Simulation of molecular transitions using classical trajectories

Energy Technology Data Exchange (ETDEWEB)

Donoso, A.; Martens, C. C. [University of California, California (United States)

2001-03-01

In the present work, we describe the implementation of a semiclassical method to study physical-chemical processes in molecular systems where electronic state transitions and quantum coherence play a dominant role. The method is based on classical trajectory propagation on the underlying coupled electronic surfaces and is derived from the semiclassical limit of the quantum Liouville equation. Unlike previous classical trajectory-based methods, quantum electronic coherence are treated naturally within this approach as complex weighted trajectory ensembles propagating on the average electronic surfaces. The method is tested on a model problem consisting of one-dimensional motion on two crossing electronic surfaces. Excellent agreement is obtained when compared to the exact results obtained by wave packet propagation. The method is applied to model quantum wave packet interferometry, where two wave packets, differing only in a relative phase, collide in the region where the two electronic surfaces cross. The dependence of the resulting population transfer on the initial relative phase of the wave packets is perfectly captured by our classical trajectory method. Comparison with an alternative method, surface hopping, shows that our approach is appropriate for modelling quantum interference phenomena. [Spanish] En este trabajo se describe la implementacion de un metodo semiclasico para estudiar procesos fisicos-quimicos en sistemas moleculares donde las transiciones entre estados electronicos y las coherencias cuanticas juegan un papel predominante. El metodo se basa en la propagacion de trayectorias clasicas sobre las correspondientes superficies electronicas acopladas y se deriva a partir del limite semiclasico de la ecuacion cuantica de Liouville. A diferencia de metodos previos basados en trayectoria clasica, dentro de este esquema, las coherencias electronicas cuanticas son tratadas de manera natural como ensamble de trayectorias con pesos complejos, moviendose en

Classical trajectory in non-relativistic scattering

International Nuclear Information System (INIS)

Williams, A.C.

1978-01-01

With the statistical interpretation of quantum mechanics as a guide, the classical trajectory is incorporated into quantum scattering theory. The Feynman path integral formalism is used as a starting point, and classical transformation theory is applied to the phase of the wave function so derived. This approach is then used to derive an expression for the scattering amplitude for potential scattering. It is found that the amplitude can be expressed in an impact parameter representation similar to the Glauber formalism. Connections are then made to the Glauber approximation and to semiclassical approximations derived from the Feynman path integral formalism. In extending this analysis to projectile-nucleus scattering, an approximation scheme is given with the first term being the same as in Glauber's multiple scattering theory. Higher-order approximations, thus, are found to give corrections to the fixed scatterer form of the impulse approximation inherent in the Glauber theory

Photon trajectories, anomalous velocities and weak measurements: a classical interpretation

International Nuclear Information System (INIS)

Bliokh, Konstantin Y; Kofman, Abraham G; Nori, Franco; Bekshaev, Aleksandr Y

2013-01-01

Recently, Kocsis et al (2011 Science 332 1170) reported the observation of ‘average trajectories of single photons’ in a two-slit interference experiment. This was possible by using the quantum weak-measurement method, which implies averaging over many events, i.e. in fact, a multi-photon limit of classical linear optics. We give a classical-optics interpretation of this experiment and other related problems. It appears that weak measurements of the local momentum of photons made by Kocsis et al represent measurements of the Poynting vector in an optical field. We consider both the real and imaginary parts of the local momentum and show that their measurements have been realized in classical optics using small-probe particles. We also examine the appearance of ‘anomalous’ values of the local momentum: either negative (backflow) or exceeding the wavenumber (superluminal propagation). These features appear to be closely related to vortices and evanescent waves. Finally, we revisit a number of older works and find examples of photon trajectories and anomalous-momentum measurements in various optical experiments. (paper)

From a quantum to a classical description of intense laser-atom physics with Bohmian trajectories

International Nuclear Information System (INIS)

Lai, X Y; Cai Qingyu; Zhan, M S

2009-01-01

In this paper, Bohmian mechanics is applied to intense laser-atom physics. The motion of an atomic electron in an intense laser field is obtained from the Bohm-Newton equation. We find that the quantum potential that dominates the quantum effect of a physical system becomes negligible as the electron is driven far from the parent ion by the intense laser field, i.e. the behavior of the electron smoothly tends towards classical soon after the electron is ionized. Our numerical calculations present direct positive evidence for semiclassical trajectory methods in intense laser-atom physics where the motion of the ionized electron is treated by classical mechanics, while quantum mechanics is needed before the ionization.

Trajectory Calculation as Forecasting Support Tool for Dust Storms

Directory of Open Access Journals (Sweden)

Sultan Al-Yahyai

2014-01-01

Full Text Available In arid and semiarid regions, dust storms are common during windy seasons. Strong wind can blow loose sand from the dry surface. The rising sand and dust is then transported to other places depending on the wind conditions (speed and direction at different levels of the atmosphere. Considering dust as a moving object in space and time, trajectory calculation then can be used to determine the path it will follow. Trajectory calculation is used as a forecast supporting tool for both operational and research activities. Predefined dust sources can be identified and the trajectories can be precalculated from the Numerical Weather Prediction (NWP forecast. In case of long distance transported dust, the tool should allow the operational forecaster to perform online trajectory calculation. This paper presents a case study for using trajectory calculation based on NWP models as a forecast supporting tool in Oman Meteorological Service during some dust storm events. Case study validation results showed a good agreement between the calculated trajectories and the real transport path of the dust storms and hence trajectory calculation can be used at operational centers for warning purposes.

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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.

Science.gov (United States)

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.

Sensitivity of trajectory calculations to the temporal frequency of wind data

Science.gov (United States)

Doty, Kevin G.; Perkey, Donald J.

1993-01-01

A mesoscale primitive equation model is used to create a 36-h simulation of the three-dimensional wind field of an intense maritime extratropical cyclone. The control experiment uses the simulated wind field every 15 min in a trajectory model to calculate back trajectories from various horizontal and vertical positions of interest relative to synoptic features of the storm. The latter trajectories are compared to trajectories that were calculated with the simulated wind data degraded in time to 30 min, 1 h, 3 h, 6h, and 12 h. Various error statistics reveal significant deterioration in trajectory accuracy between trajectories calculated with 1- and 3-h data frequencies. Trajectories calculated with 15-min, 30-min, and 1-h data frequencies yielded similar results, while trajectories calculated with data time frequencies 3 h and greater yielded results with unacceptably large errors.

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

International Nuclear Information System (INIS)

Bonhommeau, David; Truhlar, Donald G.

2008-01-01

The photodissociation dynamics of ammonia upon excitation of the out-of-plane bending mode (mode ν 2 with n 2 =0,...,6 quanta of vibration) in the A-tilde 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 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

Classical and quasi-classical trajectory calculations of isotope exchange and ozone formation proceeding through O+O2 collision complexes

Science.gov (United States)

Baker, Thomas A.; Gellene, Gregory I.

2002-10-01

The isotope exchange reaction, and the three-body ozone formation rate proceeding through an ozone complex, have been studied by classical and quasi-classical trajectory techniques. The exchange rate studies indicate that the rate of this reaction is dominantly sensitive to the O+O2 entrance channel characteristics of the potential energy surface. A detailed consideration of the dynamics of the intermediate ozone complex reveals three important classes. In one class, the complex adopts an ozonelike geometry, largely undergoing asymmetric stretchinglike motion until it dissociates. In a second class, the oxygen atom and molecule never visit the ozonelike geometry but rather remain separated by relatively large distances trapped near the angular momentum barrier in the entrance channel of a pseudo-effective potential. These complexes, which cannot undergo exchange, are, nevertheless, found to contribute significantly to ozone formation at high density of the third body suggesting that the association of the high-density effective formation rate constant with twice the exchange rate may not be valid. The third class can be considered a hybrid of the first two, spending some time as an ozonelike complex and some time as a large atom-diatomic complex. This third class provides a mechanism for rearranging atom locations in the complex (e.g., end and middle position swapping) and, consequently, would not be well accounted for by statistical treatments of the ozone complex based on a single ozonelike reference geometry. In general, the survival time distributions of the complexes are found to be nonexponential. However, when the detailed survival time distributions are coupled with a Lennard-Jones collision model for the stabilization step, the experimental ozone formation rate can be adequately modeled over a broad range of temperature and density.

Comment on the classical-trajectory Monte Carlo method for ion-atom collisions

International Nuclear Information System (INIS)

Cohen, J.S.

1982-01-01

It is shown that the procedure described by Olson and Salop for classical-trajectory Monte Carlo treatment of ion-atom collisions does not provide a uniform statistical distribution of all the parameters defining the initial conditions of a trajectory. Impact-ionization and charge-transfer cross sections for collisions of H + with H at H energies between 25 and 600 keV are recalculated eliminating this failing and compared with those obtained using the procedure of Olson and Salop and with experimental results

Microscopic classical equations of motion calculations of high-energy heavy-ion collisions

International Nuclear Information System (INIS)

Panos, C.N.

1979-01-01

Classical microscopic nonrelativistic calculations are made for collisions between equal-mass-nuclei projectile and target with A/sub P/ = A/sub T/ = 20 for laboratory energies E/sub L/ = 117, 400, and 800 MeV/A/sub P/ and also between nuclei with A/sub P/ = A/sub T/ = 40 for E/sub L/ = 400 MeV/A/sub P/. For a given initial configuration of the projectile and target nucleons the trajectories of all nucleons are calculated classically with two-body forces between all pairs of nucleons. The implementation of the CEOM calculations is discussed in detail. More limited relativistic calculations for single initial configurations are also made. The configurations representing the initial nuclei are chosen to have a reasonable radius and kinetic energy; however, they do not saturate with the two-body potentials used. The trajectory information is analyzed to give a large number of position and momentum dependent quantities such as densities, rapidity distributions, inclusive double differential cross sections, etc. The results show that a central collision (b = 0) proceeds in three stages, an initial transparent stage, a strongly interacting stage where the dissipation is large, and finally an expansion stage for which there is considerable dissipation. Appreciable potential energy effects were found for b = 0; however, the final distributions were very similar for the scattering equivalent potentials. For lower energies (E/sub L/ approx. = 100 MeV) there is some evidence of fusion into large fragments. The thermal models for b = 0 are tested. Noncentral collisions show typical nonequilibrium and transparency features. The multiplicity distribution is obtained for A/sub P/ = A/sub T/ = 20 and E/sub L/ = 800 MeV. A comparison of the impact parameter-integrated inclusive double differential cross sections is made with the experimental data for A/sub P/ = A/sub T/ = 20, E/sub L/ = 800 MeV and shows fair agreement

On the Calculation of Quantum Mechanical Ground States from Classical Geodesic Motion on Certain Spaces of Constant Negative Curvature

CERN Document Server

Tomaschitz, R

1989-01-01

We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are bounded and recurrent in both directions of the time evolution a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schrodinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories.

On the calculation of quantum mechanical ground states from classical geodesic motion on certain spaces of constant negative curvature

International Nuclear Information System (INIS)

Tomaschitz, R.

1989-01-01

We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are recurrent in both directions of the time evolution t → +∞, t → -∞ a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schroedinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories. (orig.)

Periodic trajectories for two-dimensional nonintegrable Hamiltonians

International Nuclear Information System (INIS)

Davies, K.T.R.

1990-02-01

I want to report on some calculations of classical periodic trajectories in a two-dimensional nonintegrable potential. After a brief introduction, I will present some details of the theory. The main part of this report will be devoted to showing pictures of the various families of trajectories and to discussing the topology (in E-τ space) and branching behavior of these families. Then I will demonstrate the connection between periodic trajectories and ''nearby'' nonperiodic trajectories, which nicely illustrates the relationship of this work to chaos. Finally, I will discuss very briefly how periodic trajectories can be used to calculate tori. 12 refs., 40 figs

Iterative quantum-classical path integral with dynamically consistent state hopping

Energy Technology Data Exchange (ETDEWEB)

Walters, Peter L.; Makri, Nancy [Department of Chemistry, University of Illinois, Urbana, Illinois 61801 (United States)

2016-01-28

We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.

Calculation of molecular free energies in classical potentials

International Nuclear Information System (INIS)

Farhi, Asaf; Singh, Bipin

2016-01-01

Free energies of molecules can be calculated by quantum chemistry computations or by normal mode classical calculations. However, the first can be computationally impractical for large molecules and the second is based on the assumption of harmonic dynamics. We present a novel, accurate and complete calculation of molecular free energies in standard classical potentials. In this method we transform the molecule by relaxing potential terms which depend on the coordinates of a group of atoms in that molecule and calculate the free energy difference associated with the transformation. Then, since the transformed molecule can be treated as non-interacting systems, the free energy associated with these atoms is analytically or numerically calculated. This two-step calculation can be applied to calculate free energies of molecules or free energy difference between (possibly large) molecules in a general environment. We demonstrate the method in free energy calculations for methanethiol and butane molecules in vacuum and solvent. We suggest the potential application of free energy calculation of chemical reactions in classical molecular simulations. (paper)

Bifurcations and chaos of classical trajectories in a deformed nuclear potential

International Nuclear Information System (INIS)

Carbonell, J.; Arvieu, R.

1983-01-01

The organization of the phase space of a classical nucleon in an axially symmetric deformed potential with the restriction Lsub(z)=0 is studied by drawing the Poincare surfaces of section. In the limit of small deformations three simple limits help to understand this organization. Moreover important bifurcations of periodic trajectories occur. At higher deformations multifurcations and chaos are observed. Chaos is developed to a larger extent in the heavier nuclei. (author)

Bifurcations and chaos of classical trajectories in a deformed nuclear potential

International Nuclear Information System (INIS)

Carbonell, J.; Arvieu, R.

1982-10-01

The purpose is to describe the general organization of the trajectories of a nucleon in a deformed potential both in phase space and in configuration space. This question gives rise to a very complex problem in a deformed potential. There one is in the frame of the theory of nonintegrable systems. Many very important mathematical theorems (like K.A.M. theorem) are needed as well as any results of bifurcation theory and also of numerical experiments. This work belongs entirely to classical mechanics. The main problems to be treated are: the organization of phase space, the connection with simple known limiting cases and bifurcation theory, and the occurrence of chaotic trajectories in a nuclear field. These problems must be solved as functions of the size, the deformation of the potential and the excitation energy of the particle

Bifurcations and chaos of classical trajectories in a deformed nuclear potential

Energy Technology Data Exchange (ETDEWEB)

Carbonell, J; Arvieu, R

1982-10-01

The purpose is to describe the general organization of the trajectories of a nucleon in a deformed potential both in phase space and in configuration space. This question gives rise to a very complex problem in a deformed potential. There one is in the frame of the theory of nonintegrable systems. Many very important mathematical theorems (like K.A.M. theorem) are needed as well as any results of bifurcation theory and also of numerical experiments. This work belongs entirely to classical mechanics. The main problems to be treated are: the organization of phase space, the connection with simple known limiting cases and bifurcation theory, and the occurrence of chaotic trajectories in a nuclear field. These problems must be solved as functions of the size, the deformation of the potential and the excitation energy of the particle.

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

Science.gov (United States)

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.

Single electron ionization and electron capture cross sections for (C{sup 6+}, H{sub 2}O) interaction within the Classical Trajectory Monte Carlo (CTMC) approach

Energy Technology Data Exchange (ETDEWEB)

Tran, H.N., E-mail: tranngochoang@tdt.edu.vn [Division of Nuclear Physics, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Faculty of Applied Sciences, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Dao, D.D. [Division of Nuclear Physics, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Faculty of Applied Sciences, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Incerti, S. [Division of Nuclear Physics, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Faculty of Applied Sciences, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); Université de Bordeaux, CENBG, UMR 5797, F-33170 Gradignan (France); Bernal, M.A. [Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, SP (Brazil); Karamitros, M. [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); Université de Bordeaux, CENBG, UMR 5797, F-33170 Gradignan (France); Nhan Hao, T.V. [Center of Research and Development, Duy Tan University, K7/25 Quang Trung, Danang (Viet Nam); Center for Theoretical and Computational Physics, College of Education, Hue University, 34 Le Loi Street, Hue City (Viet Nam); Dang, T.M. [VNUHCM-University of Science (Viet Nam); Francis, Z. [Saint Joseph University, Beyrouth (Lebanon)

2016-01-01

In this work, we present a derivation of cross sections for single ionization and electron capture processes within the Classical Trajectory Monte Carlo (CTMC) approach. Specifically, we have used a potential stemming from an ab initio calculation in Green et al.’s framework to describe the dynamics of the water molecule system. Proposing a modified version of the Classical Over-Barrier (COB) potential, we have found that a cut-off of roughly 28 a.u. on the initial distance of the projectile produced a reasonable accuracy. A global agreement has been obtained in our calculations compared to experimental and other theoretical results for C{sup 6+} ion energies ranging from 10 keV/u to 10 MeV/u.

Cluster dynamics: A classical trajectory study of A + A/sub n/arrow-right-leftA*/sub n/+1

International Nuclear Information System (INIS)

Brady, J.W.; Doll, J.D.; Thompson, D.L.

1979-01-01

The dynamics of the collision of an atom A with a small cluster of atoms, A/sub n/, leading to the formation of a quasibound A*/sub n/+1 complex, which subsequently decays, has been studied using classical trajectories. Pairwise Lennard-Jones potentials (with parameters appropriate for argon) were used to describe the identical point masses (Ar). The results illustrate the feasibility of direct calculations of microscopic rates for nucleation processes. The dissociation of collisionally formed A*/sub n/+1 (n=3,4, and 5) occurs by first-order exponential decay. Furthermore the energy dependence of the dissociation rate constants appears to be well described by the RRK functional form

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

Science.gov (United States)

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)].

Computational Method for Ice Crystal Trajectories in a Turbofan Compressor

NARCIS (Netherlands)

Grift, E.J.; Norde, Ellen; van der Weide, Edwin Theodorus Antonius; Hoeijmakers, Hendrik Willem Marie

2015-01-01

In this study the characteristics of ice crystals on their trajectory in a single stage of a turbofan engine compressor are determined. The particle trajectories are calculated with a Lagrangian method employing a classical fourth-order Runge-Kutta time integration scheme. The air flow field is

Rapid Calculation of Spacecraft Trajectories Using Efficient Taylor Series Integration

Science.gov (United States)

Scott, James R.; Martini, Michael C.

2011-01-01

A variable-order, variable-step Taylor series integration algorithm was implemented in NASA Glenn's SNAP (Spacecraft N-body Analysis Program) code. SNAP is a high-fidelity trajectory propagation program that can propagate the trajectory of a spacecraft about virtually any body in the solar system. The Taylor series algorithm's very high order accuracy and excellent stability properties lead to large reductions in computer time relative to the code's existing 8th order Runge-Kutta scheme. Head-to-head comparison on near-Earth, lunar, Mars, and Europa missions showed that Taylor series integration is 15.8 times faster than Runge- Kutta on average, and is more accurate. These speedups were obtained for calculations involving central body, other body, thrust, and drag forces. Similar speedups have been obtained for calculations that include J2 spherical harmonic for central body gravitation. The algorithm includes a step size selection method that directly calculates the step size and never requires a repeat step. High-order Taylor series integration algorithms have been shown to provide major reductions in computer time over conventional integration methods in numerous scientific applications. The objective here was to directly implement Taylor series integration in an existing trajectory analysis code and demonstrate that large reductions in computer time (order of magnitude) could be achieved while simultaneously maintaining high accuracy. This software greatly accelerates the calculation of spacecraft trajectories. At each time level, the spacecraft position, velocity, and mass are expanded in a high-order Taylor series whose coefficients are obtained through efficient differentiation arithmetic. This makes it possible to take very large time steps at minimal cost, resulting in large savings in computer time. The Taylor series algorithm is implemented primarily through three subroutines: (1) a driver routine that automatically introduces auxiliary variables and

Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects

Science.gov (United States)

Smith, Brendan; Akimov, Alexey V.

2018-04-01

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

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

Science.gov (United States)

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.

Computer program 'TRIO' for third order calculation of ion trajectory

International Nuclear Information System (INIS)

Matsuo, Takekiyo; Matsuda, Hisashi; Fujita, Yoshitaka; Wollnik, H.

1976-01-01

A computer program for the calculation of ion trajectory is described. This program ''TRIO'' (Third Order Ion Optics) is applicable to any ion optical system consisting of drift spaces, cylindrical or toroidal electric sector fields, homogeneous or inhomogeneous magnetic sector fields, magnetic and electrostatic Q-lenses. The influence of the fringing field is taken into consideration. A special device is introduced to the method of matrix multiplication to shorten the calculation time and the required time proves to be about 40 times shorter than the ordinary method as a result. The trajectory calculation is possible to execute with accuracy up to third order. Any one of three dispersion bases, momentum, energy, mass and energy, is possible to be selected. Full LIST of the computer program and an example are given. (auth.)

Progress in classical and quantum variational principles

International Nuclear Information System (INIS)

Gray, C G; Karl, G; Novikov, V A

2004-01-01

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The reciprocal Maupertuis principle is the classical limit of Schroedinger's variational principle of wave mechanics and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems. '... the most beautiful and important discovery of Mechanics.' Lagrange to Maupertuis (November 1756)

Calculation of the radial dose distribution around the trajectory of an ion

International Nuclear Information System (INIS)

Pretzsch, G.

1979-01-01

The dose caused in polyester by incoming protons, alpha beams, 127 I ions, and 16 O ions has been calculated as a function of the distance perpendicularly to their trajectory. Based on simplified assumptions regarding the binding state of target electrons, emission of secondary electrons and their propagation in matter, it has been found that the dose depends on the distance to the ion trajectory (R) in the form Rsup(-l), l being about 2. The calculated radial dose distributions agree well with values calculated or measured by other authors

A uniform semi-classical approach to the Coulomb fission problem

International Nuclear Information System (INIS)

Levit, S.; Smilansky, U.

1978-01-01

A semi-classical theory based on the path integral formalism is applied to the description of Coulomb fission. Complex classical trajectories are used to compute the classically forbidden transitions from the target's ground state to fission. In a simple model the energy spectrum and angular distributions of the fragments are calculated for the Coulomb fission in the Xe + U collision. Theoretical predictions are made which may be checked experimentally. (author)

Moyal dynamics and trajectories

Science.gov (United States)

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.

Calculation of the electron trajectory for 200 kV self-shielded electron accelerator

International Nuclear Information System (INIS)

Wang Shuiqing

2000-01-01

In order to calculate the electron trajectory of 200 kV self-shielded electron accelerator, the electric field is calculated with a TRAJ program. In this program, following electron track mash points one by one, the electron beam trajectories are calculated. Knowing the effect of grid voltage on electron optics and gaining grid voltage focusing effect in the various energy grades, the authors have gained scientific basis for adjusting grid voltage, and also accumulated a wealth of experience for designing self-shielded electron accelerator or electron curtain in future

A simple model for correcting the zero point energy problem in classical trajectory simulations of polyatomic molecules

International Nuclear Information System (INIS)

Miller, W.H.; Hase, W.L.; Darling, C.L.

1989-01-01

A simple model is proposed for correcting problems with zero point energy in classical trajectory simulations of dynamical processes in polyatomic molecules. The ''problems'' referred to are that classical mechanics allows the vibrational energy in a mode to decrease below its quantum zero point value, and since the total energy is conserved classically this can allow too much energy to pool in other modes. The proposed model introduces hard sphere-like terms in action--angle variables that prevent the vibrational energy in any mode from falling below its zero point value. The algorithm which results is quite simple in terms of the cartesian normal modes of the system: if the energy in a mode k, say, decreases below its zero point value at time t, then at this time the momentum P k for that mode has its sign changed, and the trajectory continues. This is essentially a time reversal for mode k (only exclamation point), and it conserves the total energy of the system. One can think of the model as supplying impulsive ''quantum kicks'' to a mode whose energy attempts to fall below its zero point value, a kind of ''Planck demon'' analogous to a Brownian-like random force. The model is illustrated by application to a model of CH overtone relaxation

A simple algorithm for calculating the scattering angle in atomic collisions

International Nuclear Information System (INIS)

Belchior, J.C.; Braga, J.P.

1996-01-01

A geometric approach to calculate the classical atomic scattering angle is presented. The trajectory of the particle is divided into several straight-lines and changing in direction from one sector to the other is used to calculate the scattering angle. In this model, calculation of the scattering angle does not involve either the direct evaluation of integrals nor classical turning points. (author)

A trajectory description of quantum processes. I. Fundamentals. A Bohmian perspective

International Nuclear Information System (INIS)

Sanz, Angel S.; Miret-Artes, Salvador

2012-01-01

Offers a thorough introduction to, and treatment of, trajectory-based quantum-mechanical calculations. Presents the fundamentals of Bohmian mechanics. Useful for a wide range of scattering problems, as described in Vol. 2. Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of ''classical'' concepts. Beginning at an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This first volume is focussed on the classical and quantum background necessary to understand the fundamentals of Bohmian mechanics, which can be considered the main topic of this work. Extensions of the formalism to the fields of open quantum systems and to optics are also proposed and discussed.

A trajectory description of quantum processes. I. Fundamentals. A Bohmian perspective

Energy Technology Data Exchange (ETDEWEB)

Sanz, Angel S.; Miret-Artes, Salvador [Consejo Superior de Investigaciones Cientificas, Madrid (Spain). Inst. de Fisica Fundamental

2012-11-01

Offers a thorough introduction to, and treatment of, trajectory-based quantum-mechanical calculations. Presents the fundamentals of Bohmian mechanics. Useful for a wide range of scattering problems, as described in Vol. 2. Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of ''classical'' concepts. Beginning at an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This first volume is focussed on the classical and quantum background necessary to understand the fundamentals of Bohmian mechanics, which can be considered the main topic of this work. Extensions of the formalism to the fields of open quantum systems and to optics are also proposed and discussed.

Adatom Bond Dissociation in the Collision Between an Adsorbed Atom and Incident Diatomic Molecule: A Classical Trajectory Study

International Nuclear Information System (INIS)

Bayhan, U.

2004-01-01

The collisional dissociation of the Atom-Surface bond in the diatomic molecule (gas) / atom (ads) collision taking place on a bcc-structure surface have been studied by classical trajectory methods over the collision energy ranges and the attractive well depth of the diatomic molecule (gas) / atom (ads) interactions

How to calculate linear absorption spectra with lifetime broadening using fewest switches surface hopping trajectories: A simple generalization of ground-state Kubo theory

International Nuclear Information System (INIS)

Petit, Andrew S.; Subotnik, Joseph E.

2014-01-01

In this paper, we develop a surface hopping approach for calculating linear absorption spectra using ensembles of classical trajectories propagated on both the ground and excited potential energy surfaces. We demonstrate that our method allows the dipole-dipole correlation function to be determined exactly for the model problem of two shifted, uncoupled harmonic potentials with the same harmonic frequency. For systems where nonadiabatic dynamics and electronic relaxation are present, preliminary results show that our method produces spectra in better agreement with the results of exact quantum dynamics calculations than spectra obtained using the standard ground-state Kubo formalism. As such, our proposed surface hopping approach should find immediate use for modeling condensed phase spectra, especially for expensive calculations using ab initio potential energy surfaces

Quantum dynamics and breakdown of classical realism in nonlinear oscillators

International Nuclear Information System (INIS)

Gat, Omri

2007-01-01

The leading nonclassical term in the quantum dynamics of nonlinear oscillators is calculated in the Moyal quasi-trajectory representation. The irreducibility of the quantum dynamics to phase-space trajectories is quantified by the discrepancy of the canonical quasi-flow and the quasi-flow of a general observable. This discrepancy is shown to imply the breakdown of classical realism that can give rise to a dynamical violation of Bell's inequalities. (fast track communication)

Partitioning of the nonfixed excess energy and the reverse critical energy in CH2OH + --> CHO + +H2: A classical trajectory study

Science.gov (United States)

Lee, Tae Geol; Kim, Myung Soo; Park, Seung C.

1996-04-01

Dynamics of the four-centered elimination reaction CH2OH+→CHO++H2 has been investigated over the internal energy range 4.6-5.9 eV using the classical trajectory method. A realistic semiempirical potential reported previously [J. Chem. Phys. (in press, 1996)] has been used for the calculation. It has been found that the disposal of the nonfixed excess energy at the transition state and of the reverse critical energy can be considered independently as manifest in the sum rule analysis. The former is determined statistically while the latter dynamically. Based on the above idea, a method to determine the kinetic energy release distribution originating only from the reverse critical energy has been developed.

Quantum-classical dynamics of scattering processes in adiabatic and diabatic representations

International Nuclear Information System (INIS)

Puzari, Panchanan; Sarkar, Biplab; Adhikari, Satrajit

2004-01-01

We demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantum-classical approach, for simulating scattering processes on a quasi-Jahn-Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The time-dependent Schroedinger equation and classical equations of motion are solved self-consistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantum-classical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive state-to-state transition probabilities, along with calculations on an adiabatic surface with ordinary Born-Oppenheimer approximation. Excellent agreement between TDDVR and DVR results is obtained in both the representations

Quantum models of classical systems

International Nuclear Information System (INIS)

Hájíček, P

2015-01-01

Quantum statistical methods that are commonly used for the derivation of classical thermodynamic properties are extended to classical mechanical properties. The usual assumption that every real motion of a classical mechanical system is represented by a sharp trajectory is not testable and is replaced by a class of fuzzy models, the so-called maximum entropy (ME) packets. The fuzzier are the compared classical and quantum ME packets, the better seems to be the match between their dynamical trajectories. Classical and quantum models of a stiff rod will be constructed to illustrate the resulting unified quantum theory of thermodynamic and mechanical properties. (paper)

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

Science.gov (United States)

Sarkadi, L.

2018-04-01

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

Classical and semi-classical treatments of Li3+, Ne10++H(1s) collisions

International Nuclear Information System (INIS)

Errea, L F; Illescas, Clara; Mendez, L; Pons, B; Riera, A; Suarez, J

2004-01-01

We perform molecular close-coupling and impact-parameter classical trajectory Monte Carlo calculations of total and partial cross sections for capture and ionization in collisions of highly charged ions on H(1s). We first consider Li 3+ +H(1s) as a benchmark to ascertain the complementarity of the methods, and then Ne 10+ +H(1s), which has been scarcely studied up to now, and has recently become of interest for fusion plasma research

Chemical reaction dynamics of Rydberg atoms with neutral molecules: A comparison of molecular-beam and classical trajectory results for the H(n)+D2→HD+D(n') reaction

International Nuclear Information System (INIS)

Song Hui; Dai Dongxu; Wu Guorong; Wang, C.-C.; Harich, Steven A.; Hayes, Michael Y.; Wang Xiuyan; Gerlich, Dieter; Yang Xueming; Skodje, Rex T.

2005-01-01

Recent molecular-beam experiments have probed the dynamics of the Rydberg-atom reaction, H(n)+D 2 →HD+D(n) at low collision energies. It was discovered that the rotationally resolved product distribution was remarkably similar to a much more limited data set obtained at a single scattering angle for the ion-molecule reaction H + +D 2 →D + +HD. The equivalence of these two problems would be consistent with the Fermi-independent-collider model (electron acting as a spectator) and would provide an important new avenue for the study of ion-molecule reactions. In this work, we employ a classical trajectory calculation on the ion-molecule reaction to facilitate a more extensive comparison between the two systems. The trajectory simulations tend to confirm the equivalence of the ion+molecule dynamics to that for the Rydberg-atom+molecule system. The theory reproduces the close relationship of the two experimental observations made previously. However, some differences between the Rydberg-atom experiments and the trajectory simulations are seen when comparisons are made to a broader data set. In particular, the angular distribution of the differential cross section exhibits more asymmetry in the experiment than in the theory. The potential breakdown of the classical model is discussed. The role of the 'spectator' Rydberg electron is addressed and several crucial issues for future theoretical work are brought out

Intersection of separatrices of periodical trajectories and non-integrability of the classical Yang-Mills equations

International Nuclear Information System (INIS)

Nikolaevskij, E.S.; Shchur, L.N.

1983-01-01

A perticular case of the Yang-Mills (YM) equations has been studied. For this system a transversal intersection of separatrices of unstable periodical trajectories is discovered, hence, it follows that there are no first real-analytical integrals of motion additional to the Hamiltonian. As a result, a complete set of integrals does not exist for the system describing the classical YM fields. Numerical methods of constructing separatrices, double-asymptotical solutions and of determining the angles between separatrices have been described

Trajectory Calculator for Finite-Radius Cutter on a Lathe

Science.gov (United States)

Savchenkov, Anatoliy; Strekalov, Dmitry; Yu, Nan

2009-01-01

A computer program calculates the two-dimensional trajectory (radial vs. axial position) of a finite-radius-of-curvature cutting tool on a lathe so as to cut a workpiece to a piecewise-continuous, analytically defined surface of revolution. (In the original intended application, the tool is a diamond cutter, and the workpiece is made of a crystalline material and is to be formed into an optical resonator disk.) The program also calculates an optimum cutting speed as F/L, where F is a material-dependent empirical factor and L is the effective instantaneous length of the cutting edge.

Classical and semiclassical treatments of highly charged ions + H(1s) collisions

International Nuclear Information System (INIS)

Errea, L.F.; Illescas, C.; Mendez, L.; Pons, B.; Riera, A.; Suarez, J.

2005-01-01

We present impact-parameter classical trajectory Monte-Carlo and molecular close-coupling calculations for total and partial cross sections for Ne 10+ , Ar 18 + H(1s) collisions, which have recently became of interest in fusion plasma research

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

Science.gov (United States)

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.

Fractional dynamics using an ensemble of classical trajectories

Science.gov (United States)

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.

An alternative phase-space distribution to sample initial conditions for classical dynamics simulations

International Nuclear Information System (INIS)

Garcia-Vela, A.

2002-01-01

A new quantum-type phase-space distribution is proposed in order to sample initial conditions for classical trajectory simulations. The phase-space distribution is obtained as the modulus of a quantum phase-space state of the system, defined as the direct product of the coordinate and momentum representations of the quantum initial state. The distribution is tested by sampling initial conditions which reproduce the initial state of the Ar-HCl cluster prepared by ultraviolet excitation, and by simulating the photodissociation dynamics by classical trajectories. The results are compared with those of a wave packet calculation, and with a classical simulation using an initial phase-space distribution recently suggested. A better agreement is found between the classical and the quantum predictions with the present phase-space distribution, as compared with the previous one. This improvement is attributed to the fact that the phase-space distribution propagated classically in this work resembles more closely the shape of the wave packet propagated quantum mechanically

Calculating trajectories for atoms in near-resonant lightfields

International Nuclear Information System (INIS)

Scholten, R.E.; O' Kane, T.J.; Mackin, T.R.; Hunt, T.A.; Farrell, P.M.

1999-01-01

We review several methods for calculating the time development of the internal state and the external motion of atoms in near-resonant light fields, with emphasis on studying the focussing of atomic beams into microscopic and potentially nanoscopic patterns. Three different approaches are considered: two-level semiclassical, multi-level semiclassical, and the Monte Carlo wavefunction method. The two-level semiclassical technique of McClelland and Scheinfein (1991) and McClelland (1995) is extended to three dimensions, and used to calculate the trajectories of atoms and the imaging properties of a simple lens formed from a near-resonant travelling TEM 01 mode laser. The model is then extended to multi-level atoms, where we calculate the density matrix for the internal state of a sample of thermal atoms in a standing wave, and show how cooling processes can be simulated. Finally, we use the Monte Carlo wavefunction method to calculate the internal state of the atom, and compare the results and required computation time to those of the multi-level semiclassical technique. (authors)

The influence of aerodynamic coefficients on the elements of classic projectile paths

Directory of Open Access Journals (Sweden)

Damir D. Jerković

2011-04-01

Full Text Available The article deals with the results of the research on the influence of aerodynamic coefficient values on the trajectory elements and the stability parameters of classic axisymmetric projectiles. It presents the characteristic functions of aerodynamic coefficients with regard to aerodynamic parameters and the projectile body shape. The trajectory elements of the model of classic axisymmetric projectiles and the analyses of their changes were presented with respect to the aerodynamic coefficient values. Introduction Classic axisymmetric projectiles fly through atmosphere using muzzle velocity as initial energy resource, so the aerodynamic force and moment have the most significant influence on the motion of projectiles. The aerodynamic force and moment components represented as aerodynamic coefficients depend on motion velocity i. e. flow velocity, the flow features produced by projectile shape and position in the flow, and angular velocity (rate of the body. The functional dependence of aerodynamic coefficients on certain influential parameters, such as angle of attack and angular velocity components is expressed by the derivative of aerodynamic coefficients. The determination of aerodynamic coefficients and derivatives enables complete definition of the aerodynamic force and moment acting on the classic projectile. The projectile motion problem is considered in relation to defining the projectile stability parameters and the conditions under which the stability occurs. The comparative analyses of aerodynamic coefficient values obtained by numerical methods, semi empirical calculations and experimental research give preliminary evaluation of the quality of the determined values. The flight simulation of the motion of a classic axisymetric projectile, which has the shape defined by the aerodynamic coefficient values, enables the comparative analyses of the trajectory elements and stability characteristics. The model of the classic projectile

Classical approach in atomic physics

International Nuclear Information System (INIS)

Solov'ev, E.A.

2011-01-01

The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of a hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's approach to Stark problem, long-lived excited states of a helium atom discovered with the help of Poincare section, inelastic transitions in slow and fast electron-atom and ion-atom collisions - is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treated as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semiclassical series such as renormalization group symmetry, criterion of accuracy and so on are reviewed as well. (author)

Oxygen transport properties estimation by classical trajectory–direct simulation Monte Carlo

Energy Technology Data Exchange (ETDEWEB)

Bruno, Domenico, E-mail: domenico.bruno@cnr.it [Istituto di Metodologie Inorganiche e dei Plasmi, Consiglio Nazionale delle Ricerche– Via G. Amendola 122, 70125 Bari (Italy); Frezzotti, Aldo, E-mail: aldo.frezzotti@polimi.it; Ghiroldi, Gian Pietro, E-mail: gpghiro@gmail.com [Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano–Via La Masa 34, 20156 Milano (Italy)

2015-05-15

Coupling direct simulation Monte Carlo (DSMC) simulations with classical trajectory calculations is a powerful tool to improve predictive capabilities of computational dilute gas dynamics. The considerable increase in computational effort outlined in early applications of the method can be compensated by running simulations on massively parallel computers. In particular, Graphics Processing Unit acceleration has been found quite effective in reducing computing time of classical trajectory (CT)-DSMC simulations. The aim of the present work is to study dilute molecular oxygen flows by modeling binary collisions, in the rigid rotor approximation, through an accurate Potential Energy Surface (PES), obtained by molecular beams scattering. The PES accuracy is assessed by calculating molecular oxygen transport properties by different equilibrium and non-equilibrium CT-DSMC based simulations that provide close values of the transport properties. Comparisons with available experimental data are presented and discussed in the temperature range 300–900 K, where vibrational degrees of freedom are expected to play a limited (but not always negligible) role.

Piezoelectric constants for ZnO calculated using classical polarizable core-shell potentials

International Nuclear Information System (INIS)

Dai Shuangxing; Dunn, Martin L; Park, Harold S

2010-01-01

We demonstrate the feasibility of using classical atomistic simulations, i.e. molecular dynamics and molecular statics, to study the piezoelectric properties of ZnO using core-shell interatomic potentials. We accomplish this by reporting the piezoelectric constants for ZnO as calculated using two different classical interatomic core-shell potentials: that originally proposed by Binks and Grimes (1994 Solid State Commun. 89 921-4), and that proposed by Nyberg et al (1996 J. Phys. Chem. 100 9054-63). We demonstrate that the classical core-shell potentials are able to qualitatively reproduce the piezoelectric constants as compared to benchmark ab initio calculations. We further demonstrate that while the presence of the shell is required to capture the electron polarization effects that control the clamped ion part of the piezoelectric constant, the major shortcoming of the classical potentials is a significant underprediction of the clamped ion term as compared to previous ab initio results. However, the present results suggest that overall, these classical core-shell potentials are sufficiently accurate to be utilized for large scale atomistic simulations of the piezoelectric response of ZnO nanostructures.

Classical calculation of radiative lifetimes of atomic hydrogen in a homogeneous magnetic field

International Nuclear Information System (INIS)

Horbatsch, M.W.; Hessels, E.A.; Horbatsch, M.

2005-01-01

Radiative lifetimes of hydrogenic atoms in a homogeneous magnetic field of moderate strength are calculated on the basis of classical radiation. The modifications of the Keplerian orbits due to the magnetic field are incorporated by classical perturbation theory. The model is complemented by a classical radiative decay calculation using the radiated Larmor power. A recently derived highly accurate formula for the transition rate of a field-free hydrogenic state is averaged over the angular momentum oscillations caused by the magnetic field. The resulting radiative lifetimes for diamagnetic eigenstates classified by n,m and the diamagnetic energy shift C compare well with quantum results

Semi-classical calculation of the spin-isospin response functions

International Nuclear Information System (INIS)

Chanfray, G.

1987-03-01

We present a semi-classical calculation of the nuclear response functions beyond the Thomas-Fermi approximation. We apply our formalism to the spin-isospin responses and show that the surface peaked h/2π corrections considerably decrease the ratio longitudinal/transverse as obtained through hadronic probes

Uncertainty in predictions of oil spill trajectories in a coastal zone

Science.gov (United States)

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.

Coherent states of the driven Rydberg atom: Quantum-classical correspondence of periodically driven systems

International Nuclear Information System (INIS)

Vela-Arevalo, Luz V.; Fox, Ronald F.

