molecular ion in a Paul trap

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

Hashemloo, A.; Dion, C. M., E-mail: claude.dion@umu.se

We present models for a heteronuclear diatomic molecular ion in a linear Paul trap in a rigid-rotor approximation, one purely classical and the other where the center-of-mass motion is treated classically, while rotational motion is quantized. We study the rotational dynamics and their influence on the motion of the center-of-mass, in the presence of the coupling between the permanent dipole moment of the ion and the trapping electric field. We show that the presence of the permanent dipole moment affects the trajectory of the ion and that it departs from the Mathieu equation solution found for atomic ions. For themore » case of quantum rotations, we also evidence the effect of the above-mentioned coupling on the rotational states of the ion.« less

Nonsequential double ionization with mid-infrared laser fields

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

Li, Ying -Bin; Wang, Xu; Yu, Ben -Hai

Using a full-dimensional Monte Carlo classical ensemble method, we present a theoretical study of atomic nonsequential double ionization (NSDI) with mid-infrared laser fields, and compare with results from near-infrared laser fields. Unlike single-electron strong-field processes, double ionization shows complex and unexpected interplays between the returning electron and its parent ion core. As a result of these interplays, NSDI for mid-IR fields is dominated by second-returning electron trajectories, instead of first-returning trajectories for near-IR fields. Here, some complex NSDI channels commonly happen with near-IR fields, such as the recollision-excitation-with-subsequent-ionization (RESI) channel, are virtually shut down by mid-IR fields. Besides, the finalmore » energies of the two electrons can be extremely unequal, leading to novel e-e momentum correlation spectra that can be measured experimentally.« less

Nonsequential double ionization with mid-infrared laser fields

DOE PAGES

Li, Ying -Bin; Wang, Xu; Yu, Ben -Hai; ...

2016-11-18

Using a full-dimensional Monte Carlo classical ensemble method, we present a theoretical study of atomic nonsequential double ionization (NSDI) with mid-infrared laser fields, and compare with results from near-infrared laser fields. Unlike single-electron strong-field processes, double ionization shows complex and unexpected interplays between the returning electron and its parent ion core. As a result of these interplays, NSDI for mid-IR fields is dominated by second-returning electron trajectories, instead of first-returning trajectories for near-IR fields. Here, some complex NSDI channels commonly happen with near-IR fields, such as the recollision-excitation-with-subsequent-ionization (RESI) channel, are virtually shut down by mid-IR fields. Besides, the finalmore » energies of the two electrons can be extremely unequal, leading to novel e-e momentum correlation spectra that can be measured experimentally.« less

Field signature for apparently superluminal particle motion

NASA Astrophysics Data System (ADS)

Land, Martin

2015-05-01

In the context of Stueckelberg's covariant symplectic mechanics, Horwitz and Aharonovich [1] have proposed a simple mechanism by which a particle traveling below light speed almost everywhere may exhibit a transit time that suggests superluminal motion. This mechanism, which requires precise measurement of the particle velocity, involves a subtle perturbation affecting the particle's recorded time coordinate caused by virtual pair processes. The Stueckelberg framework is particularly well suited to such problems, because it permits pair creation/annihilation at the classical level. In this paper, we study a trajectory of the type proposed by Horwitz and Aharonovich, and derive the Maxwell 4-vector potential associated with the motion. We show that the resulting fields carry a signature associated with the apparent superluminal motion, providing an independent test for the mechanism that does not require direct observation of the trajectory, except at the detector.

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.

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.

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.

Network-based study of Lagrangian transport and mixing

NASA Astrophysics Data System (ADS)

Padberg-Gehle, Kathrin; Schneide, Christiane

2017-10-01

Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterization of these Lagrangian objects is a topic of intense current research. While established mathematical approaches such as variational methods or transfer-operator-based schemes require full knowledge of the flow field or at least high-resolution trajectory data, this information may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from Lagrangian trajectory data, that is, numerical or measured time series of particle positions in a fluid flow. In this context, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, where Lagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph concepts are then employed to analyze the resulting network. In particular, local network measures such as the node degree, the average degree of neighboring nodes, and the clustering coefficient serve as indicators of highly mixing regions, whereas spectral graph partitioning schemes allow us to extract coherent sets. The proposed methodology is very fast to run and we demonstrate its applicability in two geophysical flows - the Bickley jet as well as the Antarctic stratospheric polar vortex.

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.

Rainbows in rotationally inelastic scattering: a comparative study of different model potential surfaces and dynamical approximations

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

Schinke, R.; Korsch, H.J.; Poppe, D.

1982-12-15

Rainbow structures in rotationally elastic and inelastic differential cross sections in atom--diatom collisions are investigated by comparison of three model potential energy surfaces labeled I, II, and III which are represented by V(R,..gamma..) = V/sub 0/(R)+V/sub 2/(R)P/sub 2/(cos ..gamma..). The cross sections are calculated within the quantal infinite-order-sudden (IOS) approximation. The anisotropic part V/sub 2/ is the same for all potentials and purely repulsive. The isotropic part V/sub 0/ for potential I is also repulsive and the differential cross sections show the well-studied rotational rainbow structures. Structural changes occur for collisions in potential II and III which have V/sub 0/more » terms being attractive at intermediate and large atom--molecule separations and having well depths of 10% and 25% of the collision energy, respectively. For example, the elastic cross section has no classical rainbow in the case of potential I but three in the case of potential III. The rainbow structures are analyzed within the classical and semiclassical versions of the IOS approximation and interpreted in terms of catastrophe theory. The quantitative comparison of the classical with the quantal IOS cross sections manifests possible quantum effects, i.e., tunneling into nonclassical regions and interference effects due to the superposition of several contributions (up to six in the present study). They can be very prominent and thus we conclude that much caution is needed if experimental data are compared with classical calculations. The accuracy of the IOS approximation is tested by comparison of classical IOS cross sections with cross sections obtained from exact classical trajectory calculations. The agreement is generally good with the exemption of the rainbow region and small angle, rotationally elastic scattering.« less

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.

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).

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.

Bio-inspired energy-harvesting mechanisms and patterns of dynamic soaring.

PubMed

Liu, Duo-Neng; Hou, Zhong-Xi; Guo, Zheng; Yang, Xi-Xiang; Gao, Xian-Zhong

2017-01-30

Albatrosses can make use of the dynamic soaring technique extracting energy from the wind field to achieve large-scale movement without a flap, which stimulates interest in effortless flight with small unmanned aerial vehicles (UAVs). However, mechanisms of energy harvesting in terms of the energy transfer from the wind to the flyer (albatross or UAV) are still indeterminate and controversial when using different reference frames in previous studies. In this paper, the classical four-phase Rayleigh cycle, includes sequentially upwind climb, downwind turn, downwind dive and upwind turn, is introduced in analyses of energy gain with the albatross's equation of motions and the simulated trajectory in dynamic soaring. Analytical and numerical results indicate that the energy gain in the air-relative frame mostly originates from large wind gradients at lower part of the climb and dive, while the energy gain in the inertial frame comes from the lift vector inclined to the wind speed direction during the climb, dive and downwind turn at higher altitude. These two energy-gain mechanisms are not equivalent in terms of energy sources and reference frames but have to be simultaneously satisfied in terms of the energy-neutral dynamic soaring cycle. For each reference frame, energy-loss phases are necessary to connect energy-gain ones. Based on these four essential phases in dynamic soaring and the albatrosses' flight trajectory, different dynamic soaring patterns are schematically depicted and corresponding optimal trajectories are computed. The optimal dynamic soaring trajectories are classified into two closed patterns including 'O' shape and '8' shape, and four travelling patterns including 'Ω' shape, 'α' shape, 'C' shape and 'S' shape. The correlation among these patterns are analysed and discussed. The completeness of the classification for different patterns is confirmed by listing and summarising dynamic soaring trajectories shown in studies over the past decades.

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.

Robust iterative learning contouring controller with disturbance observer for machine tool feed drives.

PubMed

Simba, Kenneth Renny; Bui, Ba Dinh; Msukwa, Mathew Renny; Uchiyama, Naoki

2018-04-01

In feed drive systems, particularly machine tools, a contour error is more significant than the individual axial tracking errors from the view point of enhancing precision in manufacturing and production systems. The contour error must be within the permissible tolerance of given products. In machining complex or sharp-corner products, large contour errors occur mainly owing to discontinuous trajectories and the existence of nonlinear uncertainties. Therefore, it is indispensable to design robust controllers that can enhance the tracking ability of feed drive systems. In this study, an iterative learning contouring controller consisting of a classical Proportional-Derivative (PD) controller and disturbance observer is proposed. The proposed controller was evaluated experimentally by using a typical sharp-corner trajectory, and its performance was compared with that of conventional controllers. The results revealed that the maximum contour error can be reduced by about 37% on average. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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.

When hawks attack: animal-borne video studies of goshawk pursuit and prey-evasion strategies

PubMed Central

Kane, Suzanne Amador; Fulton, Andrew H.; Rosenthal, Lee J.

2015-01-01

Video filmed by a camera mounted on the head of a Northern Goshawk (Accipiter gentilis) was used to study how the raptor used visual guidance to pursue prey and land on perches. A combination of novel image analysis methods and numerical simulations of mathematical pursuit models was used to determine the goshawk's pursuit strategy. The goshawk flew to intercept targets by fixing the prey at a constant visual angle, using classical pursuit for stationary prey, lures or perches, and usually using constant absolute target direction (CATD) for moving prey. Visual fixation was better maintained along the horizontal than vertical direction. In some cases, we observed oscillations in the visual fix on the prey, suggesting that the goshawk used finite-feedback steering. Video filmed from the ground gave similar results. In most cases, it showed goshawks intercepting prey using a trajectory consistent with CATD, then turning rapidly to attack by classical pursuit; in a few cases, it showed them using curving non-CATD trajectories. Analysis of the prey's evasive tactics indicated that only sharp sideways turns caused the goshawk to lose visual fixation on the prey, supporting a sensory basis for the surprising frequency and effectiveness of this tactic found by previous studies. The dynamics of the prey's looming image also suggested that the goshawk used a tau-based interception strategy. We interpret these results in the context of a concise review of pursuit–evasion in biology, and conjecture that some prey deimatic ‘startle’ displays may exploit tau-based interception. PMID:25609783

Buckling Instabilities and Complex Dynamics in a Model of Uniflagellar Bacterial Locomotion

NASA Astrophysics Data System (ADS)

Nguyen, Frank; Graham, Michael

2015-11-01

Locomotion of microorganisms at low Reynolds number is a long studied problem. Of particular interest are organisms using a single flagellum to undergo a wide range of motions: pushing, pulling, and tumbling or flicking. Recent experiments have connected the stability of the hook protein, connecting cell motor and flagellum, to deviations from typical straight swimming trajectories. We seek physical explanations to these phenomena by developing a computationally inexpensive, rigid-body dynamic model of a uniflagellated organism with a flexible hook connection that captures the fundamental dynamics, kinematics, and configurations. Furthermore, the model addresses the effects of hook loading and geometry on the stability of the system. Simulations with low hook flexibility produce the classic straight trajectory, but a large flexibility produces helical trajectories, leading to directional changes when coupled with transient hook stiffening. Minima for critical flexibilities are found in certain subsets of parameter space, implying preferred geometries for certain swimming dynamics. The model verifies proposed mechanisms for swimming in various modes and highlights the role of flexibility in the biology of real organisms and the engineering of artificial microswimmers. This work was supported by NSF grant PHY-1304942.

Crossing the dividing surface of transition state theory. III. Once and only once. Selecting reactive trajectories

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

Lorquet, J. C., E-mail: jc.lorquet@ulg.ac.be

2015-09-14

The purpose of the present work is to determine initial conditions that generate reacting, recrossing-free trajectories that cross the conventional dividing surface of transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) without ever returning to it. Local analytical equations of motion valid in the neighborhood of this planar surface have been derived as an expansion in Poisson brackets. We show that the mere presence of a saddle point implies that reactivity criteria can be quite simply formulated in terms of elements of thismore » series, irrespective of the shape of the potential energy function. Some of these elements are demonstrated to be equal to a sum of squares and thus to be necessarily positive, which has a profound impact on the dynamics. The method is then applied to a three-dimensional model describing an atom-diatom interaction. A particular relation between initial conditions is shown to generate a bundle of reactive trajectories that form reactive cylinders (or conduits) in phase space. This relation considerably reduces the phase space volume of initial conditions that generate recrossing-free trajectories. Loci in phase space of reactive initial conditions are presented. Reactivity is influenced by symmetry, as shown by a comparative study of collinear and bent transition states. Finally, it is argued that the rules that have been derived to generate reactive trajectories in classical mechanics are also useful to build up a reactive wave packet.« less

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

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.

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.

Quantum and quasi-classical calculations for the S+ + H2(v, j) →SH+(v′, j′)+H reactive collisions

PubMed Central

Zanchet, Alexandre; Roncero, Octavio; Bulut, Niyazi

2016-01-01

State-to-state cross sections for the S+ + H2(v, j) → SH+ (v′, j′) + H endothermic reaction are obtained with quantum wave packet(WP) and quasi-classical (QCT) methods for different initial rovibrational H2(v, j) over a wide range of translation energies. Final state distribution as a function of the initial quantum number is obtained and discussed. Additionally, the effect of the internal excitation of H2 on the reactivity is carefully studied. It appears that energy transfer among modes is very inefficient, that vibrational energy is the most favorable for reaction and rotational excitation significantly enhance reactivity when vibrational energy is sufficient to reach the product. Special attention is also paid on an unusual discrepancy between classical and quantum dynamics for low rotational levels while agreement improves with rotational excitation of H2, An interesting resonant behaviour found in WP calculations is also discussed and is associated to the existence of roaming classical trajectories that enhance the reactivity of the title reaction. Finally, a comparison with the experimental results of Stowe et al.[1] for S+ + HD and S+ +D2 reactions, finding a reasonably good agreement with those results. PMID:27055725

Quantum and quasi-classical calculations for the S⁺ + H₂(v,j) → SH⁺(v',j') + H reactive collisions.

PubMed

Zanchet, Alexandre; Roncero, Octavio; Bulut, Niyazi

2016-04-28

State-to-state cross-sections for the S(+) + H2(v,j) → SH(+)(v',j') + H endothermic reaction are obtained using quantum wave packet (WP) and quasi-classical (QCT) methods for different initial ro-vibrational H2(v,j) over a wide range of translation energies. The final state distribution as a function of the initial quantum number is obtained and discussed. Additionally, the effect of the internal excitation of H2 on the reactivity is carefully studied. It appears that energy transfer among modes is very inefficient that vibrational energy is the most favorable for the reaction, and rotational excitation significantly enhances the reactivity when vibrational energy is sufficient to reach the product. Special attention is also paid to an unusual discrepancy between classical and quantum dynamics for low rotational levels while agreement improves with rotational excitation of H2. An interesting resonant behaviour found in WP calculations is also discussed and associated with the existence of roaming classical trajectories that enhance the reactivity of the title reaction. Finally, a comparison with the experimental results of Stowe et al. for S(+) + HD and S(+) + D2 reactions exhibits a reasonably good agreement with those results.

Predictability sieve, pointer states, and the classicality of quantum trajectories

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

Dalvit, D. A. R.; Zurek, W. H.; Dziarmaga, J.

2005-12-15

We study various measures of classicality of the states of open quantum systems subject to decoherence. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and puritymore » loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity). We show that when pointer states--the most predictable states of an open quantum system selected by the predictability sieve--are well defined, all four criteria agree that they are indeed the most classical states. We illustrate this with two examples: an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion, for which most criteria select almost identical Gaussian states (although, in this case, the predictability sieve does not select well defined pointer states)« less

"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.

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.

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.

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.

The strengths and limitations of effective centroid force models explored by studying isotopic effects in liquid water

NASA Astrophysics Data System (ADS)

Yuan, Ying; Li, Jicun; Li, Xin-Zheng; Wang, Feng

2018-05-01

The development of effective centroid potentials (ECPs) is explored with both the constrained-centroid and quasi-adiabatic force matching using liquid water as a test system. A trajectory integrated with the ECP is free of statistical noises that would be introduced when the centroid potential is approximated on the fly with a finite number of beads. With the reduced cost of ECP, challenging experimental properties can be studied in the spirit of centroid molecular dynamics. The experimental number density of H2O is 0.38% higher than that of D2O. With the ECP, the H2O number density is predicted to be 0.42% higher, when the dispersion term is not refit. After correction of finite size effects, the diffusion constant of H2O is found to be 21% higher than that of D2O, which is in good agreement with the 29.9% higher diffusivity for H2O observed experimentally. Although the ECP is also able to capture the redshifts of both the OH and OD stretching modes in liquid water, there are a number of properties that a classical simulation with the ECP will not be able to recover. For example, the heat capacities of H2O and D2O are predicted to be almost identical and higher than the experimental values. Such a failure is simply a result of not properly treating quantized vibrational energy levels when the trajectory is propagated with classical mechanics. Several limitations of the ECP based approach without bead population reconstruction are discussed.

High-precision radiocarbon dating of political collapse and dynastic origins at the Maya site of Ceibal, Guatemala

PubMed Central

Inomata, Takeshi; Triadan, Daniela; MacLellan, Jessica; Burham, Melissa; Aoyama, Kazuo; Palomo, Juan Manuel; Yonenobu, Hitoshi; Pinzón, Flory; Nasu, Hiroo

2017-01-01

The lowland Maya site of Ceibal, Guatemala, had a long history of occupation, spanning from the Middle Preclassic Period through the Terminal Classic (1000 BC to AD 950). The Ceibal-Petexbatun Archaeological Project has been conducting archaeological investigations at this site since 2005 and has obtained 154 radiocarbon dates, which represent the largest collection of radiocarbon assays from a single Maya site. The Bayesian analysis of these dates, combined with a detailed study of ceramics, allowed us to develop a high-precision chronology for Ceibal. Through this chronology, we traced the trajectories of the Preclassic collapse around AD 150–300 and the Classic collapse around AD 800–950, revealing similar patterns in the two cases. Social instability started with the intensification of warfare around 75 BC and AD 735, respectively, followed by the fall of multiple centers across the Maya lowlands around AD 150 and 810. The population of Ceibal persisted for some time in both cases, but the center eventually experienced major decline around AD 300 and 900. Despite these similarities in their diachronic trajectories, the outcomes of these collapses were different, with the former associated with the development of dynasties centered on divine rulership and the latter leading to their downfalls. The Ceibal dynasty emerged during the period of low population after the Preclassic collapse, suggesting that this dynasty was placed under the influence from, or by the direct intervention of, an external power. PMID:28115691

The effect of zero-point energy differences on the isotope dependence of the formation of ozone: a classical trajectory study.

PubMed

Schinke, Reinhard; Fleurat-Lessard, Paul

2005-03-01

The effect of zero-point energy differences (DeltaZPE) between the possible fragmentation channels of highly excited O(3) complexes on the isotope dependence of the formation of ozone is investigated by means of classical trajectory calculations and a strong-collision model. DeltaZPE is incorporated in the calculations in a phenomenological way by adjusting the potential energy surface in the product channels so that the correct exothermicities and endothermicities are matched. The model contains two parameters, the frequency of stabilizing collisions omega and an energy dependent parameter Delta(damp), which favors the lower energies in the Maxwell-Boltzmann distribution. The stabilization frequency is used to adjust the pressure dependence of the absolute formation rate while Delta(damp) is utilized to control its isotope dependence. The calculations for several isotope combinations of oxygen atoms show a clear dependence of relative formation rates on DeltaZPE. The results are similar to those of Gao and Marcus [J. Chem. Phys. 116, 137 (2002)] obtained within a statistical model. In particular, like in the statistical approach an ad hoc parameter eta approximately 1.14, which effectively reduces the formation rates of the symmetric ABA ozone molecules, has to be introduced in order to obtain good agreement with the measured relative rates of Janssen et al. [Phys. Chem. Chem. Phys. 3, 4718 (2001)]. The temperature dependence of the recombination rate is also addressed.

High-precision radiocarbon dating of political collapse and dynastic origins at the Maya site of Ceibal, Guatemala.

PubMed

Inomata, Takeshi; Triadan, Daniela; MacLellan, Jessica; Burham, Melissa; Aoyama, Kazuo; Palomo, Juan Manuel; Yonenobu, Hitoshi; Pinzón, Flory; Nasu, Hiroo

2017-02-07

The lowland Maya site of Ceibal, Guatemala, had a long history of occupation, spanning from the Middle Preclassic Period through the Terminal Classic (1000 BC to AD 950). The Ceibal-Petexbatun Archaeological Project has been conducting archaeological investigations at this site since 2005 and has obtained 154 radiocarbon dates, which represent the largest collection of radiocarbon assays from a single Maya site. The Bayesian analysis of these dates, combined with a detailed study of ceramics, allowed us to develop a high-precision chronology for Ceibal. Through this chronology, we traced the trajectories of the Preclassic collapse around AD 150-300 and the Classic collapse around AD 800-950, revealing similar patterns in the two cases. Social instability started with the intensification of warfare around 75 BC and AD 735, respectively, followed by the fall of multiple centers across the Maya lowlands around AD 150 and 810. The population of Ceibal persisted for some time in both cases, but the center eventually experienced major decline around AD 300 and 900. Despite these similarities in their diachronic trajectories, the outcomes of these collapses were different, with the former associated with the development of dynasties centered on divine rulership and the latter leading to their downfalls. The Ceibal dynasty emerged during the period of low population after the Preclassic collapse, suggesting that this dynasty was placed under the influence from, or by the direct intervention of, an external power.

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.

Containment control of networked autonomous underwater vehicles: A predictor-based neural DSC design.

PubMed

Peng, Zhouhua; Wang, Dan; Wang, Wei; Liu, Lu

2015-11-01

This paper investigates the containment control problem of networked autonomous underwater vehicles in the presence of model uncertainty and unknown ocean disturbances. A predictor-based neural dynamic surface control design method is presented to develop the distributed adaptive containment controllers, under which the trajectories of follower vehicles nearly converge to the dynamic convex hull spanned by multiple reference trajectories over a directed network. Prediction errors, rather than tracking errors, are used to update the neural adaptation laws, which are independent of the tracking error dynamics, resulting in two time-scales to govern the entire system. The stability property of the closed-loop network is established via Lyapunov analysis, and transient property is quantified in terms of L2 norms of the derivatives of neural weights, which are shown to be smaller than the classical neural dynamic surface control approach. Comparative studies are given to show the substantial improvements of the proposed new method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Below-threshold harmonic generation from strong non-uniform fields

NASA Astrophysics Data System (ADS)

Yavuz, I.

2017-10-01

Strong-field photoemission below the ionization threshold is a rich/complex region where atomic emission and harmonic generation may coexist. We studied the mechanism of below-threshold harmonics (BTH) from spatially non-uniform local fields near the metallic nanostructures. Discrete harmonics are generated due to the broken inversion symmetry, suggesting enriched coherent emission in the vuv frequency range. Through the numerical solution of the time-dependent Schrödinger equation, we investigate wavelength and intensity dependence of BTH. Wavelength dependence identifies counter-regular resonances; individual contributions from the multi-photon emission and channel-closing effects due to quantum path interferences. In order to understand the underlying mechanism of BTH, we devised a generalized semi-classical model, including the influence of Coulomb and non-uniform field interactions. As in uniform fields, Coulomb potential in non-uniform fields is the determinant of BTH; we observed that the generation of BTH are due to returning trajectories with negative energies. Due to large distance effectiveness of the non-uniformity, only long trajectories are noticeably affected.

Testing sensory evidence against mnemonic templates

PubMed Central

Myers, Nicholas E; Rohenkohl, Gustavo; Wyart, Valentin; Woolrich, Mark W; Nobre, Anna C; Stokes, Mark G

2015-01-01

Most perceptual decisions require comparisons between current input and an internal template. Classic studies propose that templates are encoded in sustained activity of sensory neurons. However, stimulus encoding is itself dynamic, tracing a complex trajectory through activity space. Which part of this trajectory is pre-activated to reflect the template? Here we recorded magneto- and electroencephalography during a visual target-detection task, and used pattern analyses to decode template, stimulus, and decision-variable representation. Our findings ran counter to the dominant model of sustained pre-activation. Instead, template information emerged transiently around stimulus onset and quickly subsided. Cross-generalization between stimulus and template coding, indicating a shared neural representation, occurred only briefly. Our results are compatible with the proposal that template representation relies on a matched filter, transforming input into task-appropriate output. This proposal was consistent with a signed difference response at the perceptual decision stage, which can be explained by a simple neural model. DOI: http://dx.doi.org/10.7554/eLife.09000.001 PMID:26653854

Electron Capture in Proton Collisions with CO.

NASA Astrophysics Data System (ADS)

Stancil, P. C.; Schultz, D. R.; Kimura, M.; Gu, J.-P.; Hirsch, G.; Buenker, R. J.; Li, Y.

1999-10-01

Electron capture by protons following collisions with carbon monoxide is studied with a variety of theoretical approaches including quantal and semiclassical molecular-orbital close-coupling (MOCC) and classical trajectory Monte Carlo (CTMC) techniques. The MOCC treatments utilize potential surfaces and couplings computed for a range of H^+-CO orientation angles and C-O separations. Results including integral, differential, electronic state-selective, and vibrational state-selective cross sections will be presented for low- to intermediate-energies. Comparison with experiment will be made where possible and the relevance of the reaction in astrophysics and atmospheric physics will be discussed.

A structural and theoretical study of the alkylammonium nitrates forefather: Liquid methylammonium nitrate

NASA Astrophysics Data System (ADS)

Gontrani, Lorenzo; Caminiti, Ruggero; Salma, Umme; Campetella, Marco

2017-09-01

We present here a structural and vibrational analysis of melted methylammonium nitrate, the simplest compound of the family of alkylammonium nitrates. The static and dynamical features calculated were endorsed by comparing the experimental X-ray data with the theoretical ones. A reliable description cannot be obtained with classical molecular dynamics owing to polarization effects. Contrariwise, the structure factor and the vibrational frequencies obtained from ab initio molecular dynamics trajectories are in very good agreement with the experiment. A careful analysis has provided additional information on the complex hydrogen bonding network that exists in this liquid.

Analytical and numerical solutions of the equation for the beam propagation in a photovoltaic-photorefractive media

NASA Astrophysics Data System (ADS)

Lin, Ji; Wang, Hou

2013-07-01

We use the classical Lie-group method to study the evolution equation describing a photovoltaic-photorefractive media with the effects of diffusion process and the external electric field. We reduce it to some similarity equations firstly, and then obtain some analytically exact solutions including the soliton solution, the exponential solution and the oscillatory solution. We also obtain the numeric solitons from these similarity equations. Moreover, We show theoretically that these solutions have two types of trajectories. One type is a straight line. The other is a parabolic curve, which indicates these solitons have self-deflection.

On the possibility of negative activation energies in bimolecular reactions

NASA Technical Reports Server (NTRS)

Jaffe, R. L.

1978-01-01

The temperature dependence of the rate constants for model reacting systems was studied to understand some recent experimental measurements which imply the existence of negative activation energies. A collision theory model and classical trajectory calculations are used to demonstrate that the reaction probability can vary inversely with collision energy for bimolecular reactions occurring on attractive potential energy surfaces. However, this is not a sufficient condition to ensure that the rate constant has a negative temperature dependence. On the basis of these calculations, it seems unlikely that a true bimolecular reaction between neutral molecules will have a negative activation energy.

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

Refined method for predicting electrochemical windows of ionic liquids and experimental validation studies.

PubMed

Zhang, Yong; Shi, Chaojun; Brennecke, Joan F; Maginn, Edward J

2014-06-12

A combined classical molecular dynamics (MD) and ab initio MD (AIMD) method was developed for the calculation of electrochemical windows (ECWs) of ionic liquids. In the method, the liquid phase of ionic liquid is explicitly sampled using classical MD. The electrochemical window, estimated by the energy difference between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), is calculated at the density functional theory (DFT) level based on snapshots obtained from classical MD trajectories. The snapshots were relaxed using AIMD and quenched to their local energy minima, which assures that the HOMO/LUMO calculations are based on stable configurations on the same potential energy surface. The new procedure was applied to a group of ionic liquids for which the ECWs were also experimentally measured in a self-consistent manner. It was found that the predicted ECWs not only agree with the experimental trend very well but also the values are quantitatively accurate. The proposed method provides an efficient way to compare ECWs of ionic liquids in the same context, which has been difficult in experiments or simulation due to the fact that ECW values sensitively depend on experimental setup and conditions.

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

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.

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.

Quantization of Chirikov Map and Quantum KAM Theorem.

NASA Astrophysics Data System (ADS)

Shi, Kang-Jie

KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions agree with the numerical results of the quantum Chirikov map.

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

The potential influence of Asian and African mineral dust on ice, mixed-phase and liquid water clouds

NASA Astrophysics Data System (ADS)

Wiacek, A.; Peter, T.; Lohmann, U.

2010-02-01

This modelling study explores the availability of mineral dust particles as ice nuclei for interactions with ice, mixed-phase and liquid water clouds, also tracking the particles' history of cloud-processing. We performed 61 320 one-week forward trajectory calculations originating near the surface of major dust emitting regions in Africa and Asia using high-resolution meteorological analysis fields for the year 2007. Without explicitly modelling dust emission and deposition processes, dust-bearing trajectories were assumed to be those coinciding with known dust emission seasons. We found that dust emissions from Asian deserts lead to a higher potential for interactions with high clouds, despite being the climatologically much smaller dust emission source. This is due to Asian regions experiencing significantly more ascent than African regions, with strongest ascent in the Asian Taklimakan desert at ~25%, ~40% and 10% of trajectories ascending to 300 hPa in spring, summer and fall, respectively. The specific humidity at each trajectory's starting point was transported in a Lagrangian manner and relative humidities with respect to water and ice were calculated in 6-h steps downstream, allowing us to estimate the formation of liquid, mixed-phase and ice clouds. Practically none of the simulated air parcels reached regions where homogeneous ice nucleation can take place (T≲-40 °C) along trajectories that have not experienced water saturation first. By far the largest fraction of cloud forming trajectories entered conditions of mixed-phase clouds, where mineral dust will potentially exert the biggest influence. The majority of trajectories also passed through regions supersaturated with respect to ice but subsaturated with respect to water, where "warm" (T≳-40 °C) ice clouds may form prior to supercooled water or mixed-phase clouds. The importance of "warm" ice clouds and the general influence of dust in the mixed-phase cloud region are highly uncertain due to considerable scatter in recent laboratory data from ice nucleation experiments, which we briefly review in this work. For "classical" cirrus-forming temperatures, our results show that only mineral dust IN that underwent mixed-phase cloud-processing previously are likely to be relevant, and, therefore, we recommend further systematic studies of immersion mode ice nucleation on mineral dust suspended in atmospherically relevant coatings.

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.

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.

Weak Measurement and Quantum Smoothing of a Superconducting Qubit

NASA Astrophysics Data System (ADS)

Tan, Dian

In quantum mechanics, the measurement outcome of an observable in a quantum system is intrinsically random, yielding a probability distribution. The state of the quantum system can be described by a density matrix rho(t), which depends on the information accumulated until time t, and represents our knowledge about the system. The density matrix rho(t) gives probabilities for the outcomes of measurements at time t. Further probing of the quantum system allows us to refine our prediction in hindsight. In this thesis, we experimentally examine a quantum smoothing theory in a superconducting qubit by introducing an auxiliary matrix E(t) which is conditioned on information obtained from time t to a final time T. With the complete information before and after time t, the pair of matrices [rho(t), E(t)] can be used to make smoothed predictions for the measurement outcome at time t. We apply the quantum smoothing theory in the case of continuous weak measurement unveiling the retrodicted quantum trajectories and weak values. In the case of strong projective measurement, while the density matrix rho(t) with only diagonal elements in a given basis |n〉 may be treated as a classical mixture, we demonstrate a failure of this classical mixture description in determining the smoothed probabilities for the measurement outcome at time t with both diagonal rho(t) and diagonal E(t). We study the correlations between quantum states and weak measurement signals and examine aspects of the time symmetry of continuous quantum measurement. We also extend our study of quantum smoothing theory to the case of resonance fluorescence of a superconducting qubit with homodyne measurement and observe some interesting effects such as the modification of the excited state probabilities, weak values, and evolution of the predicted and retrodicted trajectories.

The ortho-to-para ratio of H2Cl+: Quasi-classical trajectory calculations and new simulations in light of new observations

NASA Astrophysics Data System (ADS)

Le Gal, R.; Xie, C.; Herbst, E.; Talbi, D.; Guo, H.; Muller, S.

2017-12-01

Multi-hydrogenated species with proper symmetry properties can present different spin configurations, and thus exist under different spin symmetry forms, labeled as para and ortho for two-hydrogen molecules. We investigated here the ortho-to-para ratio (OPR) of H2Cl+ in the light of new observations performed in the z = 0.89 absorber toward the lensed quasar PKS 1830-211 with the Atacama Large Millimeter/submillimeter Array (ALMA). Two independent lines of sight were observed, to the southwest (SW) and northeast (NE) images of the quasar, with OPR values found to be 3.15 ± 0.13 and 3.1 ± 0.5 in each region, respectively, in agreement with a spin statistical weight of 3:1. An OPR of 3:1 for a molecule containing two identical hydrogen nuclei can refer to either a statistical result or a high-temperature limit depending on the reaction mechanism leading to its formation. It is thus crucial to identify rigorously how OPRs are produced in order to constrain the information that these probes can provide. To understand the production of the H2Cl+ OPR, we undertook a careful theoretical study of the reaction mechanisms involved with the aid of quasi-classical trajectory calculations on a new global potential energy surface fit to a large number of high-level ab initio data. Our study shows that the major formation reaction for H2Cl+ produces this ion via a hydrogen abstraction rather than a scrambling mechanism. Such a mechanism leads to a 3:1 OPR, which is not changed by destruction and possible thermalization reactions for H2Cl+ and is thus likely to be the cause of observed 3:1 OPR ratios, contrary to the normal assumption of scrambling.

Determining of migraine prognosis using latent growth mixture models.

PubMed

Tasdelen, Bahar; Ozge, Aynur; Kaleagasi, Hakan; Erdogan, Semra; Mengi, Tufan

2011-04-01

This paper presents a retrospective study to classify patients into subtypes of the treatment according to baseline and longitudinally observed values considering heterogenity in migraine prognosis. In the classical prospective clinical studies, participants are classified with respect to baseline status and followed within a certain time period. However, latent growth mixture model is the most suitable method, which considers the population heterogenity and is not affected drop-outs if they are missing at random. Hence, we planned this comprehensive study to identify prognostic factors in migraine. The study data have been based on a 10-year computer-based follow-up data of Mersin University Headache Outpatient Department. The developmental trajectories within subgroups were described for the severity, frequency, and duration of headache separately and the probabilities of each subgroup were estimated by using latent growth mixture models. SAS PROC TRAJ procedures, semiparametric and group-based mixture modeling approach, were applied to define the developmental trajectories. While the three-group model for the severity (mild, moderate, severe) and frequency (low, medium, high) of headache appeared to be appropriate, the four-group model for the duration (low, medium, high, extremely high) was more suitable. The severity of headache increased in the patients with nausea, vomiting, photophobia and phonophobia. The frequency of headache was especially related with increasing age and unilateral pain. Nausea and photophobia were also related with headache duration. Nausea, vomiting and photophobia were the most significant factors to identify developmental trajectories. The remission time was not the same for the severity, frequency, and duration of headache.

Stability and chaos in Kustaanheimo-Stiefel space induced by the Hopf fibration

NASA Astrophysics Data System (ADS)

Roa, Javier; Urrutxua, Hodei; Peláez, Jesús

2016-07-01

The need for the extra dimension in Kustaanheimo-Stiefel (KS) regularization is explained by the topology of the Hopf fibration, which defines the geometry and structure of KS space. A trajectory in Cartesian space is represented by a four-dimensional manifold called the fundamental manifold. Based on geometric and topological aspects classical concepts of stability are translated to KS language. The separation between manifolds of solutions generalizes the concept of Lyapunov stability. The dimension-raising nature of the fibration transforms fixed points, limit cycles, attractive sets, and Poincaré sections to higher dimensional subspaces. From these concepts chaotic systems are studied. In strongly perturbed problems, the numerical error can break the topological structure of KS space: points in a fibre are no longer transformed to the same point in Cartesian space. An observer in three dimensions will see orbits departing from the same initial conditions but diverging in time. This apparent randomness of the integration can only be understood in four dimensions. The concept of topological stability results in a simple method for estimating the time-scale in which numerical simulations can be trusted. Ideally, all trajectories departing from the same fibre should be KS transformed to a unique trajectory in three-dimensional space, because the fundamental manifold that they constitute is unique. By monitoring how trajectories departing from one fibre separate from the fundamental manifold a critical time, equivalent to the Lyapunov time, is estimated. These concepts are tested on N-body examples: the Pythagorean problem, and an example of field stars interacting with a binary.

MDcons: Intermolecular contact maps as a tool to analyze the interface of protein complexes from molecular dynamics trajectories

PubMed Central

2014-01-01

Background Molecular Dynamics (MD) simulations of protein complexes suffer from the lack of specific tools in the analysis step. Analyses of MD trajectories of protein complexes indeed generally rely on classical measures, such as the RMSD, RMSF and gyration radius, conceived and developed for single macromolecules. As a matter of fact, instead, researchers engaged in simulating the dynamics of a protein complex are mainly interested in characterizing the conservation/variation of its biological interface. Results On these bases, herein we propose a novel approach to the analysis of MD trajectories or other conformational ensembles of protein complexes, MDcons, which uses the conservation of inter-residue contacts at the interface as a measure of the similarity between different snapshots. A "consensus contact map" is also provided, where the conservation of the different contacts is drawn in a grey scale. Finally, the interface area of the complex is monitored during the simulations. To show its utility, we used this novel approach to study two protein-protein complexes with interfaces of comparable size and both dominated by hydrophilic interactions, but having binding affinities at the extremes of the experimental range. MDcons is demonstrated to be extremely useful to analyse the MD trajectories of the investigated complexes, adding important insight into the dynamic behavior of their biological interface. Conclusions MDcons specifically allows the user to highlight and characterize the dynamics of the interface in protein complexes and can thus be used as a complementary tool for the analysis of MD simulations of both experimental and predicted structures of protein complexes. PMID:25077693

MDcons: Intermolecular contact maps as a tool to analyze the interface of protein complexes from molecular dynamics trajectories.

PubMed

Abdel-Azeim, Safwat; Chermak, Edrisse; Vangone, Anna; Oliva, Romina; Cavallo, Luigi

2014-01-01

Molecular Dynamics (MD) simulations of protein complexes suffer from the lack of specific tools in the analysis step. Analyses of MD trajectories of protein complexes indeed generally rely on classical measures, such as the RMSD, RMSF and gyration radius, conceived and developed for single macromolecules. As a matter of fact, instead, researchers engaged in simulating the dynamics of a protein complex are mainly interested in characterizing the conservation/variation of its biological interface. On these bases, herein we propose a novel approach to the analysis of MD trajectories or other conformational ensembles of protein complexes, MDcons, which uses the conservation of inter-residue contacts at the interface as a measure of the similarity between different snapshots. A "consensus contact map" is also provided, where the conservation of the different contacts is drawn in a grey scale. Finally, the interface area of the complex is monitored during the simulations. To show its utility, we used this novel approach to study two protein-protein complexes with interfaces of comparable size and both dominated by hydrophilic interactions, but having binding affinities at the extremes of the experimental range. MDcons is demonstrated to be extremely useful to analyse the MD trajectories of the investigated complexes, adding important insight into the dynamic behavior of their biological interface. MDcons specifically allows the user to highlight and characterize the dynamics of the interface in protein complexes and can thus be used as a complementary tool for the analysis of MD simulations of both experimental and predicted structures of protein complexes.