2005-01-01

A methodology to calculate generalized coherent states for a periodically driven system is presented. We study wave packets constructed as a linear combination of suitable Floquet states of the three-dimensional Rydberg atom in a microwave field. The driven coherent states show classical space localization, spreading, and revivals and remain localized along the classical trajectory. The microwave strength and frequency have a great effect in the localization of Floquet states, since quasienergy avoided crossings produce delocalization of the Floquet states, showing that tuning of the parameters is very important. Using wavelet-based time-frequency analysis, the classical phase-space structure is determined, which allows us to show that the driven coherent state is located in a large regular region in which the z coordinate is in resonance with the external field. The expectation values of the wave packet show that the driven coherent state evolves along the classical trajectory

Mode specific dynamics of the H2 + CH3 → H + CH4 reaction studied using quasi-classical trajectory and eight-dimensional quantum dynamics methods

International Nuclear Information System (INIS)

Wang, Yan; Li, Jun; Guo, Hua; Chen, Liuyang; Yang, Minghui; Lu, Yunpeng

2015-01-01

An eight-dimensional quantum dynamical model is proposed and applied to the title reaction. The reaction probabilities and integral cross sections have been determined for both the ground and excited vibrational states of the two reactants. The results indicate that the H 2 stretching and CH 3 umbrella modes, along with the translational energy, strongly promote the reactivity, while the CH 3 symmetric stretching mode has a negligible effect. The observed mode specificity is confirmed by full-dimensional quasi-classical trajectory calculations. The mode specificity can be interpreted by the recently proposed sudden vector projection model, which attributes the enhancement effects of the reactant modes to their strong couplings with the reaction coordinate at the transition state

On the Trajectories of Projectiles Depicted in Early Ballistic Woodcuts

Science.gov (United States)

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…

Quasi-classical integral method for spectra calculation of symmetric central problems

International Nuclear Information System (INIS)

Lobashev, A.A.; Trunov, N.N.

2000-01-01

The new approach to the quantization quasi-classical conditions is developed. It is based on general exact properties of the wave equations and their spectra and it does not use asymptotic decompositions. The quantization conditions for the central-symmetric potentials depend only on the totality of integrals, including the classical pulse degrees. The energy level values, calculated by means of this conditions, are in good agreement with the numerical data [ru

Classical-limit S-matrix for heavy ion scattering

International Nuclear Information System (INIS)

Donangelo, R.J.

1977-01-01

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, and 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

Classical trajectory Monte Carlo simulations of particle confinement using dual levitated coils

Directory of Open Access Journals (Sweden)

R. A. Lane

2014-07-01

Full Text Available The particle confinement properties of plasma confinement systems that employ dual levitated magnetic coils are investigated using classical trajectory Monte Carlo simulations. Two model systems are examined. In one, two identical current-carrying loops are coaxial and separated axially. In the second, two concentric and coplanar loops have different radii and carry equal currents. In both systems, a magnetic null circle is present between the current loops. Simulations are carried out for seven current loop separations for each system and at numerous values of magnetic field strength. Particle confinement is investigated at three locations between the loops at different distances from the magnetic null circle. Each simulated particle that did not escape the system exhibited one of four modes of confinement. Reduced results are given for both systems as the lowest magnetic field strength that exhibits complete confinement of all simulated particles for a particular loop separation.

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

Science.gov (United States)

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.

Three-stage classical molecular dynamics model for simulation of heavy-ion fusion

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Godre Subodh S.

2015-01-01

Full Text Available A three-stage Classical Molecular Dynamics (3S-CMD approach for heavy-ion fusion is developed. In this approach the Classical Rigid-Body Dynamics simulation for heavy-ion collision involving light deformed nucleus is initiated on their Rutherford trajectories at very large initial separation. Collision simulation is then followed by relaxation of the rigid-body constrains for one or both the colliding nuclei at distances close to the barrier when the trajectories of all the nucleons are obtained in a Classical Molecular Dynamics approach. This 3S-CMD approach explicitly takes into account not only the long range Coulomb reorientation of the deformed collision partner but also the internal vibrational excitations of one or both the nuclei at distances close to the barrier. The results of the dynamical simulation for 24Mg+208Pb collision show significant modification of the fusion barrier and calculated fusion cross sections due to internal excitations.

Path integrals and geometry of trajectories

International Nuclear Information System (INIS)

Blau, M.; Keski-Vakkuri, E.; Niemi, A.J.

1990-01-01

A geometrical interpretation of path integrals is developed in the space of trajectories. This yields a supersymmetric formulation of a generic path integral, with the supersymmetry resembling the BRST supersymmetry of a first class constrained system. If the classical equation of motion is a Killing vector field in the space of trajectories, the supersymmetry localizes the path integral to classical trajectories and the WKB approximation becomes exact. This can be viewed as a path integral generalization of the Duistermaat-Heckman theorem, which states the conditions for the exactness of the WKB approximation for integrals in a compact phase space. (orig.)

Classical treatment of Li2++Ar and He2++Ar collisions

International Nuclear Information System (INIS)

Jorge, A; Illescas, Clara; Pons, B

2015-01-01

Classical Trajectory Monte Carlo calculations are carried out for Li 2+ +Ar and He 2+ +Ar collisions, motivated by recent experiments on these systems. Cross sections for electron capture, projectile electron loss and target multiple ionization processes are evaluated and compared to the experimental values in the 75-500 keV/amy impact energy range. (paper)

O método das trajectórias clássicas: colisões coplanares do tipo A+BC Classical trajectory method: A+BC coplanar collisions

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Jorge M. C. Marques

2003-10-01

Full Text Available The general methodology of classical trajectories as applied to elementary chemical reactions of the A+BC type is presented. The goal is to elucidate students about the main theoretical features and potentialities in applying this versatile method to calculate the dynamical properties of reactive systems. Only the methodology for two-dimensional (2D case is described, from which the general theory for 3D follows straightforwardly. The adopted point of view is, as much as possible, that of allowing a direct translation of the concepts into a working program. An application to the reaction O(¹D+H2->O+OH with relevance in atmospheric chemistry is also presented. The FORTRAN codes used are available through the web page www.qqesc.qui.uc.pt.

Periodic trajectories for a two-dimensional nonintegrable Hamiltonian

International Nuclear Information System (INIS)

Baranger, M.; Davies, K.T.R.

1987-01-01

A numerical study is made of the classical periodic trajectories for the two-dimensional nonintegrable Hamiltonian H = 1/2(p 2 /sub x/+p 2 /sub y/)+(y-1/2x 2 ) 2 +0.05 x 2 . In addition to x--y pictures of the trajectories, E--tau (energy--period) plots of the periodic families are presented. Efforts have been ade to include all trajectories with short periods and all simple branchings of these trajectories. The monodromy matrix has been calculated in all cases, and from it the stability properties are derived. The topology of the E--tau plot has been explored, with the following results. One family may have several stable regions. The plot is not completely connected; there are islands. The plot is not a tree; there are cycles. There are isochronous branchings, period-doublings, and period-multiplyings of higher orders, and examples of each of these are presented. There is often more than one branch issuing from a branch point. Some general empirical rules are inferred. In particular, the existence of isochronous branching is seen to be a consequence of the symmetry of the Hamiltonian. All these results agree with the general classification of possible branchings derived in Ref. [10]. (M. A. M. de Aguiar, C. P. Malta, M. Baranger, and K. T. R. Davies, in preparation). Finally, some nonperiodic trajectories are calculated to illustrate the fact that stable periodic trajectories lie in ''regular'' regions of phase space, while unstable ones lie in ''chaotic'' regions

Investigation of oxygen vibrational relaxation by quasi-classical trajectory method

International Nuclear Information System (INIS)

Andrienko, Daniil; Boyd, Iain D.

2015-01-01

Highlights: • Importance of attraction for the O 2 –O energy exchange in hypersonic flows. • O 2 –O vibrational relaxation time cannot be described by the Millikan–White equation. • Weak dependence of exothermic transition rates on translational temperature. • Multiquantum jumps in molecular oxygen occur mostly via the exchange reaction. - Abstract: O 2 –O collisions are studied by the quasi-classical trajectory method. A full set of cross sections for the vibrational ladder is obtained utilizing an accurate O 3 potential energy surface. Vibrational relaxation is investigated at temperatures between 1000 and 10,000 K, that are relevant to hypersonic flows. The relaxation time is derived based on the removal rate for the first excited vibrational level. A significant deviation from the formula by Millikan and White is observed for temperatures beyond those reported in experimental work. Relaxation becomes less efficient at high temperatures, suggesting that the efficiency of the energy randomization is strongly to the attractive component of the O 3 potential energy surface. These results are explained by analyzing the microscopic parameter of collisions that reflects the number of exchanges in the shortest interatomic distance. The rates of exothermic transitions are found to be nearly independent of the translational temperature in the range of interest.

Bohmian mechanics and the emergence of classicality

International Nuclear Information System (INIS)

Matzkin, A

2009-01-01

Bohmian mechanics is endowed with an ontological package that supposedly allows to solve the main interpretational problems of quantum mechanics. We are concerned in this work by the emergence of classicality from the quantum mechanical substrate. We will argue that although being superficially attractive, the de Broglie-Bohm interpretation does not shed new light on the quantum-to-classical transition. This is due to nature of the dynamical law of Bohmian mechanics by which the particles follow the streamlines of the probability flow. As a consequence, Bohmian trajectories can be highly non-classical even when the wavefunction propagates along classical trajectories, as happens in semiclassical systems. In order to account for classical dynamics, Bohmian mechanics needs non-spreading and non-interfering wave packets: this is achieved for practical purposes by having recourse to decoherence and dense measurements. However one then faces the usual fundamental problems associated with the meaning of reduced density matrices. Moreover the specific assets of the de Broglie-Bohm interpretation - in particular the existence of point-like particles pursuing well-defined trajectories - would play no role in accounting for the emergence of classical dynamics.

Classical/quantum correspondence in state selective charge transfer and excitation reactions involving highly charged ions and hydrogen

International Nuclear Information System (INIS)

Purkait, M

2009-01-01

State selective charge transfer and excitation cross sections for collisions of Ne q+ (q = 1-10) with atomic hydrogen are calculated within the framework of Classical Trajectory Monte Carlo (CTMC) method and Boundary Corrected Continuum Intermediate State (BCCIS) approximation.

A trajectory description of quantum processes. II. Applications. A Bohmian perspective

Energy Technology Data Exchange (ETDEWEB)

Sanz, Angel S.; Miret-Artes, Salvador [CSIC, Madrid (Spain). Inst. de Fisica Fundamental (IFF-CSIC)

2014-07-01

Presents a thorough introduction to, and treatment of, trajectory-based quantum-mechanical calculations. Useful for a wide range of scattering problems. Presents the applications of the trajectory description of basic quantum processes. Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of ''classical'' concepts. Beginning as an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This second volume is focussed on simple and basic applications of quantum processes such as interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering problems. The corresponding analysis is carried out within the Bohmian framework. By stressing its interpretational aspects, the book leads the reader to an alternative and complementary way to better understand the underlying quantum dynamics.

Modeling classical and quantum radiation from laser-plasma accelerators

Directory of Open Access Journals (Sweden)

M. Chen

2013-03-01

Full Text Available The development of models and the “Virtual Detector for Synchrotron Radiation” (vdsr code that accurately describe the production of synchrotron radiation are described. These models and code are valid in the classical and linear (single-scattering quantum regimes and are capable of describing radiation produced from laser-plasma accelerators (LPAs through a variety of mechanisms including betatron radiation, undulator radiation, and Thomson/Compton scattering. Previous models of classical synchrotron radiation, such as those typically used for undulator radiation, are inadequate in describing the radiation spectra from electrons undergoing small numbers of oscillations. This is due to an improper treatment of a mathematical evaluation at the end points of an integration that leads to an unphysical plateau in the radiation spectrum at high frequencies, the magnitude of which increases as the number of oscillation periods decreases. This is important for betatron radiation from LPAs, in which the betatron strength parameter is large but the number of betatron periods is small. The code vdsr allows the radiation to be calculated in this regime by full integration over each electron trajectory, including end-point effects, and this code is used to calculate betatron radiation for cases of experimental interest. Radiation from Thomson scattering and Compton scattering is also studied with vdsr. For Thomson scattering, radiation reaction is included by using the Sokolov method for the calculation of the electron dynamics. For Compton scattering, quantum recoil effects are considered in vdsr by using Monte Carlo methods. The quantum calculation has been benchmarked with the classical calculation in a classical regime.

Trajectory calculation of a trapped particle in electro-dynamic balance for study of chemical reaction of aerosol particles

International Nuclear Information System (INIS)

Okuma, Miho; Itou, Takahiro; Harano, Azuchi; Takarada, Takayuki; James, Davis E

2013-01-01

Electrodynamic balance (EDB) is a powerful tool for investigating the chemical reactions between a fine particle and gaseous species. But the EDB device alone is inadequate to match the rapid weight change of a fine particle caused by chemical reactions, because it takes a few seconds to set a fine particle at null point. The particle trajectory calculation for the trapped particle added to the EDB is thus a very useful tool for the measurement of the transient response of a particle weight change with no need to adjust the applied DC voltage to set the null point. The purpose of this study is to develop the trajectory calculation method to track the particle oscillation pattern in the EDB and examine the possibility for kinetic studies on the reaction of a single aerosol particle with gaseous species. The results demonstrated the feasibility of applying particle trajectory calculation to realize the research purpose.

Quantum-Classical Correspondence Principle for Work Distributions

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Christopher Jarzynski

2015-09-01

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

Calculation of probabilities of rotational transitions of two-atom molecules in the collision with heavy particles

International Nuclear Information System (INIS)

Vargin, A.N.; Ganina, N.A.; Konyukhov, V.K.; Selyakov, V.I.

1975-01-01

The problem of calculation of collisional probabilities of rotational transitions (CPRT) in molecule-molecule and molecule-atom interactions in a three-dimensional space has been solved in this paper. A quasiclassical approach was used. The calculation of collisional probabilities of rotational transitions trajectory was carried out in the following way. The particle motion trajectory was calculated by a classical method and the time dependence of the perturbation operator was obtained, its averaging over wave functions of initial and finite states produced CPRT. The classical calculation of the molecule motion trajectory was justified by triviality of the de Broglie wavelength, compared with characteristic atomic distances, and by triviality of a transfered rotational quantum compared with the energy of translational motion of particles. The results of calculation depend on the chosen interaction potential of collisional particles. It follows from the Messy criterion that the region of nonadiabaticity of interaction may be compared with internuclear distances of a molecule. Therefore, for the description of the interaction a short-range potential is required. Analytical expressions were obtained appropriate for practical calculations for one- and two-quantum rotational transitions of diatomic molecules. The CPRT was averaged over the Maxwell distribution over velocities and analytical dependences on a gas temperature were obtained. The results of the numerical calculation of probabilities for the HCl-HCl, HCl-He, CO-CO interactions are presented to illustrate the method

Fluctuation theorems and atypical trajectories

International Nuclear Information System (INIS)

Sahoo, M; Lahiri, S; Jayannavar, A M

2011-01-01

In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.

Calculation of the spin-isospin response functions in an extended semi-classical theory

International Nuclear Information System (INIS)

Chanfray, G.

1987-01-01

We present a semi-classical calculation of the spin isospin response-functions beyond Thomas-Fermi theory. We show that surface-peaked ℎ 2 corrections reduce the collective effects predicted by Thomas-Fermi calculations. These effects, small for a volume response, become important for surface responses probed by hadrons. This yields a considerable improvement of the agreement with the (p, p') Los Alamos data

Absorption spectra for collinear (nonreactive) H3: Comparison between quantal and classical calculations

International Nuclear Information System (INIS)

Engel, V.; Bacic, Z.; Schinke, R.; Shapiro, M.

1985-01-01

Absorption spectra for the collinear (nonreactive) H+H 2 →H/sup number-sign/ 3 →H+H 2 are calculated quantum mechanically, using the Siegbahn--Liu--Truhlar--Horowitz (SLTH) ab initio potential and a model H( 3 surface as the ground and excited H 3 surface, respectively. They are compared to classical spectra previously computed by Mayne, Poirier, and Polanyi using the same potential energy surfaces [J. Chem. Phys. 80, 4025 (1984)]. The spectra are calculated at several collision energies and for both H+H 2 (v = 0) and H+H 2 (v = 1). The quantal and classical spectra are shown to agree with respect to basic features and trends. Nevertheless, the two sets of spectra differ considerably in their overall appearance because of some purely quantum aspects of the H+H 2 system

Trajectory calculations for the ternary cold fission of 252Cf

International Nuclear Information System (INIS)

Misicu, S.

1998-01-01

We compute the final kinetic energies of the fragments emitted in the light charged particle accompanied by cold fission of 252 Cf taking into account the deformation and the finite-size effects of the fragments and integrating the equations of motion for a three-body system subjected only to Coulomb forces. The initial conditions for the trajectory calculations were derived in the framework of a deformed cluster model which includes also the effect due to the absorbative nuclear part. Although the distributions of initial kinetic energies are rather broad we show that in cold fission the initial conditions can be better determined than in the usual spontaneous fission

Continuous quantum measurement and the quantum to classical transition

International Nuclear Information System (INIS)

Bhattacharya, Tanmoy; Habib, Salman; Jacobs, Kurt

2003-01-01

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

Importance sampling and histogrammic representations of reactivity functions and product distributions in Monte Carlo quasiclassical trajectory calculations

International Nuclear Information System (INIS)

Faist, M.B.; Muckerman, J.T.; Schubert, F.E.

1978-01-01

The application of importance sampling as a variance reduction technique in Monte Carlo quasiclassical trajectory calculations is discussed. Two measures are proposed which quantify the quality of the importance sampling used, and indicate whether further improvements may be obtained by some other choice of importance sampling function. A general procedure for constructing standardized histogrammic representations of differential functions which integrate to the appropriate integral value obtained from a trajectory calculation is presented. Two criteria for ''optimum'' binning of these histogrammic representations of differential functions are suggested. These are (1) that each bin makes an equal contribution to the integral value, and (2) each bin has the same relative error. Numerical examples illustrating these sampling and binning concepts are provided

Non-Born-Oppenheimer trajectories with self-consistent decay of mixing

International Nuclear Information System (INIS)

Zhu Chaoyuan; Jasper, Ahren W.; Truhlar, Donald G.

2004-01-01

A semiclassical trajectory method, called the self-consistent decay of mixing (SCDM) method, is presented for the treatment of electronically nonadiabatic dynamics. The SCDM method is a modification of the semiclassical Ehrenfest (SE) method (also called the semiclassical time-dependent self-consistent-field method) that solves the problem of unphysical mixed final states by including decay-of-mixing terms in the equations for the evolution of the electronic state populations. These terms generate a force, called the decoherent force (or dephasing force), that drives the electronic component of each trajectory toward a pure state. Results for several mixed quantum-classical methods, in particular the SCDM, SE, and natural-decay-of-mixing methods and several trajectory surface hopping methods, are compared to the results of accurate quantum mechanical calculations for 12 cases involving five different fully dimensional triatomic model systems. The SCDM method is found to be the most accurate of the methods tested. The method should be useful for the simulation of photochemical reactions

Classical and quantum mechanical studies of HF in an intense laser field

International Nuclear Information System (INIS)

Dardi, P.S.; Gray, S.K.

1982-01-01

The behavior of an HF molecule in an intense laser field is investigated with both classical trajectories and quantum dynamics. Vibration-rotation transition probabilities and energy absorption as a function of laser pulse time are calculated for the diatomic initially in its ground state. For comparison, results are also reported for a model nonrotating HF molecule. It is found that classical mechanics does not predict the correct time behavior of the system, nor does it predict the correct rotational state distributions. Classical mechanics does, however, predict pulse time averaged quantities to be the correct order of magnitude. There is also a correct general trend of increased multiphoton excitation for laser frequencies red-shifted from the one-photon resonance, although multiphoton resonance peaks are not observed in the classical results and far too little multiphoton excitation is predicted. The effect of laser phase has also been investigated and shown to be relatively unimportant in both the classical and quantum dynamics

Classical Methods and Calculation Algorithms for Determining Lime Requirements

Directory of Open Access Journals (Sweden)

André Guarçoni

Full Text Available ABSTRACT The methods developed for determination of lime requirements (LR are based on widely accepted principles. However, the formulas used for calculation have evolved little over recent decades, and in some cases there are indications of their inadequacy. The aim of this study was to compare the lime requirements calculated by three classic formulas and three algorithms, defining those most appropriate for supplying Ca and Mg to coffee plants and the smaller possibility of causing overliming. The database used contained 600 soil samples, which were collected in coffee plantings. The LR was estimated by the methods of base saturation, neutralization of Al3+, and elevation of Ca2+ and Mg2+ contents (two formulas and by the three calculation algorithms. Averages of the lime requirements were compared, determining the frequency distribution of the 600 lime requirements (LR estimated through each calculation method. In soils with low cation exchange capacity at pH 7, the base saturation method may fail to adequately supply the plants with Ca and Mg in many situations, while the method of Al3+ neutralization and elevation of Ca2+ and Mg2+ contents can result in the calculation of application rates that will increase the pH above the suitable range. Among the methods studied for calculating lime requirements, the algorithm that predicts reaching a defined base saturation, with adequate Ca and Mg supply and the maximum application rate limited to the H+Al value, proved to be the most efficient calculation method, and it can be recommended for use in numerous crops conditions.

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

Science.gov (United States)

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 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.

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

International Nuclear Information System (INIS)

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

2012-01-01

Room-temperature N 2 -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 CH 3 Cl-N 2 system. The excellent agreement between the theoretical and the experimental results ensures the reliability of these data.

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

Science.gov (United States)

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.

Quantum flesh on classical bones: Semiclassical bridges across the quantum-classical divide

Energy Technology Data Exchange (ETDEWEB)

Bokulich, Alisa [Center for Philosophy and History of Science, Boston University, Boston, MA (United States)

2014-07-01

Traditionally quantum mechanics is viewed as having made a sharp break from classical mechanics, and the concepts and methods of these two theories are viewed as incommensurable with one another. A closer examination of the history of quantum mechanics, however, reveals that there is a strong sense in which quantum mechanics was built on the backbone of classical mechanics. As a result, there is a considerable structural continuity between these two theories, despite their important differences. These structural continuities provide a ground for semiclassical methods in which classical structures, such as trajectories, are used to investigate and model quantum phenomena. After briefly tracing the history of semiclassical approaches, I show how current research in semiclassical mechanics is revealing new bridges across the quantum-classical divide.

Transition to classical chaos in a coupled quantum system through continuous measurement

International Nuclear Information System (INIS)

Ghose, Shohini; Alsing, Paul; Deutsch, Ivan; Bhattacharya, Tanmoy; Habib, Salman

2004-01-01

Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough that quantum backaction noise is negligible. We investigate the conditions under which classical dynamics emerges, via a continuous position measurement, for a particle moving in a harmonic well with its position coupled to internal spin. As a consequence of this coupling, we find that classical dynamics emerges only when the position and spin actions are both large compared to (ℎ/2π). These conditions are quantified by placing bounds on the size of the covariance matrix which describes the delocalized quantum coherence over extended regions of phase space. From this result, it follows that a mixed quantum-classical regime (where one subsystem can be treated classically and the other not) does not exist for a continuously observed spin-(1/2) particle. When the conditions for classicality are satisfied (in the large-spin limit), the quantum trajectories reproduce both the classical periodic orbits as well as the classically chaotic phase space regions. As a quantitative test of this convergence, we compute the largest Lyapunov exponent directly from the measured quantum trajectories and show that it agrees with the classical value

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

Science.gov (United States)

Dimitroulis, Christos; Raptis, Theophanes; Raptis, Vasilios

2015-12-01

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

Seven steps towards the classical world

International Nuclear Information System (INIS)

Allori, Valia; Duerr, Detlef; Goldstein, Shelly; Zanghi, Nino

2002-01-01

Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard quantum mechanics only the wavefunctions or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical limit becomes very simple: when do the Bohmian trajectories look Newtonian?

Calculation of Coherent Synchrotron Radiation Impedance for a Beam Moving in a Curved Trajectory

Science.gov (United States)

Zhou, Demin; Ohmi, Kazuhito; Oide, Katsunobu; Zang, Lei; Stupakov, Gennady

2012-01-01

Coherent synchrotron radiation (CSR) fields are generated when a bunched beam moves along a curved trajectory. A new code, named CSRZ, was developed using finite difference method to calculate the longitudinal CSR impedance for a beam moving along a curved chamber. The method adopted in the code was originated by Agoh and Yokoya [Phys. Rev. ST Accel. Beams 7 (2004) 054403]. It solves the parabolic equation in the frequency domain in a curvilinear coordinate system. The chamber considered has uniform rectangular cross-section along the beam trajectory. The code was used to investigate the properties of CSR impedance of a single or a series of bending magnets. The calculation results indicate that the shielding effect due to outer chamber wall can be well explained by a simple optical approximation model at high frequencies. The CSR fields reflected by the outer wall may interfere with each other along a series of bending magnets and lead to sharp narrow peaks in the CSR impedance. In a small storage ring, such interference effect can be significant and may cause microwave instability, according to a simple estimate of instability threshold.

Quantum and classical studies of collisional excitation in H + CO and two other projects in theoretical chemical dynamics

International Nuclear Information System (INIS)

Geiger, L.C.

1985-01-01

This dissertation is a collection of four projects in theoretical chemical dynamics. In the first two projects collisional excitation in H + CO was studied using the quasiclassical trajectory method and the quantum infinite order sudden approximation (QIOS). Integral cross sections calculated using these methods were found to agree well with experimental and classical IOS results. The trajectory study was also used to examine the effects of potential energy surface features on the dynamics. Two surfaces were examined: a fitted surface based on ab initio points and a global ab initio surface. Next, the quasiclassical trajectory method was used to obtain cross sections and rate constants for O + H 2 → OH + H and analogous deuterium isotope reactions. The results using the Johnson and Winter surface agreed well with those of transition state theory (TST) and experiment, except for O + HD → OH + D. TST rate constants were calculated using an ab initio surface. These results were in poor agreement with calculations using the Johnson and Winter surface. A theory of action-angle variables for coupled oscillator systems was developed in the fourth project

Calculation of the level density parameter using semi-classical approach

International Nuclear Information System (INIS)

Canbula, B.; Babacan, H.

2011-01-01

The level density parameters (level density parameter a and energy shift δ) for back-shifted Fermi gas model have been determined for 1136 nuclei for which complete level scheme is available. Level density parameter is calculated by using the semi-classical single particle level density, which can be obtained analytically through spherical harmonic oscillator potential. This method also enables us to analyze the Coulomb potential's effect on the level density parameter. The dependence of this parameter on energy has been also investigated. Another parameter, δ, is determined by fitting of the experimental level scheme and the average resonance spacings for 289 nuclei. Only level scheme is used for optimization procedure for remaining 847 nuclei. Level densities for some nuclei have been calculated by using these parameter values. Obtained results have been compared with the experimental level scheme and the resonance spacing data.

Galileo's Trajectory with Mild Resistance

Science.gov (United States)

Groetsch, C. W.

2012-01-01

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

Emergence of classical theories from quantum mechanics

International Nuclear Information System (INIS)

Hájícek, P

2012-01-01

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's 'first kind of dynamics', and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

Semi-classical approximation and the problem of boundary conditions in the theory of relativistic particle radiation

International Nuclear Information System (INIS)

Akhiezer, A.I.; Shul'ga, N.F.

1991-01-01

The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is in expressing the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation. We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation. The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics. (author)

CTMC calculation of Si2+ + H impact ionization

International Nuclear Information System (INIS)

Liu Chunlei; He Bin; Ning Ye; Yan Jun; Wang Jianguo

2005-01-01

The Si 2+ + H collision ionization is studied using classical trajectory Monte-Carlo (CTMC) method. The total cross section as functions of the energy of incident projectile, single differential cross section and double differential cross section as a functions of the energy and the angle of the ejected electron are calculated. The ionization mechanisms of soft collision, electron capture to the continuum state, binary encounter collision are demonstrated. The effect of 'saddle point' is also discussed by calculating the ejected electron distribution depending on the ratios of distances between electron and target and between electron and projectile. (author)

Calculation of trajectory parameters of long pass in basketball.

Directory of Open Access Journals (Sweden)

Charikova K.M.

2011-08-01

Full Text Available Values of a ball's flight trajectory parameters depending on a distance of long pass, a corner of a ball's start and height of a throwing point are submitted in article. Coordinates of reference points installation for training to long pass with an optimum trajectory of a ball's flight are designed. Requirements to simulators design are determined. Corners of ball's long pass performance in various game situations are recommended.

Soccer ball lift coefficients via trajectory analysis

International Nuclear Information System (INIS)

Goff, John Eric; Carre, Matt J

2010-01-01

We performed experiments in which a soccer ball was launched from a machine while two high-speed cameras recorded portions of the trajectory. Using the trajectory data and published drag coefficients, we extracted lift coefficients for a soccer ball. We determined lift coefficients for a wide range of spin parameters, including several spin parameters that have not been obtained by today's wind tunnels. Our trajectory analysis technique is not only a valuable tool for professional sports scientists, it is also accessible to students with a background in undergraduate-level classical mechanics.

Soccer ball lift coefficients via trajectory analysis

Energy Technology Data Exchange (ETDEWEB)

Goff, John Eric [Department of Physics, Lynchburg College, Lynchburg, VA 24501 (United States); Carre, Matt J, E-mail: goff@lynchburg.ed [Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD (United Kingdom)

2010-07-15

We performed experiments in which a soccer ball was launched from a machine while two high-speed cameras recorded portions of the trajectory. Using the trajectory data and published drag coefficients, we extracted lift coefficients for a soccer ball. We determined lift coefficients for a wide range of spin parameters, including several spin parameters that have not been obtained by today's wind tunnels. Our trajectory analysis technique is not only a valuable tool for professional sports scientists, it is also accessible to students with a background in undergraduate-level classical mechanics.

TRAJ - a FORTRAN 77 computer program for the calculation of trajectories on the basis of space and time varying velocity fields

International Nuclear Information System (INIS)

Zimmer, J.

1986-09-01

The computation of three dimensional trajectories is described in this report. Since measurements of the position and velocity of individual fluid parcels are difficult to be carried out and analytic solutions applicable to the trajectory problem are not available, trajectories have to be calculated by successive observations of the corresponding velocity fields using a method of successive approximation. The application is restricted to cartesian grid coordinate system with equidistant grid points. This model was developed for meteorological purposes (transport of pollutants) but can also be used for other fluids and scales. (orig./PW) [de

Technical description of the RIVM trajectory model

Energy Technology Data Exchange (ETDEWEB)

De Waal, E.S.; Van Pul, W.A.J.

1995-12-01

The RIVM trajectory model, described in this report, enables calculation of a backward or forward trajectory. These trajectories are used to `follow` previous released air pollution in a backward mode or to `find` the origin of air pollution in a forward mode. The trajectories are used in the smog forecasting and in the TREND model for the distribution of materials in Europe. Presently 6-hourly ECMWF wind fields at 1000 and 850 hPa, with 3 deg x 3 deg latitude-longitude resolution are used. Wind fields with a different resolution in latitude-longitude can also be used after simple adjustments. An iterative method, described elsewhere, is applied to calculate the trajectories. Within limits, the user is free to choose the time step (1, 2 or 6-hour), transport height, length, starting or arrival date and starting or arrival position of the trajectory. The differences between the trajectories calculated with time steps of 1, 2 and 6 h were small. For the 96-hour trajectories at 1000 and 850 hPa the deviations were generally within 1 deg latitude and longitude, i.e. 100-200 km. The trajectory calculated with the 6-hour time step could be used without a great loss in accuracy compared to the calculations with the 1-hour time step. A typical error in the trajectory path at 1000 and 850 hPa was 500 km, which is about 30% of a typical travel distance. However, close to quickly changing weather systems, such as cyclones, the error can be as large as the travel distance and makes the calculations unreliable. The error in the forecasted trajectory was found to be larger than the above error estimation due to larger uncertainties in the forecasted compared to the analyzed wind fields. A manual on how to run the model is also given. 5 figs., 3 tabs., 5 refs., 6 appendices

A classical trajectory study of the photodissociation of T1 acetaldehyde: The transition from impulsive to statistical dynamics

International Nuclear Information System (INIS)

Thompson, Keiran C.; Crittenden, Deborah L.; Kable, Scott H.; Jordan, Meredith J.T.

2006-01-01

Previous experimental and theoretical studies of the radical dissociation channel of T 1 acetaldehyde show conflicting behavior in the HCO and CH 3 product distributions. To resolve these conflicts, a full-dimensional potential-energy surface for the dissociation of CH 3 CHO into HCO and CH 3 fragments over the barrier on the T 1 surface is developed based on RO-CCSD(T)/cc-pVTZ(DZ) ab initio calculations. 20 000 classical trajectories are calculated on this surface at each of five initial excess energies, spanning the excitation energies used in previous experimental studies, and translational, vibrational, and rotational distributions of the radical products are determined. For excess energies near the dissociation threshold, both the HCO and CH 3 products are vibrationally cold; there is a small amount of HCO rotational excitation and little CH 3 rotational excitation, and the reaction energy is partitioned dominantly (>90% at threshold) into relative translational motion. Close to threshold the HCO and CH 3 rotational distributions are symmetrically shaped, resembling a Gaussian function, in agreement with observed experimental HCO rotational distributions. As the excess energy increases the calculated HCO and CH 3 rotational distributions are observed to change from a Gaussian shape at threshold to one more resembling a Boltzmann distribution, a behavior also seen by various experimental groups. Thus the distribution of energy in these rotational degrees of freedom is observed to change from nonstatistical to apparently statistical, as excess energy increases. As the energy above threshold increases all the internal and external degrees of freedom are observed to gain population at a similar rate, broadly consistent with equipartitioning of the available energy at the transition state. These observations generally support the practice of separating the reaction dynamics into two reservoirs: an impulsive reservoir, fed by the exit channel dynamics, and a

Classical and semiclassical aspects of chemical dynamics

International Nuclear Information System (INIS)

Gray, S.K.

1982-08-01

Tunneling in the unimolecular reactions H 2 C 2 → HC 2 H, HNC → HCN, and H 2 CO → H 2 + CO is studied with a classical Hamiltonian that allows the reaction coordinate and transverse vibrational modes to be considered directly. A combination of classical perturbation theory and the semiclassical WKB method allows tunneling probabilities to be obtained, and a statistical theory (RRKM) is used to construct rate constants for these reactions in the tunneling regime. In this fashion, it is found that tunneling may be important, particularly for low excitation energies. Nonadiabatic charge transfer in the reaction Na + I → Na + + I - is treated with classical trajectories based on a classical Hamiltonian that is the analogue of a quantum matrix representation. The charge transfer cross section obtained is found to agree reasonably well with the exact quantum results. An approximate semiclassical formula, valid at high energies, is also obtained. The interaction of radiation and matter is treated from a classical viewpoint. The excitation of an HF molecule in a strong laser is described with classical trajectories. Quantum mechanical results are also obtained and compared to the classical results. Although the detailed structure of the pulse time averaged energy absorption cannot be reproduced classically, classical mechanics does predict the correct magnitude of energy absorption, as well as certain other qualitative features. The classical behavior of a nonrotating diatomic molecule in a strong laser field is considered further, by generating a period advance map that allows the solution over many periods of oscillation of the laser to be obtained with relative ease. Classical states are found to form beautiful spirals in phase space as time progresses. A simple pendulum model is found to describe the major qualitative features

Three-dimensional classical-ensemble modeling of non-sequential double ionization

International Nuclear Information System (INIS)

Haan, S.L.; Breen, L.; Tannor, D.; Panfili, R.; Ho, Phay J.; Eberly, J.H.

2005-01-01

Full text: We have been using 1d ensembles of classical two-electron atoms to simulate helium atoms that are exposed to pulses of intense laser radiation. In this talk we discuss the challenges in setting up a 3d classical ensemble that can mimic the quantum ground state of helium. We then report studies in which each one of 500,000 two-electron trajectories is followed in 3d through a ten-cycle (25 fs) 780 nm laser pulse. We examine double-ionization yield for various intensities, finding the familiar knee structure. We consider the momentum spread of outcoming electrons in directions both parallel and perpendicular to the direction of laser polarization, and find results that are consistent with experiment. We examine individual trajectories and recollision processes that lead to double ionization, considering the best phases of the laser cycle for recollision events and looking at the possible time delay between recollision and emergence. We consider also the number of recollision events, and find that multiple recollisions are common in the classical ensemble. We investigate which collisional processes lead to various final electron momenta. We conclude with comments regarding the ability of classical mechanics to describe non-sequential double ionization, and a quick summary of similarities and differences between 1d and 3d classical double ionization using energy-trajectory comparisons. Refs. 3 (author)

Accurate Calculations of Rotationally Inelastic Scattering Cross Sections Using Mixed Quantum/Classical Theory.

Science.gov (United States)

Semenov, Alexander; Babikov, Dmitri

2014-01-16

For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with full-quantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the full-quantum framework.

A classical trajectory study of the adatom -surface bond dissociation in the collision reaction between an adsorbed H atom and an N2 molecule

International Nuclear Information System (INIS)

Bayhan, U.

2005-01-01

The collisionnal dissociation of the Adatom-Surface bond in the diatomic molecule N2(gas)/H(ads) collision taking place on a W(100) bcc-structure surface have been studied by classical trajectory method over the collision energy ranges (0.1-2.0 eV ) and the attractive well depth (0.19-4.0 eV). of the N2 molecule (gas)/H(ads) interactions. When the energy accumulate into the adatom bond, thus leading to a a large dissociation probability

Classical Music Clustering Based on Acoustic Features

OpenAIRE

Wang, Xindi; Haque, Syed Arefinul

2017-01-01

In this paper we cluster 330 classical music pieces collected from MusicNet database based on their musical note sequence. We use shingling and chord trajectory matrices to create signature for each music piece and performed spectral clustering to find the clusters. Based on different resolution, the output clusters distinctively indicate composition from different classical music era and different composing style of the musicians.

PERL-2 and LAVR-2 programs for Monte Carlo calculation of reactivity disturbances with trajectory correlation using random numbers

International Nuclear Information System (INIS)

Kamaeva, O.B.; Polevoj, V.B.

1983-01-01

Realization of BESM-6 computer of a technique is described for calculating a wide class of reactivity disturbances by plotting trajectories in undisturbed and disturbed systems using one sequence of random numbers. The technique was realized on the base of earlier created programs of calculation of widespreed (PERL) and local (LAVR) reactivity disturbances. The efficiency of the technique and programs is demonstrated by calculation of change of effective neutron-multiplication factor when absorber is substituted for fuel element in a BFS-40 critical assembly and by calculation of control drum characteristics

Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

Science.gov (United States)

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.

Effects of complex parameters on classical trajectories of ...

Indian Academy of Sciences (India)

2Permanent address: Department of Mathematics, University of Jaffna, Jaffna, Sri Lanka. ∗ ... is complex and k = 1 or 2) are closed and periodic only for a discrete set of parameter curves in the complex b-plane. ... are periodic for a discrete set of real energies (i.e., classical energy gets discretized or quantized by imposing ...

Conduction bands in classical periodic potentials

Indian Academy of Sciences (India)

is an infinite amount of time to perform the measurement. This paper ... the observation that when the energy is real, the classical trajectories in the com- plex plane are .... Figure 4 shows that the particle can travel smoothly from one well to the ...

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

Science.gov (United States)

Paul, Amit K; Hase, William L

2016-01-28

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

Classical analog for electronic degrees of freedom in nonadiabatic collision processes

International Nuclear Information System (INIS)

Meyer, H.; Miller, W.H.

1979-01-01

It is shown how a formally exact classical analog can be defined for a finite dimensional (in Hilbert space) quantum mechanical system. This approach is then used to obtain a classical model for the electronic degrees of freedom in a molecular collision system, and the combination of this with the usual classical description of the heavy particle (i.e., nuclear) motion provides a completely classical model for the electronic and heavy particle degrees of freedom. The resulting equations of motion are shown to be equivalent to describing the electronic degrees of freedom by the time-dependent Schroedinger equation, the time dependence arising from the classical motion of the nuclei, the trajectory of which is determined by the quantum mechanical average (i.e., Ehrenfest) force on the nuclei. Quantizing the system via classical S-matrix theory is shown to provide a dynamically consistent description of nonadiabatic collision processes; i.e., different electronic transitions have different heavy particle trajectories and, for example, the total energy of the electronic and heavy particle degrees of freedom is conserved. Application of this classical model for the electronic degrees of freedom (plus classical S-matrix theory) to the two-state model problem shows that the approach provides a good description of the electronic dynamics

Quasi-classical trajectory approach to the O(1D)+HBr→OH+Br reaction stereo-dynamics on X1A' potential energy surface

International Nuclear Information System (INIS)

Li Hong; Zheng Bin; Yin Ji-Qing; Meng Qing-Tian

2011-01-01

The vector properties of reaction O( 1 D)+HBr→OH+Br on the potential energy surface (PES) of X 1 A' ground singlet state are studied by using the quasi-classical trajectory (QCT) theory. The polarization-dependent differential cross sections (PDDCSs), the average rotational alignment factor 2 (j' · k)>, as well as the distributions reflecting vector correlations are also computed. The analysis of the results shows that the alignment and the orientation distribution of the rotation angular momentum vector of product molecule OH is influenced by both the effect of heavy—light—heavy (HLH) type mass combination and the deep well of PES. (atomic and molecular physics)

Dissociation of acetone radical cation (CH3COCH3(+*) --> CH3CO(+) + CH3(*)): an ab initio direct classical trajectory study of the energy dependence of the branching ratio.