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.

Scaling relationships for nonadiabatic energy relaxation times in warm dense matter: toward understanding the equation of state.

PubMed

Pradhan, Ekadashi; Magyar, Rudolph J; Akimov, Alexey V

2016-11-30

Understanding the dynamics of electron-ion energy transfer in warm dense (WD) matter is important to the measurement of equation of state (EOS) properties and for understanding the energy balance in dynamic simulations. In this work, we present a comprehensive investigation of nonadiabatic electron relaxation and thermal excitation dynamics in aluminum under high pressure and temperature. Using quantum-classical trajectory surface hopping approaches, we examine the role of nonadiabatic couplings and electronic decoherence in electron-nuclear energy transfer in WD aluminum. The computed timescales range from 400 fs to 4.0 ps and are consistent with existing experimental studies. We have derived general scaling relationships between macroscopic parameters of WD systems such as temperature or mass density and the timescales of energy redistribution between quantum and classical degrees of freedom. The scaling laws are supported by computational results. We show that electronic decoherence plays essential role and can change the functional dependencies qualitatively. The established scaling relationships can be of use in modelling of WD matter.

A study of the influence of the sun on optimal two-impulse Earth-to-Moon trajectories with moderate time of flight in the three-body and four-body models

NASA Astrophysics Data System (ADS)

Filho, Luiz Arthur Gagg; da Silva Fernandes, Sandro

2017-05-01

In this work, a study about the influence of the Sun on optimal two-impulse Earth-to-Moon trajectories for interior transfers with moderate time of flight is presented considering the three-body and the four-body models. The optimization criterion is the total characteristic velocity which represents the fuel consumption of an infinite thrust propulsion system. The optimization problem has been formulated using the classic planar circular restricted three-body problem (PCR3BP) and the planar bi-circular restricted four-body problem (PBR4BP), and, it consists of transferring a spacecraft from a circular low Earth orbit (LEO) to a circular low Moon orbit (LMO) with minimum fuel consumption. The Sequential Gradient Restoration Algorithm (SGRA) is applied to determine the optimal solutions. Numerical results are presented for several final altitudes of a clockwise or a counterclockwise circular low Moon orbit considering a specified altitude of a counterclockwise circular low Earth orbit. Two types of analysis are performed: in the first one, the initial position of the Sun is taken as a parameter and the major parameters describing the optimal trajectories are obtained by solving an optimization problem of one degree of freedom. In the second analysis, an optimization problem with two degrees of freedom is considered and the initial position of the Sun is taken as an additional unknown.

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.

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

The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems

NASA Astrophysics Data System (ADS)

Novaes, Douglas D.; Teixeira, Marco A.; Zeli, Iris O.

2018-05-01

Generic bifurcation theory was classically well developed for smooth differential systems, establishing results for k-parameter families of planar vector fields. In the present study we focus on a qualitative analysis of 2-parameter families, , of planar Filippov systems assuming that Z 0,0 presents a codimension-two minimal set. Such object, named elementary simple two-fold cycle, is characterized by a regular trajectory connecting a visible two-fold singularity to itself, for which the second derivative of the first return map is nonvanishing. We analyzed the codimension-two scenario through the exhibition of its bifurcation diagram.

Hawking tunneling and boomerang behaviour of massive particles with E < m

NASA Astrophysics Data System (ADS)

Jannes, Gil; Philbin, Thomas G.; Rousseaux, Germain

2012-07-01

Massive particles are radiated from black holes through the Hawking mechanism together with the more familiar radiation of massless particles. For E >= m, the emission rate is identical to the massless case. But E < m particles can also tunnel across the horizon. A study of the dispersion relation and wave packet simulations show that their classical trajectory is similar to that of a boomerang. The tunneling formalism is used to calculate the probability for detecting such E < m particles, for a Schwarzschild black hole of astrophysical size or in an analogue gravity experiment, as a function of the distance from the horizon and the energy of the particle.

Study of Transport Characteristics of Motile Microorganisms Using Micro-Scale Devices

NASA Astrophysics Data System (ADS)

Parashar, R.; Scheibe, T. D.; Plymale, A.; Hu, D.; Kelly, R.; Frederick, J. M.; Yang, X.; Sund, N. L.

2016-12-01

Accurate numerical models of microbial transport are needed to support design and evaluation of bioremediation implementations. A sequence of micro-scale experiments using advanced microfluidics and imaging techniques was conducted to quantify the movement patterns of individual microbes and their interactions with solid surfaces in unobstructed medium and simple pore geometries. The set of bacteria studied encompasses strictly anaerobic, facultatively anaerobic, fermentative, and facultatively autotrophic species, with capacities to reduce a range of metals and radionuclides, as well as nitrate, using a variety of electron donors, including acetate, lactate, carbohydrates, and molecular hydrogen. Motion of motile microorganisms recorded over time provides results that can be analyzed to determine the character and several statistical attributes of microbial motion. Individual tracks on the order of several seconds to a few minutes in duration are characterized to provide information on 1) the length (distance in microns) of microbial runs, 2) velocity distributions along individual trajectories, and 3) the angle between the directions of sequential runs. Analysis of the microbial trajectories elucidates parameters related to dynamics of their motion. Comparison of these parameters with those of a classical Brownian motion yields crucial information on selection of appropriate model to account for microbial motility in relevant applications.

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.

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

PubMed

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

Measuring the number of independent emitters in single-molecule fluorescence images and trajectories using coincident photons.

PubMed

Weston, Kenneth D; Dyck, Martina; Tinnefeld, Philip; Müller, Christian; Herten, Dirk P; Sauer, Markus

2002-10-15

A simple new approach is described and demonstrated for measuring the number of independent emitters along with the fluorescence intensity, lifetime, and emission wavelength for trajectories and images of single molecules and multichromophoric systems using a single PC plug-in card for time-correlated single-photon counting. The number of independent emitters present in the detection volume can be determined using the interphoton times in a manner similar to classical antibunching experiments. In contrast to traditional coincidence analysis based on pulsed laser excitation and direct measurement of coincident photon pairs using a time-to-amplitude converter, the interphoton distances are retrieved afterward by recording the absolute arrival time of each photon with nanosecond time resolution on two spectrally separated detectors. Intensity changes that result from fluctuations of a photophysical parameter can be distinguished from fluctuations due to changes in the number of emitters (e.g., photobleaching) in single chromophore and multichromophore intensity trajectories. This is the first report to demonstrate imaging with contrast based on the number of independently emitting species within the detection volume.

Surface-hopping dynamics and decoherence with quantum equilibrium structure.

PubMed

Grunwald, Robbie; Kim, Hyojoon; Kapral, Raymond

2008-04-28

In open quantum systems, decoherence occurs through interaction of a quantum subsystem with its environment. The computation of expectation values requires a knowledge of the quantum dynamics of operators and sampling from initial states of the density matrix describing the subsystem and bath. We consider situations where the quantum evolution can be approximated by quantum-classical Liouville dynamics and examine the circumstances under which the evolution can be reduced to surface-hopping dynamics, where the evolution consists of trajectory segments exclusively evolving on single adiabatic surfaces, with probabilistic hops between these surfaces. The justification for the reduction depends on the validity of a Markovian approximation on a bath averaged memory kernel that accounts for quantum coherence in the system. We show that such a reduction is often possible when initial sampling is from either the quantum or classical bath initial distributions. If the average is taken only over the quantum dispersion that broadens the classical distribution, then such a reduction is not always possible.

Radiation of a nonrelativistic particle during its finite motion in a central field

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

Karnakov, B. M., E-mail: karnak@theor.mephi.ru; Korneev, Ph. A., E-mail: korneev@theor.mephi.ru; Popruzhenko, S. V.

The spectrum and expressions for the intensity of dipole radiation lines are obtained for a classical nonrelativistic charged particle that executes a finite aperiodic motion in an arbitrary central field along a non-closed trajectory. It is shown that, in this case of a conditionally periodic motion, the radiaton spectrum consists of two series of equally spaced lines. It is pointed out that, according to the correspondence principle, the rise of two such series in the classical theory corresponds to the well-known selection rule |{delta}l = 1 for the dipole radiation in a central field in quantum theory, where l ismore » the orbital angular momentum of the particle. The results obtained can be applied to the description of the radiation and the absorption of a classical collisionless electron plasma in nanoparticles irradiated by an intense laser field. As an example, the rate of collisionless absorption of electromagnetic wave energy in equilibrium isotropic nanoplasma is calculated.« less

Adaptive robust motion trajectory tracking control of pneumatic cylinders with LuGre model-based friction compensation

NASA Astrophysics Data System (ADS)

Meng, Deyuan; Tao, Guoliang; Liu, Hao; Zhu, Xiaocong

2014-07-01

Friction compensation is particularly important for motion trajectory tracking control of pneumatic cylinders at low speed movement. However, most of the existing model-based friction compensation schemes use simple classical models, which are not enough to address applications with high-accuracy position requirements. Furthermore, the friction force in the cylinder is time-varying, and there exist rather severe unmodelled dynamics and unknown disturbances in the pneumatic system. To deal with these problems effectively, an adaptive robust controller with LuGre model-based dynamic friction compensation is constructed. The proposed controller employs on-line recursive least squares estimation (RLSE) to reduce the extent of parametric uncertainties, and utilizes the sliding mode control method to attenuate the effects of parameter estimation errors, unmodelled dynamics and disturbances. In addition, in order to realize LuGre model-based friction compensation, the modified dual-observer structure for estimating immeasurable friction internal state is developed. Therefore, a prescribed motion tracking transient performance and final tracking accuracy can be guaranteed. Since the system model uncertainties are unmatched, the recursive backstepping design technology is applied. In order to solve the conflicts between the sliding mode control design and the adaptive control design, the projection mapping is used to condition the RLSE algorithm so that the parameter estimates are kept within a known bounded convex set. Finally, the proposed controller is tested for tracking sinusoidal trajectories and smooth square trajectory under different loads and sudden disturbance. The testing results demonstrate that the achievable performance of the proposed controller is excellent and is much better than most other studies in literature. Especially when a 0.5 Hz sinusoidal trajectory is tracked, the maximum tracking error is 0.96 mm and the average tracking error is 0.45 mm. This paper constructs an adaptive robust controller which can compensate the friction force in the cylinder.

Classical Calculations of Scattering Signatures from a Gravitational Singularity or the Scattering and Absorption Cross-Sections of a Black Hole

NASA Astrophysics Data System (ADS)

Difilippo, Felix C.

2012-09-01

Within the context of general relativity theory we calculate, analytically, scattering signatures around a gravitational singularity: angular and time distributions of scattered massive objects and photons and the time and space modulation of Doppler effects. Additionally, the scattering and absorption cross sections for the gravitational interactions are calculated. The results of numerical simulations of the trajectories are compared with the analytical results.

Direct dynamics simulations of the unimolecular dissociation of dioxetane: Probing the non-RRKM dynamics

NASA Astrophysics Data System (ADS)

Malpathak, Shreyas; Ma, Xinyou; Hase, William L.

2018-04-01

In a previous UB3LYP/6-31G* direct dynamics simulation, non-Rice-Ramsperger-Kassel-Marcus (RRKM) unimolecular dynamics was found for vibrationally excited 1,2-dioxetane (DO); [R. Sun et al., J. Chem. Phys. 137, 044305 (2012)]. In the work reported here, these dynamics are studied in more detail using the same direct dynamics method. Vibrational modes of DO were divided into 4 groups, based on their characteristic motions, and each group excited with the same energy. To compare with the dynamics of these groups, an additional group of trajectories comprising a microcanonical ensemble was also simulated. The results of these simulations are consistent with the previous study. The dissociation probability, N(t)/N(0), for these excitation groups were all different. Groups A, B, and C, without initial excitation in the O-O stretch reaction coordinate, had a time lag to of 0.25-1.0 ps for the first dissociation to occur. Somewhat surprisingly, the C-H stretch Group A and out-of-plane motion Group C excitations had exponential dissociation probabilities after to, with a rate constant ˜2 times smaller than the anharmonic RRKM value. Groups B and D, with excitation of the H-C-H bend and wag, and ring bend and stretch modes, respectively, had bi-exponential dissociation probabilities. For Group D, with excitation localized in the reaction coordinate, the initial rate constant is ˜7 times larger than the anharmonic RRKM value, substantial apparent non-RRKM dynamics. N(t)/N(0) for the random excitation trajectories was non-exponential, indicating intrinsic non-RRKM dynamics. For the trajectory integration time of 13.5 ps, 9% of these trajectories did not dissociate in comparison to the RRKM prediction of 0.3%. Classical power spectra for these trajectories indicate they have regular intramolecular dynamics. The N(t)/N(0) for the excitation groups are well described by a two-state coupled phase space model. From the intercept of N(t)/N(0) with random excitation, the anharmonic correction to the RRKM rate constant is approximately a factor of 1.5.

OPTIMAL AIRCRAFT TRAJECTORIES FOR SPECIFIED RANGE

NASA Technical Reports Server (NTRS)

Lee, H.

1994-01-01

For an aircraft operating over a fixed range, the operating costs are basically a sum of fuel cost and time cost. While minimum fuel and minimum time trajectories are relatively easy to calculate, the determination of a minimum cost trajectory can be a complex undertaking. This computer program was developed to optimize trajectories with respect to a cost function based on a weighted sum of fuel cost and time cost. As a research tool, the program could be used to study various characteristics of optimum trajectories and their comparison to standard trajectories. It might also be used to generate a model for the development of an airborne trajectory optimization system. The program could be incorporated into an airline flight planning system, with optimum flight plans determined at takeoff time for the prevailing flight conditions. The use of trajectory optimization could significantly reduce the cost for a given aircraft mission. The algorithm incorporated in the program assumes that a trajectory consists of climb, cruise, and descent segments. The optimization of each segment is not done independently, as in classical procedures, but is performed in a manner which accounts for interaction between the segments. This is accomplished by the application of optimal control theory. The climb and descent profiles are generated by integrating a set of kinematic and dynamic equations, where the total energy of the aircraft is the independent variable. At each energy level of the climb and descent profiles, the air speed and power setting necessary for an optimal trajectory are determined. The variational Hamiltonian of the problem consists of the rate of change of cost with respect to total energy and a term dependent on the adjoint variable, which is identical to the optimum cruise cost at a specified altitude. This variable uniquely specifies the optimal cruise energy, cruise altitude, cruise Mach number, and, indirectly, the climb and descent profiles. If the optimum cruise cost is specified, an optimum trajectory can easily be generated; however, the range obtained for a particular optimum cruise cost is not known a priori. For short range flights, the program iteratively varies the optimum cruise cost until the computed range converges to the specified range. For long-range flights, iteration is unnecessary since the specified range can be divided into a cruise segment distance and full climb and descent distances. The user must supply the program with engine fuel flow rate coefficients and an aircraft aerodynamic model. The program currently includes coefficients for the Pratt-Whitney JT8D-7 engine and an aerodynamic model for the Boeing 727. Input to the program consists of the flight range to be covered and the prevailing flight conditions including pressure, temperature, and wind profiles. Information output by the program includes: optimum cruise tables at selected weights, optimal cruise quantities as a function of cruise weight and cruise distance, climb and descent profiles, and a summary of the complete synthesized optimal trajectory. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 100K (octal) of 60 bit words. This aircraft trajectory optimization program was developed in 1979.

Recent Advances and Perspectives on Nonadiabatic Mixed Quantum-Classical Dynamics.

PubMed

Crespo-Otero, Rachel; Barbatti, Mario

2018-05-16

Nonadiabatic mixed quantum-classical (NA-MQC) dynamics methods form a class of computational theoretical approaches in quantum chemistry tailored to investigate the time evolution of nonadiabatic phenomena in molecules and supramolecular assemblies. NA-MQC is characterized by a partition of the molecular system into two subsystems: one to be treated quantum mechanically (usually but not restricted to electrons) and another to be dealt with classically (nuclei). The two subsystems are connected through nonadiabatic couplings terms to enforce self-consistency. A local approximation underlies the classical subsystem, implying that direct dynamics can be simulated, without needing precomputed potential energy surfaces. The NA-MQC split allows reducing computational costs, enabling the treatment of realistic molecular systems in diverse fields. Starting from the three most well-established methods-mean-field Ehrenfest, trajectory surface hopping, and multiple spawning-this review focuses on the NA-MQC dynamics methods and programs developed in the last 10 years. It stresses the relations between approaches and their domains of application. The electronic structure methods most commonly used together with NA-MQC dynamics are reviewed as well. The accuracy and precision of NA-MQC simulations are critically discussed, and general guidelines to choose an adequate method for each application are delivered.

Mixed Quantum/Classical Theory for Molecule-Molecule Inelastic Scattering: Derivations of Equations and Application to N2 + H2 System.

PubMed

Semenov, Alexander; Babikov, Dmitri

2015-12-17

The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward.

Cycle frequency in standard Rock-Paper-Scissors games: Evidence from experimental economics

NASA Astrophysics Data System (ADS)

Xu, Bin; Zhou, Hai-Jun; Wang, Zhijian

2013-10-01

The Rock-Paper-Scissors (RPS) game is a widely used model system in game theory. Evolutionary game theory predicts the existence of persistent cycles in the evolutionary trajectories of the RPS game, but experimental evidence has remained to be rather weak. In this work, we performed laboratory experiments on the RPS game and analyzed the social-state evolutionary trajectories of twelve populations of N=6 players. We found strong evidence supporting the existence of persistent cycles. The mean cycling frequency was measured to be 0.029±0.009 period per experimental round. Our experimental observations can be quantitatively explained by a simple non-equilibrium model, namely the discrete-time logit dynamical process with a noise parameter. Our work therefore favors the evolutionary game theory over the classical game theory for describing the dynamical behavior of the RPS game.

Proton relays in anomalous carbocations dictate spectroscopy, stability, and mechanisms: case studies on C2H5+ and C3H3.

PubMed

Sager, LeeAnn M; Iyengar, Srinivasan S

2017-10-18

We present a detailed analysis of the anomalous carbocations: C 2 H 5 + and C 3 H 3 + . This work involves (a) probing electronic structural properties, (b) ab initio dynamics simulations over a range of internal energies, (c) analysis of reduced dimensional potential surfaces directed along selected conformational transition pathways, (d) dynamically averaged vibrational spectra computed from ab initio dynamics trajectories, and (e) two-dimensional time-frequency analysis to probe conformational dynamics. Key findings are as follows: (i) as noted in our previous study on C 2 H 3 + , it appears that these non-classical carbocations are stabilized by delocalized nuclear frameworks and "proton shuttles". We analyze this nuclear delocalization and find critical parallels between conformational changes in C 2 H 3 + , C 2 H 5 + , and C 3 H 3 + . (ii) The vibrational signatures of C 2 H 5 + are dominated by the "bridge-proton" conformation, but also show critical contributions from the "classical" configuration, which is a transition state at almost all levels of theory. This result is further substantiated through two-dimensional time-frequency analysis and is at odds with earlier explanations of the experimental spectra, where frequencies close to the classical region were thought to arise from an impurity. While this is still possible, our results here indicate an additional (perhaps more likely) explanation that involves the "classical" isomer. (iii) Finally, in the case of C 3 H 3 + our explanation of the experimental result includes the presence of multiple, namely, "cyclic", "straight", and propargyl, configurations. Proton shuttles and nuclear delocalization, reminiscent of those seen in the case of C 2 H 3 + , were seen all through and have a critical role in all our observations.

Mixed semiclassical-classical propagators for the Wigner phase space representation

NASA Astrophysics Data System (ADS)

Koda, Shin-ichi

2016-04-01

We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency.

Mixed semiclassical-classical propagators for the Wigner phase space representation.

PubMed

Koda, Shin-Ichi

2016-04-21

We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency.

Grain boundary, triple junction and quadruple point mobility controlled normal grain growth

NASA Astrophysics Data System (ADS)

Rios, P. R.; Glicksman, M. E.

2015-07-01

Reduction in stored free energy provides the thermodynamic driving force for grain and bubble growth in polycrystals and foams. Evolution of polycrystalline networks exhibit the additional complication that grain growth may be controlled by several kinetic mechanisms through which the decrease in network energy occurs. Polyhedral boundaries, triple junctions (TJs), and quadruple points (QPs) are the geometrically distinct elements of three dimensional networks that follow Plateau's rules, provided that grain growth is limited by diffusion through, and motion of, cell boundaries. Shvindlerman and co-workers have long recognized the kinetic influences on polycrystalline grain growth of network TJs and QPs. Moreover, the emergence of interesting polycrystalline nanomaterials underscored that TJs can indeed influence grain growth kinetics. Currently there exist few detailed studies concerned either with network distributions of grain size, number of faces per grain, or with 'grain trajectories', when grain growth is limited by the motion of its TJs or QPs. By contrast there exist abundant studies of classical grain growth limited by boundary mobility. This study is focused on a topological/geometrical representation of polycrystals to obtain statistical predictions of the grain size and face number distributions, as well as growth 'trajectories' during steady-state grain growth. Three limits to grain growth are considered, with grain growth kinetics controlled by boundary, TJ, and QP mobilities.

Collisional excitation of HC3N by para- and ortho-H2

NASA Astrophysics Data System (ADS)

Faure, Alexandre; Lique, François; Wiesenfeld, Laurent

2016-08-01

New calculations for rotational excitation of cyanoacetylene by collisions with hydrogen molecules are performed to include the lowest 38 rotational levels of HC3N and kinetic temperatures to 300 K. Calculations are based on the interaction potential of Wernli et al. whose accuracy is checked against spectroscopic measurements of the HC3N-H2 complex. The quantum coupled-channel approach is employed and complemented by quasi-classical trajectory calculations. Rate coefficients for ortho-H2 are provided for the first time. Hyperfine resolved rate coefficients are also deduced. Collisional propensity rules are discussed and comparisons between quantum and classical rate coefficients are presented. This collisional data should prove useful in interpreting HC3N observations in the cold and warm ISM, as well as in protoplanetary discs.

'I stayed with my illness': a grounded theory study of health seeking behaviour and treatment pathways of patients with obstetric fistula in Kenya.

PubMed

Khisa, Anne M; Omoni, Grace M; Nyamongo, Isaac K; Spitzer, Rachel F

2017-09-29

Obstetric fistula classic symptoms of faecal and urinary incontinence cause women to live with social stigma, isolation, psychological trauma and lose their source of livelihoods. There is a paucity of studies on the health seeking behaviour trajectories of women with fistula illness although women live with the illness for decades before surgery. We set out to establish the complete picture of women's health seeking behaviour using qualitative research. We sought to answer the question: what patterns of health seeking do women with obstetric fistula display in their quest for healing? We used grounded theory methodology to analyse data from narratives of women during inpatient stay after fistula surgery in 3 hospitals in Kenya. Emergent themes contributed to generation of substantive theory and a conceptual framework on the health seeking behaviour of fistula patients. We recruited 121 participants aged 17 to 62 years whose treatment pathways are presented. Participants delayed health seeking, living with fistula illness after their first encounter with unresponsive hospitals. The health seeking trajectory is characterized by long episodes of staying home with illness for decades and consulting multiple actors. Staying with fistula illness entailed health seeking through seven key actions of staying home, trying home remedies, consulting with private health care providers, Non-Governmental organisations, prayer, traditional medicine and formal hospitals and clinics. Long treatment trajectories at hospital resulted from multiple hospital visits and surgeries. Seeking treatment at hospital is the most popular step for most women after recognizing fistula symptoms. We conclude that the formal health system is not responsive to women's needs during fistula illness. Women suffer an illness with a chronic trajectory and seek alternative forms of care that are not ideally placed to treat fistula illness. The results suggest that a robust health system be provided with expertise and facilities to treat obstetric fistula to shorten women's treatment pathways.

Energy-level repulsion by spin-orbit coupling in two-dimensional Rydberg excitons

NASA Astrophysics Data System (ADS)

Stephanovich, V. A.; Sherman, E. Ya.; Zinner, N. T.; Marchukov, O. V.

2018-05-01

We study the effects of Rashba spin-orbit coupling on two-dimensional Rydberg exciton systems. Using analytical and numerical arguments we demonstrate that this coupling considerably modifies the wave functions and leads to a level repulsion that results in a deviation from the Poissonian statistics of the adjacent level distance distribution. This signifies the crossover to nonintegrability of the system and hints at the possibility of quantum chaos emerging. Such behavior strongly differs from the classical realization, where spin-orbit coupling produces highly entangled, chaotic electron trajectories in an exciton. We also calculate the oscillator strengths and show that randomization appears in the transitions between states with different total momenta.

A new semiclassical decoupling scheme for electronic transitions in molecular collisions - Application to vibrational-to-electronic energy transfer

NASA Technical Reports Server (NTRS)

Lee, H.-W.; Lam, K. S.; Devries, P. L.; George, T. F.

1980-01-01

A new semiclassical decoupling scheme (the trajectory-based decoupling scheme) is introduced in a computational study of vibrational-to-electronic energy transfer for a simple model system that simulates collinear atom-diatom collisions. The probability of energy transfer (P) is calculated quasiclassically using the new scheme as well as quantum mechanically as a function of the atomic electronic-energy separation (lambda), with overall good agreement between the two sets of results. Classical mechanics with the new decoupling scheme is found to be capable of predicting resonance behavior whereas an earlier decoupling scheme (the coordinate-based decoupling scheme) failed. Interference effects are not exhibited in P vs lambda results.

Generalized radially self-accelerating helicon beams.

PubMed

Vetter, Christian; Eichelkraut, Toni; Ornigotti, Marco; Szameit, Alexander

2014-10-31

We report, in theory and experiment, on a new class of optical beams that are radially self-accelerating and nondiffracting. These beams continuously evolve on spiraling trajectories while maintaining their amplitude and phase distribution in their rotating rest frame. We provide a detailed insight into the theoretical origin and characteristics of radial self-acceleration and prove our findings experimentally. As radially self-accelerating beams are nonparaxial and a solution to the full scalar Helmholtz equation, they can be implemented in many linear wave systems beyond optics, from acoustic and elastic waves to surface waves in fluids and soft matter. Our work generalized the study of classical helicon beams to a complete set of solutions for rotating complex fields.

The rotate-plus-shift C-arm trajectory: complete CT data with limited angular rotation

NASA Astrophysics Data System (ADS)

Ritschl, Ludwig; Kuntz, Jan; Kachelrieß, Marc

2015-03-01

In the last decade C-arm-based cone-beam CT became a widely used modality for intraoperative imaging. Typically a C-arm scan is performed using a circle-like trajectory around a region of interest. Therefor an angular range of at least 180° plus fan-angle must be covered to ensure a completely sampled data set. This fact defines some constraints on the geometry and technical specifications of a C-arm system, for example a larger C radius or a smaller C opening respectively. These technical modifications are usually not beneficial in terms of handling and usability of the C-arm during classical 2D applications like fluoroscopy. The method proposed in this paper relaxes the constraint of 180° plus fan-angle rotation to acquire a complete data set. The proposed C-arm trajectory requires a motorization of the orbital axis of the C and of ideally two orthogonal axis in the C plane. The trajectory consists of three parts: A rotation of the C around a defined iso-center and two translational movements parallel to the detector plane at the begin and at the end of the rotation. Combining these three parts to one trajectory enables for the acquisition of a completely sampled dataset using only 180° minus fan-angle of rotation. To evaluate the method we show animal and cadaver scans acquired with a mobile C-arm prototype. We expect that the transition of this method into clinical routine will lead to a much broader use of intraoperative 3D imaging in a wide field of clinical applications.

Consistent resolution of some relativistic quantum paradoxes

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2002-12-01

A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of the Einstein-Podolsky-Rosen paradox, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the measurement process that is less misleading than collapse models. In particular, one can employ a coarse-grained but fully quantum-mechanical description in which particles move along trajectories, with behavior under Lorentz transformations the same as in classical relativistic physics, and detectors are triggered by particles reaching them along such trajectories. States entangled between spacelike separate regions are also legitimate quantum descriptions, and can be consistently handled by the formalism presented here. The paradoxes in question arise because of using modes of reasoning which, while correct for classical physics, are inconsistent with the mathematical structure of quantum theory, and are resolved (or tamed) by using a proper quantum analysis. In particular, there is no need to invoke, nor any evidence for, mysterious long-range superluminal influences, and thus no incompatibility, at least from this source, between relativity theory and quantum mechanics.

Effect Sizes for Growth-Modeling Analysis for Controlled Clinical Trials in the Same Metric as for Classical Analysis

PubMed Central

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 intervention and control groups that captures the treatment effect is rarely reported. This article first reviews two classes of formulas for effect sizes associated with classical repeated-measures designs that use the standard deviation of either change scores or raw scores for the denominator. It then broadens the scope to subsume GMA, and demonstrates that the independent groups, within-subjects, pretest-posttest control-group, and GMA designs all estimate the same effect size when the standard deviation of raw scores is uniformly used. Finally, it is shown that the correct effect size for treatment efficacy in GMA--the difference between the estimated means of the two groups at end of study (determined from the coefficient for the slope difference and length of study) divided by the baseline standard deviation--is not reported in clinical trials. PMID:19271847

Locally enhanced sampling molecular dynamics study of the dioxygen transport in human cytoglobin.

PubMed

Orlowski, Slawomir; Nowak, Wieslaw

2007-07-01

Cytoglobin (Cyg)--a new member of the vertebrate heme globin family--is expressed in many tissues of the human body but its physiological role is still unclear. It may deliver oxygen under hypoxia, serve as a scavenger of reactive species or be involved in collagen synthesis. This protein is usually six-coordinated and binds oxygen by a displacement of the distal HisE7 imidazole. In this paper, the results of 60 ns molecular dynamics (MD) simulations of dioxygen diffusion inside Cyg matrix are discussed. In addition to a classical MD trajectory, an approximate Locally Enhanced Sampling (LES) method has been employed. Classical diffusion paths were carefully analyzed, five cavities in dynamical structures were determined and at least four distinct ligand exit paths were identified. The most probable exit/entry path is connected with a large tunnel present in Cyg. Several residues that are perhaps critical for kinetics of small gaseous diffusion were discovered. A comparison of gaseous ligand transport in Cyg and in the most studied heme protein myoglobin is presented. Implications of efficient oxygen transport found in Cyg to its possible physiological role are discussed.

Crossing the dividing surface of transition state theory. IV. Dynamical regularity and dimensionality reduction as key features of reactive trajectories

NASA Astrophysics Data System (ADS)

Lorquet, J. C.

2017-04-01

The atom-diatom interaction is studied by classical mechanics using Jacobi coordinates (R, r, θ). Reactivity criteria that go beyond the simple requirement of transition state theory (i.e., PR* > 0) are derived in terms of specific initial conditions. Trajectories that exactly fulfill these conditions cross the conventional dividing surface used in transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) only once. Furthermore, they are observed to be strikingly similar and to form a tightly packed bundle of perfectly collimated trajectories in the two-dimensional (R, r) configuration space, although their angular motion is highly specific for each one. Particular attention is paid to symmetrical transition states (i.e., either collinear or T-shaped with C2v symmetry) for which decoupling between angular and radial coordinates is observed, as a result of selection rules that reduce to zero Coriolis couplings between modes that belong to different irreducible representations. Liapunov exponents are equal to zero and Hamilton's characteristic function is planar in that part of configuration space that is visited by reactive trajectories. Detailed consideration is given to the concept of average reactive trajectory, which starts right from the saddle point and which is shown to be free of curvature-induced Coriolis coupling. The reaction path Hamiltonian model, together with a symmetry-based separation of the angular degree of freedom, provides an appropriate framework that leads to the formulation of an effective two-dimensional Hamiltonian. The success of the adiabatic approximation in this model is due to the symmetry of the transition state, not to a separation of time scales. Adjacent trajectories, i.e., those that do not exactly fulfill the reactivity conditions have similar characteristics, but the quality of the approximation is lower. At higher energies, these characteristics persist, but to a lesser degree. Recrossings of the dividing surface then become much more frequent and the phase space volumes of initial conditions that generate recrossing-free trajectories decrease. Altogether, one ends up with an additional illustration of the concept of reactive cylinder (or conduit) in phase space that reactive trajectories must follow. Reactivity is associated with dynamical regularity and dimensionality reduction, whatever the shape of the potential energy surface, no matter how strong its anharmonicity, and whatever the curvature of its reaction path. Both simplifying features persist during the entire reactive process, up to complete separation of fragments. The ergodicity assumption commonly assumed in statistical theories is inappropriate for reactive trajectories.

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

Donangelo, R.J.

An integral representation for the classical limit of the quantum mechanical S-matrix is developed and applied to heavy-ion Coulomb excitation and Coulomb-nuclear interference. The method combines the quantum principle of superposition with exact classical dynamics to describe the projectile-target system. A detailed consideration of the classical trajectories and of the dimensionless parameters that characterize the system is carried out. The results are compared, where possible, to exact quantum mechanical calculations and to conventional semiclassical calculations. It is found that in the case of backscattering the classical limit S-matrix method is able to almost exactly reproduce the quantum-mechanical S-matrix elements, andmore » therefore the transition probabilities, even for projectiles as light as protons. The results also suggest that this approach should be a better approximation for heavy-ion multiple Coulomb excitation than earlier semiclassical methods, due to a more accurate description of the classical orbits in the electromagnetic field of the target nucleus. Calculations using this method indicate that the rotational excitation probabilities in the Coulomb-nuclear interference region should be very sensitive to the details of the potential at the surface of the nucleus, suggesting that heavy-ion rotational excitation could constitute a sensitive probe of the nuclear potential in this region. The application to other problems as well as the present limits of applicability of the formalism are also discussed.« less

On the importance of an accurate representation of the initial state of the system in classical dynamics simulations

NASA Astrophysics Data System (ADS)

García-Vela, A.

2000-05-01

A definition of a quantum-type phase-space distribution is proposed in order to represent the initial state of the system in a classical dynamics simulation. The central idea is to define an initial quantum phase-space state of the system as the direct product of the coordinate and momentum representations of the quantum initial state. The phase-space distribution is then obtained as the square modulus of this phase-space state. The resulting phase-space distribution closely resembles the quantum nature of the system initial state. The initial conditions are sampled with the distribution, using a grid technique in phase space. With this type of sampling the distribution of initial conditions reproduces more faithfully the shape of the original phase-space distribution. The method is applied to generate initial conditions describing the three-dimensional state of the Ar-HCl cluster prepared by ultraviolet excitation. The photodissociation dynamics is simulated by classical trajectories, and the results are compared with those of a wave packet calculation. The classical and quantum descriptions are found in good agreement for those dynamical events less subject to quantum effects. The classical result fails to reproduce the quantum mechanical one for the more strongly quantum features of the dynamics. The properties and applicability of the phase-space distribution and the sampling technique proposed are discussed.

Convergence acceleration of molecular dynamics methods for shocked materials using velocity scaling

NASA Astrophysics Data System (ADS)

Taylor, DeCarlos E.

2017-03-01

In this work, a convergence acceleration method applicable to extended system molecular dynamics techniques for shock simulations of materials is presented. The method uses velocity scaling to reduce the instantaneous value of the Rankine-Hugoniot conservation of energy constraint used in extended system molecular dynamics methods to more rapidly drive the system towards a converged Hugoniot state. When used in conjunction with the constant stress Hugoniostat method, the velocity scaled trajectories show faster convergence to the final Hugoniot state with little difference observed in the converged Hugoniot energy, pressure, volume and temperature. A derivation of the scale factor is presented and the performance of the technique is demonstrated using the boron carbide armour ceramic as a test material. It is shown that simulation of boron carbide Hugoniot states, from 5 to 20 GPa, using both a classical Tersoff potential and an ab initio density functional, are more rapidly convergent when the velocity scaling algorithm is applied. The accelerated convergence afforded by the current algorithm enables more rapid determination of Hugoniot states thus reducing the computational demand of such studies when using expensive ab initio or classical potentials.

Electrons in strong electromagnetic fields: spin effects and radiation reaction (Conference Presentation)

NASA Astrophysics Data System (ADS)

Bauke, Heiko; Wen, Meng; Keitel, Christoph H.

2017-05-01

Various different classical models of electrons including their spin degree of freedom are commonly applied to describe the coupled dynamics of relativistic electron motion and spin precession in strong electromagnetic fields. The spin dynamics is usually governed by the Thomas-Bargmann-Michel-Telegdi equation [1, 2] in these models, while the electron's orbital motion follows the (modified) Lorentz force and a spin-dependent Stern-Gerlach force. Various classical models can lead to different or even contradicting predictions how the spin degree of freedom modifies the electron's orbital motion when the electron moves in strong electromagnetic fields. This discrepancy is rooted in the model-specific energy dependency of the spin induced relativistic Stern-Gerlach force acting on the electron. The Frenkel model [3, 4] and the classical Foldy-Wouthuysen model 5 are compared exemplarily against each other and against the quantum mechanical Dirac equation in order to identify parameter regimes where these classical models make different predictions [6, 7]. Our theoretical results allow for experimental tests of these models. In the setup of the longitudinal Stern-Gerlach effect, the Frenkel model and classical Foldy-Wouthuysen model lead in the relativistic limit to qualitatively different spin effects on the electron trajectory. Furthermore, it is demonstrated that in tightly focused beams in the near infrared the effect of the Stern-Gerlach force of the Frenkel model becomes sufficiently large to be potentially detectable in an experiment. Among the classical spin models, the Frenkel model is certainly prominent for its long history and its wide application. Our results, however, suggest that the classical Foldy-Wouthuysen model is superior as it is qualitatively in better agreement with the quantum mechanical Dirac equation. In ultra strong laser setups at parameter regimes where effects of the Stern-Gerlach force become relevant also radiation reaction effects are expected to set in. We incorporate radiation reaction classically via the Landau-Lifshitz equation and demonstrate that although radiation reaction effects can have a significant effect on the electron trajectory, the Frenkel model and the classical Foldy-Wouthuysen model remain distinguishable also if radiation reaction effects are taken into account. Our calculations are also suitable to verify the Landau-Lifshitz equation for the radiation reaction of electrons and other spin one-half particles. 1. Thomas, L. H., "I. The kinematics of an electron with an axis," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 3(13), 1-22 (1927). 2. Bargmann, V., Michel, L., and Telegdi, V. L., "Precession of the polarization of particles moving in a homogeneous electromagnetic field," Phys. Rev. Lett. 2(10), 435-436 (1959). 3. Frenkel, J., "Die Elektrodynamik des rotierenden Elektrons," Z. Phys. 37(4-5), 243-262 (1926). 4. Frenkel, J., "Spinning electrons," Nature (London) 117(2949), 653-654 (1926). 5. Silenko, A. J., "Foldy-Wouthyusen transformation and semiclassical limit for relativistic particles in strong external fields," Phys. Rev. A 77(1), 012116 (2008). 6. Wen, M., Bauke, H., and Keitel, C. H., "Identifying the Stern-Gerlach force of classical electron dynamics," Sci. Rep. 6, 31624 (2016). 7. Wen, M., Keitel, C. H., and Bauke, H., "Spin one-half particles in strong electromagnetic fields: spin effects and radiation reaction," arXiv:1610.08951 (2016).