Science.gov (United States)

Zhou, Jia; Schlegel, H Bernhard

2008-12-18

The nonstatistical dissociation of acetone radical cation has been studied by ab initio direct classical trajectory calculations at the MP2/6-31G(d) level of theory. A bond additivity correction has been used to improve the MP2 potential energy surface (BAC-MP2). The energy dependence of the branching ratio, dissociation kinetics, and translational energy distribution for the two types of methyl groups have been investigated using microcanonical ensembles and specific mode excitation. In each case, the dissociation favors the loss of the newly formed methyl group, in agreement with the experiments. For microcanonical ensembles, the branching ratios for methyl loss are calculated to be 1.43, 1.88, 1.70, and 1.50 for 1, 2, 10, and 18 kcal/mol of excess energy, respectively. The energy dependence of the branching ratio is seen more dramatically in the excitation of individual modes involving C-C-O bending. For modes 3 and 6, the branching ratio rises to 1.6 and 1.8-2.3 when 1 or 2 kcal/mol are added, respectively, but falls off when more energy is added. For mode 8, the branching ratio continues to rise monotonically from 1.5 to 2.76 when 1-8 kcal/mol of excess energy are added.

Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution

Directory of Open Access Journals (Sweden)

Yuri V. Kovchegov

2016-02-01

Full Text Available We set up a formalism for calculating transverse-momentum-dependent parton distribution functions (TMDs of a large nucleus using the tools of saturation physics. By generalizing the quasi-classical Glauber–Gribov–Mueller/McLerran–Venugopalan approximation to allow for the possibility of spin–orbit coupling, we show how any TMD can be calculated in the saturation framework. This can also be applied to the TMDs of a proton by modeling it as a large “nucleus.” To illustrate our technique, we calculate the quark TMDs of an unpolarized nucleus at large-x: the unpolarized quark distribution and the quark Boer–Mulders distribution. We observe that spin–orbit coupling leads to mixing between different TMDs of the nucleus and of the nucleons. We then consider the evolution of TMDs: at large-x, in the double-logarithmic approximation, we obtain the Sudakov form factor. At small-x the evolution of unpolarized-target quark TMDs is governed by BK/JIMWLK evolution, while the small-x evolution of polarized-target quark TMDs appears to be dominated by the QCD Reggeon.

Progress in the application of classical S-matrix theory to inelastic collision processes

International Nuclear Information System (INIS)

McCurdy, C.W.; Miller, W.H.

1980-01-01

Methods are described which effectively solve two of the technical difficulties associated with applying classical S-matrix theory to inelastic/reactive scattering. Specifically, it is shown that rather standard numerical methods can be used to solve the ''root search'' problem (i.e., the nonlinear boundary value problem necessary to impose semiclassical quantum conditions at the beginning and the end of the classical trajectories) and also how complex classical trajectories, which are necessary to describe classically forbidden (i.e., tunneling) processes, can be computed in a numerically stable way. Application is made to vibrational relaxation of H 2 by collision with He (within the helicity conserving approximation). The only remaining problem with regard to applying classical S-matrix theory to complex collision processes has to do with the availability of multidimensional uniform asymptotic formulas for interpolating the ''primitive'' semiclassical expressions between their various regions of validity

Classical-driving-assisted entanglement dynamics control

Energy Technology Data Exchange (ETDEWEB)

Zhang, Ying-Jie, E-mail: yingjiezhang@qfnu.edu.cn [Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165 (China); Han, Wei [Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165 (China); Xia, Yun-Jie, E-mail: yjxia@qfnu.edu.cn [Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165 (China); Fan, Heng, E-mail: hfan@iphy.ac.cn [Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 (China); Collaborative Innovation Center of Quantum Matter, Beijing, 100190 (China)

2017-04-15

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 entanglement 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.

The equivalence principle in classical mechanics and quantum mechanics

OpenAIRE

Mannheim, Philip D.

1998-01-01

We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all.

Conditions for the classicality of the center of mass of many-particle quantum states

International Nuclear Information System (INIS)

Oriols, Xavier; Benseny, Albert

2017-01-01

We discuss the conditions for the classicality of quantum states with a very large number of identical particles. By defining the center of mass from a large set of Bohmian particles, we show that it follows a classical trajectory when the distribution of the Bohmian particle positions in a single experiment is always equal to the marginal distribution of the quantum state in physical space. This result can also be interpreted as a single experiment generalization of the well-known Ehrenfest theorem. We also demonstrate that the classical trajectory of the center of mass is fully compatible with a quantum (conditional) wave function solution of a classical non-linear Schrödinger equation. Our work shows clear evidence for a quantum–classical inter-theory unification, and opens new possibilities for practical quantum computations with decoherence. (paper)

The dynamics of the H(+) + D(2) reaction: a comparison of quantum mechanical wavepacket, quasi-classical and statistical-quasi-classical results.

Science.gov (United States)

Jambrina, P G; Aoiz, F J; Bulut, N; Smith, Sean C; Balint-Kurti, G G; Hankel, M

2010-02-07

A detailed study of the proton exchange reaction H(+) + D(2)(v = 0, j = 0) --> HD + D(+) on its ground 1(1)A' potential energy surface has been carried out using 'exact' close-coupled quantum mechanical wavepacket (WP-EQM), quasi-classical trajectory (QCT), and statistical quasi-classical trajectory (SQCT) calculations for a range of collision energies starting from the reaction threshold to 1.3 eV. The WP-EQM calculations include all total angular momenta up to J(max) = 50, and therefore the various dynamical observables are converged up to 0.6 eV. It has been found that it is necessary to include all Coriolis couplings to obtain reliable converged results. Reaction probabilities obtained using the different methods are thoroughly compared as a function of the total energy for a series of J values. Comparisons are also made of total reaction cross sections as function of the collision energy, and rate constants. In addition, opacity functions, integral cross sections (ICS) and differential cross sections (DCS) are presented at 102 meV, 201.3 meV and 524.6 meV collision energy. The agreement between the three sets of results is only qualitative. The QCT calculations fail to describe the overall reactivity and most of the dynamical observables correctly. At low collision energies, the QCT method is plagued by the lack of conservation of zero point energy, whilst at higher collision energies and/or total angular momenta, the appearance of an effective repulsive potential associated with the centrifugal motion "over" the well causes a substantial decrease of the reactivity. In turn, the statistical models overestimate the reactivity over the whole range of collision energies as compared with the WP-EQM method. Specifically, at sufficiently high collision energies the reaction cannot be deemed to be statistical and important dynamical effects seem to be present. In general the WP-EQM results lie in between those obtained using the QCT and SQCT methods. One of the main

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

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

2016-10-15

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 for 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.

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

International Nuclear Information System (INIS)

Chou, Chia-Chun

2016-01-01

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 for 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.

Lorentz invariance from classical particle paths in quantum field theory of electric and magnetic charge

International Nuclear Information System (INIS)

Brandt, R.A.; Neri, F.; Zwanziger, D.

1979-01-01

We establish the Lorentz invariance of the quantum field theory of electric and magnetic charge. This is a priori implausible because the theory is the second-quantized version of a classical field theory which is inconsistent if the minimally coupled charged fields are smooth functions. For our proof we express the generating functional for the gauge-invariant Green's functions of quantum electrodynamics: with or without magnetic charge: as a path integral over the trajectories of classical charged point particles. The electric-electric and electric-magnetic interactions contribute factors exp(JDJ) and exp(JD'K), where J and K are the electric and magnetic currents of classical point particles and D is the usual photon propagator. The propagator D' involves the Dirac string but exp(JD'K) depends on it only through a topological integer linking string and classical particle trajectories. The charge quantization condition e/sub i/g/sub j/ - g/sub i/e/sub j/ = integer then suffices to make the gauge-invariant Green's functions string independent. By implication our formulation shows that if the Green's functions of quantum electrodynamics are expressed as usual as functional integrals over classical charged fields, the smooth field configurations have measure zero and all the support of the Feynman measure lies on the trajectories of classical point particles

Classical calculation of the total ionization energy of helium-like atoms

International Nuclear Information System (INIS)

Karastoyanov, A.

1990-01-01

Quantum mechanics rejects the classical modelling of microworld. One of the reasons is that the Bohr's rules can not be applied for many-electron atoms and molecules. But the many-body problem in classical mechanics has no analytical solution even for 3 particles. Numerical solutions should be used. The quantum Bohr's rule expressing the moment of momentum conservation for two particles is invalid in more complicated cases. Yet Bohr reached some success for helium-like atoms. The Bohr's formula concerning helim-like atoms is deduced again in this paper and its practical reliability is analyzed with contemporary data. The binding energy of the system is obtained in the simple form E=(Z-1/4) 2 α 2 mc 2 , where Z is the atomic number, α - the fine structure constant, M - the electron mass and c - the light speed in vacuum. The calculated values are compared with experimental data on the total ionization energy of the helium-like atoms from 2 He 4 to 29 Cu 64 . The error decreases quickly with the increasing of atomic mass, reaching zero for Cu. This indicated that the main source of error is the nucleus motion. The role of other possible causes is analyzed and proves negligible. (author). 1 tab, 4 refs

FPGA Implementation of an Efficient Algorithm for the Calculation of Charged Particle Trajectories in Cosmic Ray Detectors

Science.gov (United States)

Villar, Xabier; Piso, Daniel; Bruguera, Javier D.

2014-02-01

This paper presents an FPGA implementation of an algorithm, previously published, for the the reconstruction of cosmic rays' trajectories and the determination of the time of arrival and velocity of the particles. The accuracy and precision issues of the algorithm have been analyzed to propose a suitable implementation. Thus, a 32-bit fixed-point format has been used for the representation of the data values. Moreover, the dependencies among the different operations have been taken into account to obtain a highly parallel and efficient hardware implementation. The final hardware architecture requires 18 cycles to process every particle, and has been exhaustively simulated to validate all the design decisions. The architecture has been mapped over different commercial FPGAs, with a frequency of operation ranging from 300 MHz to 1.3 GHz, depending on the FPGA being used. Consequently, the number of particle trajectories processed per second is between 16 million and 72 million. The high number of particle trajectories calculated per second shows that the proposed FPGA implementation might be used also in high rate environments such as those found in particle and nuclear physics experiments.

Classical Calculations of Scattering Signatures from a Gravitational ...

Indian Academy of Sciences (India)

The objective of this section is to compile the relevant equations to compute the trajectories and the scattering cross-sections for objects with small velocities (with respect to the speed of light) and with large impact parameters (in Schwarzschild radius units), s >> sl. We are going to reference later these equations as the limit.

An hydrodynamic model for the calculation of oil spills trajectories

Energy Technology Data Exchange (ETDEWEB)

Paladino, Emilio Ernesto; Maliska, Clovis Raimundo [Santa Catarina Univ., Florianopolis, SC (Brazil). Dept. de Engenharia Mecanica. Lab. de Dinamica dos Fluidos Computacionais]. E-mails: emilio@sinmec.ufsc.br; maliska@sinmec.ufsc.br

2000-07-01

The aim of this paper is to present a mathematical model and its numerical treatment to forecast oil spills trajectories in the sea. The knowledge of the trajectory followed by an oil slick spilled on the sea is of fundamental importance in the estimation of potential risks for pipeline and tankers route selection, and in combating the pollution using floating barriers, detergents, etc. In order to estimate these slicks trajectories a new model, based on the mass and momentum conservation equations is presented. The model considers the spreading in the regimes when the inertial and viscous forces counterbalance gravity and takes into account the effects of winds and water currents. The inertial forces are considered for the spreading and the displacement of the oil slick, i.e., is considered its effects on the movement of the mass center of the slick. The mass loss caused by oil evaporation is also taken into account. The numerical model is developed in generalized coordinates, making the model easily applicable to complex coastal geographies. (author)

Semiclassical approach to mesoscopic systems classical trajectory correlations and wave interference

CERN Document Server

Waltner, Daniel

2012-01-01

This volume describes mesoscopic systems with classically chaotic dynamics using semiclassical methods which combine elements of classical dynamics and quantum interference effects. Experiments and numerical studies show that Random Matrix Theory (RMT) explains physical properties of these systems well. This was conjectured more than 25 years ago by Bohigas, Giannoni and Schmit for the spectral properties. Since then, it has been a challenge to understand this connection analytically.  The author offers his readers a clearly-written and up-to-date treatment of the topics covered. He extends previous semiclassical approaches that treated spectral and conductance properties. He shows that RMT results can in general only be obtained semiclassically when taking into account classical configurations not considered previously, for example those containing multiply traversed periodic orbits. Furthermore, semiclassics is capable of describing effects beyond RMT. In this context he studies the effect of a non-zero Eh...

OPTIMAL AIRCRAFT TRAJECTORIES FOR SPECIFIED RANGE

Science.gov (United States)

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

Collective probabilities algorithm for surface hopping calculations

International Nuclear Information System (INIS)

Bastida, Adolfo; Cruz, Carlos; Zuniga, Jose; Requena, Alberto

2003-01-01

General equations that transition probabilities of the hopping algorithms in surface hopping calculations must obey to assure the equality between the average quantum and classical populations are derived. These equations are solved for two particular cases. In the first it is assumed that probabilities are the same for all trajectories and that the number of hops is kept to a minimum. These assumptions specify the collective probabilities (CP) algorithm, for which the transition probabilities depend on the average populations for all trajectories. In the second case, the probabilities for each trajectory are supposed to be completely independent of the results from the other trajectories. There is, then, a unique solution of the general equations assuring that the transition probabilities are equal to the quantum population of the target state, which is referred to as the independent probabilities (IP) algorithm. The fewest switches (FS) algorithm developed by Tully is accordingly understood as an approximate hopping algorithm which takes elements from the accurate CP and IP solutions. A numerical test of all these hopping algorithms is carried out for a one-dimensional two-state problem with two avoiding crossings which shows the accuracy and computational efficiency of the collective probabilities algorithm proposed, the limitations of the FS algorithm and the similarity between the results offered by the IP algorithm and those obtained with the Ehrenfest method

Does the classically chaotic Henon–Heiles oscillator exhibit ...

Indian Academy of Sciences (India)

–12]. In contrast to a classically chaotic system, where the exponential divergence of trajectories in phase-space is an unambiguous and confirmatory signature of chaos. [15–17], the decision about whether a quantum system is chaotic or not is ...

Surface-hopping trajectories for OH(A{sup 2}Σ{sup +}) + Kr: Extension to the 1A″ state

Energy Technology Data Exchange (ETDEWEB)

Perkins, T.; McCrudden, G.; Brouard, M., E-mail: mark.brouard@chem.ox.ac.uk [The Department of Chemistry, The Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ (United Kingdom); Herráez-Aguilar, D.; Aoiz, F.J., E-mail: aoiz@quim.ucm.es [Departamento de Química Física, Facultad de Química, Universidad Complutense, 28040 Madrid (Spain); Kłos, J., E-mail: jklos@umd.edu [Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742 (United States)

2015-04-14

We present a new trajectory surface hopping study of the rotational energy transfer and collisional quenching of electronically excited OH(A) radicals by Kr. The trajectory surface hopping calculations include both electronic coupling between the excited 2{sup 2}A′ and ground 1{sup 2}A′ electronic states, as well as Renner-Teller and Coriolis roto-electronic couplings between the 1{sup 2}A′ and 1{sup 2}A″, and the 2{sup 2}A′ and 1{sup 2}A″ electronic states, respectively. The new calculations are shown to lead to a noticeable improvement in the agreement between theory and experiment in this system, particularly with respect to the OH(X) rotational and Λ-doublet quantum state populations, compared with a simpler two-state treatment, which only included the electronic coupling between the 2{sup 2}A′ and 1{sup 2}A′ states. Discrepancies between the predictions of theory and experiment do however remain, and could arise either due to errors in the potential energy surfaces and couplings employed, or due to the limitations in the classical treatment of non-adiabatic effects.

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

International Nuclear Information System (INIS)

Judson, R.S.; Rabitz, H.

1987-01-01

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 eta -3 /sup // 2 , with eta 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

Quantum scattering from classical field theory

International Nuclear Information System (INIS)

Gould, T.M.; Poppitz, E.R.

1995-01-01

We show that scattering amplitudes between initial wave packet states and certain coherent final states can be computed in a systematic weak coupling expansion about classical solutions satisfying initial-value conditions. The initial-value conditions are such as to make the solution of the classical field equations amenable to numerical methods. We propose a practical procedure for computing classical solutions which contribute to high energy two-particle scattering amplitudes. We consider in this regard the implications of a recent numerical simulation in classical SU(2) Yang-Mills theory for multiparticle scattering in quantum gauge theories and speculate on its generalization to electroweak theory. We also generalize our results to the case of complex trajectories and discuss the prospects for finding a solution to the resulting complex boundary value problem, which would allow the application of our method to any wave packet to coherent state transition. Finally, we discuss the relevance of these results to the issues of baryon number violation and multiparticle scattering at high energies. ((orig.))

Quantum trajectory analysis of multimode subsystem-bath dynamics.

Science.gov (United States)

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.

TALENT DEVELOPMENT IN THE WORLD OF CLASSICAL MUSIC AND VISUAL ARTS

Directory of Open Access Journals (Sweden)

Linda Jarvin

2017-12-01

Full Text Available In this article, we propose to explore the developmental trajectories of children displaying gifts and abilities in the domains of (classical music and in visual arts. A developmental model for talent development that was developed in the domain of classical music will be briefly presented and its applicability in the field of visual arts will be discussed.

Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems

International Nuclear Information System (INIS)

Prigogine, I.

1995-01-01

Nonintegrable Poincare systems with a continuous spectrum lead to the appearance of diffusive terms in the frame of classical or quantum dynamics. These terms break time symmetry. They lead, therefore, to limitations to classical trajectory theory and of wave-function formalism. These diffusive terms correspond to well-defined classes of dynamical processes. The diffusive effects are amplified in situations corresponding to persistent interactions. As a result, we have to include, already, in the fundamental dynamical description the two basic aspects, probability and irreversibility, which are so conspicuous on the macroscopic level. We have to formulate both classical and quantum mechanics on the Liouville level of probability distributions. For integrable systems, we recover the usual formulation of classical or quantum mechanics. Instead of being primitive concepts, which cannot be further analyzed, trajectories and wave functions appear as special solutions of the Liouville-von Neumann equations. This extension of classical and quantum dynamics permits us to unify the two concepts of nature that we inherited from the nineteenth century, based, on the one hand, on dynamical time-reversible laws and, on the other, on an evolutionary view associated to entropy. It leads also to a unified formulation of quantum theory, avoiding the conventional dual structure based on Schroedinger's equation, on the one hand, and on the open-quotes collapseclose quotes of the wave function, on the other. A dynamical interpretation is given to processes such as decoherence or approach to equilibrium without any appeal to extra dynamic considerations. There is a striking parallelism between classical and quantum theory. For large Poincare systems (LPS), we have, in general, both a open-quotes collapseclose quotes of trajectories and of wave functions. In both cases, we need a generalized formulation of dynamics in terms of probability distributions or density matrices

On the derivation of quasi-classical equations for superconductors or 3He

International Nuclear Information System (INIS)

Shelankov, A.L.

1984-11-01

We present a method for the derivation of the quasi-classical equations for Keldysh Green function of a superconductor or superfluid 3 He. It is shown that Green functions on the classical trajectories g(Y 1 ,Y 2 ) which depend on two trajectory coordinates y 1 and y 2 , give the full description of the system within quasi-classical accuracy. The equation of motion for g(y 1 ,y 2 ) is obtained. it is shown that g(y)=g(y+0,y)+g(y-0,y) is equal to the Green function in momentum space integrated with respect to xi=vsub(F)(p-psub(F)). The normalization condition (g(y)) 2 =1 is proved in a direct manner using the properties of g(y 1 ,y 2 ) with y 1 not=Y 2 . The different methods of introducing the distribution function are discussed. (orig.)

Classical Yang-Mills mechanics. Nonlinear colour oscillations

International Nuclear Information System (INIS)

Matinyan, S.G.; Savvidi, G.K.; Ter-Arutyunyan-Savvidi, N.G.

1981-01-01

A novel class of solutions of the classical Yang-Mills equations in the Minkowsky space which leads to nonlinear colour oscillations is studied. The system discribing these oscillations is apparently stochastic. Periodic trajectories corresponding to the solutions are found and studied and it is demonstrated that they constitute at least an enumerable set [ru

Symplectic approach to calculation of magnetic field line trajectories in physical space with realistic magnetic geometry in divertor tokamaks

Science.gov (United States)

Punjabi, Alkesh; Ali, Halima

2008-12-01

A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates (ψ,θ) from experimental data from a Grad-Shafranov equilibrium solver for a tokamak. ψ is the toroidal magnetic flux and θ is the poloidal angle. Natural canonical coordinates (ψ,θ,φ) can be transformed to physical position (R,Z,φ) using a canonical transformation. (R,Z,φ) are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonical coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates (x,y) or (R,Z), the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.

Symplectic approach to calculation of magnetic field line trajectories in physical space with realistic magnetic geometry in divertor tokamaks

International Nuclear Information System (INIS)

Punjabi, Alkesh; Ali, Halima

2008-01-01

A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates (ψ,θ) from experimental data from a Grad-Shafranov equilibrium solver for a tokamak. ψ is the toroidal magnetic flux and θ is the poloidal angle. Natural canonical coordinates (ψ,θ,φ) can be transformed to physical position (R,Z,φ) using a canonical transformation. (R,Z,φ) are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonical coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates (x,y) or (R,Z), the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.

Quantum Computing's Classical Problem, Classical Computing's Quantum Problem

OpenAIRE

Van Meter, Rodney

2013-01-01

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classica...

Dynamics in the quantum/classical limit based on selective use of the quantum potential

International Nuclear Information System (INIS)

Garashchuk, Sophya; Dell’Angelo, David; Rassolov, Vitaly A.

2014-01-01

A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the time-dependent Schrödinger equation. The quantum potential is a non-local quantity, defined in the trajectory-based form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantum-mechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed “quantum,” defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or mean-field, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction

Dynamics in the quantum/classical limit based on selective use of the quantum potential

Energy Technology Data Exchange (ETDEWEB)

Garashchuk, Sophya, E-mail: garashchuk@sc.edu; Dell’Angelo, David; Rassolov, Vitaly A. [Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208 (United States)

2014-12-21

A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the time-dependent Schrödinger equation. The quantum potential is a non-local quantity, defined in the trajectory-based form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantum-mechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed “quantum,” defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or mean-field, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction.

Regularities in hadron systematics, Regge trajectories and a string quark model

International Nuclear Information System (INIS)

Chekanov, S.V.; Levchenko, B.B.

2006-08-01

An empirical principle for the construction of a linear relationship between the total angular momentum and squared-mass of baryons is proposed. In order to examine linearity of the trajectories, a rigorous least-squares regression analysis was performed. Unlike the standard Regge-Chew-Frautschi approach, the constructed trajectories do not have non-linear behaviour. A similar regularity may exist for lowest-mass mesons. The linear baryonic trajectories are well described by a semi-classical picture based on a spinning relativistic string with tension. The obtained numerical solution of this model was used to extract the (di)quark masses. (orig.)

Most probable trajectory of a muon in a scattering medium, when input and output trajectories are known

Energy Technology Data Exchange (ETDEWEB)

Benton, Christopher J., E-mail: cjb30@bath.ac.uk [Department of Electronic and Electrical Engineering, University of Bath, Claverton Down, Bath BA2 7AY (United Kingdom); Smith, Nathan D. [Department of Electronic and Electrical Engineering, University of Bath, Claverton Down, Bath BA2 7AY (United Kingdom); Quillin, Stephen J.; Steer, Christopher A. [AWE, Aldermaston, Reading, Berkshire RG7 4PR (United Kingdom)

2012-11-21

Tomographic imaging using cosmic ray muons has a range of applications including homeland security and geological imaging. To this end, we have developed a technique to calculate the most probable muon trajectory through a scattering material, given its measured entry and exit trajectories. This method has the potential to improve tomographic algorithms, in particular by replacing the muon paths assumed by the Point Of Closest Approach (POCA) method, with more realistic paths. These paths can be calculated for arbitary matter distributions, rather than just the point scatterers assumed by POCA.

Focal points and the phase of the semi-classical propagator

International Nuclear Information System (INIS)

Levit, S.; Moehring, K.; Smilansky, U.; Dreyfus, T.

1977-01-01

The relation between the phase of the semi-classical propagator and the number of times the classical trajectory is reflected from a caustic is discussed. It is shown that the accepted prescription based on Morse's focal point theorem is valid only for a restricted class of problems (coordinate representation and a positive definite mass tensor). A more general method to evaluate the phase is derived. It applies to all problems of physical interest involving the most general representations (mixed coordinate and momentum) and complicated Hamiltonian functions. The result is of particular relevance for the classical S-matrix. (author)

Quantum trajectories in complex space: One-dimensional stationary scattering problems

International Nuclear Information System (INIS)

Chou, C.-C.; Wyatt, Robert E.

2008-01-01

One-dimensional time-independent scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. The equation for the local approximate quantum trajectories near the stagnation point of the quantum momentum function is derived, and the first derivative of the quantum momentum function is related to the local structure of quantum trajectories. Exact complex quantum trajectories are determined for two examples by numerically integrating the equations of motion. For the soft potential step, some particles penetrate into the nonclassical region, and then turn back to the reflection region. For the barrier scattering problem, quantum trajectories may spiral into the attractors or from the repellers in the barrier region. Although the classical potentials extended to complex space show different pole structures for each problem, the quantum potentials present the same second-order pole structure in the reflection region. This paper not only analyzes complex quantum trajectories and the total potentials for these examples but also demonstrates general properties and similar structures of the complex quantum trajectories and the quantum potentials for one-dimensional time-independent scattering problems

Comparison of Classical and Quantum Bremsstrahlung

International Nuclear Information System (INIS)

Pratt, R.H.; Uskov, D.B.; Korol, A.V.; Obolensky, O.I.

2003-01-01

Classical features persist in bremsstrahlung at surprisingly high energies, while quantum features are present at low energies. For Coulomb bremsstrahlung this is related to the similar properties of Coulomb scattering. For bremsstrahlung in a screened potential, the low energy spectrum and angular distribution exhibit structures. In quantum mechanics these structures are associated with zeroes of particular angular-momentum transfer matrix elements at particular energies, a continuation of the Cooper minima in atomic photoeffect. They lead to transparency windows in free-free absorption. The trajectories of these zeroes in the plane of initial and final transition energies (bound and continuum) has been explored. Corresponding features have now been seen in classical bremsstrahlung, resulting from reduced contributions from particular impact parameters at particular energies. This has suggested the possibility of a more unified treatment of classical and quantum bremsstrahlung, based on the singularities of the scattering amplitude in angular momentum

Quantum dynamics modeled by interacting trajectories

Science.gov (United States)

Cruz-Rodríguez, L.; Uranga-Piña, L.; Martínez-Mesa, A.; Meier, C.

2018-03-01

We present quantum dynamical simulations based on the propagation of interacting trajectories where the effect of the quantum potential is mimicked by effective pseudo-particle interactions. The method is applied to several quantum systems, both for bound and scattering problems. For the bound systems, the quantum ground state density and zero point energy are shown to be perfectly obtained by the interacting trajectories. In the case of time-dependent quantum scattering, the Eckart barrier and uphill ramp are considered, with transmission coefficients in very good agreement with standard quantum calculations. Finally, we show that via wave function synthesis along the trajectories, correlation functions and energy spectra can be obtained based on the dynamics of interacting trajectories.

Skipping Orbits, Traversing Trajectories, and Quantum Ballistic Transport in Microstructures

NARCIS (Netherlands)

Beenakker, C.W.J.; Houten, H. van; Wees, B.J. van

1989-01-01

Three topics of current interest in the study of quantum ballistic transport in a two-dimensional electron gas are discussed, with an emphasis on correspondences between classical trajectories and quantum states in the various experimental geometries. We consider the quantized conductance of point

The comparative roles of connected and disconnected trajectories in the evaluation of the semiclassical coherent-state propagator

International Nuclear Information System (INIS)

Rubin, A.; Klauder, J.R.

1995-01-01

The semiclassical approximation of the coherent-state propagator developed by Klauder and subsequently modified by Adachi is applied to the quartic oscillator. This approximation involves classical trajectories which must satisfy complex boundary conditions. It is found that these complex classical trajectories fall into two broad categories basically characterized by the descriptive titles ''continuously connected'' and ''disconnected'' given to the two different types. The continuously connected type is found to always contribute in the evaluation of the semiclassical propagator while the disconnected type will only contribute under specific conditions. copyright 1995 Academic Press, Inc

Tracers vs. trajectories in a coastal region

Science.gov (United States)

Engqvist, A.; Döös, K.

2008-12-01

Two different methods of estimating the water exchange through a Baltic coastal region have been used, consisting of particle trajectories and passive tracers. Water is traced from and to a small discharge region near the coast. The discharge material in this region is treated as zero dimensional particles or tracers with neutral buoyancy. The real discharge material could be a leakage of radio-nuclides through the sea floor from an underground repository of nuclear waste. Water exchange rates between the discharge region and the model domain are estimated using both forward and backward trajectories as well as passive tracers. The Lagrangian trajectories can account for the time evolution of the water exchange while the tracers give one average age per model grid box. Water exchange times such as residence time, age and transient times have been calculated with trajectories but only the average age (AvA) for tracers. The trajectory calculations provide a more detailed time evolution than the tracers. On the other hand the tracers are integrated "on-line" simultaneously in the sea circulation model with the same time step while the Lagrangian trajectories are integrated "off-line" from the stored model velocities with its inherent temporal resolution, presently one hour. The sub-grid turbulence is parameterised as a Laplacian diffusion for the passive tracers and with an extra stochastic velocity for trajectories. The importance of the parameterised sub-grid turbulence for the trajectories is estimated to give an extra diffusion of the same order as the Laplacian diffusion by comparing the Lagrangian dispersions with and without parameterisation. The results of the different methods are similar but depend on the chosen diffusivity coefficient with a slightly higher correlation between trajectories and tracers when integrated with a lower diffusivity coefficient.

Lagrangian Investigation of Auto-ignition in a Hydrogen Jet Flame in a Vitiated Co-flow: Animations of Particle Trajectories in Composition Space from PDF Model Calculations

OpenAIRE

Wang, Haifeng; Pope, Stephen B.

2007-01-01

PDF model calculations have been performed of the Cabra lifted hydrogen flame in a vitiated co-flow. Particle trajectories are extracted from the Lagrangian particle method used to solve the modeled PDF equation. The particle trajectories in the mixture fraction-temperature plane reveal (at successive downstream locations): essentially inert mixing between the cold fuel jet and the hot co-flow; the auto-ignition of very lean particles; and, subsequent mixing and reaction, leading to near-equi...

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.

Science.gov (United States)

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.

Photonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics

Science.gov (United States)

Selmke, Markus; Cichos, Frank

2013-06-01

Using Fermat's least-optical-path principle, the family of ray trajectories through a special (but common) type of a gradient refractive index lens n(r)=n0+ΔnR /r is solved analytically. The solution gives a ray equation r(ϕ) that is closely related to Rutherford scattering trajectories; we therefore refer to this refraction process as "photonic Rutherford scattering." It is shown that not only do the classical limits correspond but also the wave-mechanical pictures coincide—the time-independent Schrödingier equation and the Helmholtz equation permit the same mapping between the scattering of massive particles and optical scalar waves. Scattering of narrow beams of light finally recovers the classical trajectories. The analysis suggests that photothermal single-particle microscopy measures photonic Rutherford scattering in specific limits and allows for an individual single-scatterer probing. A macroscopic experiment is demonstrated to directly measure the scattering angle to impact parameter relation, which is otherwise accessible only indirectly in Rutherford-scattering experiments.

Data-based control trajectory planning for nonlinear systems

International Nuclear Information System (INIS)

Rhodes, C.; Morari, M.; Tsimring, L.S.; Rulkov, N.F.

1997-01-01

An open-loop trajectory planning algorithm is presented for computing an input sequence that drives an input-output system such that a reference trajectory is tracked. The algorithm utilizes only input-output data from the system to determine the proper control sequence, and does not require a mathematical or identified description of the system dynamics. From the input-output data, the controlled input trajectory is calculated in a open-quotes one-step-aheadclose quotes fashion using local modeling. Since the algorithm is calculated in this fashion, the output trajectories to be tracked can be nonperiodic. The algorithm is applied to a driven Lorenz system, and an experimental electrical circuit and the results are analyzed. Issues of stability associated with the implementation of this open-loop scheme are also examined using an analytic example of a driven Hacute enon map, problems associated with inverse controllers are illustrated, and solutions to these problems are proposed. copyright 1997 The American Physical Society

A semi-classical analysis of Dirac fermions in 2+1 dimensions

International Nuclear Information System (INIS)

Maiti, Moitri; Shankar, R

2012-01-01

We investigate the semi-classical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the α matrices by two generators of the SU(2) group in the (2S + 1)-dimensional representation and doing a certain scaling, we formulate an S → ∞ limit where the orbital and the spinor degrees become classical. We solve for the classical trajectories for a free particle on a cylinder and a particle in a constant magnetic field. We compare the semi-classical spectrum, obtained by Bohr–Sommerfeld quantization with the exact quantum spectrum for low values of S. For the free particle, the semi-classical spectrum is exact. For the particle in a constant magnetic field, the semi-classical spectrum reproduces all the qualitative features of the exact quantum spectrum at all S. The quantitative fit for S = 1/2 is reasonably good. (paper)

Calculation of three-dimensional MHD equilibria with magnetic islands and chaotic field line trajectories

International Nuclear Information System (INIS)

Reiman, A.; Monticello, D.; Pomphrey, N.

1993-01-01

The three-dimensional MHD equilibrium equation is a mixed elliptic-hyperbolic partial differential equation. Unlike more familiar equations of this sort, the source term in the elliptic part of the equation is dependent on the time-asymptotic solution of the hyperbolic part, because the pressure and the force-free part of the current are constant along magnetic field lines. The equations for the field line trajectories can be put in the form of Hamilton's equations for a one-dimensional time-dependent system. The authors require an accurate solution for the KAM surfaces of this nonintegrable Hamiltonian. They describe a new algorithm they have developed for this purpose, and discuss its relationship to previously developed algorithms for computing KAM surfaces. They also discuss the numerical issues that arise in self-consistently coupling the output of this algorithm to the elliptic piece of the equation to calculate the magnetic field driven by the current. For nominally axisymmetric devices, they describe how the code is used to directly calculate the saturated state of nonaxisymmetric instabilities by following the equilibrium solution through a bifurcation. They argue that this should be the method of choice for evaluating stability to tearing modes in toroidal magnetic confinement devices

Dopamine and Caffeine Encapsulation within Boron Nitride (14,0) Nanotubes: Classical Molecular Dynamics and First Principles Calculations.

Science.gov (United States)

García-Toral, Dolores; González-Melchor, Minerva; Rivas-Silva, Juan F; Meneses-Juárez, Efraín; Cano-Ordaz, José; H Cocoletzi, Gregorio

2018-06-07

Classical molecular dynamics (MD) and density functional theory (DFT) calculations are developed to investigate the dopamine and caffeine encapsulation within boron nitride (BN) nanotubes (NT) with (14,0) chirality. Classical MD studies are done at canonical and isobaric-isothermal conditions at 298 K and 1 bar in explicit water. Results reveal that both molecules are attracted by the nanotube; however, only dopamine is able to enter the nanotube, whereas caffeine moves in its vicinity, suggesting that both species can be transported: the first by encapsulation and the second by drag. Findings are analyzed using the dielectric behavior, pair correlation functions, diffusion of the species, and energy contributions. The DFT calculations are performed according to the BLYP approach and applying the atomic base of the divided valence 6-31g(d) orbitals. The geometry optimization uses the minimum-energy criterion, accounting for the total charge neutrality and multiplicity of 1. Adsorption energies in the dopamine encapsulation indicate physisorption, which induces the highly occupied molecular orbital-lower unoccupied molecular orbital gap reduction yielding a semiconductor behavior. The charge redistribution polarizes the BNNT/dopamine and BNNT/caffeine structures. The work function decrease and the chemical potential values suggest the proper transport properties in these systems, which may allow their use in nanobiomedicine.

Classically exact surface diffusion constants at arbitrary temperature

International Nuclear Information System (INIS)

Voter, A.F.; Cohen, J.M.

1989-01-01

An expression is presented for computing the classical diffusion constant of a point defect (e.g., an adatom) in an infinite lattice of binding sites at arbitrary temperature. The transition state theory diffusion constant is simply multiplied by a dynamical correction factor that is computed from short-time classical trajectories initiated at the site boundaries. The time scale limitations of direct molecular dynamics are thus avoided in the low- and middle-temperature regimes. The expression results from taking the time derivative of the particle mean-square displacement in the lattice-discretized coordinate system. Applications are presented for surface diffusion on fcc(100) and fcc(111) Lennard-Jones crystal faces

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

Science.gov (United States)

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.

Picking Robot Arm Trajectory Planning Method

Directory of Open Access Journals (Sweden)

Zhang Zhiyong

2014-01-01

Full Text Available The picking robot arm is scheduled to complete picking tasks in the working space, to overcome the shaking vibration to improve the picking stability, its movement should follow specific consistence trajectory points. Usually we should give definite multiple feature picking points, map their inverse kinematics to the joint space, establish motion equation for the corresponding point in the joint space, then follow these equations motion for the interpolation on the joint so that we can meet the movement requirements. Trajectory planning is decisive significance for accuracy and stability of controlling robot arm. The key issue that picking arm complete picking task will be come true by trajectory planning, namely, robot arm track the desired trajectory. which based on kinematics and statics picking analysis in a joint space according to the requirements of picking tasks, and obtain the position and orientation for picking robot arm, study and calculate the theory of trajectory parameters timely.

Adaptive density trajectory cluster based on time and space distance

Science.gov (United States)

Liu, Fagui; Zhang, Zhijie

2017-10-01

There are some hotspot problems remaining in trajectory cluster for discovering mobile behavior regularity, such as the computation of distance between sub trajectories, the setting of parameter values in cluster algorithm and the uncertainty/boundary problem of data set. As a result, based on the time and space, this paper tries to define the calculation method of distance between sub trajectories. The significance of distance calculation for sub trajectories is to clearly reveal the differences in moving trajectories and to promote the accuracy of cluster algorithm. Besides, a novel adaptive density trajectory cluster algorithm is proposed, in which cluster radius is computed through using the density of data distribution. In addition, cluster centers and number are selected by a certain strategy automatically, and uncertainty/boundary problem of data set is solved by designed weighted rough c-means. Experimental results demonstrate that the proposed algorithm can perform the fuzzy trajectory cluster effectively on the basis of the time and space distance, and obtain the optimal cluster centers and rich cluster results information adaptably for excavating the features of mobile behavior in mobile and sociology network.

Reproducing Quantum Probability Distributions at the Speed of Classical Dynamics: A New Approach for Developing Force-Field Functors.

Science.gov (United States)

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.

Introducing DInaMo: A Package for Calculating Protein Circular Dichroism Using Classical Electromagnetic Theory

Directory of Open Access Journals (Sweden)

Igor V. Uporov

2015-09-01

Full Text Available The dipole interaction model is a classical electromagnetic theory for calculating circular dichroism (CD resulting from the π-π* transitions of amides. The theoretical model, pioneered by J. Applequist, is assembled into a package, DInaMo, written in Fortran allowing for treatment of proteins. DInaMo reads Protein Data Bank formatted files of structures generated by molecular mechanics or reconstructed secondary structures. Crystal structures cannot be used directly with DInaMo; they either need to be rebuilt with idealized bond angles and lengths, or they need to be energy minimized to adjust bond lengths and bond angles because it is common for crystal structure geometries to have slightly short bond lengths, and DInaMo is sensitive to this. DInaMo reduces all the amide chromophores to points with anisotropic polarizability and all nonchromophoric aliphatic atoms including hydrogens to points with isotropic polarizability; all other atoms are ignored. By determining the interactions among the chromophoric and nonchromophoric parts of the molecule using empirically derived polarizabilities, the rotational and dipole strengths are determined leading to the calculation of CD. Furthermore, ignoring hydrogens bound to methyl groups is initially explored and proves to be a good approximation. Theoretical calculations on 24 proteins agree with experiment showing bands with similar morphology and maxima.

Trajectory attractors of equations of mathematical physics

International Nuclear Information System (INIS)

Vishik, Marko I; Chepyzhov, Vladimir V

2011-01-01

In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.

A fast computing method to distinguish the hyperbolic trajectory of an non-autonomous system

International Nuclear Information System (INIS)

Jia Meng; Fan Yang-Yu; Tian Wei-Jian

2011-01-01

Attempting to find a fast computing method to DHT (distinguished hyperbolic trajectory), this study first proves that the errors of the stable DHT can be ignored in normal direction when they are computed as the trajectories extend. This conclusion means that the stable flow with perturbation will approach to the real trajectory as it extends over time. Based on this theory and combined with the improved DHT computing method, this paper reports a new fast computing method to DHT, which magnifies the DHT computing speed without decreasing its accuracy. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

VISUAL UAV TRAJECTORY PLAN SYSTEM BASED ON NETWORK MAP

Directory of Open Access Journals (Sweden)

X. L. Li

2012-07-01

Full Text Available The base map of the current software UP-30 using in trajectory plan for Unmanned Aircraft Vehicle is vector diagram. UP-30 draws navigation points manually. But in the field of operation process, the efficiency and the quality of work is influenced because of insufficient information, screen reflection, calculate inconveniently and other factors. If we do this work in indoor, the effect of external factors on the results would be eliminated, the network earth users can browse the free world high definition satellite images through downloading a client software, and can export the high resolution image by standard file format. This brings unprecedented convenient of trajectory plan. But the images must be disposed by coordinate transformation, geometric correction. In addition, according to the requirement of mapping scale ,camera parameters and overlap degree we can calculate exposure hole interval and trajectory distance between the adjacent trajectory automatically . This will improve the degree of automation of data collection. Software will judge the position of next point according to the intersection of the trajectory and the survey area and ensure the position of point according to trajectory distance. We can undertake the points artificially. So the trajectory plan is automatic and flexible. Considering safety, the date can be used in flying after simulating flight. Finally we can export all of the date using a key

Visual Uav Trajectory Plan System Based on Network Map

Science.gov (United States)

Li, X. L.; Lin, Z. J.; Su, G. Z.; Wu, B. Y.