Development of sustainable precision farming systems for swine: estimating real-time individual amino acid requirements in growing-finishing pigs.

PubMed

Hauschild, L; Lovatto, P A; Pomar, J; Pomar, C

2012-07-01

The objective of this study was to develop and evaluate a mathematical model used to estimate the daily amino acid requirements of individual growing-finishing pigs. The model includes empirical and mechanistic model components. The empirical component estimates daily feed intake (DFI), BW, and daily gain (DG) based on individual pig information collected in real time. Based on DFI, BW, and DG estimates, the mechanistic component uses classic factorial equations to estimate the optimal concentration of amino acids that must be offered to each pig to meet its requirements. The model was evaluated with data from a study that investigated the effect of feeding pigs with a 3-phase or daily multiphase system. The DFI and BW values measured in this study were compared with those estimated by the empirical component of the model. The coherence of the values estimated by the mechanistic component was evaluated by analyzing if it followed a normal pattern of requirements. Lastly, the proposed model was evaluated by comparing its estimates with those generated by the existing growth model (InraPorc). The precision of the proposed model and InraPorc in estimating DFI and BW was evaluated through the mean absolute error. The empirical component results indicated that the DFI and BW trajectories of individual pigs fed ad libitum could be predicted 1 d (DFI) or 7 d (BW) ahead with the average mean absolute error of 12.45 and 1.85%, respectively. The average mean absolute error obtained with the InraPorc for the average individual of the population was 14.72% for DFI and 5.38% for BW. Major differences were observed when estimates from InraPorc were compared with individual observations. The proposed model, however, was effective in tracking the change in DFI and BW for each individual pig. The mechanistic model component estimated the optimal standardized ileal digestible Lys to NE ratio with reasonable between animal (average CV = 7%) and overtime (average CV = 14%) variation. Thus, the amino acid requirements estimated by model are animal- and time-dependent and follow, in real time, the individual DFI and BW growth patterns. The proposed model can follow the average feed intake and feed weight trajectory of each individual pig in real time with good accuracy. Based on these trajectories and using classical factorial equations, the model makes it possible to estimate dynamically the AA requirements of each animal, taking into account the intake and growth changes of the animal.

High-energy gravitational scattering and the general relativistic two-body problem

NASA Astrophysics Data System (ADS)

Damour, Thibault

2018-02-01

A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys. Rev. D 94, 104015 (2016), 10.1103/PhysRevD.94.104015]. Using this technique, we derive, for the first time, to second-order in Newton's constant (i.e. one classical loop) the Hamiltonian of two point masses having an arbitrary (possibly relativistic) relative velocity. The resulting (second post-Minkowskian) Hamiltonian is found to have a tame high-energy structure which we relate both to gravitational self-force studies of large mass-ratio binary systems, and to the ultra high-energy quantum scattering results of Amati, Ciafaloni and Veneziano. We derive several consequences of our second post-Minkowskian Hamiltonian: (i) the need to use special phase-space gauges to get a tame high-energy limit; and (ii) predictions about a (rest-mass independent) linear Regge trajectory behavior of high-angular-momenta, high-energy circular orbits. Ways of testing these predictions by dedicated numerical simulations are indicated. We finally indicate a way to connect our classical results to the quantum gravitational scattering amplitude of two particles, and we urge amplitude experts to use their novel techniques to compute the two-loop scattering amplitude of scalar masses, from which one could deduce the third post-Minkowskian effective one-body Hamiltonian.

Nanotube Tunneling as a Consequence of Probable Discrete Trajectories

NASA Technical Reports Server (NTRS)

Robinson, Daryl C.

2001-01-01

It has been recently reported that the electrical charge in a semiconductive carbon nanotube is not evenly distributed, but is divided into charge "islands." A clear understanding of tunneling phenomena can be useful to elucidate the mechanism for electrical conduction in nanotubes. This paper represents the first attempt to shed light on the aforementioned phenomenon through viewing tunneling as a natural consequence of "discrete trajectories." The relevance of this analysis is that it may provide further insight into the higher rate of tunneling processes, which makes tunneling devices attractive. In a situation involving particles impinging on a classically impenetrable barrier, the result of quantum mechanics that the probability of detecting transmitted particles falls off exponentially is derived without wave theory. This paper should provide a basis for calculating the charge profile over the length of the tube so that nanoscale devices' conductive properties may be fully exploited.

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

Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu

The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packetmore » in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.« less

A practical method to avoid zero-point leak in molecular dynamics calculations: application to the water dimer.

PubMed

Czakó, Gábor; Kaledin, Alexey L; Bowman, Joel M

2010-04-28

We report the implementation of a previously suggested method to constrain a molecular system to have mode-specific vibrational energy greater than or equal to the zero-point energy in quasiclassical trajectory calculations [J. M. Bowman et al., J. Chem. Phys. 91, 2859 (1989); W. H. Miller et al., J. Chem. Phys. 91, 2863 (1989)]. The implementation is made practical by using a technique described recently [G. Czako and J. M. Bowman, J. Chem. Phys. 131, 244302 (2009)], where a normal-mode analysis is performed during the course of a trajectory and which gives only real-valued frequencies. The method is applied to the water dimer, where its effectiveness is shown by computing mode energies as a function of integration time. Radial distribution functions are also calculated using constrained quasiclassical and standard classical molecular dynamics at low temperature and at 300 K and compared to rigorous quantum path integral calculations.

Combining Charge Couple Devices and Rate Sensors for the Feedforward Control System of a Charge Coupled Device Tracking Loop.

PubMed

Tang, Tao; Tian, Jing; Zhong, Daijun; Fu, Chengyu

2016-06-25

A rate feed forward control-based sensor fusion is proposed to improve the closed-loop performance for a charge couple device (CCD) tracking loop. The target trajectory is recovered by combining line of sight (LOS) errors from the CCD and the angular rate from a fiber-optic gyroscope (FOG). A Kalman filter based on the Singer acceleration model utilizes the reconstructive target trajectory to estimate the target velocity. Different from classical feed forward control, additive feedback loops are inevitably added to the original control loops due to the fact some closed-loop information is used. The transfer function of the Kalman filter in the frequency domain is built for analyzing the closed loop stability. The bandwidth of the Kalman filter is the major factor affecting the control stability and close-loop performance. Both simulations and experiments are provided to demonstrate the benefits of the proposed algorithm.

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions.

PubMed

Liu, Jian; Miller, William H

2011-03-14

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.

Dissipative tunnelling by means of scaled trajectories

NASA Astrophysics Data System (ADS)

Mousavi, S. V.; Miret-Artés, S.

2018-06-01

Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schrödinger-Langevin or Kostin quantum-classical transition wave equation is used and applied resulting in a scaled differential equation of motion. A Gaussian wave packet solution to the resulting scaled Kostin nonlinear equation is assumed and compared to the same solution for the scaled linear Caldirola-Kanai equation. The resulting scaled trajectories are obtained at different dynamical regimes and friction cases, showing the gradual decoherence process in this open dynamics. Theoretical results show that the transmission probabilities are always higher in the Kostin approach than in the Caldirola-Kanai approach in the presence or not of an external electric field. This discrepancy should be understood due to the presence of an environment since the corresponding open dynamics should be governed by nonlinear quantum equations, whereas the second approach is issued from an effective Hamiltonian within a linear theory.

Quantum Tunneling and Chaos in Classical Scale Walkers

NASA Astrophysics Data System (ADS)

Su, Jenny; Dijksman, Joshua; Ward, Jeremy; Behringer, Robert

2014-03-01

We study the behavior of `walkers' small droplets bouncing on a fluid layer vibrated at amplitudes just below the onset of Faraday instability. It was shown recently that despite their macroscopic size, the droplet dynamics are stochastic in nature and reminiscent of the dual particle-wave dynamics in the realm of quantum mechanics (Couder PRL 2006). We use these walkers to study how chaos, which is macroscopically unpredictable, will manifest in a quantum setting. Pecora showed in 2011 that tunneling for particles that have a chaotic ground state is different from tunneling for particles with a regular ground state (PRE 2011). In the experiment we gather data that illustrates the particle trajectory and tunneling behavior as particles transition across the barrier in the double well system with both integrable and chaotic shapes.

Random walks of colloidal probes in viscoelastic materials

NASA Astrophysics Data System (ADS)

Khan, Manas; Mason, Thomas G.

2014-04-01

To overcome limitations of using a single fixed time step in random walk simulations, such as those that rely on the classic Wiener approach, we have developed an algorithm for exploring random walks based on random temporal steps that are uniformly distributed in logarithmic time. This improvement enables us to generate random-walk trajectories of probe particles that span a highly extended dynamic range in time, thereby facilitating the exploration of probe motion in soft viscoelastic materials. By combining this faster approach with a Maxwell-Voigt model (MVM) of linear viscoelasticity, based on a slowly diffusing harmonically bound Brownian particle, we rapidly create trajectories of spherical probes in soft viscoelastic materials over more than 12 orders of magnitude in time. Appropriate windowing of these trajectories over different time intervals demonstrates that random walk for the MVM is neither self-similar nor self-affine, even if the viscoelastic material is isotropic. We extend this approach to spatially anisotropic viscoelastic materials, using binning to calculate the anisotropic mean square displacements and creep compliances along different orthogonal directions. The elimination of a fixed time step in simulations of random processes, including random walks, opens up interesting possibilities for modeling dynamics and response over a highly extended temporal dynamic range.

Zero-point Energy is Needed in Molecular Dynamics Calculations to Access the Saddle Point for H+HCN→H2CN* and cis/trans-HCNH* on a New Potential Energy Surface.

PubMed

Wang, Xiaohong; Bowman, Joel M

2013-02-12

We calculate the probabilities for the association reactions H+HCN→H2CN* and cis/trans-HCNH*, using quasiclassical trajectory (QCT) and classical trajectory (CT) calculations, on a new global ab initio potential energy surface (PES) for H2CN including the reaction channels. The surface is a linear least-squares fit of roughly 60 000 CCSD(T)-F12b/aug-cc-pVDZ electronic energies, using a permutationally invariant basis with Morse-type variables. The reaction probabilities are obtained at a variety of collision energies and impact parameters. Large differences in the threshold energies in the two types of dynamics calculations are traced to the absence of zero-point energy in the CT calculations. We argue that the QCT threshold energy is the realistic one. In addition, trajectories find a direct pathway to trans-HCNH, even though there is no obvious transition state (TS) for this pathway. Instead the saddle point (SP) for the addition to cis-HCNH is evidently also the TS for direct formation of trans-HCNH.

Sensitivity of peptide conformational dynamics on clustering of a classical molecular dynamics trajectory

NASA Astrophysics Data System (ADS)

Jensen, Christian H.; Nerukh, Dmitry; Glen, Robert C.

2008-03-01

We investigate the sensitivity of a Markov model with states and transition probabilities obtained from clustering a molecular dynamics trajectory. We have examined a 500ns molecular dynamics trajectory of the peptide valine-proline-alanine-leucine in explicit water. The sensitivity is quantified by varying the boundaries of the clusters and investigating the resulting variation in transition probabilities and the average transition time between states. In this way, we represent the effect of clustering using different clustering algorithms. It is found that in terms of the investigated quantities, the peptide dynamics described by the Markov model is sensitive to the clustering; in particular, the average transition times are found to vary up to 46%. Moreover, inclusion of nonphysical sparsely populated clusters can lead to serious errors of up to 814%. In the investigation, the time step used in the transition matrix is determined by the minimum time scale on which the system behaves approximately Markovian. This time step is found to be about 100ps. It is concluded that the description of peptide dynamics with transition matrices should be performed with care, and that using standard clustering algorithms to obtain states and transition probabilities may not always produce reliable results.

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

NASA Astrophysics Data System (ADS)

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

2001-05-01

Charge transfer processes due to collisions of ground state S^4+ ions with atomic hydrogen were investigated for energies between 1 meV/u and 10 MeV/u 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 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 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 S^3+ excited classical states. Hydrogen target isotope effects were explored and rate coefficients for temperatures between 100 and 10^6 K will be presented

Time Domain Stability Margin Assessment Method

NASA Technical Reports Server (NTRS)

Clements, Keith

2017-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

Time-Domain Stability Margin Assessment

NASA Technical Reports Server (NTRS)

Clements, Keith

2016-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

Experimental Observation of Classical Dynamical Monodromy

NASA Astrophysics Data System (ADS)

Nerem, M. P.; Salmon, D.; Aubin, S.; Delos, J. B.

2018-03-01

A Hamiltonian system is said to have nontrivial monodromy if its fundamental action-angle loops do not return to their initial topological state at the end of a closed circuit in angular momentum-energy space. This process has been predicted to have consequences which can be seen in dynamical systems, called dynamical monodromy. Using an apparatus consisting of a spherical pendulum subject to magnetic potentials and torques, we observe nontrivial monodromy by the associated topological change in the evolution of a loop of trajectories.

Non linear predictive control of a LEGO mobile robot

NASA Astrophysics Data System (ADS)

Merabti, H.; Bouchemal, B.; Belarbi, K.; Boucherma, D.; Amouri, A.

2014-10-01

Metaheuristics are general purpose heuristics which have shown a great potential for the solution of difficult optimization problems. In this work, we apply the meta heuristic, namely particle swarm optimization, PSO, for the solution of the optimization problem arising in NLMPC. This algorithm is easy to code and may be considered as alternatives for the more classical solution procedures. The PSO- NLMPC is applied to control a mobile robot for the tracking trajectory and obstacles avoidance. Experimental results show the strength of this approach.

The Conference on the Dynamics of Molecular Collisions Held in Oglebay Park, Wheeling, West Virginia on 12-17 July 1987.

DTIC Science & Technology

1987-07-17

Yuhua Guan, Gillian C. Lynch and Donald L. Thompson Department of Chemistry, Oklahoma State University, Stillwater, OK 74078 Classical trajectories...P20 PHOTOFRAGMrTATION OF ALKYL IODIDES -- Photofragmentation Channels and Energy Partitioning of the Fragments Qihe Zhu, Shouling Huang, J.R. Cao , Ye...Chemistry (314) 553-5344 Upton, NY 11973 (516) 282-4348 Dr. William L. Hase Wayne State University Dr. Yuhua Guan 435 Chemistry Department of Chemistry

Vibrational effects in x-ray absorption and resonant inelastic x-ray scattering using a semiclassical scheme

NASA Astrophysics Data System (ADS)

Ljungberg, Mathias P.

2017-12-01

A method is presented for describing vibrational effects in x-ray absorption spectroscopy and resonant inelastic x-ray scattering (RIXS) using a combination of the classical Franck-Condon (FC) approximation and classical trajectories run on the core-excited state. The formulation of RIXS is an extension of the semiclassical Kramers-Heisenberg formalism of Ljungberg et al. [Phys. Rev. B 82, 245115 (2010), 10.1103/PhysRevB.82.245115] to the resonant case, retaining approximately the same computational cost. To overcome difficulties with connecting the absorption and emission processes in RIXS, the classical FC approximation is used for the absorption, which is seen to work well provided that a zero-point-energy correction is included. In the case of core-excited states with dissociative character, the method is capable of closely reproducing the main features for one-dimensional test systems, compared to the quantum-mechanical formulation. Due to the good accuracy combined with the relatively low computational cost, the method has great potential of being used for complex systems with many degrees of freedom, such as liquids and surface adsorbates.

Correlated electron-nuclear dissociation dynamics: classical versus quantum motion

NASA Astrophysics Data System (ADS)

Schaupp, Thomas; Albert, Julian; Engel, Volker

2017-01-01

We investigate the coupled electron-nuclear dynamics in a model system which undergoes dissociation. In choosing different initial conditions, the cases of adiabatic and non-adiabatic dissociation are realized. We treat the coupled electronic and nuclear motion in the complete configuration space so that classically, no surface hopping procedures have to be incorporated in the case that more than a single adiabatic electronic state is populated during the fragmentation. Due to the anharmonic interaction potential, it is expected that classical mechanics substantially deviate from quantum mechanics. However, we provide examples where the densities and fragmentation yields obtained from the two treatments are in astonishingly strong agreement in the case that one starts in the electronic ground state initially. As expected, larger deviations are found if one starts in electronically excited states where trajectories are sampled from the more spatially extended electronic wave function. In that case, higher initial energies are accessed, and the motion proceeds in regions with increasing degree of anharmonicity. Contribution to the Topical Issue "Dynamics of Molecular Systems (MOLEC 2016)", edited by Alberto Garcia-Vela, Luis Banares and Maria Luisa Senent.

A position-dependent mass harmonic oscillator and deformed space

NASA Astrophysics Data System (ADS)

da Costa, Bruno G.; Borges, Ernesto P.

2018-04-01

We consider canonically conjugated generalized space and linear momentum operators x^ q and p^ q in quantum mechanics, associated with a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter q. A canonical transformation (x ^ ,p ^ ) →(x^ q,p^ q ) leads the Hamiltonian of a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space. The equation of motion for the classical phase space (x, p) may be expressed in terms of the deformed (dual) q-derivative. We revisit the problem of a q-deformed oscillator in both classical and quantum formalisms. Particularly, this canonical transformation leads a particle with position-dependent mass in a harmonic potential to a particle with constant mass in a Morse potential. The trajectories in phase spaces (x, p) and (xq, pq) are analyzed for different values of the deformation parameter. Finally, we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.

Steepest Ascent Low/Non-Low-Frequency Ratio in Empirical Mode Decomposition to Separate Deterministic and Stochastic Velocities From a Single Lagrangian Drifter

NASA Astrophysics Data System (ADS)

Chu, Peter C.

2018-03-01

SOund Fixing And Ranging (RAFOS) floats deployed by the Naval Postgraduate School (NPS) in the California Current system from 1992 to 2001 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/) are used to study 2-D turbulent characteristics. Each drifter trajectory is adaptively decomposed using the empirical mode decomposition (EMD) into a series of intrinsic mode functions (IMFs) with corresponding specific scale for each IMF. A new steepest ascent low/non-low-frequency ratio is proposed in this paper to separate a Lagrangian trajectory into low-frequency (nondiffusive, i.e., deterministic) and high-frequency (diffusive, i.e., stochastic) components. The 2-D turbulent (or called eddy) diffusion coefficients are calculated on the base of the classical turbulent diffusion with mixing length theory from stochastic component of a single drifter. Statistical characteristics of the calculated 2-D turbulence length scale, strength, and diffusion coefficients from the NPS RAFOS data are presented with the mean values (over the whole drifters) of the 2-D diffusion coefficients comparable to the commonly used diffusivity tensor method.

3-D high-speed imaging of volcanic bomb trajectory in basaltic explosive eruptions

USGS Publications Warehouse

Gaudin, D.; Taddeucci, J; Houghton, Bruce F.; Orr, Tim R.; Andronico, D.; Del Bello, E.; Kueppers, U.; Ricci, T.; Scarlato, P.

2016-01-01

Imaging, in general, and high speed imaging in particular are important emerging tools for the study of explosive volcanic eruptions. However, traditional 2-D video observations cannot measure volcanic ejecta motion toward and away from the camera, strongly hindering our capability to fully determine crucial hazard-related parameters such as explosion directionality and pyroclasts' absolute velocity. In this paper, we use up to three synchronized high-speed cameras to reconstruct pyroclasts trajectories in three dimensions. Classical stereographic techniques are adapted to overcome the difficult observation conditions of active volcanic vents, including the large number of overlapping pyroclasts which may change shape in flight, variable lighting and clouding conditions, and lack of direct access to the target. In particular, we use a laser rangefinder to measure the geometry of the filming setup and manually track pyroclasts on the videos. This method reduces uncertainties to 10° in azimuth and dip angle of the pyroclasts, and down to 20% in the absolute velocity estimation. We demonstrate the potential of this approach by three examples: the development of an explosion at Stromboli, a bubble burst at Halema'uma'u lava lake, and an in-flight collision between two bombs at Stromboli.

Comparison of different interpolation operators including nonlinear subdivision schemes in the simulation of particle trajectories

NASA Astrophysics Data System (ADS)

Bensiali, Bouchra; Bodi, Kowsik; Ciraolo, Guido; Ghendrih, Philippe; Liandrat, Jacques

2013-03-01

In this work, we compare different interpolation operators in the context of particle tracking with an emphasis on situations involving velocity field with steep gradients. Since, in this case, most classical methods give rise to the Gibbs phenomenon (generation of oscillations near discontinuities), we present new methods for particle tracking based on subdivision schemes and especially on the Piecewise Parabolic Harmonic (PPH) scheme which has shown its advantage in image processing in presence of strong contrasts. First an analytic univariate case with a discontinuous velocity field is considered in order to highlight the effect of the Gibbs phenomenon on trajectory calculation. Theoretical results are provided. Then, we show, regardless of the interpolation method, the need to use a conservative approach when integrating a conservative problem with a velocity field deriving from a potential. Finally, the PPH scheme is applied in a more realistic case of a time-dependent potential encountered in the edge turbulence of magnetically confined plasmas, to compare the propagation of density structures (turbulence bursts) with the dynamics of test particles. This study highlights the difference between particle transport and density transport in turbulent fields.

A mapping variable ring polymer molecular dynamics study of condensed phase proton-coupled electron transfer

NASA Astrophysics Data System (ADS)

Pierre, Sadrach; Duke, Jessica R.; Hele, Timothy J. H.; Ananth, Nandini

2017-12-01

We investigate the mechanisms of condensed phase proton-coupled electron transfer (PCET) using Mapping-Variable Ring Polymer Molecular Dynamics (MV-RPMD), a recently developed method that employs an ensemble of classical trajectories to simulate nonadiabatic excited state dynamics. Here, we construct a series of system-bath model Hamiltonians for the PCET, where four localized electron-proton states are coupled to a thermal bath via a single solvent mode, and we employ MV-RPMD to simulate state population dynamics. Specifically, for each model, we identify the dominant PCET mechanism, and by comparing against rate theory calculations, we verify that our simulations correctly distinguish between concerted PCET, where the electron and proton transfer together, and sequential PCET, where either the electron or the proton transfers first. This work represents a first application of MV-RPMD to multi-level condensed phase systems; we introduce a modified MV-RPMD expression that is derived using a symmetric rather than asymmetric Trotter discretization scheme and an initialization protocol that uses a recently derived population estimator to constrain trajectories to a dividing surface. We also demonstrate that, as expected, the PCET mechanisms predicted by our simulations are robust to an arbitrary choice of the initial dividing surface.

The potential influence of Asian and African mineral dust on ice, mixed-phase and liquid water clouds

NASA Astrophysics Data System (ADS)

Wiacek, A.; Peter, T.; Lohmann, U.

2010-09-01

This modelling study explores the availability of mineral dust particles as ice nuclei for interactions with ice, mixed-phase and liquid water clouds, also tracking the particles' history of cloud-processing. We performed 61 320 one-week forward trajectory calculations originating near the surface of major dust emitting regions in Africa and Asia using high-resolution meteorological analysis fields for the year 2007. Dust-bearing trajectories were assumed to be those coinciding with known dust emission seasons, without explicitly modelling dust emission and deposition processes. We found that dust emissions from Asian deserts lead to a higher potential for interactions with high ice clouds, despite being the climatologically much smaller dust emission source. This is due to Asian regions experiencing significantly more ascent than African regions, with strongest ascent in the Asian Taklimakan desert at ~25%, ~40% and 10% of trajectories ascending to 300 hPa in spring, summer and fall, respectively. The specific humidity at each trajectory's starting point was transported in a Lagrangian manner and relative humidities with respect to water and ice were calculated in 6-h steps downstream, allowing us to estimate the formation of liquid, mixed-phase and ice clouds. Downstream of the investigated dust sources, practically none of the simulated air parcels reached conditions of homogeneous ice nucleation (T≲-40 °C) along trajectories that have not experienced water saturation first. By far the largest fraction of cloud forming trajectories entered conditions of mixed-phase clouds, where mineral dust will potentially exert the biggest influence. The majority of trajectories also passed through atmospheric regions supersaturated with respect to ice but subsaturated with respect to water, where so-called "warm ice clouds" (T≳-40 °C) theoretically may form prior to supercooled water or mixed-phase clouds. The importance of "warm ice clouds" and the general influence of dust in the mixed-phase cloud region are highly uncertain due to both a considerable scatter in recent laboratory data from ice nucleation experiments, which we briefly review in this work, and due to uncertainties in sub-grid scale vertical transport processes unresolved by the present trajectory analysis. For "classical" cirrus-forming temperatures (T≲-40 °C), our results show that only mineral dust ice nuclei that underwent mixed-phase cloud-processing, most likely acquiring coatings of organic or inorganic material, are likely to be relevant. While the potential paucity of deposition ice nuclei shown in this work dimishes the possibility of deposition nucleation, the absence of liquid water droplets at T≲-40 °C makes the less explored contact freezing mechanism (involving droplet collisions with bare ice nuclei) highly inefficient. These factors together indicate the necessity of further systematic studies of immersion mode ice nucleation on mineral dust suspended in atmospherically relevant coatings.

Feasibility of Modified Anterior Odontoid Screw Fixation: Analysis of a New Trajectory Using 3-Dimensional Simulation Software.

PubMed

Zhang, Li-Lian; Chen, Qi; Wang, Hao-Li; Xu, Hua-Zi; Tian, Nai-Feng

2018-05-03

Anterior odontoid screw fixation (AOSF) has been suggested as the optimal treatment for type II and some shallow type III odontoid fractures. However, only the classical surgical trajectory is available; no newer entry points or trajectories have been reported. We evaluated the anatomic feasibility of a new trajectory for AOSF using 3-dimensional (3D) screw insertion simulation software (Mimics). Computed tomography (CT) scans of patients (65 males and 59 females) with normal cervical structures were obtained consecutively, and the axes were reconstructed in 3 dimensions by Mimics software. Then simulated operations were performed using 2 new entry points below the superior articular process using bilateral screws of different diameters (group 1: 4 mm and 4 mm; group 2: 4 mm and 3.5 mm; group 3: 3.5 mm and 3.5 mm). The success rates and the required screw lengths were recorded and analyzed. The success rates were 79.03% for group 1, 95.16% for group 2, and 98.39% for group 3. The success rates for groups 2 and 3 did not differ significantly, and both were significantly better than the rate for group 1. The success rate was much higher in males than in females in group 1, but the success rate was similar in males and females in the other 2 groups. Screw lengths did not differ significantly among the 3 groups, but an effect of sex was apparent. Our modified trajectory is anatomically feasible for fixation of anterior odontoid fractures, but further anatomic experiments and clinical research are needed. Copyright © 2018 Elsevier Inc. All rights reserved.

Nonadiabatic Molecular Dynamics and Orthogonality Constrained Density Functional Theory

NASA Astrophysics Data System (ADS)

Shushkov, Philip Georgiev

The exact quantum dynamics of realistic, multidimensional systems remains a formidable computational challenge. In many chemical processes, however, quantum effects such as tunneling, zero-point energy quantization, and nonadiabatic transitions play an important role. Therefore, approximate approaches that improve on the classical mechanical framework are of special practical interest. We propose a novel ring polymer surface hopping method for the calculation of chemical rate constants. The method blends two approaches, namely ring polymer molecular dynamics that accounts for tunneling and zero-point energy quantization, and surface hopping that incorporates nonadiabatic transitions. We test the method against exact quantum mechanical calculations for a one-dimensional, two-state model system. The method reproduces quite accurately the tunneling contribution to the rate and the distribution of reactants between the electronic states for this model system. Semiclassical instanton theory, an approach related to ring polymer molecular dynamics, accounts for tunneling by the use of periodic classical trajectories on the inverted potential energy surface. We study a model of electron transfer in solution, a chemical process where nonadiabatic events are prominent. By representing the tunneling electron with a ring polymer, we derive Marcus theory of electron transfer from semiclassical instanton theory after a careful analysis of the tunneling mode. We demonstrate that semiclassical instanton theory can recover the limit of Fermi's Golden Rule rate in a low-temperature, deep-tunneling regime. Mixed quantum-classical dynamics treats a few important degrees of freedom quantum mechanically, while classical mechanics describes affordably the rest of the system. But the interface of quantum and classical description is a challenging theoretical problem, especially for low-energy chemical processes. We therefore focus on the semiclassical limit of the coupled nuclear-electronic dynamics. We show that the time-dependent Schrodinger equation for the electrons employed in the widely used fewest switches surface hopping method is applicable only in the limit of nearly identical classical trajectories on the different potential energy surfaces. We propose a short-time decoupling algorithm that restricts the use of the Schrodinger equation only to the interaction regions. We test the short-time approximation on three model systems against exact quantum-mechanical calculations. The approximation improves the performance of the surface hopping approach. Nonadiabatic molecular dynamics simulations require the efficient and accurate computation of ground and excited state potential energy surfaces. Unlike the ground state calculations where standard methods exist, the computation of excited state properties is a challenging task. We employ time-independent density functional theory, in which the excited state energy is represented as a functional of the total density. We suggest an adiabatic-like approximation that simplifies the excited state exchange-correlation functional. We also derive a set of minimal conditions to impose exactly the orthogonality of the excited state Kohn-Sham determinant to the ground state determinant. This leads to an efficient, variational algorithm for the self-consistent optimization of the excited state energy. Finally, we assess the quality of the excitation energies obtained by the new method on a set of 28 organic molecules. The new approach provides results of similar accuracy to time-dependent density functional theory.

Theory of time-resolved x-ray photoelectron diffraction from transient conformational molecules

NASA Astrophysics Data System (ADS)

Tsuru, Shota; Sako, Tokuei; Fujikawa, Takashi; Yagishita, Akira

2017-04-01

We formulate x-ray photoelectron diffraction (XPD) from molecules undergoing photochemical reactions induced by optical laser pulses, and then apply the formula to the simulation of time-dependent XPD profiles from both dissociating I2 molecules and bending C S2 molecules. The dependence of nuclear wave-packet motions on the intensity and shape of the optical laser pulses is examined. As a result, the XPD simulations based on such nuclear wave-packet calculations are observed to exhibit characteristic features, which are compared with the XPD profiles due to classical trajectories of nuclear motions. The present study provides a methodology toward creating "molecular movies" of ultrafast photochemical reactions by means of femtosecond XPD with x-ray free-electron lasers.

Time-Frequency Analysis Reveals Pairwise Interactions in Insect Swarms

NASA Astrophysics Data System (ADS)

Puckett, James G.; Ni, Rui; Ouellette, Nicholas T.

2015-06-01

The macroscopic emergent behavior of social animal groups is a classic example of dynamical self-organization, and is thought to arise from the local interactions between individuals. Determining these interactions from empirical data sets of real animal groups, however, is challenging. Using multicamera imaging and tracking, we studied the motion of individual flying midges in laboratory mating swarms. By performing a time-frequency analysis of the midge trajectories, we show that the midge behavior can be segmented into two distinct modes: one that is independent and composed of low-frequency maneuvers, and one that consists of higher-frequency nearly harmonic oscillations conducted in synchrony with another midge. We characterize these pairwise interactions, and make a hypothesis as to their biological function.

Phase-space analysis of the Schwinger effect in inhomogeneous electromagnetic fields

NASA Astrophysics Data System (ADS)

Kohlfürst, Christian

2018-05-01

Schwinger pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied. The focus is on the particle phase-space distribution within a high-intensity few-cycle pulse. Accurate numerical solutions of a quantum kinetic theory (DHW formalism) are presented in momentum space and, with the aid of coarse-graining techniques, in a mixed spatial-momentum representation. Additionally, signatures of the carrier-envelope phase as well as spin-field interactions are discussed on the basis of a trajectory-based model taking into account instantaneous pair production and relativistic single-particle dynamics. Although our simple semi-classical single-particle model cannot describe every aspect of the particle production process (quantum interferences), essential features such as spin-field interactions are captured.

Physics of badminton shuttlecocks. Part 1 : aerodynamics

NASA Astrophysics Data System (ADS)

Cohen, Caroline; Darbois Texier, Baptiste; Quéré, David; Clanet, Christophe

2011-11-01

We study experimentally shuttlecocks dynamics. In this part we show that shuttlecock trajectory is highly different from classical parabola. When one takes into account the aerodynamic drag, the flight of the shuttlecock quickly curves downwards and almost reaches a vertical asymptote. We solve the equation of motion with gravity and drag at high Reynolds number and find an analytical expression of the reach. At high velocity, this reach does not depend on velocity anymore. Even if you develop your muscles you will not manage to launch the shuttlecock very far because of the ``aerodynamic wall.'' As a consequence you can predict the length of the field. We then discuss the extend of the aerodynamic wall to other projectiles like sports balls and its importance.

Stability Assessment and Tuning of an Adaptively Augmented Classical Controller for Launch Vehicle Flight Control

NASA Technical Reports Server (NTRS)

VanZwieten, Tannen; Zhu, J. Jim; Adami, Tony; Berry, Kyle; Grammar, Alex; Orr, Jeb S.; Best, Eric A.

2014-01-01

Recently, a robust and practical adaptive control scheme for launch vehicles [ [1] has been introduced. It augments a classical controller with a real-time loop-gain adaptation, and it is therefore called Adaptive Augmentation Control (AAC). The loop-gain will be increased from the nominal design when the tracking error between the (filtered) output and the (filtered) command trajectory is large; whereas it will be decreased when excitation of flex or sloshing modes are detected. There is a need to determine the range and rate of the loop-gain adaptation in order to retain (exponential) stability, which is critical in vehicle operation, and to develop some theoretically based heuristic tuning methods for the adaptive law gain parameters. The classical launch vehicle flight controller design technics are based on gain-scheduling, whereby the launch vehicle dynamics model is linearized at selected operating points along the nominal tracking command trajectory, and Linear Time-Invariant (LTI) controller design techniques are employed to ensure asymptotic stability of the tracking error dynamics, typically by meeting some prescribed Gain Margin (GM) and Phase Margin (PM) specifications. The controller gains at the design points are then scheduled, tuned and sometimes interpolated to achieve good performance and stability robustness under external disturbances (e.g. winds) and structural perturbations (e.g. vehicle modeling errors). While the GM does give a bound for loop-gain variation without losing stability, it is for constant dispersions of the loop-gain because the GM is based on frequency-domain analysis, which is applicable only for LTI systems. The real-time adaptive loop-gain variation of the AAC effectively renders the closed-loop system a time-varying system, for which it is well-known that the LTI system stability criterion is neither necessary nor sufficient when applying to a Linear Time-Varying (LTV) system in a frozen-time fashion. Therefore, a generalized stability metric for time-varying loop=gain perturbations is needed for the AAC.

High prices for rare species can drive large populations extinct: the anthropogenic Allee effect revisited.

PubMed

Holden, Matthew H; McDonald-Madden, Eve

2017-09-21

Consumer demand for plant and animal products threatens many populations with extinction. The anthropogenic Allee effect (AAE) proposes that such extinctions can be caused by prices for wildlife products increasing with species rarity. This price-rarity relationship creates financial incentives to extract the last remaining individuals of a population, despite higher search and harvest costs. The AAE has become a standard approach for conceptualizing the threat of economic markets on endangered species. Despite its potential importance for conservation, AAE theory is based on a simple graphical model with limited analysis of possible population trajectories. By specifying a general class of functions for price-rarity relationships, we show that the classic theory can understate the risk of species extinction. AAE theory proposes that only populations below a critical Allee threshold will go extinct due to increasing price-rarity relationships. Our analysis shows that this threshold can be much higher than the original theory suggests, depending on initial harvest effort. More alarmingly, even species with population sizes above this Allee threshold, for which AAE predicts persistence, can be destined to extinction. Introducing even a minimum price for harvested individuals, close to zero, can cause large populations to cross the classic anthropogenic Allee threshold on a trajectory towards extinction. These results suggest that traditional AAE theory may give a false sense of security when managing large harvested populations. Copyright © 2017 Elsevier Ltd. All rights reserved.

How can we model selectively neutral density dependence in evolutionary games.

PubMed

Argasinski, Krzysztof; Kozłowski, Jan

2008-03-01

The problem of density dependence appears in all approaches to the modelling of population dynamics. It is pertinent to classic models (i.e., Lotka-Volterra's), and also population genetics and game theoretical models related to the replicator dynamics. There is no density dependence in the classic formulation of replicator dynamics, which means that population size may grow to infinity. Therefore the question arises: How is unlimited population growth suppressed in frequency-dependent models? Two categories of solutions can be found in the literature. In the first, replicator dynamics is independent of background fitness. In the second type of solution, a multiplicative suppression coefficient is used, as in a logistic equation. Both approaches have disadvantages. The first one is incompatible with the methods of life history theory and basic probabilistic intuitions. The logistic type of suppression of per capita growth rate stops trajectories of selection when population size reaches the maximal value (carrying capacity); hence this method does not satisfy selective neutrality. To overcome these difficulties, we must explicitly consider turn-over of individuals dependent on mortality rate. This new approach leads to two interesting predictions. First, the equilibrium value of population size is lower than carrying capacity and depends on the mortality rate. Second, although the phase portrait of selection trajectories is the same as in density-independent replicator dynamics, pace of selection slows down when population size approaches equilibrium, and then remains constant and dependent on the rate of turn-over of individuals.

Comparative ontogeny in humans and chimpanzees: similarities, differences and paradoxes in postnatal growth and development of the skull.

PubMed

Bastir, Markus; Rosas, Antonio

2004-12-01

The hypothesis of retarded development is a classic and controversial issue in human evolution. It depends directly on the understanding of ontogenetic trajectories and their basic constituents: timing, rate and associated patterns of maturation. In the present study, we applied geometric morphometrics to investigate postnatal ontogeny in human and chimpanzee skulls (N = 302). We evaluated postnatal ontogenetic rates, based on comparisons of properties of size and shape in adults. At different dental ages the percentage of the adult mean size (growth) and adult mean shape (development) was used to quantify patterns of maturation. We found significantly higher levels of ontogenetic maturity in humans than chimpanzees during pre-M1 and M1 eruption. However, during this ontogenetic period the human increments were lower than those of chimpanzees suggesting lower rates. During and after M2-eruption species did not differ in their ontogenetic trajectories. The results indicate that higher prenatal and lower peri- and postnatal maturation rates characterize human ontogeny when compared with chimpanzees. If mandibular ontogeny is considered alone, a paradox was found. Whereas growth maturation proceeded in an expected trajectory continuously approximating 100% adult mean size, developmental maturity was different. After M1-eruption in both species the morphological distance, which had increased before, became reduced again, and reached adult mean shape in a second developmental peak. Such a tendency was found in humans and chimpanzees. This indicates that both size and shape maturation must be considered to understand the complexity of postnatal mandibular ontogeny.

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.

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.

Thermal quantum time-correlation functions from classical-like dynamics

NASA Astrophysics Data System (ADS)

Hele, Timothy J. H.