2012-07-01

The base map of the current software UP-30 using in trajectory plan for Unmanned Aircraft Vehicle is vector diagram. UP-30 draws navigation points manually. But in the field of operation process, the efficiency and the quality of work is influenced because of insufficient information, screen reflection, calculate inconveniently and other factors. If we do this work in indoor, the effect of external factors on the results would be eliminated, the network earth users can browse the free world high definition satellite images through downloading a client software, and can export the high resolution image by standard file format. This brings unprecedented convenient of trajectory plan. But the images must be disposed by coordinate transformation, geometric correction. In addition, according to the requirement of mapping scale ,camera parameters and overlap degree we can calculate exposure hole interval and trajectory distance between the adjacent trajectory automatically . This will improve the degree of automation of data collection. Software will judge the position of next point according to the intersection of the trajectory and the survey area and ensure the position of point according to trajectory distance. We can undertake the points artificially. So the trajectory plan is automatic and flexible. Considering safety, the date can be used in flying after simulating flight. Finally we can export all of the date using a key

Electron trajectory program

International Nuclear Information System (INIS)

Herrmannsfeldt, W.B.

1979-11-01

The SLAC Electron Trajectory Program is described and instructions and examples for users are given. The program is specifically written to compute trajectories of charged particles in electrostatic and magnetostatic focusing systems including the effects of space charge and self-magnetic fields. Starting options include Child's Law conditions on cathodes of various shapes. Either rectangular or cylindrically symmetric geometry may be used. Magntic fields may be specified using arbitrary configurations of coils, or the output of a magnet program such as Poisson or by an externally calculated array of the axial fields. The program is available in IBM FORTRAN but can be easily converted for use on other brands of hardware. The program is intended to be used with a plotter whose interface the user must provide

Computer programmes for high current ion trajectories in a magnetic sector-type mass separator

International Nuclear Information System (INIS)

Nakai, Akira

1988-01-01

According to theoretical calculations previously proposed by the author, a new programme 'MALT' for electronic computers has been developed for numerical calculations of ion trajectories of a high current ion beam traversing a magnetic sector-type mass separator. In the programme, both effects of the fringing field and the space charge are taken into account in an analytical way, so that numerical calculations can be done straightforwardly. Furthermore, it becomes also possible to analyze and cotrol the trajectories of the high current ion beam. The programme MALT contains several subroutine programmes which are separated individually for the convenience of various calculations with respect to the high current ion beam. To demonstrate the calculations by the use of these subroutine programmes, a main programme for the calculation of the trajectories in the whole region of the separator is shown, which also makes it possible to draw the traces of the trajectories. The trajectories calculated by the proposed programme have been compared with the images of the ion beams recorded on novel dry plates developed by the author: the comparison enables us to evaluate the effective space charge and the effective space charge potential, and to analyze the behaviour of the beam of neutral particles accompanying the ion beam. (author)

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

Science.gov (United States)

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.

Trajectory phases of a quantum dot model

International Nuclear Information System (INIS)

Genway, Sam; Hickey, James M; Garrahan, Juan P; Armour, Andrew D

2014-01-01

We present a thermodynamic formalism to study the trajectories of charge transport through a quantum dot coupled to two leads in the resonant-level model. We show that a close analogue of equilibrium phase transitions exists for the statistics of transferred charge; by tuning an appropriate ‘counting field’, crossovers to different trajectory phases are possible. Our description reveals a mapping between the statistics of a given device and current measurements over a range of devices with different dot–lead coupling strengths. Furthermore insight into features of the trajectory phases are found by studying the occupation of the dot conditioned on the transported charge between the leads; this is calculated from first principles using a trajectory biased two-point projective measurement scheme. (paper)

Classical kinematic model for direct reactions of oriented reagents

International Nuclear Information System (INIS)

Schechter, I.; Prisant, M.G.; Levine, R.D.

1987-01-01

A simple kinematic model based on the concept of an orientation-dependent critical configuration for reaction is introduced and applied. The model serves two complementary purposes. In the predictive mode the model provides an easily implemented procedure for computing the reactivity of oriented reagents (including those actually amenable to measure) from a given potential energy surface. The predictions of the model are compared against classical trajectory results for the H + D 2 reaction. By use of realistic potential energy surfaces the model is applied to the Li + HF and O + HCl reactions where the HX molecules are pumped by a polarized laser. A given classical trajectory is deemed reactive or not according to whether it can surmount the barrier at that particular orientation. The essential difference with the model of Levine and Bernstein is that the averaging over initial conditions is performed by using a Monte Carlo integration. One can therefore use the correct orientation-dependent shape (and not only height) of the barrier to reaction and, furthermore, use oriented or aligned reagents. Since the only numerical step is a Monte Carlo sampling of initial conditions, very many trajectories can be run. This suffices to determine the reaction cross section for different initial conditions. To probe the products, they have employed the kinematic approach of Elsum and Gordon. The result is a model where, under varying initial conditions, examining final-state distributions or screening different potential energy surfaces can be efficiently carried out

Classical model for nuclear collisions including the meson degree of freedom

International Nuclear Information System (INIS)

Babinet, R.; Kunz, J.; Mosel, U.; Wilets, L.

1980-01-01

Many different approaches have been taken to describe high energy heavy ion collisions. L. Wilets et al proposed a classical treatment of the problem. In his model non-relativistic nucleons move on classical trajectories. However, the Pauli-principle is simulated by a momentum dependent potential acting between the nucleons. This model is extended in two ways. The nucleons are coupled to a pionfield, which enables us to describe inelastic processes. Nucleons and pionfiled are treated completely relativistically, this also assures Lorentz invariance. We aim at a set of classical equations of motion describing the interacting system of nucleons and pionfield. These classical equations should have a quantum mechanical basis. Further, they should contain such fundamental properties of the pion-nucleon system as the Δ(3,3)-resonance, at least in a qualitative manner. (orig./FKS)

Computer modeling of oil spill trajectories with a high accuracy method

International Nuclear Information System (INIS)

Garcia-Martinez, Reinaldo; Flores-Tovar, Henry

1999-01-01

This paper proposes a high accuracy numerical method to model oil spill trajectories using a particle-tracking algorithm. The Euler method, used to calculate oil trajectories, can give adequate solutions in most open ocean applications. However, this method may not predict accurate particle trajectories in certain highly non-uniform velocity fields near coastal zones or in river problems. Simple numerical experiments show that the Euler method may also introduce artificial numerical dispersion that could lead to overestimation of spill areas. This article proposes a fourth-order Runge-Kutta method with fourth-order velocity interpolation to calculate oil trajectories that minimise these problems. The algorithm is implemented in the OilTrack model to predict oil trajectories following the 'Nissos Amorgos' oil spill accident that occurred in the Gulf of Venezuela in 1997. Despite lack of adequate field information, model results compare well with observations in the impacted area. (Author)

KOBRA 3 - a code for the calculation of space-charge-influenced trajectories in 3-dimensions

International Nuclear Information System (INIS)

Spaedtke, P.; Wipf, S.

1989-06-01

KOBRA3 is a three-dimensional multi-purpose program, written in standard FORTRAN77. The main purpose of the program is to calculate the trajectories of charged particles through a static electro-magnetic field in three dimensions. If space charge is not negligible its influence is taken into account by an iterative process. The Laplace equation is solved for the scalar potential. During the ray tracing, in which the equations of motion for charged particles are solved, the space charge term in the Poisson equation is distributed onto the mesh. By repeating this procedure the steady-state Vlasov equation is solved: ∇ 2 φ+∫∫∫f p dxdydz = 0, where φ is the electro-static potential and f p (r vector, v vector) describes the distribution of the charged particles in space. KOBRA3 can handle finite plasma boundaries, which are found by the program automatically. Special features are included within the program to investigate the beam quality (emittance, transverse energy), and to display the geometry, the trajectories and the potential and magnetic fields graphically. The modular structure of the program enables the user to create his (her) own diagnostic programs or interfaces to the main program. This report is intended to facilitate the use of KOBRA3 by describing the theory, structure and numerical methods used. At GSI (Gesellschaft fuer Schwerionenforschung) the program runs on an IBM 3090-40E. The program has been installed on other machines e.g. CRAY XM-P, CRAY II, VAX 8600, IBM 3090-200, IBM 3033, ATARI ST, IBM-AT. (orig./HSI)

Increasing the efficiency and accuracy of time-resolved electronic spectra calculations with on-the-fly ab initio quantum dynamics methods

Science.gov (United States)

Vanicek, Jiri

2014-03-01

Rigorous quantum-mechanical calculations of coherent ultrafast electronic spectra remain difficult. I will present several approaches developed in our group that increase the efficiency and accuracy of such calculations: First, we justified the feasibility of evaluating time-resolved spectra of large systems by proving that the number of trajectories needed for convergence of the semiclassical dephasing representation/phase averaging is independent of dimensionality. Recently, we further accelerated this approximation with a cellular scheme employing inverse Weierstrass transform and optimal scaling of the cell size. The accuracy of potential energy surfaces was increased by combining the dephasing representation with accurate on-the-fly ab initio electronic structure calculations, including nonadiabatic and spin-orbit couplings. Finally, the inherent semiclassical approximation was removed in the exact quantum Gaussian dephasing representation, in which semiclassical trajectories are replaced by communicating frozen Gaussian basis functions evolving classically with an average Hamiltonian. Among other examples I will present an on-the-fly ab initio semiclassical dynamics calculation of the dispersed time-resolved stimulated emission spectrum of the 54-dimensional azulene. This research was supported by EPFL and by the Swiss National Science Foundation NCCR MUST (Molecular Ultrafast Science and Technology) and Grant No. 200021124936/1.

Baryon exchange in dual unitarisation - the f and ω-trajectories

International Nuclear Information System (INIS)

Hansson, T.H.

1978-11-01

Intercepts and quark content of the f and ω-trajectories are calculated by considering the effects of baryon exchange and SU(3)-breaking within the dual unitarisation scheme. The coupling of the ω-trajectory to external particles is discussed. (author)

Electron trajectory program

Energy Technology Data Exchange (ETDEWEB)

Herrmannsfeldt, W.B.

1979-11-01

The SLAC Electron Trajectory Program is described and instructions and examples for users are given. The program is specifically written to compute trajectories of charged particles in electrostatic and magnetostatic focusing systems including the effects of space charge and self-magnetic fields. Starting options include Child's Law conditions on cathodes of various shapes. Either rectangular or cylindrically symmetric geometry may be used. Magntic fields may be specified using arbitrary configurations of coils, or the output of a magnet program such as Poisson or by an externally calculated array of the axial fields. The program is available in IBM FORTRAN but can be easily converted for use on other brands of hardware. The program is intended to be used with a plotter whose interface the user must provide.

Frame dependence of world lines for directly interacting classical relativistic particles

International Nuclear Information System (INIS)

Molotkov, V.V.; Todorov, I.T.

1979-06-01

The motion of world lines is studied in the constraint Hamiltonian formulation of relativistic point particle dynamics. The particle world lines are shown to depend, in general (in the presence of interaction) on the choice of the equal time hyperplane (the only exception being the elastic scattering of rigid balls). However, the relative motion of a 2-particle system and the (classical) S-matrix are independent of this choice. This inferred that particle trajectories should not be regarded as frame independent observables in the classical theory of relativistic particles. (author)

Hybrid classical/quantum simulation for infrared spectroscopy of water

Science.gov (United States)

Maekawa, Yuki; Sasaoka, Kenji; Ube, Takuji; Ishiguro, Takashi; Yamamoto, Takahiro

2018-05-01

We have developed a hybrid classical/quantum simulation method to calculate the infrared (IR) spectrum of water. The proposed method achieves much higher accuracy than conventional classical molecular dynamics (MD) simulations at a much lower computational cost than ab initio MD simulations. The IR spectrum of water is obtained as an ensemble average of the eigenvalues of the dynamical matrix constructed by ab initio calculations, using the positions of oxygen atoms that constitute water molecules obtained from the classical MD simulation. The calculated IR spectrum is in excellent agreement with the experimental IR spectrum.

Classical geometry from the quantum Liouville theory

Science.gov (United States)

Hadasz, Leszek; Jaskólski, Zbigniew; Piaţek, Marcin

2005-09-01

Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.

Classical geometry from the quantum Liouville theory

International Nuclear Information System (INIS)

Hadasz, Leszek; Jaskolski, Zbigniew; Piatek, Marcin

2005-01-01

Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere

Why aortic elasticity differs among classical and non-classical mitral valve prolapsed?

Science.gov (United States)

Unlu, Murat; Demirkol, Sait; Aparci, Mustafa; Arslan, Zekeriya; Balta, Sevket; Dogan, Umuttan; Kilicarslan, Baris; Ozeke, Ozcan; Celik, Turgay; Iyisoy, Atila

2014-01-01

Mitral valve prolapse (MVP) is the most common valvular heart disease and characterized by the displacement of an abnormally thickened mitral valve leaflet into the left atrium during systole. There are two types of MVP, broadly classified as classic (thickness ≥5 mm) and non-classic (thickness elastic properties of the aorta in young male patients with classical and non-classical MVP. In the present study, 63 young adult males (mean age: 22.7 ± 4.2) were included. Patients were divided into classic MVP (n = 27) and non-classic MVP (n = 36) groups. Aortic strain, aortic distensibility and aortic stiffness index were calculated by using aortic diameters obtained by echocardiography and blood pressures measured by sphygmomanometer. There was no significant difference between the groups in terms of age, body mass index, left ventricular mass and ejection fraction. When comparing the MVP group it was found that aortic strain and aortic distensibility were increased (p = 0.0027, p = 0.016, respectively) whereas the aortic stiffness index was decreased (p = 0.06) in the classical MVP group. We concluded that the elastic properties of the aorta is increased in patients with classic MVP. Further large scale studies should be performed to understand of morphological and physiological properties of the aorta in patients with MVP.

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

Science.gov (United States)

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.

Quantum-classical correspondence for the inverted oscillator

Science.gov (United States)

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)

Quantization in classical mechanics and its relation to the Bohmian Ψ-field

International Nuclear Information System (INIS)

Rusov, V.D.; Vlasenko, D.S.; Mavrodiev, S.Cht.

2011-01-01

Research highlights: →The Schroedinger equation is derived from the classical Hamiltonian mechanics. →This derivation is based on the Chetaev theorem on stable dynamical trajectories. →The conditions for correctness of trajectory quantum mechanics are discussed. - Abstract: Based on the Chetaev theorem on stable dynamical trajectories in the presence of dissipative forces, we obtain the generalized condition for stability of Hamilton systems in the form of the Schroedinger equation. It is shown that the energy of dissipative forces, which generate the Chetaev generalized condition of stability, coincides exactly with the Bohm 'quantum' potential. Within the frame-work of Bohmian quantum mechanics supplemented by the generalized Chetaev theorem and on the basis of the principle of least action for dissipative forces, we show that the squared amplitude of a wave function in the Schroedinger equation is equivalent semantically and syntactically to the probability density function for the number of particle trajectories, relative to which the velocity and the position of the particle are not hidden parameters. The conditions for the correctness of trajectory interpretation of quantum mechanics are discussed.

The shell effects in s-wave neutron resonance level densities ρ according to combinatorial calculations and on the basis of the semi-classical approach

International Nuclear Information System (INIS)

Kaczmarczyk, Maria

2005-01-01

The results of calculations of level densities ρ, in the vicinity of the neutron binding energy S n , are presented. These results were obtained using the Boehning combinatorial method for the calculation of particle-hole state densities dependent on the number of decompositions of the nucleus excitation energy to energies of independent fermions. The calculation was based on the semi-classical model description in the computation of particle-hole state densities and then of the level densities ρ, and takes into account the existence of energy gaps Δ, located near the Fermi level, in a single particle level scheme. This procedure considerably improved and extended the Boehning calculation method. The results, which were obtained in this way for ρ, for 220 nuclei, reproduce the regularities observed in the experimental values of ρ, which are dependent on the neutron number N, and they agree with the experimental data within two orders of magnitude. In addition, the neutron resonance densities ρ were calculated on the basis of the particle-hole state densities obtained using the analytical formula from Boehning's paper. To make the calculations possible, the values of 'complexity' k, as given in the semi-classical model, and the spin factors R(J), according to the paper by Ryckbosch, were used

Communication: Rate coefficients from quasiclassical trajectory calculations from the reverse reaction: The Mu + H2 reaction re-visited

Science.gov (United States)

Homayoon, Zahra; Jambrina, Pablo G.; Aoiz, F. Javier; Bowman, Joel M.

2012-07-01

In a previous paper [P. G. Jambrina et al., J. Chem. Phys. 135, 034310 (2011), 10.1063/1.3611400] various calculations of the rate coefficient for the Mu + H2 → MuH + H reaction were presented and compared to experiment. The widely used standard quasiclassical trajectory (QCT) method was shown to overestimate the rate coefficients by several orders of magnitude over the temperature range 200-1000 K. This was attributed to a major failure of that method to describe the correct threshold for the reaction owing to the large difference in zero-point energies (ZPE) of the reactant H2 and product MuH (˜0.32 eV). In this Communication we show that by performing standard QCT calculations for the reverse reaction and then applying detailed balance, the resulting rate coefficient is in very good agreement with the other computational results that respect the ZPE, (as well as with the experiment) but which are more demanding computationally.

The trapping of K and Na atoms by a clean W(110) surface. Dynamic trajectory calculations. ch.3

International Nuclear Information System (INIS)

Hurkmans, A.; Overbosch, E.G.; Los, J.

1976-01-01

The fraction of K and Na atoms which are initially trapped by a clean W(110) surface has been measured as a function of incident energy (0.5 < approximately Esub(i) < approximately 15 eV) at several angles of incidence. At the same time the desorption energies Qsub(i) of the trapped potassium and sodium atoms were measured: Qsub(i) = 2.05 +- 0.02 eV and Qsub(i) = 2.60 +- 0.04 eV respectively. The measured trapping probabilities can be described well by Trillings 'partially screened spherical cap' model, except fos the small angles of incidence. Dynamic trajectory calculations were performed for a particle scattered from a diatomic molecule to explain the screening and the descrepancy at normal incidence. The calculations give good quantitative agreement with the measured trapping probability at small angles both for potassium and sodium atoms and show that simultaneous interaction with two adjacent surface atoms affects the trapping particularly at small angles of incidence. (Auth.)

Dispersions in Semi-Classical Dynamics

International Nuclear Information System (INIS)

Zielinska-Pfabe, M.; Gregoire, C.

1987-01-01

Dispersions around mean values of one-body observables are obtained by restoring classical many-body correlations in Vlasov and Landau-Vlasov dynamics. The method is applied to the calculation of fluctuations in mass, charge and linear momentum in heavy-ion collisions. Results are compared to those obtained by the Balian-Veneroni variational principle in semi-classical approximation

Dynamical coupling of plasmons and molecular excitations by hybrid quantum/classical calculations: time-domain approach

International Nuclear Information System (INIS)

Sakko, Arto; Rossi, Tuomas P; Nieminen, Risto M

2014-01-01

The presence of plasmonic material influences the optical properties of nearby molecules in untrivial ways due to the dynamical plasmon-molecule coupling. We combine quantum and classical calculation schemes to study this phenomenon in a hybrid system that consists of a Na 2 molecule located in the gap between two Au/Ag nanoparticles. The molecule is treated quantum-mechanically with time-dependent density-functional theory, and the nanoparticles with quasistatic classical electrodynamics. The nanoparticle dimer has a plasmon resonance in the visible part of the electromagnetic spectrum, and the Na 2 molecule has an electron-hole excitation in the same energy range. Due to the dynamical interaction of the two subsystems the plasmon and the molecular excitations couple, creating a hybridized molecular-plasmon excited state. This state has unique properties that yield e.g. enhanced photoabsorption compared to the freestanding Na 2 molecule. The computational approach used enables decoupling of the mutual plasmon-molecule interaction, and our analysis verifies that it is not legitimate to neglect the backcoupling effect when describing the dynamical interaction between plasmonic material and nearby molecules. Time-resolved analysis shows nearly instantaneous formation of the coupled state, and provides an intuitive picture of the underlying physics. (paper)

CLASSICAL CALCULATION METHODS OF COSTS AND THEIR LIMITS IN ACTUAL FRAME OF ROMANIAN ECONOMY. PRESENT TENDENCIES IN COSTS ACCOUNTANCY

Directory of Open Access Journals (Sweden)

Simona Dragomirescu

2008-12-01

Full Text Available Classical accountancy shaped and coagulated in an informational system grafted on traditional production systems, characterized by mass productions, planning etc. The powerful concentrations and grouping, economies globalization, both as offer and as demand, the new restrictions and economical opportunities and global environment technologies lead to a redefining of enterprises’ objectives. From the well-known “quantity and productivity”, the enterprise faced a new system of objectives: quality’s increase; terms and costs decrease; productivity; flexibility. In such conditions the need of “defining new methods” appeared, the need of adapting the fundamental calculation methods, their improvement – respective the appearance of modern methods of costs calculation.

Communication: Proper treatment of classically forbidden electronic transitions significantly improves detailed balance in surface hopping

Energy Technology Data Exchange (ETDEWEB)

Sifain, Andrew E. [Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0485 (United States); Wang, Linjun [Department of Chemistry, Zhejiang University, Hangzhou 310027 (China); Prezhdo, Oleg V. [Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0485 (United States); Department of Chemistry, University of Southern California, Los Angeles, California 90089-1062 (United States)

2016-06-07

Surface hopping is the most popular method for nonadiabatic molecular dynamics. Many have reported that it does not rigorously attain detailed balance at thermal equilibrium, but does so approximately. We show that convergence to the Boltzmann populations is significantly improved when the nuclear velocity is reversed after a classically forbidden hop. The proposed prescription significantly reduces the total number of classically forbidden hops encountered along a trajectory, suggesting that some randomization in nuclear velocity is needed when classically forbidden hops constitute a large fraction of attempted hops. Our results are verified computationally using two- and three-level quantum subsystems, coupled to a classical bath undergoing Langevin dynamics.

Aircraft path planning with the use of smooth trajectories

Science.gov (United States)

Belokon', S. A.; Zolotukhin, Yu. N.; Nesterov, A. A.

2017-01-01

A simplified method of plane trajectory calculation is proposed for solving the problem of planning a path defined by a sequence of waypoints. The trajectory consists of oriented segments of straight lines joined by clothoids (Cornu spirals). The efficiency of the method is validated by means of numerical simulations in the MATLAB/Simulink environment.

Calculation of the cross section of the H2+(D2+)+Li→Li++2H(2D) charge-exchange reaction

International Nuclear Information System (INIS)

Voronin, A.I.; Osherov, V.I.; Poluyanov, L.V.; Ushakov, V.G.

1983-01-01

The method of classic trajectories with account for non-adiabatic transitions has been used to calculate Li atoms charge-exchange cross sections on H 2 + and D 2 + ions depending on collision energy and oscillatory excitation of molecular ion. Surfaces of potentil energy of nuclei interaction corresponding to essential for the chargeexchange process electron states are plotted by the diatomics-in-molecules (DIM) method. Qualitative characteristics of calculated cross sections (dependence on collision energy, oscillatory number, deuteration effect) coincide well with those obtained during the experiment. However the experimental cross section value approximately two times surpasses the theoretical one. This is connected with insufficient accuracy of the DIM method

Classical geometry from the quantum Liouville theory

Energy Technology Data Exchange (ETDEWEB)

Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: jask@ift.uni.wroc.pl; Piatek, Marcin [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: piatek@ift.uni.wroc.pl

2005-09-26

Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.

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

Science.gov (United States)

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…

Trajectory approach to dissipative quantum phase space dynamics: Application to barrier scattering

International Nuclear Information System (INIS)

Hughes, Keith H.; Wyatt, Robert E.

2004-01-01

The Caldeira-Leggett master equation, expressed in Lindblad form, has been used in the numerical study of the effect of a thermal environment on the dynamics of the scattering of a wave packet from a repulsive Eckart barrier. The dynamics are studied in terms of phase space trajectories associated with the distribution function, W(q,p,t). The equations of motion for the trajectories include quantum terms that introduce nonlocality into the motion, which imply that an ensemble of correlated trajectories needs to be propagated. However, use of the derivative propagation method (DPM) allows each trajectory to be propagated individually. This is achieved by deriving equations of motion for the partial derivatives of W(q,p,t) that appear in the master equation. The effects of dissipation on the trajectories are studied and results are shown for the transmission probability. On short time scales, decoherence is demonstrated by a swelling of trajectories into momentum space. For a nondissipative system, a comparison is made of the DPM with the 'exact' transmission probability calculated from a fixed grid calculation

Classical and quantum dynamics from classical paths to path integrals

CERN Document Server

Dittrich, Walter

2017-01-01

Graduate students who wish to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals. The fifth edition has been revised and enlarged to include chapters on quantum electrodynamics, in particular, Schwinger’s proper time method and the treatment of classical and quantum mechanics with Lie brackets and pseudocanonical transformations. It is shown that operator quantum electrodynamics can be equivalently described with c-numbers, as demonstrated by calculating the propagation function for an electron in a prescribed classical electromagnetic field.

Evaluation of Small Unmanned Aircraft Flight Trajectory Accuracy

Directory of Open Access Journals (Sweden)

Ramūnas Kikutis

2014-12-01

Full Text Available Today small unmanned aircraft are being more widely adapted for practical tasks. These tasks require high reliability and flight path accuracy. For such aircraft we have to deal with the chalenge how to compensate external factors and how to ensure the accuracy of the flight trajectory according to new regulations and standards. In this paper, new regulations for the flights of small unmanned aircraft in Lithuanian air space are discussed. Main factors, which affect errors of the autonomous flight path tracking, are discussed too. The emphasis is on the wind factor and the flight path of Dubbin’s trajectories. Research was performed with mathematical-dynamic model of UAV and it was compared with theoretical calculations. All calculations and experiments were accomplished for the circular part of Dubbin’s paths when the airplane was trimmed for circular trajectory flight in calm conditions. Further, for such flight the wind influence was analysed.

Classical-quantal coupling in the capture of muons by hydrogen atoms

International Nuclear Information System (INIS)

Kwong, N.H.; Garcia, J.D.

1989-01-01

We describe a self-consistent semiclassical approach to the problem of muon capture by hydrogen atoms. The dynamics of the heavier muon and proton are treated classically, and the electron quantally, with the potentials for both being self-consistently determined. Our numerical results are compared to classical-trajectory Monte Carlo (CTMC) and adiabatic ionisation (AI) results. Our capture cross sections are larger at low energy but fall more rapidly to zero. Our results provide the corrections to the dynamics beyond the adiabatic picture, which were missing in other approaches; interesting questions concerning the quantal nature of the events are discussed. (author)

Non-classicality criteria: Glauber-Sudarshan P function and Mandel ? parameter

Science.gov (United States)

Alexanian, Moorad

2018-01-01

We calculate exactly the quantum mechanical, temporal Wigner quasiprobability density for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state. The Wigner function allows us to calculate the fluctuations in photon number and the quadrature variance. We contrast the difference between the non-classicality criteria, which is independent of the displacement parameter ?, based on the Glauber-Sudarshan quasiprobability distribution ? and the classical/non-classical behaviour of the Mandel ? parameter, which depends strongly on ?. We find a phase transition as a function of ? such that at the critical point ?, ?, as a function of ?, goes from strictly classical, for ?, to a mixed classical/non-classical behaviour, for ?.

A stepping stone from classical to quantum mechanics

International Nuclear Information System (INIS)

Tzara, C.

1984-01-01

A microscopic mechanics is constructed in order to incorporate the Planck constant while retaining the concept of particle location. In the one-dimensional stationary case, the first integral of the equation of motion can be solved explicitly with the help of the Schroedinger equation. It is thus shown that, in describing bound-state motions, this mechanics meets a serious difficulty. It can be overcome only by renouncing the classical concepts of trajectories and opting for quantum mechanics

Career Trajectories of Municipal Servants: Two Types of Professional Mobility (Case Study in Novgorod Region

Directory of Open Access Journals (Sweden)

A A Kurakin

2013-12-01

Full Text Available The case study of a district in the Novgorod region shows some scenarios of recruiting new employees in the district and town municipalities, their work motivation and the most plausible career trajectories. The author argues that on the municipal level (district or its administrative center there are parallel career ladders for the top-ranked municipal clerks and for the rest of the municipal staff: the career trajectory of the high-ranked clerks can be described as a step-by-step trajectory, while the one of the lower-ranked employees — as a shuttle trajectory. There is an almost insurmountable border line between these two levels of municipal hierarchy, an obstacle for implementing the classical Weberian characteristics of “proper” bureaucracy: meritocratic recruitment and workers’ promotion and predictable long-term career ladders.

The classical limit of non-integrable quantum systems, a route to quantum chaos

International Nuclear Information System (INIS)

Castagnino, Mario; Lombardi, Olimpia

2006-01-01

The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those, which have, as their classical limit, a non-integrable classical system. This quantum systems will be the candidates to be the models of quantum chaos. In order to obtain this limit, the self-induced decoherence approach and the corresponding classical limit are generalized from integrable to non-integrable systems. In this approach, the lost of information, usually conceived as the result of a coarse-graining or the trace of an environment, is produced by a particular choice of the algebra of observables and the systematic use of mean values, that project the unitary evolution onto an effective non-unitary one. By means of our method, we can obtain the classical limit of the quantum state of a non-integrable system, which turns out to be a set of unstable, potentially chaotic classical trajectories contained in the Wigner transformation of the quantum state

The classical limit of non-integrable quantum systems, a route to quantum chaos

Energy Technology Data Exchange (ETDEWEB)

Castagnino, Mario [CONICET-UNR-UBA, Institutos de Fisica de Rosario y de Astronomia y Fisica del Espacio, Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina)]. E-mail: mariocastagnino@citynet.net.ar; Lombardi, Olimpia [CONICET-Universidad de Buenos Aires-Universidad de Quilmes Rivadavia 2358, 6to. Derecha, Buenos Aires (Argentina)

2006-05-15

The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those, which have, as their classical limit, a non-integrable classical system. This quantum systems will be the candidates to be the models of quantum chaos. In order to obtain this limit, the self-induced decoherence approach and the corresponding classical limit are generalized from integrable to non-integrable systems. In this approach, the lost of information, usually conceived as the result of a coarse-graining or the trace of an environment, is produced by a particular choice of the algebra of observables and the systematic use of mean values, that project the unitary evolution onto an effective non-unitary one. By means of our method, we can obtain the classical limit of the quantum state of a non-integrable system, which turns out to be a set of unstable, potentially chaotic classical trajectories contained in the Wigner transformation of the quantum state.

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

Science.gov (United States)

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.

Trajectory tracking control for underactuated stratospheric airship

Science.gov (United States)

Zheng, Zewei; Huo, Wei; Wu, Zhe

2012-10-01

Stratospheric airship is a new kind of aerospace system which has attracted worldwide developing interests for its broad application prospects. Based on the trajectory linearization control (TLC) theory, a novel trajectory tracking control method for an underactuated stratospheric airship is presented in this paper. Firstly, the TLC theory is described sketchily, and the dynamic model of the stratospheric airship is introduced with kinematics and dynamics equations. Then, the trajectory tracking control strategy is deduced in detail. The designed control system possesses a cascaded structure which consists of desired attitude calculation, position control loop and attitude control loop. Two sub-loops are designed for the position and attitude control loops, respectively, including the kinematics control loop and dynamics control loop. Stability analysis shows that the controlled closed-loop system is exponentially stable. Finally, simulation results for the stratospheric airship to track typical trajectories are illustrated to verify effectiveness of the proposed approach.

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

Science.gov (United States)

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

Reactive scattering for H{sup -} + H{sub 2} and H{sup +} + H{sub 2} and its isotopologues. Classical versus quantum investigation

Energy Technology Data Exchange (ETDEWEB)

Wang, Dequan

2016-07-01

reaction preferentially occurs adiabatically, but at higher collision energies non-adiabatic effects have to be taken into account. Reaction probabilities and reaction cross sections for the collision H{sup -} with H{sub 2} and its isotopologues using quasi-classical trajectories and quantum wavepackets were presented in the main part of Chapter 5. It was found that, at low collision energies, the reaction probabilities using SM-PES and AY-PES are very similar. The reaction probabilities based on the PS-PES are lower than those based on the SM-PES and AY-PES. At lower collision energies the reaction cross sections calculated with SM-PES are higher than those calculated with PS-PES. The reaction cross sections investigated with quasi-classical trajectories are higher than those calculated with quantum wavepackets (using the same potential). The last section of Chapter 5 showed results for the collision of H{sup -} and D{sup -} with HD. The total I reaction probabilities, the reaction cross sections, and the product ratios were determined using quasi-classical trajectories. One can learn from these calculations that for the H{sup -} + HD(v=0-1, j=0) reaction and low collision energies, the main product are H{sub 2} + D{sup -}. At high collision energies, the product channel HD + H{sup -} is slightly dominant. For the collision of D{sup -} with HD and low collision energies the product channel HD + D{sup -} is strongly favored, but in the high collision energy range, the product channel D{sub 2} + H{sup -} dominates.

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

International Nuclear Information System (INIS)

Albaugh, Alex; Demerdash, Omar; Head-Gordon, Teresa

2015-01-01

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 course 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

EGUN, Charged Particle Trajectories in Electromagnetic Focusing System

International Nuclear Information System (INIS)

Herrmannsfeldt, W.B.

2002-01-01

1 - Description of problem or function: EGUN computes trajectories of charged particles in electrostatic and magnetostatic focusing systems including the effects of space charge and self-magnetic fields. Starting options include Child's Law conditions on cathodes of various shapes, user-specified conditions input for each ray, and a combination of Child's Law conditions and user specifications. Either rectangular or cylindrically symmetric geometry may be used. Magnetic fields may be specified using an arbitrary configuration of coils, or the output of a magnet program, such as Poisson, or by an externally calculated array of the axial fields. 2 - Method of solution: The program first solves Laplace's equation. Next, the first iteration of electron trajectories is started using one of the four starting options. On the first iteration cycle, space charge forces are calculated from the assumption of paraxial flow. As the rays are traced, space charge is computed and stored. After all the electron trajectories have been calculated, the program begins the second cycle by solving the Poisson equation with the space charge from the first iteration. Subsequent iteration cycles follow this pattern. The Poisson equation is solved by an alternate column relaxation technique known as the semi-iterative Chebyshev method. A fourth-order Runge-Kutta method is used to solve the relativistic differential equations of the trajectory calculations. 3 - Restrictions on the complexity of the problem - Maxima of: 9001 mesh points in a square mesh, 300 mesh points in the axial direction, 100 mesh points in the radial direction, 101 potentials, 51 rays. In the cylindrical coordinates, the magnetic fields are axially symmetric. In rectangular coordinates, the external field is assumed to be normal to the plane of the problem, which is assumed to be the median plane

Visualizing the solutions for the circular infinite well in quantum and classical mechanics

International Nuclear Information System (INIS)

Robinett, R.W.

1996-01-01

The classical and quantum mechanical problem of a particle in the infinite circular well has recently surfaced in two quite different manifestations: (i) the observation of open-quote open-quote electron standing waves close-quote close-quote in circular open-quote open-quote corrals close-quote close-quote of atoms adsorbed on surfaces and (ii) as a benchmark example of an integrable system for comparison to the classical and quantum chaotic behavior of the open-quote open-quote stadium billiards close-quote close-quote problem. Motivated by this, we review the quantum and classical probability distributions for both position and momentum for this familiar problem, focusing on the visualization of the quantum wave functions and classical trajectories as well as the semiclassical connections between the two. copyright 1996 American Association of Physics Teachers

Ensemble simulations with discrete classical dynamics

DEFF Research Database (Denmark)

Toxværd, Søren

2013-01-01

For discrete classical Molecular dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment $h$ there exist a shadow Hamiltonian $\\tilde{H}$ with energy $\\tilde{E}(h)$, for which the discrete particle positions lie on the analytic trajectories for $\\tilde{H}$. $\\tilde......{E}(h)$ is employed to determine the relation with the corresponding energy, $E$ for the analytic dynamics with $h=0$ and the zero-order estimate $E_0(h)$ of the energy for discrete dynamics, appearing in the literature for MD with VA. We derive a corresponding time reversible VA algorithm for canonical dynamics...

Exact classical scaling formalism for nonreactive processes

International Nuclear Information System (INIS)

DePristo, A.E.

1981-01-01

A general nonreactive collision system is considered with internal molecular variables (p, r) and/or (I, theta) of arbitrary dimensions and relative translational variables (P, R) of three or less dimensions. We derive an exact classical scaling formalism which relates the collisional change in any function of molecular variables directly to the initial values of these variables. The collision dynamics is then described by an explicit function of the initial point in the internal molecular phase space, for a fixed point in the relative translational phase space. In other words, the systematic variation of the internal molecular properties (e.g., actions and average internal kinetic energies) is given as a function of the initial internal action-angle variables. A simple three term approximation to the exact formalism is derived, the natural variables of which are the internal action I and internal linear momenta p. For the final average internal kinetic energies T, the result is T-T/sup( 0 ) = α+βp/sup( 0 )+γI/sup( 0 ), where the superscripted ''0'' indicates the initial value. The parameters α, β, and γ in this scaling theory are directly related to the moments of the change in average internal kinetic energy. Utilizing a very limited number of input moments generated from classical trajectory calculations, the scaling can be used to predict the entire distribution of final internal variables as a function of initial internal actions and linear momenta. Initial examples for atom--collinear harmonic oscillator collision systems are presented in detail, with the scaling predictions (e.g., moments and quasiclassical histogram transition probabilities) being generally very good to excellent quantitatively

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

Science.gov (United States)

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

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

Science.gov (United States)

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.

Classical-quantum correspondence in electron-positron pair creation

International Nuclear Information System (INIS)

Chott, N. I.; Su, Q.; Grobe, R.

2007-01-01

We examine the creation of electron-positron pairs in a very strong force field. Using numerical solutions to quantum field theory we calculate the spatial and momentum probability distributions for the created particles. A comparison with classical mechanical phase space calculations suggests that despite the fully relativistic and quantum mechanical nature of the matter creation process, most aspects can be reproduced accurately in terms of classical mechanics

Simulation of planar channeling-radiation spectra of relativistic electrons and positrons channeled in a diamond-structure or tungsten single crystal (classical approach)

International Nuclear Information System (INIS)

Azadegan, B.; Wagner, W.

2015-01-01

We present a Mathematica package for simulation of spectral-angular distributions and energy spectra of planar channeling radiation of relativistic electrons and positrons channeled along major crystallographic planes of a diamond-structure or tungsten single crystal. The program is based on the classical theory of channeling radiation which has been successfully applied to study planar channeling of light charged particles at energies higher than 100 MeV. Continuous potentials for different planes of diamond, Si, Ge and W single crystals are calculated using the Doyle–Turner approximation to the atomic scattering factor and taking thermal vibrations of the crystal atoms into account. Numerical methods are applied to solve the classical one-dimensional equation of motion. The code is designed to calculate the trajectories, velocities and accelerations of electrons (positrons) channeled by the planar continuous potential. In the framework of classical electrodynamics, these data allow realistic simulations of spectral-angular distributions and energy spectra of planar channeling radiation. Since the generated output is quantitative, the results of calculation may be useful, e.g., for setup configuration and crystal alignment in channeling experiments, for the study of the dependence of channeling radiation on the input parameters of particle beams with respect to the crystal orientation, but also for the simulation of positron production by means of pair creation what is mandatory for the design of efficient positron sources necessary in high-energy and collider physics. Although the classical theory of channeling is well established for long time, there is no adequate library program for simulation of channeling radiation up to now, which is commonly available, sufficiently simple and effective to employ and, therefore, of benefit as for special investigations as for a quick overview of basic features of this type of radiation

Quantifying ataxia: ideal trajectory analysis--a technical note

Science.gov (United States)

McPartland, M. D.; Krebs, D. E.; Wall, C. 3rd

2000-01-01

We describe a quantitative method to assess repeated stair stepping stability. In both the mediolateral (ML) and anterioposterior (AP) directions, the trajectory of the subject's center of mass (COM) was compared to an ideal sinusoid. The two identified sinusoids were unique in each direction but coupled. Two dimensionless numbers-the mediolateral instability index (IML) and AP instability index (IAP)-were calculated using the COM trajectory and ideal sinusoids for each subject with larger index values resulting from less stable performance. The COM trajectories of nine nonimpaired controls and six patients diagnosed with unilateral or bilateral vestibular labyrinth hypofunction were analyzed. The average IML and IAP values of labyrinth disorder patients were respectively 127% and 119% greater than those of controls (panalysis distinguishes persons with labyrinth disorder from those without. The COM trajectories also identify movement inefficiencies attributable to vestibulopathy.

Let the trajectories tell a quantum story: Post-entangling the SHARC scheme

International Nuclear Information System (INIS)

Ruiz, Pablo Sampedro; Sola, Ignacio R; González-Vázquez, Jesús

2015-01-01

A new method is proposed to perform Quantum Wave Packet Nuclear Dynamics on large systems, by making use of information obtained by Semi-Classical Quantum Dynamics. The key of the method resides in expressing the nuclear wave function of the system in a basis set determined by the positions of multiple trajectories at each time. (paper)

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

Science.gov (United States)

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.