2017-07-01

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here, we review recent progress in the field with the development of methods including centroid molecular dynamics , ring polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from 'Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also apply the Matsubara formalism to reaction rate theory, rederiving t → 0+ quantum transition-state theory (QTST) and showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

Time Domain Stability Margin Assessment of the NASA Space Launch System GN&C Design for Exploration Mission One

NASA Technical Reports Server (NTRS)

Clements, Keith; Wall, John

2017-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

Time Domain Stability Margin Assessment of the NS Space Launch System GN&C Design for Exploration Mission One

NASA Technical Reports Server (NTRS)

Clements, Keith; Wall, John

2017-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

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

Chu, S.; Wang, K.; Layton, E.

In this paper we accomplish three goals. First, we present new nonperturbative results of complex quasi-energies (shifts and widths) for several low-lying excited states of atomic H in strong fields, using the {ital L}{sup 2} non-Hermitian Floquet matrix technique. Second, we present a new nonperturbative {ital L}{sup 2} technique for the treatment of ac Stark shifts of arbitrary excited states. We found that all the Rydberg states in weak fields are upshifted and closely follow the quadratic field dependence described by the ponderomotive potential {ital e}{sup 2}{ital F}{sup 2}/4{ital mgw}{sup 2}. Large deviation from the ponderomotive shift and intricate level-shiftmore » behaviors, however, occur in strong fields. Finally, we present a classical nonperturbative treatment of the electronic motion in intense laser fields. We show that the spectral analysis of classical trajectories can provide detailed insights regarding the mechanisms responsible for the multiple-harmonic generation recently observed in high-intensity experiments.« less

Energy Scaling of Cold Atom-Atom-Ion Three-Body Recombination

NASA Astrophysics Data System (ADS)

Krükow, Artjom; Mohammadi, Amir; Härter, Arne; Denschlag, Johannes Hecker; Pérez-Ríos, Jesús; Greene, Chris H.

2016-05-01

We study three-body recombination of Ba++Rb +Rb in the mK regime where a single 138Ba+ ion in a Paul trap is immersed into a cloud of ultracold 87Rb atoms. We measure the energy dependence of the three-body rate coefficient k3 and compare the results to the theoretical prediction, k3∝Ecol-3 /4, where Ecol is the collision energy. We find agreement if we assume that the nonthermal ion energy distribution is determined by at least two different micromotion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed in an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s -wave regime.

Potential energy surfaces and reaction dynamics of polyatomic molecules

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

Chang, Yan-Tyng

A simple empirical valence bond (EVB) model approach is suggested for constructing global potential energy surfaces for reactions of polyatomic molecular systems. This approach produces smooth and continuous potential surfaces which can be directly utilized in a dynamical study. Two types of reactions are of special interest, the unimolecular dissociation and the unimolecular isomerization. For the first type, the molecular dissociation dynamics of formaldehyde on the ground electronic surface is investigated through classical trajectory calculations on EVB surfaces. The product state distributions and vector correlations obtained from this study suggest very similar behaviors seen in the experiments. The intramolecular hydrogenmore » atom transfer in the formic acid dimer is an example of the isomerization reaction. High level ab initio quantum chemistry calculations are performed to obtain optimized equilibrium and transition state dimer geometries and also the harmonic frequencies.« less

Suppression of progesterone synthesis in human trophoblast cells by fine particulate matter primarily derived from industry.

PubMed

Wang, Cui; Yang, Jinhuan; Hao, Zhengliang; Gong, Chenxue; Tang, Lihua; Xu, Yingling; Lu, Dezhao; Li, Zhuoyu; Zhao, Meirong

2017-12-01

Epidemiological studies have exhibited a positive association between fine particulate matter (PM 2.5 ) exposure and adverse pregnancy outcome (APO). However, source-related effect and the potential mechanism have not been thoroughly elucidated in toxicology. In this study, PM 2.5 was collected during a severe winter haze episode in an energy-base city of China. We coupled this approach with the source appointment by applying the Lagrangian Integrated Trajectory and Concentration Weighted Trajectory model. We observed that the primary trajectory with high polluted air mass came from the northwest of the sampling site. Approximately 90% or more of PM 2.5 was derived from the industry at this haze period. Next, the sampled PM 2.5 was used to study the classical hormone synthesis pathway on trophoblast JEG-3 cells. PM 2.5 induced the secretion of human chorionic gonadotrophin (HCG) and the proliferation of JEG-3 cells at a noncytotoxic concentration. However, the synthesis of progesterone was significantly suppressed, even if both hCG and cyclic adenosine monophosphate (cAMP) were increased, suggesting that PM 2.5 may interfere the downstream of cAMP. As expected, the phosphorylated activity of protein kinase A (PKA) was attenuated. Subsequently, the downstream molecules of steroidogenesis, such as ferredoxin reductase (FDXR), CYP11A1 (encoded P450scc), and 3β-Hydroxysteroid dehydrogenase type 1 (3β-HSD1), were inhibited. Therefore, PM 2.5, primarily derived from industry, may directly inhibit the phosphorylation status of PKA in JEG-3 which, in turn, inhibited the proteins expression in progesterone-synthesis to suppress progesterone levels. Considering the pivotal role of progesterone in pregnancy maintenance, the mechanism on hormone synthesis may provide a better understanding for PM 2.5 -caused APO. Industry-emanated PM 2.5 , though not specific, could threaten the placenta, which needs to be verified by further epidemiological studies. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

Composition and structure of surfaces by time-of-flight scattering and recoiling spectrometry (TOF-SARS)

NASA Astrophysics Data System (ADS)

Ahn, Jeongheon

1997-10-01

Time-of-flight scattering and recoiling spectrometry (TOF-SARS) was applied to characterize surface structures in order to understand the chemical and physical phenomena on various surfaces. The combination of TOF-SARS, LEED, and classical ion trajectory simulations has allowed characterization of the elemental composition in the outermost atomic layers, surface symmetry, and possible reconstruction or relaxation. The composition and structure of the CdS\\{0001\\}-(1 x 1) and CdS\\{000bar1\\}-(1 x 1) surfaces were investigated. The termination layer of each surface was determined by grazing incidence TOF-SARS. Both (1 x 1) surfaces are bulk-terminated without any reconstruction or relaxation detected by TOF-SARS. Each surface has two domains which are rotated by 60sp° from each other and there exist steps on both surfaces. The CdS\\{0001\\}-(1 x 1) surface is stabilized by O and H covering half a monolayer which are structurally ordered on the surface, while the O and H on the CdS\\{000bar1\\}-(1 x 1) stabilize the surface without ordering. The study of GaN\\{000bar1\\}-(1 x 1) shows the bulk-termination of the surface with no detectable reconstruction or relaxation. The surface is terminated in a N layer with Ga in the 2sp{nd}-layer. H atoms are bound to the outermost N atoms with a coverage of ˜3/4 monolayer and protrude outward from the surface. The surface termination, composition and structure of the Alsb2Osb3 (sapphire) were examined. The surface relaxation was studied quantitatively using classical ion trajectory simulations along with TOF-SARS. The surface undergoes 1sp{st}{-}2sp{nd}-layer relaxation as large as 0.5 A from the bulk value resulting in near coplanarity of Al and O atoms. The reconstruction of the Ni\\{100\\}-(2 x 2)-C surface was studied by TOF-SARS. The surface contained 80% of the (2 x 2)p4g phase and 20% of the unreconstructed (2 x 2) phase. The displacement of Ni atoms was determined by comparing the experimental and simulated results.

Towards apparent convergence in asymptotically safe quantum gravity

NASA Astrophysics Data System (ADS)

Denz, T.; Pawlowski, J. M.; Reichert, M.

2018-04-01

The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in Christiansen et al. (Phys Lett B 728:114, 2014), Christiansen et al. (Phy Rev D 93:044036, 2016), and implemented in Christiansen et al. (Phys Rev D 92:121501, 2015) for propagators and three-point functions. In the present work this expansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows. In terms of a covariant operator expansion the current approximation gives access to Λ , R, R^2 as well as R_{μ ν }^2 and higher derivative operators. We find a UV fixed point with three attractive and two repulsive directions, thus confirming previous studies on the relevance of the first three operators. In the infrared we find trajectories that correspond to classical general relativity and further show non-classical behaviour in some fluctuation couplings. We also find signatures for the apparent convergence of the systematic vertex expansion. This opens a promising path towards establishing asymptotically safe gravity in terms of apparent convergence.

Experimental studies by complementary terahertz techniques and semi-classical calculations of N2- broadening coefficients of CH335Cl

NASA Astrophysics Data System (ADS)

Guinet, M.; Rohart, F.; Buldyreva, J.; Gupta, V.; Eliet, S.; Motiyenko, R. A.; Margulès, L.; Cuisset, A.; Hindle, F.; Mouret, G.

2012-07-01

Room-temperature N2-broadening coefficients of methyl chloride rotational lines are measured over a large interval of quantum numbers (6≤J≤50, 0≤K≤18) by a submillimeter frequency-multiplication chain (J≤31) and a terahertz photomixing continuous-wave spectrometer (J≥31). In order to check the accuracy of both techniques, the measurements of identical lines are compared for J=31. The pressure broadening coefficients are deduced from line fits using mainly a Voigt profile model. The excellent signal-to-noise ratio of the frequency-multiplication scheme highlights some speed dependence effect on the line shape. Theoretical values of these coefficients are calculated by a semi-classical approach with exact trajectories. An intermolecular potential including atom-atom interactions is used for the first time. It is shown that, contrary to the previous theoretical predictions, the contributions of short-range forces are important for all values of the rotational quantum numbers. Additional testing of modifications required in the semi-classical formalism for a correct application of the cumulant expansion is also performed. It is stated that the use of the cumulant average on the rotational states of the perturbing molecule leads, for high J and small K values, to slightly higher line-broadening coefficients, as expected for the relatively strong interacting CH3Cl-N2 system. The excellent agreement between the theoretical and the experimental results ensures the reliability of these data.

Electron removal from H and He atoms in collisions with C q+ , O q+ ions

NASA Astrophysics Data System (ADS)

Janev, R. K.; McDowell, M. R. C.

1984-06-01

Cross sections for electron capture and ionisation in collision of partially and completely stripped C q+ , N q+ and O q+ ions with hydrogen and helium atoms have been calculated at selected energies. The classical trajectory Monte Carlo method was used with a variable-charge pseudopotential to describe the interaction of the active electron with the projectile ion. A scalling relationship has been derived for the electron removal (capture and ionisation) cross section which allows a unifield representation of the data.

Catenaries in viscous fluid

NASA Astrophysics Data System (ADS)

Hanna, James; Chakrabarti, Brato

2015-11-01

Slender structures live in fluid flows across many scales, from towed instruments to plant blades to microfluidic valves. The present work details a simple model of a flexible structure in a uniform flow. We present analytical solutions for the translating, axially flowing equilibria of strings subjected to a uniform body force and linear drag forces. This is an extension of the classical catenaries to a five-parameter family of solutions, represented as trajectories in angle-curvature ``phase space.'' Limiting cases include neutrally buoyant towed cables and freely sedimenting flexible filaments. Now at University of California, San Diego.

In situ realization of particlelike scattering states in a microwave cavity

NASA Astrophysics Data System (ADS)

Böhm, Julian; Brandstötter, Andre; Ambichl, Philipp; Rotter, Stefan; Kuhl, Ulrich

2018-02-01

We realize scattering states in a lossy and chaotic two-dimensional microwave cavity which follow bundles of classical particle trajectories. To generate such particlelike scattering states, we measure the system's complex transmission matrix and apply an adapted Wigner-Smith time-delay formalism to it. The necessary shaping of the incident wave is achieved in situ using phase- and amplitude-regulated microwave antennas. Our experimental findings pave the way for establishing spatially confined communication channels that avoid possible intruders or obstacles in wave-based communication systems.

The divine clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state

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

Durran, Richard; Neate, Andrew; Truman, Aubrey

2008-03-15

We consider the Bohr correspondence limit of the Schroedinger wave function for an atomic elliptic state. We analyze this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Keplerian orbit for eccentricities greater than (1/{radical}(2)) which do not occur classically.

Vertical incidence of slow Ne 10+ ions on an LiF surface: Suppression of the trampoline effect

NASA Astrophysics Data System (ADS)

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

2001-08-01

We present a Monte Carlo simulation of the neutralization of a slow Ne 10+ ion in vertical incidence on an LiF(1 0 0) surface. The rates for resonant electron transfer between surface F - ions and the projectile are calculated using a classical trajectory Monte Carlo simulation. We investigate the influence of the hole mobility on the neutralization sequence. It is shown that backscattering above the surface due to the local positive charge up of the surface ("trampoline effect") does not take place.

Atom optics in the time domain

NASA Astrophysics Data System (ADS)

Arndt, M.; Szriftgiser, P.; Dalibard, J.; Steane, A. M.

1996-05-01

Atom-optics experiments are presented using a time-modulated evanescent light wave as an atomic mirror in the trampoline configuration, i.e., perpendicular to the direction of the atomic free fall. This modulated mirror is used to accelerate cesium atoms, to focus their trajectories, and to apply a ``multiple lens'' to separately focus different velocity classes of atoms originating from a point source. We form images of a simple two-slit object to show the resolution of the device. The experiments are modelled by a general treatment analogous to classical ray optics.

How decoherence affects the probability of slow-roll eternal inflation

NASA Astrophysics Data System (ADS)

Boddy, Kimberly K.; Carroll, Sean M.; Pollack, Jason

2017-07-01

Slow-roll inflation can become eternal if the quantum variance of the inflaton field around its slowly rolling classical trajectory is converted into a distribution of classical spacetimes inflating at different rates, and if the variance is large enough compared to the rate of classical rolling that the probability of an increased rate of expansion is sufficiently high. Both of these criteria depend sensitively on whether and how perturbation modes of the inflaton interact and decohere. Decoherence is inevitable as a result of gravitationally sourced interactions whose strength are proportional to the slow-roll parameters. However, the weakness of these interactions means that decoherence is typically delayed until several Hubble times after modes grow beyond the Hubble scale. We present perturbative evidence that decoherence of long-wavelength inflaton modes indeed leads to an ensemble of classical spacetimes with differing cosmological evolutions. We introduce the notion of per-branch observables—expectation values with respect to the different decohered branches of the wave function—and show that the evolution of modes on individual branches varies from branch to branch. Thus, single-field slow-roll inflation fulfills the quantum-mechanical criteria required for the validity of the standard picture of eternal inflation. For a given potential, the delayed decoherence can lead to slight quantitative adjustments to the regime in which the inflaton undergoes eternal inflation.

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix

DOE PAGES

Miller, William H.; Cotton, Stephen J.

2016-08-28

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory - e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer valuesmore » of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states - and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.« less

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix.

PubMed

Miller, William H; Cotton, Stephen J

2016-08-28

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory-e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states-and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.

A round trip from Caldirola to Bateman systems

NASA Astrophysics Data System (ADS)

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

2011-03-01

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

Periodic orbit spectrum in terms of Ruelle-Pollicott resonances

NASA Astrophysics Data System (ADS)

Leboeuf, P.

2004-02-01

Fully chaotic Hamiltonian systems possess an infinite number of classical solutions which are periodic, e.g., a trajectory “p” returns to its initial conditions after some fixed time τp. Our aim is to investigate the spectrum {τ1,τ2,…} of periods of the periodic orbits. An explicit formula for the density ρ(τ)=∑pδ(τ-τp) is derived in terms of the eigenvalues of the classical evolution operator. The density is naturally decomposed into a smooth part plus an interferent sum over oscillatory terms. The frequencies of the oscillatory terms are given by the imaginary part of the complex eigenvalues (Ruelle-Pollicott resonances). For large periods, corrections to the well-known exponential growth of the smooth part of the density are obtained. An alternative formula for ρ(τ) in terms of the zeros and poles of the Ruelle ζ function is also discussed. The results are illustrated with the geodesic motion in billiards of constant negative curvature. Connections with the statistical properties of the corresponding quantum eigenvalues, random-matrix theory, and discrete maps are also considered. In particular, a random-matrix conjecture is proposed for the eigenvalues of the classical evolution operator of chaotic billiards.

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.

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

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory—e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of themore » action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states—and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.« less

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

Miller, William H.; Cotton, Stephen J.

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory - e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer valuesmore » of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states - and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.« less

On the long time behavior of non-autonomous Lotka-Volterra models with diffusion via the sub-supertrajectory method

NASA Astrophysics Data System (ADS)

Langa, José A.; Rodríguez-Bernal, Aníbal; Suárez, Antonio

In this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non-autonomous Lotka-Volterra systems in all the three cases of competition, symbiosis or prey-predator. In particular, under some conditions on the parameters, we prove the existence of a unique nondegenerate global solution for these models, which attracts any other complete bounded trajectory. Thus, we generalize the existence of a unique strictly positive stable (stationary) solution from the autonomous case and we extend to Lotka-Volterra systems the result for scalar logistic equations. To this end we present the sub-supertrajectory tool as a generalization of the now classical sub-supersolution method. In particular, we also conclude pullback and forwards permanence for the above models.

Slow-roll approximation in loop quantum cosmology

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

Luc, Joanna; Mielczarek, Jakub, E-mail: joanna.luc@uj.edu.pl, E-mail: jakub.mielczarek@uj.edu.pl

The slow-roll approximation is an analytical approach to study dynamical properties of the inflationary universe. In this article, systematic construction of the slow-roll expansion for effective loop quantum cosmology is presented. The analysis is performed up to the fourth order in both slow-roll parameters and the parameter controlling the strength of deviation from the classical case. The expansion is performed for three types of the slow-roll parameters: Hubble slow-roll parameters, Hubble flow parameters and potential slow-roll parameters. An accuracy of the approximation is verified by comparison with the numerical phase space trajectories for the case with a massive potential term.more » The results obtained in this article may be helpful in the search for the subtle quantum gravitational effects with use of the cosmological data.« less

Generalized entropy production fluctuation theorems for quantum systems

NASA Astrophysics Data System (ADS)

Rana, Shubhashis; Lahiri, Sourabh; Jayannavar, A. M.

2013-02-01

Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for three different cases: (i) the system is evolving in isolation from its surroundings; (ii) the system being weakly coupled to a heat bath; and (iii) system in contact with reservoir using quantum Crooks fluctuation theorem. In case (iii), we build on the treatment carried out in [H. T. Quan and H. Dong, arxiv/cond-mat: 0812.4955], where a quantum trajectory has been defined as a sequence of alternating work and heat steps. The obtained entropy production fluctuation theorems retain the same form as in the classical case. The inequality of second law of thermodynamics gets modified in the presence of information. These fluctuation theorems are robust against intermediate measurements of any observable performed with respect to von Neumann projective measurements as well as weak or positive operator valued measurements.

Effects of polymers on the spatial structure of turbulent flows

NASA Astrophysics Data System (ADS)

Sinhuber, Michael; Ballouz, Joseph G.; Ouellette, Nicholas T.

2017-11-01

It is well known that the addition of minor amounts of polymers to a turbulent water flow can significantly change its properties. One of the most prominent effects is the observed drastic reduction of drag in wall-bounded flows that is utilized in many engineering applications. Much of the research on polymers in turbulence has focused on their influence on the turbulent energy cascade and their interaction with the energy transfer processes. Much less investigated are their effects on the spatial structure of turbulent flows. In a classical von-Kárman swirling flow setup, we used Lagrangian particle tracking to obtain three-dimensional particle trajectories, velocities, and accelerations and find that polymers have a significant effect on Lagrangian measures of the turbulence structure such as radial distribution functions and the curvature of particle trajectories. We find that not only do the statistical distributions change, but also that polymers appear to affect the spatial statistics well beyond the size of the polymers themselves.

Machine learning of accurate energy-conserving molecular force fields.

PubMed

Chmiela, Stefan; Tkatchenko, Alexandre; Sauceda, Huziel E; Poltavsky, Igor; Schütt, Kristof T; Müller, Klaus-Robert

2017-05-01

Using conservation of energy-a fundamental property of closed classical and quantum mechanical systems-we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio molecular dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized molecules with an accuracy of 0.3 kcal mol -1 for energies and 1 kcal mol -1 Å̊ -1 for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.

Deciphering Front-Side Complex Formation in SN2 Reactions via Dynamics Mapping.

PubMed

Szabó, István; Olasz, Balázs; Czakó, Gábor

2017-07-06

Due to their importance in organic chemistry, the atomistic understanding of bimolecular nucleophilic substitution (S N 2) reactions shows exponentially growing interest. In this publication, the effect of front-side complex (FSC) formation is uncovered via quasi-classical trajectory computations combined with a novel analysis method called trajectory orthogonal projection (TOP). For both F - + CH 3 Y [Y = Cl,I] reactions, the lifetime distributions of the F - ···YCH 3 front-side complex revealed weakly trapped nucleophiles (F - ). However, only the F - + CH 3 I reaction features strongly trapped nucleophiles in the front-side region of the prereaction well. Interestingly, both back-side and front-side attack show propensity to long-lived FSC formation. Spatial distributions of the nucleophile demonstrate more prominent FSC formation in case of the F - + CH 3 I reaction compared to F - + CH 3 Cl. The presence of front-side intermediates and the broad spatial distribution in the back-side region may explain the indirect nature of the F - + CH 3 I reaction.

Machine learning of accurate energy-conserving molecular force fields

PubMed Central

Chmiela, Stefan; Tkatchenko, Alexandre; Sauceda, Huziel E.; Poltavsky, Igor; Schütt, Kristof T.; Müller, Klaus-Robert

2017-01-01

Using conservation of energy—a fundamental property of closed classical and quantum mechanical systems—we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio molecular dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized molecules with an accuracy of 0.3 kcal mol−1 for energies and 1 kcal mol−1 Å̊−1 for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods. PMID:28508076

Decentralized robust nonlinear model predictive controller for unmanned aerial systems

NASA Astrophysics Data System (ADS)

Garcia Garreton, Gonzalo A.

The nonlinear and unsteady nature of aircraft aerodynamics together with limited practical range of controls and state variables make the use of the linear control theory inadequate especially in the presence of external disturbances, such as wind. In the classical approach, aircraft are controlled by multiple inner and outer loops, designed separately and sequentially. For unmanned aerial systems in particular, control technology must evolve to a point where autonomy is extended to the entire mission flight envelope. This requires advanced controllers that have sufficient robustness, track complex trajectories, and use all the vehicles control capabilities at higher levels of accuracy. In this work, a robust nonlinear model predictive controller is designed to command and control an unmanned aerial system to track complex tight trajectories in the presence of internal and external perturbance. The Flight System developed in this work achieves the above performance by using: 1. A nonlinear guidance algorithm that enables the vehicle to follow an arbitrary trajectory shaped by moving points; 2. A formulation that embeds the guidance logic and trajectory information in the aircraft model, avoiding cross coupling and control degradation; 3. An artificial neural network, designed to adaptively estimate and provide aerodynamic and propulsive forces in real-time; and 4. A mixed sensitivity approach that enhances the robustness for a nonlinear model predictive controller overcoming the effect of un-modeled dynamics, external disturbances such as wind, and measurement additive perturbations, such as noise and biases. These elements have been integrated and tested in simulation and with previously stored flight test data and shown to be feasible.

Target tracking and surveillance by fusing stereo and RFID information

NASA Astrophysics Data System (ADS)

Raza, Rana H.; Stockman, George C.

2012-06-01

Ensuring security in high risk areas such as an airport is an important but complex problem. Effectively tracking personnel, containers, and machines is a crucial task. Moreover, security and safety require understanding the interaction of persons and objects. Computer vision (CV) has been a classic tool; however, variable lighting, imaging, and random occlusions present difficulties for real-time surveillance, resulting in erroneous object detection and trajectories. Determining object ID via CV at any instance of time in a crowded area is computationally prohibitive, yet the trajectories of personnel and objects should be known in real time. Radio Frequency Identification (RFID) can be used to reliably identify target objects and can even locate targets at coarse spatial resolution, while CV provides fuzzy features for target ID at finer resolution. Our research demonstrates benefits obtained when most objects are "cooperative" by being RFID tagged. Fusion provides a method to simplify the correspondence problem in 3D space. A surveillance system can query for unique object ID as well as tag ID information, such as target height, texture, shape and color, which can greatly enhance scene analysis. We extend geometry-based tracking so that intermittent information on ID and location can be used in determining a set of trajectories of N targets over T time steps. We show that partial-targetinformation obtained through RFID can reduce computation time (by 99.9% in some cases) and also increase the likelihood of producing correct trajectories. We conclude that real-time decision-making should be possible if the surveillance system can integrate information effectively between the sensor level and activity understanding level.

Localization and Poincaré catastrophe in the problem of a photon scattering on a pair of Rayleigh particles

NASA Astrophysics Data System (ADS)

Maksimenko, V. V.; Zagaynov, V. A.; Agranovski, I. E.

2013-11-01

It is shown that complexities in a problem of elastic scattering of a photon on a pair of Rayleigh particles (two small metallic spheres) are similar to the complexities of the classic problem of three bodies in celestial mechanics. In the latter problem, as is well known, the phase trajectory of a system becomes a nonanalytical function of its variables. In our problem, the trajectory of a virtual photon at some frequency could be considered such as the well-known Antoine set (Antoine's necklace) or a chain with interlaced sections having zero topological dimension and fractal structure. Such a virtual “zero-dimensional” photon could be localized between the particles of the pair. The topology suppresses the photon's exit to the real world with dimensional equal-to-or-greater-than units. The physical reason for this type of photon localization is related to the “mechanical rigidity” of interlaced sections of the photon trajectory due to a singularity of energy density along these sections. Within the approximations used in this paper, the effect is possible if the frequency of the incident radiation is equal to double the frequency of the dipole surface plasmon in an isolated particle, which is the only character frequency in the problem. This condition and transformation of the photon trajectory to the zero-dimensional Antoine set reminds of some of the simplest variants of Poincaré's catastrophe in the dynamics of some nonintegrable systems. The influence of the localization on elastic light scattering by the pair is investigated.

Senescence or selective disappearance? Age trajectories of body mass in wild and captive populations of a small-bodied primate.

PubMed

Hämäläinen, Anni; Dammhahn, Melanie; Aujard, Fabienne; Eberle, Manfred; Hardy, Isabelle; Kappeler, Peter M; Perret, Martine; Schliehe-Diecks, Susanne; Kraus, Cornelia

2014-09-22

Classic theories of ageing consider extrinsic mortality (EM) a major factor in shaping longevity and ageing, yet most studies of functional ageing focus on species with low EM. This bias may cause overestimation of the influence of senescent declines in performance over condition-dependent mortality on demographic processes across taxa. To simultaneously investigate the roles of functional senescence (FS) and intrinsic, extrinsic and condition-dependent mortality in a species with a high predation risk in nature, we compared age trajectories of body mass (BM) in wild and captive grey mouse lemurs (Microcebus murinus) using longitudinal data (853 individuals followed through adulthood). We found evidence of non-random mortality in both settings. In captivity, the oldest animals showed senescence in their ability to regain lost BM, whereas no evidence of FS was found in the wild. Overall, captive animals lived longer, but a reversed sex bias in lifespan was observed between wild and captive populations. We suggest that even moderately condition-dependent EM may lead to negligible FS in the wild. While high EM may act to reduce the average lifespan, this evolutionary process may be counteracted by the increased fitness of the long-lived, high-quality individuals. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Dynamical model of binary asteroid systems through patched three-body problems

NASA Astrophysics Data System (ADS)

Ferrari, Fabio; Lavagna, Michèle; Howell, Kathleen C.

2016-08-01

The paper presents a strategy for trajectory design in the proximity of a binary asteroid pair. A novel patched approach has been used to design trajectories in the binary system, which is modeled by means of two different three-body systems. The model introduces some degrees of freedom with respect to a classical two-body approach and it is intended to model to higher accuracy the peculiar dynamical properties of such irregular and low gravity field bodies, while keeping the advantages of having a full analytical formulation and low computational cost required. The neighborhood of the asteroid couple is split into two regions of influence where two different three-body problems describe the dynamics of the spacecraft. These regions have been identified by introducing the concept of surface of equivalence (SOE), a three-dimensional surface that serves as boundary between the regions of influence of each dynamical model. A case of study is presented, in terms of potential scenario that may benefit of such an approach in solving its mission analysis. Cost-effective solutions to land a vehicle on the surface of a low gravity body are selected by generating Poincaré maps on the SOE, seeking intersections between stable and unstable manifolds of the two patched three-body systems.

Understanding How Isotopes Affect Charge Transfer in P3HT/PCBM: A Quantum Trajectory-Electronic Structure Study with Nonlinear Quantum Corrections

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

Wang, Lei; Jakowski, Jacek; Garashchuk, Sophya

The experimentally observed effect of selective deuterium substitution on the open circuit voltage for a blend of poly(3-hexylthiophene)(P3HT) and [6,6]-phenyl-C 61- butyric acid methyl ester (PCBM) (Nat. Commun. 5:3180, 2014) is explored using a 221-atom model of a polymer-wrapped PCBM molecule. We describe the protonic and deuteronic wavefunctions for the H/D isotopologues of the hexyl side chains within a Quantum Trajectory/Electronic Structure approach where the dynamics is performed with newly developed nonlinear corrections to the quantum forces, necessary to describe the nuclear wavefunctions; the classical forces are generated with a Density Functional Tight Binding method. We used the resulting protonicmore » and deuteronic time-dependent wavefunctions to assess the effects of isotopic substitution (deuteration) on the energy gaps relevant to the charge transfer for the donor and acceptor electronic states. Furthermore, while the isotope effect on the electronic energy levels is found negligible, the quantum-induced fluctuations of the energy gap between the charge transfer and charge separated states due to nuclear wavefunctions may account for experimental trends by promoting charge transfer in P3HT/PCBM and increasing charge recombination on the donor in the deuterium substituted P3HT/PCBM.« less

Understanding How Isotopes Affect Charge Transfer in P3HT/PCBM: A Quantum Trajectory-Electronic Structure Study with Nonlinear Quantum Corrections

DOE PAGES

Wang, Lei; Jakowski, Jacek; Garashchuk, Sophya; ...

2016-08-09

The experimentally observed effect of selective deuterium substitution on the open circuit voltage for a blend of poly(3-hexylthiophene)(P3HT) and [6,6]-phenyl-C 61- butyric acid methyl ester (PCBM) (Nat. Commun. 5:3180, 2014) is explored using a 221-atom model of a polymer-wrapped PCBM molecule. We describe the protonic and deuteronic wavefunctions for the H/D isotopologues of the hexyl side chains within a Quantum Trajectory/Electronic Structure approach where the dynamics is performed with newly developed nonlinear corrections to the quantum forces, necessary to describe the nuclear wavefunctions; the classical forces are generated with a Density Functional Tight Binding method. We used the resulting protonicmore » and deuteronic time-dependent wavefunctions to assess the effects of isotopic substitution (deuteration) on the energy gaps relevant to the charge transfer for the donor and acceptor electronic states. Furthermore, while the isotope effect on the electronic energy levels is found negligible, the quantum-induced fluctuations of the energy gap between the charge transfer and charge separated states due to nuclear wavefunctions may account for experimental trends by promoting charge transfer in P3HT/PCBM and increasing charge recombination on the donor in the deuterium substituted P3HT/PCBM.« less

Beam tracking with micromegas & wire chambers in secondary electron detection configuration

NASA Astrophysics Data System (ADS)

Voštinar, M.; Fernández, B.; Pancin, J.; Alvarez, M. A. G.; Chaminade, T.; Damoy, S.; Doré, D.; Drouart, A.; Druillole, F.; Frémont, G.; Kebbiri, M.; Materna, T.; Monmarthe, E.; Panebianco, S.; Papaevangelou, T.; Riallot, M.; Savajols, H.; Spitaels, C.

2013-12-01

The focal plane of S3 (Super Separator Spectrometer), a new experimental area of SPIRAL2 at GANIL, will be used for identification of nuclei, and requires the reconstruction of their trajectories and velocities by the Time Of Flight (TOF) method. Classical tracking detectors used in-beam would generate a lot of angular and energy straggling due to their thickness. One solution is the use of a SED (Secondary Electron Detection), which consists of a thin emissive foil in beam coupled to a low pressure gaseous detector out of the beam, for the detection of secondary electrons ejected from the foil. Moreover, this type of detector can be used for classical beam tracking at low energies, or for example at NFS (GANIL) for the FALSTAFF experiment for the reconstruction of fission fragments trajectories. Several low pressure gaseous detectors such as wire chambers and Micromegas have been constructed and tested since 2008. High counting rate capabilities and good time resolution obtained in previous tests motivated the construction of a new real-size 2D prototype wire chamber and a 2D bulk Micromegas at low pressure. For the first time, spatial resolution of the Micromegas at low pressure (below 20 mbar) in the SED configuration was measured. Different tests have been performed in order to characterize time and spatial properties of both prototypes, giving spatial resolution in the horizontal (X) direction of 0.90(0.02) mm FWHM for the real size prototype and 0.72(0.08) mm FWHM for Micromegas, and a time resolution of ~ 110(25) ps for the real size prototype.

High-order above-threshold photoemission from nanotips controlled with two-color laser fields

NASA Astrophysics Data System (ADS)

Seiffert, Lennart; Paschen, Timo; Hommelhoff, Peter; Fennel, Thomas

2018-07-01

We investigate the process of phase-controlled high-order above-threshold photoemission from metallic nanotips under bichromatic laser fields. Experimental photoelectron spectra resulting from two-color excitation with a moderately intense near-infrared fundamental field (1560 nm) and its weak second harmonic show a strong sensitivity on the relative phase and clear indications for a plateau-like structure that is attributed to elastic backscattering. To explore the relevant control mechanisms, characteristic features, and particular signatures from the near-field inhomogeneity, we performed systematic quantum simulations employing a one-dimensional nanotip model. Besides rich phase-dependent structures in the simulated above-threshold ionization photoelectron spectra we find ponderomotive shifts as well as substantial modifications of the rescattering cutoff as function of the decay length of the near-field. To explore the quantum or classical nature of the observed features and to discriminate the two-color effects stemming from electron propagation and from the ionization rate we compare the quantum results to classical trajectory simulations. We show that signatures from direct electrons as well as the modulations in the plateau region mainly stem from control of the ionization probability, while the modulation in the cutoff region can only be explained by the impact of the two-color field on the electron trajectory. Despite the complexity of the phase-dependent features that render two-color strong-field photoemission from nanotips intriguing for sub-cycle strong-field control, our findings support that the recollision features in the cutoff region provide a robust and reliable method to calibrate the relative two-color phase.

Dynamical tachyons on fuzzy spheres

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

Berenstein, David; Institute for Advanced Study, School of Natural Science, Princeton, New Jersey 08540; Trancanelli, Diego

2011-05-15

We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the Berenstein-Maldacena-Nastase plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles, classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills theory on a sphere, of which this system is a truncation. We also set upmore » a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.« less

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

LOP- LONG-TERM ORBIT PREDICTOR

NASA Technical Reports Server (NTRS)

Kwok, J. H.

1994-01-01

The Long-Term Orbit Predictor (LOP) trajectory propagation program is a useful tool in lifetime analysis of orbiting spacecraft. LOP is suitable for studying planetary orbit missions with reconnaissance (flyby) and exploratory (mapping) trajectories. Sample data is included for a geosynchronous station drift cycle study, a Venus radar mapping strategy, a frozen orbit about Mars, and a repeat ground trace orbit. LOP uses the variation-of-parameters method in formulating the equations of motion. Terms involving the mean anomaly are removed from numerical integrations so that large step sizes, on the order of days, are possible. Consequently, LOP executes much faster than programs based on Cowell's method, such as the companion program ASAP (the Artificial Satellite Analysis Program, NPO-17522, also available through COSMIC). The program uses a force model with a gravity field of up to 21 by 21, lunisolar perturbation, drag, and solar radiation pressure. The input includes classical orbital elements (either mean or oscillating), orbital elements of the sun relative to the planet, reference time and dates, drag coefficients, gravitational constants, planet radius, rotation rate. The printed output contains the classical elements for each time step or event step, and additional orbital data such as true anomaly, eccentric anomaly, latitude, longitude, periapsis altitude, and the rate of change per day of certain elements. Selected output is additionally written to a plot file for postprocessing by the user. LOP is written in FORTRAN 77 for batch execution on IBM PC compatibles running MS-DOS with a minimum of 256K RAM. Recompiling the source requires the Lahey F77 v2.2 compiler. The LOP package includes examples that use LOTUS 1-2-3 for graphical displays, but any graphics software package should be able to handle the ASCII plot file. The program is available on two 5.25 inch 360K MS-DOS format diskettes. The program was written in 1986 and last updated in 1989. LOP is a copyrighted work with all copyright vested in NASA. IBM PC is a registered trademark of International Business Machines Corporation. Lotus 1-2-3 is a registered trademark of Lotus Development Corporation. MS-DOS is a trademark of Microsoft Corporation.

Computer Simulations and Theoretical Studies of Complex Systems: from complex fluids to frustrated magnets

NASA Astrophysics Data System (ADS)

Choi, Eunsong

Computer simulations are an integral part of research in modern condensed matter physics; they serve as a direct bridge between theory and experiment by systemactically applying a microscopic model to a collection of particles that effectively imitate a macroscopic system. In this thesis, we study two very differnt condensed systems, namely complex fluids and frustrated magnets, primarily by simulating classical dynamics of each system. In the first part of the thesis, we focus on ionic liquids (ILs) and polymers--the two complementary classes of materials that can be combined to provide various unique properties. The properties of polymers/ILs systems, such as conductivity, viscosity, and miscibility, can be fine tuned by choosing an appropriate combination of cations, anions, and polymers. However, designing a system that meets a specific need requires a concrete understanding of physics and chemistry that dictates a complex interplay between polymers and ionic liquids. In this regard, molecular dynamics (MD) simulation is an efficient tool that provides a molecular level picture of such complex systems. We study the behavior of Poly (ethylene oxide) (PEO) and the imidazolium based ionic liquids, using MD simulations and statistical mechanics. We also discuss our efforts to develop reliable and efficient classical force-fields for PEO and the ionic liquids. The second part is devoted to studies on geometrically frustrated magnets. In particular, a microscopic model, which gives rise to an incommensurate spiral magnetic ordering observed in a pyrochlore antiferromagnet is investigated. The validation of the model is made via a comparison of the spin-wave spectra with the neutron scattering data. Since the standard Holstein-Primakoff method is difficult to employ in such a complex ground state structure with a large unit cell, we carry out classical spin dynamics simulations to compute spin-wave spectra directly from the Fourier transform of spin trajectories. We conclude the study by showing an excellent agreement between the simulation and the experiment.

The rotate-plus-shift C-arm trajectory. Part I. Complete data with less than 180° rotation.

PubMed

Ritschl, Ludwig; Kuntz, Jan; Fleischmann, Christof; Kachelrieß, Marc

2016-05-01

In the last decade, C-arm-based cone-beam CT became a widely used modality for intraoperative imaging. Typically a C-arm CT scan is performed using a circular or elliptical trajectory around a region of interest. Therefore, an angular range of at least 180° plus fan angle must be covered to ensure a completely sampled data set. However, mobile C-arms designed with a focus on classical 2D applications like fluoroscopy may be limited to a mechanical rotation range of less than 180° to improve handling and usability. The method proposed in this paper allows for the acquisition of a fully sampled data set with a system limited to a mechanical rotation range of at least 180° minus fan angle using a new trajectory design. This enables CT like 3D imaging with a wide range of C-arm devices which are mainly designed for 2D imaging. The proposed trajectory extends the mechanical rotation range of the C-arm system with two additional linear shifts. Due to the divergent character of the fan-beam geometry, these two shifts lead to an additional angular range of half of the fan angle. Combining one shift at the beginning of the scan followed by a rotation and a second shift, the resulting rotate-plus-shift trajectory enables the acquisition of a completely sampled data set using only 180° minus fan angle of rotation. The shifts can be performed using, e.g., the two orthogonal positioning axes of a fully motorized C-arm system. The trajectory was evaluated in phantom and cadaver examinations using two prototype C-arm systems. The proposed trajectory leads to reconstructions without limited angle artifacts. Compared to the limited angle reconstructions of 180° minus fan angle, image quality increased dramatically. Details in the rotate-plus-shift reconstructions were clearly depicted, whereas they are dominated by artifacts in the limited angle scan. The method proposed here employs 3D imaging using C-arms with less than 180° rotation range adding full 3D functionality to a C-arm device retaining both handling comfort and the usability of 2D imaging. This method has a clear potential for clinical use especially to meet the increasing demand for an intraoperative 3D imaging.

The rotate-plus-shift C-arm trajectory. Part I. Complete data with less than 180° rotation

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

Ritschl, Ludwig; Fleischmann, Christof; Kuntz, Jan, E-mail: j.kuntz@dkfz.de

Purpose: In the last decade, C-arm-based cone-beam CT became a widely used modality for intraoperative imaging. Typically a C-arm CT scan is performed using a circular or elliptical trajectory around a region of interest. Therefore, an angular range of at least 180° plus fan angle must be covered to ensure a completely sampled data set. However, mobile C-arms designed with a focus on classical 2D applications like fluoroscopy may be limited to a mechanical rotation range of less than 180° to improve handling and usability. The method proposed in this paper allows for the acquisition of a fully sampled datamore » set with a system limited to a mechanical rotation range of at least 180° minus fan angle using a new trajectory design. This enables CT like 3D imaging with a wide range of C-arm devices which are mainly designed for 2D imaging. Methods: The proposed trajectory extends the mechanical rotation range of the C-arm system with two additional linear shifts. Due to the divergent character of the fan-beam geometry, these two shifts lead to an additional angular range of half of the fan angle. Combining one shift at the beginning of the scan followed by a rotation and a second shift, the resulting rotate-plus-shift trajectory enables the acquisition of a completely sampled data set using only 180° minus fan angle of rotation. The shifts can be performed using, e.g., the two orthogonal positioning axes of a fully motorized C-arm system. The trajectory was evaluated in phantom and cadaver examinations using two prototype C-arm systems. Results: The proposed trajectory leads to reconstructions without limited angle artifacts. Compared to the limited angle reconstructions of 180° minus fan angle, image quality increased dramatically. Details in the rotate-plus-shift reconstructions were clearly depicted, whereas they are dominated by artifacts in the limited angle scan. Conclusions: The method proposed here employs 3D imaging using C-arms with less than 180° rotation range adding full 3D functionality to a C-arm device retaining both handling comfort and the usability of 2D imaging. This method has a clear potential for clinical use especially to meet the increasing demand for an intraoperative 3D imaging.« less

Problem solving stages in the five square problem

PubMed Central

Fedor, Anna; Szathmáry, Eörs; Öllinger, Michael

2015-01-01

According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight, and search again for someone, who solves the task. The order of these stages was determined through self-reports of problem solvers and has never been verified behaviorally. We asked whether individual analysis of problem solving attempts of participants revealed the same order of problem solving stages as defined by the theory and whether their subjective feelings corresponded to the problem solving stages they were in. Our participants tried to solve the Five-Square problem in an online task, while we recorded the time and trajectory of their stick movements. After the task they were asked about their feelings related to insight and some of them also had the possibility of reporting impasse while working on the task. We found that the majority of participants did not follow the classic four-stage model of insight, but had more complex sequences of problem solving stages, with search and impasse recurring several times. This means that the classic four-stage model is not sufficient to describe variability on the individual level. We revised the classic model and we provide a new model that can generate all sequences found. Solvers reported insight more often than non-solvers and non-solvers reported impasse more often than solvers, as expected; but participants did not report impasse more often during behaviorally defined impasse stages than during other stages. This shows that impasse reports might be unreliable indicators of impasse. Our study highlights the importance of individual analysis of problem solving behavior to verify insight theory. PMID:26300794

Problem solving stages in the five square problem.

PubMed

Fedor, Anna; Szathmáry, Eörs; Öllinger, Michael

2015-01-01

According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight, and search again for someone, who solves the task. The order of these stages was determined through self-reports of problem solvers and has never been verified behaviorally. We asked whether individual analysis of problem solving attempts of participants revealed the same order of problem solving stages as defined by the theory and whether their subjective feelings corresponded to the problem solving stages they were in. Our participants tried to solve the Five-Square problem in an online task, while we recorded the time and trajectory of their stick movements. After the task they were asked about their feelings related to insight and some of them also had the possibility of reporting impasse while working on the task. We found that the majority of participants did not follow the classic four-stage model of insight, but had more complex sequences of problem solving stages, with search and impasse recurring several times. This means that the classic four-stage model is not sufficient to describe variability on the individual level. We revised the classic model and we provide a new model that can generate all sequences found. Solvers reported insight more often than non-solvers and non-solvers reported impasse more often than solvers, as expected; but participants did not report impasse more often during behaviorally defined impasse stages than during other stages. This shows that impasse reports might be unreliable indicators of impasse. Our study highlights the importance of individual analysis of problem solving behavior to verify insight theory.

On the fly quantum dynamics of electronic and nuclear wave packets

NASA Astrophysics Data System (ADS)

Komarova, Ksenia G.; Remacle, F.; Levine, R. D.

2018-05-01

Multielectronic states quantum dynamics on a grid is described in a manner motivated by on the fly classical trajectory computations. Non stationary electronic states are prepared by a few cycle laser pulse. The nuclei respond and begin moving. We solve the time dependent Schrödinger equation for the electronic and nuclear dynamics for excitation from the ground electronic state. A satisfactory accuracy is possible using a localized description on a discrete grid. This enables computing on the fly for both the nuclear and electronic dynamics including non-adiabatic couplings. Attosecond dynamics in LiH is used as an example.

Unique Non-Keplerian Orbit Vantage Locations for Sun-Earth Connection and Earth Science Vision Roadmaps

NASA Technical Reports Server (NTRS)

Folta, David; Young, Corissa; Ross, Adam

2001-01-01

The purpose of this investigation is to determine the feasibility of attaining and maintaining unique non-Keplerian orbit vantage locations in the Earth/Moon environment in order to obtain continuous scientific measurements. The principal difficulty associated with obtaining continuous measurements is the temporal nature of astrodynamics, i.e., classical orbits. This investigation demonstrates advanced trajectory designs to meet demanding science requirements which cannot be met following traditional orbital mechanic logic. Examples of continuous observer missions addressed include Earth pole-sitters and unique vertical libration orbits that address Sun-Earth Connection and Earth Science Vision roadmaps.

Stable long-time semiclassical description of zero-point energy in high-dimensional molecular systems.

PubMed

Garashchuk, Sophya; Rassolov, Vitaly A

2008-07-14

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.

Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models

NASA Astrophysics Data System (ADS)

Le Deunff, Jérémy; Mouchet, Amaury; Schlagheck, Peter

2013-10-01

Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit resonance island chain structures with accurately controlled sizes and positions of the islands. Using complex classical trajectories that evolve along suitably defined paths in the complex time domain, we construct a semiclassical theory of the resonance-assisted tunneling process. This semiclassical approach yields a compact analytical expression for tunnelling-induced level splittings which is found to be in very good agreement with the exact splittings obtained through numerical diagonalization.

An Exploration Of Fuel Optimal Two-impulse Transfers To Cyclers in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Hosseinisianaki, Saghar

2011-12-01

This research explores the optimum two-impulse transfers between a low Earth orbit and cycler orbits in the Earth-Moon circular restricted three-body framework, emphasizing the optimization strategy. Cyclers are those types of periodic orbits that meet both the Earth and the Moon periodically. A spacecraft on such trajectories are under the influence of both the Earth and the Moon gravitational fields. Cyclers have gained recent interest as baseline orbits for several Earth-Moon mission concepts, notably in relation to human exploration. In this thesis it is shown that a direct optimization starting from the classic lambert initial guess may not be adequate for these problems and propose a three-step optimization solver to improve the domain of convergence toward an optimal solution. The first step consists of finding feasible trajectories with a given transfer time. I employ Lambert's problem to provide initial guess to optimize the error in arrival position. This includes the analysis of the liability of Lambert's solution as an initial guess. Once a feasible trajectory is found, the velocity impulse is only a function of transfer time, departure, and arrival points' phases. The second step consists of the optimization of impulse over transfer time which results in the minimum impulse transfer for fixed end points. Finally, the third step is mapping the optimal solutions as the end points are varied.

An Exploration Of Fuel Optimal Two-impulse Transfers To Cyclers in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Hosseinisianaki, Saghar

This research explores the optimum two-impulse transfers between a low Earth orbit and cycler orbits in the Earth-Moon circular restricted three-body framework, emphasizing the optimization strategy. Cyclers are those types of periodic orbits that meet both the Earth and the Moon periodically. A spacecraft on such trajectories are under the influence of both the Earth and the Moon gravitational fields. Cyclers have gained recent interest as baseline orbits for several Earth-Moon mission concepts, notably in relation to human exploration. In this thesis it is shown that a direct optimization starting from the classic lambert initial guess may not be adequate for these problems and propose a three-step optimization solver to improve the domain of convergence toward an optimal solution. The first step consists of finding feasible trajectories with a given transfer time. I employ Lambert's problem to provide initial guess to optimize the error in arrival position. This includes the analysis of the liability of Lambert's solution as an initial guess. Once a feasible trajectory is found, the velocity impulse is only a function of transfer time, departure, and arrival points' phases. The second step consists of the optimization of impulse over transfer time which results in the minimum impulse transfer for fixed end points. Finally, the third step is mapping the optimal solutions as the end points are varied.

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes back to the classic monograph of Fiacco & McCormick. This idea was further developed by Gould who obtained a two-steps quadratically convergent algorithm using prediction steps and Newton correction. Dussault interpreted the prediction step as a combined extrapolation with respect to the penalty parameter and the residual of the first order optimality conditions. Extrapolation with respect to the residual coincides with a Newton step.We explore here higher-order extrapolations, thus higher-order Newton-like methods. We first consider high-order variants of the Newton-Raphson method applied to non-linear systems of equations. Next, we obtain improved asymptotic convergence results for the quadratic loss penalty algorithm by using high-order extrapolation steps.

Classical trajectories in polar-asymmetric laser fields: Synchronous THz and XUV emission

NASA Astrophysics Data System (ADS)

Gragossian, Aram; Seletskiy, Denis V.; Sheik-Bahae, Mansoor

2016-10-01

The interaction of intense near- and mid-infrared laser pulses with rare gases has produced bursts of radiation with spectral content extending into the extreme ultraviolet and soft x-ray region of electromagnetic spectrum. On the other end of the spectrum, laser-driven gas plasmas has been shown to produce coherent sub-harmonic optical waveforms, covering from terahertz (THz) to mid- and near-infrared frequency spectral band. Both processes can be enhanced via a combination of a driving field and its second harmonic. Despite this striking similarity, only limited experimental and theoretical attempts have been made to address these two regimes simultaneously. Here we present systematic experiments and a unifying picture of these processes, based on our extension of the semi-classical three-step model. Further understanding of the generation and coherent control of time-synchronized transients with photon energies from meV to 1 keV can lead to numerous technological advances and to an intriguing possibilities of ultra-broadband investigations into complex condensed matter systems.

Image charge effects on electron capture by dust grains in dusty plasmas.

PubMed

Jung, Y D; Tawara, H

2001-07-01

Electron-capture processes by negatively charged dust grains from hydrogenic ions in dusty plasmas are investigated in accordance with the classical Bohr-Lindhard model. The attractive interaction between the electron in a hydrogenic ion and its own image charge inside the dust grain is included to obtain the total interaction energy between the electron and the dust grain. The electron-capture radius is determined by the total interaction energy and the kinetic energy of the released electron in the frame of the projectile dust grain. The classical straight-line trajectory approximation is applied to the motion of the ion in order to visualize the electron-capture cross section as a function of the impact parameter, kinetic energy of the projectile ion, and dust charge. It is found that the image charge inside the dust grain plays a significant role in the electron-capture process near the surface of the dust grain. The electron-capture cross section is found to be quite sensitive to the collision energy and dust charge.

Quantum and classical dynamics of water dissociation on Ni(111): A test of the site-averaging model in dissociative chemisorption of polyatomic molecules

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

Jiang, Bin; Department of Chemical Physics, University of Science and Technology of China, Hefei 230026; Guo, Hua, E-mail: hguo@unm.edu

Recently, we reported the first highly accurate nine-dimensional global potential energy surface (PES) for water interacting with a rigid Ni(111) surface, built on a large number of density functional theory points [B. Jiang and H. Guo, Phys. Rev. Lett. 114, 166101 (2015)]. Here, we investigate site-specific reaction probabilities on this PES using a quasi-seven-dimensional quantum dynamical model. It is shown that the site-specific reactivity is largely controlled by the topography of the PES instead of the barrier height alone, underscoring the importance of multidimensional dynamics. In addition, the full-dimensional dissociation probability is estimated by averaging fixed-site reaction probabilities with appropriatemore » weights. To validate this model and gain insights into the dynamics, additional quasi-classical trajectory calculations in both full and reduced dimensions have also been performed and important dynamical factors such as the steering effect are discussed.« less

A Novel DEM Approach to Simulate Block Propagation on Forested Slopes

NASA Astrophysics Data System (ADS)

Toe, David; Bourrier, Franck; Dorren, Luuk; Berger, Frédéric

2018-03-01

In order to model rockfall on forested slopes, we developed a trajectory rockfall model based on the discrete element method (DEM). This model is able to take the complex mechanical processes at work during an impact into account (large deformations, complex contact conditions) and can explicitly simulate block/soil, block/tree contacts as well as contacts between neighbouring trees. In this paper, we describe the DEM model developed and we use it to assess the protective effect of different types of forest. In addition, we compared it with a more classical rockfall simulation model. The results highlight that forests can significantly reduce rockfall hazard and that the spatial structure of coppice forests has to be taken into account in rockfall simulations in order to avoid overestimating the protective role of these forest structures against rockfall hazard. In addition, the protective role of the forests is mainly influenced by the basal area. Finally, the advantages and limitations of the DEM model were compared with classical rockfall modelling approaches.

Femtosecond dynamics and laser control of charge transport in trans-polyacetylene.

PubMed

Franco, Ignacio; Shapiro, Moshe; Brumer, Paul

2008-06-28

The induction of dc electronic transport in rigid and flexible trans-polyacetylene oligomers according to the omega versus 2omega coherent control scenario is investigated using a quantum-classical mean field approximation. The approach involves running a large ensemble of mixed quantum-classical trajectories under the influence of omega+2omega laser fields and choosing the initial conditions by sampling the ground-state Wigner distribution function for the nuclei. The vibronic couplings are shown to change the mean single-particle spectrum, introduce ultrafast decoherence, and enhance intramolecular vibrational and electronic relaxation. Nevertheless, even in the presence of significant couplings, limited coherent control of the electronic dynamics is still viable, the most promising route involving the use of femtosecond pulses with a duration that is comparable to the electronic dephasing time. The simulations offer a realistic description of the behavior of a simple coherent control scenario in a complex system and provide a detailed account of the femtosecond photoinduced vibronic dynamics of a conjugated polymer.

Relativistic Newtonian dynamics

NASA Astrophysics Data System (ADS)

Friedman, Yaakov; Mendel Steiner, Joseph

2017-05-01

A new Relativistic Newtonian Dynamics (RND) for motion under a conservative force capable to describe non-classical behavior in astronomy is proposed. The rotor experiments using Mössbauer spectroscopy with synchrotron radiation, described in the paper, indicate the influence of non-gravitational acceleration or potential energy on time. Similarly, the observed precession of Mercury and the periastron advance of binaries can be explained by the influence of gravitational potential energy on spacetime. The proposed RND incorporates the influence of potential energy on spacetime in Newton’s dynamics. The effect of this influence on time intervals, space increments and velocities is described explicitly by the use of the concept of escape trajectory. For an attracting conservative static potential we derived the RND energy conservation and the dynamics equation for motion of objects with non-zero mass and for massless particles. These equations are subsequently simplified for motion under a central force. Without the need to curve spacetime, this model predicts accurately the four non-classical observations in astronomy used to test the General Relativity.

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

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

2015-07-29

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

Scaling analysis and instantons for thermally assisted tunneling and quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

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

2017-01-01

We develop an instantonic calculus to derive an analytical expression for the thermally assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path-integral quantum Monte Carlo (QMC). We show analytically that the exponential scaling with the number of spins of the thermally assisted quantum tunneling rate and the escape rate of the QMC process are identical. We relate this effect to the existence of a dominant instantonic tunneling path. The instanton trajectory is described by nonlinear dynamical mean-field theory equations for a single-site magnetization vector, which we solve exactly. Finally, we derive scaling relations for the "spiky" barrier shape when the spin tunneling and QMC rates scale polynomially with the number of spins N while a purely classical over-the-barrier activation rate scales exponentially with N .

Computational simulations of hydrogen circular migration in protonated acetylene induced by circularly polarized light

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

Shi, Xuetao; Li, Wen; Schlegel, H. Bernhard, E-mail: hbs@chem.wayne.edu

2016-08-28

The hydrogens in protonated acetylene are very mobile and can easily migrate around the C{sub 2} core by moving between classical and non-classical structures of the cation. The lowest energy structure is the T-shaped, non-classical cation with a hydrogen bridging the two carbons. Conversion to the classical H{sub 2}CCH{sup +} ion requires only 4 kcal/mol. The effect of circularly polarized light on the migration of hydrogens in oriented C{sub 2}H{sub 3}{sup +} has been simulated by Born-Oppenheimer molecular dynamics. Classical trajectory calculations were carried out with the M062X/6-311+G(3df,2pd) level of theory using linearly and circularly polarized 32 cycle 7 μmmore » cosine squared pulses with peak intensity of 5.6 × 10{sup 13} W/cm{sup 2} and 3.15 × 10{sup 13} W/cm{sup 2}, respectively. These linearly and circularly polarized pulses transfer similar amounts of energy and total angular momentum to C{sub 2}H{sub 3}{sup +}. The average angular momentum vectors of the three hydrogens show opposite directions of rotation for right and left circularly polarized light, but no directional preference for linearly polarized light. This difference results in an appreciable amount of angular displacement of the three hydrogens relative to the C{sub 2} core for circularly polarized light, but only an insignificant amount for linearly polarized light. Over the course of the simulation with circularly polarized light, this corresponds to a propeller-like motion of the three hydrogens around the C{sub 2} core of protonated acetylene.« less

Born’s rule as signature of a superclassical current algebra

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

Fussy, S.; Mesa Pascasio, J.; Institute for Atomic and Subatomic Physics, Vienna University of Technology, Operng. 9, 1040 Vienna

2014-04-15

We present a new tool for calculating the interference patterns and particle trajectories of a double-, three- and N-slit system on the basis of an emergent sub-quantum theory developed by our group throughout the last years. The quantum itself is considered as an emergent system representing an off-equilibrium steady state oscillation maintained by a constant throughput of energy provided by a classical zero-point energy field. We introduce the concept of a “relational causality” which allows for evaluating structural interdependences of different systems levels, i.e. in our case of the relations between partial and total probability density currents, respectively. Combined with themore » application of 21st century classical physics like, e.g., modern nonequilibrium thermodynamics, we thus arrive at a “superclassical” theory. Within this framework, the proposed current algebra directly leads to a new formulation of the guiding equation which is equivalent to the original one of the de Broglie–Bohm theory. By proving the absence of third order interferences in three-path systems it is shown that Born’s rule is a natural consequence of our theory. Considering the series of one-, double-, or, generally, of N-slit systems, with the first appearance of an interference term in the double slit case, we can explain the violation of Sorkin’s first order sum rule, just as the validity of all higher order sum rules. Moreover, the Talbot patterns and Talbot distance for an arbitrary N-slit device can be reproduced exactly by our model without any quantum physics tool. -- Highlights: •Calculating the interference patterns and particle trajectories of a double-, three- and N-slit system. •Deriving a new formulation of the guiding equation equivalent to the de Broglie–Bohm one. •Proving the absence of third order interferences and thus explaining Born’s rule. •Explaining the violation of Sorkin’s order sum rules. •Classical simulation of Talbot patterns and exact reproduction of Talbot distance for N slits.« less

Semiclassical treatment of fusion and breakup processes of ^{6,8}He halo nuclei

NASA Astrophysics Data System (ADS)

Majeed, Fouad A.; Abdul-Hussien, Yousif A.

2016-06-01

A semiclassical approach has been used to study the effect of channel coupling on the calculations of the total fusion reaction cross section σ _{fus}, and the fusion barrier distribution D_{fus} for the systems 6He +^{238}U and 8He +^{197}Au. Since these systems invloves light exotic nuclei, breakup states channel play an important role that should be considered in the calculations. In semiclassical treatment, the relative motion between the projectile and target nuclei is approximated by a classical trajectory while the intrinsic dynamics is handled by time-dependent quantum mechanics. The calculations of the total fusion cross section σ _{fus}, and the fusion barrier distribution D_{fus} are compared with the full quantum mechanical calculations using the coupled-channels calculations with all order coupling using the computer code and with the available experimental data.

Trapping dynamics of xenon on Pt(111)

NASA Astrophysics Data System (ADS)

Arumainayagam, Christopher R.; Madix, Robert J.; Mcmaster, Mark C.; Suzawa, Valerie M.; Tully, John C.

1990-02-01

The dynamics of Xe trapping on Pt(111) was studied using supersonic atomic beam techniques. Initial trapping probabilities ( S0) were measured directly as a function of incident translational energy ( EinT) and angle of incidence (θ i) at a surface temperature ( Tins) 95 K. The initial trapping probability decreases smoothly with increasing ET cosθ i;, rather than ET cos 2θ i, suggesting participation of parallel momentum in the trapping process. Accordingly, the measured initial trapping probability falls off more slowly with increasing incident translational energy than predicted by one-dimensional theories. This finding is in near agreement with previous mean translational energy measurements for Xe desorbing near the Pt(111) surface normal, assuming detailed balance applies. Three-dimensional stochastic classical trajectory calculations presented herein also exhibit the importance of tangential momentum in trapping and satisfactorily reproduce the experimental initial trapping probabilities.

Organogenesis in deep time: A problem in genomics, development, and paleontology.

PubMed

Pieretti, Joyce; Gehrke, Andrew R; Schneider, Igor; Adachi, Noritaka; Nakamura, Tetsuya; Shubin, Neil H

2015-04-21

The fossil record is a unique repository of information on major morphological transitions. Increasingly, developmental, embryological, and functional genomic approaches have also conspired to reveal evolutionary trajectory of phenotypic shifts. Here, we use the vertebrate appendage to demonstrate how these disciplines can mutually reinforce each other to facilitate the generation and testing of hypotheses of morphological evolution. We discuss classical theories on the origins of paired fins, recent data on regulatory modulations of fish fins and tetrapod limbs, and case studies exploring the mechanisms of digit loss in tetrapods. We envision an era of research in which the deep history of morphological evolution can be revealed by integrating fossils of transitional forms with direct experimentation in the laboratory via genome manipulation, thereby shedding light on the relationship between genes, developmental processes, and the evolving phenotype.

Discrete-time pilot model. [human dynamics and digital simulation

NASA Technical Reports Server (NTRS)

Cavalli, D.

1978-01-01

Pilot behavior is considered as a discrete-time process where the decision making has a sequential nature. This model differs from both the quasilinear model which follows from classical control theory and from the optimal control model which considers the human operator as a Kalman estimator-predictor. An additional factor considered is that the pilot's objective may not be adequately formulated as a quadratic cost functional to be minimized, but rather as a more fuzzy measure of the closeness with which the aircraft follows a reference trajectory. All model parameters, in the digital program simulating the pilot's behavior, were successfully compared in terms of standard-deviation and performance with those of professional pilots in IFR configuration. The first practical application of the model was in the study of its performance degradation when the aircraft model static margin decreases.

Fitness in time-dependent environments includes a geometric phase contribution

PubMed Central

Tănase-Nicola, Sorin; Nemenman, Ilya

2012-01-01

Phenotypic evolution implies sequential rise in frequency of new genomic sequences. The speed of the rise depends, in part, on the relative fitness (selection coefficient) of the mutant versus the ancestor. Using a simple population dynamics model, we show that the relative fitness in dynamical environments is not equal to the geometric average of the fitness over individual environments. Instead, it includes a term that explicitly depends on the sequence of the environments. For slowly varying environments, this term depends only on the oriented area enclosed by the trajectory taken by the system in the environment state space. It is closely related to the well-studied geometric phases in classical and quantum physical systems. We discuss possible biological implications of these observations, focusing on evolution of novel metabolic or stress-resistant functions. PMID:22112653

Quasi-soliton scattering in quantum spin chains

NASA Astrophysics Data System (ADS)

Vlijm, R.; Ganahl, M.; Fioretto, D.; Brockmann, M.; Haque, M.; Evertz, H. G.; Caux, J.-S.

2015-12-01

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time-evolution fits on the displacements. The time-evolved block decimation algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.

Quasi-soliton scattering in quantum spin chains

NASA Astrophysics Data System (ADS)

Fioretto, Davide; Vljim, Rogier; Ganahl, Martin; Brockmann, Michael; Haque, Masud; Evertz, Hans-Gerd; Caux, Jean-Sébastien

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time evolution fits on the displacements. The TEBD algorithm allows for the study of scattering displacements from spin-block states, showing similar displacement scattering features.

Posttraumatic Stress Symptom Trajectories Among Children After Disaster Exposure: A Review

PubMed Central

Lai, Betty S.; Lewis, Rayleen; Livings, Michelle S.; La Greca, Annetate M.; Esnard, Ann-Margaret

2018-01-01

Natural disasters, such as hurricanes and floods, are increasing in frequency and scope. Youth exposed to disasters are at risk for developing posttraumatic stress symptoms (PTSS). However, not all youth who report initially elevated PTSS report persistent PTSS that last beyond the first three to six months postdisaster. Thus, it is crucial to understand how and why youth differ in their patterns of PTSS. This study reviewed the literature on children’s postdisaster PTSS, evaluating the typical number and types of patterns for children’s PTSS trajectories, as well as risk and protective factors predicting trajectory membership. This review identified eight empirical studies on youth PTSS trajectories following natural disasters; these studies included 8,306 children aged 3 to 18 years. All studies identified resilience, recovery, and chronic trajectories. Evidence for a delayed trajectory was mixed. Proportions of children falling into each trajectory varied widely across studies, but overall, resilience was the most prevalent trajectory. These findings were consistent across study factors (i.e., analytic strategy, assessment timing, and study selection criteria). Female gender, disaster exposure, negative coping, and lack of social support were significant risk factors for chronic trajectories across several studies. Future research should combine individual level participant data across studies of children’s responses to disasters to better understand PTSS trajectories. PMID:29193316

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.

Trajectory and Relative Dispersion Case Studies and Statistics from the Green River Mesoscale Deformation, Dispersion, and Dissipation Program

NASA Astrophysics Data System (ADS)

Niemann, Brand Lee

A major field program to study beta-mesoscale transport and dispersion over complex mountainous terrain was conducted during 1969 with the cooperation of three government agencies at the White Sands Missile Range in central Utah. The purpose of the program was to measure simultaneously on a large number of days the synoptic and mesoscale wind fields, the relative dispersion between pairs of particle trajectories and the rate of small scale turbulence dissipation. The field program included measurements during more than 60 days in the months of March, June, and November. The large quantity of data generated from this program has been processed and analyzed to provide case studies and statistics to evaluate and refine Lagrangian variable trajectory models. The case studies selected to illustrate the complexities of mesoscale transport and dispersion over complex terrain include those with terrain blocking, lee waves, and stagnation, as well as those with large vertical wind shears and horizontal wind field deformation. The statistics of relative particle dispersion were computed and compared to the classical theories of Richardson and Batchelor and the more recent theories of Lin and Kao among others. The relative particle dispersion was generally found to increase with travel time in the alongwind and crosswind directions, but in a more oscillatory than sustained or even accelerated manner as predicted by most theories, unless substantial wind shears or finite vertical separations between particles were present. The relative particle dispersion in the vertical was generally found to be small and bounded even when substantial vertical motions due to lee waves were present because of the limiting effect of stable temperature stratification. The data show that velocity shears have a more significant effect than turbulence on relative particle dispersion and that sufficient turbulence may not always be present above the planetary boundary layer for "wind direction shear induced dispersion" to become effective horizontal dispersion by vertical mixing over the shear layer. The statistics of relative particle dispersion in the three component directions have been summarized and stratified by flow parameters for use in practical prediction problems.

The ortho-to-para ratio of interstellar NH2: quasi-classical trajectory calculations and new simulations

NASA Astrophysics Data System (ADS)

Le Gal, R.; Herbst, E.; Xie, C.; Li, A.; Guo, H.

2016-11-01

Based on recent Herschel results, the ortho-to-para ratio (OPR) of NH2 has been measured towards the following high-mass star-forming regions: W31C (G10.6-0.4), W49N (G43.2-0.1), W51 (G49.5-0.4), and G34.3+0.1. The OPR at thermal equilibrium ranges from the statistical limit of three at high temperatures to infinity as the temperature tends toward zero, unlike the case of H2. Depending on the position observed along the lines-of-sight, the OPR was found to lie either slightly below the high temperature limit of three (in the range 2.2-2.9) or above this limit ( 3.5, ≳ 4.2, and ≳5.0). In low temperature interstellar gas, where the H2 is para-enriched, our nearly pure gas-phase astrochemical models with nuclear-spin chemistry can account for anomalously low observed NH2-OPR values. We have tentatively explained OPR values larger than three by assuming that spin thermalization of NH2 can proceed at least partially by H-atom exchange collisions with atomic hydrogen, thus increasing the OPR with decreasing temperature. In this paper, we present quasi-classical trajectory calculations of the H-exchange reaction NH2 + H, which show the reaction to proceed without a barrier, confirming that the H-exchange will be efficient in the temperature range of interest. With the inclusion of this process, our models suggest both that OPR values below three arise in regions with temperatures ≳20-25 K, depending on time, and values above three but lower than the thermal limit arise at still lower temperatures.

Ground-based telescope pointing and tracking optimization using a neural controller.

PubMed

Mancini, D; Brescia, M; Schipani, P

2003-01-01

Neural network models (NN) have emerged as important components for applications of adaptive control theories. Their basic generalization capability, based on acquired knowledge, together with execution rapidity and correlation ability between input stimula, are basic attributes to consider NN as an extremely powerful tool for on-line control of complex systems. By a control system point of view, not only accuracy and speed, but also, in some cases, a high level of adaptation capability is required in order to match all working phases of the whole system during its lifetime. This is particularly remarkable for a new generation ground-based telescope control system. Infact, strong changes in terms of system speed and instantaneous position error tolerance are necessary, especially in case of trajectory disturb induced by wind shake. The classical control scheme adopted in such a system is based on the proportional integral (PI) filter, already applied and implemented on a large amount of new generation telescopes, considered as a standard in this technological environment. In this paper we introduce the concept of a new approach, the neural variable structure proportional integral, (NVSPI), related to the implementation of a standard multi layer perceptron network in new generation ground-based Alt-Az telescope control systems. Its main purpose is to improve adaptive capability of the Variable structure proportional integral model, an already innovative control scheme recently introduced by authors [Proc SPIE (1997)], based on a modified version of classical PI control model, in terms of flexibility and accuracy of the dynamic response range also in presence of wind noise effects. The realization of a powerful well tested and validated telescope model simulation system allowed the possibility to directly compare performances of the two control schemes on simulated tracking trajectories, revealing extremely encouraging results in terms of NVSPI control robustness and reliability.

Toward quantum-like modeling of financial processes

NASA Astrophysics Data System (ADS)

Choustova, Olga

2007-05-01

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Trajectories of prices are determined by two financial potentials: classical-like V(q) ("hard" market conditions, e.g., natural resources) and quantum-like U(q) (behavioral market conditions). On the one hand, our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven, E. W. Piotrowski, J. Sladkowski. On the other hand, (since Bohmian mechanics provides the possibility to describe individual price trajectories) it belongs to the domain of extended research on deterministic dynamics for financial assets (C.W.J. Granger, W.A. Barnett, A. J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay, A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D. Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many others).

Transition state theory for activated systems with driven anharmonic barriers.

PubMed

Revuelta, F; Craven, Galen T; Bartsch, Thomas; Borondo, F; Benito, R M; Hernandez, Rigoberto

2017-08-21

Classical transition state theory has been extended to address chemical reactions across barriers that are driven and anharmonic. This resolves a challenge to the naive theory that necessarily leads to recrossings and approximate rates because it relies on a fixed dividing surface. We develop both perturbative and numerical methods for the computation of a time-dependent recrossing-free dividing surface for a model anharmonic system in a solvated environment that interacts strongly with an oscillatory external field. We extend our previous work, which relied either on a harmonic approximation or on periodic force driving. We demonstrate that the reaction rate, expressed as the long-time flux of reactive trajectories, can be extracted directly from the stability exponents, namely, Lyapunov exponents, of the moving dividing surface. Comparison to numerical results demonstrates the accuracy and robustness of this approach for the computation of optimal (recrossing-free) dividing surfaces and reaction rates in systems with Markovian solvation forces. The resulting reaction rates are in strong agreement with those determined from the long-time flux of reactive trajectories.

Graviton mass bounds from an analysis of bright star trajectories at the Galactic Center

NASA Astrophysics Data System (ADS)

Zakharov, Alexander; Jovanović, Predrag; Borka, Dusko; Jovanović, Vesna Borka

2017-03-01

In February 2016 the LIGO & VIRGO collaboration reported the discovery of gravitational waves in merging black holes, therefore, the team confirmed GR predictions about an existence of black holes and gravitational waves in the strong gravitational field limit. Moreover, in their papers the joint LIGO & VIRGO team presented an upper limit on graviton mass such as mg < 1.2 × 10-22 eV (Abbott et al. 2016). So, the authors concluded that their observational data do not show any violation of classical general relativity. We show that an analysis of bright star trajectories could constrain graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and the estimate is consistent with the one obtained by the LIGO & VIRGO collaboration. This analysis gives an opportunity to treat observations of bright stars near the Galactic Center as a useful tool to obtain constraints on the fundamental gravity law such as modifications of the Newton gravity law in a weak field approximation. In that way, based on a potential reconstruction at the Galactic Center we obtain bounds on a graviton mass.

Generalized trajectory surface hopping method based on the Zhu-Nakamura theory

NASA Astrophysics Data System (ADS)

Oloyede, Ponmile; Mil'nikov, Gennady; Nakamura, Hiroki

2006-04-01

We present a generalized formulation of the trajectory surface hopping method applicable to a general multidimensional system. The method is based on the Zhu-Nakamura theory of a nonadiabatic transition and therefore includes the treatment of classically forbidden hops. The method uses a generalized recipe for the conservation of angular momentum after forbidden hops and an approximation for determining a nonadiabatic transition direction which is crucial when the coupling vector is unavailable. This method also eliminates the need for a rigorous location of the seam surface, thereby ensuring its applicability to a wide class of chemical systems. In a test calculation, we implement the method for the DH2+ system, and it shows a remarkable agreement with the previous results of C. Zhu, H. Kamisaka, and H. Nakamura, [J. Chem. Phys. 116, 3234 (2002)]. We then apply it to a diatomic-in-molecule model system with a conical intersection, and the results compare well with exact quantum calculations. The successful application to the conical intersection system confirms the possibility of directly extending the present method to an arbitrary potential of general topology.

Bayesian Lagrangian Data Assimilation and Drifter Deployment Strategies

NASA Astrophysics Data System (ADS)

Dutt, A.; Lermusiaux, P. F. J.

2017-12-01

Ocean currents transport a variety of natural (e.g. water masses, phytoplankton, zooplankton, sediments, etc.) and man-made materials and other objects (e.g. pollutants, floating debris, search and rescue, etc.). Lagrangian Coherent Structures (LCSs) or the most influential/persistent material lines in a flow, provide a robust approach to characterize such Lagrangian transports and organize classic trajectories. Using the flow-map stochastic advection and a dynamically-orthogonal decomposition, we develop uncertainty prediction schemes for both Eulerian and Lagrangian variables. We then extend our Bayesian Gaussian Mixture Model (GMM)-DO filter to a joint Eulerian-Lagrangian Bayesian data assimilation scheme. The resulting nonlinear filter allows the simultaneous non-Gaussian estimation of Eulerian variables (e.g. velocity, temperature, salinity, etc.) and Lagrangian variables (e.g. drifter/float positions, trajectories, LCSs, etc.). Its results are showcased using a double-gyre flow with a random frequency, a stochastic flow past a cylinder, and realistic ocean examples. We further show how our Bayesian mutual information and adaptive sampling equations provide a rigorous efficient methodology to plan optimal drifter deployment strategies and predict the optimal times, locations, and types of measurements to be collected.

Event-Based Sensing and Control for Remote Robot Guidance: An Experimental Case

PubMed Central

Santos, Carlos; Martínez-Rey, Miguel; Santiso, Enrique

2017-01-01

This paper describes the theoretical and practical foundations for remote control of a mobile robot for nonlinear trajectory tracking using an external localisation sensor. It constitutes a classical networked control system, whereby event-based techniques for both control and state estimation contribute to efficient use of communications and reduce sensor activity. Measurement requests are dictated by an event-based state estimator by setting an upper bound to the estimation error covariance matrix. The rest of the time, state prediction is carried out with the Unscented transformation. This prediction method makes it possible to select the appropriate instants at which to perform actuations on the robot so that guidance performance does not degrade below a certain threshold. Ultimately, we obtained a combined event-based control and estimation solution that drastically reduces communication accesses. The magnitude of this reduction is set according to the tracking error margin of a P3-DX robot following a nonlinear trajectory, remotely controlled with a mini PC and whose pose is detected by a camera sensor. PMID:28878144

Machine Learning of Accurate Energy-Conserving Molecular Force Fields

NASA Astrophysics Data System (ADS)

Chmiela, Stefan; Tkatchenko, Alexandre; Sauceda, Huziel; Poltavsky, Igor; Schütt, Kristof; Müller, Klaus-Robert; GDML Collaboration

Efficient and accurate access to the Born-Oppenheimer potential energy surface (PES) is essential for long time scale molecular dynamics (MD) simulations. Using conservation of energy - a fundamental property of closed classical and quantum mechanical systems - we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio MD trajectories (AIMD). The GDML implementation is able to reproduce global potential-energy surfaces of intermediate-size molecules with an accuracy of 0.3 kcal/mol for energies and 1 kcal/mol/Å for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, malonaldehyde, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative MD simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.

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

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.