New calculations of gross β-decay properties for astrophysical applications: Speeding-up the classical r process

International Nuclear Information System (INIS)

Moeller, Peter; Pfeiffer, Bernd; Kratz, Karl-Ludwig

2003-01-01

Recent compilations of experimental gross β-decay properties, i.e., half-lives (T 1/2 ) and neutron-emission probabilities (P n ), are compared to improved global macroscopic-microscopic model predictions. The model combines calculations within the quasiparticle (QP) random-phase approximation for the Gamow-Teller (GT) part with an empirical spreading of the QP strength and the gross theory for the first-forbidden part of β - decay. Nuclear masses are either taken from the 1995 data compilation of Audi et al., when available, otherwise from the finite-range droplet model. Especially for spherical and neutron-(sub-)magic isotopes a considerable improvement compared to our earlier predictions for pure GT decay (ADNDT, 1997) is observed. T 1/2 and P n values up to the neutron drip line have been used in r-process calculations within the classical 'waiting-point' approximation. With the new nuclear-physics input, a considerable speeding-up of the r-matter flow is observed, in particular at those r-abundance peaks which are related to magic neutron-shell closures

Graphical Method for Determining Projectile Trajectory

Science.gov (United States)

Moore, J. C.; Baker, J. C.; Franzel, L.; McMahon, D.; Songer, D.

2010-01-01

We present a nontrigonometric graphical method for predicting the trajectory of a projectile when the angle and initial velocity are known. Students enrolled in a general education conceptual physics course typically have weak backgrounds in trigonometry, making inaccessible the standard analytical calculation of projectile range. Furthermore,…

Comparing Classical Water Models Using Molecular Dynamics to Find Bulk Properties

Science.gov (United States)

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…

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

Science.gov (United States)

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.

Trajectory Control of Rendezvous with Maneuver Target Spacecraft

Science.gov (United States)

Zhou, Zhinqiang

2012-01-01

In this paper, a nonlinear trajectory control algorithm of rendezvous with maneuvering target spacecraft is presented. The disturbance forces on the chaser and target spacecraft and the thrust forces on the chaser spacecraft are considered in the analysis. The control algorithm developed in this paper uses the relative distance and relative velocity between the target and chaser spacecraft as the inputs. A general formula of reference relative trajectory of the chaser spacecraft to the target spacecraft is developed and applied to four different proximity maneuvers, which are in-track circling, cross-track circling, in-track spiral rendezvous and cross-track spiral rendezvous. The closed-loop differential equations of the proximity relative motion with the control algorithm are derived. It is proven in the paper that the tracking errors between the commanded relative trajectory and the actual relative trajectory are bounded within a constant region determined by the control gains. The prediction of the tracking errors is obtained. Design examples are provided to show the implementation of the control algorithm. The simulation results show that the actual relative trajectory tracks the commanded relative trajectory tightly. The predicted tracking errors match those calculated in the simulation results. The control algorithm developed in this paper can also be applied to interception of maneuver target spacecraft and relative trajectory control of spacecraft formation flying.

Classical treatments of quantum mechanical effects in collisions of weakly bound complexes

International Nuclear Information System (INIS)

Lopez, Jose G.; McCoy, Anne B.

2005-01-01

Classical and quantum simulations of Ne + Ar 2 collision dynamics are performed in order to investigate where quantum mechanical effects are most important and where classical simulations provide good descriptions of the dynamics. It is found that when Ar 2 is in a low-lying vibrational state, the differences between the results of quantum and quasiclassical simulations are profound. However, excellent agreement between the results of the quantum and classical simulations can be achieved when the initial conditions for the classical trajectories are sampled from the quantum phase space distribution given by the Wigner function. These effects are largest when collisions occur under constrained geometries or when Ar 2 is in its ground vibrational state. The results of this work suggest that sampling the initial conditions using the Wigner function provides a straightforward way to incorporate the most important quantum mechanical effects in simulations of collisions involving very cold weakly bound complexes

Classical oscillator with position-dependent mass in a complex domain

International Nuclear Information System (INIS)

Ghosh, Subir; Modak, Sujoy Kumar

2009-01-01

We study complexified Harmonic Oscillator with a position-dependent mass, termed as Complex Exotic Oscillator (CEO). The complexification induces a gauge invariance [A.V. Smilga, J. Phys. A 41 (2008) 244026, (arXiv:0706.4064); A. Mostafazadeh, J. Math. Phys. 43 (2002) 205; A. Mostafazadeh, J. Math. Phys. 43 (2002) 2814; A. Mostafazadeh, J. Math. Phys. 43 (2002) 3944]. The role of PT-symmetry is discussed from the perspective of classical trajectories of CEO for real energy. Some trajectories of CEO are similar to those for the particle in a quartic potential in the complex domain [C.M. Bender, S. Boettcher, P.N. Meisinger, J. Math. Phys. 40 (1999) 2201; C.M. Bender, D.D. Holm, D. Hook, J. Phys. A 40 (2007) F793, (arXiv:0705.3893)

Classical theory of radiating strings

Science.gov (United States)

Copeland, Edmund J.; Haws, D.; Hindmarsh, M.

1990-01-01

The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities.

Classical hair in string theory. II. Explicit calculations

International Nuclear Information System (INIS)

Larsen, F.

1997-01-01

For pt.I see ibid., vol.475, p.627-44, 1996. After emphasizing the importance of obtaining a space-time understanding of black hole entropy, we further elaborate our program to identify the degrees of freedom of black holes with classical space-time degrees of freedom. The Cvetic-Youm dyonic black holes are discussed in some detail as an example. In this example hair degrees of freedom transforming as an effective string can be identified explicitly. We discuss issues concerning charge quantization, identification of winding, and tension renormalization that arise in counting the associated degrees of freedom. The possibility of other forms of hair in this example, and the prospects for making contact with D-brane ideas, are briefly considered. (orig.)

Microscopic phenomenon in light of classical and quantum theory

International Nuclear Information System (INIS)

Mandal, C.R.

1999-01-01

Quantum mechanical boundary corrected continuum intermediate state (BCCIS) approximation and classical trajectory Monte Carlo (CTMC) simulation method have been employed to study total charge transfer cross sections in collisions of Be q+ (q = 2-4) and B q+ (q = 3-5) with atomic hydrogen in ground state in the energy range of 30 - 200 keV/amu. Results have been found to be in reasonable agreement with each other. Attempts have been made to find justifications for such resemblance. (author)

Calculation of beam source geometry of electron accelerator for radiation technologies

International Nuclear Information System (INIS)

Balalykin, N.I.; Derendyaev, Yu.S.; Dolbilov, G.V.; Karlov, A.A.; Korenev, S.A.; Petrov, V.A.; Smolyakova, T.F.

1994-01-01

ELLIPT and GRAFOR programmes written in FORTRAN language were developed to calculate the geometry of an electron source. The programmes enable calculation of electromagnetic field of the source and electron trajectories in the source under preset boundary and initial conditions. The GRAFOR programme allows to display electric field curves and calculated trajectories of large particles. 4 refs., 1 fig

Parametric Approach to Trajectory Tracking Control of Robot Manipulators

Directory of Open Access Journals (Sweden)

Shijie Zhang

2013-01-01

Full Text Available The mathematic description of the trajectory of robot manipulators with the optimal trajectory tracking problem is formulated as an optimal control problem, and a parametric approach is proposed for the optimal trajectory tracking control problem. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, a practical method is presented to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results of 2-link robot manipulator are presented to show the effectiveness of the proposed method.

Classical and quantum mechanics of the damped harmonic oscillator

International Nuclear Information System (INIS)

Dekker, H.

1981-01-01

The relations between various treatments of the classical linearly damped harmonic oscillator and its quantization are investigated. In the course of a historical survey typical features of the problem are discussed on the basis of Havas' classical Hamiltonian and the quantum mechanical Suessmann-Hasse-Albrecht models as coined by the Muenchen/Garching nuclear physics group. It is then shown how by imposing a restriction on the classical trajectories in order to connect the Hamiltonian with the energy, the time-independent Bateman-Morse-Feshbach-Bopp Hamiltonian leads to the time-dependent Caldirola-Kanai Hamiltonian. Canonical quantization of either formulation entails a violation of Heisenberg's principle. By means of a unified treatment of both the electrical and mechanical semi-infinite transmission line, this defect is related to the disregard of additional quantum fluctuations that are intrinsically connected with the dissipation. The difficulties of these models are discussed. Then it is proved that the Bateman dual Hamiltonian is connected to a recently developed complex symplectic formulation by a simple canonical transformation. (orig.)

Developing learning trajectory on the circumference of a cycle with realistic mathematics education (RME)

Science.gov (United States)

Indriani, Novi; Julie, Hongki

2017-08-01

According Nuranisa, the students' difficulties on a lesson about the circumference of a circle were to understand the concept of what was the circumference of a circle and solve problems associated with the circumference of a circle [8]. According Nuranisa, this is because the teacher only gives a formula to find the circumference of a circle without helping students to construct the formula [8]. The purposes of this study were (1) to develop the hypothetical learning trajectory (HLT) for the cycle circumference material, (2) to describe the student results from the HLT implementation. The type of research used in this research was the design research developed by Gravemeijer and Cobb (2006). According Gravemeijer and Cobb, the design research was divided into three stages: (1) preparing for the experiment, (2) design experiments, and (3) retrospective analysis [6]. In this study, researchers developed the student learning trajectories which were help students to construct their knowledge about the understanding and how to calculate the circumference of a circle. The context used on the students' learning trajectory was sports and arts event. The learning trajectory has been tried out for 15 grade five students on the Budya Wacana elementary school in Yogyakarta. In this paper, researchers would describe how the learning trajectory traversed students to construct their knowledge about the understanding and how to calculate the circumference of the circle and the student thinking process on the understanding and how to calculate the circumference of a circle. The results showed that students could construct about the understanding of the circumference of a circle and how to calculate the circumference of a circle through the student learning trajectory.

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

Science.gov (United States)

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.

Reference trajectory tracking for a multi-DOF robot arm

Directory of Open Access Journals (Sweden)

Krasňanský Róbert

2015-12-01

Full Text Available This paper presents the problem of tracking the generated reference trajectory by the simulation model of a multi-DOF robot arm. The kinematic transformation between task space and joint configuration coordinates is nonlinear and configuration dependent. To obtain the solution of the forward kinematics problem, the homogeneous transformation matrix is used. A solution to the inverse kinematics is a vector of joint configuration coordinates calculated using of pseudoinverse Jacobian technique. These coordinates correspond to a set of task space coordinates. The algorithm is presented which uses iterative solution and is simplified by considering stepper motors in robot arm joints. The reference trajectory in Cartesian coordinate system is generated on-line by the signal generator previously developed in MS Excel. Dynamic Data Exchange communication protocol allows sharing data with Matlab-Simulink. These data represent the reference tracking trajectory of the end effector. Matlab-Simulink software is used to calculate the representative joint rotations. The proposed algorithm is demonstrated experimentally on the model of 7-DOF robot arm system.

Multiphase Return Trajectory Optimization Based on Hybrid Algorithm

Directory of Open Access Journals (Sweden)

Yi Yang

2016-01-01

Full Text Available A hybrid trajectory optimization method consisting of Gauss pseudospectral method (GPM and natural computation algorithm has been developed and utilized to solve multiphase return trajectory optimization problem, where a phase is defined as a subinterval in which the right-hand side of the differential equation is continuous. GPM converts the optimal control problem to a nonlinear programming problem (NLP, which helps to improve calculation accuracy and speed of natural computation algorithm. Through numerical simulations, it is found that the multiphase optimal control problem could be solved perfectly.

Classical realizability in the CPS target language

DEFF Research Database (Denmark)

Frey, Jonas

2016-01-01

Motivated by considerations about Krivine's classical realizability, we introduce a term calculus for an intuitionistic logic with record types, which we call the CPS target language. We give a reformulation of the constructions of classical realizability in this language, using the categorical...... techniques of realizability triposes and toposes. We argue that the presentation of classical realizability in the CPS target language simplifies calculations in realizability toposes, in particular it admits a nice presentation of conjunction as intersection type which is inspired by Girard's ludics....

Mean motion and trajectories of heavy particles falling through a boundary layer

Energy Technology Data Exchange (ETDEWEB)

Stout, J.E.; Arya, S.P. [North Carolina State Univ., Raleigh, NC (United States)

1994-12-31

As particles fall through a turbulent boundary layer they experience a rather complex and unique time series of aerodynamic forces and, thus, each individual particle follows a rather complex and unique trajectory to the surface. For sufficiently large and heavy particles, the turbulence induced particle motion can be thought of as a small perturbation superimposed on the mean trajectory. By ignoring the turbulent contribution to particle motion it is possible to calculate the trajectory of a particle due to the mean flow alone. The mean trajectory provides an estimate of the ensemble-averaged path of a set of particles released from a given point in the atmosphere. The effect of turbulence on individual particle trajectories, the distribution of particle displacements from the mean trajectory, and their deposition patterns on the surface will be investigated in a separate study, using a random walk model.

Reconstruction of equilibrium trajectories during whole-body movements.

Science.gov (United States)

Domen, K; Latash, M L; Zatsiorsky, V M

1999-03-01

The framework of the equilibrium-point hypothesis was used to reconstruct equilibrium trajectories (ETs) of the ankle, hip and body center of mass during quick voluntary hip flexions ('Japanese courtesy bow') by standing subjects. Different spring loads applied to the subject's back were used to introduce smooth perturbations that are necessary to reconstruct ETs based on a series of trials at the same task. Time patterns of muscle torques were calculated using inverse dynamics techniques. A second-order linear model was employed to calculate the instantaneous position of the spring-like joint or center of mass characteristic at different times during the movement. ETs of the joints and of the center of mass had significantly different shapes from the actual trajectories. Integral measures of electromyographic bursts of activity in postural muscles demonstrated a relation to muscle length corresponding to the equilibrium-point hypothesis.

The importance of trajectory modelling in accident consequence assessments

International Nuclear Information System (INIS)

Jones, J.A.; Williams, J.A.; Hill, M.D.

1988-01-01

Most atmospheric dispersion models used at present or probabilistic risk assessment (PRA) are linear: they take account of the wind speed but not the direction after the first hour. Therefore, the trajectory model is a more realistic description of the cloud's behaviour. However, the extra complexity means that the computing costs increase. This is an important factor for the MARIA code which is intended to be run on computers of varying power. The numbers of early effects predicted by a linear model and a trajectory model in a probabilistic risk assessment were compared to see which model should be preferred. The trajectory model predicted about 25% fewer expected early deaths and 30% more people evacuated than the linear model. However, the trajectory model took about ten times longer to calculate its results. The choice between the two models may depend on the speed of the computer available

Wigner's dynamical transition state theory in phase space: classical and quantum

International Nuclear Information System (INIS)

Waalkens, Holger; Schubert, Roman; Wiggins, Stephen

2008-01-01

We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs the evolution from reactants to products in high dimensional systems. In the classical case this is the standard Poincaré–Birkhoff normal form. In the quantum case we develop a normal form based on the Weyl calculus and an explicit algorithm for computing this quantum normal form. The classical normal form allows us to discover and compute the phase space structures that govern classical reaction dynamics. From this knowledge we are able to provide a direct construction of an energy dependent dividing surface in phase space having the properties that trajectories do not locally 're-cross' the surface and the directional flux across the surface is minimal. Using this, we are able to give a formula for the directional flux through the dividing surface that goes beyond the harmonic approximation. We relate this construction to the flux–flux autocorrelation function which is a standard ingredient in the expression for the reaction rate in the chemistry community. We also give a classical mechanical interpretation of the activated complex as a normally hyperbolic invariant manifold (NHIM), and further describe the structure of the NHIM. The quantum normal form provides us with an efficient algorithm to compute quantum reaction rates and we relate this algorithm to the quantum version of the flux–flux autocorrelation function formalism. The significance of the classical phase space structures for the quantum mechanics of reactions is elucidated by studying the phase space distribution of scattering states. The quantum normal form also provides an efficient way of computing Gamov–Siegert resonances. We relate these resonances to the lifetimes of the quantum activated

Examples of Complete Solvability of 2D Classical Superintegrable Systems

Science.gov (United States)

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.

New Search Space Reduction Algorithm for Vertical Reference Trajectory Optimization

Directory of Open Access Journals (Sweden)

Alejandro MURRIETA-MENDOZA

2016-06-01

Full Text Available Burning the fuel required to sustain a given flight releases pollution such as carbon dioxide and nitrogen oxides, and the amount of fuel consumed is also a significant expense for airlines. It is desirable to reduce fuel consumption to reduce both pollution and flight costs. To increase fuel savings in a given flight, one option is to compute the most economical vertical reference trajectory (or flight plan. A deterministic algorithm was developed using a numerical aircraft performance model to determine the most economical vertical flight profile considering take-off weight, flight distance, step climb and weather conditions. This algorithm is based on linear interpolations of the performance model using the Lagrange interpolation method. The algorithm downloads the latest available forecast from Environment Canada according to the departure date and flight coordinates, and calculates the optimal trajectory taking into account the effects of wind and temperature. Techniques to avoid unnecessary calculations are implemented to reduce the computation time. The costs of the reference trajectories proposed by the algorithm are compared with the costs of the reference trajectories proposed by a commercial flight management system using the fuel consumption estimated by the FlightSim® simulator made by Presagis®.

Quantum-classical correspondence in the vicinity of periodic orbits

Science.gov (United States)

Kumari, Meenu; Ghose, Shohini

2018-05-01

Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical correspondence near periodic orbits of Floquet systems. Our method shows how the stability of classical periodic orbits affects quantum dynamics. We demonstrate our method by analyzing quantum-classical correspondence in the quantum kicked top (QKT), which exhibits both regular and chaotic behavior. We use our correspondence conditions to identify signatures of classical bifurcations even in a deep quantum regime. Our method can be used to explain the breakdown of quantum-classical correspondence in chaotic systems.

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

International Nuclear Information System (INIS)

Mastromatteo, Michael; Jackson, Bret

2013-01-01

Electronic structure methods based on density functional theory are used to construct a reaction path Hamiltonian for CH 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 vibrational 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

A quasi-classical study of energy transfer in collisions of hyperthermal H atoms with SO2 molecules.

Science.gov (United States)

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.

Taylor Series Trajectory Calculations Including Oblateness Effects and Variable Atmospheric Density

Science.gov (United States)

Scott, James R.

2011-01-01

Taylor series integration is implemented in NASA Glenn's Spacecraft N-body Analysis Program, and compared head-to-head with the code's existing 8th- order Runge-Kutta Fehlberg time integration scheme. This paper focuses on trajectory problems that include oblateness and/or variable atmospheric density. Taylor series is shown to be significantly faster and more accurate for oblateness problems up through a 4x4 field, with speedups ranging from a factor of 2 to 13. For problems with variable atmospheric density, speedups average 24 for atmospheric density alone, and average 1.6 to 8.2 when density and oblateness are combined.

Simulations of High Speed Fragment Trajectories

Science.gov (United States)

Yeh, Peter; Attaway, Stephen; Arunajatesan, Srinivasan; Fisher, Travis

2017-11-01

Flying shrapnel from an explosion are capable of traveling at supersonic speeds and distances much farther than expected due to aerodynamic interactions. Predicting the trajectories and stable tumbling modes of arbitrary shaped fragments is a fundamental problem applicable to range safety calculations, damage assessment, and military technology. Traditional approaches rely on characterizing fragment flight using a single drag coefficient, which may be inaccurate for fragments with large aspect ratios. In our work we develop a procedure to simulate trajectories of arbitrary shaped fragments with higher fidelity using high performance computing. We employ a two-step approach in which the force and moment coefficients are first computed as a function of orientation using compressible computational fluid dynamics. The force and moment data are then input into a six-degree-of-freedom rigid body dynamics solver to integrate trajectories in time. Results of these high fidelity simulations allow us to further understand the flight dynamics and tumbling modes of a single fragment. Furthermore, we use these results to determine the validity and uncertainty of inexpensive methods such as the single drag coefficient model.

Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation.

Science.gov (United States)

Zamstein, Noa; Tannor, David J

2012-12-14

We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys. 125, 231103 (2006)] to treat non-adiabatic transitions. Each trajectory evolves on a single surface according to Newton's laws with complex positions and momenta. The transfer of amplitude between surfaces stems naturally from the equations of motion, without the need for surface hopping. In this paper we derive the equations of motion and show results in the diabatic representation, which is rarely used in trajectory methods for calculating non-adiabatic dynamics. We apply our method to the first two benchmark models introduced by Tully [J. Chem. Phys. 93, 1061 (1990)]. Besides giving the probability branching ratios between the surfaces, the method also allows the reconstruction of the time-dependent wavepacket. Our results are in quantitative agreement with converged quantum mechanical calculations.

Evaluation of Adherence to Nutritional Intervention Through Trajectory Analysis.

Science.gov (United States)

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.

Entropy method of measuring and evaluating periodicity of quasi-periodic trajectories

Science.gov (United States)

Ni, Yanshuo; Turitsyn, Konstantin; Baoyin, Hexi; Junfeng, Li

2018-06-01

This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform (DFT) to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem (CRTBP) are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator (OFLI). The results show that entropy is a better tool for discriminating periodicity in quasiperiodic trajectories than OFLI and can detect periodicity while excluding the spirals that are judged as periodic cases by OFLI. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.

The quantum potential and ''causal'' trajectories for stationary states and for coherent states

International Nuclear Information System (INIS)

Barut, A.O.; Bozic, M.

1988-07-01

We show for stationary states in a central potential that the quantum action S is only a part of the classical action W and derive an expression for the ''quantum potential'' U Q in terms of the other part. The association of momenta of some ''particles'' in the causal interpretation of quantum mechanics by p-vector=∇S and by dp-vector'/dt=-∇(V+U Q ) gives for stationary states very different orbits which have no relation to classical orbits but express some flow properties of the quantum mechanical current. For coherent states, on the other hand, p-vector and p-vector' as well as the quantum mechanical average p-vector and classical momenta, all four, lead to essentially the same trajectories except for different integration constants. The spinning particle is also considered. (author). 27 refs, 2 figs

Wilson loop, Regge trajectory and hadron masses in a Yang-Mills theory from semiclassical strings

International Nuclear Information System (INIS)

Bigazzi, F.; Cotrone, A.L.; Martucci, L.; Pando Zayas, L.A.

2004-07-01

We compute the one-loop string corrections to the Wilson loop, glueball Regge trajectory and stringy hadron masses in the Witten model of non supersymmetric, large-N Yang-Mills theory. The classical string configurations corresponding to the above field theory objects are respectively: open straight strings, folded closed spinning strings, and strings orbiting in the internal part of the supergravity background. For the rectangular Wilson loop we show that besides the standard Luscher term, string corrections provide a rescaling of the field theory string tension. The one-loop corrections to the linear glueball Regge trajectories render them nonlinear with a positive intercept, as in the experimental soft Pomeron trajectory. Strings orbiting in the internal space predict a spectrum of hadronic-like states charged under global flavor symmetries which falls in the same universality class of other confining models. (author)

Matricial theory in classical photoelasticity

International Nuclear Information System (INIS)

Apostol, D.

1980-01-01

The matrix calculus in classical photoelasticity is used. Transfer functions for different polariscope arrangements are calculated. Linear polariscopes, circular polariscopes, double-exposure method to obtain isochromatics and Tardy and Senarmont method of measuring fractional relative retardations are analysed using coherency matrix formalism. (author)

Classical region of a trapped Bose gas

Energy Technology Data Exchange (ETDEWEB)

Blakie, P Blair [Jack Dodd Centre for Photonics and Ultra-Cold Atoms, University of Otago, Dunedin (New Zealand); Davis, Matthew J [ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, QLD 4072 (Australia)

2007-06-14

The classical region of a Bose gas consists of all single particle modes that have a high average occupation and are well described by a classical field. Highly occupied modes only occur in massive Bose gases at ultra-cold temperatures, in contrast to the photon case where there are highly occupied modes at all temperatures. For the Bose gas the number of these modes is dependent on the temperature, the total number of particles and their interaction strength. In this paper, we characterize the classical region of a harmonically trapped Bose gas over a wide parameter regime. We use a Hartree-Fock approach to account for the effects of interactions, which we observe to significantly change the classical region as compared to the idealized case. We compare our results to full classical field calculations and show that the Hartree-Fock approach provides a qualitatively accurate description of a classical region for the interacting gas.

Classical Liouville action on the sphere with three hyperbolic singularities

Energy Technology Data Exchange (ETDEWEB)

Hadasz, Leszek E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew E-mail: jask@ift.uniwroc.pl

2004-08-30

The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.

Classical Liouville action on the sphere with three hyperbolic singularities

Science.gov (United States)

Hadasz, Leszek; Jaskólski, Zbigniew

2004-08-01

The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.

Classical Liouville action on the sphere with three hyperbolic singularities

International Nuclear Information System (INIS)

Hadasz, Leszek; Jaskolski, Zbigniew

2004-01-01

The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory

To calculation of electron-optical characteristics of crossed lenses

International Nuclear Information System (INIS)

Afanas'ev, V.P.; Gritsyuk, N.P.; Lachashvili, R.A.; Yavor, S.Ya.

1979-01-01

Two approaches are used for theoretical study of crossed lenses (CL), which are formed by plates with slits turned by 90 deg: 1) aberration determination according to axial determination of potential and 2) trajectory analysis of CL. While studying CL of definite configuration it is necessary to take into account aberrations of the highest order. The following conclusions are drawn: the classical method is applied for fast determination of the main characteristics, of CL by means of average power computers (the ''M-220'' or the ''Minsk-32'' computers); the trajectory analysis should be performed by means of power computer (the BESM-6) when it is necessary to obtain more detailed information of the CL, including the trajectory deflection along the system axis, the dimensions of the point source image taking into account the aberrations of the highest order

Complex dynamics in diatomic molecules. Part II: Quantum trajectories

International Nuclear Information System (INIS)

Yang, C.-D.; Weng, H.-J.

2008-01-01

The second part of this paper deals with quantum trajectories in diatomic molecules, which has not been considered before in the literature. Morse potential serves as a more accurate function than a simple harmonic oscillator for illustrating a realistic picture about the vibration of diatomic molecules. However, if we determine molecular dynamics by integrating the classical force equations derived from a Morse potential, we will find that the resulting trajectories do not consist with the probabilistic prediction of quantum mechanics. On the other hand, the quantum trajectory determined by Bohmian mechanics [Bohm D. A suggested interpretation of the quantum theory in terms of hidden variable. Phys. Rev. 1952;85:166-179] leads to the conclusion that a diatomic molecule is motionless in all its vibrational eigen-states, which also contradicts probabilistic prediction of quantum mechanics. In this paper, we point out that the quantum trajectory of a diatomic molecule completely consistent with quantum mechanics does exist and can be solved from the quantum Hamilton equations of motion derived in Part I, which is based on a complex-space formulation of fractal spacetime [El Naschie MS. A review of E-Infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons and Fractals 2004;19:209-36; El Naschie MS. E-Infinity theory - some recent results and new interpretations. Chaos, Solitons and Fractals 2006;29:845-853; El Naschie MS. The concepts of E-infinity. An elementary introduction to the cantorian-fractal theory of quantum physics. Chaos, Solitons and Fractals 2004;22:495-511; El Naschie MS. SU(5) grand unification in a transfinite form. Chaos, Solitons and Fractals 2007;32:370-374; Nottale L. Fractal space-time and microphysics: towards a theory of scale relativity. Singapore: World Scientific; 1993; Ord G. Fractal space time and the statistical mechanics of random works. Chaos, Soiltons and Fractals 1996;7:821-843] approach to quantum

Quantum trajectory approach to the geometric phase: open bipartite systems

International Nuclear Information System (INIS)

Yi, X X; Liu, D P; Wang, W

2005-01-01

Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other and then are entangled in the evolution. The geometric phase due to the quantum jump for both the bipartite system and its subsystems is calculated and analysed. As an example, we present two coupled spin-1/2 particles to detail the calculations

Trajectory data privacy protection based on differential privacy mechanism

Science.gov (United States)

Gu, Ke; Yang, Lihao; Liu, Yongzhi; Liao, Niandong

2018-05-01

In this paper, we propose a trajectory data privacy protection scheme based on differential privacy mechanism. In the proposed scheme, the algorithm first selects the protected points from the user’s trajectory data; secondly, the algorithm forms the polygon according to the protected points and the adjacent and high frequent accessed points that are selected from the accessing point database, then the algorithm calculates the polygon centroids; finally, the noises are added to the polygon centroids by the differential privacy method, and the polygon centroids replace the protected points, and then the algorithm constructs and issues the new trajectory data. The experiments show that the running time of the proposed algorithms is fast, the privacy protection of the scheme is effective and the data usability of the scheme is higher.

Analytic Electron Trajectories in an Extremely Relativistic Helical Wiggler an Application to the Proposed SLAC E166 Experiment.

CERN Document Server

ThomasDonohue, John

2004-01-01

The proposed experiment SLAC E166 intends to generate circularly polarized gamma rays of energy 10 MeV by passing a 15 GeV electron beam through a meter long wiggler with approximately 400 periods. Using an analytic model formulated by Rullier and me, I present calculations of electron trajectories. At this extremely high energy the trajectories are described quite well by the model, and an extremely simple picture emerges, even for trajectories that that fail to encircle the axis of the wiggler. Our calculations are successfully compared with standard numerical integration of the Lorentz force equations of motion. In addition, the calculation of the spectrum and angular distribution of the radiated photons is easily carried out.

Crack trajectory near a weld: Modeling and simulation

DEFF Research Database (Denmark)

Rashid, M.M.; Tvergaard, Viggo

2008-01-01

A 2D computational model of ductile fracture, in which arbitrary crack extension through the mesh is accommodated without mesh bias, is used to study ductile fracture near the weld line in welded aluminum plates. Comparisons of the calculated toughness behavior and crack trajectory are made...

TH-EF-BRB-10: Dosimetric Validation of a Trajectory Based Cranial SRS Treatment Technique On a Varian TrueBeam Linac

Energy Technology Data Exchange (ETDEWEB)

Wilson, B [University of British Columbia, Vancouver, BC (Canada); Vancouver Cancer Centre, Vancouver, BC (Canada); Gete, E [Vancouver Cancer Centre, Vancouver, BC (Canada)

2016-06-15

Purpose: This work investigates the dosimetric accuracy of a trajectory based delivery technique in which an optimized radiation beam is delivered along a Couch-Gantry trajectory that is formed by simultaneous rotation of the linac gantry and the treatment couch. Methods: Nine trajectory based cranial SRS treatment plans were created using in-house optimization software. The plans were calculated for delivery on the TrueBeam STx linac with 6MV photon beam. Dose optimization was performed along a user-defined trajectory using MLC modulation, dose rate modulation and jaw tracking. The pre-defined trajectory chosen for this study is formed by a couch rotation through its full range of 180 degrees while the gantry makes four partial arc sweeps which are 170 degrees each. For final dose calculation, the trajectory based plans were exported to the Varian Eclipse Treatment Planning System. The plans were calculated on a homogeneous cube phantom measuring 18.2×18.2×18.2 cm3 with the analytical anisotropic algorithm (AAA) using a 1mm3 calculation voxel. The plans were delivered on the TrueBeam linac via the developer’s mode. Point dose measurements were performed on 9 patients with the IBA CC01 mini-chamber with a sensitive volume of 0.01 cc. Gafchromic film measurements along the sagittal and coronal planes were performed on three of the 9 treatment plans. Point dose values were compared with ion chamber measurements. Gamma analysis comparing film measurement and AAA calculations was performed using FilmQA Pro. Results: The AAA calculations and measurements were in good agreement. The point dose difference between AAA and ion chamber measurements were within 2.2%. Gamma analysis test pass rates (2%, 2mm passing criteria) for the Gafchromic film measurements were >95%. Conclusion: We have successfully tested TrueBeam’s ability to deliver accurate trajectory based treatments involving simultaneous gantry and couch rotation with MLC and dose rate modulation along the

Bell trajectories for revealing quantum control mechanisms

International Nuclear Information System (INIS)

Dennis, Eric; Rabitz, Herschel

2003-01-01

The dynamics induced while controlling quantum systems by optimally shaped laser pulses have often been difficult to understand in detail. A method is presented for quantifying the importance of specific sequences of quantum transitions involved in the control process. The method is based on a ''beable'' formulation of quantum mechanics due to John Bell that rigorously maps the quantum evolution onto an ensemble of stochastic trajectories over a classical state space. Detailed mechanism identification is illustrated with a model seven-level system. A general procedure is presented to extract mechanism information directly from closed-loop control experiments. Application to simulated experimental data for the model system proves robust with up to 25% noise

Classical properties and semiclassical calculations in a spherical nuclear average potential

International Nuclear Information System (INIS)

Carbonell, J.; Brut, F.; Arvieu, R.; Touchard, J.

1984-03-01

We study the relation between the classical properties or an average nuclear potential and its spectral properties. We have drawn the energy-action surface of this potential and related its properties to the spectral ones in the framework of the EBK semiclassical method. We also describe a method allowing us to get the evolution of the spectrum with the mass number

A New Computational Technique for the Generation of Optimised Aircraft Trajectories

Science.gov (United States)

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.

Dynamic treatment of fission and fusion in two dimensions

International Nuclear Information System (INIS)

Nazareth, R.A.M.S.

1977-01-01

The barrier penetrability in two dimensions for nuclear fusion and fission phenomena is studied. The equations of fission static trajectories (minimum potential) in Hofmann formalism are derived and the influence of inertia parameters on the penetrability is verified. For fusion case, a realistic potential for exactly penetrability calculation is proposed. The transverse momentum to the fusion and the unidimensional calculation in classical approximation by choose the trajectory which turn into maximum the penetrability are considered. The exact penetrability is compared with calculation in the classical approximation which takes in account the possibility of appearing discontinuity in the barrier along of fusion pathway. (M.C.K.) [pt

Classical Electrodynamics Coupled to Quantum Mechanics for Calculation of Molecular Optical Properties: a RT-TDDFT/FDTD Approach

Energy Technology Data Exchange (ETDEWEB)

Chen, Hanning; McMahon, J. M.; Ratner, Mark A.; Schatz, George C.

2010-09-02

A new multiscale computational methodology was developed to effectively incorporate the scattered electric field of a plasmonic nanoparticle into a quantum mechanical (QM) optical property calculation for a nearby dye molecule. For a given location of the dye molecule with respect to the nanoparticle, a frequency-dependent scattering response function was first determined by the classical electrodynamics (ED) finite-difference time-domain (FDTD) approach. Subsequently, the time-dependent scattered electric field at the dye molecule was calculated using the FDTD scattering response function through a multidimensional Fourier transform to reflect the effect of polarization of the nanoparticle on the local field at the molecule. Finally, a real-time time-dependent density function theory (RT-TDDFT) approach was employed to obtain a desired optical property (such as absorption cross section) of the dye molecule in the presence of the nanoparticle’s scattered electric field. Our hybrid QM/ED methodology was demonstrated by investigating the absorption spectrum of the N3 dye molecule and the Raman spectrum of pyridine, both of which were shown to be significantly enhanced by a 20 nm diameter silver sphere. In contrast to traditional quantum mechanical optical calculations in which the field at the molecule is entirely determined by intensity and polarization direction of the incident light, in this work we show that the light propagation direction as well as polarization and intensity are important to nanoparticle-bound dye molecule response. At no additional computation cost compared to conventional ED and QM calculations, this method provides a reliable way to couple the response of the dye molecule’s individual electrons to the collective dielectric response of the nanoparticle.

Ion beam trajectory simulation of carbon isotopes in cyclotron DECY-13

International Nuclear Information System (INIS)

Pramudita Anggraita

2014-01-01

A simulation on the ion beam trajectories of various carbon isotopes "1"2C, "1"3C, and "1"4C in DECY-13 cyclotron has been carried out using Scilab 5.4.1 software. Calculations in the simulation were carried out in 3 dimensions. The simulation shows trajectory separations, which provide possibility for "1"4C measurement such as in carbon dating at accelerating voltage frequency of about 72 MHz. (author)

Path integral density matrix dynamics: a method for calculating time-dependent properties in thermal adiabatic and non-adiabatic systems.

Science.gov (United States)

Habershon, Scott

2013-09-14

We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.

Path integral density matrix dynamics: A method for calculating time-dependent properties in thermal adiabatic and non-adiabatic systems

International Nuclear Information System (INIS)

Habershon, Scott

2013-01-01

We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency

Quantum calculations of the carrier mobility: Methodology, Matthiessen's rule, and comparison with semi-classical approaches

Energy Technology Data Exchange (ETDEWEB)

Niquet, Yann-Michel, E-mail: yniquet@cea.fr; Nguyen, Viet-Hung; Duchemin, Ivan [L-Sim, SP2M, UMR-E CEA/UJF-Grenoble 1, INAC, Grenoble (France); Triozon, François [CEA, LETI-MINATEC, Grenoble (France); Nier, Olivier; Rideau, Denis [ST Microelectronics, Crolles (France)

2014-02-07

We discuss carrier mobilities in the quantum Non-Equilibrium Green's Functions (NEGF) framework. We introduce a method for the extraction of the mobility that is free from contact resistance contamination and with minimal needs for ensemble averages. We focus on silicon thin films as an illustration, although the method can be applied to various materials such as semiconductor nanowires or carbon nanostructures. We then introduce a new paradigm for the definition of the partial mobility μ{sub M} associated with a given elastic scattering mechanism “M,” taking phonons (PH) as a reference (μ{sub M}{sup −1}=μ{sub PH+M}{sup −1}−μ{sub PH}{sup −1}). We argue that this definition makes better sense in a quantum transport framework as it is free from long range interference effects that can appear in purely ballistic calculations. As a matter of fact, these mobilities satisfy Matthiessen's rule for three mechanisms [e.g., surface roughness (SR), remote Coulomb scattering (RCS) and phonons] much better than the usual, single mechanism calculations. We also discuss the problems raised by the long range spatial correlations in the RCS disorder. Finally, we compare semi-classical Kubo-Greenwood (KG) and quantum NEGF calculations. We show that KG and NEGF are in reasonable agreement for phonon and RCS, yet not for SR. We discuss the reasons for these discrepancies.

Report on the achievements in fiscal 1999 of research and development of fusion zones. Calculation science; 1999 nendo yugo ryoiki kenkyu kaihatsu seika hokokusho. Keisan kagaku

Energy Technology Data Exchange (ETDEWEB)

NONE

2000-03-01

In order to elucidate the mechanism for specific phenomena from the atom scale to the meso-scale, developmental research has been performed on a fusion type calculation method. This paper reports the achievements in fiscal 1999. In planning the policy of structuring the program package TACPAC and its application method, the program for materials STATE using the classical molecule dynamics method and the biological program, Peach, were selected as the programs to act as the nuclei. In continuing performance improvements respectively in the computer programs to be fused, and improving the performance of the software fused with them, the programs were transferred into a super-computer. As a result, it was found that the classical and the first principle quantum molecular dynamics method program STATE can be executed at high efficiency on the super-computer. In executing the challenging computer simulation and developing a calculation method for large scale systems, researches were performed on alcohol synthesizing reaction on copper surface and the status of association of gene DNA molecules with enzymes, and development was carried out on a matrix generation method to calculate non-empirical molecule trajectories of the large scale systems. (NEDO)

Ion trajectories of the MFTF unshielded 80-keV neutral-beam sources

International Nuclear Information System (INIS)

Ling, R.C.; Bulmer, R.H.; Cutler, T.A.; Foote, J.H.; Horvath, J.A.

1978-01-01

The trajectories of ions from the Magnetic Fusion Test Facility (MFTF) 80-keV neutral-beam sources are calculated to obtain a preliminary understanding of the ion-beam paths and the magnitude of the power densities. This information will be needed for locating and designing thermal (kinetic-energy) absorbers for the ions. The calculations are made by employing a number of previously written computer codes. The TIBRO code is used to calculate the trajectories of the ions in the fringe magnetic field of the MFTF machine, which can operate with a center-field intensity of up to 2 T. The SAMPP code gives three-dimensional views of the ion beams for better visualization of the ion-beam paths. Also used are the codes MIG, XPICK, and MERGE, which were all previously written for manipulating data

Kick-Off Point (KOP and End of Buildup (EOB Data Analysis in Trajectory Design

Directory of Open Access Journals (Sweden)

Novrianti Novrianti

2017-06-01

Full Text Available Well X is a development well which is directionally drilled. Directional drilling is choosen because the coordinate target of Well X is above the buffer zone. The directional track plan needs accurate survey calculation in order to make the righ track for directional drilling. There are many survey calculation in directional drilling such as tangential, underbalance, average angle, radius of curvature, and mercury method. Minimum curvature method is used in this directional track plan calculation. This method is used because it gives less error than other method.  Kick-Off Point (KOP and End of Buildup (EOB analysis is done at 200 ft, 400 ft, and 600 ft depth to determine the trajectory design and optimal inclination. The hole problem is also determined in this trajectory track design. Optimal trajectory design determined at 200 ft depth because the inclination below 35º and also already reach the target quite well at 1632.28 ft TVD and 408.16 AHD. The optimal inclination at 200 ft KOP depth because the maximum inclination is 18.87º which is below 35º. Hole problem will occur if the trajectory designed at 600 ft. The problems are stuck pipe and the casing or tubing will not able to bend.

A classical statistical model of heavy ion collisions

International Nuclear Information System (INIS)

Schmidt, R.; Teichert, J.

1980-01-01

The use of the computer code TRAJEC which represents the numerical realization of a classical statistical model for heavy ion collisions is described. The code calculates the results of a classical friction model as well as various multi-differential cross sections for heavy ion collisions. INPUT and OUTPUT information of the code are described. Two examples of data sets are given [ru

Ion trajectories quadrupole mass filters

International Nuclear Information System (INIS)

Ursu, D.; Lupsa, N.; Muntean, F.

1994-01-01

The present paper aims at bringing some contributions to the understanding of ion motion in quadrupole mass filters. The theoretical treatment of quadrupole mass filter is intended to be a concise derivation of the important physical relationships using Mathieu functions. A simple iterative method of numerical computation has been used to simulate ion trajectories in an ideal quadrupole field. Finally, some examples of calculation are presented with the aid of computer graphics. (Author) 14 Figs., 1 Tab., 20 Refs

Fluctuations of wavefunctions about their classical average

International Nuclear Information System (INIS)

Benet, L; Flores, J; Hernandez-Saldana, H; Izrailev, F M; Leyvraz, F; Seligman, T H

2003-01-01

Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations of the quantum wavefunctions around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes whose width is determined by the classical shape of the eigenfunction. To compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators, we develop a rescaling method for the components. The expectations are broadly confirmed, but deviations due to scars are observed. This effect is much reduced when both Hamiltonians have chaotic dynamics

[Brief survey of some foreign currents of classical acupuncture].

Science.gov (United States)

Andrews, Z; Zhang, S J

2017-05-28

This paper reviews the history of acupuncture's dissemination to Japan, France, and England in the modern period. In particular, it examines how Chinese acupuncture methods were modified in each of these countries and how these modifications were theoretically justified based on new readings of classical texts. In each country, these currents of acupuncture practice all claimed to be transmitting true traditional acupuncture, even as they developed along different trajectories and created new and different theories and practices of acupuncture. Some of these foreign methods were re-exported back to China, where they, in turn, have influenced the development of Chinese acupuncture.

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

Science.gov (United States)

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

2009-03-06

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

Statistical trajectory of an approximate EM algorithm for probabilistic image processing

International Nuclear Information System (INIS)

Tanaka, Kazuyuki; Titterington, D M

2007-01-01

We calculate analytically a statistical average of trajectories of an approximate expectation-maximization (EM) algorithm with generalized belief propagation (GBP) and a Gaussian graphical model for the estimation of hyperparameters from observable data in probabilistic image processing. A statistical average with respect to observed data corresponds to a configuration average for the random-field Ising model in spin glass theory. In the present paper, hyperparameters which correspond to interactions and external fields of spin systems are estimated by an approximate EM algorithm. A practical algorithm is described for gray-level image restoration based on a Gaussian graphical model and GBP. The GBP approach corresponds to the cluster variation method in statistical mechanics. Our main result in the present paper is to obtain the statistical average of the trajectory in the approximate EM algorithm by using loopy belief propagation and GBP with respect to degraded images generated from a probability density function with true values of hyperparameters. The statistical average of the trajectory can be expressed in terms of recursion formulas derived from some analytical calculations

Macroscopic and microscopic description of HE-HI collisions; classical equations of motion calculations

International Nuclear Information System (INIS)

Bodmer, A.R.

1978-01-01

The study of high energy heavy ion reactions includes the three principle a priori approaches used for central collisions, namely, hydrodynamics, cascade--Boltzman equation, and the classical equations of motion. While no clearly justified central or near central collisions are found, the classical equations of motion are used to illustrate some general features of these reactions. It is expected that the hot nuclear matter produced in such collisions is a dense, viscous, and thermally conductive fluid with important nonequilibrium and nonclassical features, rapidity, distribution, noncentral collisions, potential dependent effects for a given two-body scattering, and c.m. cross sections for a central collision with given parameters are among the properties considered. 12 references

Analytical calculation of spin tunneling effect in single molecule magnet Fe8 with considering quadrupole excitation

Directory of Open Access Journals (Sweden)

Y Yousefi

2018-02-01

Full Text Available Spin tunneling effect in Single Molecule Magnet Fe8 is studied by instanton calculation technique using SU(3 generalized spin coherent state in real parameter as a trial function. For this SMM, tunnel splitting arises due to the presence of a Berry like phase in action, which causes interference between tunneling trajectories (instantons. For this SMM, it is established that the use of quadrupole excitation (g dependence changes not only the location of the quenching points, but also the number of these points. Also, these quenching points are the steps in hysteresis loops of this SMM. If dipole and quadrupole excitations in classical energy considered, the number of these steps equals to the number that obtained from experimental data.

Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality

International Nuclear Information System (INIS)

Dai, Zhiping; Yang, Zhenjun; Ling, Xiaohui; Zhang, Shumin; Pang, Zhaoguang

2016-01-01

The interaction trajectory of solitons in nonlocal nonlinear media is investigated. A simple differential equation describing the interaction trajectories is derived based on the light ray equation. Numerical calculations are carried out to illustrate the interaction trajectories with different parameters. The results show that the degree of nonlocality greatly affects the interaction of solitons. For a strongly nonlocal case, the interaction trajectory can be described by a cosine function. Analytical expressions describing the trajectory and the oscillation period are obtained. For generally and weakly nonlocal cases, the interaction trajectories still oscillate periodically, however it is no longer sinusoidal and the oscillation period increases with the nonlocal degree decreasing. In addition, the trajectory of two solitons launched with a relative angle at the entrance plane is investigated. It is found that there exists a critical angle. When the initial relative angle is larger than the critical angle, the two solitons do not collide on propagation. The influence of the degree of nonlocality on the critical angle is also discussed.

Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases

Science.gov (United States)

Zhou, Chi-Chun; Dai, Wu-Sheng

2018-02-01

In statistical mechanics, for a system with a fixed number of particles, e.g. a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the canonical partition function is difficult. In this paper, based on the mathematical theory of the symmetric function, we suggest a method for the calculation of the canonical partition function of ideal quantum gases, including ideal Bose, Fermi, and Gentile gases. Moreover, we express the canonical partition functions of interacting classical and quantum gases given by the classical and quantum cluster expansion methods in terms of the Bell polynomial in mathematics. The virial coefficients of ideal Bose, Fermi, and Gentile gases are calculated from the exact canonical partition function. The virial coefficients of interacting classical and quantum gases are calculated from the canonical partition function by using the expansion of the Bell polynomial, rather than calculated from the grand canonical potential.

Lane changing trajectory planning and tracking control for intelligent vehicle on curved road.

Science.gov (United States)

Wang, Lukun; Zhao, Xiaoying; Su, Hao; Tang, Gongyou

2016-01-01

This paper explores lane changing trajectory planning and tracking control for intelligent vehicle on curved road. A novel arcs trajectory is planned for the desired lane changing trajectory. A kinematic controller and a dynamics controller are designed to implement the trajectory tracking control. Firstly, the kinematic model and dynamics model of intelligent vehicle with non-holonomic constraint are established. Secondly, two constraints of lane changing on curved road in practice (LCCP) are proposed. Thirdly, two arcs with same curvature are constructed for the desired lane changing trajectory. According to the geometrical characteristics of arcs trajectory, equations of desired state can be calculated. Finally, the backstepping method is employed to design a kinematic trajectory tracking controller. Then the sliding-mode dynamics controller is designed to ensure that the motion of the intelligent vehicle can follow the desired velocity generated by kinematic controller. The stability of control system is proved by Lyapunov theory. Computer simulation demonstrates that the desired arcs trajectory and state curves with B-spline optimization can meet the requirements of LCCP constraints and the proposed control schemes can make tracking errors to converge uniformly.

Long range trajectories

Energy Technology Data Exchange (ETDEWEB)

Allen, P. W.; Jessup, E. A.; White, R. E. [Air Resources Field Research Office, Las Vegas, Nevada (United States)

1967-07-01

A single air molecule can have a trajectory that can be described with a line, but most meteorologists use single lines to represent the trajectories of air parcels. A single line trajectory has the disadvantage that it is a categorical description of position. Like categorized forecasts it provides no qualification, and no provision for dispersion in case the parcel contains two or more molecules which may take vastly different paths. Diffusion technology has amply demonstrated that an initial aerosol cloud or volume of gas in the atmosphere not only grows larger, but sometimes divides into puffs, each having a different path or swath. Yet, the average meteorologist, faced with the problem of predicting the future motion of a cloud, usually falls back on the line trajectory approach with the explanation that he had no better tool for long range application. In his more rational moments, he may use some arbitrary device to spread his cloud with distance. One such technique has been to separate the trajectory into two or more trajectories, spaced about the endpoint of the original trajectory after a short period of travel, repeating this every so often like a chain reaction. This has the obvious disadvantage of involving a large amount of labor without much assurance of improved accuracy. Another approach is to draw a circle about the trajectory endpoint, to represent either diffusion or error. The problem then is to know what radius to give the circle and also whether to call it diffusion or error. Meteorologists at the Nevada Test Site (NTS) are asked frequently to provide advice which involves trajectory technology, such as prediction of an aerosol cloud path, reconstruction of the motion of a volume of air, indication of the dilution, and the possible trajectory prediction error over great distances. Therefore, we set out, nearly three years ago, to provide some statistical knowledge about the status of our trajectory technology. This report contains some of the

Variable trajectory model for regional assessments of air pollution from sulfur compounds.

Energy Technology Data Exchange (ETDEWEB)

Powell, D.C.; McNaughton, D.J.; Wendell, L.L.; Drake, R.L.

1979-02-01

This report describes a sulfur oxides atmospheric pollution model that calculates trajectories using single-layer historical wind data as well as chemical transformation and deposition following discrete contaminant air masses. Vertical diffusion under constraints is calculated, but all horizontal dispersion is a funcion of trajectory variation. The ground-level air concentrations and deposition are calculated in a rectangular area comprising the northeastern United States and southeastern Canada. Calculations for a 29-day assessment period in April 1974 are presented along with a limited verification. Results for the studies were calculated using a source inventory comprising 61% of the anthropogenic SO/sub 2/ emissions. Using current model parameterization levels, predicted concentration values are most sensitive to variations in dry deposition of SO/sub 2/, wet deposition of sulfate, and transformation of SO/sub 2/ to sulfate. Replacing the variable mixed-layer depth and variable stability features of the model with constant definitions of each results in increased ground-level concentration predicions for SO/sub 2/ and particularly for sulfate.

Brane classical and quantum cosmology from an effective action

International Nuclear Information System (INIS)

Seahra, Sanjeev S.; Sepangi, H.R.; Ponce de Leon, J.

2003-01-01

Motivated by the Randall-Sundrum braneworld scenario, we discuss the classical and quantum dynamics of a (d+1)-dimensional boundary wall between a pair of (d+2)-dimensional topological Schwarzschild-AdS black holes. We assume there are quite general--but not completely arbitrary--matter fields living on the boundary 'brane universe', and that its geometry is that of a Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The effective action governing the model in the minisuperspace approximation is derived. We find that the presence of black hole horizons in the bulk gives rise to a complex action for certain classically allowed brane configurations, but that the imaginary contribution plays no role in the equations of motion. Classical and instanton brane trajectories are examined in general and for special cases, and we find a subset of configuration space that is not allowed at the classical or semiclassical level; this subset corresponds to spacelike branes carrying tachyonic matter. The Hamiltonization and Dirac quantization of the model is then performed for the general case; the latter involves the manipulation of the Hamiltonian constraint before it is transformed into an operator that annihilates physical state vectors. The ensuing covariant Wheeler-DeWitt equation is examined at the semiclassical level, and we consider the possible localization of the brane universe's wave function away from the cosmological singularity. This is easier to achieve for branes with low density and/or spherical spatial sections

Brane classical and quantum cosmology from an effective action

Science.gov (United States)

Seahra, Sanjeev S.; Sepangi, H. R.; Ponce de Leon, J.

2003-09-01

Motivated by the Randall-Sundrum braneworld scenario, we discuss the classical and quantum dynamics of a (d+1)-dimensional boundary wall between a pair of (d+2)-dimensional topological Schwarzschild-AdS black holes. We assume there are quite general—but not completely arbitrary—matter fields living on the boundary “brane universe,” and that its geometry is that of a Friedmann-Lemaître-Robertson-Walker (FLRW) model. The effective action governing the model in the minisuperspace approximation is derived. We find that the presence of black hole horizons in the bulk gives rise to a complex action for certain classically allowed brane configurations, but that the imaginary contribution plays no role in the equations of motion. Classical and instanton brane trajectories are examined in general and for special cases, and we find a subset of configuration space that is not allowed at the classical or semiclassical level; this subset corresponds to spacelike branes carrying tachyonic matter. The Hamiltonization and Dirac quantization of the model is then performed for the general case; the latter involves the manipulation of the Hamiltonian constraint before it is transformed into an operator that annihilates physical state vectors. The ensuing covariant Wheeler-DeWitt equation is examined at the semiclassical level, and we consider the possible localization of the brane universe’s wave function away from the cosmological singularity. This is easier to achieve for branes with low density and/or spherical spatial sections.

Trajectory Browser Website

Science.gov (United States)

Foster, Cyrus; Jaroux, Belgacem A.

2012-01-01

The Trajectory Browser is a web-based tool developed at the NASA Ames Research Center to be used for the preliminary assessment of trajectories to small-bodies and planets and for providing relevant launch date, time-of-flight and V requirements. The site hosts a database of transfer trajectories from Earth to asteroids and planets for various types of missions such as rendezvous, sample return or flybys. A search engine allows the user to find trajectories meeting desired constraints on the launch window, mission duration and delta V capability, while a trajectory viewer tool allows the visualization of the heliocentric trajectory and the detailed mission itinerary. The anticipated user base of this tool consists primarily of scientists and engineers designing interplanetary missions in the context of pre-phase A studies, particularly for performing accessibility surveys to large populations of small-bodies. The educational potential of the website is also recognized for academia and the public with regards to trajectory design, a field that has generally been poorly understood by the public. The website is currently hosted on NASA-internal URL http://trajbrowser.arc.nasa.gov/ with plans for a public release as soon as development is complete.

TRAJECTORIES AND DISTRIBUTION OF INTERSTELLAR DUST GRAINS IN THE HELIOSPHERE

International Nuclear Information System (INIS)

Slavin, Jonathan D.; Frisch, Priscilla C.; Müller, Hans-Reinhard; Heerikhuisen, Jacob; Pogorelov, Nikolai V.; Reach, William T.; Zank, Gary

2012-01-01

The solar wind carves a bubble in the surrounding interstellar medium (ISM) known as the heliosphere. Charged interstellar dust grains (ISDG) encountering the heliosphere may be diverted around the heliopause or penetrate it depending on their charge-to-mass ratio. We present new calculations of trajectories of ISDG in the heliosphere, and the dust density distributions that result. We include up-to-date grain charging calculations using a realistic UV radiation field and full three-dimensional magnetohydrodynamic fluid + kinetic models for the heliosphere. Models with two different (constant) polarities for the solar wind magnetic field (SWMF) are used, with the grain trajectory calculations done separately for each polarity. Small grains a gr ∼ gr ∼> 1.0 μm, pass into the inner solar system and are concentrated near the Sun by its gravity. Trajectories of intermediate size grains depend strongly on the SWMF polarity. When the field has magnetic north pointing to ecliptic north, the field de-focuses the grains resulting in low densities in the inner heliosphere, while for the opposite polarity the dust is focused near the Sun. The ISDG density outside the heliosphere inferred from applying the model results to in situ dust measurements is inconsistent with local ISM depletion data for both SWMF polarities but is bracketed by them. This result points to the need to include the time variation in the SWMF polarity during grain propagation. Our results provide valuable insights for interpretation of the in situ dust observations from Ulysses.

Enhanced tunneling through nonstationary barriers

International Nuclear Information System (INIS)

Palomares-Baez, J. P.; Rodriguez-Lopez, J. L.; Ivlev, B.

2007-01-01

Quantum tunneling through a nonstationary barrier is studied analytically and by a direct numerical solution of Schroedinger equation. Both methods are in agreement and say that the main features of the phenomenon can be described in terms of classical trajectories which are solutions of Newton's equation in complex time. The probability of tunneling is governed by analytical properties of a time-dependent perturbation and the classical trajectory in the plane of complex time. Some preliminary numerical calculations of Euclidean resonance (an easy penetration through a classical nonstationary barrier due to an underbarrier interference) are presented

Management by Trajectory: Trajectory Management Study Report

Science.gov (United States)

Leiden, Kenneth; Atkins, Stephen; Fernandes, Alicia D.; Kaler, Curt; Bell, Alan; Kilbourne, Todd; Evans, Mark

2017-01-01

In order to realize the full potential of the Next Generation Air Transportation System (NextGen), improved management along planned trajectories between air navigation service providers (ANSPs) and system users (e.g., pilots and airline dispatchers) is needed. Future automation improvements and increased data communications between aircraft and ground automation would make the concept of Management by Trajectory (MBT) possible.

Classical theory of electric and magnetic fields

CERN Document Server

Good, Roland H

1971-01-01

Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction. The book also focuses on electrostatics and the general methods for solving electrostatic problems concerning images, inversion, complex variable, or separation of variables. The text also explains ma

WE-AB-209-06: Dynamic Collimator Trajectory Algorithm for Use in VMAT Treatment Deliveries

Energy Technology Data Exchange (ETDEWEB)

MacDonald, L [Department of Medical Physics, Dalhousie University, Halifax, Nova Scotia, CA (Canada); Thomas, C; Syme, A [Department of Medical Physics, Dalhousie University, Halifax, Nova Scotia, CA (Canada); Department of Radiation Oncology, Dalhousie University, Halifax, Nova Scotia (Canada); Medical Physics, Nova Scotia Cancer Centre, Halifax, Nova Scotia (Canada)

2016-06-15

Purpose: To develop advanced dynamic collimator positioning algorithms for optimal beam’s-eye-view (BEV) fitting of targets in VMAT procedures, including multiple metastases stereotactic radiosurgery procedures. Methods: A trajectory algorithm was developed, which can dynamically modify the angle of the collimator as a function of VMAT control point to provide optimized collimation of target volume(s). Central to this algorithm is a concept denoted “whitespace”, defined as area within the jaw-defined BEV field, outside of the PTV, and not shielded by the MLC when fit to the PTV. Calculating whitespace at all collimator angles and every control point, a two-dimensional topographical map depicting the tightness-of-fit of the MLC was generated. A variety of novel searching algorithms identified a number of candidate trajectories of continuous collimator motion. Ranking these candidate trajectories according to their accrued whitespace value produced an optimal solution for navigation of this map. Results: All trajectories were normalized to minimum possible (i.e. calculated without consideration of collimator motion constraints) accrued whitespace. On an acoustic neuroma case, a random walk algorithm generated a trajectory with 151% whitespace; random walk including a mandatory anchor point improved this to 148%; gradient search produced a trajectory with 137%; and bi-directional gradient search generated a trajectory with 130% whitespace. For comparison, a fixed collimator angle of 30° and 330° accumulated 272% and 228% of whitespace, respectively. The algorithm was tested on a clinical case with two metastases (single isocentre) and identified collimator angles that allow for simultaneous irradiation of the PTVs while minimizing normal tissue irradiation. Conclusion: Dynamic collimator trajectories have the potential to improve VMAT deliveries through increased efficiency and reduced normal tissue dose, especially in treatment of multiple cranial metastases

WE-AB-209-06: Dynamic Collimator Trajectory Algorithm for Use in VMAT Treatment Deliveries

International Nuclear Information System (INIS)

MacDonald, L; Thomas, C; Syme, A

2016-01-01

Purpose: To develop advanced dynamic collimator positioning algorithms for optimal beam’s-eye-view (BEV) fitting of targets in VMAT procedures, including multiple metastases stereotactic radiosurgery procedures. Methods: A trajectory algorithm was developed, which can dynamically modify the angle of the collimator as a function of VMAT control point to provide optimized collimation of target volume(s). Central to this algorithm is a concept denoted “whitespace”, defined as area within the jaw-defined BEV field, outside of the PTV, and not shielded by the MLC when fit to the PTV. Calculating whitespace at all collimator angles and every control point, a two-dimensional topographical map depicting the tightness-of-fit of the MLC was generated. A variety of novel searching algorithms identified a number of candidate trajectories of continuous collimator motion. Ranking these candidate trajectories according to their accrued whitespace value produced an optimal solution for navigation of this map. Results: All trajectories were normalized to minimum possible (i.e. calculated without consideration of collimator motion constraints) accrued whitespace. On an acoustic neuroma case, a random walk algorithm generated a trajectory with 151% whitespace; random walk including a mandatory anchor point improved this to 148%; gradient search produced a trajectory with 137%; and bi-directional gradient search generated a trajectory with 130% whitespace. For comparison, a fixed collimator angle of 30° and 330° accumulated 272% and 228% of whitespace, respectively. The algorithm was tested on a clinical case with two metastases (single isocentre) and identified collimator angles that allow for simultaneous irradiation of the PTVs while minimizing normal tissue irradiation. Conclusion: Dynamic collimator trajectories have the potential to improve VMAT deliveries through increased efficiency and reduced normal tissue dose, especially in treatment of multiple cranial metastases

The trajectory prediction of spacecraft by grey method

International Nuclear Information System (INIS)

Wang, Qiyue; Wang, Zhongyu; Zhang, Zili; Wang, Yanqing; Zhou, Weihu

2016-01-01

The real-time and high-precision trajectory prediction of a moving object is a core technology in the field of aerospace engineering. The real-time monitoring and tracking technology are also significant guarantees of aerospace equipment. A dynamic trajectory prediction method called grey dynamic filter (GDF) which combines the dynamic measurement theory and grey system theory is proposed. GDF can use coordinates of the current period to extrapolate coordinates of the following period. At meantime, GDF can also keep the instantaneity of measured coordinates by the metabolism model. In this paper the optimal model length of GDF is firstly selected to improve the prediction accuracy. Then the simulation for uniformly accelerated motion and variably accelerated motion is conducted. The simulation results indicate that the mean composite position error of GDF prediction is one-fifth to that of Kalman filter (KF). By using a spacecraft landing experiment, the prediction accuracy of GDF is compared with the KF method and the primitive grey method (GM). The results show that the motion trajectory of spacecraft predicted by GDF is much closer to actual trajectory than the other two methods. The mean composite position error calculated by GDF is one-eighth to KF and one-fifth to GM respectively. (paper)

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

Science.gov (United States)

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

Citation classics in pediatrics: a bibliometric analysis.

Science.gov (United States)

Chhapola, Viswas; Tiwari, Soumya; Deepthi, Bobbity; Kanwal, Sandeep Kumar

2018-03-06

Citation analysis provides insights into the history and developmental trajectory of scientific fields. Our objective was to perform an analysis of citation classics in the journals of pediatric specialty and to examine their characteristics. Initially, all the journals listed under the category of pediatrics (n = 120) were identified using Journal Citation Reports. Web of science database was then searched (1950-2016) to select the top-100 cited articles in the above identified pediatric journals. The top-100 cited article were categorized according the study design, sub-specialty, country, institutional affiliation, and language. The top-100 articles were published in 18 different journals, with Pediatrics having the highest numbers (n = 40), followed by The Journal of Pediatrics (n = 17). The majority (n = 62) of classics were published after 1990. The most cited article had citation count of 3516 and the least cited had a citation count of 593. The USA (n = 71) was the most commonly represented country, and 60 institutions contributed to 100 articles. Fifteen authors contributed to more than one classic as first or second author. Observational study (n = 55) was the commonest study design across all decades, followed by reviews (n = 12), scale development studies (n = 11), and guidelines (n = 11). Among the pediatric sub-specialties, growth and development articles were highly cited (n = 24), followed by pediatric psychiatry and behavior (n = 21), endocrinology (n = 15), and neonatology (n = 12). The top-100 cited articles in pediatrics identify the impactful authors, journals, institutes, and countries. Observational study design was predominant-implying that inclusion among citation classics is not related to soundness of study design.

Calculation of pion form factor

International Nuclear Information System (INIS)

Vahedi, N.; Amirarjomand, S.

1975-09-01

The pion form factor is calculated using the structure function Wsub(2), which incorporates kinematical constraints, threshold behaviour and scaling. The Bloom-Gilman sum rule is used and only the two leading Regge trajectories are taken into account

Wind field and trajectory models for tornado-propelled objects

International Nuclear Information System (INIS)

Anon

1978-01-01

This report contains the results of the second phase of a research program which has as its objective the development of a mathematical model to predict the trajectory of tornado-borne objects postulated to be in the vicinity of nuclear power plants. An improved tornado wind field model satisfies the no-slip ground boundary condition of fluid mechanics and includes the functional dependence of eddy viscosity with altitude. Sub-scale wind tunnel data are obtained for all of the missiles currently specified for nuclear plant design. Confirmatory full-scale data are obtained for a 12-inch pipe and automobile. The original six-degree-of-freedom trajectory model is modified to include the improved wind field and increased capability as to body shapes and inertial characteristics that can be handled. The improved trajectory model is used to calculate maximum credible speeds, which for all of the heavy missiles are considerably less than those currently specified for design. Equivalent coefficients for use in three-degree-of-freedom models are developed and the sensitivity of range and speed to various trajectory parameters for the 12-inch diameter pipe is examined

Trajectories of martian habitability.

Science.gov (United States)

Cockell, Charles S

2014-02-01

Beginning from two plausible starting points-an uninhabited or inhabited Mars-this paper discusses the possible trajectories of martian habitability over time. On an uninhabited Mars, the trajectories follow paths determined by the abundance of uninhabitable environments and uninhabited habitats. On an inhabited Mars, the addition of a third environment type, inhabited habitats, results in other trajectories, including ones where the planet remains inhabited today or others where planetary-scale life extinction occurs. By identifying different trajectories of habitability, corresponding hypotheses can be described that allow for the various trajectories to be disentangled and ultimately a determination of which trajectory Mars has taken and the changing relative abundance of its constituent environments.

Classical quantum theory of wobbling modes

International Nuclear Information System (INIS)

Onishi, Naoki

1986-01-01

Wobbling modes are studied extensively in terms of time-dependent variational theory. Quantum states and their energies are determined by the Bohr-Sommerfeld rule of classical quantization. Numerical calculations are performed for states of 166 Er with vertical strokejvertical stroke=30-40 (h/2π). (orig.)

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

International Nuclear Information System (INIS)

Miller, William H.; Cotton, Stephen J.

2016-01-01

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.

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.

Science.gov (United States)

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.

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

Energy Technology Data Exchange (ETDEWEB)

Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com [Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)

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.

Ionization of atoms or ions by electron or proton impact; calculations with the classical three-body theory. ch. 3

International Nuclear Information System (INIS)

Boesten, L.G.J.

1978-01-01

Calculations on the threshold ionization of H, He + and Li 2+ by electrons have been performed to study the so-called 'post-collision interaction' (P.C.I.) effects which appear to affect the threshold ionization process significantly. These effects are caused by the long range Coulomb interactions between the two electrons as they move away from the nucleus. The long range interactions are fully taken into account in the classical three-body collision theory. In quantum mechanical theories, however, it is difficult to account for these interactions. This theory has been used to study the ionization of He + -ions by electron impact up to much higher energies (up till ten times the threshold energy). The results are compared with experimental results of Dolder et al. (1961) and with results of quantum mechanical calculations. Results are given for ionization of helium atoms by electron or proton impact. This collision process, in which four particles are involved, can under certain circumstances be treated as a collision process in which only three particles are involved. Calculations are performed concerning: a) cross sections for ionization of metastable helium atoms by electron impact, b) cross sections for ionization of ground-state helium atoms by fast proton impact (energy and angular distributions of ejected electrons), c) generalized oscillator strengths for ionization of helium by fast proton impact

Description of classical and quantum interference in view of the concept of flow line

OpenAIRE

Davidovic, M.; Sanz, A. S.; Bozic, M.

2015-01-01

© 2015, Springer Science+Business Media New York. Bohmian mechanics, a hydrodynamic formulation of quantum mechanics, relies on the concept of trajectory, which evolves in time in compliance with dynamical information conveyed by the wave function. Here, this appealing idea is considered to analyze both classical and quantum interference, thus providing an alternative and more intuitive framework to understand the time evolution of waves either in terms of the flow of energy (for instance, fo...

Coordinated trajectory planning of dual-arm space robot using constrained particle swarm optimization

Science.gov (United States)

Wang, Mingming; Luo, Jianjun; Yuan, Jianping; Walter, Ulrich

2018-05-01

Application of the multi-arm space robot will be more effective than single arm especially when the target is tumbling. This paper investigates the application of particle swarm optimization (PSO) strategy to coordinated trajectory planning of the dual-arm space robot in free-floating mode. In order to overcome the dynamics singularities issue, the direct kinematics equations in conjunction with constrained PSO are employed for coordinated trajectory planning of dual-arm space robot. The joint trajectories are parametrized with Bézier curve to simplify the calculation. Constrained PSO scheme with adaptive inertia weight is implemented to find the optimal solution of joint trajectories while specific objectives and imposed constraints are satisfied. The proposed method is not sensitive to the singularity issue due to the application of forward kinematic equations. Simulation results are presented for coordinated trajectory planning of two kinematically redundant manipulators mounted on a free-floating spacecraft and demonstrate the effectiveness of the proposed method.

On the Optimization of Aerospace Plane Ascent Trajectory

Science.gov (United States)

Al-Garni, Ahmed; Kassem, Ayman Hamdy

A hybrid heuristic optimization technique based on genetic algorithms and particle swarm optimization has been developed and tested for trajectory optimization problems with multi-constraints and a multi-objective cost function. The technique is used to calculate control settings for two types for ascending trajectories (constant dynamic pressure and minimum-fuel-minimum-heat) for a two-dimensional model of an aerospace plane. A thorough statistical analysis is done on the hybrid technique to make comparisons with both basic genetic algorithms and particle swarm optimization techniques with respect to convergence and execution time. Genetic algorithm optimization showed better execution time performance while particle swarm optimization showed better convergence performance. The hybrid optimization technique, benefiting from both techniques, showed superior robust performance compromising convergence trends and execution time.

Classical solutions in lattice gauge theories

International Nuclear Information System (INIS)

Mitrjushkin, V.K.

1996-08-01

The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non-abelian theories. Possible applications of these solutions to the calculation of gauge dependent and gauge invariant observables are discussed. (orig.)

TRAJECTORIES AND DISTRIBUTION OF INTERSTELLAR DUST GRAINS IN THE HELIOSPHERE

Energy Technology Data Exchange (ETDEWEB)

Slavin, Jonathan D. [Harvard-Smithsonian Center for Astrophysics, MS 83, 60 Garden Street, Cambridge, MA 02138 (United States); Frisch, Priscilla C. [Department of Astronomy and Astrophysics, University of Chicago, 5460 S. Ellis Avenue, Chicago, IL 60637 (United States); Mueller, Hans-Reinhard [Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755 (United States); Heerikhuisen, Jacob; Pogorelov, Nikolai V. [Department of Physics and Center for Space Physics and Aeronomic Research, University of Alabama, Huntsville, AL 35899 (United States); Reach, William T. [Universities Space Research Association, MS 211-3, Moffett Field, CA 94035 (United States); Zank, Gary [Department of Physics and Center for Space Plasma and Aeronomic Research, University of Alabama, Huntsville, AL 35805 (United States)

2012-11-20

The solar wind carves a bubble in the surrounding interstellar medium (ISM) known as the heliosphere. Charged interstellar dust grains (ISDG) encountering the heliosphere may be diverted around the heliopause or penetrate it depending on their charge-to-mass ratio. We present new calculations of trajectories of ISDG in the heliosphere, and the dust density distributions that result. We include up-to-date grain charging calculations using a realistic UV radiation field and full three-dimensional magnetohydrodynamic fluid + kinetic models for the heliosphere. Models with two different (constant) polarities for the solar wind magnetic field (SWMF) are used, with the grain trajectory calculations done separately for each polarity. Small grains a {sub gr} {approx}< 0.01 {mu}m are completely excluded from the inner heliosphere. Large grains, a {sub gr} {approx}> 1.0 {mu}m, pass into the inner solar system and are concentrated near the Sun by its gravity. Trajectories of intermediate size grains depend strongly on the SWMF polarity. When the field has magnetic north pointing to ecliptic north, the field de-focuses the grains resulting in low densities in the inner heliosphere, while for the opposite polarity the dust is focused near the Sun. The ISDG density outside the heliosphere inferred from applying the model results to in situ dust measurements is inconsistent with local ISM depletion data for both SWMF polarities but is bracketed by them. This result points to the need to include the time variation in the SWMF polarity during grain propagation. Our results provide valuable insights for interpretation of the in situ dust observations from Ulysses.

Pairing effects in rotating nuclei: a semi classical approach

International Nuclear Information System (INIS)

Durand, M.

1985-10-01

The semi-classical phase-space distribution ρ(r,p) is calculated for rotating superfluid nuclei, taking into account the reaction of the pairing field to the rotational motion. Moments of inertia and current distributions calculated by means of this distribution pass continuously from a rigid to an irrotational behaviour

Power spectral density of a single Brownian trajectory: what one can and cannot learn from it

Science.gov (United States)

Krapf, Diego; Marinari, Enzo; Metzler, Ralf; Oshanin, Gleb; Xu, Xinran; Squarcini, Alessio

2018-02-01

The power spectral density (PSD) of any time-dependent stochastic process X t is a meaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of X t over an infinitely large observation time T, that is, it is defined as an ensemble-averaged property taken in the limit T\\to ∞ . A legitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a single trajectory recorded for a finite observation time T. In quest for this answer, for a d-dimensional Brownian motion (BM) we calculate the probability density function of a single-trajectory PSD for arbitrary frequency f, finite observation time T and arbitrary number k of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of BM trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is a fluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single-particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of BM, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for BM and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories.

A quasiclassical trajectory analysis of stereodynamics of the H + FCl ...

Indian Academy of Sciences (India)

Abstract. The chemical stereodynamics for the title reaction are studied by the quasiclassical trajectory method. Employing the recent works of Deskevich, Hayes, Takahashi, Skodje, and Nesbitt (DHTSN) potential energy surface of the ground 12A′ electronic state, the present work calculates the polarization- dependent ...

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

Science.gov (United States)

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.

Exact quantum dynamics study of the O++H2(v=0,j=0)→OH++H ion-molecule reaction and comparison with quasiclassical trajectory calculations

International Nuclear Information System (INIS)

Martinez, Rodrigo; Lucas, Josep M.; Gimenez, Xavier; Aguilar, Antonio; Gonzalez, Miguel

2006-01-01

The close-coupling hyperspherical (CCH) exact quantum method was used to study the title barrierless reaction up to a collision energy (E T ) of 0.75 eV, and the results compared with quasiclassical trajectory (QCT) calculations to determine the importance of quantum effects. The CCH integral cross section decreased with E T and, although the QCT results were in general quite similar to the CCH ones, they presented a significant deviation from the CCH data within the 0.2-0.6 eV collision energy range, where the QCT method did not correctly describe the reaction probability. A very good accord between both methods was obtained for the OH + vibrational distribution, where no inversion of population was found. For the OH + rotational distributions, the agreement between the CCH and QCT results was not as good as in the vibrational case, but it was satisfactory in many conditions. The kk ' angular distribution showed a preferential forward character, and the CCH method produced higher forward peaks than the QCT one. All the results were interpreted considering the potential energy surface and plots of a representative sampling of reactive trajectories

PANTHER. Trajectory Analysis

Energy Technology Data Exchange (ETDEWEB)

Rintoul, Mark Daniel [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Wilson, Andrew T. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Valicka, Christopher G. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Kegelmeyer, W. Philip [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Shead, Timothy M. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Newton, Benjamin D. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Czuchlewski, Kristina Rodriguez [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

2015-09-01

We want to organize a body of trajectories in order to identify, search for, classify and predict behavior among objects such as aircraft and ships. Existing compari- son functions such as the Fr'echet distance are computationally expensive and yield counterintuitive results in some cases. We propose an approach using feature vectors whose components represent succinctly the salient information in trajectories. These features incorporate basic information such as total distance traveled and distance be- tween start/stop points as well as geometric features related to the properties of the convex hull, trajectory curvature and general distance geometry. Additionally, these features can generally be mapped easily to behaviors of interest to humans that are searching large databases. Most of these geometric features are invariant under rigid transformation. We demonstrate the use of different subsets of these features to iden- tify trajectories similar to an exemplar, cluster a database of several hundred thousand trajectories, predict destination and apply unsupervised machine learning algorithms.

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

Science.gov (United States)

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.

Classical optics and curved spaces

International Nuclear Information System (INIS)

Bailyn, M.; Ragusa, S.

1976-01-01

In the eikonal approximation of classical optics, the unit polarization 3-vector of light satisfies an equation that depends only on the index, n, of refraction. It is known that if the original 3-space line element is d sigma 2 , then this polarization direction propagates parallely in the fictitious space n 2 d sigma 2 . Since the equation depends only on n, it is possible to invent a fictitious curved 4-space in which the light performs a null geodesic, and the polarization 3-vector behaves as the 'shadow' of a parallely propagated 4-vector. The inverse, namely, the reduction of Maxwell's equation, on a curve 'dielectric free) space, to a classical space with dielectric constant n=(-g 00 ) -1 / 2 is well known, but in the latter the dielectric constant epsilon and permeability μ must also equal (-g 00 ) -1 / 2 . The rotation of polarization as light bends around the sun by utilizing the reduction to the classical space, is calculated. This (non-) rotation may then be interpreted as parallel transport in the 3-space n 2 d sigma 2 [pt

Study on classical and excess eddy currents losses of Terfenol-D

Energy Technology Data Exchange (ETDEWEB)

Talebian, Soheil; Hojjat, Yousef [Department of Mechanical Engineering, Tarbiat Modares University, Tehran (Iran, Islamic Republic of); Ghodsi, Mojtaba [Department of Mechanical and Industrial Engineering, Sultan Qaboos University, Muscat (Oman); Karafi, Mohammad Reza [Department of Mechanical Engineering, Tarbiat Modares University, Tehran (Iran, Islamic Republic of)

2015-08-15

In the present paper, classical and excess eddy currents losses of Terfenol-D are studied and effects of magnetic field frequency, peak of magnetic flux density and diameter of Terfenol-D on the eddy currents losses are investigated. To provide reliable data for the purpose of the paper, an experimental laboratory is fabricated and used to obtain major and minor hysteresis loops of Terfenol-D at different frequencies. In theoretical study, initially an analytical model based on uniform distribution of magnetic flux is developed which yields to calculation of classical eddy currents losses. Then, another eddy currents model based on non-uniform distribution of magnetic flux and nonlinear diffusion of electromagnetic fields is presented. The difference between output values of the two models is identified as excess eddy currents losses. Obtained results show that the values of excess losses are generally larger than classical losses and applying just classical model leads to wrong calculation of actual value of eddy currents losses. For the results obtained from two above models, empirical models with respect to the magnetic field frequency and the peak value of magnetic flux density are achieved which can predict the eddy currents losses precisely. To validate the empirical relations, experiments are repeated at a new frequency and values of power losses calculated from analytical equations are compared with the predicted values of the empirical models. The results point towards possibility to use the obtained empirical relations in order to calculate the classical and excess eddy currents losses of Terfenol-D at the frequencies below 200 Hz and different values of magnetic flux density. - Highlights: • Classical eddy currents loss of Terfenol-D is studied using Maxwell's laws. • Excess eddy currents loss of Terfenol-D is studied using Mayergoyz nonlinear model. • Effects of Terfenol-D geometry on the eddy currents losses are investigated. • Power

Application of Back Trajectory Model to Predict Long Range Transport of Pollutant

International Nuclear Information System (INIS)

Shamsiah Abdul Rahman; Mohd Suhaimi Hamzah; Mohd Suhaimi Elias

2011-01-01

Trans-boundary haze pollution in Malaysia has become an issue that created a public attention over the past several years. The presence of haze not only caused by internal and external sources but it sometime coincided with the El Nino phenomenon which prolonged the dry season during the southwest monsoon in May to September. In this study fine particulate data (PM 2.5) of Klang Valley region covering the period from 1997 to 2008 were used to investigate the source location that responsible for the long range transport of pollutant. Back trajectory model the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) was used to calculate the air mass backward trajectories up to 120 hours (5 days) for the days when fine particle were sampled. (author)

The Monte Carlo applied for calculation dose

International Nuclear Information System (INIS)

Peixoto, J.E.

1988-01-01

The Monte Carlo method is showed for the calculation of absorbed dose. The trajectory of the photon is traced simulating sucessive interaction between the photon and the substance that consist the human body simulator. The energy deposition in each interaction of the simulator organ or tissue per photon is also calculated. (C.G.C.) [pt

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

Energy Technology Data Exchange (ETDEWEB)

Schubert, Alexander, E-mail: schubert@irsamc.ups-tlse.fr; Meier, Christoph [Laboratoire Collisions Agrégats et Réactivité, IRSAMC, UMR CNRS 5589, Université Paul Sabatier, 31062 Toulouse (France); Falvo, Cyril [Institut des Sciences Moléculaires d’Orsay (ISMO), CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France)

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 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.

Orbital magnetism in ensembles of ballistic billiards

International Nuclear Information System (INIS)

Ullmo, D.; Richter, K.; Jalabert, R.A.

1993-01-01

The magnetic response of ensembles of small two-dimensional structures at finite temperatures is calculated. Using semiclassical methods and numerical calculation it is demonstrated that only short classical trajectories are relevant. The magnetic susceptibility is enhanced in regular systems, where these trajectories appear in families. For ensembles of squares large paramagnetic susceptibility is obtained, in good agreement with recent measurements in the ballistic regime. (authors). 20 refs., 2 figs

Adaptive Trajectory Design

Data.gov (United States)

National Aeronautics and Space Administration — Adaptive Trajectory Design (ATD) is an original concept for quick and efficient end-to-end trajectory designs using proven piece-wise dynamical methods. With ongoing...