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

Creating Rydberg electron wave packets using terahertz pulses

NASA Astrophysics Data System (ADS)

Bromage, Jake

1999-10-01

In this thesis I present experiments in which we excited classical-limit states of an atom using terahertz pulses. In a classical-limit state, an atom's outer electron is confined to a wave packet that orbits the core along a classical trajectory. Researchers have excited states with classical traits, but wave packets localized in all three dimensions have proved elusive. Theoretical studies have shown such states can be created using terahertz pulses. Using these techniques, we created a linear-orbit wave packet (LOWP), that is three-dimensionally localized and orbits along a line on one side of the atom's core. Terahertz pulses are sub-picosecond bursts of far- infrared radiation. Unlike ultrashort optical pulses, the electric field of terahertz pulses barely completes a single cycle. Our simulations of the atom-pulse interaction show that this electric field profile is critical in determining the quality of the wave packet. To characterize our terahertz pulses, we invented dithered-edge sampling which time- resolves the electric field using a photoconductive receiver and a triggered attenuator. We also studied how pulses are distorted after propagating through metallic structures, and used our findings to design our atomic experiments. We excited wave packets in atomic sodium using a two-step process. First, we used tunable, nanosecond dye lasers to excite an extreme Stark state. Next, we used a terahertz pump pulse to coherently redistribute population among extreme Stark states in neighboring manifolds. Interference between the final states produces a localized, dynamic LOWP. To analyze the LOWP, we ionized it with a stronger terahertz probe pulse, varying the pump-probe delay to map out its motion. We observed two strong LOWP signatures. Changing the static electric field produced small changes (2%) in the orbital period that agreed with our theoretical predictions. Secondly, because the LOWP scatters off the core, the pump-probe signal depended on the direction of the kick the LOWP received from the robe pulse. These observations, combined with our detailed simulations that used sodium parameters and the actual shape of the terahertz pulse, lead us to conclude that we excited a LOWP.

Analysis of Chemical, REP, and SEP missions to the Trojan asteroids

NASA Technical Reports Server (NTRS)

Bonfiglio, Eugene P.; Oh, David; Yen, Chen-Wan

2005-01-01

Recent studies suggest significant benefits from using 1st and 2nd generation Radioisotope Power Systems (RPS) as a power source for electric propulsion (EP) missions to the outer planets. This study focuses on trajectories to the Trojan asteroids. A high level analysis is performed with chemical trajectories to determine potential canidates for REP trajectory optimization. Extensive analysis of direct trajectories using REP is performed on these candidates. Solar Electric Propulsion (SEP) trajectories are also considered for comparison against REP trajectories.

Trajectories of self-evaluation bias in primary and secondary school: Parental antecedents and academic consequences.

PubMed

Bonneville-Roussy, Arielle; Bouffard, Thérèse; Vezeau, Carole

2017-08-01

Using a longitudinal approach spanning nine years of children's formal education, this study investigated the developmental trajectories of self-evaluation bias of academic competence. The study also examined how parenting styles were associated with the trajectories of bias in mid-primary school, and how those trajectories predicted academic outcomes at the end of secondary school and the beginning of college. A total of 711 children in 4th and 5th grades (mean age=10.71years old; 358 girls) participated in this study. Using a latent class growth modeling framework, results indicated that children can be classified in three latent growth trajectories of self-evaluation bias: the optimistic, realistic and pessimistic trajectories. These trajectories differed in their initial status of bias and also in their development over time. Children's adherence to a specific trajectory was associated with parenting variables in childhood. Finally, the optimistic, realistic, or pessimistic trajectories distinctively predicted achievement and persistence. Copyright © 2017 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Quantization and Quantum-Like Phenomena: A Number Amplitude Approach

NASA Astrophysics Data System (ADS)

Robinson, T. R.; Haven, E.

2015-12-01

Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.

The Production of Black Ph.D.’s in Economics at Harvard University, 1905–19551

PubMed Central

Myers, Samuel L.

2018-01-01

Harvard University’s Economics Department produced some of the leading African American economists between World War I and the Korean War. This essay explores the factors that contributed to this accomplishment and documents the career trajectories of the six blacks who obtained the Doctorate in Economics from Harvard University during the period 1905–1955. The analysis reveals the pivotal roles of the Rosenwald Fund, Classical High Schools, Black Fraternal Organizations and former University of Minnesota Applied Economics Professor, John D. Black. A common outcome of the careers of these six pioneers was a commitment to black economic empowerment. PMID:29937590

Experimental Evidence for Quantum Tunneling Time.

PubMed

Camus, Nicolas; Yakaboylu, Enderalp; Fechner, Lutz; Klaiber, Michael; Laux, Martin; Mi, Yonghao; Hatsagortsyan, Karen Z; Pfeifer, Thomas; Keitel, Christoph H; Moshammer, Robert

2017-07-14

The first hundred attoseconds of the electron dynamics during strong field tunneling ionization are investigated. We quantify theoretically how the electron's classical trajectories in the continuum emerge from the tunneling process and test the results with those achieved in parallel from attoclock measurements. An especially high sensitivity on the tunneling barrier is accomplished here by comparing the momentum distributions of two atomic species of slightly deviating atomic potentials (argon and krypton) being ionized under absolutely identical conditions with near-infrared laser pulses (1300 nm). The agreement between experiment and theory provides clear evidence for a nonzero tunneling time delay and a nonvanishing longitudinal momentum of the electron at the "tunnel exit."

Experimental Evidence for Quantum Tunneling Time

NASA Astrophysics Data System (ADS)

Camus, Nicolas; Yakaboylu, Enderalp; Fechner, Lutz; Klaiber, Michael; Laux, Martin; Mi, Yonghao; Hatsagortsyan, Karen Z.; Pfeifer, Thomas; Keitel, Christoph H.; Moshammer, Robert

2017-07-01

The first hundred attoseconds of the electron dynamics during strong field tunneling ionization are investigated. We quantify theoretically how the electron's classical trajectories in the continuum emerge from the tunneling process and test the results with those achieved in parallel from attoclock measurements. An especially high sensitivity on the tunneling barrier is accomplished here by comparing the momentum distributions of two atomic species of slightly deviating atomic potentials (argon and krypton) being ionized under absolutely identical conditions with near-infrared laser pulses (1300 nm). The agreement between experiment and theory provides clear evidence for a nonzero tunneling time delay and a nonvanishing longitudinal momentum of the electron at the "tunnel exit."

Persistent stability of a chaotic system

NASA Astrophysics Data System (ADS)

Huber, Greg; Pradas, Marc; Pumir, Alain; Wilkinson, Michael

2018-02-01

We report that trajectories of a one-dimensional model for inertial particles in a random velocity field can remain stable for a surprisingly long time, despite the fact that the system is chaotic. We provide a detailed quantitative description of this effect by developing the large-deviation theory for fluctuations of the finite-time Lyapunov exponent of this system. Specifically, the determination of the entropy function for the distribution reduces to the analysis of a Schrödinger equation, which is tackled by semi-classical methods. The system has 'generic' instability properties, and we consider the broader implications of our observation of long-term stability in chaotic systems.

Boost-phase discrimination research activities

NASA Technical Reports Server (NTRS)

Cooper, David M.; Deiwert, George S.

1989-01-01

Theoretical research in two areas was performed. The aerothermodynamics research focused on the hard-body and rocket plume flows. Analytical real gas models to describe finite rate chemistry were developed and incorporated into the three-dimensional flow codes. New numerical algorithms capable of treating multi-species reacting gas equations and treating flows with large gradients were also developed. The computational chemistry research focused on the determination of spectral radiative intensity factors, transport properties and reaction rates. Ab initio solutions to the Schrodinger equation provided potential energy curves transition moments (radiative probabilities and strengths) and potential energy surfaces. These surfaces were then coupled with classical particle reactive trajectories to compute reaction cross-sections and rates.

Imprints of the Molecular Electronic Structure in the Photoelectron Spectra of Strong-Field Ionized Asymmetric Triatomic Model Molecules

NASA Astrophysics Data System (ADS)

Paul, Matthias; Yue, Lun; Gräfe, Stefanie

2018-06-01

We examine the circular dichroism in the angular distribution of photoelectrons of triatomic model systems ionized by strong-field ionization. Following our recent work on this effect [Paul, Yue, and Gräfe, J. Mod. Opt. 64, 1104 (2017), 10.1080/09500340.2017.1299883], we demonstrate how the symmetry and electronic structure of the system is imprinted into the photoelectron momentum distribution. We use classical trajectories to reveal the origin of the threefolded pattern in the photoelectron momentum distribution, and show how an asymmetric nuclear configuration of the triatomic system effects the photoelectron spectra.

Analysis of a semiclassical model for rotational transition probabilities. [in highly nonequilibrium flow of diatomic molecules

NASA Technical Reports Server (NTRS)

Deiwert, G. S.; Yoshikawa, K. K.

1975-01-01

A semiclassical model proposed by Pearson and Hansen (1974) for computing collision-induced transition probabilities in diatomic molecules is tested by the direct-simulation Monte Carlo method. Specifically, this model is described by point centers of repulsion for collision dynamics, and the resulting classical trajectories are used in conjunction with the Schroedinger equation for a rigid-rotator harmonic oscillator to compute the rotational energy transition probabilities necessary to evaluate the rotation-translation exchange phenomena. It is assumed that a single, average energy spacing exists between the initial state and possible final states for a given collision.

Quantum design rules for single molecule logic gates.

PubMed

Renaud, N; Hliwa, M; Joachim, C

2011-08-28

Recent publications have demonstrated how to implement a NOR logic gate with a single molecule using its interaction with two surface atoms as logical inputs [W. Soe et al., ACS Nano, 2011, 5, 1436]. We demonstrate here how this NOR logic gate belongs to the general family of quantum logic gates where the Boolean truth table results from a full control of the quantum trajectory of the electron transfer process through the molecule by very local and classical inputs practiced on the molecule. A new molecule OR gate is proposed for the logical inputs to be also single metal atoms, one per logical input.

Theory and algorithms for image reconstruction on chords and within regions of interest

NASA Astrophysics Data System (ADS)

Zou, Yu; Pan, Xiaochuan; Sidky, Emilâ Y.

2005-11-01

We introduce a formula for image reconstruction on a chord of a general source trajectory. We subsequently develop three algorithms for exact image reconstruction on a chord from data acquired with the general trajectory. Interestingly, two of the developed algorithms can accommodate data containing transverse truncations. The widely used helical trajectory and other trajectories discussed in literature can be interpreted as special cases of the general trajectory, and the developed theory and algorithms are thus directly applicable to reconstructing images exactly from data acquired with these trajectories. For instance, chords on a helical trajectory are equivalent to the n-PI-line segments. In this situation, the proposed algorithms become the algorithms that we proposed previously for image reconstruction on PI-line segments. We have performed preliminary numerical studies, which include the study on image reconstruction on chords of two-circle trajectory, which is nonsmooth, and on n-PI lines of a helical trajectory, which is smooth. Quantitative results of these studies verify and demonstrate the proposed theory and algorithms.

The Human Cell Atlas.

PubMed

Regev, Aviv; Teichmann, Sarah A; Lander, Eric S; Amit, Ido; Benoist, Christophe; Birney, Ewan; Bodenmiller, Bernd; Campbell, Peter; Carninci, Piero; Clatworthy, Menna; Clevers, Hans; Deplancke, Bart; Dunham, Ian; Eberwine, James; Eils, Roland; Enard, Wolfgang; Farmer, Andrew; Fugger, Lars; Göttgens, Berthold; Hacohen, Nir; Haniffa, Muzlifah; Hemberg, Martin; Kim, Seung; Klenerman, Paul; Kriegstein, Arnold; Lein, Ed; Linnarsson, Sten; Lundberg, Emma; Lundeberg, Joakim; Majumder, Partha; Marioni, John C; Merad, Miriam; Mhlanga, Musa; Nawijn, Martijn; Netea, Mihai; Nolan, Garry; Pe'er, Dana; Phillipakis, Anthony; Ponting, Chris P; Quake, Stephen; Reik, Wolf; Rozenblatt-Rosen, Orit; Sanes, Joshua; Satija, Rahul; Schumacher, Ton N; Shalek, Alex; Shapiro, Ehud; Sharma, Padmanee; Shin, Jay W; Stegle, Oliver; Stratton, Michael; Stubbington, Michael J T; Theis, Fabian J; Uhlen, Matthias; van Oudenaarden, Alexander; Wagner, Allon; Watt, Fiona; Weissman, Jonathan; Wold, Barbara; Xavier, Ramnik; Yosef, Nir

2017-12-05

The recent advent of methods for high-throughput single-cell molecular profiling has catalyzed a growing sense in the scientific community that the time is ripe to complete the 150-year-old effort to identify all cell types in the human body. The Human Cell Atlas Project is an international collaborative effort that aims to define all human cell types in terms of distinctive molecular profiles (such as gene expression profiles) and to connect this information with classical cellular descriptions (such as location and morphology). An open comprehensive reference map of the molecular state of cells in healthy human tissues would propel the systematic study of physiological states, developmental trajectories, regulatory circuitry and interactions of cells, and also provide a framework for understanding cellular dysregulation in human disease. Here we describe the idea, its potential utility, early proofs-of-concept, and some design considerations for the Human Cell Atlas, including a commitment to open data, code, and community.

Influence of nuclear exchange on nonadiabatic electron processes in H(+)+H2 collisions.

PubMed

Errea, L F; Illescas, Clara; Macías, A; Méndez, L; Pons, B; Rabadán, I; Riera, A

2010-12-28

H(+)+H(2) collisions are studied by means of a semiclassical approach that explicitly accounts for nuclear rearrangement channels in nonadiabatic electron processes. A set of classical trajectories is used to describe the nuclear motion, while the electronic degrees of freedom are treated quantum mechanically in terms of a three-state expansion of the collision wavefunction. We describe electron capture and vibrational excitation, which can also involve nuclear exchange and dissociation, in the E = 2-1000 eV impact energy range. We compare dynamical results obtained with two parametrizations of the potential energy surface of H(3)(+) ground electronic state. Total cross sections for E > 10 eV agree with previous results using a vibronic close-coupling expansion, and with experimental data for E < 10 eV. Additionally, some prototypical features of both nuclear and electron dynamics at low E are discussed.

Path suppression of strongly collapsing bubbles at finite and low Reynolds numbers.

PubMed

Rechiman, Ludmila M; Dellavale, Damián; Bonetto, Fabián J

2013-06-01

We study, numerically and experimentally, three different methods to suppress the trajectories of strongly collapsing and sonoluminescent bubbles in a highly viscous sulfuric acid solution. A new numerical scheme based on the window method is proposed to account for the history force acting on a spherical bubble with variable radius. We could quantify the history force, which is not negligible in comparison with the primary Bjerknes force in this type of problem, and results are in agreement with the classical primary Bjerknes force trapping threshold analysis. Moreover, the present numerical implementation reproduces the spatial behavior associated with the positional and path instability of sonoluminescent argon bubbles in strongly gassed and highly degassed sulfuric acid solutions. Finally, the model allows us to demonstrate that spatially stationary bubbles driven by biharmonic excitation could be obtained with a different mode from the one used in previous reported experiments.

Observation of the Topological Change Associated with the Dynamical Monodromy

NASA Astrophysics Data System (ADS)

Salmon, Daniel; Nerem, Matthew; Aubin, Seth; Delos, John

2017-04-01

Classical mechanics is an old theory and new phenomena do not often appear. A recently predicted phenomenon is called ``Dynamical Monodromy.'' Monodromy is the study of the behavior of a system as it evolves ``once around a closed circuit''. Systems that do not return to their original state after forming a closed circuit in some space are said to exhibit ``nontrivial monodromy.'' One such system is a collection of non-interacting particles moving in a ``champagne bottle'' potential. A loop of trajectories of this system exhibits a topological change when each of the particles traverse a monodromy circuit in Energy-Angular Momentum space (any closed path that encloses the singular point at the origin). This system has been realized using a rigid spherical pendulum, with a permanent magnet at its end. Magnetic fields generated by coils are used to create the champagne-bottle potential, as well as drive the pendulum through the monodromy circuit.

The Human Cell Atlas

PubMed Central

Amit, Ido; Benoist, Christophe; Birney, Ewan; Bodenmiller, Bernd; Campbell, Peter; Carninci, Piero; Clatworthy, Menna; Clevers, Hans; Deplancke, Bart; Dunham, Ian; Eberwine, James; Eils, Roland; Enard, Wolfgang; Farmer, Andrew; Fugger, Lars; Göttgens, Berthold; Hacohen, Nir; Haniffa, Muzlifah; Hemberg, Martin; Kim, Seung; Klenerman, Paul; Kriegstein, Arnold; Lein, Ed; Linnarsson, Sten; Lundberg, Emma; Lundeberg, Joakim; Majumder, Partha; Marioni, John C; Merad, Miriam; Mhlanga, Musa; Nawijn, Martijn; Netea, Mihai; Nolan, Garry; Pe'er, Dana; Phillipakis, Anthony; Ponting, Chris P; Quake, Stephen; Reik, Wolf; Rozenblatt-Rosen, Orit; Sanes, Joshua; Satija, Rahul; Schumacher, Ton N; Shalek, Alex; Shapiro, Ehud; Sharma, Padmanee; Shin, Jay W; Stegle, Oliver; Stratton, Michael; Stubbington, Michael J T; Theis, Fabian J; Uhlen, Matthias; van Oudenaarden, Alexander; Wagner, Allon; Watt, Fiona; Weissman, Jonathan; Wold, Barbara; Xavier, Ramnik; Yosef, Nir

2017-01-01

The recent advent of methods for high-throughput single-cell molecular profiling has catalyzed a growing sense in the scientific community that the time is ripe to complete the 150-year-old effort to identify all cell types in the human body. The Human Cell Atlas Project is an international collaborative effort that aims to define all human cell types in terms of distinctive molecular profiles (such as gene expression profiles) and to connect this information with classical cellular descriptions (such as location and morphology). An open comprehensive reference map of the molecular state of cells in healthy human tissues would propel the systematic study of physiological states, developmental trajectories, regulatory circuitry and interactions of cells, and also provide a framework for understanding cellular dysregulation in human disease. Here we describe the idea, its potential utility, early proofs-of-concept, and some design considerations for the Human Cell Atlas, including a commitment to open data, code, and community. PMID:29206104

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

Cui, Jie; Krems, Roman V.; Li, Zhiying

We use classical trajectory calculations to study the effects of the interaction strength and the geometry of rigid polyatomic molecules on the formation of long-lived collision complexes at low collision energies. We first compare the results of the calculations for collisions of benzene molecules with rare gas atoms He, Ne, Ar, Kr, and Xe. The comparison illustrates that the mean lifetimes of the collision complexes increase monotonically with the strength of the atom–molecule interaction. We then compare the results of the atom–benzene calculations with those for benzene–benzene collisions. The comparison illustrates that the mean lifetimes of the benzene–benzene collision complexesmore » are significantly reduced due to non-ergodic effects prohibiting the molecules from sampling the entire configuration space. We find that the thermally averaged lifetimes of the benzene–benzene collisions are much shorter than those for Xe with benzene and similar to those for Ne with benzene.« less

Theory of the stopping power of fast multicharged ions

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

Yudin, G.L.

1991-12-01

The processes of Coulomb excitation and ionization of atoms by a fast charged particle moving along a classical trajectory are studied. The target electrons are described by the Dirac equation, while the field of the incident particle is described by the Lienard-Wiechert potential. The theory is formulated in the form most convenient for investigation of various characteristics of semiclassical atomic collisions. The theory of sudden perturbations, which is valid at high enough velocities for a high projectile charge, is employed to obtain probabilities and cross sections of the Coulomb excitation and ionization of atomic hydrogen by fast multiply charged ions.more » Based on the semiclassical sudden Born approximation, the ionization cross section and the average electronic energy loss of a fast ion in a single collision with an atom are investigated over a wide specific energy range from 500 keV/amu to 50 MeV/amu.« less

Magnetoresistance of an Anderson insulator of bosons.

PubMed

Gangopadhyay, Anirban; Galitski, Victor; Müller, Markus

2013-07-12

We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the change in spatial decay of localized excitations in response to a magnetic field, which is given by an interference sum over alternative tunneling trajectories. The excitations become more localized with increasing field (in sharp contrast to generic fermionic excitations which get weakly delocalized): the localization length ξ(B) is found to change as ξ(-1)(B)-ξ(-1)(0)~B(4/5). The quantum interference problem maps onto the classical statistical mechanics of directed polymers in random media (DPRM). We explain the observed scaling using a simplified droplet model which incorporates the nontrivial DPRM exponents. Our results have implications for a variety of experiments on magnetic-field-tuned superconductor-to-insulator transitions observed in disordered films, granular superconductors, and Josephson junction arrays, as well as for cold atoms in artificial gauge fields.

First principles calculations of thermal conductivity with out of equilibrium molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Puligheddu, Marcello; Gygi, Francois; Galli, Giulia

The prediction of the thermal properties of solids and liquids is central to numerous problems in condensed matter physics and materials science, including the study of thermal management of opto-electronic and energy conversion devices. We present a method to compute the thermal conductivity of solids by performing ab initio molecular dynamics at non equilibrium conditions. Our formulation is based on a generalization of the approach to equilibrium technique, using sinusoidal temperature gradients, and it only requires calculations of first principles trajectories and atomic forces. We discuss results and computational requirements for a representative, simple oxide, MgO, and compare with experiments and data obtained with classical potentials. This work was supported by MICCoM as part of the Computational Materials Science Program funded by the U.S. Department of Energy (DOE), Office of Science , Basic Energy Sciences (BES), Materials Sciences and Engineering Division under Grant DOE/BES 5J-30.

Failure tolerance strategy of space manipulator for large load carrying tasks

NASA Astrophysics Data System (ADS)

Chen, Gang; Yuan, Bonan; Jia, Qingxuan; Sun, Hanxu; Guo, Wen

2018-07-01

During the execution of large load carrying tasks in long term service, there is a notable risk of space manipulator suffering from locked-joint failure, thus space manipulator should be with enough failure tolerance performance. A research on evaluating failure tolerance performance and re-planning feasible task trajectory for space manipulator performing large load carrying tasks is conducted in this paper. The effects of locked-joint failure on critical performance(reachability and load carrying capacity) of space manipulator are analyzed at first. According to the requirements of load carrying tasks, we further propose a new concept of failure tolerance workspace with load carrying capacity(FTWLCC) to evaluate failure tolerance performance, and improve the classic A* algorithm to search the feasible task trajectory. Through the normalized FTWLCC and the improved A* algorithm, the reachability and load carrying capacity of the degraded space manipulator are evaluated, and the reachable and capable trajectory can be obtained. The establishment of FTWLCC provides a novel idea that combines mathematical statistics with failure tolerance performance to illustrate the distribution of load carrying capacity in three-dimensional space, so multiple performance indices can be analyzed simultaneously and visually. And the full consideration of all possible failure situations and motion states makes FTWLCC and improved A* algorithm be universal and effective enough to be appropriate for random joint failure and variety of requirement of large load carrying tasks, so they can be extended to other types of manipulators.

Why Pteropods Flap Their Wings, Periodically Pitch Their Shell, and Swim in a Sawtooth-like Trajectory

NASA Astrophysics Data System (ADS)

Adhikari, D.; Webster, D. R.; Yen, J.

2016-02-01

Antarctic pteropods (Limacina helicina antarctica), which are currently threatened by ocean acidification, swim in seawater with a pair of gelatinous parapodia (or "wings") via a distinctive propulsion mechanism. By flapping their parapodia in a way that resembles insect flight, they exhibit a unique shell wobble (or periodic shell pitching) motion and sawtooth-like trajectory. We present three-dimensional kinematics and volumetric fluid velocity fields for upward-swimming pteropods. Time-resolved data were collected with a unique infrared tomographic particle image velocimetry (tomo-PIV) system that was transported to Palmer Station, Antarctica. Both power and recovery strokes of the parapodia propel the pteropod (1.5 - 5 mm in size) upward in a sawtooth-like trajectory with average speed of 14 - 30 mm/s and periodically pitch the shell at 1.9 - 3 Hz with up to 110° difference in pitching angle. The pitch motion effectively positions the parapodia such that they stroke downward during both the power and recovery strokes. We use the kinematics measurement to illustrate the relationship between flapping, swimming and pitching, where the corresponding Reynolds numbers (i.e. Ref, ReU, and ReΩ) characterize the motion of the pteropod. For example, when Ref < 50, the shell does not pitch and the pteropod swims abnormally with little or no vertical translation. We show that the flow field and vortices generated during pteropod propulsion resemble some aspects of insect-flight aerodynamics reported in classic literature, albeit with distinct aquatic variations.

Trajectories of positive, negative and general psychopathology symptoms in first episode psychosis and their relationship with functioning over a 2-year follow-up period.

PubMed

Abdin, Edimansyah; Chong, Siow Ann; Vaingankar, Janhavi Ajit; Peh, Chao Xu; Poon, Lye Yin; Rao, Sujatha; Verma, Swapna; Subramaniam, Mythily

2017-01-01

Few studies have examined the trajectories of symptom severity in first episode psychosis (FEP) and their impact on functioning. This study aimed to identify discrete trajectories of positive, negative and general psychopathological symptoms and functioning, determine predictors of the identified symptom trajectories and subsequently investigate the relationship between symptom and functioning trajectories over the 2-year follow-up period. Data were extracted from the Singapore Early Psychosis Intervention Programme clinical database. Trajectories of the Positive and Negative Syndrome Scale and Global Assessment of Functioning (GAF) scale over the two-year follow up were modelled using latent class growth curve modelling. Two distinct trajectories (early response and stable trajectory and delayed response trajectory) for positive symptoms, four distinct trajectories (early response and stable trajectory, early response and relapse trajectory, slower response and no response trajectory and delayed response trajectory) for negative and general psychopathology symptoms and three distinct trajectories for functioning (high functioning trajectory, moderately stable functioning trajectory and deterioration in functioning trajectory) were identified in our sample. Compared to individuals in the early response and stable trajectory, those in the delayed response trajectory for positive and negative symptoms, early response and relapse for negative and general psychopathology symptoms and slower response and no response trajectories for general psychopathology symptoms were significantly associated with higher odds of having deterioration in functioning over time. Poor symptom trajectories were also significantly predicted by younger age, male gender, unemployed and economically inactive status, lower education, longer duration of untreated psychosis and diagnosis of schizophrenia spectrum and delusional disorders. The results confirm that the symptoms trajectories among patients with FEP are heterogeneous and suggest that a small group of patients may be at higher risk of deterioration in symptom severity and functioning over the 2-year follow-up.

US Decadal Survey Outer Solar System Missions: Trajectory Options

NASA Astrophysics Data System (ADS)

Spilker, T. R.; Atkinson, D. H.; Strange, N. J.; Landau, D.

2012-04-01

The report of the US Planetary Science Decadal Survey (PSDS), released in draft form March 7, 2011, identifies several mission concepts involving travel to high-priority outer solar system (OSS) destinations. These include missions to Europa and Jupiter, Saturn and two of its satellites, and Uranus. Because travel to the OSS involves much larger distances and larger excursions out of the sun's gravitational potential well than inner solar system (ISS) missions, transfer trajectories for OSS missions are stronger drivers of mission schedule and resource requirements than for ISS missions. Various characteristics of each planet system, such as obliquity, radiation belts, rings, deep gravity wells, etc., carry ramifications for approach trajectories or trajectories within the systems. The maturity of trajectory studies for each of these destinations varies significantly. Europa has been the focus of studies for well over a decade. Transfer trajectory options from Earth to Jupiter are well understood. Current studies focus on trajectories within the Jovian system that could reduce the total mission cost of a Europa orbiter mission. Three missions to the Saturn system received high priority ratings in the PSDS report: two flagship orbital missions, one to Titan and one to Enceladus, and a Saturn atmospheric entry probe mission for NASA's New Frontiers Program. The Titan Saturn System Mission (TSSM) studies of 2007-2009 advanced our understanding of trajectory options for transfers to Saturn, including solar electric propulsion (SEP) trajectories. But SEP trajectories depend more on details of spacecraft and propulsion system characteristics than chemical trajectories, and the maturity of SEP trajectory search tools has not yet caught up with chemical trajectory tools, so there is still more useful research to be done on Saturn transfers. The TSSM studies revealed much about Saturn-orbiting trajectories that yield efficient and timely delivery to Titan or Enceladus orbits. PSDS studies suggest there is significant flexibility in trajectory options for a Saturn entry probe. Many different trajectory approaches and a wide range of trajectory parameters yield probe-to-carrier data relay communications of sufficient duration and at data rates surpassing those of the 1995 Galileo probe at Jupiter. Research into trajectories to Uranus and within the Uranian system is the least mature. SEP and chemical transfer trajectories have been examined but the searches are not yet comprehensive, though the fundamentals of such transfers are fairly well understood. Study of orbital tours within the Uranian system suggests they can be analogous to such tours in the Jovian system, though in the time frame of launches within the next couple of decades arrivals at Uranus would be from high declinations, so the transition from an initial orbit to an equatorial satellite tour could be lengthy. This paper will present results from the most recent work on these trajectories. This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. Copyright 2012 California Institute of Technology. Government sponsorship acknowledged.

Construction of a coarse-grain quasi-classical trajectory method. II. Comparison against the direct molecular simulation method

NASA Astrophysics Data System (ADS)

Macdonald, R. L.; Grover, M. S.; Schwartzentruber, T. E.; Panesi, M.

2018-02-01

This work presents the analysis of non-equilibrium energy transfer and dissociation of nitrogen molecules (N2(g+1Σ) ) using two different approaches: the direct molecular simulation (DMS) method and the coarse-grain quasi-classical trajectory (CG-QCT) method. The two methods are used to study thermochemical relaxation in a zero-dimensional isochoric and isothermal reactor in which the nitrogen molecules are heated to several thousand degrees Kelvin, forcing the system into strong non-equilibrium. The analysis considers thermochemical relaxation for temperatures ranging from 10 000 to 25 000 K. Both methods make use of the same potential energy surface for the N2(g+1Σ ) -N2(g+1Σ ) system taken from the NASA Ames quantum chemistry database. Within the CG-QCT method, the rovibrational energy levels of the electronic ground state of the nitrogen molecule are lumped into a reduced number of bins. Two different grouping strategies are used: the more conventional vibrational-based grouping, widely used in the literature, and energy-based grouping. The analysis of both the internal state populations and concentration profiles show excellent agreement between the energy-based grouping and the DMS solutions. During the energy transfer process, discrepancies arise between the energy-based grouping and DMS solution due to the increased importance of mode separation for low energy states. By contrast, the vibrational grouping, traditionally considered state-of-the-art, captures well the behavior of the energy relaxation but fails to consistently predict the dissociation process. The deficiency of the vibrational grouping model is due to the assumption of strict mode separation and equilibrium of rotational energy states. These assumptions result in errors predicting the energy contribution to dissociation from the rotational and vibrational modes, with rotational energy actually contributing 30%-40% of the energy required to dissociate a molecule. This work confirms the findings discussed in Paper I [R. L. Macdonald et al., J. Chem. Phys. 148, 054309 (2018)], which underlines the importance of rotational energy to the dissociation process, and demonstrates that an accurate non-equilibrium chemistry model must accurately predict the deviation of rovibrational distribution from equilibrium.

Construction of a coarse-grain quasi-classical trajectory method. II. Comparison against the direct molecular simulation method.

PubMed

Macdonald, R L; Grover, M S; Schwartzentruber, T E; Panesi, M

2018-02-07

This work presents the analysis of non-equilibrium energy transfer and dissociation of nitrogen molecules (N 2 (Σg+1)) using two different approaches: the direct molecular simulation (DMS) method and the coarse-grain quasi-classical trajectory (CG-QCT) method. The two methods are used to study thermochemical relaxation in a zero-dimensional isochoric and isothermal reactor in which the nitrogen molecules are heated to several thousand degrees Kelvin, forcing the system into strong non-equilibrium. The analysis considers thermochemical relaxation for temperatures ranging from 10 000 to 25 000 K. Both methods make use of the same potential energy surface for the N 2 (Σg+1)-N 2 (Σg+1) system taken from the NASA Ames quantum chemistry database. Within the CG-QCT method, the rovibrational energy levels of the electronic ground state of the nitrogen molecule are lumped into a reduced number of bins. Two different grouping strategies are used: the more conventional vibrational-based grouping, widely used in the literature, and energy-based grouping. The analysis of both the internal state populations and concentration profiles show excellent agreement between the energy-based grouping and the DMS solutions. During the energy transfer process, discrepancies arise between the energy-based grouping and DMS solution due to the increased importance of mode separation for low energy states. By contrast, the vibrational grouping, traditionally considered state-of-the-art, captures well the behavior of the energy relaxation but fails to consistently predict the dissociation process. The deficiency of the vibrational grouping model is due to the assumption of strict mode separation and equilibrium of rotational energy states. These assumptions result in errors predicting the energy contribution to dissociation from the rotational and vibrational modes, with rotational energy actually contributing 30%-40% of the energy required to dissociate a molecule. This work confirms the findings discussed in Paper I [R. L. Macdonald et al., J. Chem. Phys. 148, 054309 (2018)], which underlines the importance of rotational energy to the dissociation process, and demonstrates that an accurate non-equilibrium chemistry model must accurately predict the deviation of rovibrational distribution from equilibrium.

Power spectra as a diagnostic tool in probing statistical/nonstatistical behavior in unimolecular reactions

NASA Astrophysics Data System (ADS)

Chang, Xiaoyen Y.; Sewell, Thomas D.; Raff, Lionel M.; Thompson, Donald L.

1992-11-01

The possibility of utilizing different types of power spectra obtained from classical trajectories as a diagnostic tool to identify the presence of nonstatistical dynamics is explored by using the unimolecular bond-fission reactions of 1,2-difluoroethane and the 2-chloroethyl radical as test cases. In previous studies, the reaction rates for these systems were calculated by using a variational transition-state theory and classical trajectory methods. A comparison of the results showed that 1,2-difluoroethane is a nonstatistical system, while the 2-chloroethyl radical behaves statistically. Power spectra for these two systems have been generated under various conditions. The characteristics of these spectra are as follows: (1) The spectra for the 2-chloroethyl radical are always broader and more coupled to other modes than is the case for 1,2-difluoroethane. This is true even at very low levels of excitation. (2) When an internal energy near or above the dissociation threshold is initially partitioned into a local C-H stretching mode, the power spectra for 1,2-difluoroethane broaden somewhat, but discrete and somewhat isolated bands are still clearly evident. In contrast, the analogous power spectra for the 2-chloroethyl radical exhibit a near complete absence of isolated bands. The general appearance of the spectrum suggests a very high level of mode-to-mode coupling, large intramolecular vibrational energy redistribution (IVR) rates, and global statistical behavior. (3) The appearance of the power spectrum for the 2-chloroethyl radical is unaltered regardless of whether the initial C-H excitation is in the CH2 or the CH2Cl group. This result also suggests statistical behavior. These results are interpreted to mean that power spectra may be used as a diagnostic tool to assess the statistical character of a system. The presence of a diffuse spectrum exhibiting a nearly complete loss of isolated structures indicates that the dissociation dynamics of the molecule will be well described by statistical theories. If, however, the power spectrum maintains its discrete, isolated character, as is the case for 1,2-difluoroethane, the opposite conclusion is suggested. Since power spectra are very easily computed, this diagnostic method may prove to be useful.

Trajectories of Delinquency among Puerto Rican Children and Adolescents at Two Sites

ERIC Educational Resources Information Center

Maldonado-Molina, Mildred M.; Piquero, Alex R.; Jennings, Wesley G.; Bird, Hector; Canino, Glorisa

2009-01-01

This study examined the trajectories of delinquency among Puerto Rican children and adolescents in two cultural contexts. Relying on data from the Boricua Youth Study, a longitudinal study of children and youth from Bronx, New York, and San Juan, Puerto Rico, a group-based trajectory procedure estimated the number of delinquency trajectories,…

Developmental trajectories of DSM-IV symptoms of attention-deficit/hyperactivity disorder: genetic effects, family risk and associated psychopathology.

PubMed

Larsson, Henrik; Dilshad, Rezin; Lichtenstein, Paul; Barker, Edward D

2011-09-01

DSM-IV specifies three ADHD subtypes; the combined, the hyperactive-impulsive and the inattentive. Little is known about the developmental relationships underlying these subtypes. The objective of this study was to describe the development of parent-reported hyperactivity-impulsivity and inattention symptoms from childhood to adolescence and to study their associations with genetic factors, family risk, and later adjustment problems in early adulthood. Data in this study comes from 1,450 twin pairs participating in a population-based, longitudinal twin study. Developmental trajectories were defined using parent-ratings of hyperactivity-impulsivity and inattention symptoms at age 8-9, 13-14, and 16-17. Twin methods were used to explore genetic influences on trajectories. Family risk measures included low socioeconomic status, large family size and divorce. Self-ratings of externalizing and internalizing problems in early adulthood were used to examine adjustment problems related to the different trajectory combinations. We found two hyperactivity-impulsivity trajectories (low, high/decreasing) and two inattention trajectories (low, high/increasing). Twin modeling revealed a substantial genetic component underlying both the hyperactivity-impulsivity and the inattention trajectory. Joint trajectory analyses identified four groups of adolescents with distinct developmental patterns of hyperactivity-impulsivity and inattention: a low/low group, a primarily hyperactive, a primarily inattentive and a combined (high/high) trajectory type. These trajectory combinations showed discriminant relations to adjustment problems in early adulthood. The hyperactive, inattentive and combined trajectory subtypes were associated with higher rates of family risk environments compared to the low/low group. Study results showed that for those on a high trajectory, hyperactivity decreased whereas inattention increased. The combinations of these trajectories lend developmental insight into how children shift from (i) a combined to inattentive subtype, and (ii) a hyperactive-impulsive to a combined subtype. This study suggests that ADHD subtypes cannot be viewed as discrete and stable categories. © 2011 The Authors. Journal of Child Psychology and Psychiatry © 2011 Association for Child and Adolescent Mental Health.

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

Song, Hongwei, E-mail: hwsong@wipm.ac.cn; Yang, Minghui; Lu, Yunpeng

An initial state selected time-dependent wave packet method is applied to study the dynamics of the OH + CHD{sub 3} reaction with a six-dimensional model on a newly developed full-dimensional ab initio potential energy surface (PES). This quantum dynamical (QD) study is complemented by full-dimensional quasi-classical trajectory (QCT) calculations on the same PES. The QD results indicate that both translational energy and the excitation of the CH stretching mode significantly promote the reaction while the excitation of the umbrella mode has a negligible effect on the reactivity. For this early barrier reaction, interestingly, the CH stretching mode is more effectivemore » than translational energy in promoting the reaction except at very low collision energies. These QD observations are supported by QCT results. The higher efficacy of the CH stretching model in promoting this early barrier reaction is inconsistent with the prediction of the naively extended Polanyi’s rules, but can be rationalized by the recently proposed sudden vector projection model.« less

High-level ab initio potential energy surface and dynamics of the F– + CH3I SN2 and proton-transfer reactions† †Electronic supplementary information (ESI) available: Benchmark classical and adiabatic relative energies (Table S1), vibrational frequencies of all the stationary points (Tables S2 and S3), direct/indirect trajectory separation function parameters (Table S4), entrance-channel potential (Fig. S1), structures of the minima and saddle points corresponding to the abstraction channel (Fig. S2), reaction probabilities (Fig. S3), trajectory integration time distributions (Fig. S4), trajectory integration time vs. I– velocity distributions (Fig. S5), and mechanism-specific reaction probabilities (Fig. S6). See DOI: 10.1039/c7sc00033b Click here for additional data file.

PubMed Central

Olasz, Balázs; Szabó, István

2017-01-01

Bimolecular nucleophilic substitution (SN2) and proton transfer are fundamental processes in chemistry and F– + CH3I is an important prototype of these reactions. Here we develop the first full-dimensional ab initio analytical potential energy surface (PES) for the F– + CH3I system using a permutationally invariant fit of high-level composite energies obtained with the combination of the explicitly-correlated CCSD(T)-F12b method, the aug-cc-pVTZ basis, core electron correlation effects, and a relativistic effective core potential for iodine. The PES accurately describes the SN2 channel producing I– + CH3F via Walden-inversion, front-side attack, and double-inversion pathways as well as the proton-transfer channel leading to HF + CH2I–. The relative energies of the stationary points on the PES agree well with the new explicitly-correlated all-electron CCSD(T)-F12b/QZ-quality benchmark values. Quasiclassical trajectory computations on the PES show that the proton transfer becomes significant at high collision energies and double-inversion as well as front-side attack trajectories can occur. The computed broad angular distributions and hot internal energy distributions indicate the dominance of indirect mechanisms at lower collision energies, which is confirmed by analyzing the integration time and leaving group velocity distributions. Comparison with available crossed-beam experiments shows usually good agreement. PMID:28507692

Benefit finding trajectories in cancer patients receiving psychological care: Predictors and relations to depressive and anxiety symptoms.

PubMed

Zhu, Lei; Ranchor, Adelita V; Helgeson, Vicki S; van der Lee, Marije; Garssen, Bert; Stewart, Roy E; Sanderman, Robbert; Schroevers, Maya J

2018-05-01

This study aimed to (1) identify benefit finding trajectories in cancer patients receiving psychological care; (2) examine associations of benefit finding trajectories with levels of and changes in psychological symptoms; and (3) examine whether socio-demographic and medical characteristics distinguished trajectories. Naturalistic longitudinal study design. Participants were 241 cancer patients receiving psychological care at specialized psycho-oncological institutions in the Netherlands. Data were collected before starting psychological care, and three and 9 months thereafter. Latent class growth analysis was performed to identify benefit finding trajectories. Five benefit finding trajectories were identified: 'high level-stable' (8%), 'very low level-small increase' (16%), 'low level-small increase' (39%), 'low level-large increase' (9%), and 'moderate level-stable' (28%). People in distinct benefit finding trajectories reported significant differential courses of depression but not of anxiety symptoms. Compared with the other four trajectories, people in the 'low level-large increase' trajectory reported the largest decreases in depression over time. Perceptions of cancer prognosis distinguished these trajectories, such that people with a favourable prognosis were more likely to belong to the 'high level-stable' trajectory, while people perceiving an uncertain prognosis were more likely to belong to the 'low level-large increase' trajectory of benefit finding. Cancer patients showed distinct benefit finding trajectories during psychological care. A small proportion reporting a large increase in benefit finding were also most likely to show decreases in depressive symptoms over time. These findings suggest a relation between perceiving benefits from cancer experience and improved psychological functioning in cancer patients receiving psychological care. Statement of contribution What is already known on this subject? People vary in course of benefit finding (BF) after trauma, with some experiencing enhanced BF and others decreased BF. Empirical studies have identified subgroups of cancer patients with distinct BF trajectories. What does this study add? This is the first study showing that cancer patients followed different BF trajectories during psychological care. Only a small proportion experienced clinically meaningful increases in BF over time. More attention is needed for cancer patients with decreased BF, as they are at a higher risk of remaining depressed. © 2017 The British Psychological Society.

Longitudinal investigation of anxiety sensitivity growth trajectories and relations with anxiety and depression symptoms in adolescence.

PubMed

Allan, Nicholas P; Felton, Julia W; Lejuez, Carl W; MacPherson, Laura; Schmidt, Norman B

2016-05-01

Anxiety sensitivity (AS), the belief that anxious arousal is harmful, is a malleable risk factor that has been implicated in anxiety and depression symptoms in adolescents. Although there is some evidence that adolescents possess distinct developmental trajectories, few studies have explored this topic. This study examined the developmental trajectory of AS in 248 adolescents (M age = 11.0 years, SD = 0.82; 56% male) across 6 years, beginning when children were age 11. This study also examined the influence of AS trajectories on anxiety and depression at age 16. Finally, this study examined the utility of AS classes in identifying anxiety and depression growth. Three AS classes were found, described by normative-stable, high-stable, and high-unstable trajectories. Adolescents in the high-stable and the high-unstable AS classes had higher levels of anxiety and depression at age 16 than did adolescents in the normative-stable AS class. In addition, the anxiety and depression trajectories fit by AS class mirrored the AS class trajectories. These findings suggest three AS trajectories can be identified in adolescents. These trajectories are discussed in relation to a developmental perspective of AS.

Integrability versus Thermalizability in Isolated Quantum Systems

NASA Astrophysics Data System (ADS)

Olshanii, Maxim

2012-02-01

The purpose of this presentation is to assess the status of our understanding of the transition from integrability to thermalizability in isolated quantum systems. In Classical Mechanics, the boundary stripe between the two is relatively sharp: its integrability edge is marked by the appearance of finite Lyapunov's exponents that further converge to a unique value when the ergodicity edge is reached. Classical ergodicity is a universal property: if a system is ergodic, then every observable attains its microcanonical value in the infinite time average over the trajectory. On the contrary, in Quantum Mechanics, Lyapunov's exponents are always zero. Furthermore, since quantum dynamics necessarily invokes coherent superpositions of eigenstates of different energy, projectors to the eigenstates become more relevant; those in turn never thermalize. All of the above indicates that in quantum many-body systems, (a) the integrability-thermalizability transition is smooth, and (b) the degree of thermalizability is not absolute like in classical mechanics, but it is relative to the class of observables of interest. In accordance with these observations, we propose a concrete measure of the degree of quantum thermalizability, consistent with the expected empirical manifestations of it. As a practical application of this measure, we devise a unified recipe for choosing an optimal set of conserved quantities to govern the after-relaxation values of observables, in both integrable quantum systems and in quantum systems in between integrable and thermalizable.

An efficient and stable hybrid extended Lagrangian/self-consistent field scheme for solving classical mutual induction

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

Albaugh, Alex; Demerdash, Omar; Head-Gordon, Teresa, E-mail: thg@berkeley.edu

2015-11-07

We have adapted a hybrid extended Lagrangian self-consistent field (EL/SCF) approach, developed for time reversible Born Oppenheimer molecular dynamics for quantum electronic degrees of freedom, to the problem of classical polarization. In this context, the initial guess for the mutual induction calculation is treated by auxiliary induced dipole variables evolved via a time-reversible velocity Verlet scheme. However, we find numerical instability, which is manifested as an accumulation in the auxiliary velocity variables, that in turn results in an unacceptable increase in the number of SCF cycles to meet even loose convergence tolerances for the real induced dipoles over the coursemore » of a 1 ns trajectory of the AMOEBA14 water model. By diagnosing the numerical instability as a problem of resonances that corrupt the dynamics, we introduce a simple thermostating scheme, illustrated using Berendsen weak coupling and Nose-Hoover chain thermostats, applied to the auxiliary dipole velocities. We find that the inertial EL/SCF (iEL/SCF) method provides superior energy conservation with less stringent convergence thresholds and a correspondingly small number of SCF cycles, to reproduce all properties of the polarization model in the NVT and NVE ensembles accurately. Our iEL/SCF approach is a clear improvement over standard SCF approaches to classical mutual induction calculations and would be worth investigating for application to ab initio molecular dynamics as well.« less

Health care professionals' perspectives of living and dying with primary malignant glioma: Implications for a unique cancer trajectory.

PubMed

Philip, Jennifer; Collins, Anna; Brand, Caroline A; Gold, Michelle; Moore, Gaye; Sundararajan, Vijaya; Murphy, Michael A; Lethborg, Carrie

2015-12-01

Health care professionals (HCPs) caring for people with primary malignant glioma (PMG) and their carers see many of the profound challenges facing this group, yet their perspectives are not documented. This study aimed to understand and document the unique perspective of HCPs in relation to the supportive and palliative care needs of patients with PMG and their carers, with a view to developing a model of care. Qualitative study involving semi-structured focus groups and interviews with 35 medical, nursing and allied health staff actively engaged in providing care for this patient group. Purposive and theoretical sampling from two major metropolitan hospitals and one community palliative care service in Australia was utilised to seek perspectives from a variety of disciplines and health care settings. Thematic analysis was conducted by three independent researchers, using a constant comparative method influenced by grounded theory. Key themes relating to the needs of people with PMG which were apparent from the HCPs included: The difference in the illness course of glioma compared to other cancers; Limitations of current medical care; Challenges in balancing hope with reality of the illness; and Recommendations to improve care, including recognising the role of family and moving from a model where services are offered in response to demonstrated needs. Significance of the results: Current models of care based upon the classic cancer trajectory are unresponsive to the needs of people with PMG. Care may be enhanced by moving towards a proactive approach, extending the goals of care beyond medical needs and broadening the focus of care to include family needs.

Indeterminism in Classical Dynamics of Particle Motion

NASA Astrophysics Data System (ADS)

Eyink, Gregory; Vishniac, Ethan; Lalescu, Cristian; Aluie, Hussein; Kanov, Kalin; Burns, Randal; Meneveau, Charles; Szalay, Alex

2013-03-01

We show that ``God plays dice'' not only in quantum mechanics but also in the classical dynamics of particles advected by turbulent fluids. With a fixed deterministic flow velocity and an exactly known initial position, the particle motion is nevertheless completely unpredictable! In analogy with spontaneous magnetization in ferromagnets which persists as external field is taken to zero, the particle trajectories in turbulent flow remain random as external noise vanishes. The necessary ingredient is a rough advecting field with a power-law energy spectrum extending to smaller scales as noise is taken to zero. The physical mechanism of ``spontaneous stochasticity'' is the explosive dispersion of particle pairs proposed by L. F. Richardson in 1926, so the phenomenon should be observable in laboratory and natural turbulent flows. We present here the first empirical corroboration of these effects in high Reynolds-number numerical simulations of hydrodynamic and magnetohydrodynamic fluid turbulence. Since power-law spectra are seen in many other systems in condensed matter, geophysics and astrophysics, the phenomenon should occur rather widely. Fast reconnection in solar flares and other astrophysical systems can be explained by spontaneous stochasticity of magnetic field-line motion

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.

Simulation of vibrational dephasing of I(2) in solid Kr using the semiclassical Liouville method.

PubMed

Riga, Jeanne M; Fredj, Erick; Martens, Craig C

2006-02-14

In this paper, we present simulations of the decay of quantum coherence between vibrational states of I(2) in its ground (X) electronic state embedded in a cryogenic Kr matrix. We employ a numerical method based on the semiclassical limit of the quantum Liouville equation, which allows the simulation of the evolution and decay of quantum vibrational coherence using classical trajectories and ensemble averaging. The vibrational level-dependent interaction of the I(2)(X) oscillator with the rare-gas environment is modeled using a recently developed method for constructing state-dependent many-body potentials for quantum vibrations in a many-body classical environment [J. M. Riga, E. Fredj, and C. C. Martens, J. Chem. Phys. 122, 174107 (2005)]. The vibrational dephasing rates gamma(0n) for coherences prepared between the ground vibrational state mid R:0 and excited vibrational state mid R:n are calculated as a function of n and lattice temperature T. Excellent agreement with recent experiments performed by Karavitis et al. [Phys. Chem. Chem. Phys. 7, 791 (2005)] is obtained.

Computing Wigner distributions and time correlation functions using the quantum thermal bath method: application to proton transfer spectroscopy.

PubMed

Basire, Marie; Borgis, Daniel; Vuilleumier, Rodolphe

2013-08-14

Langevin dynamics coupled to a quantum thermal bath (QTB) allows for the inclusion of vibrational quantum effects in molecular dynamics simulations at virtually no additional computer cost. We investigate here the ability of the QTB method to reproduce the quantum Wigner distribution of a variety of model potentials, designed to assess the performances and limits of the method. We further compute the infrared spectrum of a multidimensional model of proton transfer in the gas phase and in solution, using classical trajectories sampled initially from the Wigner distribution. It is shown that for this type of system involving large anharmonicities and strong nonlinear coupling to the environment, the quantum thermal bath is able to sample the Wigner distribution satisfactorily and to account for both zero point energy and tunneling effects. It leads to quantum time correlation functions having the correct short-time behavior, and the correct associated spectral frequencies, but that are slightly too overdamped. This is attributed to the classical propagation approximation rather than the generation of the quantized initial conditions themselves.

Experimental Apparatus for the Observation of the Topological Change Associated with Dynamical Monodromy

NASA Astrophysics Data System (ADS)

Salmon, Daniel; Nerem, M. Perry; Aubin, Seth; Delos, John

Monodromy means ``once around a path,'' therefore systems that have non-trivial monodromy are systems such that, when taken around a closed circuit in some space, the system has changed state in some way. Classical systems that exhibit non-trivial Hamiltonian monodromy have action and angle variables that are multivalued functions. A family, or loop, of trajectories of this system has a topological change upon traversing a monodromy circuit. We present an experimental apparatus for observing this topological change. A family of particles moving in a cylindrically symmetric champagne-bottle potential exhibits non-trivial Hamiltonian monodromy. At the center of this system is a classically forbidden region. By following a monodromy circuit, a loop of initial conditions on one side of the forbidden region can be made to evolve continuously into a loop that surrounds the forbidden region. We realize this system using a spherical pendulum, having at its end a permanent magnet. Magnetic fields generated by coils can then be used to create the champagne-bottle potential, as well as drive the pendulum through the monodromy circuit.

A stochastic vision-based model inspired by zebrafish collective behaviour in heterogeneous environments

PubMed Central

Collignon, Bertrand; Séguret, Axel; Halloy, José

2016-01-01

Collective motion is one of the most ubiquitous behaviours displayed by social organisms and has led to the development of numerous models. Recent advances in the understanding of sensory system and information processing by animals impels one to revise classical assumptions made in decisional algorithms. In this context, we present a model describing the three-dimensional visual sensory system of fish that adjust their trajectory according to their perception field. Furthermore, we introduce a stochastic process based on a probability distribution function to move in targeted directions rather than on a summation of influential vectors as is classically assumed by most models. In parallel, we present experimental results of zebrafish (alone or in group of 10) swimming in both homogeneous and heterogeneous environments. We use these experimental data to set the parameter values of our model and show that this perception-based approach can simulate the collective motion of species showing cohesive behaviour in heterogeneous environments. Finally, we discuss the advances of this multilayer model and its possible outcomes in biological, physical and robotic sciences. PMID:26909173

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.

Extending geometrical optics: A Lagrangian theory for vector waves

DOE PAGES

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

2017-03-16

Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wavemore » spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.« less

Extending geometrical optics: A Lagrangian theory for vector waves

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

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

Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wavemore » spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.« less

Dynamics and Novel Mechanisms of SN2 Reactions on ab Initio Analytical Potential Energy Surfaces.

PubMed

Szabó, István; Czakó, Gábor

2017-11-30

We describe a novel theoretical approach to the bimolecular nucleophilic substitution (S N 2) reactions that is based on analytical potential energy surfaces (PESs) obtained by fitting a few tens of thousands high-level ab initio energy points. These PESs allow computing millions of quasi-classical trajectories thereby providing unprecedented statistical accuracy for S N 2 reactions, as well as performing high-dimensional quantum dynamics computations. We developed full-dimensional ab initio PESs for the F - + CH 3 Y [Y = F, Cl, I] systems, which describe the direct and indirect, complex-forming Walden-inversion, the frontside attack, and the new double-inversion pathways as well as the proton-transfer channels. Reaction dynamics simulations on the new PESs revealed (a) a novel double-inversion S N 2 mechanism, (b) frontside complex formation, (c) the dynamics of proton transfer, (d) vibrational and rotational mode specificity, (e) mode-specific product vibrational distributions, (f) agreement between classical and quantum dynamics, (g) good agreement with measured scattering angle and product internal energy distributions, and (h) significant leaving group effect in accord with experiments.

Oligopolies with contingent workforce and unemployment insurance systems

NASA Astrophysics Data System (ADS)

Matsumoto, Akio; Merlone, Ugo; Szidarovszky, Ferenc

2015-10-01

In the recent literature the introduction of modified cost functions has added reality into the classical oligopoly analysis. Furthermore, the market evolution requires much more flexibility to firms, and in several countries contingent workforce plays an important role in the production choices by the firms. Therefore, an analysis of dynamic adjustment costs is in order to understand oligopoly dynamics. In this paper, dynamic single-product oligopolies without product differentiation are first examined with the additional consideration of production adjustment costs. Linear inverse demand and cost functions are considered and it is assumed that the firms adjust their outputs partially toward best response. The set of the steady states is characterized by a system of linear inequalities and there are usually infinitely many steady states. The asymptotic behavior of the output trajectories is examined by using computer simulation. The numerical results indicate that the resulting dynamics is richer than in the case of the classical Cournot model. This model and results are then compared to oligopolies with unemployment insurance systems when the additional cost is considered if firms do not use their maximum capacities.

Quasi-classical trajectory study of the role of vibrational and translational energy in the Cl(2P) + NH3 reaction.

PubMed

Monge-Palacios, M; Corchado, J C; Espinosa-Garcia, J

2012-05-28

A detailed state-to-state dynamics study was performed to analyze the effects of vibrational excitation and translational energy on the dynamics of the Cl((2)P) + NH(3)(v) gas-phase reaction, effects which are connected to such issues as mode selectivity and Polanyi's rules. This reaction evolves along two deep wells in the entry and exit channels. At low and high collision energies quasi-classical trajectory calculations were performed on an analytical potential energy surface previously developed by our group, together with a simplified model surface in which the reactant well is removed to analyze the influence of this well. While at high energy the independent vibrational excitation of all NH(3)(v) modes increases the reactivity by a factor ≈1.1-2.9 with respect to the vibrational ground-state, at low energy the opposite behaviour is found (factor ≈ 0.4-0.9). However, when the simplified model surface is used at low energy the independent vibrational excitation of all NH(3)(v) modes increases the reactivity, showing that the behaviour at low energies is a direct consequence of the existence of the reactant well. Moreover, we find that this reaction exhibits negligible mode selectivity, first because the independent excitation of the N-H symmetric and asymmetric stretch modes, which lie within 200 cm(-1) of each other, leads to reactions with similar reaction probabilities, and second because the vibrational excitation of the reactive N-H stretch mode is only partially retained in the products. For this "late transition-state" reaction, we also find that vibrational energy is more effective in driving the reaction than an equivalent amount of energy in translation, consistent with an extension of Polanyi's rules. Finally, we find that the non-reactive events, Cl((2)P)+NH(3)(v) → Cl((2)P) + NH(3)(v'), lead to a great number of populated vibrational states in the NH(3)(v') product, even starting from the NH(3)(v = 0) vibrational ground state at low energies, which is unphysical in a quantum world. This result is interpreted on the basis of non-conservation of the ZPE per mode.

A theoretical study of the dynamic behavior of alkane hydroxylation by a compound I model of cytochrome P450.

PubMed

Yoshizawa, K; Kamachi, T; Shiota, Y

2001-10-10

Dynamic aspects of alkane hydroxylation mediated by Compound I of cytochrome P450 are discussed from classical trajectory calculations at the B3LYP level of density functional theory. The nuclei of the reacting system are propagated from a transition state to a reactant or product direction according to classical dynamics on a Born-Oppenheimer potential energy surface. Geometric and energetic changes in both low-spin doublet and high-spin quartet states are followed along the ethane to ethanol reaction pathway, which is partitioned into two chemical steps: the first is the H-atom abstraction from ethane by the iron-oxo species of Compound I and the second is the rebound step in which the resultant iron-hydroxo complex and the ethyl radical intermediate react to form the ethanol complex. Molecular vibrations of the C-H bond being dissociated and the O-H bond being formed are significantly activated before and after the transition state, respectively, in the H-atom abstraction. The principal reaction coordinate that can represent the first chemical step is the C-H distance or the O-H distance while other geometric parameters remain almost unchanged. The rebound process begins with the iron-hydroxo complex and the ethyl radical intermediate and ends with the formation of the ethanol complex, the essential process in this reaction being the formation of the C-O bond. The H-O-Fe-C dihedral angle corresponds to the principal reaction coordinate for the rebound step. When sufficient kinetic energy is supplied to this rotational mode, the rebound process should efficiently take place. Trajectory calculations suggest that about 200 fs is required for the rebound process under specific initial conditions, in which a small amount of kinetic energy (0.1 kcal/mol) is supplied to the transition state exactly along the reaction coordinate. An important issue about which normal mode of vibration is activated during the hydroxylation reaction is investigated in detail from trajectory calculations. A large part of the kinetic energy is distributed to the C-H and O-H stretching modes before and after the transition state for the H-atom abstraction, respectively, and a small part of the kinetic energy is distributed to the Fe-O and Fe-S stretching modes and some characteristic modes of the porphyrin ring. The porphyrin marker modes of nu(3) and nu(4) that explicitly involve Fe-N stretching motion are effectively enhanced in the hydroxylation reaction. These vibrational modes of the porphyrin ring can play an important role in the energy transfer during the enzymatic process.

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.

Decoherence, discord, and the quantum master equation for cosmological perturbations

NASA Astrophysics Data System (ADS)

Hollowood, Timothy J.; McDonald, Jamie I.

2017-05-01

We examine environmental decoherence of cosmological perturbations in order to study the quantum-to-classical transition and the impact of noise on entanglement during inflation. Given an explicit interaction between the system and environment, we derive a quantum master equation for the reduced density matrix of perturbations, drawing parallels with quantum Brownian motion, where we see the emergence of fluctuation and dissipation terms. Although the master equation is not in Lindblad form, we see how typical solutions exhibit positivity on super-horizon scales, leading to a physically meaningful density matrix. This allows us to write down a Langevin equation with stochastic noise for the classical trajectories which emerge from the quantum system on super-horizon scales. In particular, we find that environmental decoherence increases in strength as modes exit the horizon, with the growth driven essentially by white noise coming from local contributions to environmental correlations. Finally, we use our master equation to quantify the strength of quantum correlations as captured by discord. We show that environmental interactions have a tendency to decrease the size of the discord and that these effects are determined by the relative strength of the expansion rate and interaction rate of the environment. We interpret this in terms of the competing effects of particle creation versus environmental fluctuations, which tend to increase and decrease the discord respectively.

Clinical Interpretations of Patient Experience in a Trial of Psilocybin-Assisted Psychotherapy for Alcohol Use Disorder.

PubMed

Bogenschutz, Michael P; Podrebarac, Samantha K; Duane, Jessie H; Amegadzie, Sean S; Malone, Tara C; Owens, Lindsey T; Ross, Stephen; Mennenga, Sarah E

2018-01-01

After a hiatus of some 40 years, clinical research has resumed on the use of classic hallucinogens to treat addiction. Following completion of a small open-label feasibility study, we are currently conducting a double-blind placebo-controlled clinical trial of psilocybin-assisted treatment of alcohol use disorder. Although treatment effects cannot be analyzed until the study is complete, descriptive case studies provide a useful window into the therapeutic process of psychedelic-assisted treatment of addiction. Here we describe treatment trajectories of three participants in the ongoing trial to illustrate the range of experiences and persisting effects of psilocybin treatment. Although it is difficult to generalize from a few cases, several qualitative conclusions can be drawn from the data presented here. Although participants often find it difficult to describe much of their psilocybin experience, pivotal moments tend to be individualized, extremely vivid, and memorable. Often, the qualitative content extends beyond the clinical problem that is being addressed. The participants discussed in this paper experienced acute and lasting alterations in their perceptions of self, in the quality of their baseline consciousness, and in their relationship with alcohol and drinking. In these cases, experiences of catharsis, forgiveness, self-compassion, and love were at least as salient as classic mystical content. Finally, feelings of increased "spaciousness" or mindfulness, and increased control over choices and behavior were reported following the drug administration sessions. Ultimately, psilocybin-assisted treatment appears to elicit experiences that are extremely variable, yet seem to meet the particular needs of the individual.

Clinical Interpretations of Patient Experience in a Trial of Psilocybin-Assisted Psychotherapy for Alcohol Use Disorder

PubMed Central

Bogenschutz, Michael P.; Podrebarac, Samantha K.; Duane, Jessie H.; Amegadzie, Sean S.; Malone, Tara C.; Owens, Lindsey T.; Ross, Stephen; Mennenga, Sarah E.

2018-01-01

After a hiatus of some 40 years, clinical research has resumed on the use of classic hallucinogens to treat addiction. Following completion of a small open-label feasibility study, we are currently conducting a double-blind placebo-controlled clinical trial of psilocybin-assisted treatment of alcohol use disorder. Although treatment effects cannot be analyzed until the study is complete, descriptive case studies provide a useful window into the therapeutic process of psychedelic-assisted treatment of addiction. Here we describe treatment trajectories of three participants in the ongoing trial to illustrate the range of experiences and persisting effects of psilocybin treatment. Although it is difficult to generalize from a few cases, several qualitative conclusions can be drawn from the data presented here. Although participants often find it difficult to describe much of their psilocybin experience, pivotal moments tend to be individualized, extremely vivid, and memorable. Often, the qualitative content extends beyond the clinical problem that is being addressed. The participants discussed in this paper experienced acute and lasting alterations in their perceptions of self, in the quality of their baseline consciousness, and in their relationship with alcohol and drinking. In these cases, experiences of catharsis, forgiveness, self-compassion, and love were at least as salient as classic mystical content. Finally, feelings of increased “spaciousness” or mindfulness, and increased control over choices and behavior were reported following the drug administration sessions. Ultimately, psilocybin-assisted treatment appears to elicit experiences that are extremely variable, yet seem to meet the particular needs of the individual. PMID:29515439

Optimization of interplanetary trajectories with unpowered planetary swingbys

NASA Technical Reports Server (NTRS)

Sauer, Carl G., Jr.

1988-01-01

A method is presented for calculating and optimizing unpowered planetary swingby trajectories using a patched conic trajectory generator. Examples of unpowered swingby trajectories are given to demonstrate the method. The method, which uses primer vector theory, is not highly accurate, but provides projections for preliminary mission definition studies. Advantages to using a patched conic trajectory simulation for preliminary studies which examine many different and complex missions include calculation speed and adaptability to changes or additions to the formulation.

Stereodirectional Origin of anti-Arrhenius Kinetics for a Tetraatomic Hydrogen Exchange Reaction: Born-Oppenheimer Molecular Dynamics for OH + HBr.

PubMed

Coutinho, Nayara D; Aquilanti, Vincenzo; Silva, Valter H C; Camargo, Ademir J; Mundim, Kleber C; de Oliveira, Heibbe C B

2016-07-14

Among four-atom processes, the reaction OH + HBr → H2O + Br is one of the most studied experimentally: its kinetics has manifested an unusual anti-Arrhenius behavior, namely, a marked decrease of the rate constant as the temperature increases, which has intrigued theoreticians for a long time. Recently, salient features of the potential energy surface have been characterized and most kinetic aspects can be considered as satisfactorily reproduced by classical trajectory simulations. Motivation of the work reported in this paper is the investigation of the stereodirectional dynamics of this reaction as the prominent reason for the peculiar kinetics: we started in a previous Letter ( J. Phys. Chem. Lett. 2015 , 6 , 1553 - 1558 ) a first-principles Born-Oppenheimer "canonical" molecular dynamics approach. Trajectories are step-by-step generated on a potential energy surface quantum mechanically calculated on-the-fly and are thermostatically equilibrated to correspond to a specific temperature. Here, refinements of the method permitted a major increase of the number of trajectories and the consideration of four temperatures -50, +200, +350, and +500 K, for which the sampling of initial conditions allowed us to characterize the stereodynamical effect. The role is documented of the adjustment of the reactants' mutual orientation to encounter the entrance into the "cone of acceptance" for reactivity. The aperture angle of this cone is dictated by a range of directions of approach compatible with the formation of the specific HOH angle of the product water molecule; and consistently the adjustment is progressively less effective the higher the kinetic energy. Qualitatively, this emerging picture corroborates experiments on this reaction, involving collisions of aligned and oriented molecular beams, and covering a range of energies higher than the thermal ones. The extraction of thermal rate constants from this molecular dynamics approach is discussed and the systematic sampling of the canonical ensemble is indicated as needed for quantitative comparison with the kinetic experiments.

Psychological and sociocultural adjustment of first-year international students: Trajectories and predictors.

PubMed

Hirai, Reiko; Frazier, Patricia; Syed, Moin

2015-07-01

Despite the increasing number of international students in U.S. universities, the temporal course of international students' adjustment has not been adequately tested, and only 1 study to date has examined multiple trajectories of adjustment. Therefore, the first goal of the current study was to explore multiple trajectories of adjustment among first-year international students using a broader range of adjustment measures (i.e., psychological distress, positive psychological adjustment, sociocultural adjustment). The second goal was to identify important predictors of trajectories. A wide range of individual and interpersonal predictor variables was examined, including academic stress and perceived control over academic stress, personality, social relationships, and language-related factors. Undergraduate and graduate international students in their first semester at a large midwestern university participated in this 5-wave longitudinal study (N = 248) that spanned 1 academic year. Multiple trajectories emerged, and the trajectories varied across the 3 adjustment measures. Average trajectories masked the trajectories of small groups of students who maintained or increased in terms of adjustment difficulties across outcomes. Contrary to popular theories, the U-shape adjustment trajectory (characterized by initial euphoria, distress, and then recovery) did not emerge. The most consistent predictors of adjustment trajectories were perceived present control over academic stress and Neuroticism. (c) 2015 APA, all rights reserved).

Young adults' trajectories of Ecstasy use: a population based study.

PubMed

Smirnov, Andrew; Najman, Jake M; Hayatbakhsh, Reza; Plotnikova, Maria; Wells, Helene; Legosz, Margot; Kemp, Robert

2013-11-01

Young adults' Ecstasy use trajectories have important implications for individual and population-level consequences of Ecstasy use, but little relevant research has been conducted. This study prospectively examines Ecstasy trajectories in a population-based sample. Data are from the Natural History Study of Drug Use, a retrospective/prospective cohort study conducted in Australia. Population screening identified a probability sample of Ecstasy users aged 19-23 years. Complete data for 30 months of follow-up, comprising 4 time intervals, were available for 297 participants (88.4% of sample). Trajectories were derived using cluster analysis based on recent Ecstasy use at each interval. Trajectory predictors were examined using a generalized ordered logit model and included Ecstasy dependence (World Mental Health Composite International Diagnostic Instrument), psychological distress (Hospital Anxiety Depression Scale), aggression (Young Adult Self Report) and contextual factors (e.g. attendance at electronic/dance music events). Three Ecstasy trajectories were identified (low, intermediate and high use). At its peak, the high-use trajectory involved 1-2 days Ecstasy use per week. Decreasing frequency of use was observed for intermediate and high-use trajectories from 12 months, independently of market factors. Intermediate and high-use trajectory membership was predicted by past Ecstasy consumption (>70 pills) and attendance at electronic/dance music events. High-use trajectory members were unlikely to have used Ecstasy for more than 3 years and tended to report consistently positive subjective effects at baseline. Given the social context and temporal course of Ecstasy use, Ecstasy trajectories might be better understood in terms of instrumental rather than addictive drug use patterns. © 2013 Elsevier Ltd. All rights reserved.

Positive and negative mood trajectories and their relationship with work ability, self-rated health, and life satisfaction: a 13-year follow-up study.

PubMed

Airila, Auli; Hakanen, Jari J; Luukkonen, Ritva; Lusa, Sirpa; Punakallio, Anne

2013-07-01

To investigate the change trajectories of positive and negative moods and their relationship to work ability, self-rated health, and life satisfaction in a three-wave 13-year follow-up study. The data, consisting of Finnish firefighters (n = 360), were collected via questionnaires in 1996, 1999, and 2009. Four distinct mood trajectories were identified by latent class growth modeling: (1) high positive, (2) high positive but decreasing, (3) moderately positive, and (4) high negative. The trajectory groups were differentially related to well-being. Members of the high positive trajectory had better well-being than members of other latent mood trajectories. Different trajectories exist in positive and negative moods, and these trajectories are differentially related to well-being. Developing work environments in which a positive mood can flourish is beneficial in terms of better well-being among employees.

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

Toward simulating complex systems with quantum effects

NASA Astrophysics Data System (ADS)

Kenion-Hanrath, Rachel Lynn

Quantum effects like tunneling, coherence, and zero point energy often play a significant role in phenomena on the scales of atoms and molecules. However, the exact quantum treatment of a system scales exponentially with dimensionality, making it impractical for characterizing reaction rates and mechanisms in complex systems. An ongoing effort in the field of theoretical chemistry and physics is extending scalable, classical trajectory-based simulation methods capable of capturing quantum effects to describe dynamic processes in many-body systems; in the work presented here we explore two such techniques. First, we detail an explicit electron, path integral (PI)-based simulation protocol for predicting the rate of electron transfer in condensed-phase transition metal complex systems. Using a PI representation of the transferring electron and a classical representation of the transition metal complex and solvent atoms, we compute the outer sphere free energy barrier and dynamical recrossing factor of the electron transfer rate while accounting for quantum tunneling and zero point energy effects. We are able to achieve this employing only a single set of force field parameters to describe the system rather than parameterizing along the reaction coordinate. Following our success in describing a simple model system, we discuss our next steps in extending our protocol to technologically relevant materials systems. The latter half focuses on the Mixed Quantum-Classical Initial Value Representation (MQC-IVR) of real-time correlation functions, a semiclassical method which has demonstrated its ability to "tune'' between quantum- and classical-limit correlation functions while maintaining dynamic consistency. Specifically, this is achieved through a parameter that determines the quantumness of individual degrees of freedom. Here, we derive a semiclassical correction term for the MQC-IVR to systematically characterize the error introduced by different choices of simulation parameters, and demonstrate the ability of this approach to optimize MQC-IVR simulations.

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.

Trajectories of bright stars at the Galactic Center as a tool to evaluate a graviton mass

NASA Astrophysics Data System (ADS)

Zakharov, Alexander; Jovanović, Predrag; Borka, Dusko; Jovanović, Vesna Borka

2016-10-01

Scientists worked in Saint-Petersburg (Petrograd, Leningrad) played the extremely important role in creation of scientific school and development of general relativity in Russia. Very recently LIGO collaboration discovered gravitational waves [1] predicted 100 years ago by A. Einstein. In the papers reporting about this discovery, the joint LIGO & VIRGO team presented an upper limit on graviton mass such as mg < 1.2 × 10-22eV [1, 2]. The authors concluded that their observational data do not show violations of classical general relativity because the graviton mass limit is very small. We show that an analysis of bright star trajectories could bound graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and expected with forthcoming pulsar timing observations for gravitational wave detection. This analysis gives an opportunity to treat observations of bright stars near the Galactic Center as a tool for an evaluation specific parameters of the black hole and also to obtain constraints on the fundamental gravity law such as a modifications of Newton gravity law in a weak field approximation. In that way, based on a potential reconstruction at the Galactic Center we give a bounds on a graviton mass.

E-Invariant Quantized Motion of Valence Quarks

NASA Astrophysics Data System (ADS)

Kreymer, E. L.

2018-06-01

In sub-proton space wave processes are impossible. The analog of the Klein-Gordon equation in sub-proton space is elliptical and describes a stationary system with a constant number of particles. For dynamical processes, separation of variables is used and in each quantum of motion of the quark two states are distinguished: a localization state and a translation state with infinite velocity. Alternation of these states describes the motion of a quark. The mathematical expectations of the lifetimes of the localization states and the spatial extents of the translation states for a free quark and for a quark in a centrally symmetric potential are found. The action after one quantum of motion is equal to the Planck constant. The one-sided Laplace transform is used to determine the Green's function. Use of path integrals shows that the quantized trajectory of a quark is a broken line enveloping the classical trajectory of oscillation of the quark. Comparison of the calculated electric charge distribution in a proton with its experimental value gives satisfactory results. A hypothesis is formulated, according to which the three Grand Geometries of space correspond to the three main interactions of elementary particles.

Probing periodic potential of crystals via strong-field re-scattering

NASA Astrophysics Data System (ADS)

You, Yong Sing; Cunningham, Eric; Reis, David A.; Ghimire, Shambhu

2018-06-01

Strong-field ionization and re-scattering phenomena have been used to image angstrom-scale structures of isolated molecules in the gas phase. These methods typically make use of the anisotropic response of the participating molecular orbital. Recently, an anisotropic strong-field response has also been observed in high-order harmonic generation (HHG) from bulk crystals (2016 Nat. Phys. 13 345). In a (100) cut magnesium oxide crystal, extreme ultraviolet high-harmonics are found to depend strongly on the crystal structure and inter-atomic bonding. Here, we extend these measurements to other two important crystal orientations: (111) and (110). We find that HHG from these orientations is also strongly anisotropic. The underlying dynamics is understood using a real-space picture, where high-harmonics are produced via coherent collision of strong-field driven electrons from the atomic sites, including from the nearest neighbor atoms. We find that harmonic efficiency is enhanced when semi-classical electron trajectories connect to the concentrated valence charge distribution regions around the atomic cores. Similarly, the efficiency is suppressed when the trajectories miss the atomic cores. These results further support the real-space picture of HHG with implications for retrieving the periodic potential of the crystal, if not the wavefunctions in three-dimensions.

Polarization characteristics of radiation in both 'light' and conventional undulators

NASA Astrophysics Data System (ADS)

Potylitsyn, A. P.; Kolchuzhkin, A. M.; Strokov, S. A.

2017-07-01

As a rule, an intensity spectrum of undulator radiation (UR) is calculated by using the classical approach, even for electron energy higher than 10 GeV. Such a spectrum is determined by an electron trajectory in an undulator while neglecting radiation loss. Using Planck's law, the UR photon spectrum can be calculated from the obtained intensity spectrum, for both linear and nonlinear regimes. The electron radiation process in a field of strong electromagnetic waves is considered within the quantum electrodynamics framework, using the Compton scattering process or radiation in a 'light' undulator. A comparison was made of the results from using these two approaches, for UR spectra generated by 250-GeV electrons in an undulator with a 11.5-mm period; this comparison shows that they coincide with high accuracy. The characteristics of the collimated UR beam (i.e. spectrum and circular polarization) were simulated while taking into account the discrete process of photon emission along an electron trajectory in both undulator types. Both spectral photon distributions and polarization dependence on photon energy are 'smoothed', in comparison to that expected for a long undulator-the latter of which considers the ILC positron source (ILC Technical Design Report).

Uniform function constants of motion and their first-order perturbation

NASA Astrophysics Data System (ADS)

Prato, Domingo; Hamity, Victor H.