Minimum distance determination between consecutive carriers in the gamma irradiator IR-200 K trajectory

International Nuclear Information System (INIS)

Achmad Suntoro

2014-01-01

A design to determine the minimum distance between the consecutive carriers at the trajectory of gamma irradiators IR-200K is implemented. Equilibrium between centrifugal force of a moving carrier in circular trajectory and its gravity force as well as carrier dimensions are used as parameters in determining such a minimum distance. The minimum distance between the consecutive carriers in the design is defined 1.2 meters. The distance is 11.5% greater than the minimum distance theoretically calculated, namely 1,076 meters. Errors tolerance in construction/installation of the trajectory and other unexpected things during irradiator's operation are part of the consideration to enlarge the minimum distance from its theoretical value. The distance between the consecutive carriers will not affect throughput and efficiency of using radiation due to the straight trajectory segments do not need to follow such the minimum distance between the carriers, as the trajectory segments around the i radiation sources are straight. (author)

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

Science.gov (United States)

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. �

The evaluation of cutoff rigidities and reentrant albedo calculations for Palestine, Dallas, and Midland, Texas

International Nuclear Information System (INIS)

Shea, M.A.; Smart, D.F.

1975-01-01

By using the trajectory-tracing technique, cutoff rigidities for Palestine, Dallas, and Midland, Texas, have been calculated as a function of various zenith and azimuth angles. Extensive analysis of the trajectory calculations shows that there is a systematic uncertainty involved in computing the lowest allowed rigidity, and this uncertainty may be a significant fraction of the penumbral width. Continuation of the trajectory-tracing process below the Stormer cutoff allows an evaluation of the reentrant albedo, showing that the average invariant latitude of the guiding center of the trajectory at the albedo origin is the same as the average invariant latitude of the guiding center of the particle trajectory at the detection point. No significant difference in the cutoff rigidities for these locations is found when the external magnetic fields present in the magnetosphere are added to the geomagnetic field of internal origin

Classically dynamical behaviour of single particle in heavy nuclei

International Nuclear Information System (INIS)

Gu Jianzhong; Zhuo Yizhong; Wu Xizhen

1998-01-01

A detailed analysis of the classically dynamical behaviour of a nucleon in heavy nuclei in terms of the TCSM (two-center shell model) is presented. Poincare section is a convenient and reliable criterion to judge the regularity (or chaoticity) of a classical system. The numerical calculations in this work are carried out for a nucleon in 238 U. The Poincare section map and the Poincare surface of section for different conditions are presented

Energy Optimal Trajectories in Human Arm Motion Aiming for Assistive Robots

Directory of Open Access Journals (Sweden)

Lelai Zhou

2017-01-01

Full Text Available The energy expenditure in human arm has been of great interests for seeking optimal human arm trajectories. This paper presents a new way for calculating metabolic energy consumption of human arm motions. The purpose is to reveal the relationship between the energy consumption and the trajectory of arm motion, and further, the acceleration and arm orientation contributions. Human arm motion in horizontal plane is investigated by virtue of Qualisys motion capture system. The motion data is post-processed by a biomechanical model to obtain the metabolic expenditure. Results on the arm motion kinematics, dynamics and metabolic energy consumption, are included.

Numerical calculation of beam coupling impedances in synchrotron accelerators

International Nuclear Information System (INIS)

Haenichen, Lukas

2016-01-01

Beams of charged particles are of interest in various fields of research including particle and nuclear physics, material and medical science and many more. In synchrotron accelerators the accelerating section is passed periodically. A closed loop trajectory is enforced, by increasing the frequency of the accelerating electric field and the magnitude of the dipolar magnetic guide field synchronously. A synchrotron therefore consists of a circular assembly of various beamline elements which serve the purposes of accelerating and guiding the particle beam. For the flawless operation of such a machine it has to be assured that the particles perform a controlled motion along predefined trajectories. Amongst others, the fulfillment of the corresponding stability criteria is in close conjuction with the so-called beam coupling impedances which are an important figure of merit for collective effects in synchrotron accelerators. This work focuses on analytical and numerical methods for the calculation of beam coupling impedances. One of the primary objectives is to gain a better understanding of the electrodynamics related to charged particle beams, furthermore to recapitulate the mathematical description of charged particle beams in both time and frequency domain and finally establish the links between actual physics and numerical modeling. Analytical methods are usually restricted to symmetrical geometry and may solely serve for the approximate determination of the field distribution in real geometries or to validate certain numerical methods. More accurate prognosis is only possible with three-dimensional simulation models. Numerical simulation techniques have been established in the second half of the last century accompanying the evolution of many particle accelerators. Classical time domain codes were the prevailing simulation tools where the actual process of the particle motion sequence is reproduced. For the present case of a heavy ion synchrotron accelerator

Numerical calculation of beam coupling impedances in synchrotron accelerators

Energy Technology Data Exchange (ETDEWEB)

Haenichen, Lukas

2016-07-01

Beams of charged particles are of interest in various fields of research including particle and nuclear physics, material and medical science and many more. In synchrotron accelerators the accelerating section is passed periodically. A closed loop trajectory is enforced, by increasing the frequency of the accelerating electric field and the magnitude of the dipolar magnetic guide field synchronously. A synchrotron therefore consists of a circular assembly of various beamline elements which serve the purposes of accelerating and guiding the particle beam. For the flawless operation of such a machine it has to be assured that the particles perform a controlled motion along predefined trajectories. Amongst others, the fulfillment of the corresponding stability criteria is in close conjuction with the so-called beam coupling impedances which are an important figure of merit for collective effects in synchrotron accelerators. This work focuses on analytical and numerical methods for the calculation of beam coupling impedances. One of the primary objectives is to gain a better understanding of the electrodynamics related to charged particle beams, furthermore to recapitulate the mathematical description of charged particle beams in both time and frequency domain and finally establish the links between actual physics and numerical modeling. Analytical methods are usually restricted to symmetrical geometry and may solely serve for the approximate determination of the field distribution in real geometries or to validate certain numerical methods. More accurate prognosis is only possible with three-dimensional simulation models. Numerical simulation techniques have been established in the second half of the last century accompanying the evolution of many particle accelerators. Classical time domain codes were the prevailing simulation tools where the actual process of the particle motion sequence is reproduced. For the present case of a heavy ion synchrotron accelerator

Economic calculation in socialist countries

NARCIS (Netherlands)

Ellman, M.; Durlauf, S.N.; Blume, L.E.

2008-01-01

In the 1930s, when the classical socialist system emerged, economic decisions were based not on detailed and precise economic methods of calculation but on rough and ready political methods. An important method of economic calculation - particularly in the post-Stalin period - was that of

Lagrangian Transport Calculations Using UARS Data. Part I: Passive Tracers

Science.gov (United States)

Manney, G. L.; Lahoz, W. A.; Harwood, R. S.; Zurek, R. W.; Kumer, J. B.; Mergenthaler, J. L.; Roche, A. E.; O'Neill, A; Swinbank, R.; Waters, J. W.

1994-01-01

The transport of passive tracers observed by UARS has been simulated using computed trajectories of thousands of air parcels initialized on a three-dimensional stratospheric grid. These trajectories are calculated in isentropic coordinates using horizontal winds provided by the United Kingdom Meteorological Office data assimilation system and vertical (cross-isentropic) velocities computed using a fast radiation code.

Global aspects of classical integrable systems

CERN Document Server

Cushman, Richard H

2015-01-01

This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.

Trajectory modeling of gestational weight: A functional principal component analysis approach.

Directory of Open Access Journals (Sweden)

Menglu Che

Full Text Available Suboptimal gestational weight gain (GWG, which is linked to increased risk of adverse outcomes for a pregnant woman and her infant, is prevalent. In the study of a large cohort of Canadian pregnant women, our goals are to estimate the individual weight growth trajectory using sparsely collected bodyweight data, and to identify the factors affecting the weight change during pregnancy, such as prepregnancy body mass index (BMI, dietary intakes and physical activity. The first goal was achieved through functional principal component analysis (FPCA by conditional expectation. For the second goal, we used linear regression with the total weight gain as the response variable. The trajectory modeling through FPCA had a significantly smaller root mean square error (RMSE and improved adaptability than the classic nonlinear mixed-effect models, demonstrating a novel tool that can be used to facilitate real time monitoring and interventions of GWG. Our regression analysis showed that prepregnancy BMI had a high predictive value for the weight changes during pregnancy, which agrees with the published weight gain guideline.

Migration and spatial assimilation among U.S. Latinos: classical versus segmented trajectories.

Science.gov (United States)

South, Scott J; Crowder, Kyle; Chavez, Erick

2005-08-01

We used merged data from the Latino National Political Survey, the Panel Study of Income Dynamics, and the U.S. census to examine patterns and determinants of interneighborhood residential mobility between 1990 and 1995 for 2,074 U.S. residents of Mexican, Puerto Rican, and Cuban ethnicity. In several respects, our findings confirm the central tenets of spatial assimilation theory: Latino residential mobility into neighborhoods that are inhabited by greater percentages of non-Hispanic whites (i.e., Anglos) increases with human and financial capital and English-language use. However, these results also point to variations in the residential mobility process among Latinos that are broadly consistent with the segmented assimilation perspective on ethnic and immigrant incorporation. Net of controls, Puerto Ricans are less likely than Mexicans to move to neighborhoods with relatively large Anglo populations, and the generational and socioeconomic differences that are anticipated by the classical assimilation model emerge more strongly for Mexicans than for Puerto Ricans or Cubans. Among Puerto Ricans and Cubans, darker skin color inhibits mobility into Anglo neighborhoods.

Surface modeling of workpiece and tool trajectory planning for spray painting robot.

Directory of Open Access Journals (Sweden)

Yang Tang

Full Text Available Automated tool trajectory planning for spray-painting robots is still a challenging problem, especially for a large free-form surface. A grid approximation of a free-form surface is adopted in CAD modeling in this paper. A free-form surface model is approximated by a set of flat patches. We describe here an efficient and flexible tool trajectory optimization scheme using T-Bézier curves calculated in a new way from trigonometrical bases. The distance between the spray gun and the free-form surface along the normal vector is varied. Automotive body parts, which are large free-form surfaces, are used to test the scheme. The experimental results show that the trajectory planning algorithm achieves satisfactory performance. This algorithm can also be extended to other applications.

Entropy in the classical and quantum polymer black hole models

International Nuclear Information System (INIS)

Livine, Etera R; Terno, Daniel R

2012-01-01

We investigate the entropy counting for black hole horizons in loop quantum gravity (LQG). We argue that the space of 3D closed polyhedra is the classical counterpart of the space of SU(2) intertwiners at the quantum level. Then computing the entropy for the boundary horizon amounts to calculating the density of polyhedra or the number of intertwiners at fixed total area. Following the previous work (Bianchi 2011 Class. Quantum Grav. 28 114006) we dub these the classical and quantum polymer models for isolated horizons in LQG. We provide exact micro-canonical calculations for both models and we show that the classical counting of polyhedra accounts for most of the features of the intertwiner counting (leading order entropy and log-correction), thus providing us with a simpler model to further investigate correlations and dynamics. To illustrate this, we also produce an exact formula for the dimension of the intertwiner space as a density of ‘almost-closed polyhedra’. (paper)

Classical algebraic chromodynamics

International Nuclear Information System (INIS)

Adler, S.L.

1978-01-01

I develop an extension of the usual equations of SU(n) chromodynamics which permits the consistent introduction of classical, noncommuting quark source charges. The extension involves adding a singlet gluon, giving a U(n) -based theory with outer product P/sup a/(u,v) = (1/2)(d/sup a/bc + if/sup a/bc)(u/sup b/v/sup c/ - v/sup b/u/sup c/) which obeys the Jacobi identity, inner product S (u,v) = (1/2)(u/sup a/v/sup a/ + v/sup a/u/sup a/), and with the n 2 gluon fields elevated to algebraic fields over the quark color charge C* algebra. I show that provided the color charge algebra satisfies the condition S (P (u,v),w) = S (u,P (v,w)) for all elements u,v,w of the algebra, all the standard derivations of Lagrangian chromodynamics continue to hold in the algebraic chromodynamics case. I analyze in detail the color charge algebra in the two-particle (qq, qq-bar, q-barq-bar) case and show that the above consistency condition is satisfied for the following unique (and, interestingly, asymmetric) choice of quark and antiquark charges: Q/sup a//sub q/ = xi/sup a/, Q/sup a//sub q/ = xi-bar/sup a/ + delta/sup a/0(n/2)/sup 3/2/1, with xi/sup a/xi/sup b/ = (1/2)(d/sup a/bc + if/sup a/bc) xi/sup c/, xi-bar/sup a/xi-bar/sup b/ = -(1/2)(d/sup a/bc - if/sup a/bc) xi-bar/sup c/. The algebraic structure of the two-particle U(n) force problem, when expressed on an appropriately diagonalized basis, leads for all n to a classical dynamics problem involving an ordinary SU(2) Yang-Mills field with uniquely specified classical source charges which are nonparallel in the color-singlet state. An explicit calculation shows that local algebraic U(n) gauge transformations lead only to a rigid global rotation of axes in the overlying classical SU(2) problem, which implies that the relative orientations of the classical source charges have physical significance

Resonance charge exchange mechanism at high and moderate energies

International Nuclear Information System (INIS)

Bogdanov, A.V.; Gevorkyan, A.S.

1984-01-01

Charge exchange mechanisms at high and medium energies are investigated, ta king the resonance charge exchange of a proton by an hydrogen atom as an example . It is established that there are two classical charge exchange mechanisms rel ated to direct proton knockout from the bound state and one quantum-mechanical mechanism corresponding to the electron tunnelling from one bound state to anoth er. The classical cross-section diverges for two of these mechanisms, and the quasiclassical scattering amplitude must be calculated on the base of a complex classical trajectory. Physical grounds for the choice of such trajectories are discussed and calculations of the Van Vleck determinant for these mechanisms a re presented. Contributions from different mechanisms to the total charge excha nge cross-section are analyzed. A comparison with experimental data and results of other authors is made

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

Science.gov (United States)

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.

Computing with spatial trajectories

CERN Document Server

2011-01-01

Covers the fundamentals and the state-of-the-art research inspired by the spatial trajectory data Readers are provided with tutorial-style chapters, case studies and references to other relevant research work This is the first book that presents the foundation dealing with spatial trajectories and state-of-the-art research and practices enabled by trajectories

SU-F-BRB-16: A Spreadsheet Based Automatic Trajectory GEnerator (SAGE): An Open Source Tool for Automatic Creation of TrueBeam Developer Mode Robotic Trajectories

International Nuclear Information System (INIS)

Etmektzoglou, A; Mishra, P; Svatos, M

2015-01-01

Purpose: To automate creation and delivery of robotic linac trajectories with TrueBeam Developer Mode, an open source spreadsheet-based trajectory generation tool has been developed, tested and made freely available. The computing power inherent in a spreadsheet environment plus additional functions programmed into the tool insulate users from the underlying schema tedium and allow easy calculation, parameterization, graphical visualization, validation and finally automatic generation of Developer Mode XML scripts which are directly loadable on a TrueBeam linac. Methods: The robotic control system platform that allows total coordination of potentially all linac moving axes with beam (continuous, step-and-shoot, or combination thereof) becomes available in TrueBeam Developer Mode. Many complex trajectories are either geometric or can be described in analytical form, making the computational power, graphing and programmability available in a spreadsheet environment an easy and ideal vehicle for automatic trajectory generation. The spreadsheet environment allows also for parameterization of trajectories thus enabling the creation of entire families of trajectories using only a few variables. Standard spreadsheet functionality has been extended for powerful movie-like dynamic graphic visualization of the gantry, table, MLC, room, lasers, 3D observer placement and beam centerline all as a function of MU or time, for analysis of the motions before requiring actual linac time. Results: We used the tool to generate and deliver extended SAD “virtual isocenter” trajectories of various shapes such as parameterized circles and ellipses. We also demonstrated use of the tool in generating linac couch motions that simulate respiratory motion using analytical parameterized functions. Conclusion: The SAGE tool is a valuable resource to experiment with families of complex geometric trajectories for a TrueBeam Linac. It makes Developer Mode more accessible as a vehicle to quickly

SU-F-BRB-16: A Spreadsheet Based Automatic Trajectory GEnerator (SAGE): An Open Source Tool for Automatic Creation of TrueBeam Developer Mode Robotic Trajectories

Energy Technology Data Exchange (ETDEWEB)

Etmektzoglou, A; Mishra, P; Svatos, M [Varian Medical Systems, Palo Alto, CA (United States)

2015-06-15

Purpose: To automate creation and delivery of robotic linac trajectories with TrueBeam Developer Mode, an open source spreadsheet-based trajectory generation tool has been developed, tested and made freely available. The computing power inherent in a spreadsheet environment plus additional functions programmed into the tool insulate users from the underlying schema tedium and allow easy calculation, parameterization, graphical visualization, validation and finally automatic generation of Developer Mode XML scripts which are directly loadable on a TrueBeam linac. Methods: The robotic control system platform that allows total coordination of potentially all linac moving axes with beam (continuous, step-and-shoot, or combination thereof) becomes available in TrueBeam Developer Mode. Many complex trajectories are either geometric or can be described in analytical form, making the computational power, graphing and programmability available in a spreadsheet environment an easy and ideal vehicle for automatic trajectory generation. The spreadsheet environment allows also for parameterization of trajectories thus enabling the creation of entire families of trajectories using only a few variables. Standard spreadsheet functionality has been extended for powerful movie-like dynamic graphic visualization of the gantry, table, MLC, room, lasers, 3D observer placement and beam centerline all as a function of MU or time, for analysis of the motions before requiring actual linac time. Results: We used the tool to generate and deliver extended SAD “virtual isocenter” trajectories of various shapes such as parameterized circles and ellipses. We also demonstrated use of the tool in generating linac couch motions that simulate respiratory motion using analytical parameterized functions. Conclusion: The SAGE tool is a valuable resource to experiment with families of complex geometric trajectories for a TrueBeam Linac. It makes Developer Mode more accessible as a vehicle to quickly

Classical photodissociation dynamics with Bohr quantization: Application to the fragmentation of a van der Waals cluster

International Nuclear Information System (INIS)

Arbelo-González, W.; Bonnet, L.; Larrégaray, P.; Rayez, J.-C.; Rubayo-Soneira, J.

2012-01-01

Graphical abstract: A recent classical description of photodissociation dynamics in a quantum spirit is applied for the first time to a realistic process, the fragmentation of NeBr 2 . Highlights: ► The photo-dissociation of NeBr 2 is studied by means of two approaches. ► The first is the standard classical one with Gaussian binning. ► The second is a new method applied for the first time to a realistic system. ► The new method leads to exactly the same results as the standard one. ► However, it requires about 10 times less trajectories in the present case. - Abstract: The recent classical dynamical approach of photodissociations with Bohr quantization [L. Bonnet, J. Chem. Phys. 133 (2010) 174108] is applied for the first time to a realistic process, the photofragmentation of the van der Waals cluster NeBr 2 . We illustrate the fact that this approach, formally equivalent to the standard one, may be numerically much more efficient.

A New Methodology for Solving Trajectory Planning and Dynamic Load-Carrying Capacity of a Robot Manipulator

Directory of Open Access Journals (Sweden)

Wanjin Guo

2016-01-01

Full Text Available A new methodology using a direct method for obtaining the best found trajectory planning and maximum dynamic load-carrying capacity (DLCC is presented for a 5-degree of freedom (DOF hybrid robot manipulator. A nonlinear constrained multiobjective optimization problem is formulated with four objective functions, namely, travel time, total energy involved in the motion, joint jerks, and joint acceleration. The vector of decision variables is defined by the sequence of the time-interval lengths associated with each two consecutive via-points on the desired trajectory of the 5-DOF robot generalized coordinates. Then this vector of decision variables is computed in order to minimize the cost function (which is the weighted sum of these four objective functions subject to constraints on joint positions, velocities, acceleration, jerks, forces/torques, and payload mass. Two separate approaches are proposed to deal with the trajectory planning problem and the maximum DLCC calculation for the 5-DOF robot manipulator using an evolutionary optimization technique. The adopted evolutionary algorithm is the elitist nondominated sorting genetic algorithm (NSGA-II. A numerical application is performed for obtaining best found solutions of trajectory planning and maximum DLCC calculation for the 5-DOF hybrid robot manipulator.

Optimal trajectory planning and train scheduling for urban rail transit systems

CERN Document Server

Wang, Yihui; van den Boom, Ton; De Schutter, Bart

2016-01-01

This book contributes to making urban rail transport fast, punctual and energy-efficient –significant factors in the importance of public transportation systems to economic, environmental and social requirements at both municipal and national levels. It proposes new methods for shortening passenger travel times and for reducing energy consumption, addressing two major topics: (1) train trajectory planning: the authors derive a nonlinear model for the operation of trains and present several approaches for calculating optimal and energy-efficient trajectories within a given schedule; and (2) train scheduling: the authors develop a train scheduling model for urban rail systems and optimization approaches with which to balance total passenger travel time with energy efficiency and other costs to the operator. Mixed-integer linear programming and pseudospectral methods are among the new methods proposed for single- and multi-train systems for the solution of the nonlinear trajectory planning problem which involv...

Periodicity and quasi-periodicity for super-integrable hamiltonian systems

International Nuclear Information System (INIS)

Kibler, M.; Winternitz, P.

1990-01-01

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single-valued integrals of motion each. All finite trajectories are quasi-periodical; they become truly periodical if a commensurability condition is imposed on an angular momentum component

Classical diffusion in a field-reversed mirror

International Nuclear Information System (INIS)

Auerbach, S.P.; Condit, W.C.

1981-01-01

Classical transport of particles and heat in field-reversed mirrors is discussed. The X-points (field nulls on axis) are shown to have no deleterious effect on transport; this conclusion is true for any transport model. For an elongated Hill's vortex equilibrium the classical diffusion coefficient is calculated analytically and used to construct an analytic solution to the transport equation for particles or energy; this yields exact results for particle and energy confinement times. These life-times are roughly 3 to 6 times shorter than previous heuristic estimates. Experimentally determined life-times are within a factor of 3 to 4 of our estimates. To assess the impact of these results on reactor designs, the authors construct an analytic reactor model in which neutral-beam input balances ion heat loss. Energy loss due to synchrotron radiation is calculated analytically and shown to be negligible, even with no wall reflection. Formulas are presented which give the reactor parameters in terms of plasma temperature, energy multiplication factor Q, and allowed neutron wall loading. The effect of anomalous resistivity is incorporated heuristically by assuming an anomalous resistivity which is enhanced by a factor A over classical resistivity. For large A the minimum power of a reactor scales as Asup(11/6). A=50 gives a reactor design which still seems reasonable, but A=200 leads to extremely large, high-power reactors. (author)

An oilspill trajectory analysis model with a variable wind deflection angle

Science.gov (United States)

Samuels, W.B.; Huang, N.E.; Amstutz, D.E.

1982-01-01

The oilspill trajectory movement algorithm consists of a vector sum of the surface drift component due to wind and the surface current component. In the U.S. Geological Survey oilspill trajectory analysis model, the surface drift component is assumed to be 3.5% of the wind speed and is rotated 20 degrees clockwise to account for Coriolis effects in the Northern Hemisphere. Field and laboratory data suggest, however, that the deflection angle of the surface drift current can be highly variable. An empirical formula, based on field observations and theoretical arguments relating wind speed to deflection angle, was used to calculate a new deflection angle at each time step in the model. Comparisons of oilspill contact probabilities to coastal areas calculated for constant and variable deflection angles showed that the model is insensitive to this changing angle at low wind speeds. At high wind speeds, some statistically significant differences in contact probabilities did appear. ?? 1982.

Classical dynamics and its quantum analogues

International Nuclear Information System (INIS)

Park, D.

1979-01-01

In this book the author establishes mathematical connections between classical and quantum mechanics, between ray optics and wave optics. The approach is to consider classical mechanics as a limiting case of quantum mechanics, and ray optics as a limiting case of wave optics. The conceptual background is discussed where necessary, so the reader should be already fairly familiar with it. The main goal of this approach is the revelation that classical and quantum theory are not so different conceptually as one thinks at first exposure. The first chapters recall the basic facts about light waves and light rays and demonstrate the construction of Newtonian orbits from Schroedinger waves. In the following the Lagrangian and Hamiltonian formulation of few-body system is developed showing as often as possible the relations to the corresponding quantum systems. To illustrate the theory planetary motion using perturbation theory is treated in some detail and several calculations in general relativity such as the deflection and retardation of light by the sun and the precession of planetary perikelia are included. The final parts deal with the motions of systems of many particles. The quantum mechanics of rigid bodies is presented in analogy with the classical theory and contrasts are noted. There is also a discussion of the roles of spinors in the two theories. The book is intended as a text in classical mechanics for readers which have already some knowledge in classical and quantum mechanics. It may help to deepen their understanding of the relation between the old and new theory and show something of the ways in which new discoveries are made. (orig.) 891 HJ/orig. 892 BRE

The (ℎ/2π)-expansion for Regge-trajectories. 2. Relativistic equations

International Nuclear Information System (INIS)

Stepanov, S.S.; Tutik, R.S.

1992-01-01

The (h/2π)-expansion method, proposed earlier for deriving Regge trajectories for bound states of central potentials in the Schroedinger equation framework, is extended to the Klein-Gordon and Dirac equations with potentials having vector and scalar components. The simple recursion formulae, with the same form both for the parent and daughter Regge trajectories, are obtained. They provide, in principle, the calculation of the (h/2π)-expansion terms up to an arbitrary order. As an illustration, a superposition of the vector and scalar Coulomb potentials, and the funnel-shaped potential are treated with the technique developed. 20 refs.; 3 figs.; 1 table. (author)

Generic trajectory representation and trajectory following for wheeled robots

DEFF Research Database (Denmark)

Kjærgaard, Morten; Andersen, Nils Axel; Ravn, Ole

2014-01-01

will drive. Safe: Avoid fatal collisions. Based on a survey of existing methods and algorithms the article presents a generic way to represent constraints for different types of robots, a generic way to represent trajectories using Bëzier curves, a method to convert the trajectory so it can be driven...... in a smooth motion, a method to create a safe velocity profile for the robot, and a path following controller....

A users manual for a computer program which calculates time optical geocentric transfers using solar or nuclear electric and high thrust propulsion

Science.gov (United States)

Sackett, L. L.; Edelbaum, T. N.; Malchow, H. L.

1974-01-01

This manual is a guide for using a computer program which calculates time optimal trajectories for high-and low-thrust geocentric transfers. Either SEP or NEP may be assumed and a one or two impulse, fixed total delta V, initial high thrust phase may be included. Also a single impulse of specified delta V may be included after the low thrust state. The low thrust phase utilizes equinoctial orbital elements to avoid the classical singularities and Kryloff-Boguliuboff averaging to help insure more rapid computation time. The program is written in FORTRAN 4 in double precision for use on an IBM 360 computer. The manual includes a description of the problem treated, input/output information, examples of runs, and source code listings.

Automatic Generation of Complex Spatial Trajectories of the UAV and Synthesis of Control

Directory of Open Access Journals (Sweden)

S. B. Tkachev

2015-01-01

Full Text Available In this paper, we propose a new method and algorithms that allow us to design complex spatial trajectories for an unmanned aerial vehicle (UAV passing through a given sequence of waypoints in the three-dimensional space.The nonlinear six-dimensional model of the UAV center-of-mass motion given in the trajectory frame is used for calculations. The state vector includes the altitude, the along-track deviation, the cross-track position, the velocity, the flight-path angle and the heading angle. The longitudinal and transverse overloads and the angle between the cross overload vector and vertical plane are considered as controls. This angle is often named as the roll angle.The feature of the problem is that both positions at waypoints and additional conditions are given. These conditions determine orientation of the velocity vector at each point (using the flight path angle and the heading angle. We also set either the point-visiting time or the pointvisiting velocity. The full state vector and controls are fixed at the starting waypoint.To construct a spatial trajectory, the concept of inverse dynamics problems is applied, as well as modern results of mathematical control theory of nonlinear dynamical systems. The introduction of new virtual controls allows us to represent the original system as an affine (linear in control system. Then, the designed system is converted into the regular canonical form.When we set flight times between any two waypoints, the corresponding segments of the trajectory are designed using time-dependent polynomials of the fifth degree. These polynomials specify the altitude variation, the variation of the along-track deviation and that of the cross-track position. If the point-visiting times are not fixed, the transition to a new independent variable (the normalized mechanical energy of the system is used. This transition is possible if the energy varies monotonically. In this case, the spatial trajectory is defined as a

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

International Nuclear Information System (INIS)

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

2013-01-01

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

Quantum and classical vacuum forces at zero and finite temperature

International Nuclear Information System (INIS)

Niekerken, Ole

2009-06-01

In this diploma thesis the Casimir-Polder force at zero temperature and at finite temperatures is calculated by using a well-defined quantum field theory (formulated in position space) and the method of image charges. For the calculations at finite temperature KMS-states are used. The so defined temperature describes the temperature of the electromagnetic background. A one oscillator model for inhomogeneous dispersive absorbing dielectric material is introduced and canonically quantized to calculate the Casimir-Polder force at a dielectric interface at finite temperature. The model fulfils causal commutation relations and the dielectric function of the model fulfils the Kramer-Kronig relations. We then use the same methods to calculate the van der Waals force between two neutral atoms at zero temperature and at finite temperatures. It is shown that the high temperature behaviour of the Casimir-Polder force and the van der Waals force are independent of ℎ. This means that they have to be understood classically, what is then shown in an algebraic statistical theory by using classical KMS states. (orig.)

Structure evolution of mononuclear tungsten and molybdenum species in the protonation process: Insight from FPMD and DFT calculations

Science.gov (United States)

Zhang, Ning; Yi, Haibo; Zeng, Dewen; Zhao, Zhongwei; Wang, Wenlei; Costanzo, Francesca

2018-03-01

In this work, we apply static density functional theory (DFT) calculations, as well as classical and first-principles molecular dynamics (FPMD) simulations, using the free-energy perturbation method to study the protonation ability, active site and structures of W(VI) and Mo(VI) in acidic aqueous solution. Using FPMD simulations, utilizing the pKa's calculation technique, we concluded that the octahedral WO2(OH)2(H2O)2 is the true formula for tungstic acid (H2WO4), and the hydroxyl ligands are the acidic site. This aqueous structure of H2WO4 is analogous to the previously reported structure of molybdic acid (H2MoO4). The FPMD trajectories of the tungstic acid deprotonation show that the mono-protonated monotungstate ion (HWO4-) may partially exist as a five-coordinated WO3(OH)(H2O)- species except for the four-coordinated WO3(OH)- species. This result is supported by DFT calculations, with an isoenergetic point (ΔE = 1.9 kcal·mol-1) for the WO3(OH)(H2O)- and WO3(OH)- species, when explicit solvent molecules are taken into account. In contrast, for the H2MoO4 acid, FPMD trajectories during the deprotonation process show that two H2O ligands immediately escape from the first coordinated sphere of Mo(VI) to form the four-coordinated MoO3(OH)- species. This difference indicates that structural expansion of W(VI) began in the first protonated step, while that of Mo(VI) only occurs in the second step. In addition, our calculated first and second acid constants for tungstic acid are higher than previously reported values for molybdic acid. This result suggests that WO42- is more easily protonated than the MoO42- anion in the same acidic solution, which is further confirmed by DFT calculations of hydrated oxoanions and its protonated species, based upon the hydration energy.

Quantum versus classical dynamics in the optical centrifuge

Science.gov (United States)

Armon, Tsafrir; Friedland, Lazar

2017-09-01

The interplay between classical and quantum-mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum-mechanical formalism starting from either the ground state or a thermal ensemble. Two resonant mechanisms are identified, i.e., the classical autoresonance and the quantum-mechanical ladder climbing, yielding different dynamics and rotational excitation efficiencies. The rotating-wave approximation is used to analyze the two resonant regimes in the associated dimensionless two-parameter space and calculate the OC excitation efficiency. The results show good agreement between numerical simulations and theory and are relevant to existing experimental setups.

Reason of method of density functional in classical and quantum statistical mechanisms

International Nuclear Information System (INIS)

Dinariev, O.Yu.

2000-01-01

Interaction between phenomenological description of a multi-component mixture on the basis of entropy functional with members, square in terms of component density gradients and temperature, on the one hand, and description in the framework of classical and quantum statistical mechanics, on the other hand, was investigated. Explicit expressions for the entropy functional in the classical and quantum theory were derived. Then a square approximation for the case of minor disturbances of uniform state was calculated. In the approximation the addends square in reference to the gradient were singlet out. It permits calculation of the relevant phenomenological coefficients from the leading principles [ru

State-selective charge transfer and excitation in ion-ion interactions at intermediate and high energies

International Nuclear Information System (INIS)

Samanta, R; Purkait, M

2012-01-01

Boundary Corrected Continuum Intermediate State (BCCIS) approximation and Classical Trajectory Monte Carlo (CTMC) methods are applied to calculate the charge transfer and excitation cross sections for ion-ion collisions.

Construction of classical and non-classical coherent photon states

International Nuclear Information System (INIS)

Honegger, Reinhard; Rieckers, Alfred

2001-01-01

It is well known that the diagonal matrix elements of all-order coherent states for the quantized electromagnetic field have to constitute a Poisson distribution with respect to the photon number. The present work gives first the summary of a constructive scheme, developed previously, which determines in terms of an auxiliary Hilbert space all possible off-diagonal elements for the all-order coherent density operators in Fock space and which identifies all extremal coherent states. In terms of this formalism it is then demonstrated that each pure classical coherent state is a uniformly phase locked (quantum) coherent superposition of number states. In a mixed classical coherent state the exponential of the locked phase is shown to be replaced by a rather arbitrary unitary operator in the auxiliary Hilbert space. On the other hand classes for density operators--and for their normally ordered characteristic functions--of non-classical coherent states are obtained, especially by rather weak perturbations of classical coherent states. These illustrate various forms of breaking the classical uniform phase locking and exhibit rather peculiar properties, such as asymmetric fluctuations for the quadrature phase operators. Several criteria for non-classicality are put forward and applied to the elaborated non-classical coherent states, providing counterexamples against too simple arguments for classicality. It is concluded that classicality is only a stable concept for coherent states with macroscopic intensity

Fundamental theories of waves and particles formulated without classical mass

Science.gov (United States)

Fry, J. L.; Musielak, Z. E.

2010-12-01

Quantum and classical mechanics are two conceptually and mathematically different theories of physics, and yet they do use the same concept of classical mass that was originally introduced by Newton in his formulation of the laws of dynamics. In this paper, physical consequences of using the classical mass by both theories are explored, and a novel approach that allows formulating fundamental (Galilean invariant) theories of waves and particles without formally introducing the classical mass is presented. In this new formulation, the theories depend only on one common parameter called 'wave mass', which is deduced from experiments for selected elementary particles and for the classical mass of one kilogram. It is shown that quantum theory with the wave mass is independent of the Planck constant and that higher accuracy of performing calculations can be attained by such theory. Natural units in connection with the presented approach are also discussed and justification beyond dimensional analysis is given for the particular choice of such units.

Classical, Semi-classical and Quantum Noise

CERN Document Server

Poor, H; Scully, Marlan

2012-01-01

David Middleton was a towering figure of 20th Century engineering and science and one of the founders of statistical communication theory. During the second World War, the young David Middleton, working with Van Fleck, devised the notion of the matched filter, which is the most basic method used for detecting signals in noise. Over the intervening six decades, the contributions of Middleton have become classics. This collection of essays by leading scientists, engineers and colleagues of David are in his honor and reflect the wide  influence that he has had on many fields. Also included is the introduction by Middleton to his forthcoming book, which gives a wonderful view of the field of communication, its history and his own views on the field that he developed over the past 60 years. Focusing on classical noise modeling and applications, Classical, Semi-Classical and Quantum Noise includes coverage of statistical communication theory, non-stationary noise, molecular footprints, noise suppression, Quantum e...

Lunar and interplanetary trajectories

CERN Document Server

Biesbroek, Robin

2016-01-01

This book provides readers with a clear description of the types of lunar and interplanetary trajectories, and how they influence satellite-system design. The description follows an engineering rather than a mathematical approach and includes many examples of lunar trajectories, based on real missions. It helps readers gain an understanding of the driving subsystems of interplanetary and lunar satellites. The tables and graphs showing features of trajectories make the book easy to understand. .

Optimal trajectories of aircraft and spacecraft

Science.gov (United States)

Miele, A.

1990-01-01

Work done on algorithms for the numerical solutions of optimal control problems and their application to the computation of optimal flight trajectories of aircraft and spacecraft is summarized. General considerations on calculus of variations, optimal control, numerical algorithms, and applications of these algorithms to real-world problems are presented. The sequential gradient-restoration algorithm (SGRA) is examined for the numerical solution of optimal control problems of the Bolza type. Both the primal formulation and the dual formulation are discussed. Aircraft trajectories, in particular, the application of the dual sequential gradient-restoration algorithm (DSGRA) to the determination of optimal flight trajectories in the presence of windshear are described. Both take-off trajectories and abort landing trajectories are discussed. Take-off trajectories are optimized by minimizing the peak deviation of the absolute path inclination from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. The survival capability of an aircraft in a severe windshear is discussed, and the optimal trajectories are found to be superior to both constant pitch trajectories and maximum angle of attack trajectories. Spacecraft trajectories, in particular, the application of the primal sequential gradient-restoration algorithm (PSGRA) to the determination of optimal flight trajectories for aeroassisted orbital transfer are examined. Both the coplanar case and the noncoplanar case are discussed within the frame of three problems: minimization of the total characteristic velocity; minimization of the time integral of the square of the path inclination; and minimization of the peak heating rate. The solution of the second problem is called nearly-grazing solution, and its merits are pointed out as a useful

Semantic Enrichment of GPS Trajectories

NARCIS (Netherlands)

de Graaff, V.; van Keulen, Maurice; de By, R.A.

2012-01-01

Semantic annotation of GPS trajectories helps us to recognize the interests of the creator of the GPS trajectories. Automating this trajectory annotation circumvents the requirement of additional user input. To annotate the GPS traces automatically, two types of automated input are required: 1) a

X-ray computed tomography reconstruction on non-standard trajectories for robotized inspection

International Nuclear Information System (INIS)

Banjak, Hussein

2016-01-01

The number of industrial applications of computed tomography (CT) is large and rapidly increasing with typical areas of use in the aerospace, automotive and transport industry. To support this growth of CT in the industrial field, the identified requirements concern firstly software development to improve the reconstruction algorithms and secondly the automation of the inspection process. Indeed, the use of robots gives more flexibility in the acquisition trajectory and allows the control of large and complex objects, which cannot be inspected using classical CT systems. In this context of new CT trend, a robotic platform has been installed at CEA LIST to better understand and solve specific challenges linked to the robotization of the CT process. The considered system integrates two robots that move the X-ray generator and detector. This thesis aims at achieving this new development. In particular, the objective is to develop and implement analytical and iterative reconstruction algorithms adapted to such robotized trajectories. The main focus of this thesis is concerned with helical-like scanning trajectories. We consider two main problems that could occur during acquisition process: truncated and limited-angle data. We present in this work experimental results for reconstruction on such non-standard trajectories. CIVA software is used to simulate these complex inspections and our developed algorithms are integrated as reconstruction tools. This thesis contains three parts. In the first part, we introduce the basic principles of CT and we present an overview of existing analytical and iterative algorithms for non-standard trajectories. In the second part, we modify the approximate helical FDK algorithm to deal with transversely truncated data and we propose a modified FDK algorithm adapted to reverse helical trajectory with the scan range less than 360 degrees. For iterative reconstruction, we propose two algebraic methods named SART-FISTA-TV and DART

Computational Approaches to Simulation and Optimization of Global Aircraft Trajectories

Science.gov (United States)

Ng, Hok Kwan; Sridhar, Banavar

2016-01-01

This study examines three possible approaches to improving the speed in generating wind-optimal routes for air traffic at the national or global level. They are: (a) using the resources of a supercomputer, (b) running the computations on multiple commercially available computers and (c) implementing those same algorithms into NASAs Future ATM Concepts Evaluation Tool (FACET) and compares those to a standard implementation run on a single CPU. Wind-optimal aircraft trajectories are computed using global air traffic schedules. The run time and wait time on the supercomputer for trajectory optimization using various numbers of CPUs ranging from 80 to 10,240 units are compared with the total computational time for running the same computation on a single desktop computer and on multiple commercially available computers for potential computational enhancement through parallel processing on the computer clusters. This study also re-implements the trajectory optimization algorithm for further reduction of computational time through algorithm modifications and integrates that with FACET to facilitate the use of the new features which calculate time-optimal routes between worldwide airport pairs in a wind field for use with existing FACET applications. The implementations of trajectory optimization algorithms use MATLAB, Python, and Java programming languages. The performance evaluations are done by comparing their computational efficiencies and based on the potential application of optimized trajectories. The paper shows that in the absence of special privileges on a supercomputer, a cluster of commercially available computers provides a feasible approach for national and global air traffic system studies.

Classical behavior of few-electron parabolic quantum dots

International Nuclear Information System (INIS)

Ciftja, O.