2005-05-01

The main purpose of this work is to present some uniform function constants of motion rather than the well-known quantities arising from spacetime symmetries. These constants are usually associated with the intrinsic characteristics of the trajectories of a particle in a central potential field. We treat two cases. The first is the Lenz vector which sometimes is found in the literature [1, 2]; the other is associated with the isotropic harmonic oscillator, of relative importance in some simple models of the classical molecular interaction. The first example is applied to describe the perturbation of the trajectories in the Rutherford scattering and the precession of the Keplerian orbit of a planet. In the other case the conserved quantity is a symmetric tensor. We find the eigenvectors and eigenvalues of that tensor while at the same time we obtain the solution to the problem of calculating the rotation rate of the orbits in first order of a perturbation parameter in the potential energy, by performing a simple coordinate transformation in the Cartesian plane. We think that the present work addresses many aspects of mechanics with a didactical interest in other physics or mathematics courses.

Quantitative prediction of collision-induced vibration-rotation distributions from physical data

NASA Astrophysics Data System (ADS)

Marsh, Richard J.; McCaffery, Anthony J.

2003-04-01

We describe a rapid, accurate technique for computing state-to-state cross-sections in collision-induced vibration-rotation transfer (VRT) using only physical data, i.e. spectroscopic constants, bond length, mass and velocity distribution. The probability of linear-to-angular momentum (AM) conversion is calculated for a set of trajectories, each of which is subjected to energy conservation boundary conditions. No mechanism is specified for inducing vibrational state change. In the model, this constitutes a velocity or momentum barrier that must be overcome before rotational AM may be generated in the new vibrational state. The method is subjected to stringent testing by calculating state-to-state VRT probabilities for diatomics in highly excited vibrational, rotational and electronic states. Comparison is made to experimental data and to results from quantum mechanical and from quasi-classical trajectory calculations. There is quantitative agreement with data from all three sources, indicating that despite its simplicity the essential physics of collisions involving highly excited species is captured in the model. We develop further the concept of the molecular efficiency factor as an indicative parameter in collision dynamics, and derive an expression for ji > 0 and for VRT.

ab initio calculation of the rate of vibrational relaxation and thermal dissociation of hydrogen by helium at high temperatures

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

Dove, J.E.; Raynor, S.

The master equation for the thermal dissociation of para-H/sub 2/ infinitely dilute in He, was solved for temperatures of 1000 to 10,000/sup 0/K. Transition probabilities, used in the master equation, were obtained, in the case of energy transfer transitions, from distorted wave and quasi-classical trajectory calculations and, for dissociative processes, from trajectory calculations alone. An ab initio potential was used. From the solution, values of the dissociation rate constant, vibrational relaxation times, and incubation times for dissociation and vibrational relaxation were calculated. The sensitivity of the calculated results to variations in the transition probabilities was examined. Vibrational relaxation is mostmore » sensitive to simultaneous transitions in vibration and rotation (VRT processes); pure rotational (RT) transitions also have a substantial effect. Dissociation is most strongly affected by RT processes, but changes in VRT and groups of dissociative transitions also have a significant effect. However complete suppression of all dissociative transitions except those from levels immediately next to the continuum lowers the dissociation rates only by a factor of about 2. The location of the dissociation ''bottleneck'' is discussed. 5 figures, 3 tables.« less

Aeroassisted orbit transfer vehicle trajectory analysis

NASA Technical Reports Server (NTRS)

Braun, Robert D.; Suit, William T.

1988-01-01

The emphasis in this study was on the use of multiple pass trajectories for aerobraking. However, for comparison, single pass trajectories, trajectories using ballutes, and trajectories corrupted by atmospheric anomolies were run. A two-pass trajectory was chosen to determine the relation between sensitivity to errors and payload to orbit. Trajectories that used only aerodynamic forces for maneuvering could put more weight into the target orbits but were very sensitive to variations from the planned trajectors. Using some thrust control resulted in less payload to orbit, but greatly reduced the sensitivity to variations from nominal trajectories. When compared to the non-thrusting trajectories investigated, the judicious use of thrusting resulted in multiple pass trajectories that gave 97 percent of the payload to orbit with almost none of the sensitivity to variations from the nominal.

Congenitally Deaf Children's Care Trajectories in the Context of Universal Neonatal Hearing Screening: A Qualitative Study of the Parental Experiences

ERIC Educational Resources Information Center

Hardonk, Stefan; Desnerck, Greetje; Loots, Gerrit; Van Hove, Geert; Van Kerschaver, Erwin; Sigurjonsdottir, Hanna Bjorg; Vanroelen, Christophe; Louckx, Fred

2011-01-01

The objective of this study is to examine the early care trajectories of congenitally deaf children from a parental perspective, starting with universal neonatal hearing screenings. The analysis using a three-dimensional care trajectory concept is aimed at developing a basic typology of postscreening care trajectories. Children with…

The behavior of bouncing disks and pizza tossing

NASA Astrophysics Data System (ADS)

Liu, K.-C.; Friend, J.; Yeo, L.

2009-03-01

We investigate the dynamics of a disk bouncing on a vibrating platform - a variation of the classic bouncing ball problem - that captures the physics of pizza tossing and the operation of certain standing-wave ultrasonic motors (SWUMs). The system's dynamics explains why certain tossing motions are used by dough-toss performers for different tricks: a helical trajectory is used in single tosses because it maximizes energy efficiency and the dough's airborne rotational speed, a semi-elliptical motion is used in multiple tosses because it is easier for maintaining dough rotation at the maximum rotational speed. The system's bifurcation diagram and basins of attraction also informs SWUM designers about the optimal design for high speed and minimal sensitivity to perturbation.

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.

HYM-flation: Yang-Mills cosmology with Horndeski coupling

NASA Astrophysics Data System (ADS)

Davydov, E.; Gal'tsov, D.

2016-02-01

We propose new mechanism for inflation using classical SU (2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.

PBMC: Pre-conditioned Backward Monte Carlo code for radiative transport in planetary atmospheres

NASA Astrophysics Data System (ADS)

García Muñoz, A.; Mills, F. P.

2017-08-01

PBMC (Pre-Conditioned Backward Monte Carlo) solves the vector Radiative Transport Equation (vRTE) and can be applied to planetary atmospheres irradiated from above. The code 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. In accounting for the polarization in the sampling of photon propagation directions and pre-conditioning the scattering matrix with information from the scattering matrices of prior (in the BMC integration order) photon collisions, PBMC avoids the unstable and biased solutions of classical BMC algorithms for conservative, optically-thick, strongly-polarizing media such as Rayleigh atmospheres.

Analysis of single quantum-dot mobility inside 1D nanochannel devices

NASA Astrophysics Data System (ADS)

Hoang, H. T.; Segers-Nolten, I. M.; Tas, N. R.; van Honschoten, J. W.; Subramaniam, V.; Elwenspoek, M. C.

2011-07-01

We visualized individual quantum dots using a combination of a confining nanochannel and an ultra-sensitive microscope system, equipped with a high numerical aperture lens and a highly sensitive camera. The diffusion coefficients of the confined quantum dots were determined from the experimentally recorded trajectories according to the classical diffusion theory for Brownian motion in two dimensions. The calculated diffusion coefficients were three times smaller than those in bulk solution. These observations confirm and extend the results of Eichmann et al (2008 Langmuir 24 714-21) to smaller particle diameters and more narrow confinement. A detailed analysis shows that the observed reduction in mobility cannot be explained by conventional hydrodynamic theory.

On the n-body problem on surfaces of revolution

NASA Astrophysics Data System (ADS)

Stoica, Cristina

2018-05-01

We explore the n-body problem, n ≥ 3, on a surface of revolution with a general interaction depending on the pairwise geodesic distance. Using the geometric methods of classical mechanics we determine a large set of properties. In particular, we show that Saari's conjecture fails on surfaces of revolution admitting a geodesic circle. We define homographic motions and, using the discrete symmetries, prove that when the masses are equal, they form an invariant manifold. On this manifold the dynamics are reducible to a one-degree of freedom system. We also find that for attractive interactions, regular n-gon shaped relative equilibria with trajectories located on geodesic circles typically experience a pitchfork bifurcation. Some applications are included.

Orbital-resolved nonadiabatic tunneling ionization

NASA Astrophysics Data System (ADS)

Zhang, Qingbin; Basnayake, Gihan; Winney, Alexander; Lin, Yun Fei; Debrah, Duke; Lee, Suk Kyoung; Li, Wen

2017-08-01

In this theoretical work, we show that both the orbital helicity (p+ vs p-) and the adiabaticity of tunneling have a significant effect on the initial conditions of tunneling ionization. We developed a hybrid quantum (numerical solution of the time-dependent Schrödinger equation) and classical (back propagation of trajectories) approach to extract orbital-specific initial conditions of electrons at the tunneling exit. Clear physical insight connecting these initial conditions with the final momentum and deflection angles of electrons are presented. Moreover, the adiabaticity of tunneling ionization is characterized by comparing the initial conditions with those with a static field. Significant nonadiabatic tunneling is found to persist beyond a Keldysh parameter of less than 0.5.

Orbital and Landing Operations at Near-Earth

NASA Technical Reports Server (NTRS)

Scheeres, D. J.

1995-01-01

Orbital and landing operations about near-Earth asteroids are different than classical orbital operations about large bodies. The major differences lie with the small mass of the asteroid, the lower orbital velocities, the larger Solar tide and radiation pressure perturbations, the irregular shape of the asteroid and the potential for non-uniform rotation of the asteroid. These differences change the nature of orbits about an asteroid to where it is often common to find trajectories that evolve from stable, near-circular orbits to crashing or escaping orbits in a matter of days. The understanding and control of such orbits is important if a human or robotic presence at asteroids is to be commonplace in the future.

Easy GROMACS: A Graphical User Interface for GROMACS Molecular Dynamics Simulation Package

NASA Astrophysics Data System (ADS)

Dizkirici, Ayten; Tekpinar, Mustafa

2015-03-01

GROMACS is a widely used molecular dynamics simulation package. Since it is a command driven program, it is difficult to use this program for molecular biologists, biochemists, new graduate students and undergraduate researchers who are interested in molecular dynamics simulations. To alleviate the problem for those researchers, we wrote a graphical user interface that simplifies protein preparation for a classical molecular dynamics simulation. Our program can work with various GROMACS versions and it can perform essential analyses of GROMACS trajectories as well as protein preparation. We named our open source program `Easy GROMACS'. Easy GROMACS can give researchers more time for scientific research instead of dealing with technical intricacies.

Mode-Specific SN2 Reaction Dynamics.

PubMed

Wang, Yan; Song, Hongwei; Szabó, István; Czakó, Gábor; Guo, Hua; Yang, Minghui

2016-09-01

Despite its importance in chemistry, the microscopic dynamics of bimolecular nucleophilic substitution (SN2) reactions is still not completely elucidated. In this publication, the dynamics of a prototypical SN2 reaction (F(-) + CH3Cl → CH3F + Cl(-)) is investigated using a high-dimensional quantum mechanical model on an accurate potential energy surface (PES) and further analyzed by quasi-classical trajectories on the same PES. While the indirect mechanism dominates at low collision energies, the direct mechanism makes a significant contribution. The reactivity is found to depend on the specific reactant vibrational mode excitation. The mode specificity, which is more prevalent in the direct reaction, is rationalized by a transition-state-based model.

Trajectories of depressive symptoms over two years postpartum among overweight or obese women

PubMed Central

Lee, Chien-Ti; Stroo, Marissa; Fuemmeler, Bernard; Malhotra, Rahul; Østbye, Truls

2014-01-01

Background Although depressive symptoms are common postpartum, few studies have followed women beyond 12 months postpartum to investigate changes in the number and severity of these symptoms over time, especially in overweight and obese women. Using two complementary analytical methods, this study aims to identify trajectories of depressive symptoms over two years postpartum among overweight or obese mothers, and assess the demographic, socio-economic , and health covariates for these trajectories. Methods Using longitudinal data from two behavioral intervention studies (KAN-DO and AMP; N = 844), we used latent growth modeling to identify the overall trajectory of depressive symptoms and how it was related to key covariates. Next, we used latent class growth analysis to assess the heterogeneity in the depressive symptom trajectories over time, and thereby, identify subgroups of women with distinct trajectories. Findings The overall trajectory of depressive symptoms over two years postpartum was relatively stable in our sample. However, the presence of three distinct latent class trajectories [stable-low (82.5%), decreasing symptoms (7.3%) and increasing symptoms (10.2%)], identified based on trajectory shape and mean depressive symptom score, supported heterogeneity in depressive symptom trajectories over time. Lower maternal education was related to a higher symptom score, and poorer subjective health status at baseline predicted inclusion in the increasing symptoms trajectory. Conclusions In some overweight or obese mothers postpartum depressive symptoms do not resolve quickly. Practitioners should be aware of this phenomenon and continue to screen for depression for longer periods of time postpartum. PMID:25213748

Controlling electron quantum paths for generation of circularly polarized high-order harmonics by H2+ subject to tailored (ω , 2 ω ) counter-rotating laser fields

NASA Astrophysics Data System (ADS)

Heslar, John; Telnov, Dmitry A.; Chu, Shih-I.

2018-04-01

Recently, studies of high-order harmonics (HHG) from atoms driven by bichromatic counter-rotating circularly polarized laser fields as a source of coherent circularly polarized extreme ultraviolet (XUV) and soft-x-ray beams in a tabletop-scale setup have received considerable attention. Here, we demonstrate the ability to control the electron recollisions giving three returns per one cycle of the fundamental frequency ω by using tailored bichromatic (ω , 2 ω ) counter-rotating circularly polarized laser fields with a molecular target. The full control of the electronic pathway is first analyzed by a classical trajectory analysis and then extended to a detailed quantum study of H2+ molecules in bichromatic (ω , 2 ω ) counter-rotating circularly polarized laser fields. The radiation spectrum contains doublets of left- and right-circularly polarized harmonics in the XUV ranges. We study in detail the below-, near-, and above-threshold harmonic regions and describe how excited-state resonances alter the ellipticity and phase of the generated harmonic peaks.

Accurate orbit propagation in the presence of planetary close encounters

NASA Astrophysics Data System (ADS)

Amato, Davide; Baù, Giulio; Bombardelli, Claudio

2017-09-01

We present an efficient strategy for the numerical propagation of small Solar system objects undergoing close encounters with massive bodies. The trajectory is split into several phases, each of them being the solution of a perturbed two-body problem. Formulations regularized with respect to different primaries are employed in two subsequent phases. In particular, we consider the Kustaanheimo-Stiefel regularization and a novel set of non-singular orbital elements pertaining to the Dromo family. In order to test the proposed strategy, we perform ensemble propagations in the Earth-Sun Circular Restricted 3-Body Problem (CR3BP) using a variable step size and order multistep integrator and an improved version of Everhart's radau solver of 15th order. By combining the trajectory splitting with regularized equations of motion in short-term propagations (1 year), we gain up to six orders of magnitude in accuracy with respect to the classical Cowell's method for the same computational cost. Moreover, in the propagation of asteroid (99942) Apophis through its 2029 Earth encounter, the position error stays within 100 metres after 100 years. In general, as to improve the performance of regularized formulations, the trajectory must be split between 1.2 and 3 Hill radii from the Earth. We also devise a robust iterative algorithm to stop the integration of regularized equations of motion at a prescribed physical time. The results rigorously hold in the CR3BP, and similar considerations may apply when considering more complex models. The methods and algorithms are implemented in the naples fortran 2003 code, which is available online as a GitHub repository.

Walking Ahead: The Headed Social Force Model.

PubMed

Farina, Francesco; Fontanelli, Daniele; Garulli, Andrea; Giannitrapani, Antonio; Prattichizzo, Domenico

2017-01-01

Human motion models are finding an increasing number of novel applications in many different fields, such as building design, computer graphics and robot motion planning. The Social Force Model is one of the most popular alternatives to describe the motion of pedestrians. By resorting to a physical analogy, individuals are assimilated to point-wise particles subject to social forces which drive their dynamics. Such a model implicitly assumes that humans move isotropically. On the contrary, empirical evidence shows that people do have a preferred direction of motion, walking forward most of the time. Lateral motions are observed only in specific circumstances, such as when navigating in overcrowded environments or avoiding unexpected obstacles. In this paper, the Headed Social Force Model is introduced in order to improve the realism of the trajectories generated by the classical Social Force Model. The key feature of the proposed approach is the inclusion of the pedestrians' heading into the dynamic model used to describe the motion of each individual. The force and torque representing the model inputs are computed as suitable functions of the force terms resulting from the traditional Social Force Model. Moreover, a new force contribution is introduced in order to model the behavior of people walking together as a single group. The proposed model features high versatility, being able to reproduce both the unicycle-like trajectories typical of people moving in open spaces and the point-wise motion patterns occurring in high density scenarios. Extensive numerical simulations show an increased regularity of the resulting trajectories and confirm a general improvement of the model realism.

Growth Trajectories of Health Behaviors from Adolescence through Young Adulthood.

PubMed

Wiium, Nora; Breivik, Kyrre; Wold, Bente

2015-10-28

Based on nine waves of data collected during a period of 17 years (1990-2007), the present study explored different developmental trajectories of the following unhealthy behaviors: regular smoking, lack of regular exercise, lack of daily fruit intake, and drunkenness. A baseline sample of 1195 13-year-old pupils was from 22 randomly selected schools in the Hordaland County in western Norway. Latent class growth analysis revealed three developmental trajectories. The first trajectory was a conventional trajectory, comprising 36.3% of participants, who showed changes in smoking, physical exercise, fruit intake, and drunkenness consistent with the prevailing age specific norms of these behaviors in the Norwegian society at the time. The second trajectory was a passive trajectory, comprising 25.5% of participants, who reported low levels of both healthy and unhealthy behaviors during the 17-year period. The third trajectory was an unhealthy trajectory, comprising 38.2% of participants, who had high levels of unhealthy behaviors over time. Several covariates were examined, but only sex and mother's and father's educational levels were found to be significantly associated with the identified trajectories. While these findings need to be replicated in future studies, the identification of the different trajectories suggests the need to tailor intervention according to specific needs.

The Trajectory and the Related Physical and Social Determinants of Body Mass Index in Elementary School Children: Results from the Child and Adolescent Behaviors in Long-Term Evolution Study

PubMed Central

Chang, Hsing-Yi; Luh, Dih-Ling; Hurng, Baai-Shyun; Yen, Lee-Lan

2014-01-01

This study explored developmental trajectory patterns of BMI and associated factors. Participants included 1,609 students who were followed from age 7 to 12 years. Data collection involved annual self-administered questionnaires and records of height and weight. An ecological model was used to identify the factors associated with BMI trajectories. Group-based trajectory models and multinomial logit models were used in the statistical analysis. There were gender differences in BMI trajectories. Among boys, four BMI trajectories were normal or slightly underweight, persistently normal weight, overweight becoming obese, and persistently obese. Among girls, four BMI trajectories were persistently slightly underweight, persistently normal weight, persistently overweight, and persistently obese. The mean BMI in each trajectory group demonstrated an upward trend over time. In boys, BMI trajectories were significantly associated with after-school exercise, academic performance, family interactions, overweight parents, and father's education level. In girls, BMI trajectories were significantly associated with television viewing or computer use, family interactions, peer interactions, and overweight parents. Children under age 7 years who are already overweight or obese are an important target for interventions. The different factors associated with BMI trajectories can be used for targeting high risk groups. PMID:25114800

Growth Trajectories of Health Behaviors from Adolescence through Young Adulthood

PubMed Central

Wiium, Nora; Breivik, Kyrre; Wold, Bente

2015-01-01

Based on nine waves of data collected during a period of 17 years (1990–2007), the present study explored different developmental trajectories of the following unhealthy behaviors: regular smoking, lack of regular exercise, lack of daily fruit intake, and drunkenness. A baseline sample of 1195 13-year-old pupils was from 22 randomly selected schools in the Hordaland County in western Norway. Latent class growth analysis revealed three developmental trajectories. The first trajectory was a conventional trajectory, comprising 36.3% of participants, who showed changes in smoking, physical exercise, fruit intake, and drunkenness consistent with the prevailing age specific norms of these behaviors in the Norwegian society at the time. The second trajectory was a passive trajectory, comprising 25.5% of participants, who reported low levels of both healthy and unhealthy behaviors during the 17-year period. The third trajectory was an unhealthy trajectory, comprising 38.2% of participants, who had high levels of unhealthy behaviors over time. Several covariates were examined, but only sex and mother’s and father’s educational levels were found to be significantly associated with the identified trajectories. While these findings need to be replicated in future studies, the identification of the different trajectories suggests the need to tailor intervention according to specific needs. PMID:26516889

Phase transitions in trajectories of a superconducting single-electron transistor coupled to a resonator.

PubMed

Genway, Sam; Garrahan, Juan P; Lesanovsky, Igor; Armour, Andrew D

2012-05-01

Recent progress in the study of dynamical phase transitions has been made with a large-deviation approach to study trajectories of stochastic jumps using a thermodynamic formalism. We study this method applied to an open quantum system consisting of a superconducting single-electron transistor, near the Josephson quasiparticle resonance, coupled to a resonator. We find that the dynamical behavior shown in rare trajectories can be rich even when the mean dynamical activity is small, and thus the formalism gives insights into the form of fluctuations. The structure of the dynamical phase diagram found from the quantum-jump trajectories of the resonator is studied, and we see that sharp transitions in the dynamical activity may be related to the appearance and disappearance of bistabilities in the state of the resonator as system parameters are changed. We also demonstrate that for a fast resonator, the trajectories of quasiparticles are similar to the resonator trajectories.

Extension of classical hydrological risk analysis to non-stationary conditions due to climate change - application to the Fulda catchment, Germany

NASA Astrophysics Data System (ADS)

Fink, G.; Koch, M.

2010-12-01

An important aspect in water resources and hydrological engineering is the assessment of hydrological risk, due to the occurrence of extreme events, e.g. droughts or floods. When dealing with the latter - as is the focus here - the classical methods of flood frequency analysis (FFA) are usually being used for the proper dimensioning of a hydraulic structure, for the purpose of bringing down the flood risk to an acceptable level. FFA is based on extreme value statistics theory. Despite the progress of methods in this scientific branch, the development, decision, and fitting of an appropriate distribution function stills remains a challenge, particularly, when certain underlying assumptions of the theory are not met in real applications. This is, for example, the case when the stationarity-condition for a random flood time series is not satisfied anymore, as could be the situation when long-term hydrological impacts of future climate change are to be considered. The objective here is to verify the applicability of classical (stationary) FFA to predicted flood time series in the Fulda catchment in central Germany, as they may occur in the wake of climate change during the 21st century. These discharge time series at the outlet of the Fulda basin have been simulated with a distributed hydrological model (SWAT) that is forced by predicted climate variables of a regional climate model for Germany (REMO). From the simulated future daily time series, annual maximum (extremes) values are computed and analyzed for the purpose of risk evaluation. Although the 21st century estimated extreme flood series of the Fulda river turn out to be only mildly non-stationary, alleviating the need for further action and concern at the first sight, the more detailed analysis of the risk, as quantified, for example, by the return period, shows non-negligent differences in the calculated risk levels. This could be verified by employing a new method, the so-called flood series maximum analysis (FSMA) method, which consists in the stochastic simulation of numerous trajectories of a stochastic process with a given GEV-distribution over a certain length of time (> larger than a desired return period). Then the maximum value for each trajectory is computed, all of which are then used to determine the empirical distribution of this maximum series. Through graphical inversion of this distribution function the size of the design flood for a given risk (quantile) and given life duration can be inferred. The results of numerous simulations show that for stationary flood series, the new FSMA method results, expectedly, in nearly identical risk values as the classical FFA approach. However, once the flood time series becomes slightly non-stationary - for reasons as discussed - and regardless of whether the trend is increasing or decreasing, large differences in the computed risk values for a given design flood occur. Or in other word, for the same risk, the new FSMA method would lead to different values in the design flood for a hydraulic structure than the classical FFA method. This, in turn, could lead to some cost savings in the realization of a hydraulic project.

Direct dynamics trajectory study of the reaction of formaldehyde cation with D2: vibrational and zero-point energy effects on quasiclassical trajectories.

PubMed

Liu, Jianbo; Song, Kihyung; Hase, William L; Anderson, Scott L

2005-12-22

Quasiclassical, direct dynamics trajectories have been used to study the reaction of formaldehyde cation with molecular hydrogen, simulating the conditions in an experimental study of H2CO+ vibrational effects on this reaction. Effects of five different H2CO+ modes were probed, and we also examined different approaches to treating zero-point energy in quasiclassical trajectories. The calculated absolute cross-sections are in excellent agreement with experiments, and the results provide insight into the reaction mechanism, product scattering behavior, and energy disposal, and how they vary with impact parameter and reactant state. The reaction is sharply orientation-dependent, even at high collision energies, and both trajectories and experiment find that H2CO+ vibration inhibits reaction. On the other hand, the trajectories do not reproduce the anomalously strong effect of nu2(+) (the CO stretch). The origin of the discrepancy and approaches for minimizing such problems in quasiclassical trajectories are discussed.

RORA and posttraumatic stress trajectories: main effects and interactions with childhood physical abuse history

PubMed Central

Lowe, Sarah R; Meyers, Jacquelyn L; Galea, Sandro; Aiello, Allison E; Uddin, Monica; Wildman, Derek E; Koenen, Karestan C

2015-01-01

Background Longitudinal studies of posttraumatic stress (PTS) have documented environmental factors as predictors of trajectories of higher, versus lower, symptoms, among them experiences of childhood physical abuse. Although it is now well-accepted that genes and environments jointly shape the risk of PTS, no published studies have investigated genes, or gene-by-environment interactions (GxEs), as predictors of PTS trajectories. The purpose of this study was to fill this gap. Methods and Materials We examined associations between variants of the retinoid-related orphan receptor alpha (RORA) gene and trajectory membership among a sample of predominantly non-Hispanic Black urban adults (N = 473). The RORA gene was selected based on its association with posttraumatic stress disorder (PTSD) in the first PTSD genome wide association study. Additionally, we explored GxEs between RORA variants and childhood physical abuse history. Results We found that the minor allele of the RORA SNP rs893290 was a significant predictor of membership in a trajectory of consistently high PTS, relatively to a trajectory of consistently low PTS. Additionally, the GxE of rs893290 with childhood physical abuse was significant. Decomposition of the interaction showed that minor allele frequency was more strongly associated with membership in consistently high or decreasing PTS trajectories, relative to a consistently low PTS trajectory, among participants with higher levels of childhood physical abuse. Conclusion The results of the study provide preliminary evidence that variation in the RORA gene is associated with membership in trajectories of higher PTS and that these associations are stronger among persons exposed to childhood physical abuse. Replication and analysis of functional data are needed to further our understanding of how RORA relates to PTS trajectories. PMID:25798337

Developmental Links between Trajectories of Physical Violence, Vandalism, Theft, and Alcohol-Drug Use from Childhood to Adolescence

ERIC Educational Resources Information Center

van Lier, Pol A. C.; Vitaro, Frank; Barker, Edward D.; Koot, Hans M.; Tremblay, Richard E.

2009-01-01

Differences in developmental trajectories of physical violence, vandalism, theft, and alcohol-drug use from ages 10 to 15 were studied. For females and for males, three trajectories of theft and of alcohol-drug use increased from 10 years to 15 years, while only the high trajectory of vandalism increased from ten to 14. All trajectories of…

HYDROCORTISONE THERAPY AND GROWTH TRAJECTORY IN CHILDREN WITH CLASSICAL CONGENITAL ADRENAL HYPERPLASIA.

PubMed

Bizzarri, Carla; Improda, Nicola; Maggioli, Chiara; Capalbo, Donatella; Roma, Silvia; Porzio, Ottavia; Salerno, Mariacarolina; Cappa, Marco

2017-05-01

Poor linear growth is one of the main concerns in children with congenital adrenal hyperplasia (CAH). We aimed to analyze factors affecting growth trajectory in children with classical CAH. Clinical records of children followed from infancy up to the end of growth at two Italian tertiary referral hospitals were reviewed. Fifty-seven patients (31 males), treated with hydrocortisone and fludrocortisone only, were included. Clinical observations were divided into three groups: 0 to 2 years, 172 observations; from 2 years to puberty onset, 813 observations; after puberty onset, 527 observations. Height velocity, pubertal growth spurt, and final height were evaluated as outcomes. Final height standard deviation score (SDS) was lower than target height SDS (-0.74 ± 1.1 versus -0.31 ± 1.01; P<.001). Target-adjusted final height SDS was -0.44 ± 1.8 in males and -0.13 ± 1.1 in females (P = .001). Total pubertal growth was 21.9 ± 7.3 cm in males and 19.2 ± 8.2 cm in females (P = .19). Hydrocortisone dose increased and height-velocity SDS decreased during puberty. At multivariable analysis, height-velocity SDS was adversely affected by hydrocortisone dose (P = .038) and directly related to adrenocorticotropic hormone (ACTH) levels (P = .023). Target-adjusted final-height SDS was adversely affected by hydrocortisone dose (P<.001) and positively related to mineralocorticoid therapy (P = .001) and ACTH levels (P = .02). Total pubertal growth (cm) was positively related to ACTH levels (P = .01). Height outcome of CAH patients is now better than previously reported. During puberty, the lowest effective dose of hydrocortisone should be used to optimize pubertal growth spurt and final height. 17-OHP = 17-alpha-hydroxyprogesterone ACTH = adrenocorticotropic hormone BMI = body mass index CAH = congenital adrenal hyperplasia GH = growth hormone HPA = hypothalamus-pituitary-adrenal PRA = plasma renin activity SDS = standard deviation score SV = simple virilizing SW = salt-wasting.

Educational Aspirations Trajectories in England

ERIC Educational Resources Information Center

McCulloch, Andrew

2017-01-01

This study used latent class analysis to examine the trajectories followed by young people's educational aspirations in England over the age range from 13 to 16 years and their relationship to educational achievement. The results suggested that young people's aspirations followed six trajectories. Four trajectories showed overall patterns of…

Maternal posttraumatic stress disorder symptom trajectories following Hurricane Katrina: An initial examination of the impact of maternal trajectories on the well-being of disaster-exposed youth.

PubMed

Self-Brown, Shannon; Lai, Betty S; Harbin, Shannon; Kelley, Mary Lou

2014-12-01

This study examined trajectories of posttraumatic stress disorder symptoms in impoverished mothers impacted by Hurricane Katrina, as well as how predictive the maternal trajectories were for youth posttraumatic stress symptoms 2 years post-Katrina. 360 mother participants displaced by Hurricane Katrina completed self-report measures across four time points related to Hurricane exposure, trauma history, and posttraumatic stress symptoms. Additionally, the youth offspring completed a self-report measure of posttraumatic stress symptoms. Latent Class Growth Analysis demonstrated three primary trajectories emerged among females impacted by Katrina, namely, (1) chronic (4 %), (2) recovering (30 %), and (3) resilient (66 %), respectively. These trajectories were significantly impacted by prior trauma history, but not hurricane exposure. Additionally, data indicated that children whose parents fell into the chronic PTS trajectory also reported high levels of PTS symptoms. This study identified three main trajectories typical of female PTS symptoms following disaster and was the first known study to document associations between PTS outcomes among adults and their offspring impacted by a large natural disaster. Future research is warranted and should explore additional risk and protective factors that impact both the parental and child outcomes.

Car and Parrinello meet Green and Kubo: simulating atomic heat transport from equilibrium ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Baroni, Stefano

Modern simulation methods based on electronic-structure theory have long been deemed unfit to compute heat transport coefficients within the Green-Kubo formalism. This is so because the quantum-mechanical energy density from which the heat flux is derived is inherently ill defined, thus allegedly hampering the use of the Green-Kubo formula. While this objection would actually apply to classical systems as well, I will demonstrate that the thermal conductivity is indeed independent of the specific microscopic expression for the energy density and current from which it is derived. This fact results from a kind of gauge invariance stemming from energy conservation and extensivity, which I will illustrate numerically for a classical Lennard-Jones fluid. I will then introduce an expression for the adiabatic energy flux, derived within density-functional theory, that allows simulating atomic heat transport using equilibrium ab initio molecular dynamics. The resulting methodology is demonstrated by comparing results from ab-initio and classical molecular-dynamics simulations of a model liquid-Argon system, for which accurate inter-atomic potentials are derived by the force-matching method, and applied to compute the thermal conductivity of heavy water at ambient conditions. The problem of evaluating transport coefficients along with their accuracy from relatively short trajectories is finally addressed and discussed with a few representative examples. Partially funded by the European Union through the MaX Centre of Excellence (Grant No. 676598).

Stereodynamics in NO(X) + Ar inelastic collisions

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

Brouard, M., E-mail: mark.brouard@chem.ox.ac.uk; Chadwick, H.; Gordon, S. D. S.

2016-06-14

The effect of orientation of the NO(X) bond axis prior to rotationally inelastic collisions with Ar has been investigated experimentally and theoretically. A modification to conventional velocity-map imaging ion optics is described, which allows the orientation of hexapole state-selected NO(X) using a static electric field, followed by velocity map imaging of the resonantly ionized scattered products. Bond orientation resolved differential cross sections are measured experimentally for a series of spin-orbit conserving transitions and compared with quantum mechanical calculations. The agreement between experimental results and those from quantum mechanical calculations is generally good. Parity pairs, which have previously been observed inmore » collisions of unpolarized NO with various rare gases, are not observed due to the coherent superposition of the two j = 1/2, Ω = 1/2 Λ-doublet levels in the orienting field. The normalized difference differential cross sections are found to depend predominantly on the final rotational state, and are not very sensitive to the final Λ-doublet level. The differential steric effect has also been investigated theoretically, by means of quantum mechanical and classical calculations. Classically, the differential steric effect can be understood by considering the steric requirement for different types of trajectories that contribute to different regions of the differential cross section. However, classical effects cannot account quantitatively for the differential steric asymmetry observed in NO(X) + Ar collisions, which reflects quantum interference from scattering at either end of the molecule. This quantum interference effect is dominated by the repulsive region of the potential.« less

Multivariate trajectories across multiple domains of health-related quality of life in children with new-onset epilepsy.

PubMed

Sajobi, Tolulope T; Wang, Meng; Ferro, Mark A; Brobbey, Anita; Goodwin, Shane; Speechley, Kathy N; Wiebe, Samuel

2017-10-01

The diagnosis of epilepsy in children is known to impact the trajectory of their health-related quality of life (HRQOL) over time. However, there is limited knowledge about variations in longitudinal trajectories across multiple domains of HRQOL. This study aims to characterize the heterogeneity in HRQOL trajectories across multiple HRQOL domains and to evaluate predictors of differences among the identified trajectory groups in children with new-onset epilepsy. Data were obtained from the Health Related Quality of Life in Children with Epilepsy Study (HERQULES), a prospective multi-center study of 373 children newly diagnosed with new-onset epilepsy who were followed up over 2years. Child HRQOL and family factors were reported by parents, and clinical characteristics were reported by neurologists. Group-based multi-trajectory modeling was adopted to characterize longitudinal trajectories of HRQOL as measured by the individual domains of cognitive, emotional, physical, and social functioning in the 55-item Quality of Life in Childhood Epilepsy Questionnaire (QOLCE-55). Multinomial logistic regression was used to assess potential factors that explain differences among the identified latent trajectory groups. Three distinct HRQOL trajectory subgroups were identified in children with new-onset epilepsy based on HRQOL scores: "High" (44.7%), "Intermediate" (37.0%), and "Low" (18.3%). While most trajectory groups exhibited increasing scores over time on physical and social domains, both flat and declining trajectories were noted on emotional and cognitive domains. Less severe epilepsy, an absence of cognitive and behavioral problems, lower parental depression scores, better family functioning, and fewer family demands were associated with a "Higher" or "Intermediate" HRQOL trajectory. The course of HRQOL over time in children with new-onset epilepsy appears to follow one of three different trajectories. Addressing the clinical and psychosocial determinants identified for each pattern can help clinicians provide more targeted care to these children and their families. Copyright © 2017 Elsevier Inc. All rights reserved.

Mixed membership trajectory models of cognitive impairment in the multicenter AIDS cohort study.

PubMed

Molsberry, Samantha A; Lecci, Fabrizio; Kingsley, Lawrence; Junker, Brian; Reynolds, Sandra; Goodkin, Karl; Levine, Andrew J; Martin, Eileen; Miller, Eric N; Munro, Cynthia A; Ragin, Ann; Sacktor, Ned; Becker, James T

2015-03-27

The longitudinal trajectories that individuals may take from a state of normal cognition to HIV-associated dementia are unknown. We applied a novel statistical methodology to identify trajectories to cognitive impairment, and factors that affected the 'closeness' of an individual to one of the canonical trajectories. The Multicenter AIDS Cohort Study (MACS) is a four-site longitudinal study of the natural and treated history of HIV disease among gay and bisexual men. Using data from 3892 men (both HIV-infected and HIV-uninfected) enrolled in the neuropsychology substudy of the MACS, a Mixed Membership Trajectory Model (MMTM) was applied to capture the pathways from normal cognitive function to mild impairment to severe impairment. MMTMs allow the data to identify canonical pathways and to model the effects of risk factors on an individual's 'closeness' to these trajectories. First, we identified three distinct trajectories to cognitive impairment: 'normal aging' (low probability of mild impairment until age 60); 'premature aging' (mild impairment starting at age 45-50); and 'unhealthy' (mild impairment in 20s and 30s) profiles. Second, clinically defined AIDS, and not simply HIV disease, was associated with closeness to the premature aging trajectory, and, third, hepatitis-C infection, depression, race, recruitment cohort and confounding conditions all affected individual's closeness to these trajectories. These results provide new insight into the natural history of cognitive dysfunction in HIV disease and provide evidence for a potential difference in the pathophysiology of the development of cognitive impairment based on trajectories to impairment.

Trajectories of Depressive Symptoms Throughout the Peri- and Postpartum Period: Results from the First Baby Study.

PubMed

McCall-Hosenfeld, Jennifer S; Phiri, Kristen; Schaefer, Eric; Zhu, Junjia; Kjerulff, Kristen

2016-11-01

Postpartum depression (PPD) is a common complication of childbearing, but the course of PPD is not well understood. We analyze trajectories of depression and key risk factors associated with these trajectories in the peripartum and postpartum period. Women in The First Baby Study, a cohort of 3006 women pregnant with their first baby, completed telephone surveys measuring depression during the mother's third trimester, and at 1, 6, and 12 months postpartum. Depression was assessed using the Edinburgh Postnatal Depression Scale. A semiparametric mixture model was used to estimate distinct group-based developmental trajectories of depression and determine whether trajectory group membership varied according to maternal characteristics. A total of 2802 (93%) of mothers completed interviews through 12 months. The mixture model indicated six distinct depression trajectories. A history of anxiety or depression, unattached marital status, and inadequate social support were significantly associated with higher odds of belonging to trajectory groups with greater depression. Most of the depression trajectories were stable or slightly decreased over time, but one depression trajectory, encompassing 1.7% of the mothers, showed women who were nondepressed at the third trimester, but became depressed at 6 months postpartum and were increasingly depressed at 12 months after birth. This trajectory study indicates that women who are depressed during pregnancy tend to remain depressed during the first year postpartum or improve slightly, but an important minority of women become newly and increasingly depressed over the course of the first year after first childbirth.