2009-01-01

Quantum dots are intricate and fascinating systems to study novel phenomena of great theoretical and practical interest because low dimensionality coupled with the interplay between strong correlations, quantum confinement and magnetic field creates unique conditions for emergence of fundamentally new physics. In this work we consider two-dimensional semiconductor quantum dot systems consisting of few interacting electrons confined in an isotropic parabolic potential. We study the many-electron quantum ground state properties of such systems in presence of a perpendicular magnetic field as the number of electrons is varied using exact numerical diagonalizations and other approaches. The results derived from the calculations of the quantum model are then compared to corresponding results for a classical model of parabolically confined point charges who interact with a Coulomb potential. We find that, for a wide range of parameters and magnetic fields considered in this work, the quantum ground state energy is very close to the classical energy of the most stable classical configuration under the condition that the classical energy is properly adjusted to incorporate the quantum zero point motion.

Constructing quantum dynamics from mixed quantum-classical descriptions

International Nuclear Information System (INIS)

Barsegov, V.; Rossky, P.J.

2004-01-01

The influence of quantum bath effects on the dynamics of a quantum two-level system linearly coupled to a harmonic bath is studied when the coupling is both diagonal and off-diagonal. It is shown that the pure dephasing kernel and the non-adiabatic quantum transition rate between Born-Oppenheimer states of the subsystem can be decomposed into a contribution from thermally excited bath modes plus a zero point energy contribution. This quantum rate can be modewise factorized exactly into a product of a mixed quantum subsystem-classical bath transition rate and a quantum correction factor. This factor determines dynamics of quantum bath correlations. Quantum bath corrections to both the transition rate and the pure dephasing kernel are shown to be readily evaluated via a mixed quantum-classical simulation. Hence, quantum dynamics can be recovered from a mixed quantum-classical counterpart by incorporating the missing quantum bath corrections. Within a mixed quantum-classical framework, a simple approach for evaluating quantum bath corrections in calculation of the non-adiabatic transition rate is presented

The influence of work-family conflict trajectories on self-rated health trajectories in Switzerland: a life course approach.

Science.gov (United States)

Cullati, Stéphane

2014-07-01

Self-rated health (SRH) trajectories tend to decline over a lifetime. Moreover, the Cumulative Advantage and Disadvantage (CAD) model indicates that SRH trajectories are known to consistently diverge along socioeconomic positions (SEP) over the life course. However, studies of working adults to consider the influence of work and family conflict (WFC) on SRH trajectories are scarce. We test the CAD model and hypothesise that SRH trajectories diverge over time according to socioeconomic positions and WFC trajectories accentuate this divergence. Using longitudinal data from the Swiss Household Panel (N = 2327 working respondents surveyed from 2004 to 2010), we first examine trajectories of SRH and potential divergence over time across age, gender, SEP and family status using latent growth curve analysis. Second, we assess changes in SRH trajectories in relation to changes in WFC trajectories and divergence in SRH trajectories according to gender, SEP and family status using parallel latent growth curve analysis. Three measures of WFC are used: exhaustion after work, difficulty disconnecting from work, and work interference in private family obligations. The results show that SRH trajectories slowly decline over time and that the rate of change is not influenced by age, gender or SEP, a result which does not support the CAD model. SRH trajectories are significantly correlated with exhaustion after work trajectories but not the other two WFC measures. When exhaustion after work trajectories are taken into account, SRH trajectories of higher educated people decline slower compared to less educated people, supporting the CAD hypothesis. Copyright © 2014 Elsevier Ltd. All rights reserved.

Semi-classical estimation of ground state energies on a sphere

International Nuclear Information System (INIS)

Sollie, R.

1989-01-01

It is considered electrons confined to the surface of a sphere, and calculate the classical electrostatic energies for up to 32 electrons. It is introduced a magnetic field perpendicular to the surface of the sphere, by placing a magnetic monopole at the origin. The classical analysis can be extended by replacing the pair-potential by an effective potential, defined as the quantum mechanical energy of a pair of electrons at the appropriate distance. (A.C.A.S.) [pt

Quasi-Classical Description of Heavy Ion Reactions

International Nuclear Information System (INIS)

Luk'yanov, V.K.

1994-01-01

A method for calculating the distorted waves for a realistic nuclear complex potential with the Coulomb forces included is developed using the quasi-classical and high energy approximations. The distorted waves are obtained in the analytical form and applications are made to elastic, inelastic scattering and to the one-nucleon transfer reactions. 9 refs., 2 figs

Statistical characteristics of trajectories of diamagnetic unicellular organisms in a magnetic field.

Science.gov (United States)

Gorobets, Yu I; Gorobets, O Yu

2015-01-01

The statistical model is proposed in this paper for description of orientation of trajectories of unicellular diamagnetic organisms in a magnetic field. The statistical parameter such as the effective energy is calculated on basis of this model. The resulting effective energy is the statistical characteristics of trajectories of diamagnetic microorganisms in a magnetic field connected with their metabolism. The statistical model is applicable for the case when the energy of the thermal motion of bacteria is negligible in comparison with their energy in a magnetic field and the bacteria manifest the significant "active random movement", i.e. there is the randomizing motion of the bacteria of non thermal nature, for example, movement of bacteria by means of flagellum. The energy of the randomizing active self-motion of bacteria is characterized by the new statistical parameter for biological objects. The parameter replaces the energy of the randomizing thermal motion in calculation of the statistical distribution. Copyright © 2014 Elsevier Ltd. All rights reserved.

A new circulation type classification based upon Lagrangian air trajectories

Directory of Open Access Journals (Sweden)

Alexandre M. Ramos

2014-10-01

Full Text Available A new classification method of the large-scale circulation characteristic for a specific target area (NW Iberian Peninsula is presented, based on the analysis of 90-h backward trajectories arriving in this area calculated with the 3-D Lagrangian particle dispersion model FLEXPART. A cluster analysis is applied to separate the backward trajectories in up to five representative air streams for each day. Specific measures are then used to characterise the distinct air streams (e.g., curvature of the trajectories, cyclonic or anticyclonic flow, moisture evolution, origin and length of the trajectories. The robustness of the presented method is demonstrated in comparison with the Eulerian Lamb weather type classification.A case study of the 2003 heatwave is discussed in terms of the new Lagrangian circulation and the Lamb weather type classifications. It is shown that the new classification method adds valuable information about the pertinent meteorological conditions, which are missing in an Eulerian approach. The new method is climatologically evaluated for the five-year time period from December 1999 to November 2004. The ability of the method to capture the inter-seasonal circulation variability in the target region is shown. Furthermore, the multi-dimensional character of the classification is shortly discussed, in particular with respect to inter-seasonal differences. Finally, the relationship between the new Lagrangian classification and the precipitation in the target area is studied.

Trajectory grouping structure

Directory of Open Access Journals (Sweden)

Maike Buchin

2015-03-01

Full Text Available The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology. The trajectory grouping structure has three natural parameters that allow more global views of the data in group size, group duration, and entity inter-distance. We prove complexity bounds on the maximum number of maximal groups that can be present, and give algorithms to compute the grouping structure efficiently. We also study how the trajectory grouping structure can be made robust, that is, how brief interruptions of groups can be disregarded in the global structure, adding a notion of persistence to the structure. Furthermore, we showcase the results of experiments using data generated by the NetLogo flocking model and from the Starkey project. The Starkey data describe the movement of elk, deer, and cattle. Although there is no ground truth for the grouping structure in this data, the experiments show that the trajectory grouping structure is plausible and has the desired effects when changing the essential parameters. Our research provides the first complete study of trajectory group evolvement, including combinatorial,algorithmic, and experimental results.

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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

2005-01-01

The energetics and dynamics of collision-induced dissociation of O 2 - 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 O 2 - 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 Ar/Xe to the molecular axis of O 2 - , 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

BMI Trajectories from Birth to Young Adulthood.

Science.gov (United States)

McGinty, Shannon M; Osganian, Stavroula K; Feldman, Henry A; Milliren, Carly E; Field, Alison E; Richmond, Tracy K

2018-04-19

This study aimed to compare BMI trajectories from childhood to early adulthood in those with overweight and/or obesity versus severe obesity. Longitudinal BMI values (2,542 measurements) were calculated from measured heights and weights for 103 children, adolescents, or young adults with overweight, obesity, or severe obesity. Segmented regression with splines was used to model BMI trajectories. Sixty-nine participants were classified as ever having severe obesity versus 34 who never had severe obesity. Trajectories and slopes did not differ by sex or race/ethnicity. Compared with those who never had severe obesity, BMI was higher in the group with severe obesity at all ages, and BMI slope was higher for those with severe obesity at age 14 (P = 0.002), with peak slope occurring later (18 years vs. 16 years) and higher (4.5 ± 0.5 kg/m 2 /y vs. 2.9 ± 0.5 kg/m 2 /y; P BMI fell below zero by the mid-20s (-0.3 ± 0.6 kg/m 2 /y); in those with severe obesity, BMI slope never reached zero (0.9 ± 0.5 kg/m 2 /y). Youth with severe obesity, compared with their peers without, started with higher BMIs, had more rapid rates of BMI increase beginning at age 14, as well as a higher peak and longer period of increase, and never achieved weight stabilization. © 2018 The Obesity Society.

Beam trajectories through the upgraded XTU tandem

International Nuclear Information System (INIS)

Guan Xialing

1988-01-01

The paper deals with a problem applicable to all electrostatic accelerators with inclined field accelerating tubes, how the trajectory of the central beam particle is affected if one of the accelerating gaps must be shorted out due to insulator failure. For the long tube of the Legnaro XTU tandem the effect of each accelerator gap is calculated and a method of compensation either by shorting out an appropriate gap with reversed incline or by appropriately steering the beam into the entrance of the low energy tube is given. (orig.)

Trajectory separation of channeled ions in crystalline materials

International Nuclear Information System (INIS)

Temkin, Misha; Chakarov, Ivan; Webb, Roger

2000-01-01

Spatial distributions of ions implanted into crystals can be of a very complex shape with 'lobes' due to ions penetrating through open channels in several directions. This paper suggests an analytical model which represents such a distribution as a linear combination of 'random' distribution and one or more 'channeled' distributions. This study is focused on the algorithm of the separation of ion trajectories into several distributions. The first distribution includes those ions which have undergone predominantly random collisions. The other distributions include those ions which have undergone mainly 'weak' collisions and traveled mostly along the main channeling directions. Our binary collision approximation (BCA) simulator is used for generating and analyzing ion trajectories. The spatial moments can be extracted from each separated distribution. It is shown that 2D analytical distributions obtained as a linear combination of distributions derived from these moments and aligned along corresponding channeling direction are in a very good agreement with direct BCA calculations

Strategic Deconfliction of 4D Trajectory and Perturbation Analysis for Air Traffic Control and Automation System

Directory of Open Access Journals (Sweden)

Xinmin Tang

2016-01-01

Full Text Available Strategic 4D trajectory conflict-free planning is recognized as one of the core technologies of next-generation air traffic control and automation systems. To resolve potential conflicts during strategic 4D conflict-free trajectory planning, a protection-zone conflict-control model based on air traffic control separation constraints was proposed, in which relationships between expected arrival time and adjusted arrival time at conflicting waypoints for aircraft queues were built and transformed into dynamic linear equations under the definition of max-plus algebra. A method for strategic deconfliction of 4D trajectory was then proposed using two strategies: arrival time adjustment and departure time adjustment. In addition, departure time and flight duration perturbations were introduced to analyze the sensitivity of the planned strategic conflict-free 4D trajectories, and a robustness index for the conflict-free 4D trajectories was calculated. Finally, the proposed method was tested for the Shanghai air traffic control terminal area. The outcomes demonstrated that the planned strategic conflict-free 4D trajectories could avoid potential conflicts, and the slack time could be used to indicate their robustness. Complexity analysis demonstrated that deconfliction using max-plus algebra is more suitable for deconfliction of 4D trajectory with random sampling period in fix air route.

Classical limit for scalar fields at high temperature

International Nuclear Information System (INIS)

Buchmueller, W.; Jakovac, A.

1998-01-01

We study real-time correlation functions in scalar quantum field theories at temperature T=1/β. We show that the behaviour of soft, long-wavelength modes is determined by classical statistical field theory. The loss of quantum coherence is due to interactions with the soft modes of the thermal bath. The soft modes are separated from the hard modes by an infrared cutoff Λ<<1/(ℎβ). Integrating out the hard modes yields an effective theory for the soft modes. The infrared cutoff Λ controls corrections to the classical limit which are O(ℎβΛ). As an application, the plasmon damping rate is calculated. (orig.)

Semiclassical methods in chemical reaction dynamics

Energy Technology Data Exchange (ETDEWEB)

Keshavamurthy, Srihari [Univ. of California, Berkeley, CA (United States)

1994-12-01

Semiclassical approximations, simple as well as rigorous, are formulated in order to be able to describe gas phase chemical reactions in large systems. We formulate a simple but accurate semiclassical model for incorporating multidimensional tunneling in classical trajectory simulations. This model is based on the existence of locally conserved actions around the saddle point region on a multidimensional potential energy surface. Using classical perturbation theory and monitoring the imaginary action as a function of time along a classical trajectory we calculate state-specific unimolecular decay rates for a model two dimensional potential with coupling. Results are in good comparison with exact quantum results for the potential over a wide range of coupling constants. We propose a new semiclassical hybrid method to calculate state-to-state S-matrix elements for bimolecular reactive scattering. The accuracy of the Van Vleck-Gutzwiller propagator and the short time dynamics of the system make this method self-consistent and accurate. We also go beyond the stationary phase approximation by doing the resulting integrals exactly (numerically). As a result, classically forbidden probabilties are calculated with purely real time classical trajectories within this approach. Application to the one dimensional Eckart barrier demonstrates the accuracy of this approach. Successful application of the semiclassical hybrid approach to collinear reactive scattering is prevented by the phenomenon of chaotic scattering. The modified Filinov approach to evaluating the integrals is discussed, but application to collinear systems requires a more careful analysis. In three and higher dimensional scattering systems, chaotic scattering is suppressed and hence the accuracy and usefulness of the semiclassical method should be tested for such systems.

Semiclassical methods in chemical reaction dynamics

International Nuclear Information System (INIS)

Keshavamurthy, S.

1994-12-01

Semiclassical approximations, simple as well as rigorous, are formulated in order to be able to describe gas phase chemical reactions in large systems. We formulate a simple but accurate semiclassical model for incorporating multidimensional tunneling in classical trajectory simulations. This model is based on the existence of locally conserved actions around the saddle point region on a multidimensional potential energy surface. Using classical perturbation theory and monitoring the imaginary action as a function of time along a classical trajectory we calculate state-specific unimolecular decay rates for a model two dimensional potential with coupling. Results are in good comparison with exact quantum results for the potential over a wide range of coupling constants. We propose a new semiclassical hybrid method to calculate state-to-state S-matrix elements for bimolecular reactive scattering. The accuracy of the Van Vleck-Gutzwiller propagator and the short time dynamics of the system make this method self-consistent and accurate. We also go beyond the stationary phase approximation by doing the resulting integrals exactly (numerically). As a result, classically forbidden probabilties are calculated with purely real time classical trajectories within this approach. Application to the one dimensional Eckart barrier demonstrates the accuracy of this approach. Successful application of the semiclassical hybrid approach to collinear reactive scattering is prevented by the phenomenon of chaotic scattering. The modified Filinov approach to evaluating the integrals is discussed, but application to collinear systems requires a more careful analysis. In three and higher dimensional scattering systems, chaotic scattering is suppressed and hence the accuracy and usefulness of the semiclassical method should be tested for such systems

Semi-classical description of matter wave interferometers and hybrid quantum systems

Energy Technology Data Exchange (ETDEWEB)

Schneider, Mathias

2015-02-16

This work considers the semi-classical description of two applications involving cold atoms. This is, on one hand, the behavior of a BOSE-EINSTEIN condensate in hybrid systems, i.e. in contact with a microscopic object (carbon nanotubes, fullerenes, etc.). On the other, the evolution of phase space distributions in matter wave interferometers utilizing ray tracing methods was discussed. For describing condensates in hybrid systems, one can map the GROSS-PITAEVSKII equation, a differential equation in the complex-valued macroscopic wave function, onto a system of two differential equations in density and phase. Neglecting quantum dispersion, one obtains a semiclassical description which is easily modified to incorporate interactions between condensate and microscopical object. In our model, these interactions comprise attractive forces (CASIMIR-POLDER forces) and loss of condensed atoms due to inelastic collisions at the surface of the object. Our model exhibited the excitation of sound waves that are triggered by the object's rapid immersion, and spread across the condensate thereafter. Moreover, local particle loss leads to a shrinking of the bulk condensate. We showed that the total number of condensed particles is decreasing potentially in the beginning (large condensate, strong mean field interaction), while it decays exponentially in the long-time limit (small condensate, mean field inetraction negligible). For representing the physics of matter wave interferometers in phase space, we utilized the WIGNER function. In semi-classical approximation, which again consists in ignoring the quantum dispersion, this representation is subject to the same equation of motion as classical phase space distributions, i.e. the LIOUVILLE equation. This implies that time evolution of theWIGNER function follows a phase space flow that consists of classical trajectories (classical transport). This means, for calculating a time-evolved distribution, one has know the initial

Fractal analysis on a classical hard-wall billiard with openings using a two-dimensional set of initial conditions

International Nuclear Information System (INIS)

Ree, Suhan

2003-01-01

Fractal analysis is performed to measure the chaoticity of a classical hard-wall billiard with openings. We use the circular billiard with a straight cut with two openings, and a two-dimensional (2D) set of initial conditions that produce all possible trajectories of a particle injected from one opening. We numerically compute the fractal dimension of singular points of the function that maps an initial condition to the number of collisions with the wall before the exit, using the box-counting algorithm that uses uniformly distributed points inside the 2D set of initial conditions. Finally, the classical chaotic properties are observed while the parameters of the billiard are varied, and the results are compared with those with the one-dimensional set of initial conditions

Trajectory Optimization of Spray Painting Robot for Complex Curved Surface Based on Exponential Mean Bézier Method

Directory of Open Access Journals (Sweden)

Wei Chen

2017-01-01

Full Text Available Automated tool trajectory planning for spray painting robots is still a challenging problem, especially for a large complex curved surface. This paper presents a new method of trajectory optimization for spray painting robot based on exponential mean Bézier method. The definition and the three theorems of exponential mean Bézier curves are discussed. Then a spatial painting path generation method based on exponential mean Bézier curves is developed. A new simple algorithm for trajectory optimization on complex curved surfaces is introduced. A golden section method is adopted to calculate the values. The experimental results illustrate that the exponential mean Bézier curves enhanced flexibility of the path planning, and the trajectory optimization algorithm achieved satisfactory performance. This method can also be extended to other applications.

Classical and quantum gravity of brane black holes

International Nuclear Information System (INIS)

Gregory, Ruth; Ross, Simon F.; Zegers, Robin

2008-01-01

We test the holographic conjecture of brane black holes: that a full classical 5D solution will correspond to a quantum corrected 4D black hole. Using the Schwarzschild-AdS black string, we compare the braneworld back reaction at strong coupling with the calculation of the quantum stress tensor on Schwarzschild-AdS 4 at weak coupling. The two calculations give different results and provide evidence that the stress tensor at strong coupling is indeed different to the weak coupling calculations, and hence does not conform to our notion of a quantum corrected black hole. We comment on the implications for an asymptotically flat black hole.

Space shuttle launch vehicle performance trajectory, exchange ratios, and dispersion analysis

Science.gov (United States)

Toelle, R. G.; Blackwell, D. L.; Lott, L. N.

1973-01-01

A baseline space shuttle performance trajectory for Mission 3A launched from WTR has been generated. Design constraints of maximum dynamic pressure, longitudinal acceleration, and delivered payload were satisfied. Payload exchange ratios are presented with explanation on use. Design envelopes of dynamic pressure, SRB staging point, aerodynamic heating and flight performance reserves are calculated and included.

Trajectory similarity join in spatial networks

KAUST Repository

Shang, Shuo

2017-09-07

The matching of similar pairs of objects, called similarity join, is fundamental functionality in data management. We consider the case of trajectory similarity join (TS-Join), where the objects are trajectories of vehicles moving in road networks. Thus, given two sets of trajectories and a threshold θ, the TS-Join returns all pairs of trajectories from the two sets with similarity above θ. This join targets applications such as trajectory near-duplicate detection, data cleaning, ridesharing recommendation, and traffic congestion prediction. With these applications in mind, we provide a purposeful definition of similarity. To enable efficient TS-Join processing on large sets of trajectories, we develop search space pruning techniques and take into account the parallel processing capabilities of modern processors. Specifically, we present a two-phase divide-and-conquer algorithm. For each trajectory, the algorithm first finds similar trajectories. Then it merges the results to achieve a final result. The algorithm exploits an upper bound on the spatiotemporal similarity and a heuristic scheduling strategy for search space pruning. The algorithm\\'s per-trajectory searches are independent of each other and can be performed in parallel, and the merging has constant cost. An empirical study with real data offers insight in the performance of the algorithm and demonstrates that is capable of outperforming a well-designed baseline algorithm by an order of magnitude.

The sufficient condition for an extremum in the classical action integral as an eingenvalue problem

International Nuclear Information System (INIS)

Hussein, M.S.; Pereira, J.G.

The sufficient condition for an extremum in the classical action integral is studied using Morse's theory. Applications to the classical harmonic and anharmonic oscillators are made. The analogy of the calculations to the quantum mechanical problems in one dimension is stressed. (Author) [pt

Personalized trajectory matching in spatial networks

KAUST Repository

Shang, Shuo

2013-07-31

With the increasing availability of moving-object tracking data, trajectory search and matching is increasingly important. We propose and investigate a novel problem called personalized trajectory matching (PTM). In contrast to conventional trajectory similarity search by spatial distance only, PTM takes into account the significance of each sample point in a query trajectory. A PTM query takes a trajectory with user-specified weights for each sample point in the trajectory as its argument. It returns the trajectory in an argument data set with the highest similarity to the query trajectory. We believe that this type of query may bring significant benefits to users in many popular applications such as route planning, carpooling, friend recommendation, traffic analysis, urban computing, and location-based services in general. PTM query processing faces two challenges: how to prune the search space during the query processing and how to schedule multiple so-called expansion centers effectively. To address these challenges, a novel two-phase search algorithm is proposed that carefully selects a set of expansion centers from the query trajectory and exploits upper and lower bounds to prune the search space in the spatial and temporal domains. An efficiency study reveals that the algorithm explores the minimum search space in both domains. Second, a heuristic search strategy based on priority ranking is developed to schedule the multiple expansion centers, which can further prune the search space and enhance the query efficiency. The performance of the PTM query is studied in extensive experiments based on real and synthetic trajectory data sets. © 2013 Springer-Verlag Berlin Heidelberg.

A study of variable thrust, variable specific impulse trajectories for solar system exploration

Science.gov (United States)

Sakai, Tadashi

A study has been performed to determine the advantages and disadvantages of variable thrust and variable Isp (specific impulse) trajectories for solar system exploration. There have been several numerical research efforts for variable thrust, variable Isp, power-limited trajectory optimization problems. All of these results conclude that variable thrust, variable Isp (variable specific impulse, or VSI) engines are superior to constant thrust, constant Isp (constant specific impulse; or CSI) engines. However, most of these research efforts assume a mission from Earth to Mars, and some of them further assume that these planets are circular and coplanar. Hence they still lack the generality. This research has been conducted to answer the following questions: (1) Is a VSI engine always better than a CSI engine or a high thrust engine for any mission to any planet with any time of flight considering lower propellant mass as the sole criterion? (2) If a planetary swing-by is used for a VSI trajectory, is the fuel savings of a VSI swing-by trajectory better than that of a CSI swing-by or high thrust swing-by trajectory? To support this research, an unique, new computer-based interplanetary trajectory calculation program has been created. This program utilizes a calculus of variations algorithm to perform overall optimization of thrust, Isp, and thrust vector direction along a trajectory that minimizes fuel consumption for interplanetary travel. It is assumed that the propulsion system is power-limited, and thus the compromise between thrust and Isp is a variable to be optimized along the flight path. This program is capable of optimizing not only variable thrust trajectories but also constant thrust trajectories in 3-D space using a planetary ephemeris database. It is also capable of conducting planetary swing-bys. Using this program, various Earth-originating trajectories have been investigated and the optimized results have been compared to traditional CSI and high

Alternative perturbation approaches in classical mechanics

International Nuclear Information System (INIS)

Amore, Paolo; Raya, Alfredo; Fernandez, Francisco M

2005-01-01

We discuss two alternative methods, based on the Lindstedt-Poincare technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches and show that one of them is more accurate for all values of the coupling constant. We believe that present discussion and comparison may be a suitable exercise for teaching perturbation theory in advanced undergraduate courses on classical mechanics

Measurement and Calculation of Absolute Single- and Multiple-Charge-Exchange Cross Sections for Fe^q+ Ions Impacting CO and CO₂

Energy Technology Data Exchange (ETDEWEB)

Simcic, J. [Jet Propulsion Laboratory/Caltech; Schultz, David Robert [ORNL; Mawhorter, R. J. [Pomona College; Cadez, I. [Jozef Stefan Institute, Slovenia; Greenwood, J. B. [Queen' s University, Belfast; Chutjian, A. [Jet Propulsion Laboratory/Caltech; Lisse, Carey M. [Johns Hopkins University; Smith, S. J. [Indiana Wesleyan University, Marion

2010-01-01

Absolute cross sections are reported for single, double, and triple charge exchange of Feq+ (q=5- 13) ions with CO and CO2. The highly-charged Fe ions are generated in an electron cyclotron resonance ion source. Absolute data are derived from knowledge of the target gas pressure, target path length, and incident and charge-exchanged ion currents. Experimental results are compared with new calculations of these cross sections in the n-electron classical trajectory Monte-Carlo approximation, in which the ensuing radiative and non-radiative cascades are approximated with scaled hydrogenic transition probabilities and scaled Auger rates. The present data are needed in astrophysical applications of solar- and stellar-wind charge-exchange with comets, planetary atmospheres, and circumstellar clouds.

Classical equation of motion and anomalous dimensions at leading order

International Nuclear Information System (INIS)

Nii, Keita

2016-01-01

Motivated by a recent paper by Rychkov-Tan http://dx.doi.org/10.1088/1751-8113/48/29/29FT01 , we calculate the anomalous dimensions of the composite operators at the leading order in various models including a ϕ"3-theory in (6−ϵ) dimensions. The method presented here relies only on the classical equation of motion and the conformal symmetry. In case that only the leading expressions of the critical exponents are of interest, it is sufficient to reduce the multiplet recombination discussed in http://dx.doi.org/10.1088/1751-8113/48/29/29FT01 to the classical equation of motion. We claim that in many cases the use of the classical equations of motion and the CFT constraint on two- and three-point functions completely determine the leading behavior of the anomalous dimensions at the Wilson-Fisher fixed point without any input of the Feynman diagrammatic calculation. The method developed here is closely related to the one presented in http://dx.doi.org/10.1088/1751-8113/48/29/29FT01 but based on a more perturbative point of view.

Direct iterative reconstruction of computed tomography trajectories (DIRECTT)

International Nuclear Information System (INIS)

Lange, A.; Hentschel, M.P.; Schors, J.

2004-01-01

The direct reconstruction approach employs an iterative procedure by selection of and angular averaging over projected trajectory data of volume elements. This avoids the blur effects of the classical Fourier method due to the sampling theorem. But longer computing time is required. The reconstructed tomographic images reveal at least the spatial resolution of the radiation detector. Any set of projection angles may be selected for the measurements. Limited rotation of the object yields still good reconstruction of details. Projections of a partial region of the object can be reconstructed without additional artifacts thus reducing the overall radiation dose. Noisy signal data from low dose irradiation have low impact on spatial resolution. The image quality is monitored during all iteration steps and is pre-selected according to the specific requirements. DIRECTT can be applied independently from the measurement equipment in addition to conventional reconstruction or as a refinement filter. (author)

On the integration scheme along a trajectory for the characteristics method

International Nuclear Information System (INIS)

Le Tellier, Romain; Hebert, Alain

2006-01-01

The issue of the integration scheme along a trajectory which appears for all tracking-based transport methods is discussed from the point of view of the method of characteristics. The analogy with the discrete ordinates method in slab geometry is highlighted along with the practical limitation in transposing high-order S N schemes to a trajectory-based method. We derived an example of such a transposition starting from the linear characteristic scheme. This new scheme is compared with the standard flat-source approximation of the step characteristic scheme and with the diamond differencing scheme. The numerical study covers a 1D analytical case, 2D one-group critical and fixed-source benchmarks and finally a realistic multigroup calculation on a BWR-MOX assembly

Trajectory planning and trajectory tracking for a small-scale helicopter in autorotation

NARCIS (Netherlands)

Taamallah, Skander; Bombois, Xavier; Van den Hof, Paul M.J.

2017-01-01

The design of a high-performance guidance and control system for a small-scale helicopterUnmanned Aerial Vehicle (UAV), with an engine OFF flight condition (i.e. autorotation), is known to be a challenging task. It is the purpose of this paper to present a Trajectory Planning (TP) and Trajectory

Robotic excavator trajectory control using an improved GA based PID controller

Science.gov (United States)

Feng, Hao; Yin, Chen-Bo; Weng, Wen-wen; Ma, Wei; Zhou, Jun-jing; Jia, Wen-hua; Zhang, Zi-li

2018-05-01

In order to achieve excellent trajectory tracking performances, an improved genetic algorithm (IGA) is presented to search for the optimal proportional-integral-derivative (PID) controller parameters for the robotic excavator. Firstly, the mathematical model of kinematic and electro-hydraulic proportional control system of the excavator are analyzed based on the mechanism modeling method. On this basis, the actual model of the electro-hydraulic proportional system are established by the identification experiment. Furthermore, the population, the fitness function, the crossover probability and mutation probability of the SGA are improved: the initial PID parameters are calculated by the Ziegler-Nichols (Z-N) tuning method and the initial population is generated near it; the fitness function is transformed to maintain the diversity of the population; the probability of crossover and mutation are adjusted automatically to avoid premature convergence. Moreover, a simulation study is carried out to evaluate the time response performance of the proposed controller, i.e., IGA based PID against the SGA and Z-N based PID controllers with a step signal. It was shown from the simulation study that the proposed controller provides the least rise time and settling time of 1.23 s and 1.81 s, respectively against the other tested controllers. Finally, two types of trajectories are designed to validate the performances of the control algorithms, and experiments are performed on the excavator trajectory control experimental platform. It was demonstrated from the experimental work that the proposed IGA based PID controller improves the trajectory accuracy of the horizontal line and slope line trajectories by 23.98% and 23.64%, respectively in comparison to the SGA tuned PID controller. The results further indicate that the proposed IGA tuning based PID controller is effective for improving the tracking accuracy, which may be employed in the trajectory control of an actual excavator.

Depressed trajectory SLBMs: A technical evaluation and arms control possibilities

International Nuclear Information System (INIS)

Gronlund, L.; Wright, D.C.

1992-01-01

SLBMs (sea-launched ballistic missiles) flown on depressed trajectories would have short flight times, comparable to escape times of bombers and launch times of ICBMs, thus raising the possibility of short time-of-flight (STOF) nuclear attacks. We assess the depressed trajectory (DT) capability of existing SLBMs by calculating the flight times, atmospheric loading on the booster, reentry heating on the reentry vehicle (RV), and degradation of accuracy for a DT SLBM. We find that current US and CIS SLBMs flown on depressed trajectories would have the capability to attack bomber bases at ranges of up to about 2,000 kilometers, and possibly at ranges up to 3,000 kilometers. To target bombers based furthest inland, a new high-velocity booster might be required, and attacking hardened targets would require a maneuvering RV (MaRV). We conclude that DT capabilities could be effectively controlled by the combination of an apogee restriction on the flight testing of existing SLBMs and bans on the development of high-velocity boosters and MaRVs, and that, in view of their inherent STOF capabilities, deep cuts in the number of SLBMs or their elimination might be desirable for an optimal minimum-deterrent force structure

The probability of false positives in zero-dimensional analyses of one-dimensional kinematic, force and EMG trajectories.

Science.gov (United States)

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.

Regularity of Center of Pressure Trajectories in Expert Gymnasts during Bipedal Closed-Eyes Quiet Standing

Directory of Open Access Journals (Sweden)

Brice Isableu

2017-06-01

Full Text Available We compared postural control of expert gymnasts (G to that of non-gymnasts (NG during bipedal closed-eyes quiet standing using conventional and nonlinear dynamical measures of center of foot pressure (COP trajectories. Earlier findings based on COP classical variables showed that gymnasts exhibited a better control of postural balance but only in demanding stances. We examined whether the effect of expertise in Gymnastic can be uncovered in less demanding stances, from the analysis of the dynamic patterns of COP trajectories. Three dependent variables were computed to describe the subject’s postural behavior: the variability of COP displacements (ACoP, the variability of the COP velocities (VCoP and the sample entropy of COP (SEnCoP to quantify COP regularity (i.e., predictability. Conventional analysis of COP trajectories showed that NG and G exhibited similar amount and control of postural sway, as indicated by similar ACoP and VCoP values observed in NG and G, respectively. These results suggest that the specialized balance training received by G may not transfer to less challenging balance conditions such as the bipedal eyes-closed stance condition used in the present experiment. Interestingly, nonlinear dynamical analysis of COP trajectories regarding COP regularity showed that G exhibited more irregular COP fluctuations relative to NG, as indicated by the higher SEnCoP values observed for the G than for the NG. The present results showed that a finer-grained analysis of the dynamic patterns of the COP displacements is required to uncover an effect of gymnastic expertise on postural control in nondemanding postural stance. The present findings shed light on the surplus value in the nonlinear dynamical analysis of COP trajectories to gain further insight into the mechanisms involved in the control of bipedal posture.

Ab Initio Calculations of Transport in Titanium and Aluminum Mixtures

Science.gov (United States)

Walker, Nicholas; Novak, Brian; Tam, Ka Ming; Moldovan, Dorel; Jarrell, Mark

In classical molecular dynamics simulations, the self-diffusion and shear viscosity of titanium about the melting point have fallen within the ranges provided by experimental data. However, the experimental data is difficult to collect and has been rather scattered, making it of limited value for the validation of these calculations. By using ab initio molecular dynamics simulations within the density functional theory framework, the classical molecular dynamics data can be validated. The dynamical data from the ab initio molecular dynamics can also be used to calculate new potentials for use in classical molecular dynamics, allowing for more accurate classical dynamics simulations for the liquid phase. For metallic materials such as titanium and aluminum alloys, these calculations are very valuable due to an increasing demand for the knowledge of their thermophysical properties that drive the development of new materials. For example, alongside knowledge of the surface tension, viscosity is an important input for modeling the additive manufacturing process at the continuum level. We are developing calculations of the viscosity along with the self-diffusion for aluminum, titanium, and titanium-aluminum alloys with ab initio molecular dynamics. Supported by the National Science Foundation through cooperative agreement OIA-1541079 and the Louisiana Board of Regents.

Computation of disordered system from the first principles of classical mechanics and ℕℙ hard problem

Energy Technology Data Exchange (ETDEWEB)

Gevorkyan, A. S., E-mail: g-ashot@sci.am; Sahakyan, V. V. [National Academy of Sciences of the Republic of Armenia, Institute for Informatics and Automation Problems (Armenia)

2017-03-15

We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.

Mathematica for Theoretical Physics Classical Mechanics and Nonlinear Dynamics

CERN Document Server

Baumann, Gerd

2005-01-01

Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A...

Longitudinal Estimated GFR Trajectories in Patients With and Without Type 2 Diabetes and Nephropathy

DEFF Research Database (Denmark)

Weldegiorgis, Misghina; de Zeeuw, Dick; Li, Liang

2017-01-01

-renin-angiotensin-aldosterone-system antihypertensives were independently associated with a greater probability of a nonlinear eGFR trajectory. LIMITATIONS: Relatively short follow-up and no measured GFR. CONCLUSIONS: In both diabetes and nondiabetes trials, the majority of patients show a more or less linear eGFR decline. These data support...... with and without diabetes. STUDY DESIGN: Longitudinal observational study. SETTING & PARTICIPANTS: 6 clinical trials with repeated measurements of serum creatinine. PREDICTOR: Patient demographic and clinical parameters. OUTCOMES: Probability of nonlinear eGFR function trajectory calculated for each patient from...... a Bayesian model of individual eGFR trajectories. RESULTS: The median probability of a nonlinear eGFR decline in all trials was 0.26 (interquartile range, 0.13-0.48). The median probability was 0.28 in diabetes versus 0.09 in nondiabetes trials (P50% probability...

Lunar Cube Transfer Trajectory Options

Science.gov (United States)

Folta, David; Dichmann, Donald James; Clark, Pamela E.; Haapala, Amanda; Howell, Kathleen

2015-01-01

Numerous Earth-Moon trajectory and lunar orbit options are available for Cubesat missions. Given the limited Cubesat injection infrastructure, transfer trajectories are contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these transfers can be restricted by the selection or designs of Cubesat subsystems such as propulsion or communication. Nonetheless, many trajectory options can b e considered which have a wide range of transfer duration, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several options including deployment from low Earth orbit (LEO) geostationary transfer orbits (GTO) and higher energy direct lunar transfer and the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory.

Towards Efficient Search for Activity Trajectories

DEFF Research Database (Denmark)

Zheng, Kai; Shang, Shuo; Yuan, Jing

2013-01-01

, recent proliferation in location-based web applications (e.g., Foursquare, Facebook) has given rise to large amounts of trajectories associated with activity information, called activity trajectory. In this paper, we study the problem of efficient similarity search on activity trajectory database. Given...

Classical Electron Model with QED Corrections

OpenAIRE

Lenk, Ron

2010-01-01

In this article we build a metric for a classical general relativistic electron model with QED corrections. We calculate the stress-energy tensor for the radiative corrections to the Coulomb potential in both the near-field and far-field approximations. We solve the three field equations in both cases by using a perturbative expansion to first order in alpha (the fine-structure constant) while insisting that the usual (+, +, -, -) structure of the stress-energy tensor is maintained. The resul...

Efficient Trajectory Options Allocation for the Collaborative Trajectory Options Program

Science.gov (United States)

Rodionova, Olga; Arneson, Heather; Sridhar, Banavar; Evans, Antony

2017-01-01

The Collaborative Trajectory Options Program (CTOP) is a Traffic Management Initiative (TMI) intended to control the air traffic flow rates at multiple specified Flow Constrained Areas (FCAs), where demand exceeds capacity. CTOP allows flight operators to submit the desired Trajectory Options Set (TOS) for each affected flight with associated Relative Trajectory Cost (RTC) for each option. CTOP then creates a feasible schedule that complies with capacity constraints by assigning affected flights with routes and departure delays in such a way as to minimize the total cost while maintaining equity across flight operators. The current version of CTOP implements a Ration-by-Schedule (RBS) scheme, which assigns the best available options to flights based on a First-Scheduled-First-Served heuristic. In the present study, an alternative flight scheduling approach is developed based on linear optimization. Results suggest that such an approach can significantly reduce flight delays, in the deterministic case, while maintaining equity as defined using a Max-Min fairness scheme.

Flight test trajectory control analysis

Science.gov (United States)

Walker, R.; Gupta, N.

1983-01-01

Recent extensions to optimal control theory applied to meaningful linear models with sufficiently flexible software tools provide powerful techniques for designing flight test trajectory controllers (FTTCs). This report describes the principal steps for systematic development of flight trajectory controllers, which can be summarized as planning, modeling, designing, and validating a trajectory controller. The techniques have been kept as general as possible and should apply to a wide range of problems where quantities must be computed and displayed to a pilot to improve pilot effectiveness and to reduce workload and fatigue. To illustrate the approach, a detailed trajectory guidance law is developed and demonstrated for the F-15 aircraft flying the zoom-and-pushover maneuver.

Trajectories of Depressive Symptoms in Older Adults and Risk of Dementia.

Science.gov (United States)

Kaup, Allison R; Byers, Amy L; Falvey, Cherie; Simonsick, Eleanor M; Satterfield, Suzanne; Ayonayon, Hilsa N; Smagula, Stephen F; Rubin, Susan M; Yaffe, Kristine

2016-05-01

Depression has been identified as a risk factor for dementia. However, most studies have measured depressive symptoms at only one time point, and older adults may show different patterns of depressive symptoms over time. To investigate the association between trajectories of depressive symptoms and risk of dementia in older adults. This was a prospective cohort investigation of black and white community-dwelling older adults in the Health, Aging, and Body Composition study. Participants were enrolled between May 1997 and June 1998 and followed up through 2001-2002. The dates of this analysis were September 2014 to December 2015. The setting was community research centers in Memphis, Tennessee, and Pittsburgh, Pennsylvania. Trajectories of depressive symptoms were assessed from baseline to year 5. Symptoms were measured with the Center for Epidemiologic Studies Depression Scale Short Form, and trajectories were calculated using latent class growth curve analysis. Incident dementia through year 11, determined by dementia medication use, hospital records, or significant cognitive decline (≥1.5 SD race-specific decline on the Modified Mini-Mental State Examination). We examined the association between depressive symptom trajectories and dementia incidence using Cox proportional hazards regression models adjusted for demographics, health factors that differed between groups, and cognition during the depressive symptom assessment period (baseline to year 5). The analytic cohort included 2488 black and white older adults with repeated depressive symptom assessments from baseline to year 5 who were free of dementia throughout that period. Their mean (SD) age at baseline was 74.0 (2.8) years, and 53.1% (n = 1322) were female. The following 3 depressive symptom trajectories were identified: consistently minimal symptoms (62.0% [n = 1542] of participants), moderate and increasing symptoms (32.2% [n = 801] of participants), and high and increasing symptoms (5

Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics