Efficient ab initio free energy calculations by classically assisted trajectory sampling
Wilson, Hugh F.
2015-12-01
A method for efficiently performing ab initio free energy calculations based on coupling constant thermodynamic integration is demonstrated. By the use of Boltzmann-weighted sums over states generated from a classical ensemble, the free energy difference between the classical and ab initio ensembles is readily available without the need for time-consuming integration over molecular dynamics trajectories. Convergence and errors in this scheme are discussed and characterised in terms of a quantity representing the degree of misfit between the classical and ab initio systems. Smaller but still substantial efficiency gains over molecular dynamics are also demonstrated for the calculation of average properties such as pressure and total energy for systems in equilibrium.
Belyaev, Andrey K; Lasser, Caroline; Trigila, Giulio
2014-01-01
The Landau--Zener (LZ) type classical-trajectory surface-hopping algorithm is applied to the nonadiabatic nuclear dynamics of the ammonia cation after photoionization of the ground-state neutral molecule to the excited states of the cation. The algorithm employs the recently proposed formula for nonadiabatic LZ transition probabilities derived from the adiabatic potential energy surfaces. The evolution of the populations of the ground state and the two lowest excited adiabatic states is calculated up to 200 fs. The results agree well with quantum simulations available for the first 100 fs based on the same potential energy surfaces. Four different time scales are detected for the nuclear dynamics: Ultrafast Jahn--Teller dynamics between the excited states on a 5 fs time scale; fast transitions between the excited state and the ground state within a time scale of 20 fs; relatively slow partial conversion of a first-excited-state population to the ground state within a time scale of 100 fs; and nearly constant ...
Energy Technology Data Exchange (ETDEWEB)
Belyaev, Andrey K., E-mail: belyaev@herzen.spb.ru [Department of Theoretical Physics, Herzen University, St. Petersburg 191186 (Russian Federation); Domcke, Wolfgang, E-mail: wolfgang.domcke@ch.tum.de [Department Chemie, Technische Universität München, D-85747 Garching (Germany); Lasser, Caroline, E-mail: classer@ma.tum.de; Trigila, Giulio, E-mail: trigila@ma.tum.de [Zentrum Mathematik, Technische Universität München, D-85747 Garching (Germany)
2015-03-14
The Landau–Zener (LZ) type classical-trajectory surface-hopping algorithm is applied to the nonadiabatic nuclear dynamics of the ammonia cation after photoionization of the ground-state neutral molecule to the excited states of the cation. The algorithm employs a recently proposed formula for nonadiabatic LZ transition probabilities derived from the adiabatic potential energy surfaces. The evolution of the populations of the ground state and the two lowest excited adiabatic states is calculated up to 200 fs. The results agree well with quantum simulations available for the first 100 fs based on the same potential energy surfaces. Three different time scales are detected for the nuclear dynamics: Ultrafast Jahn–Teller dynamics between the excited states on a 5 fs time scale; fast transitions between the excited state and the ground state within a time scale of 20 fs; and relatively slow partial conversion of a first-excited-state population to the ground state within a time scale of 100 fs. Beyond 100 fs, the adiabatic electronic populations are nearly constant due to a dynamic equilibrium between the three states. The ultrafast nonradiative decay of the excited-state populations provides a qualitative explanation of the experimental evidence that the ammonia cation is nonfluorescent.
Energy Technology Data Exchange (ETDEWEB)
Kaganovich, I. D., Shnidman, Ariel, Mebane, Harrison, Davidson, R.C.
2008-10-10
Evaluation of ion-atom charge-changing cross sections is needed for many accelerator applications. A classical trajectory Monte Carlo (CTMC) simulation has been used to calculate ionization and charge exchange cross sections. For benchmarking purposes, an extensive study has been performed for the simple case of hydrogen and helium targets in collisions with various ions. Despite the fact that the simulation only accounts for classical mechanics, the calculations are comparable to experimental results for projectile velocities in the region corresponding to the vicinity of the maximum cross section. Shortcomings of the CTMC method for multielectron target atoms are discussed.
International Nuclear Information System (INIS)
Evaluation of ion-atom charge-changing cross sections is needed for many accelerator applications. A classical trajectory Monte Carlo (CTMC) simulation has been used to calculate ionization and charge exchange cross sections. For benchmarking purposes, an extensive study has been performed for the simple case of hydrogen and helium targets in collisions with various ions. Despite the fact that the simulation only accounts for classical mechanics, the calculations are comparable to experimental results for projectile velocities in the region corresponding to the vicinity of the maximum cross section. Shortcomings of the CTMC method for multielectron target atoms are discussed
Kaganovich, Igor D.; Startsev, Edward A.; Davidson, Ronald C.
2003-01-01
Stripping cross sections in nitrogen have been calculated using the classical trajectory approximation and the Born approximation of quantum mechanics for the outer shell electrons of 3.2GeV I$^{-}$ and Cs$^{+}$ ions. A large difference in cross section, up to a factor of six, calculated in quantum mechanics and classical mechanics, has been obtained. Because at such high velocities the Born approximation is well validated, the classical trajectory approach fails to correctly predict the stri...
International Nuclear Information System (INIS)
We describe classical-trajectory calculations of sputtering yields for Ar+-ion collisions with a Si(001) surface. The Ar+-Si and short-ranged Si-Si interaction potentials were calculated using the ab initio Hartree-Fock and configuration-interaction methods. The low-energy potential describing the silicon solid is the two- and three-body form due to Stillinger and Weber. We compare the calculated sputtering yields with experiment. The potential-energy surface strongly influences the calculated sputtering yields, and it is found that the most reasonable agreement is obtained from our potentials using the (2 x 1) Si(001) reconstructed surface rather than the bulk-terminated surface. Analysis of the kinetic energy and angular distributions of the sputtered silicon atoms and of cluster yields has provided a mechanism of ejection
Sarkadi, L
2015-01-01
The three-body dynamics of the ionization of the atomic hydrogen by 30 keV antiproton impact has been investigated by calculation of fully differential cross sections (FDCS) using the classical trajectory Monte Carlo (CTMC) method. The results of the calculations are compared with the predictions of quantum mechanical descriptions: The semi-classical time-dependent close-coupling theory, the fully quantal, time-independent close-coupling theory, and the continuum-distorted-wave-eikonal-initial-state model. In the analysis particular emphasis was put on the role of the nucleus-nucleus (NN) interaction played in the ionization process. For low-energy electron ejection CTMC predicts a large NN interaction effect on FDCS, in agreement with the quantum mechanical descriptions. By examining individual particle trajectories it was found that the relative motion between the electron and the nuclei is coupled very weakly with that between the nuclei, consequently the two motions can be treated independently. A simple ...
Anderson localization from classical trajectories
Brouwer, Piet W.; Altland, Alexander
2008-01-01
We show that Anderson localization in quasi-one dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron trajectories only. At large length scales, an exponential proliferation of trajectories of nearly identical classical action generates an abundance of interference terms, which eventually leads to a suppression of transport coefficients. We quantitatively descri...
Kaganovich, I D; Davidson, R C; Kaganovich, Igor D.; Startsev, Edward A.; Davidson, Ronald C.
2003-01-01
Stripping cross sections in nitrogen have been calculated using the classical trajectory approximation and the Born approximation of quantum mechanics for the outer shell electrons of 3.2GeV I$^{-}$ and Cs$^{+}$ ions. A large difference in cross section, up to a factor of six, calculated in quantum mechanics and classical mechanics, has been obtained. Because at such high velocities the Born approximation is well validated, the classical trajectory approach fails to correctly predict the stripping cross sections at high energies for electron orbitals with low ionization potential.
Classical trajectory calculations for anisotropy-dependent cross sections for He-N2 mixtures
International Nuclear Information System (INIS)
The classical expressions for kinetic theory cross sections which are related to the Senftleben-Beenakker effect on viscosity, diffusion, conductivity and thermal diffusion are evaluated, in the temperature range 77.3-1100 K. The depolarised Rayleigh scattering and rotational-relaxation cross sections are also obtained. Comparisons with experiment show that the present values for these cross sections are 10-80% larger than the measurments. These consistent discrepancies suggest that this potential surface is too anisotropic. (author)
International Nuclear Information System (INIS)
Evaluation of ion-atom charge-changing cross-sections is needed for many accelerator applications. A Classical Trajectory Monte Carlo (CTMC) simulation has been used to calculate ionization and charge-exchange cross-sections. For benchmarking purposes, an extensive study has been performed for the simple case of hydrogen and helium targets in collisions with various ions. Despite the fact that the simulation only accounts for classical mechanics, the calculations are comparable to experimental results for projectile velocities in the region corresponding to the vicinity of the maximum cross-section. The shortcomings of the CTMC method for multielectron target atoms are discussed.
International Nuclear Information System (INIS)
Stripping cross sections in nitrogen have been calculated using the classical trajectory approximation and the Born approximation of quantum mechanics for the outer shell electrons of 3.2 GeV I- and Cs+ ions. A large difference in cross section, up to a factor of 6, calculated in quantum mechanics and classical mechanics, has been obtained. Because at such high velocities the Born approximation is well validated, the classical trajectory approach fails to correctly predict the stripping cross sections at high energies for electron orbitals with low ionization potential
Bonnet, L; Corchado, J
2015-01-01
Ten years ago, Liu and co-workers measured pair-correlated product speed and angular distributions for the OH+CH4/CD4 reactions at the collision energy of ~ 10 kcal/mol [B. Zhang, W. Shiu, J. J. Lin and K. Liu, J. Chem. Phys 122, 131102 (2005); B. Zhang, W. Shiu and K. Liu, J. Phys. Chem. A 2005, 109, 8989]. Recently, two of us could semi-quantitatively reproduce these measurements by performing full-dimensional classical trajectory calculations in a quantum spirit on an ab-initio potential energy surface of their own [J. Espinosa-Garcia and J. C. Corchado, Theor Chem Acc, 2015, 134, 6 ; J. Phys. Chem. B, Article ASAP, DOI: 10.1021/acs.jpcb.5b04290]. The goal of the present work is to show that these calculations can be significantly improved by adding a few more constraints to better comply with the experimental conditions. Overall, the level of agreement between theory and experiment is remarkable considering the large dimensionality of the processes under scrutiny.
Nonadiabatic nuclear dynamics of atomic collisions based on branching classical trajectories
International Nuclear Information System (INIS)
The branching classical trajectory method for inelastic atomic collision processes is proposed. The approach is based on two features: (i) branching of a classical trajectory in a nonadiabatic region and (ii) the nonadiabatic transition probability formulas particularly adapted for a classical trajectory treatment. In addition to transition probabilities and inelastic cross sections, the proposed approach allows one to calculate incoming and outgoing currents. The method is applied to inelastic Na + H collisions providing the results in reasonable agreement with full quantum calculations.
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
Decoherence and the Branching of Chaos-less Classical Trajectory
Ishikawa, Takuji
2016-01-01
This study was started to know mysterious classicality of nuclei. This time, I found a new rule for decoherence. I used a model without chaos. As a result, it was shown that not only the intersection of classical trajectories but also branching of classical trajectories are needed for decoherence. In other words, it was shown that interactions between a main system and environments have to make enough branchings of classical trajectories of the main system for decoherence.
Classical trajectory study of rotational excitation in collisions of hydrogen molecules
International Nuclear Information System (INIS)
The results of classical trajectory calculations for rigid rotator p-H2-p-H2 collisions are presented. Several trajectory methodologies are compared. Over the range for which quantal results are available classical-quantal comparisons are poor. (Auth.)
Effects of complex parameters on classical trajectories of Hamiltonian systems
Indian Academy of Sciences (India)
Asiri Nanayakkara; Thilagarajah Mathanaranjan
2014-06-01
Anderson et al have shown that for complex energies, the classical trajectories of real quartic potentials are closed and periodic only on a discrete set of eigencurves. Moreover, recently it was revealed that when time is complex $t(t = t_r e^{i_})$, certain real Hermitian systems possess close periodic trajectories only for a discrete set of values of . On the other hand, it is generally true that even for real energies, classical trajectories of non-PT symmetric Hamiltonians with complex parameters are mostly non-periodic and open. In this paper, we show that for given real energy, the classical trajectories of complex quartic Hamiltonians $H = p^2 + ax^4 + bx^k$ (where is real, is complex and = 1 or 2) are closed and periodic only for a discrete set of parameter curves in the complex -plane. It was further found that given complex parameter , the classical trajectories are periodic for a discrete set of real energies (i.e., classical energy gets discretized or quantized by imposing the condition that trajectories are periodic and closed). Moreover, we show that for real and positive energies (continuous), the classical trajectories of complex Hamiltonian $H = p^2 + x^4$, ($= _r$ e$^{i}$) are periodic when $ = 4 \\tan^{−1}$[($n/(2m + n)$)] for $\\forall n$ and $m \\mathbb{Z}$.
Numerical Calculation of Model Rocket Trajectories.
Keeports, David
1990-01-01
Discussed is the use of model rocketry to teach the principles of Newtonian mechanics. Included are forces involved; calculations for vertical launches; two-dimensional trajectories; and variations in mass, drag, and launch angle. (CW)
Numerical calculation of classical and non-classical electrostatic potentials
Christensen, D; Neyenhuis, B; Christensen, Dan; Durfee, Dallin S.; Neyenhuis, Brian
2006-01-01
We present a numerical exercise in which classical and non-classical electrostatic potentials were calculated. The non-classical fields take into account effects due to a possible non-zero photon rest mass. We show that in the limit of small photon rest mass, both the classical and non-classical potential can be found by solving Poisson's equation twice, using the first calculation as a source term in the second calculation. Our results support the assumptions in a recent proposal to use ion interferometry to search for a non-zero photon rest mass.
Trajectory Calculations in Light-Particle Fission
International Nuclear Information System (INIS)
Trajectory calculations based on a three-point-charge model were carried out for fission accompanied by 1H, 2H, 3H, 4He, 6He, 3He emission. The calculations were carried out with the intent of obtaining for each of these modes of fission the initial conditions which best fit the experimental results. The results indicate that both the initial distances between the fission fragments at scission and the initial kinetic energies of the particles tend to decrease as the mass of the light particle increases. In addition it was found that the experimental results could be better fitted by assuming that the particles are emitted off the axis connecting both fission fragments rather than on this axis. (author)
International Nuclear Information System (INIS)
For an arbitrary potential V with classical trajectories x-vector=g-vector(t) we construct localized oscillating three-dimensional wave lumps ψ(x-vector,t,g-vector) representing a single quantum particle. The crest of the envelope of the ripple follows the classical orbit g-vector(t) slightly modified due to potential V and ψ(x-vector,t;g-vector) satisfies the Schroedinger equation. The field energy, momentum and angular momentum calculated as integrals over all space are equal to particle energy, momentum and angular momentum. The relation to coherent states and to Schroedinger waves are also discussed. (author). 6 refs
International Nuclear Information System (INIS)
We compare the sensitivities to initial conditions for both direct (regular) and long-lived (chaotic) trajectories in classical scattering calculations with the corresponding properties of trajectories of position and momentum expectation values for quantum wave packets. The collinear H+H2 reaction is used as an example. The results show that the high sensitivity seen in chaotic trajectories is not reflected in the quantum dynamics. We conclude that it is possible for a classical ensemble consisting of only regular trajectories to respond trajectory by trajectory to perturbations in much the same way as a quantum wave packet. (There will of course be cases that are exceptions to this rule.) The response of an ensemble consisting of chaotic trajectories may on the average be similar to that of a wave packet, but not at the level of individual trajectories. In addition, the sensitivities of these trajectories to variations in the potential are analyzed. We conclude that the large contributions to the sensitivities from particular long-lived trajectories must approximately cancel when an exact ensemble average is taken. An algorithm is presented to smoothly account for the contributions to the sensitivities from these trajectories
A coupled-trajectory quantum-classical approach to decoherence in non-adiabatic processes
Min, Seung Kyu; Gross, E K U
2015-01-01
We present a novel quantum-classical approach to non-adiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the quasi-classical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as effect of the coupling to the nuclei and correctly reproduces the expected quantum behaviour. Moreover, the splitting of the nuclear wave packet is captured as consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in the Letter is supported by numerical results that are compared to quantum mechanical calculations.
Classical trajectory study of the photodissociation spectrum of H+3
International Nuclear Information System (INIS)
The photodissociation spectrum of H+3 is studied using classical mechanical methods. Tunneling rates and product translational energies are computed for a large range of total angular momentum and energy. We predict that the experimentally measured spectrum of Carrington and Kennedy is dominated by low total angular momentum and low energy (relative to dissociation). There is an almost one to one correspondence between the measured product translational energy and the total angular momentum. The classical dipole spectrum of chaotic trajectories is found to be relatively structureless, changes slowly with total J, and does not show any correspondence or indication of the experimentally measured regular structure found in the coarse grained spectrum. We conclude that the regularity found in the coarse grained spectrum should be associated with a stable manifold of trajectories. We find that the horseshoe periodic orbit previously found to be stable at J = 0 exists also for nonzero J and is stable with respect to small perturbations in 3D. The rotational constant of the rotating horseshoe is 30 cm-1 in interesting agreement with the experiment. The properties of the rotating horseshoe are studied in detail, a novel adiabatic switching method is used to study the stability of the orbit. A quantum formalism of Taylor and Zakrzewski that shows how periodic orbits may cause structure in quantal spectra is used to indicate why the features of the rotating horseshoe orbit may appear in the coarse grained spectrum. The experimental coarse grained features are interpreted as an R branch of the ν3 mode of the rotating horseshoe
Coupled-Trajectory Quantum-Classical Approach to Electronic Decoherence in Nonadiabatic Processes
Min, Seung Kyu; Agostini, Federica; Gross, E. K. U.
2015-08-01
We present a novel quantum-classical approach to nonadiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the quasiclassical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as an effect of the coupling to the nuclei and correctly reproduces the expected quantum behavior. Moreover, the splitting of the nuclear wave packet is captured as a consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in this Letter is supported by numerical results that are compared to quantum mechanical calculations.
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.
Trajectory description of the quantum-classical transition for wave packet interference
Chou, Chia-Chun
2016-08-01
The quantum-classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum-classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum-classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow the main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum-classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightful trajectory interpretation for the quantum-classical transition of wave packet interference.
Classical trajectory Monte Carlo investigation for Lorentz ionization of H (1s)
Institute of Scientific and Technical Information of China (English)
He Bin; Wang Jian-Guo; Liu Chun-Lei
2013-01-01
Lorentz ionization of H(1s) is investigated by classical trajectory Monte Carlo (CTMC) simulation.The effect of the transverse magnetic field on the considered process is analyzed in terms of the time evolution of interactions in the system,total electron energy,and electron trajectories.A classical mechanism for the ionization is found,where the variation of the kinetic energy of the nuclei is found to be important in the process.Compared with the results of tunneling ionization,the classical mechanism becomes more and more important with the increase of the velocity of the H-atom or the strength of the magnetic field.
Real-time quantum trajectories for classically allowed dynamics in strong laser fields
Plimak, L I
2015-01-01
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are distinctly quantum features of these trajectories, such as the complex-valued coordinates, physically relevant in the classically allowed region of phase space, and what is their origin? First, we argue that solutions of classical equations of motion can account for quantum effects. To this end, we construct an exact solution to the classical Hamilton-Jacobi equation which accounts for dynamics of the wave packet, and show that this solution is physically correct in the limit $\\hbar \\to 0$. Second, we show that imaginary components of classical trajectories are directly linked to the finite size of the initial wavepacket in momentum space. This way, if the electronic wavepacket produced by optical tunneling in strong infrared fiels is localised both in coordinate and momentum, its m...
A model of carbon ion interactions in water using the classical trajectory Monte Carlo method
International Nuclear Information System (INIS)
In this paper, model calculations for interactions of C6+ of energies from 1 keV u-1 to 1 MeV u-1 in water are presented. The calculations were carried out using the classical trajectory Monte Carlo method, taking into account the dynamic screening of the target core. The total cross sections (TCS) for electron capture and ionisation, and the singly and doubly differential cross sections (SDCS and DDCS) for ionisation were calculated for the five potential energy levels of the water molecule. The peaks in the DDCS for the electron capture to continuum and for the binary-encounter collision were obtained for 500-keV u-1 carbon ions. The calculated SDCS agree reasonably well with the z2 scaled proton data for 500 keV u-1 and 1 MeV u-1 projectiles, but a large deviation of up to 8-folds was observed for 100-keV u-1 projectiles. The TCS for ionisation are in agreement with the values calculated from the first born approximation (FBA) at the highest energy region investigated, but become smaller than the values from the FBA at the lower-energy region. (authors)
Comparison of classical and quantal calculations of helium three-body recombination
Pérez-Ríos, Jesús; Wang, Jia; Greene, Chris H
2013-01-01
A general method to study classical scattering in $n$-dimension is developed. Through classical trajectory calculations, the three-body recombination is computed as a function of the collision energy for helium atoms, as an example. Quantum calculations are also performed for the $J^{\\Pi}$ = $0^{+}$ symmetry of the three-body recombination rate in order to compare with the classical results, yielding good agreement for $E\\gtrsim$ 1 K. The classical threshold law is derived and numerically confirmed for the Newtonian three-body recombination rate. Finally, a relationship is found between the quantum and classical three-body hard hypersphere elastic cross sections which is analogous to the well-known shadow scattering in two-body collisions.
Classical trajectory perspective of atomic ionization in strong laser fields semiclassical modeling
Liu, Jie
2014-01-01
The ionization of atoms and molecules in strong laser fields is an active field in modern physics and has versatile applications in such as attosecond physics, X-ray generation, inertial confined fusion (ICF), medical science and so on. Classical Trajectory Perspective of Atomic Ionization in Strong Laser Fields covers the basic concepts in this field and discusses many interesting topics using the semiclassical model of classical trajectory ensemble simulation, which is one of the most successful ionization models and has the advantages of a clear picture, feasible computing and accounting for many exquisite experiments quantitatively. The book also presents many applications of the model in such topics as the single ionization, double ionization, neutral atom acceleration and other timely issues in strong field physics, and delivers useful messages to readers with presenting the classical trajectory perspective on the strong field atomic ionization. The book is intended for graduate students and researchers...
Quantum-Classical Nonadiabatic Dynamics: Coupled- vs Independent-Trajectory Methods.
Agostini, Federica; Min, Seung Kyu; Abedi, Ali; Gross, E K U
2016-05-10
Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic nonadiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper, we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron-nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods. PMID:27030209
Stegmann, Thomas; Szpak, Nikodem
2016-05-01
In this work we compare two fundamentally different approaches to the electronic transport in deformed graphene: (a) the condensed matter approach in which current flow paths are obtained by applying the non-equilibrium Green’s function (NEGF) method to the tight-binding model with local strain, (b) the general relativistic approach in which classical trajectories of relativistic point particles moving in a curved surface with a pseudo-magnetic field are calculated. The connection between the two is established in the long-wave limit via an effective Dirac Hamiltonian in curved space. Geometrical optics approximation, applied to focused current beams, allows us to directly compare the wave and the particle pictures. We obtain very good numerical agreement between the quantum and the classical approaches for a fairly wide set of parameters, improving with the increasing size of the system. The presented method offers an enormous reduction of complexity from irregular tight-binding Hamiltonians defined on large lattices to geometric language for curved continuous surfaces. It facilitates a comfortable and efficient tool for predicting electronic transport properties in graphene nanostructures with complicated geometries. Combination of the curvature and the pseudo-magnetic field paves the way to new interesting transport phenomena such as bending or focusing (lensing) of currents depending on the shape of the deformation. It can be applied in designing ultrasensitive sensors or in nanoelectronics.
Tropical troposphere-to-stratosphere transport inferred from trajectory calculations
Fueglistaler, S.; Wernli, H.; Peter, T.
2004-02-01
We present an analysis of trajectory calculations in the tropical tropopause layer (TTL) based on European Centre for Medium-Range Weather Forecasts (ECMWF) analysis wind and temperature fields. Over 500,000 forward and backward trajectories were calculated for January/February and July/August 2001. We analyze the pathways between 340 K and 400 K potential temperature (θ) of those trajectories involved in troposphere-to-stratosphere transport (TST). Even though trajectory calculations in this region may suffer from deficiencies in the underlying vertical wind field, they incorporate not only slow radiative ascent but also effects of deep convection, zonal and meridional transport, and their regional variability. From the trajectory calculations we derive a mean residence time of air parcels in the TTL, which shows a maximum at θ ≈360 K of ˜13 days for a change in potential temperature of ±10 K. The analysis of trajectory pathways reveals that approximately 80% of the trajectories ascending into the stratosphere enter the TTL over the western Pacific. Upon further ascent, they typically travel ˜5000-10,000 km before they arrive at the location where they assume minimum water mixing ratios. These pathways show regional and seasonal patterns and are largely controlled by the upper level circulation of the Asian-Australian monsoon, the northern hemispherical subtropical jet and the equatorial easterly jet from South Asia to Africa. As a consequence of the interplay of these meteorological systems, about 70% of TST trajectories assume their minimum water mixing ratio over the western Pacific, which shows also a global minimum in tropopause temperatures. Average water mixing ratios of air after TST are χH2O = 1.6 ppmv for January/February and χH2O = 3.6 ppmv for July/August 2001. Mixing of stratospherically young air, which just underwent TST, with older air masses entering the lower tropical stratosphere sideways yields an estimate of χH2O = 2.3 ppmv for
Real-time quantum trajectories for classically allowed dynamics in strong laser fields
Plimak, L. I.; Ivanov, Misha Yu.
2015-10-01
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here, we address a key question which arises in this context: Are distinctly quantum features of these trajectories, such as the complex-valued coordinates, physically relevant in the classically allowed region of phase space, and what is their origin? First, we argue that solutions of classical equations of motion can account for quantum effects. To this end, we construct an exact solution to the classical Hamilton-Jacobi equation which accounts for dynamics of the wave packet, and show that this solution is physically correct in the limit ?. Second, we show that imaginary components of classical trajectories are directly linked to the finite size of the initial wave packet in momentum space. This way, if the electronic wave packet produced by optical tunnelling in strong infrared fields is localised both in coordinate and momentum, its motion after tunnelling ipso facto cannot be described with purely classical trajectories - in contrast to popular models in the literature.
International Nuclear Information System (INIS)
Quasiclassical trajectory calculations are compared, with classical and Wigner sampling of transition state (TS) energy levels, for C2H5F≠→HF+C2H4 product energy partitioning and [Cl···CH3···Cl]- central barrier dynamics. The calculations with Wigner sampling are reported here for comparison with the previously reported calculations with classical sampling [Y. J. Cho et al., J. Chem. Phys. 96, 8275 (1992); L. Sun and W. L. Hase, J. Chem. Phys. 121, 8831 (2004)]. The C2H5F≠ calculations were performed with direct dynamics at the MP2/6-31G* level of theory. Classical and Wigner sampling give post-transition state dynamics, for these two chemical systems, which are the same within statistical uncertainties. This is a result of important equivalences in these two sampling methods for selecting initial conditions at a TS. In contrast, classical and Wigner sampling often give different photodissociation dynamics [R. Schinke, J. Phys. Chem. 92, 3195 (1988)]. Here the sampling is performed for a vibrational state of the ground electronic state potential energy surface (PES), which is then projected onto the excited electronic state's PES. Differences between the ground and the excited PESs may give rise to substantially different excitations of the vibrational and dissociative coordinates on the excited state PES by classical and Wigner sampling, resulting in different photodissociation dynamics.
Convergence and accuracy of numerical methods for trajectory calculations
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Computation of trajectories by a kinematic method requires the numerical solution of the differential equation by which the trajectory is defined. A widely used method is the iterative scheme of Petterssen which has second-order accuracy. The convergence and accuracy of this scheme is investigated for some simple flow types where analytical solutions are available. The results are discussed in comparison to other methods, especially a method similar to the Patterssen scheme, which has been recommended for use in semi-Lagrangian advection schemes. The truncation error in trajectory calculations should be kept about one order of magnitude smaller than the total uncertainty, which is mainly due to analysis errors and limited resolution of the wind data. It is shown that for trajectory calculations based on the typical output of current numerical weather prediction models or comparable data, this requires a time step 15% of the time step necessary to achieve convergence. If a fixed time step is used, it should not exceed about 0.5 h. Flexible time steps, based on the estimate of the truncation error which is provided by the difference between the first and the second iteration, are an attractive alternative. 26 refs., 8 figs
Classical trajectory perspective of atomic ionization in strong laser fields. Semiclassical modeling
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Dealing with timely and interesting issues in strong laser physics. Illustrates complex strong field atomic ionization with the simple semiclassical model of classical trajectory perspective for the first time. Provides a theoretical model that can be used to account for recent experiments. The ionization of atoms and molecules in strong laser fields is an active field in modern physics and has versatile applications in such as attosecond physics, X-ray generation, inertial confined fusion (ICF), medical science and so on. Classical Trajectory Perspective of Atomic Ionization in Strong Laser Fields covers the basic concepts in this field and discusses many interesting topics using the semiclassical model of classical trajectory ensemble simulation, which is one of the most successful ionization models and has the advantages of a clear picture, feasible computing and accounting for many exquisite experiments quantitatively. The book also presents many applications of the model in such topics as the single ionization, double ionization, neutral atom acceleration and other timely issues in strong field physics, and delivers useful messages to readers with presenting the classical trajectory perspective on the strong field atomic ionization. The book is intended for graduate students and researchers in the field of laser physics, atom molecule physics and theoretical physics. Dr. Jie Liu is a professor of Institute of Applied Physics and Computational Mathematics, China and Peking University.
Rapid Calculation of Spacecraft Trajectories Using Efficient Taylor Series Integration
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
Institute of Scientific and Technical Information of China (English)
Zhao Dan; Chu Tian-Shu; Hao Ce
2013-01-01
The stereodynamic properties of the F + HO (v,j) reaction are explored by quasi-classical trajectory (QCT) calculations performed on the 1A′ and 3A′ potential energy surfaces (PESs).Based on the polarization-dependent differential cross sections (PDDCSs) and the angular distributions of the product angular momentum with the reactant at different values of initial v or j,the results show that the product scattering and product polarization have strong links with initial vibrationalrotational numbers of v and j.The significant manifestation of the normal DCSs is that the forward scattering gradually becomes predominant with the initial vibrational excitation increasing,and the scattering angle of the HF product taking place on the 3A′ potential energy surface is found to be more sensitive to the initial value of v.The product orientation and alignment are strongly dependent on the initial rovibrational excitation effect.With enhancement in the initial rovibrational excitation effect,there is an overall decrease in the product orientation as well as in the product alignment either perpendicular to the reagent relative velocity vector k or along the direction of the y axis,for which the initial rotational excitation effect is much more noticeable than the vibrational excitation effect.Moreover,the initial rovibrational excitation effect on the product polarization is more pronounced for the 3A′ potential energy surface than for the 1A′ potential energy surface.
Voelkel, Stephen; Raman, Venkat; Varghese, Philip
2015-11-01
In high-speed reactive flows in scramjets, thermal nonequilibrium is introduced in the flow via shock waves. Though rotational and translational energy modes relax back to equilibrium quickly, vibrational relaxation is comparable to the bulk mixing and reaction timescales. The discrepancy between vibration and rotation/translation energy distributions can dramatically alter on the initiation of the fuel oxidation process. For continuum-scale applications, thermal nonequilibrium effects are derived from the rovibrational state-specific reaction and scattering rates associated with the chemical mechanism. In this work, the state-specific reaction rates are calculated for the chain branching reactions in the hydrogen combustion mechanism using a quasi-classical trajectory (QCT) framework. The state-specific rates are incorporated into a multiple temperature continuum-scale model whereby each species is characterized by a Boltzmann distribution parametrized by its own vibrational temperature. The flame ignition rates are implemented in a CFD code to simulate a reactive coflow. Funded by AFOSR FA9550-12-1-0460.
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We have computed the surface self-diffusion constants on four different crystal faces [fcc(111), fcc(100), bcc(110), and bcc(211)] using classical transition state theory methods. These results can be compared directly with previous classical-trajectory results which used the same Lennard-Jones 6-12 potential and template model; the agreement is good, though dynamical effects are evident for the fcc(111) and bcc(110) surfaces. Implications are discussed for low-temperature diffusion studies, which are inaccessible to direct molecular dynamics, and the use of ab initio potentials rather than approximate pairwise potentials
Use of hyperfunctions for classical radiation-reaction calculations
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It is shown that the use of hyperfunctions for the evaluation of radiation reaction in classical field theories leads to calculational simplifications compared to other methods. As illustrations, we calculate the radiation-reaction terms for systems of point particles in electrodynamics and in the lowest nontrivial order of the ''fast motion'' approximation of general relativity. Applications to other field theories are discussed briefly
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A previous rigid rotor potential surface for Li+-CO has been improved by computing surface points for two additional CO bond lengths at three different angles of orientation. The CI calculations including all single and double excitations which can be generated within the Hartree-Fock SCF molecular orbital basis have been improved by taking certain quadrupole excitations into account in an approximate way. Classical trajectories computed on this surface have been used to determine differential cross sections at scattering angles of 37.10, 43.20 and 49.20, and for a relative kinetic energy of 4.23 eV. Comparison with experiment shows that inclusion of CO vibrations does not account for the discrepancy found previously between the classical rigid rotor and the experimental results. When summed over all final vibrational levels the vibrotor results are nearly identical to the rigid rotor cross sections. (Auth.)
Calculating trajectories for atoms in near-resonant lightfields
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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 TEM01 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)
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Dynamic equations in the theory of a relativistic string with point masses at the ends are formulated in terms of geometric invariants of the world trajectories of the massive ends of the string (curvature ki and torsion κi(τ), i=1,2 of the trajectories). With these characteristics we reproduce the string world surface up to its position in Minkowski space E21. The torsions κi(τ), i=1,2 obey a system of second order differential equations with delay arguments describing the retardation effects of the interaction of masses through the string, ki being constants. The constant torsions are investigated in detail. In this case the string world sheet is a helicoid in E21. A nonlinear relation (the Regge trajectory) between the angular momentum of the system, J and the mass squared, M2, is derived. For given meson masses (M) and spin (J), the masses of quarks are calculated. 14 refs., 1 fig., 1 tab
Koide, T
2016-01-01
We derive a model of quantum-classical hybrids for a simplified model of quantum electrodynamics in the framework of the stochastic variational method. In this model, charged particle trajectories are affected by the interaction with quantized electromagnetic fields, and this quantum-classical interaction induces a displacement current. We further investigate a geometric phase in the wave functional of the gauge field configuration, which is induced by adiabatic motions of the charged particles. This phase contains the quantum-classical backreaction effect and usual Berry's phase is reproduced in the vanishing limit of the fluctuation of the charged particle trajectories.
Saydanzad, Erfan; Thumm, Uwe
2016-05-01
Attosecond time-resolved (XUV-pump, IR-probe) spectroscopy has been shown to be a powerful method for investigating the electron dynamics in atoms, and this technique is now being transferred to the investigation of electronic excitations, electron propagation, and collective electronic (plasmonic) effects in solids. Based on classical trajectory calculations, we simulated (i) the final photoelectron velocity distribution in order to provide observable velocity-map images for gold nanospheres of 10 and 100 nm diameter and (ii) streaked photoemission spectra. By analyzing our numerical results, we illustrate how spatio-temporal information about the sub-IR-cycle plasmonic and electronic dynamics is encoded in velocity-map images and streaked photoelectron spectra. Supported by the NE/KS NSF-EPSCOR program.
The calculation of the ion trajectory in an accelerating tube
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An accelerating tube is an electrostatic lens system. The author has deduced the ion trajectory in an accelerating tube by integrating the one in a unit electrostatic lens. The results show that tube focusing effect on ion trajectory is greatly affected by ion incident angle and the electrode dimension but almost independent of the number of the electrodes
Solid body equations to calculate the trajectory of ramjet
Imai, Kenji
1982-01-01
Six-degree-of-freedom trajectory equations for a ranrjet propelled, gun launched projectile are formulated. An outline for FORTRAN computer program flow charts also appear in the report. Special emphasis is given to the effect of wind on trajectory errors.
Diaz-Torres, Alexis
2007-01-01
A self-contained Fortran-90 program based on a classical trajectory model with stochastic breakup is presented, which should be a powerful tool for quantifying complete and incomplete fusion, and breakup in reactions induced by weakly-bound two-body projectiles near the Coulomb barrier. The code calculates complete and incomplete fusion cross sections and their angular momentum distribution, as well as breakup observables (angle, kinetic energy and relative energy distributions).
Torpedo's Search Trajectory Design Based on Acquisition and Hit Probability Calculation
Institute of Scientific and Technical Information of China (English)
LI Wen-zhe; ZHANG Yu-wen; FAN Hui; WANG Yong-hu
2008-01-01
Taking aim at light torpedo search trajectory characteristic of warship, by analyzing common used torpedo search trajectory, a better torpedo search trajectory is designed, a mathematic model is built up, and the simulation calculation taking MK46 torpedo for example is carried out. The calculation results testify that this method can increase acquisition probability and hit probability by about 10%-30% at some situations and becomes feasible for the torpedo trajectory design. The research is of great reference value for the acoustic homing torpedo trajectory design and the torpedo combat efficiency research.
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Analytical potential energy surfaces have been constructed for the four-center elimination of HCl from 1,1-dichloroethylene. The potential functions are Morse-type functions which are modified by appropriate switching and attenuating functions with adjustable parameters. The parameters have been found by fitting the calculated vibrational frequencies, reaction endothermicity, equilibrium geometries of the reactant and products to those of experiments and ab initio calculations. The translational energy release obtained from classical trajectory calculations on this surface is in good agreement with the experiment
Calculation of trajectory parameters of long pass in basketball.
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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.
Conditions for the quantum-to-classical transition: trajectories versus phase-space distributions.
Greenbaum, Benjamin D; Jacobs, Kurt; Sundaram, Bala
2007-09-01
We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the "strong" transition) [Bhattacharya et al., Phys. Rev. Lett. 85, 4852 (2000)], and the second by considering phase-space densities (the "weak" transition) [Greenbaum et al., Chaos 15, 033302 (2005)]. On the face of it these conditions appear rather different. We show, however, that in the semiclassical regime, in which the action of the system is large compared to h, and the measurement noise is small, they both offer an essentially equivalent local picture. Within this regime, the weak conditions dominate while in the opposite regime where the action is not much larger than h, the strong conditions dominate. PMID:17930329
Quasi-classical trajectory approach to the stereo-dynamics of the reaction F+HO→HF+O
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Quasi-classical trajectory (QCT) calculations are employed for the reaction F + HO(0,0)→HF + O based on the adiabatic potential energy surface (PES) of the ground 3A″triplet state. The average rotational alignment factor
Kelley, H. J.; Lefton, L.
1976-01-01
The computation of composite differential-turn trajectory pairs is studied for 'fast-evader' and 'neutral-evader' idealizations introduced in earlier publications. Transversality and generalized corner conditions are examined and the joining of trajectory segments discussed. A criterion is given for the screening of 'tandem-motion' trajectory segments. Main focus is upon the computation of barrier surfaces. Fortunately, from a computational viewpoint, the trajectory pairs defining these surfaces need not be calculated completely, the final subarc of multiple-subarc pairs not being required. Some calculations for pairs of example aircraft are presented.
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The semiclassical model RB (Robert, D. and Bonamy, J. (Journal de Physique (Paris), 1979, 40, 923 for calculation of line width and line shift has been used in many applications. It contains an approximate 'parabolic' trajectory. Bykov, A.D. et al, Atmospheric and Oceanic Optics (1992) 5, 587, have recently proposed an analytical expression for an exact treatment of the classical path. This paper analyses the consequence of introducing the exact trajectory within the RB model for the H2-He Q(1) line chosen as a simple test. Moreover, a comparison with results of exact close-coupling calculations is also given for this molecular system. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
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)
Heavy-ion fusion: comparison of experimental data with classical trajectory models
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Currently available data on fusion excitation functions for heavy-ion induced reactions over a wide mass range are compared to results calculated with a classical dynamical model based on the proximity nuclear potential of Blocki et al., the Coulomb potential of Bondorf et al., and one-body nuclear friction in the proximity formalism of Randrup. With these conservative and dissipative forces and the radial parameters of Myers, overall good agreement is obtained between the theoretical excitation functions and most of the available data. Extensive calculations have been performed to test the sensitivity of the calculated fusion cross-sections to a number of parameters, including the radial dependence of the Coulomb and nuclear potentials, the radial and tangential friction form factors as well as the projectile and target radii. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Nagy, Tibor; Vikár, Anna; Lendvay, György, E-mail: lendvay.gyorgy@ttk.mta.hu [Institute of Materials and Environmental Chemistry, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Magyar tudósok körútja 2., H-1117 Budapest (Hungary)
2016-01-07
The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH{sub 4} + H → CH{sub 3} + H{sub 2} and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C–H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C–H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling.
Nagy, Tibor; Vikár, Anna; Lendvay, György
2016-01-01
The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH4 + H → CH3 + H2 and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C-H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C-H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling. PMID:26747798
International Nuclear Information System (INIS)
The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH4 + H → CH3 + H2 and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C–H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C–H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling
International Nuclear Information System (INIS)
A classical explanation of interference effects in the double slit experiment is proposed. We claim that for every single “particle” a thermal context can be defined, which reflects its embedding within boundary conditions as given by the totality of arrangements in an experimental apparatus. To account for this context, we introduce a “path excitation field”, which derives from the thermodynamics of the zero-point vacuum and which represents all possible paths a “particle” can take via thermal path fluctuations. The intensity distribution on a screen behind a double slit is calculated, as well as the corresponding trajectories and the probability density current. The trajectories are shown to obey a “no crossing” rule with respect to the central line, i.e., between the two slits and orthogonal to their connecting line. This agrees with the Bohmian interpretation, but appears here without the necessity of invoking the quantum potential. - Highlights: ► We model quantum mechanical interference with classical means. ► The intensity distribution on a screen behind a double slit is calculated. ► Also, the corresponding trajectories and the probability density current are obtained.
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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.)
Calculating tumor trajectory and dose-of-the-day using cone-beam CT projections
Energy Technology Data Exchange (ETDEWEB)
Jones, Bernard L., E-mail: bernard.jones@ucdenver.edu; Westerly, David; Miften, Moyed [Department of Radiation Oncology, University of Colorado School of Medicine, Aurora, Colorado 80045 (United States)
2015-02-15
Purpose: Cone-beam CT (CBCT) projection images provide anatomical data in real-time over several respiratory cycles, forming a comprehensive picture of tumor movement. The authors developed and validated a method which uses these projections to determine the trajectory of and dose to highly mobile tumors during each fraction of treatment. Methods: CBCT images of a respiration phantom were acquired, the trajectory of which mimicked a lung tumor with high amplitude (up to 2.5 cm) and hysteresis. A template-matching algorithm was used to identify the location of a steel BB in each CBCT projection, and a Gaussian probability density function for the absolute BB position was calculated which best fit the observed trajectory of the BB in the imager geometry. Two modifications of the trajectory reconstruction were investigated: first, using respiratory phase information to refine the trajectory estimation (Phase), and second, using the Monte Carlo (MC) method to sample the estimated Gaussian tumor position distribution. The accuracies of the proposed methods were evaluated by comparing the known and calculated BB trajectories in phantom-simulated clinical scenarios using abdominal tumor volumes. Results: With all methods, the mean position of the BB was determined with accuracy better than 0.1 mm, and root-mean-square trajectory errors averaged 3.8% ± 1.1% of the marker amplitude. Dosimetric calculations using Phase methods were more accurate, with mean absolute error less than 0.5%, and with error less than 1% in the highest-noise trajectory. MC-based trajectories prevent the overestimation of dose, but when viewed in an absolute sense, add a small amount of dosimetric error (<0.1%). Conclusions: Marker trajectory and target dose-of-the-day were accurately calculated using CBCT projections. This technique provides a method to evaluate highly mobile tumors using ordinary CBCT data, and could facilitate better strategies to mitigate or compensate for motion during
Dispersive calculation of complex Regge trajectories for the lightest $f_2$ resonances
Carrasco, J A; Pelaez, J R; Szczepaniak, A P
2015-01-01
We apply a recently developed dispersive formalism to calculate the Regge trajectories of the $f_2(1270)$ and $f_2'(1525)$ mesons. Trajectories are calculated, not fitted to a family of resonances. Assuming that these spin-2 resonances can be treated in the elastic approximation the only input are the pole position and residue of the resonances. In both cases, the predicted Regge trajectories are almost real and linear, with slopes in agreement with the universal value of order 1 GeV$^{-2}$.
Knyazev, Vadim D; Stein, Stephen E
2010-06-10
The two-channel reaction of collision-induced dissociation (CID) of the n-butylbenzene cation under the conditions of multipole collision cells of tandem mass spectrometers was studied computationally. The results were compared with the experimental data from earlier CID studies. The Monte Carlo method used includes simulation of the trajectories of flight of the parent (n-C(4)H(9)C(6)H(5)(+)) and the product (C(7)H(7)(+) and C(7)H(8)(+)) ions in the electromagnetic field of multipole ion guides and collision cells, classical trajectory modeling of collisional activation and scattering of ions, and RRKM modeling of the parent ion decomposition. Experimental information on the energy dependences of the rates of the n-butylbenzene cation dissociation via two channels was used to create an RRKM model of the reaction. Effects of uncertainties in the critical parameters of the model of the reaction and the collision cells on the results of calculations were evaluated and shown to be minor. The results of modeling demonstrate a good agreement with experiment, providing support for the applied computational method in general and the use of classical trajectory modeling of collisional activation of ions in particular. PMID:20481494
Calculating tumor trajectory and dose-of-the-day using cone-beam CT projections
Jones, Bernard L; Miften, Moyed
2015-01-01
Purpose: Cone-beam CT (CBCT) projection images provide anatomical data in real-time over several respiratory cycles, forming a comprehensive picture of tumor movement. We developed and validated a method which uses these projections to determine the trajectory of and dose to highly mobile tumors during each fraction of treatment. Methods: CBCT images of a respiration phantom were acquired, the trajectory of which mimicked a lung tumor with high amplitude (up to 2.5 cm) and hysteresis. A template-matching algorithm was used to identify the location of a steel BB in each CBCT projection, and a Gaussian probability density function for the absolute BB position was calculated which best fit the observed trajectory of the BB in the imager geometry. Two modifications of the trajectory reconstruction were investigated: first, using respiratory phase information to refine the trajectory estimation (Phase), and second, using the Monte Carlo (MC) method to sample the estimated Gaussian tumor position distribution. Resu...
International Nuclear Information System (INIS)
It has recently been shown [S. J. Cotton and W. H. Miller, J. Chem. Phys. 139, 234112 (2013)] that a symmetrical windowing quasi-classical (SQC) approach [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] applied to the Meyer-Miller model [H.-D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] for the electronic degrees of freedom in electronically non-adiabatic dynamics is capable of quantitatively reproducing quantum mechanical results for a variety of test applications, including cases where “quantum” coherence effects are significant. Here we apply this same SQC methodology, within a flux-side correlation function framework, to calculate thermal rate constants corresponding to several proposed models of electron transfer processes [P. Huo, T. F. Miller III, and D. F. Coker, J. Chem. Phys. 139, 151103 (2013); A. R. Menzeleev, N. Ananth, and T. F. Miller III, J. Chem. Phys. 135, 074106 (2011)]. Good quantitative agreement with Marcus Theory is obtained over several orders of magnitude variation in non-adiabatic coupling. Moreover, the “inverted regime” in thermal rate constants (with increasing bias) known from Marcus Theory is also reproduced with good accuracy by this very simple classical approach. The SQC treatment is also applied to a recent model of photoinduced proton coupled electron transfer [C. Venkataraman, A. V. Soudackov, and S. Hammes-Schiffer, J. Chem. Phys. 131, 154502 (2009)] and population decay of the photoexcited donor state is found to be in reasonable agreement with results calculated via reduced density matrix theory
Mission design applications of QUICK. [software for interactive trajectory calculation
Skinner, David L.; Bass, Laura E.; Byrnes, Dennis V.; Cheng, Jeannie T.; Fordyce, Jess E.; Knocke, Philip C.; Lyons, Daniel T.; Pojman, Joan L.; Stetson, Douglas S.; Wolf, Aron A.
1990-01-01
An overview of an interactive software environment for space mission design termed QUICK is presented. This stand-alone program provides a programmable FORTRAN-like calculator interface to a wide range of both built-in and user defined functions. QUICK has evolved into a general-purpose software environment that can be intrinsically and dynamically customized for a wide range of mission design applications. Specific applications are described for some space programs, e.g., the earth-Venus-Mars mission, the Cassini mission to Saturn, the Mars Observer, the Galileo Project, and the Magellan Spacecraft.
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We present a mixed time-dependent density-functional theory (TDDFT)/classical trajectory surface hopping (SH) study of the photochemical ring opening in oxirane. Previous preparatory work limited to the symmetric CC ring-opening pathways of oxirane concluded that the Tamm-Dancoff approximation (TDA) is important for improving the performance of TDDFT away from the equilibrium geometry. This observation is supported by the present TDDFT TDA/SH calculations which successfully confirm the main experimentally derived Gomer-Noyes mechanism for the photochemical CO ring opening of oxirane and, in addition, provide important state-specific information not easily accessible from experiments. In particular, we find that, while one of the lowest two excited states is photochemically relatively inert, excitation into the other excited state leads predominantly to rapid ring opening, cyclic-C2H4O→CH2CH2O. This is followed by hopping to the electronic ground state where hot (4000 K) dynamics leads to further reactions, namely, CH2CH2O→CH3CHO→CH3+CHO and CH4+CO. We note that, in the dynamics, we are not limited to following minimum energy pathways and several surface hops may actually be needed before products are finally reached. The performance of different functionals is then assessed by comparison of TDDFT and diffusion Monte Carlo potential energy curves along a typical TDDFT TDA/SH reaction path. Finally, although true (S0,S1) conical intersections are expected to be absent in adiabatic TDDFT, we show that the TDDFT TDA is able to approximate a conical intersection in this system.
Tapavicza, Enrico; Tavernelli, Ivano; Rothlisberger, Ursula; Filippi, Claudia; Casida, Mark E.
2008-09-01
We present a mixed time-dependent density-functional theory (TDDFT)/classical trajectory surface hopping (SH) study of the photochemical ring opening in oxirane. Previous preparatory work limited to the symmetric CC ring-opening pathways of oxirane concluded that the Tamm-Dancoff approximation (TDA) is important for improving the performance of TDDFT away from the equilibrium geometry. This observation is supported by the present TDDFT TDA/SH calculations which successfully confirm the main experimentally derived Gomer-Noyes mechanism for the photochemical CO ring opening of oxirane and, in addition, provide important state-specific information not easily accessible from experiments. In particular, we find that, while one of the lowest two excited states is photochemically relatively inert, excitation into the other excited state leads predominantly to rapid ring opening, cyclic-C2H4O→C•H2CH2O•. This is followed by hopping to the electronic ground state where hot (4000K) dynamics leads to further reactions, namely, C•H2CH2O•→CH3CHO→C•H3+C•HO and CH4+CO. We note that, in the dynamics, we are not limited to following minimum energy pathways and several surface hops may actually be needed before products are finally reached. The performance of different functionals is then assessed by comparison of TDDFT and diffusion Monte Carlo potential energy curves along a typical TDDFT TDA/SH reaction path. Finally, although true (S0,S1) conical intersections are expected to be absent in adiabatic TDDFT, we show that the TDDFT TDA is able to approximate a conical intersection in this system.
Quasi-classical Trajectory Study of Reaction O (3P) + HCl (v = 2; j = 1,6,9) → OH + Cl
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The reaction O (3P) + HCl (v = 2; j = 1,6,9) → OH+ Cl is theoretically studied with a quasi-classical trajectory method (QCT) on the benchmark potential energy surface of the ground 3A'' state [J. Chem. Phys. 119(2003)9550]. The QCT-calculated state-resolved rotational distributions are in good agreement with the experimental results. The rotational polarization of the product OH molecule becomes weaker as the initial HCl rotation is excited. The calculated results can be explained from the large mass factor cos2 β of the title reaction, the van der Waals well in the potential energy surface and the secondary encounters in the exit channel. (atomic and molecular physics)
Boyle, Jason M; Liu, Jianbo; Anderson, Scott L
2009-04-23
A large set of quasi-classical trajectories were calculated at the PBE1PBE/6-311G** level of theory, in an attempt to understand the mechanistic origins of the large, mode-specific enhancement of the O-transfer reaction by NO2+ bending vibration and the surprisingly large suppressing effect of bending angular momentum. The trajectories reproduce the magnitude of the absolute reaction cross section, and also get the dependence of reactivity on NO2+ vibrational state, and the vibrational state dependent scattering behavior qualitatively correct. Analysis of the trajectories shows that the bending effect is not simply a consequence of enhanced reactivity in bent geometries but, rather, that excitation of bending motion allows reaction in a wider range of orientation angles, even if the NO2+ is not bent at the onset of the collisional interaction. There is a strong interplay between NO2+ bending and transient charge transfer during the collisions. Such charge transfer enhances reactivity, but only if the reactants are oriented correctly. PMID:19182967
Suzuki, Yasumitsu; Watanabe, Kazuyuki; Abedi, Ali; Agostini, Federica; Min, Seung Kyu; Maitra, Neepa; Gross, E. K. U.
The exact factorization of the electron-nuclear wave function allows to define the time-dependent potential energy surfaces (TDPESs) responsible for the nuclear dynamics and electron dynamics. Recently a novel coupled-trajectory mixed quantum-classical (CT-MQC) approach based on this TDPES has been developed, which accurately reproduces both nuclear and electron dynamics. Here we study the TDPES for laser-induced electron localization with a view to developing a MQC method for strong-field processes. We show our recent progress in applying the CT-MQC approach to the systems with many degrees of freedom.
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We present converged quantum dynamics for the H + D2 reaction at a total energy high enough to produce HD in the v' = 3, j' = 7 vibrational-rotational state and for total angular momenta J = 0, 1, and 2. We compare state-to-state partial cross sections for H + D2 (v = 0-2, j = 0, J = 0-2) → HD (v' = 0-2, j') + H and H + D2 (v = 1, j = 6, J = 0-2) → HD (v' = 0-2, j') + H as calculated from classical trajectory calculations with quantized initial conditions, i.e., a quasiclassical trajectory (QCT) simulation, to the results of converged quantum dynamics calculations involving up to 654 coupled channels. Final states in the QCT calculations are assigned by the quadratic smooth sampling (QSS) method. Since the quasiclassical and quantal calculations are carried out with the same potential energy surface, the comparison provides a direct test of the accuracy of the quasiclassical simulations as a function of the initial vibrational-rotational state and the final vibrational-rotational state
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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 H2 stretching and CH3 umbrella modes, along with the translational energy, strongly promote the reactivity, while the CH3 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
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The vector correlations in the reaction F+H2 (v = 0–3, j = 0–3) → HF(v', j')+H are investigated using the quasi-classical trajectory method on the Stark–Werner potential energy surface at a collision energy of 1.0eV. The potential distribution P(θr) to angles between k and j', the distribution P(ør) to dihedral angles, denoting k – k' – j' correlation and the polarization-dependent generalized differential cross sections, are calculated. The effect of reagent vibrational and rotational excitation on the F+H2 reaction is discussed in detail. The results suggest that the different vibrational and rotational quantum states of H2 have different influences on the product polarization. (atomic and molecular physics)
Scattering of fast N-2 from Pd(111) : A classical trajectory study
Schlathölter, Thomas; Vicanek, M; Heiland, W
1997-01-01
Molecular nitrogen is well known for its chemical inactivity. Experimental results for grazing incidence N-2 scattering from Pd(111) surfaces in the keV range also reveal negligible influences of electronical processes on molecular fragmentation. Therefore, we carry out gn appropriate classical trea
Semiclassical approach to mesoscopic systems. Classical trajectory correlations and wave interface
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Waltner, Daniel [Regensburg Univ. (Germany). Institut fuer Theoretische Physik
2012-07-01
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 Ehrenfest time, which is the minimal time needed for an initially spatially localized wave packet to show interference. He derives its signature on several quantities characterizing mesoscopic systems, e. g. dc and ac conductance, dc conductance variance, n-pair correlation functions of scattering matrices and the gap in the density of states of Andreev billiards. (orig.)
Indian Academy of Sciences (India)
Jinghan Zou; Shuhui Yin; Dan Wu; Mingxing Guo; Xuesong Xu; Hong Gao; Lei Li; Li Che
2013-09-01
Theoretical study on the dynamics of reactions H' + HS( = 0, = 0)→H2 + S and H' + HS( =0, = 0)→ H + H'S is performed with quasi-classical trajectory (QCT) method on a new ab initio potential energy surface for the lowest triplet state of H2S (3A") constructed in 2012 by Lv et al. The QCT-calculated reaction integral cross-sections are in good agreement with previous quantum wave packet results over the collision energy range of 0-50 kcal/mol. Both the abstraction and exchange reactions are governed by direct reaction dynamics and the trajectories follow the minimum energy path. The rotational angular momentum vector ' of products in the two reaction channels are not only aligned perpendicular to scattering plane but also oriented along the negative direction of the axis perpendicular to the scattering plane. With the increase in collision energy, the variation trends of product polarization in the two reaction channels are different and that may be attributed to the obviously different characteristic of the two channels on the potential energy surface.
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We theoretically investigate high-order harmonic generation by employing strong-field approximation (SFA) and present a new approach to the extension of the high-order harmonic cutoff frequency via an exploration of the dependence of high-order harmonic generation on the waveform of laser fields. The dependence is investigated via detailed analysis of the classical trajectories of the ionized electron moving in the continuum in the velocity—position plane. The classical trajectory consists of three sections (Acceleration Away, Deceleration Away, and Acceleration Back), and their relationship with the electron recollision energy is investigated. The analysis of classical trajectories indicates that, besides the final (Acceleration Back) section, the electron recollision energy also relies on the previous two sections. We simultaneously optimize the waveform in all three sections to increase the electron recollision energy, and an extension of the cutoff frequency up to Ip + 20.26Up is presented with a theoretically synthesized waveform of the laser field
Comparison of 3D Classical Trajectory and Transition-State Theory Reaction Cross Sections
Koeppl, G. W.; Karplus, Martin
1970-10-01
Although there is excellent agreement for a system such as H+H{sub 2} --> H{sub 2}+H, in which both the potential and the particle masses are symmetric, significant deviations occur for more asymmetric reactions. A detailed analysis show that the calculated differences are from the violation of two assumptions of transition-state theory.
Lesniak, Joseph; Behrman, Elizabeth; Zandler, Melvin; Kumar, Preethika
2008-03-01
Very few quantum algorithms are currently useable today. When calculating molecular energies, using a quantum algorithm takes advantage of the quantum nature of the algorithm and calculation. A few small molecules have been used to show that this method is possible. This method will be applied to larger molecules and compared to classical computer methods.
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Graphical abstract: The theoretical studies of the dynamics of the exchange reaction H′ + BrH (ν = 0, j = 0) → H′Br + H reactions are presented by stereodynamics calculations with quasiclassical trajectory method. Highlights: ► The cross sections for collision energies from 0.5 to 2.0 eV are determined. ► The rotational, vibrational and translational fractions are presented. ► The repulsive character of the potential energy surface is explored. ► The alignment and the orientation of H′Br are found to be close relation to Ec. - Abstract: Theoretical studies on the dynamics of the exchange reaction H′ + BrH (ν = 0, j = 0) → H′Br + H are performed on potential energy surface (PES) (Kurosaki et al., private communication) for the ground state using the quasi-classical trajectory method. The cross sections, computed at the collision energies (Ec) of 0.5–2.0 eV, are in good agreement with the earlier quantum wave packet results. The rotational, vibrational, and translational fractions in the total energy and the vibrational distribution for the product molecule are calculated at the same collision-energy range. The results support the repulsive character of the PES. In the considered Ec range, it has little chance to occur in an indirect reaction. The alignment and orientation of the product H′Br are investigated in detail with stereodynamics. The results show that Ec can effect on both the alignment and the orientation of product.
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We report rigid-rotator close coupling calculations and quasiclassical trajectory calculations for HF--HF collisions with total angular momentum zero. The results are compared to test the trajectory method
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We have measured the temperature-dependent kinetics for the reactions of OH+ with H2 and D2 using a selected ion flow tube apparatus. Reaction occurs via atom abstraction to result in H2O+/HDO+ + H/D. Room temperature rate coefficients are in agreement with prior measurements and resulting temperature dependences are T0.11 for the hydrogen and T0.25 for the deuterated reactions. This work is prompted in part by recent theoretical work that mapped a full-dimensional global potential energy surface of H3O+ for the OH+ + H2 → H + H2O+ reaction [A. Li and H. Guo, J. Phys. Chem. A 118, 11168 (2014)], and reported results of quasi-classical trajectory calculations, which are extended to a wider temperature range and initial rotational state specification here. Our experimental results are in excellent agreement with these calculations which accurately predict the isotope effect in addition to an enhancement of the reaction rate constant due to the molecular rotation of OH+. The title reaction is of high importance to astrophysical models, and the temperature dependence of the rate coefficients determined here should now allow for better understanding of this reaction at temperatures more relevant to the interstellar medium
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Accurate quantum total reaction probabilities for the collinear reaction X + F2 (upsilon = 0.1) → XF + F (X = Mu, H, D, T) have been used to calculate collinear rate constants and activation energies. Comparison is made with collinear quasi-classical trajectory calculations and transition state theory assuming classical motion along a separable reaction coordinate and vibrational adiabaticity. Considerable differences between the quantum and quasi-classical and transition state theory results are found only for the Mu reaction at low temperatures. 5 figures, 35 references, 6 tables
A simple calculator of ballistic trajectories for blocks ejected during volcanic eruptions
Mastin, Larry G.
2001-01-01
During the past century, numerous observers have described the violent ejection of large blocks and bombs from volcanoes during volcanic explosions. Minakami (1942) mapped the locations of blocks ejected from Asama Volcano during explosions in 1937. He developed a mathematical expression relating initial velocity and trajectory angle of ejected blocks to the ejection distance, taking into account air drag and assuming a constant drag coefficient. In the late 1950’s, Gorshkov (1959) estimated ejection velocities at Bezymianny volcano during its sector-collapse eruption. Wilson (1972) developed the first mathematical algorithm for ballistic trajectories in the volcanological literature (earlier ones had been available for military applications) that considered variations in drag coefficient with Reynolds number. Fagents and Wilson (1993) advanced the method of Wilson (1972) by considering the effect of reduced drag near the vent. From the 1970’s through the 1990’s other papers, too numerous to mention, have estimated volcanic ejection velocities from ballistic blocks. Since the early 1990’s there has been a decrease in the number of published papers that quantify ejection velocities from ballistic trajectories. This decrease has resulted in part from the appreciation that ejection velocities cannot be uniquely determined by ejection distance due to uncertainties in initial trajectory angle and drag force. On the other hand, the decrease in usage has coincided with an increase in the ease with which ballistic calculations can be made, due to the vast improvement in computer power and in the user-friendliness of computers. During the 1970’s, only volcanologists with mathematical acumen or those who could collaborate with applied mathematicians were able to make such estimates. With 21st century computer power, ballistic computation should be available to anyone as a back-of-the-envelope indicator of explosive power; the only factor preventing such usage is
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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.
Kovács, S. T. S.; Herczku, P.; Juhász, Z.; Sarkadi, L.; Gulyás, L.; Sulik, B.
2016-07-01
We report the energy and angular distribution of ejected electrons from C H4 and H2O molecules impacted by 1 MeV H+, H e+ , and 650 keV N+ ions. Spectra were measured at different observation angles, from 2 to 2000 eV. The obtained absolute double-differential electron-emission cross sections (DDCSs) were compared with the results of classical trajectory Monte Carlo (CTMC) and continuum distorted wave, eikonal initial state (CDW-EIS) calculations. For the bare H+ projectile both theories show remarkable agreement with the experiment at all observed angles and energies. The CTMC results are in similarly good agreement with the DDCS spectra obtained for impact by dressed H e+ and N+ ions, where screening effects and electron loss from the projectile gain importance. The CDW-EIS calculations slightly overestimate the electron loss for 1 MeV H e+ impact, and overestimate both the target and projectile ionization at low emitted electron energies for 650 keV N+ impact. The contribution of multiple electron scattering by the projectile and target centers (Fermi shuttle) dominates the N+-impact spectra at higher electron energies, and it is well reproduced by the nonperturbative CTMC calculations. The contributions of different processes in medium-velocity collisions of dressed ions with molecules are determined.
Directory of Open Access Journals (Sweden)
M. A. Hernández-Ceballos
2011-01-01
Full Text Available The Guadalquivir valley favors the channeling of air masses from coastal areas to inland Andalusia. This paper presents a first approximation of the spatial variation along the Guadalquivir valley in some of the representative thermodynamic properties of air masses. We have selected three representative sites of its lower, middle and high course, analyzing all of them on their daily trajectories and hourly records of potential temperature, specific humidity and wind speed during the period 2000-2007. The set of trajectories has been calculated using the HYSPLIT model (Hybrid Single-Particle Lagrangian Integrated Trajectory, establishing 12 UTC as the arrivaltime, a duration of 120 hours and a final height of incidence of 500 m. The cluster analysis has allowed the selection of ten different types of air masses, and those with a clear origin from the west were selected from this group. Analysis in the three sites of the daily cycles of potential temperature show a gradual cooling (3-4 K during the cold period (November-February of the year and warming during the warm period (June-September in the range of 5-6 K between the ends of the valley. The specific humidity experiences a drop, regardless of the period and type of air mass, as the air mass travels through the valley, being more intense during the warm period with up to 8 g kg-1 instead of the 1-2 g kg-1 in the cold period. The wind speed cycles show a progressive drop of intensity along the valley, more marked in the final section with a reduction of up to 3 m s-1 per 100 km, the more intense values being recorded during the warm period of the year with average values of up to 4 m s-1.
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In this paper, classical particle transport processes in field-reversed configuration plasma is investigated by particle-tracking calculations. The end-loss rate is found to increase with ion temperature, and the temperature dependence is much stronger than that of the Bohm scaling and the empirical scaling. (author)
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The isotope effect on the stereodynamic properties in the title reaction is investigated by a quasi-classical trajectory (QCT) method on the 11A' potential energy surface at a collision energy of 23.06 kcal/mol. The angular distributions P(θr), P(φr), P(θr,φr), and the polarization-dependent generalized differential cross sections are calculated, which demonstrate the observable influences on the rotational polarization of the product by the isotopic substitution of H with D. (atomic and molecular physics)
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Recent molecular-beam experiments have probed the dynamics of the Rydberg-atom reaction, H(n)+D2→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++D2→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
Scission-point configurations in ternary fission of 252Cf from trajectory calculations
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Trajectory calculations have been carried out in a three-point- charge model for the case of spontaneous ternary fission of 252Cf with a view to obtain the initial parameters characterizing the scission configuration. Without any a priori assumptions regarding the distribution of the points of emission of the α particle and the fragment velocity at the time of scission, the values of the initial parameters were obtained by fitting the observed energy distributions by making use of the method of multivariate analysis. It was found that there exist two points of α particle emission, nearer to either of the two fragments and off the axis joining the fragment centers, which reproduce the experijmental distributions equally well. This result does not support the often made assumption that the point of α particle emission coincides with the potential energy minimum on the line joining the fragment centers. With the initial parameters thus obtained, an inverse Monte Carlo calculation was carried out to obtain various correlations between the final values of the energy and the angle of emission of the α particle and the fission fragment kinetic energy. The calculated results agree well with the experiments. The implication of present results on the emission mechanism of the α particle in ternary fission is discussed
Uporov, Igor V.; Forlemu, Neville Y.; Rahul Nori; Tsvetan Aleksandrov; Sango, Boris A.; Yvonne E. Bongfen Mbote; Sandeep Pothuganti; Thomasson, Kathryn A.
2015-01-01
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...
Calculation of electron trajectory and energy deposition in no screening region
Kia, Mohammad Reza; Noshad, Houshyar
2016-01-01
The probability density function (PDF) of energy for inelastic collision is obtained by solving the integro-differential form of the quantity equation with the Bhabha differential cross section for particles with spin 1/2. Hence, the total PDF in no screening region is determined by folding theory with the following two assumptions: (1) the electron loses energy by collision and radiation and (2) the electron velocity does not change with a thin absorber. Therefore, a set of coupled stochastic differential equations based on the deviation and energy loss PDFs for electron is presented to obtain the electron trajectory inside the target. The energy PDFs for an electron beam with incident energy of 15.7 MeV inside aluminum and copper are calculated. Besides, the dose distributions for an electron beam with incident energies of 20, 10.2, 6, and 0.5 MeV in water are obtained. The results are in excellent agreement with the experimental data reported in the literature.
Buryak, Ilya; Vigasin, Andrey A.
2015-12-01
The present paper aims at deriving classical expressions which permit calculation of the equilibrium constant for weakly interacting molecular pairs using a complete multidimensional potential energy surface. The latter is often available nowadays as a result of the more and more sophisticated and accurate ab initio calculations. The water dimer formation is considered as an example. It is shown that even in case of a rather strongly bound dimer the suggested expression permits obtaining quite reliable estimate for the equilibrium constant. The reliability of our obtained water dimer equilibrium constant is briefly discussed by comparison with the available data based on experimental observations, quantum calculations, and the use of RRHO approximation, provided the latter is restricted to formation of true bound states only.
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Buryak, Ilya; Vigasin, Andrey A., E-mail: vigasin@ifaran.ru [Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 3 Pyzhevsky per., 119017 Moscow (Russian Federation)
2015-12-21
The present paper aims at deriving classical expressions which permit calculation of the equilibrium constant for weakly interacting molecular pairs using a complete multidimensional potential energy surface. The latter is often available nowadays as a result of the more and more sophisticated and accurate ab initio calculations. The water dimer formation is considered as an example. It is shown that even in case of a rather strongly bound dimer the suggested expression permits obtaining quite reliable estimate for the equilibrium constant. The reliability of our obtained water dimer equilibrium constant is briefly discussed by comparison with the available data based on experimental observations, quantum calculations, and the use of RRHO approximation, provided the latter is restricted to formation of true bound states only.
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.
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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
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A vibrationally selected beam of H2+ was used to investigate experimentally the reaction dynamics of the lowest two (endoergic) channels of the process H2+(γ=0,1)+He=HeH++H at the relative collision energy 3.58 eV, and to provide data for comparison with quasi-classical trajectory calculations. The process proceeds via a direct mechanism. In comparison with the reaction dynamics observed for the non-selected beam, where various vibrationally excited reactant ions participated, the results show - in a good agreement between theory and experiment - a prominent decrease of the forward 'stripping' scattering, and apparently an increased peak value of the recoil translational energy. This is consistent with the simple idea that small impact-parameter collisions leading to large-angle scattering are required to achieve an effective translational energy transfer necessary to overcome the reaction barrier. (Auth.)
Peláez, J R
2016-01-01
We review how the Regge trajectory of an elastic resonance can be obtained just from its pole position and coupling, using a dispersive formalism. This allows us to deal correctly with the finite widths of resonances in Regge trajectories. In this way we can calculate the Regge trajectories for the $K^*(892)$, $K_1(1400)$ and $K^*_0(1430)$, obtaining ordinary linear Regge trajectories, expected for $q \\bar q$ resonances. In contrast, for the $K^*_0(800)$ meson, the resulting Regge trajectory is non-linear and with much smaller slope, strongly supporting its non-ordinary nature.
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.
Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution
Kovchegov, Yuri V.; Sievert, Matthew D.
2016-02-01
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.
Calculating TMDs of an Unpolarized Target: Quasi-Classical Approximation and Quantum Evolution
Kovchegov, Yuri V
2016-01-01
We set up a formalism for calculating transverse-momentum-dependent parton distribution functions (TMDs) 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 dom...
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
Periodic trajectories for two-dimensional nonintegrable Hamiltonians
International Nuclear Information System (INIS)
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
Energy Technology Data Exchange (ETDEWEB)
Wang, Yan [Key Laboratory of Magnetic Resonance in Biological Systems, National Center for Magnetic Resonance in Wuhan, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China); School of Chemical and Environmental Engineering, Hubei University for Nationalities, Enshi 445000 (China); Li, Jun; Guo, Hua, E-mail: yangmh@wipm.ac.cn, E-mail: hguo@unm.edu [Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131 (United States); Chen, Liuyang; Yang, Minghui, E-mail: yangmh@wipm.ac.cn, E-mail: hguo@unm.edu [Key Laboratory of Magnetic Resonance in Biological Systems, National Center for Magnetic Resonance in Wuhan, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China); Lu, Yunpeng [Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371 (Singapore)
2015-10-21
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{sub 2} stretching and CH{sub 3} umbrella modes, along with the translational energy, strongly promote the reactivity, while the CH{sub 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.
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Recently a generalized topological unitarization scheme has been developed in which the effect of ''sea''-quark loops is taken into account from the beginning. At the lowest-order planar ''zero-entropy'' level, a self-consistent calculation of the leading Regge trajectory α (t) gives a ground-state mass m0=0.13 α'-1 and a coupling g02/4π of the order of the fine structure constant, suggesting a strong-electroweak unification. This calculation does not entail any free (input) parameters
Quantum and quasi-classical calculations for the S⁺ + H₂(v,j) → SH⁺(v',j') + H reactive collisions.
Zanchet, Alexandre; Roncero, Octavio; Bulut, Niyazi
2016-04-28
State-to-state cross-sections for the S(+) + H2(v,j) → SH(+)(v',j') + H endothermic reaction are obtained using quantum wave packet (WP) and quasi-classical (QCT) methods for different initial ro-vibrational H2(v,j) over a wide range of translation energies. The final state distribution as a function of the initial quantum number is obtained and discussed. Additionally, the effect of the internal excitation of H2 on the reactivity is carefully studied. It appears that energy transfer among modes is very inefficient that vibrational energy is the most favorable for the reaction, and rotational excitation significantly enhances the reactivity when vibrational energy is sufficient to reach the product. Special attention is also paid to an unusual discrepancy between classical and quantum dynamics for low rotational levels while agreement improves with rotational excitation of H2. An interesting resonant behaviour found in WP calculations is also discussed and associated with the existence of roaming classical trajectories that enhance the reactivity of the title reaction. Finally, a comparison with the experimental results of Stowe et al. for S(+) + HD and S(+) + D2 reactions exhibits a reasonably good agreement with those results. PMID:27055725
Institute of Scientific and Technical Information of China (English)
Bai Meng-Meng; Ge Mei-Hua; Yang Huan; Zheng Yu-Jun
2012-01-01
The quasi-classical trajectory (QCT) method is used to study the H+HS reaction on a newly built potential energy surface (PES) of the triplet state of H2S (3A") in a collision energy range of 0-60 kcal/mol.Both scalar properties,such as the reaction probability and the integral cross section (ICS),and the vector properties,such as the angular distribution between the relative velocity vector of the reactant and that of the product,etc.,are investigated using the QCT method.It is found that the ICSs obtained by the QCT method and the quantum mechanical (QM) method accord well with each other.In addition,the distribution for the product vibrational states is cold,while that for the product rotational states is hot for both reaction channels in the whole energy range studied here.
Espinosa-Garcia, Joaquin; Corchado, Jose C
2016-03-01
For the OH + CH4/CD4 hydrogen abstraction reactions, the methyl radical (CH3 and CD3) product translational distributions and the water (H2O and HOD) product vibrational distributions experimentally reported by Liu's group are reproduced by quasi-classical trajectory (QCT) calculations on an analytical full-dimensional potential energy surface when a quantum spirit is included in the analysis. Our simulations correctly predict: (i) the vibrational excitation of the water product, (ii) the inversion of the water vibrational population, and (iii) the propensity of transfer from reactant kinetic energy to product translational energy. These reactions therefore present a marked isotopic effect. In addition, the water product vibrational distributions for the OH/OD + CH4 reactions agree reasonably well with Butkovskaya and Setser's experiments for a similar alkane reaction. The theory/experiment agreement is better for the HOD than for the H2O product due to the mode coupling in the H2O molecule, which is absent in the HOD stretching modes, which show a more "local" character. In summary, for polyatomic systems with many degrees of freedom (15 in the present reaction), QCT calculations analyzed with a quantum spirit represent a useful alternative to quantum scattering methods. PMID:26061483
Communication: Overcoming the root search problem in complex quantum trajectory calculations
Energy Technology Data Exchange (ETDEWEB)
Zamstein, Noa; Tannor, David J. [Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)
2014-01-28
Three new developments are presented regarding the semiclassical coherent state propagator. First, we present a conceptually different derivation of Huber and Heller's method for identifying complex root trajectories and their equations of motion [D. Huber and E. J. Heller, J. Chem. Phys. 87, 5302 (1987)]. Our method proceeds directly from the time-dependent Schrödinger equation and therefore allows various generalizations of the formalism. Second, we obtain an analytic expression for the semiclassical coherent state propagator. We show that the prefactor can be expressed in a form that requires solving significantly fewer equations of motion than in alternative expressions. Third, the semiclassical coherent state propagator is used to formulate a final value representation of the time-dependent wavefunction that avoids the root search, eliminates problems with caustics and automatically includes interference. We present numerical results for the 1D Morse oscillator showing that the method may become an attractive alternative to existing semiclassical approaches.
Communication: Overcoming the root search problem in complex quantum trajectory calculations
International Nuclear Information System (INIS)
Three new developments are presented regarding the semiclassical coherent state propagator. First, we present a conceptually different derivation of Huber and Heller's method for identifying complex root trajectories and their equations of motion [D. Huber and E. J. Heller, J. Chem. Phys. 87, 5302 (1987)]. Our method proceeds directly from the time-dependent Schrödinger equation and therefore allows various generalizations of the formalism. Second, we obtain an analytic expression for the semiclassical coherent state propagator. We show that the prefactor can be expressed in a form that requires solving significantly fewer equations of motion than in alternative expressions. Third, the semiclassical coherent state propagator is used to formulate a final value representation of the time-dependent wavefunction that avoids the root search, eliminates problems with caustics and automatically includes interference. We present numerical results for the 1D Morse oscillator showing that the method may become an attractive alternative to existing semiclassical approaches
Algebraic-numeric calculations of proton trajectories in bending magnets of synchrotron accelerator
International Nuclear Information System (INIS)
We study a solution of nonlinear differential equation of the second degree which describes the trajectories of the charged particles in the fully inhomogeneous field of cyclic accelerator. We give the clear mathematical statement of the problem and algorithm of solving it. We realize this algorithm on the Computer Algebra System REDUCE 3.2. Our algorithm is based both on the existence of exact solution in terms of hyperelliptic integral and on the existence of power series solution of specific inversion problem. We use the known REDUCE procedures of operation on generalized power series. Using the FORTRAN code we give the numerical analysis of these series in the close relation to the concrete physical situation. We apply our results to the beam dynamics modelling of the protons in the bending magnets in synchrotron accelerator. 18 refs.; 2 figs
International Nuclear Information System (INIS)
In heavy-ion induced nuclear reactions one can produce transient systems with excitation energies up to 5 MeV per nucleon and spins up to ≅100 ℎ. The equilibrium statistical model can predict the mean lifetime for particle emission from moderately hot nuclei provided they are completely thermalized. However, as the excitation energy is increased, one expects to reach a situation of incomplete equilibration and hence a breakdown of the simplest equilibrium model. Determinations of the lifetime for (or intervals between) particle or fragment emissions can be useful both for testing the equilibrium model at low temperatures as well as for characterizing pre-equilibrium emission from partially thermalized nuclei. The net effect is best demonstrated by means of a correlation function, which can be interpreted by comparison to a reaction simulation. By such comparisons one can characterize the mean time intervals between emissions. The simulation programs MENEKA and COULGAN have been written for this purpose; they are Monte Carlo programs based on the following elements: a) Particles are emitted from the surface of an excited nucleus with a distribution of orbital angular momenta. b) Emission energies of the particles are chosen to reproduce experimental measurements or theoretical calculations. c) The distribution of time delays between particle emissions is given by exponential decay laws. d) A three-body trajectory is followed for the two particles and for the recoil nucleus. e) An event is accepted as a valid coincidence if the particle pair satisfies experimental requirements of detector thresholds and geometry. Particle trajectories are calculated numerically using time steps that are controlled by the requirement for energy conservation. An ancillary program SHOWTRAJ can be used to display and study trajectories event by event. (orig.)
Knyazev, Vadim D; Stein, Stephen E
2010-03-01
Collision-induced dissociation of the benzylammonium and the 4-tert-butyl benzylammonium ions was studied experimentally in an electrospray ionization quadrupole-hexapole-quadrupole tandem mass spectrometer. Ion fragmentation efficiencies were determined as functions of the kinetic energy of ions and the collider gas (argon) pressure. A theoretical Monte Carlo model of ion collisional excitation, scattering, and decomposition was developed. The model includes simulation of the trajectories of the parent and the product ions flight through the hexapole collision cell, quasiclassical trajectory modeling of collisional activation and scattering of ions, and Rice-Ramsperger-Kassel-Marcus (RRKM) modeling of the parent ion decomposition. The results of modeling demonstrate a general agreement between calculations and experiment. Calculated values of ion fragmentation efficiency are sensitive to initial vibrational excitation of ions, scattering of product ions from the collision cell, and distribution of initial ion velocities orthogonal to the axis of the collision cell. Three critical parameters of the model were adjusted to reproduce the experimental data on the dissociation of the benzylammonium ion: reaction enthalpy and initial internal and translational temperatures of the ions. Subsequent application of the model to decomposition of the t-butyl benzylammonium ion required adjustment of the internal ion temperature only. Energy distribution functions obtained in modeling depend on the average numbers of collisions between the ion and the atoms of the collider gas and, in general, have non-Boltzmann shapes. PMID:20060316
Chattaraj, Pratim Kumar
2010-01-01
The application of quantum mechanics to many-particle systems has been an active area of research in recent years as researchers have looked for ways to tackle difficult problems in this area. The quantum trajectory method provides an efficient computational technique for solving both stationary and time-evolving states, encompassing a large area of quantum mechanics. Quantum Trajectories brings the expertise of an international panel of experts who focus on the epistemological significance of quantum mechanics through the quantum theory of motion.Emphasizing a classical interpretation of quan
Chen, Chao; Shepler, Benjamin C; Braams, Bastiaan J; Bowman, Joel M
2007-09-14
We report a full-dimensional potential energy surface (PES) for the OH+NO(2) reaction based on fitting more than 55,000 energies obtained with density functional theory-B3LYP6-311G(d,p) calculations. The PES is invariant with respect to permutation of like nuclei and describes all isomers of HOONO, HONO(2), and the fragments OH+NO(2) and HO(2)+NO. Detailed comparison of the structures, energies, and harmonic frequencies of various stationary points on the PES are made with previous and present high-level ab initio calculations. Two hydrogen-bond complexes are found on the PES and confirmed by new ab initio CASPT2 calculations. Quasiclassical trajectory calculations of the cross sections for ground rovibrational OH+NO(2) association reactions to form HOONO and HONO(2) are done using this PES. The cross section to form HOONO is larger than the one to form HONO(2) at low collision energies but the reverse is found at higher energies. The enhancement of the HOONO complex at low collision energies is shown to be due, in large part, to the transient formation of a H-bond complex, which decays preferentially to HOONO. The association cross sections are used to obtain rate constants for formation of HOONO and HONO(2) for the ground rovibrational states in the high-pressure limit. PMID:17867750
Probabilities for classically forbidden transitions using classical and classical path methods
International Nuclear Information System (INIS)
Limits are established for the applicability of purely classical methods for calculating nonreactive, inelastic transition probabilities in collinear collisions of a structureless atom and a harmonic oscillator. These limits, obtained by comparison with previous exact quantum mechanical results, indicate that such methods are inappropriate not only for ''classically forbidden'' but for many ''classically allowed'' transitions (in spite of the fact that they are widely used to calculate probabilities for such processes). A classical path method in the context of infinite-order time-dependent perturbation theory is described which yields extremely accurate transition probabilities even for the most classically forbidden transitions in the collinear atom--harmonic oscillator system. The essential features of this method are: (1) the use of the expectation value of the total interaction potential in determining the atom--oscillator (central force) trajectory, and (2) the use of the arithmetic mean of the initial and final velocities of relative motion in the (elastic) central force trajectory. This choice of interaction potential allows the relative motion to be coupled to changes in the internal state of the oscillator. The present classical method is further applied to three-dimensional atom-breathing sphere collisions, and exact quantum mechanical calculations are also carried out. Comparison of the classical path and exact quantum results shows excellent agreement both in the specific inelastic cross section and in the individual partial-wave contributions
WOLF: a computer code package for the calculation of ion beam trajectories
International Nuclear Information System (INIS)
The WOLF code solves POISSON'S equation within a user-defined problem boundary of arbitrary shape. The code is compatible with ANSI FORTRAN and uses a two-dimensional Cartesian coordinate geometry represented on a triangular lattice. The vacuum electric fields and equipotential lines are calculated for the input problem. The use may then introduce a series of emitters from which particles of different charge-to-mass ratios and initial energies can originate. These non-relativistic particles will then be traced by WOLF through the user-defined region. Effects of ion and electron space charge are included in the calculation. A subprogram PISA forms part of this code and enables optimization of various aspects of the problem. The WOLF package also allows detailed graphics analysis of the computed results to be performed
Freixas-Lemus, Victor Manuel; Martínez-Mesa, Aliezer; Uranga-Piña, Llinersy
2016-04-01
We investigate the reactive dynamics of the triatomic system F + HCl → HF + Cl for total angular momentum equal zero and for different low-lying rovibrational states of the diatomic molecule. For each of the initial vibrational quantum numbers, the time evolution of the atom-diatom collision process is investigated for a wide range of impact angles and collision energies. To this purpose, the Quasi-Classical Trajectories (QCT) method was implemented in a hyperspherical configuration space. The Hamilton equations of motion are solved numerically in an intermediate effective Cartesian space to exploit the relative simplicity of this intermediate representation. Interatomic interactions are described by a London-Eyring-Polanyi-Sato potential energy surface, specifically developed for the title reaction, and the results of the QCT simulations are discussed in terms of the time-evolution of the hyperangles. The analysis of the collision dynamics using symmetric hyperspherical coordinates provides, in addition to the description in terms of a natural reaction coordinate (the hyperradius), a more striking representation of the exchange dynamics, in terms of the time-dependent probability distribution along the kinematic rotation hyperangle, and a precise distinction between direct and indirect mechanisms of the reaction. PMID:27002240
Indian Academy of Sciences (India)
Juan Zhang; Shunle Dong
2013-07-01
To investigate the effects of reagent vibrational and rotational states on the stereodynamical properties of the N(4S) + H2(, )→NH + H reaction and its reverse reaction of H(2S) + NH(, )→N(4S) + H2, we reported a detailed quasiclassical trajectory study using the 4A" double many-body expansion potential energy surface and at the collision energy of 35 kcal/mol. The density distribution of (r) as a function of the angle between and ', and that of (r) as a function of the dihedral angle between the plane containing -' and the plane containing '- ', the normal differential cross-sections as well as the averaged product rotational alignment parameter 〈 2('.) 〉 are calculated and reported. Comparison between the two reactions has showed that the degrees of alignment and orientation of products related to reagent rovibrational state have marked differences for the two reactive systems.
Gal, Romane Le; Xie, Changjian; Li, Anyang; Guo, Hua
2016-01-01
Based on recent $Herschel$ results, the ortho-to-para ratio (OPR) of NH$_2$ has been measured towards the following high-mass star-forming regions: W31C (G10.6-0.4), W49N (G43.2-0.1), W51 (G49.5-0.4), and G34.3+0.1. The OPR at thermal equilibrium ranges from the statistical limit of three at high temperatures to infinity as the temperature tends toward zero, unlike the case of H$_{2}$. Depending on the position observed along the lines-of-sight, the OPR was found to lie either slightly below the high temperature limit of three (in the range $2.2-2.9$) or above this limit ($\\sim3.5$, $\\gtrsim 4.2$, and $\\gtrsim 5.0$). In low temperature interstellar gas, where the H$_{2}$ is para-enriched, our nearly pure gas-phase astrochemical models with nuclear-spin chemistry can account for anomalously low observed NH$_2$-OPR values. We have tentatively explained OPR values larger than three by assuming that spin thermalization of NH$_2$ can proceed at least partially by H-atom exchange collisions with atomic hydrogen, th...
Semi-classical calculations of ultracold and cold collisions with frequency-chirped light
International Nuclear Information System (INIS)
There has been considerable interest in using shaped laser pulses as a means to control the dynamics of atoms and molecules. We conduct semi-classical Monte-Carlo simulations of ultracold collisions utilizing frequency-chirped laser light on a nanosecond timescale. Recent experiments demonstrated partial control of light-assisted collisional mechanisms with relatively slow chirp rates (10 GHz/μs). Collisions induced with positive chirped light enhance the inelastic collisional loss rate of atoms from a magneto-optical trap due to rapid adiabatic passage, whereas trap loss collisions can be coherently blocked when negative chirped light is used. Early quantum and classical simulations show that for negative chirps, laser frequency continually interacts with the atom pair during the collision. We investigate how this process depends on the chirp rate and show that by moderately speeding up the chirp (>50 GHz/μs), we can significantly enhance coherent processes. We extend our semi-classical model to examine using pulse shaping as a means to coherently control collisions and show that features in the pulse shape should be on the order of or less than 1 ns. We also show that coherent control of collisions using this technique can be extended to temperatures exceeding 1 K. (author)
International Nuclear Information System (INIS)
Numerical methods and computer programs are given to evaluate, for an arbitrary intermolecular potential, the classical transport collision integrals which appear in the kinetic theory of dilute gases. The method of Gaussian quadrature was employed to integrate the triple integral. A detailed discussion is given of the mathematics necessary to determine the boundaries of the individual integrations as well as a detailed analysis of errors introduced by the numerical procedures. Results for a recently published helium potential, the HFDHE2, are given. 5 references
Barghouty, A. F.
2014-01-01
Accurate estimates of electroncapture cross sections at energies relevant to the modeling of the transport, acceleration, and interaction of energetic neutral atoms (ENA) in space (approximately few MeV per nucleon) and especially for multi-electron ions must rely on detailed, but computationally expensive, quantum-mechanical description of the collision process. Kuang's semi-classical approach is an elegant and efficient way to arrive at these estimates. Motivated by ENA modeling efforts for apace applications, we shall briefly present this approach along with sample applications and report on current progress.
Energy Technology Data Exchange (ETDEWEB)
Jones, B; Miften, M [University of Colorado School of Medicine, Aurora, CO (United States)
2014-06-15
Purpose: Cone-beam CT (CBCT) projection images provide anatomical data in real-time over several respiratory cycles, forming a comprehensive picture of tumor movement. We developed a method using these projections to determine the trajectory and dose of highly mobile tumors during each fraction of treatment. Methods: CBCT images of a respiration phantom were acquired, where the trajectory mimicked a lung tumor with high amplitude (2.4 cm) and hysteresis. A template-matching algorithm was used to identify the location of a steel BB in each projection. A Gaussian probability density function for tumor position was calculated which best fit the observed trajectory of the BB in the imager geometry. Two methods to improve the accuracy of tumor track reconstruction were investigated: first, using respiratory phase information to refine the trajectory estimation, and second, using the Monte Carlo method to sample the estimated Gaussian tumor position distribution. 15 clinically-drawn abdominal/lung CTV volumes were used to evaluate the accuracy of the proposed methods by comparing the known and calculated BB trajectories. Results: With all methods, the mean position of the BB was determined with accuracy better than 0.1 mm, and root-mean-square (RMS) trajectory errors were lower than 5% of marker amplitude. Use of respiratory phase information decreased RMS errors by 30%, and decreased the fraction of large errors (>3 mm) by half. Mean dose to the clinical volumes was calculated with an average error of 0.1% and average absolute error of 0.3%. Dosimetric parameters D90/D95 were determined within 0.5% of maximum dose. Monte-Carlo sampling increased RMS trajectory and dosimetric errors slightly, but prevented over-estimation of dose in trajectories with high noise. Conclusions: Tumor trajectory and dose-of-the-day were accurately calculated using CBCT projections. This technique provides a widely-available method to evaluate highly-mobile tumors, and could facilitate better
Díez, Pedro
2016-01-01
This work provides an overview of a posteriori error assessment techniques for Finite Element (FE) based numerical models. These tools aim at estimating and controlling the discretization error in scientific computational models, being the basis for the numerical verification of the FE solutions. The text discusses the capabilities and limitations of classical methods to build error estimates which can be used to control the quality of numerical simulations and drive adaptive algorithms, with a focus on Computational Mechanics engineering applications. Fundamentals principles of residual methods, smoothing (recovery) methods, and constitutive relation error (duality based) methods are thus addressed along the manuscript. Attention is paid to recent advances and forthcoming research challenges on related topics. The book constitutes a useful guide for students, researchers, or engineers wishing to acquire insights into state-of-the-art techniques for numerical verification.
Indian Academy of Sciences (India)
Felix C. Difilippo
2012-09-01
Within the context of general relativity theory we calculate, analytically, scattering signatures around a gravitational singularity: angular and time distributions of scattered massive objects and photons and the time and space modulation of Doppler effects. Additionally, the scattering and absorption cross sections for the gravitational interactions are calculated. The results of numerical simulations of the trajectories are compared with the analytical results.
International Nuclear Information System (INIS)
In the framework of the present thesis by comparison of the experimental measurement data obtained by means of the detector system DIOGENES with calculated trajectories possible scission-point configurations of the fissioning nucleus should be stated. Special interest was dedicated to the evaluation of the so-called particle-accompanied fission in which beside the two fission fragments yet a light particle is additionally emitted. The initial conditions of a fission searched for are obtained by means of trajectory calculations which yield for assumed starting values the physical quantities as result which are also experimental accessible like final energies of all three contributing particles and angle between the light particle and the light fragment. The calculations were performed both for spherical and for rotational-ellipsoidally deformed fragments. All calculations were performed including the Coulomb and nuclear interaction forces between the three contributing nuclei, the fission fragment, and the α particle. (orig./HSI)
Lee, Chaohong; Duan, Yiwu; Liu, Wing-Ki; Yuan, Jian-Min; Shi, Lei; Zhu, Xiwen; Gao, Kelin
2001-01-01
Based upon our previous works (Eur.Phys.J.D 6, 319(1999); Chin.Phys.Lett. 18, 236(2001)), we develop a classical approach to calculate the high-order harmonic generation of the laser driven atoms and molecules. The Coulomb singularities in the system have been removed by a regularization procedure. Action-angle variables have been used to generate the initial microcanonical distribution which satisfies the inversion symmetry of the system. The numerical simulation show, within a proper laser ...
International Nuclear Information System (INIS)
We have derived, by the standard trajectory-tracing procedure, vertical cutoff rigidities for the locations of the stratospheric balloon measurements made during the 22nd Soviet Antarctic Expedition (1975-1976). Using the International Geomagnetic Reference Field Model for Epoch 1975, trajectories were calculated at 0.01 GV rigidity intervals to determine the vertical cutoff rigidities for each location. A comparison of the cosmic ray intensity vs. vertical cutoff rigidities for the entire survey shows a reasonable ordering of the data with an asymmetry between the northen and southern hemispheres
International Nuclear Information System (INIS)
The method of nuclear elastic scattering cross sections calculations has proposed for incident hadrons and complex particles within quasi-classic approximation using scattering phases. The calculation have performed for proton-nucleus elastic scattering cross sections from 182 MeV to 1 GeV. The calculating cross sections angular dependencies describe satisfactorily the experimental data behaviour in secondary maxima neighbourhood
International Nuclear Information System (INIS)
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 Na2 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 Na2 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 Na2 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)
Sakko, Arto; Rossi, Tuomas P.; Nieminen, Risto M.
2014-08-01
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 Na2 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 Na2 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 Na2 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.
Lee, C; Liu, W K; Yuan Jian Min; Shi, L; Zhu, X; Gao, K; Lee, Chaohong; Duan, Yiwu; Liu, Wing-Ki; Yuan, Jian-Min; Shi, Lei; Zhu, Xiwen; Gao, Kelin
2001-01-01
Based upon our previous works (Eur.Phys.J.D 6, 319(1999); Chin.Phys.Lett. 18, 236(2001)), we develop a classical approach to calculate the high-order harmonic generation of the laser driven atoms and molecules. The Coulomb singularities in the system have been removed by a regularization procedure. Action-angle variables have been used to generate the initial microcanonical distribution which satisfies the inversion symmetry of the system. The numerical simulation show, within a proper laser intensity, a harmonic plateau with only odd harmonics appears. At higher intensities, the spectra become noisier because of the existence of chaos. With further increase in laser intensity, ionization takes place, and the high-order harmonics disappear. Thus chaos introduces noise in the spectra, and ionization suppresses the harmonic generation, with the onset of the ionization follows the onset of chaos.
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Consideration is being given to a new way of approach of second and third order transformations for charged particle trajectories, performed by dipole, quadrupole magnets, widely used for acceleration and transport, separation and monochromatization of particles. The Way is based on the fact that for determination of transformation factors is necessary to conjugate two parts of particle trajectory, one of which is determined by initial particle coordinates, and another one - by terminal coordinates, presented in the form of series expansion according to initial coordinates and small parameters. Two trajectory parts are conjugated in that spot of transformation, where trajectories, typical for one out of four possible types of tra ectory brush transformation (''point to point'', ''point to parallels'', ''parallels to point'', ''parallels to parallels'') are parallel to the optical axis of transforming element or cross it. A new way of approach was used to obtain the system of unified, compact and symmetrical analytical expression for the first order coefficient with the obvious geometrical interpretation and simple algorithms for parameter search and calculation of characteristics of focusing and analyzing magnetic and electric elements (dipole magnets, electric deflectors, magnetic and electric quadrupole lenses)
Jorge, A.; Errea, L. F.; Illescas, Clara; Méndez, L.
2016-06-01
Cariatore et al. [Phys. Rev. A 91, 042709 (2015), 10.1103/PhysRevA.91.042709] have introduced a modification of the classical trajectory Monte Carlo (CTMC) method, specially conceived to provide an accurate representation of charge-exchange processes between highly charged ions and H (1 s ) , H*(n =2 ) . We point out that this new CTMC treatment is based on nonstable initial distributions for H*(n =2 ) targets and an improper description of the H (1 s ) target.
On the Trajectories of Projectiles Depicted in Early Ballistic Woodcuts
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…
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The rapid neutron-capture process (r-process) encounters unstable nuclei far from β-stability. Therefore its observable features, like the abundances, witness (still uncertain) nuclear structure as well as the conditions in the appropriate astrophysical environment. With the remaining lack of a full understanding of its astrophysical origin, parameterized calculations are still needed. We consider two approaches: (1) the classical approach is based on (constant) neutron number densities nn and temperatures T over duration timescales τ; (2) recent investigations, motivated by the neutrino wind scenario from hot neutron stars after a supernova explosion, followed the expansion of matter with initial entropies S and electron fractions Ye over expansion timescales τ. In the latter case the freezeout of reactions with declining temperatures and densities can be taken into account explicitly. We compare the similarities and differences between the two approaches with respect to resulting abundance features and their relation to solar r-process abundances, applying for the first time different nuclear mass models in entropy-based calculations. Special emphasis is given to the questions of (a) whether the same nuclear properties far from stability lead to similar abundance patterns and possible deficiencies in (1) and (2), and (b) whether some features can also provide clear constraints on the astrophysical conditions in terms of permitted entropies, Ye values, and expansion timescales in (2). This relates mostly to the A<110 mass range, where a fit to solar r-abundances in high-entropy supernova scenarios seems to be hard to attain. Possible low-entropy alternatives are presented. copyright copyright 1999. The American Astronomical Society
Hatz, Florian; Hardmeier, Martin; Bousleiman, Habib; Rüegg, Stephan; Schindler, Christian; Fuhr, Peter
2016-07-01
Connectivity analysis characterizes normal and altered brain function, for example, using the phase lag index (PLI), which is based on phase relations. However, reliability of PLI over time is limited, especially for single- or regional-link analysis. One possible cause is repeated changes of network configuration during registration. These network changes may be associated with changes of the surface potential fields, which can be characterized by microstate analysis. Microstate analysis describes repeating periods of quasistable surface potential fields lasting in the subsecond time range. This study aims to describe a novel combination of PLI with microstate analysis (microstate-segmented PLI = msPLI) and to determine its impact on the reliability of single links, regional links, and derived graph measures. msPLI was calculated in a cohort of 34 healthy controls three times over 2 years. A fully automated processing of electroencephalography was used. Resulting connectomes were compared using Pearson correlation, and test-retest reliability (TRT reliability) was assessed using the intraclass correlation coefficient. msPLI resulted in higher TRT reliability than classical PLI analysis for single or regional links, average clustering coefficient, average shortest path length, and degree diversity. Combination of microstates and phase-derived connectivity measures such as PLI improves reliability of single-link, regional-link, and graph analysis. PMID:27220459
Onida, Giovanni; Andreoni, Wanda
1995-09-01
A classical trajectory mapping method was developed to study chemical reactions in solution and in enzymes. In this method, the trajectories were calculated on a classical potential surface and the free energy profile was obtained by mapping the classical surface to the quantum mechanical surface obtained by the semiempirical AM1 method. There is no need to perform expensive quantum mechanical calculations at each iteration step. This method was applied to proton transfer reactions both in aqueous solution and in papain. The results are encouraging, indicating the applicability of this hybrid method to chemical reactions both in solution and in enzymes.
Doubleday, Charles; Boguslav, Mayla; Howell, Caronae; Korotkin, Scott D; Shaked, David
2016-06-22
An unusual H/D kinetic isotope effect (KIE) is described, in which isotopic selectivity arises primarily from nonstatistical dynamics in the product. In DFT-based quasiclassical trajectories of Bergman cyclization of (Z)-3-hexen-1,5-diyne (1) at 470 K, the new CC bond retains its energy, and 28% of nascent p-benzyne recrosses back to the enediyne on a vibrational time scale. The competing process of intramolecular vibrational redistribution (IVR) in p-benzyne is too slow to prevent this. Deuteration increases the rate of IVR, which decreases the fraction of recrossing and increases the yield of statistical (trapable) p-benzyne, 2. Trapable yields for three isotopomers of 2 range from 72% to 86%. The resulting KIEs for Bergman cyclization differ substantially from KIEs predicted by transition state theory, which suggests that IVR in this reaction can be studied by conventional KIEs. Leakage of vibrational zero point energy (ZPE) into the reaction coordinate was probed by trajectories in which initial ZPE in the CH/CD stretching modes was reduced by 25%. This did not change the predicted KIEs. PMID:27281683
Groessing, Gerhard; Fussy, Siegfried; Pascasio, Johannes Mesa; Schwabl, Herbert
2011-01-01
A classical explanation of interference effects in the double slit experiment is proposed. We claim that for every single "particle" a thermal context can be defined, which reflects its embedding within boundary conditions as given by the totality of arrangements in an experimental apparatus. To account for this context, we introduce a "path excitation field", which derives from the thermodynamics of the zero-point vacuum and which represents all possible paths a "particle" can take via therm...
Dey, Arghya; Fernando, Ravin; Abeysekera, Chamara; Homayoon, Zahra; Bowman, Joel M.; Suits, Arthur G.
2014-02-01
We combine the techniques of infrared multiphoton dissociation (IRMPD) with state selective ion imaging to probe roaming dynamics in the unimolecular dissociation of nitromethane and methyl nitrite. Recent theoretical calculations suggest a "roaming-mediated isomerization" pathway of nitromethane to methyl nitrite prior to decomposition. State-resolved imaging of the NO product coupled with infrared multiphoton dissociation was carried out to examine this unimolecular decomposition near threshold. The IRMPD images for the NO product from nitromethane are consistent with the earlier IRMPD studies that first suggested the importance of an isomerization pathway. A significant Λ-doublet propensity is seen in nitromethane IRMPD but not methyl nitrite. The experimental observations are augmented by quasiclassical trajectory calculations for nitromethane and methyl nitrite near threshold for each dissociation pathway. The observation of distinct methoxy vibrational excitation for trajectories from nitromethane and methyl nitrite dissociation at the same total energy show that the nitromethane dissociation bears a nonstatistical signature of the roaming isomerization pathway, and this is possibly responsible for the nitromethane Λ-doublet propensity as well.
Galileo's Trajectory with Mild Resistance
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.)
Theory of spontaneous radiation by electrons in a trajectory-coherent approximation
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The first-order quantum correction for the characterization of spontaneous radiation is calculated by means of electron quasi-classical trajectory-coherent states in an arbitrary electromagnetic field. Well known expressions for the characterization of spontaneous radiation are obtained using quasi-classical approximation. The first-order quantum correction is derived as a function from a classical trajectory (among which is a classical spin vector). Transitions with spin flip and without spin flip are distinguished. Those elements connected with photon kick and quantum motion characteristics are selected for first-order quantum correction. It is shown that, using an ultra-relativistic approximation, the latter may be ignored, but when using a non-relativistic approximation their contributions are approximately equal. A special trajectory-coherent representation that significantly simplifies the investigation of spontaneous radiation is proposed. (author)
Hermsdorf, D; Dörschel, B; Henniger, J
1999-01-01
The calculation of the response of CR-39 detectors exposed to neutrons is of high importance for their dosimetric application. A computer code system has been developed for this purpose. Whereas the generation of secondary charged particles is carried out using non-analogue Monte-Carlo techniques with variance reduction the simulation of the track formation process is treated without any free parameter starting from the etch rate ratio V(REL) only. Results are given for the contribution of recoil protons to the response as a function of the neutron energy and angle of incidence. Furthermore, the influence of an external radiator has been studied. The comparison of the calculated values with experimental data confirm the reliability of the track etch model applied.
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In describing the collision dynamics of processes SEC and DEC (single and double electron capture, respectively) in case of the He target the one active electron approximation was used with a single-centre effective potential for calculations of the dominant (n,l)-level state selective and total charge exchange cross sections. For He target part of the diexcited states of the projectile ions produced by DEC decay by Auger emission of one electron. This autoionizing double capture channel (ADEC) is not taken into account in the present work. (R.P.)
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In this work, Complex Robert-Bonamy calculations of half-widths and line shifts were done for N2-broadening of water for 1639 transitions in the rotational band using two models for the trajectories. The first is a model correct to second order in time, the Robert-Bonamy parabolic approximation. The second is the solution of Hamilton's equations. Both models use the isotropic part of the atom-atom potential to determine the trajectories. The present calculations used an intermolecular potential expanded to 20th order to assure the convergence of the half-widths and line shifts. The aim of the study is to assess if the difference in the half-widths and line shifts determined from the two trajectory models is greater than the accuracy requirements of the spectroscopic and remote sensing communities. The results of the calculations are compared with measurements of the half-widths and line shifts. It is shown that the effects of the trajectory model greatly exceed the needs of current remote sensing measurements and that line shape parameters calculated using trajectories determined by solving Hamilton's equations agree better with measurement.
Dynamical conservation of invariants by toroidal trajectories of guiding centres
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The classical problem of calculating toroidal trajectories is treated here by comparing the results of two different methods in a given magnetic configuration, a standard divergence-free magnetic field model. The present work consists of adapting the analytical criteria of MERCIER et al. for classical toroidal trajectories, and to examine numerically the dynamical conservation of the toroidal invariant. The first method is based on the evolution equations for the guiding centres. These equations are then solved numerically (code TRATORIA) and the trajectories are drawn for different initial conditions. We use a modified standard model for the magnetic field, which insures a manifestly divergence-free field. Moreover we take into account the contribution of the poloidal field to the total strength of the magnetic field. These corrections contribute to the analytical expression of the conserved toroidal momentum. The latter is verified to be conserved by the present numerical simulation with a precision generally of the order of 10-14. The second method is based on the analytical treatment of the invariants to yield a semi-analytical (semi graphical) determination of the intersection point of a given trajectory with the equatorial plane. Both methods allows one to recover well-known toroidal trajectories with passing and trapped particles (bananas). The present analysis brings a clear description of some other, less well-known types of trajectories, namely the stagnation orbits, the smallest D-shape banana, some small circulating de-flated bananas, some huge classical bananas (potatoes), and the largest puffed bananas which exhibit only local mirroring, along with several kind of escaping or open trajectories which are of importance for fast ion losses and target damages in the machines
Horzela, Andrzej; Kapuscik, Edward
1993-01-01
An alternative picture of classical many body mechanics is proposed. In this picture particles possess individual kinematics but are deprived from individual dynamics. Dynamics exists only for the many particle system as a whole. The theory is complete and allows to determine the trajectories of each particle. It is proposed to use our picture as a classical prototype for a realistic theory of confined particles.
Merzel, F; Johnson, M R; Fontaine-Vive, Fabien; Johnson, Mark R.; Merzel, Franci
2006-01-01
Computational tools for normal mode analysis, which are widely used in physics and materials science problems, are designed here in a single package called NMscatt (Normal Modes & scattering) that allows arbitrarily large systems to be handled. The package allows inelastic neutron and X-ray scattering observables to be calculated, allowing comparison with experimental data produced at large scale facilities. Various simplification schemes are presented for analysing displacement vectors, which are otherwise too complicated to understand in very large systems.
Inverse variational problem and ambiguity of classical system quantization
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It is shown that the problem of ambiguity of classical systems quantization is not limited by substitution of classical values for operators and by ordering of noncommutating operators. It is demonstrated that one and the same classical system can be described. Using an infinite number of various (differing more than for a total derivative) Lagrangians or Hamiltonians. The Feynman quantization is used by means of trajectory integrals. The problem of quantization of the classical system of equations of motion turns to be closely related to the inverse variational calculation problem. The inverse variational problem consists in finding a functional proceeding, from given equations, the extremals of which coincide with the solutions of the given equations. It is shown by concrete examples that with different Lagrangians though leading to identical classic equations of motion various quantum systems are obtained
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; True, Hans
2012-01-01
This paper describes the results of the application of Uncertainty Quantification methods to a railway vehicle dynamical example. Uncertainty Quantification methods take the probability distribution of the system parameters that stems from the parameter tolerances into account in the result. In...... this paper the methods are applied to a lowdimensional vehicle dynamical model composed by a two-axle bogie, which is connected to a car body by a lateral linear spring, a lateral damper and a torsional spring. Their characteristics are not deterministically defined, but they are defined by probability...... distributions. The model - but with deterministically defined parameters - was studied in [1], and this article will focus on the calculation of the critical speed of the model, when the distribution of the parameters is taken into account. Results of the application of the traditional Monte Carlo sampling...
Institute of Scientific and Technical Information of China (English)
Liu Yu-Fang; Sun Jin-Feng; Ma Heng; Zhu Zun-Lue
2007-01-01
The accurate dissociation energy and harmonic frequency for the highly excited 21 Πu state of dimer 7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space.The calculated results are in excellent agreement with experimental measurements.The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4ao to 37.0ao.And the conclusion is gained that the basis set 6-311++G(d,p) is a most suitable one.The calculated spectroscopic constants De,Re,ωe,ωeχe,αe and Be at 6-311++G(d,p) are 0.9670 eV,0.3125 nm,238.6 cm-1,1.3705cm-1,0.0039 cm-1 and 0.4921 cm-1.respectively.The vibrational levels are calculated by solving the radial Schr(o)dinger equation of nuclear motion.A total of 53 vibrational levels are found and reported for the first time.The classical turning points have been computed.Comparing with the measurements,in which only the first nine vibrational levels have been obtained so far,the present calculations are very encouraging.A careful comparison of the present results of the parameters De and ωe with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results,thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.
International Nuclear Information System (INIS)
It is easily demonstrated that a trajectory picture of low energy electron transport in condensed matter is not compatible with the Heisenberg uncertainty principle. The uncertainty in the position of a low energy electron is large and may in fact be larger than an entire simulated trajectory. This might be interpreted to mean that trajectory methods are not applicable. However, this conclusion is not correct. In the present paper, the evidence for the validity of low energy electron trajectory simulation is discussed, as well as the wave aspects and quantum nature of low energy electron transport in liquids and amorphous solids. It is pointed out that the validity of a trajectory approach to low energy electron transport in a liquid or amorphous solid partly is due to its ability to reproduce the average results of coherent elastic multiple wave scattering in a randomlike medium, and moreover that this ability may be further enhanced by the presence of inelastic scattering. The resulting validity of the trajectory method may be referred to as circumstancial validity, which is of a nature different from the explicit validity of trajectory methods which are compatible with the uncertainty principle. A previous systematic analysis of the limits of circumstancial validity is revisited and discussed for the basic case of multiple elastic scattering of a particle in a random medium of point scatterers. The detailed limits of circumstancial validity are graphically demonstrated in terms of particle wavelength, average distance between scatterers and elastic mean free path. Their immediate applicability to neutron transport is noted. The approximate nature of the point scatterer model as regards electron transport is adressed. In order to obtain an extrapolation of the result of the point scatterer model, it is observed that an increasing error of the trajectory method appears together with an increased amplitude of the multiple wave scattering taking place within the
Wigner phase space distribution via classical adiabatic switching
Energy Technology Data Exchange (ETDEWEB)
Bose, Amartya [Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States); Makri, Nancy [Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States); Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801 (United States)
2015-09-21
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.
Wigner phase space distribution via classical adiabatic switching
International Nuclear Information System (INIS)
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations
Institute of Scientific and Technical Information of China (English)
李艳青; 王美山; 朱子亮
2016-01-01
基于Lv等人最新构建的高精度的最低三重态势能面H2 S(3 A″),利用准经典轨线(QCT)方法计算了H+HS反应的两个反应通道提取反应和交换反应的动力学性质.主要研究了在反应物HS的碰撞能为0.1-2.0 eV时,不同振转态(v=0-3,j=0-3)对积分反应截面和产物极化的影响.研究结果表明:在总角动量J=0时,QCT方法计算出的动力学结果和吕等人的量子力学(QM)结果符合的很好.因此,对标题反应的动力学性质进行了进一步的研究.%The quasi-classical trajectory ( QCT) calculation are carried out for both exchange and abstraction processes of the reaction H+HS on a newly constructed high-quality lowest triplet state potential energy surface ( 3 A″) of H2 S. The integral cross section and the product polarization are investigated over the collision energy range of 0. 1-2. 0 eV for the reagent HS at the different vibrational and rotational states (v=0-3, j=0-3). The QCT-calculated integral cross sections are in good agreement with the previous QM results at the total angu-lar momentum J=0 as a function of collision energy for the H+HS ( v=0 , j=0 ) reaction. The detailed study of the dynamics properties for the title reaction is presented.
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.
On the classical limit of Bohmian mechanics for Hagedorn wave packets
Dürr, Detlef
2010-01-01
We consider the classical limit of quantum mechanics in terms of Bohmian trajectories. For wave packets as defined by Hagedorn we show that the Bohmian trajectories converge to Newtonian trajectories in probability.
Classical approach to H2+-H(1s) collisions
International Nuclear Information System (INIS)
Collisions between H2+ ion projectiles with H targets have been investigated in the 2.5-1000 keV energy range by means of classical-trajectory Monte Carlo calculations. It has been possible to simulate classically a dynamical H2+ molecule and, therefore, the approach includes all the Coulomb interactions between the five classical particles. Particular attention is paid to the description of the H2+ ion projectile, initially in its first vibration (v=0) ground state, and to the identification of the various reaction products after collision. Total cross sections for all the possible reaction channels are calculated, and are found in fair agreement with recent experimental data in the 20-100 keV energy range. Final n-state distributions for the hydrogen fragments are also determined
International Nuclear Information System (INIS)
The calculations of total cross sections of electron capture in collisions of Cq+ with H(1s) are reviewed. At low collision energies, new calculations have been performed, using molecular expansions, to analyze isotope effects. The Classical Trajectory Monte Carlo method have been also applied to discuss the accuracy of previous calculations and to extend the energy range of the available cross sections
International Nuclear Information System (INIS)
Full text: Classical cyclotron U-150, located in the Institute of Nuclear Physics of Academy of Sciences of Republic of Uzbekistan (Tashkent). The cyclotron was created more than 50 years ago and assumed it to accelerate different particles (protons, deuterons, ions, He), for the restructuring of the magnetic field used the coil current. In recent decades, the cyclotron is used to accelerate protons to energies of 15-20 MeV, which is produced at the target isotopes for medical or industrial applications. In order to save electric energy and help control the accelerator requested to create a decaying average magnetic field of the cyclotron only ferromagnetic rings and discs. To do this, we calculated the magnetic system with additional steel components (instead of the current), which create a decaying focusing magnetic field. The selected steel parts are made the cyclotron, an accelerator installed in the magnet and the measured magnetic field settings. Current coils are controlled only by the amplitude and phase of the first harmonic of magnetic field. Estimated processing of measurement results showed that using the resulting field of the accelerator can get the required isotopes, and the electric energy savings is about 15%. (author)
Smalley, Joseph S T; Shahin, Shiva; Kanté, Boubacar; Fainman, Yeshaiahu
2015-01-01
We analyze the steady-state transmission of high-momentum (high-$k$) electromagnetic waves through metal-semiconductor multilayer systems with loss and gain in the near-infrared (NIR). Using a semi-classical optical gain model in conjunction with the scattering matrix method (SMM), we study indium gallium arsenide phosphide (InGaAsP) quantum wells as the active semiconductor, in combination with the metals, aluminum-doped zinc oxide (AZO) and silver (Ag). Under moderate external pumping levels, we find that NIR transmission through Ag/InGaAsP systems may be enhanced by several orders of magnitude relative to the unpumped case, over a large angular and frequency bandwidth. Conversely, transmission enhancement through AZO/InGaAsP systems is orders of magnitude smaller, and has a strong frequency dependence. We discuss the relative importance of Purcell enhancement on our results and validate analytical calculations based on the SMM with numerical finite-difference time domain simulations.
Energy Technology Data Exchange (ETDEWEB)
Costella, J.P.; McKellar, B.H.J.; Rawlinson, A.A.
1997-03-01
We review how antiparticles may be introduced in classical relativistic mechanics, and emphasize that many of their paradoxical properties can be more transparently understood in the classical than in the quantum domain. (authors). 13 refs., 1 tab.
Quantum corrections to transport in graphene: a trajectory-based semiclassical analysis
International Nuclear Information System (INIS)
We review a calculation of the quantum corrections to electrical transport in graphene, using the trajectory-based semiclassical method. Compared to conventional metals, for graphene the semiclassical propagator contains an additional pseudospin structure that influences the results for weak localization, and interaction-induced effects, such as the Altshuler–Aronov correction and dephasing. Our results apply to a sample of graphene that is doped away from the Dirac point and subject to a smooth disorder potential, such that electrons follow classical trajectories. In such a system, the Ehrenfest time enters as an additional timescale. (paper)
Total and differential cross sections for charge transfer in He2+-He+ collisions: trajectory effects
International Nuclear Information System (INIS)
Cross sections have been computed for charge transfer in collisions between 4He+ and 4He2+ ions for centre-of-mass collision energies 0.21 ≤ E ≤ 2.50 keV. The semi-classical impact parameter method was employed, with a basis of atomic orbitals modified by plane-wave translation factors. Both rectilinear and Coulomb trajectories were used, and the differential cross sections were found to be sensitive to the assumed form of trajectory. Comparison is made with molecular orbital calculations by previous workers. (author)
Bender, D. F.
1978-01-01
The only ballistic trajectory mode feasible for a close solar probe or for an orbit inclined approximately 90 degrees to the ecliptic is the Jupiter gravity assisted mode. A comparison of the trajectories of the Solar Polar and the Solar Probe Mission for 1983 launches is shown. The geometry of the solar encounter phase is practically the same for the 4.3 year orbit achieved by a Jupiter gravity assist and for a one year orbit. Data describing the geometry of an orbit with perihelion at 4 solar radii and aphelion at Jupiter are listed. The range of apparent directions of the solar wind if it is flowing radially outward from the Sun with a speed of either 150 or 300 km/sec is shown. The minimum sun-earth-probe angle during the solar encounter as a function of the earth-node angle and the orbital inclination is also shown. If the inclination is 60 degrees or more, the minimum SEP angle is not greatly different from the 90 degree value.
Iterative quantum-classical path integral with dynamically consistent state hopping.
Walters, Peter L; Makri, Nancy
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. PMID:26827203
Iterative quantum-classical path integral with dynamically consistent state hopping
Walters, Peter L.; Makri, Nancy
2016-01-01
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.
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.
Iterative quantum-classical path integral with dynamically consistent state hopping
International Nuclear Information System (INIS)
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
Trajectory of the harmonic oscillator in the Schreodinger wave
Nishiyama, Yoshio
2001-01-01
A trajectory of a harmonic oscillator obeying the Schreodinger wave equation is exactly derived and illustrated. The trajectory resembles well the classical orbit between the turning points, and also runs through the tunneling region. The dynamics of the `particle' motion and the wave function associated with the motion are proposed. The period of a round trip on the trajectory is exactly equal to that obtained in classical mechanics.
Trajectory of the harmonic oscillator in the Schrodinger wave
Nishiyama, Yoshio
1999-01-01
A trajectory of a harmonic oscillator obeying the Schrodinger equation is exactly derived and illustrated. The trajectory resembles well the classical orbit between the turning points, and also runs through the tunneling region. The dynamics of the 'particle' motion and the wave function associated with the motion are proposed. The period of a round trip on the trajectory is exactly equal to that obtained in classical mechanics.
Dörschel, B; Hermsdorf, D; Kadner, K; Kuehne, H
1999-01-01
Computation of the neutron response of CR-39 detectors needs to simulate the track formation by neutron induced charged particles taking into account the bulk etch rate and the track etch rate varying along the particle trajectories. The latter one was determined experimentally by track length measurement. The results allowed to derive the relationship between the track etch rate and the restricted energy loss of the charged particles. On this basis, the geometrical track parameters and track etch rates as well as the critical angle of particle incidence could be determined for protons and alpha particles in the energy range from 0.2 to 8.8 MeV. The energy dependence of the critical angle enabled to determine the detection efficiency for a charged particle of given energy and direction.
Evaluation of photoexcitation and photoionization probabilities by the trajectory method
International Nuclear Information System (INIS)
A new trajectory-based method of transition probability evaluation in quantum system was developed. It is based on a path integral representation of probability and uses Weyl symbols for initial and final states. The method belongs to the efficient initial value representation (IVR) schemes. The pre-exponential factor specific to the semi-classical method is equal to one, and does not need be separately calculated. This eliminates problems with caustics and Maslov indices of trajectories. The method is equally efficient for evaluation of the transition probabilities into separate states and groups of states, including an entire ionization continuum, for example. The capabilities of the method are demonstrated by the evaluation of the photo-excitation and photo-ionization probabilities in the hydrogen atom exposed to an ultrashort photo-pulse, and total photo-ionization probability in the helium atom. (authors)
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.
International Nuclear Information System (INIS)
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
Three-stage classical molecular dynamics model for simulation of heavy-ion fusion
Directory of Open Access Journals (Sweden)
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.
Torrielli, Alessandro
2016-08-01
We review some essential aspects of classically integrable systems. The detailed outline of the sections consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schrödinger model, principal chiral field); 4. Features of classical r-matrices: Belavin–Drinfeld theorems, analyticity properties, and lift of the classical structures to quantum groups; 5. Classical inverse scattering method to solve integrable differential equations: soliton solutions, spectral properties and the Gel’fand–Levitan–Marchenko equation, with examples (KdV equation, Sine-Gordon model). Prepared for the Durham Young Researchers Integrability School, organised by the GATIS network. This is part of a collection of lecture notes.
Rydberg atoms in external fields as an example of open quantum systems with classical chaos
International Nuclear Information System (INIS)
We examine the quantum spectra of hydrogen atoms in external magnetic and electric fields above the ionization threshold with respect to signatures of classical chaos characteristics of open systems. The spectra are obtained by calculating wavefunctions and photionization cross sections in the continuum region with the aid of the complex-coordinate-rotation method. We find that the photoionization cross sections exhibit strong Ericson fluctuations, a quantum feature characteristic of classically chaotic scattering, in energy-field regions where classical trajectory calculations reveal a fractal dependence of the classical ionization time on the initial conditions. We also compare the nearest-neighbour-spacing distributions of complex resonance energies with predictions of random-matrix theories and find that our results are well reproduced by a Ginibre distribution. (author)
Energy Technology Data Exchange (ETDEWEB)
Khrushchev, Yu.V.; Danilov, S.N.; Savich, V.A.
1983-01-01
In the proposed method for forming controlling effects in dynamic transition of EPS, an additional system of equations is used of small order which can be solved at each step of integration of the system of differential equations of motion. The calculation algorithm for smooth control in this case is relatively simple and makes it possible to use standard programs. The program of formation and solution to the additional system of equations can be built into the known programs for calculating the dynamic stability of the EPS without their significant change, as a result of which a considerable improvement in their efficient use is possible.
Cohn, A G; Rabinowitz, Mario
2003-01-01
A classical representation of an extended body over barriers of height greater than the energy of the incident body is shown to have many features in common with quantum tunneling as the center-of-mass literally goes through the barrier. It is even classically possible to penetrate any finite barrier with a body of arbitrarily low energy if the body is sufficiently long. A distribution of body lengths around the de Broglie wavelength leads to reasonable agreement with the quantum transmission coefficient.
Cohn, Arthur; Rabinowitz, Mario
2003-01-01
A classical representation of an extended body over barriers of height greater than the energy of the incident body is shown to have many features in common with quantum tunneling as the center-of-mass literally goes through the barrier. It is even classically possible to penetrate any finite barrier with a body of arbitrarily low energy if the body is sufficiently long. A distribution of body lengths around the de Broglie wavelength leads to reasonable agreement with the quantum transmission...
Mould, Richard A
2003-01-01
Preciously given rules allow conscious systems to be included in quantum mechanical systems. There rules are derived from the empirical experience of an observer who witnesses a quantum mechanical interaction leading to the capture of a single particle. In the present paper it is shown that purely classical changes experienced by an observer are consistent with these rules. Three different interactions are considered, two of which combine classical and quantum mechanical changes. The previous...
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.
Exceptional points in quantum and classical dynamics
Smilga, A V
2008-01-01
We notice that, when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the corresponding classical system also exhibits a singular behaviour associated with restructuring of classical trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2 -igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies with supersymmetric Yang-Mills dynamics are elucidated.
Exceptional points in quantum and classical dynamics
Smilga, A. V.
2009-03-01
We note that when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the corresponding classical system also exhibits singular behaviour associated with the restructuring of classical trajectories. A system with the crypto-Hermitian Hamiltonian H = (p2 + z2)/2 - igz5 and hyper-elliptic classical dynamics is studied in detail. Analogies with supersymmetric Yang-Mills dynamics are elucidated.
Trajectory Optimization: OTIS 4
Riehl, John P.; Sjauw, Waldy K.; Falck, Robert D.; Paris, Stephen W.
2010-01-01
The latest release of the Optimal Trajectories by Implicit Simulation (OTIS4) allows users to simulate and optimize aerospace vehicle trajectories. With OTIS4, one can seamlessly generate optimal trajectories and parametric vehicle designs simultaneously. New features also allow OTIS4 to solve non-aerospace continuous time optimal control problems. The inputs and outputs of OTIS4 have been updated extensively from previous versions. Inputs now make use of objectoriented constructs, including one called a metastring. Metastrings use a greatly improved calculator and common nomenclature to reduce the user s workload. They allow for more flexibility in specifying vehicle physical models, boundary conditions, and path constraints. The OTIS4 calculator supports common mathematical functions, Boolean operations, and conditional statements. This allows users to define their own variables for use as outputs, constraints, or objective functions. The user-defined outputs can directly interface with other programs, such as spreadsheets, plotting packages, and visualization programs. Internally, OTIS4 has more explicit and implicit integration procedures, including high-order collocation methods, the pseudo-spectral method, and several variations of multiple shooting. Users may switch easily between the various methods. Several unique numerical techniques such as automated variable scaling and implicit integration grid refinement, support the integration methods. OTIS4 is also significantly more user friendly than previous versions. The installation process is nearly identical on various platforms, including Microsoft Windows, Apple OS X, and Linux operating systems. Cross-platform scripts also help make the execution of OTIS and post-processing of data easier. OTIS4 is supplied free by NASA and is subject to ITAR (International Traffic in Arms Regulations) restrictions. Users must have a Fortran compiler, and a Python interpreter is highly recommended.
Using Selectively Applied Accelerated Molecular Dynamics to Enhance Free Energy Calculations
Wereszczynski, Jeff; McCammon, J. Andrew
2010-01-01
Accelerated molecular dynamics (aMD) has been shown to enhance conformational space sampling relative to classical molecular dynamics; however, the exponential reweighting of aMD trajectories, which is necessary for the calculation of free energies relating to the classical system, is oftentimes problematic, especially for systems larger than small poly peptides. Here, we propose a method of accelerating only the degrees of freedom most pertinent to sampling, thereby reducing the total accele...
Mould, R A
2003-01-01
Preciously given rules allow conscious systems to be included in quantum mechanical systems. There rules are derived from the empirical experience of an observer who witnesses a quantum mechanical interaction leading to the capture of a single particle. In the present paper it is shown that purely classical changes experienced by an observer are consistent with these rules. Three different interactions are considered, two of which combine classical and quantum mechanical changes. The previously given rules support all of these cases. Key Words: brain states, conscious observer, detector, measurement, probability current, state reduction, von Neumann, wave collapse.
International Nuclear Information System (INIS)
There are several theoretical models which treat the fusion process and energy dissipation in heavy ion collision in terms of a fluctuating force represented by the coupling between macroscopic and intrinsic degrees of freedom. One such dynamical model has been developed by Feldmeier (1987), where the properties of the dissipative force are determined from a microscopic picture of particle exchange between two nuclei. The macroscopic shapes of the nuclear system are represented by axially symmetric configuration with sharp surfaces. We have used the above model to calculate the fusion time scales for the systems 11B + 237Np, 12C +232Th and 16O + 232Th at 77, 86 and 104 MeV bombarding energies to examine the effect of mass asymmetry in fusion dynamics. (author). 2 figs
Method and Apparatus for Generating Flight-Optimizing Trajectories
Ballin, Mark G. (Inventor); Wing, David J. (Inventor)
2015-01-01
An apparatus for generating flight-optimizing trajectories for a first aircraft includes a receiver capable of receiving second trajectory information associated with at least one second aircraft. The apparatus also includes a traffic aware planner (TAP) module operably connected to the receiver to receive the second trajectory information. The apparatus also includes at least one internal input device on board the first aircraft to receive first trajectory information associated with the first aircraft and a TAP application capable of calculating an optimal trajectory for the first aircraft based at least on the first trajectory information and the second trajectory information. The optimal trajectory at least avoids conflicts between the first trajectory information and the second trajectory information.
Danforth, Douglas G.
2001-01-01
Classical systems can be entangled. Entanglement is defined by coincidence correlations. Quantum entanglement experiments can be mimicked by a mechanical system with a single conserved variable and 77.8% conditional efficiency. Experiments are replicated for four particle entanglement swapping and GHZ entanglement.
Gallavotti, Giovanni
1999-01-01
This is the English version of a friendly graduate course on Classical Mechanics, containing about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. For the Spanish version, see physics/9906066
Emergence of classical theories from quantum mechanics
Hajicek, Petr
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 ...
Quantum trajectories based on the weak value
Mori, Takuya; Tsutsui, Izumi
2015-04-01
The notion of the trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any quantum observable, can offer a possible description of trajectory on account of its statistical nature. In this paper, we explore the physical significance provided by this "weak trajectory" by considering various situations where interference takes place simultaneously with the observation of particles, that is, in prototypical quantum situations for which no classical treatment is available. These include the double slit experiment and Lloyd's mirror, where in the former case it is argued that the real part of the weak trajectory describes an average over the possible classical trajectories involved in the process, and that the imaginary part is related to the variation of interference. It is shown that this average interpretation of the weak trajectory holds universally under the complex probability defined from the given transition process. These features remain essentially unaltered in the case of Lloyd's mirror where interference occurs with a single slit.
Modularity-Based Clustering for Network-Constrained Trajectories
EL MAHRSI, Mohamed Khalil; Rossi, Fabrice
2012-01-01
We present a novel clustering approach for moving object trajectories that are constrained by an underlying road network. The approach builds a similarity graph based on these trajectories then uses modularity-optimization hiearchical graph clustering to regroup trajectories with similar profiles. Our experimental study shows the superiority of the proposed approach over classic hierarchical clustering and gives a brief insight to visualization of the clustering results.
Quantum trajectories for Brownian motion
Strunz, W T; Gisin, Nicolas; Yu, T; Strunz, Walter T.; Diosi, Lajos; Gisin, Nicolas
1999-01-01
We present the stochastic Schroedinger equation for the dynamics of a quantum particle coupled to a high temperature environment and apply it the dynamics of a driven, damped, nonlinear quantum oscillator. Apart from an initial slip on the environmental memory time scale, in the mean, our result recovers the solution of the known non-Lindblad quantum Brownian motion master equation. A remarkable feature of our approach is its localization property: individual quantum trajectories remain localized wave packets for all times, even for the classically chaotic system considered here, the localization being stronger the smaller $\\hbar$.
Nonadiabatic Molecular Dynamics Based on Trajectories
Directory of Open Access Journals (Sweden)
Felipe Franco de Carvalho
2013-12-01
Full Text Available Performing molecular dynamics in electronically excited states requires the inclusion of nonadiabatic effects to properly describe phenomena beyond the Born-Oppenheimer approximation. This article provides a survey of selected nonadiabatic methods based on quantum or classical trajectories. Among these techniques, trajectory surface hopping constitutes an interesting compromise between accuracy and efficiency for the simulation of medium- to large-scale molecular systems. This approach is, however, based on non-rigorous approximations that could compromise, in some cases, the correct description of the nonadiabatic effects under consideration and hamper a systematic improvement of the theory. With the help of an in principle exact description of nonadiabatic dynamics based on Bohmian quantum trajectories, we will investigate the origin of the main approximations in trajectory surface hopping and illustrate some of the limits of this approach by means of a few simple examples.
Properties of Regge Trajectories
Tang, A; Tang, Alfred; Norbury, John W.
2000-01-01
Early Chew-Frautschi plots show that meson and baryon Regge trajectoies are approximately linear and non-intersecting. In this paper, we reconstruct all Regge trajectories from the most recent data. Our plots show that meson trajectories are non-linear and intersecting. We also show that all current meson Regge trajectories models are ruled out by data.
Computing with spatial trajectories
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
Detection of Bohmian trajectories for mixed states
Luis, A
2013-01-01
Here Bohmian mechanics is used to explore the dynamics of mixed states, often regarded as the result of classical-like ignorance, or incoherence inhibiting interference. Because of the nonlinear nature of the Bohmian guidance equation, it is shown that the corresponding trajectories do not exhibit the behavior expected from a typical context of classical ignorance. On the contrary, they preserve their full nonlocal quantum signature. This fact is illustrated by means of a simple Young-type experiment with incoherent slits, where the lack of interference usually involves a classical interpretation in terms of path (which-way) knowledge. The experimental evidence of this behavior entails important fundamental implications: even if trajectories can be measured, as claimed in recent years, they cannot remove uncertainty, which is intrinsic to quantum systems.
International Nuclear Information System (INIS)
The present state of modeling radio-induced effects at the cellular level does not account for the microscopic inhomogeneity of the nucleus from the non-aqueous contents (i.e. proteins, DNA) by approximating the entire cellular nucleus as a homogenous medium of water. Charged particle track-structure calculations utilizing this approximation are therefore neglecting to account for approximately 30% of the molecular variation within the nucleus. To truly understand what happens when biological matter is irradiated, charged particle track-structure calculations need detailed knowledge of the secondary electron cascade, resulting from interactions with not only the primary biological component—water-–but also the non-aqueous contents, down to very low energies. This paper presents our work on a generic approach for calculating low-energy interaction cross-sections between incident charged particles and individual molecules. The purpose of our work is to develop a self-consistent computational method for predicting molecule-specific interaction cross-sections, such as the component molecules of DNA and proteins (i.e. nucleotides and amino acids), in the very low-energy regime. These results would then be applied in a track-structure code and thereby reduce the homogenous water approximation. The present methodology—inspired by seeking a combination of the accuracy of quantum mechanics and the scalability, robustness, and flexibility of Monte Carlo methods—begins with the calculation of a solution to the many-body Schrödinger equation and proceeds to use Monte Carlo methods to calculate the perturbations in the internal electron field to determine the interaction processes, such as ionization and excitation. As a test of our model, the approach is applied to a water molecule in the same method as it would be applied to a nucleotide or amino acid and compared with the low-energy cross-sections from the GEANT4-DNA physics package of the Geant4 simulation toolkit
Madsen, J. R.; Akabani, G.
2014-05-01
The present state of modeling radio-induced effects at the cellular level does not account for the microscopic inhomogeneity of the nucleus from the non-aqueous contents (i.e. proteins, DNA) by approximating the entire cellular nucleus as a homogenous medium of water. Charged particle track-structure calculations utilizing this approximation are therefore neglecting to account for approximately 30% of the molecular variation within the nucleus. To truly understand what happens when biological matter is irradiated, charged particle track-structure calculations need detailed knowledge of the secondary electron cascade, resulting from interactions with not only the primary biological component—water--but also the non-aqueous contents, down to very low energies. This paper presents our work on a generic approach for calculating low-energy interaction cross-sections between incident charged particles and individual molecules. The purpose of our work is to develop a self-consistent computational method for predicting molecule-specific interaction cross-sections, such as the component molecules of DNA and proteins (i.e. nucleotides and amino acids), in the very low-energy regime. These results would then be applied in a track-structure code and thereby reduce the homogenous water approximation. The present methodology—inspired by seeking a combination of the accuracy of quantum mechanics and the scalability, robustness, and flexibility of Monte Carlo methods—begins with the calculation of a solution to the many-body Schrödinger equation and proceeds to use Monte Carlo methods to calculate the perturbations in the internal electron field to determine the interaction processes, such as ionization and excitation. As a test of our model, the approach is applied to a water molecule in the same method as it would be applied to a nucleotide or amino acid and compared with the low-energy cross-sections from the GEANT4-DNA physics package of the Geant4 simulation toolkit
International Nuclear Information System (INIS)
A review of tachyons, with particular attention to their classical theory, is presented. The extension of Special Relativity to tachyons in two dimensional is first presented, an elegant model-theory which allows a better understanding also of ordinary physics. Then, the results are extended to the four-dimensional case (particular on tachyon mechanics) that can be derived without assuming the existence of Super-luminal reference-frames. Localizability and the unexpected apparent shape of tachyonic objects are discussed, and it is shown (on the basis of tachyon kinematics) how to solve the common causal paradoxes. In connection with General Relativity, particularly the problem of the apparent superluminal expansions in astrophysics is reviewed. The problem (still open) of the extension of relativitic theories to tachyons in four dimensions is tackled, and the electromagnetic theory of tachyons, a topic that can be relevant also for the experimental side, is reviewed. (Author)
Are superparamagnetic spins classical?
Garanin, D. A.
2008-01-01
Effective giant spins of magnetic nanoparticles are considered classically in the conventional theory of superparamagnetism based on the Landau-Lifshitz-Langevin equation. However, microscopic calculations for a large spin with uniaxial anisotropy, coupled to the lattice via the simplest generic mechanism, show that the results of the conventional theory are not reproduced in the limit S ->\\infty. In particular, the prefactor Gamma_0 in the Arrhenius escape rate over the barrier Gamma =Gamma_...
Bohmian mechanics and the emergence of classicality
International Nuclear Information System (INIS)
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.
Bohmian mechanics and the emergence of classicality
Matzkin, A.
2009-06-01
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.
Cross-correlation trajectory study of vibrational relaxation of HF (v=1--7) by HF (v=0)
International Nuclear Information System (INIS)
Results are presented for a three-dimensional quasiclassical trajectory study of the vibrational deactivation of vibrationally excited HF (v=1--7) by ground vibrational HF. A cross-correlation method of analysis is used to calculate probabilities and rate constants for V--V and V--RT transitions using trajectory results. Comparisons are made of calculated total deactivation rate constants (V--V plus V--RT) with experimental values. The V--RT dominates the relaxation for higher v states, and increases particularly rapidly with increasing v. Comparisons are made with recent classical-path calculations for this system, and in the use of Morse versus equivalent harmonic oscillator potentials
Proposal for an experiment to measure the Hausdorff dimension of quantum mechanical trajectories
Kr{ö}ger, H.
1997-01-01
We make a proposal for a Gedanken experiment, based on the Aharonov-Bohm effect, how to measure in principle the zig-zagness of the trajectory of propagation (abberation from its classical trajectory) of a massive particle in quantum mechanics. Experiment I is conceived to show that contributions from quantum paths abberating from the classical trajectory are directly observable. Experiment II is conceived to measure average length, scaling behavior and critical exponent (Hausdorff dimension)...
Lunar and interplanetary trajectories
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. .
Trajectories of Martian Habitability
Cockell, Charles S.
2014-01-01
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-sc...
Trajectory analysis of the rotational dynamics of molecules
Energy Technology Data Exchange (ETDEWEB)
Petrov, S. V., E-mail: spswix@rambler.ru; Lokshtanov, S. E. [Moscow State University (Russian Federation)
2015-08-15
A method for analysis of the rotational dynamics of molecular systems has been proposed on the basis of the calculation of the set of exact classical vibrational–rotational trajectories. It has been proposed to compose and to numerically solve the complete system of dynamic equations consisting of Hamilton’s equations and generalized Euler equations for an arbitrary system. The computer algebra system can be applied to automatize the process of derivation and subsequent solution of dynamic equations. The variation of the picture of known bifurcation in the rotational dynamics of symmetric triatomic hydride molecules with an increase in vibrational excitation has been studied within the proposed approach. It has been shown that manifestations of bifurcation completely disappear at a quite high level of vibrational excitations.
Quantum Dynamics with Gaussian Bases Defined by the Quantum Trajectories.
Gu, Bing; Garashchuk, Sophya
2016-05-19
Development of a general approach to construction of efficient high-dimensional bases is an outstanding challenge in quantum dynamics describing large amplitude motion of molecules and fragments. A number of approaches, proposed over the years, utilize Gaussian bases whose parameters are somehow-usually by propagating classical trajectories or by solving coupled variational equations-tailored to the shape of a wave function evolving in time. In this paper we define the time-dependent Gaussian bases through an ensemble of quantum or Bohmian trajectories, known to provide a very compact representation of a wave function due to conservation of the probability density associated with each trajectory. Though the exact numerical implementation of the quantum trajectory dynamics itself is, generally, impractical, the quantum trajectories can be obtained from the wave function expanded in a basis. The resulting trajectories are used to guide compact Gaussian bases, as illustrated on several model problems. PMID:26735750
Classical-limit S-matrix for heavy ion scattering. [S matrix
Energy Technology Data Exchange (ETDEWEB)
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.
International Nuclear Information System (INIS)
Rotationally and vibrationally inelastic collisions between Li+-ions and N2-molecules have been investigated in a classical trajectory study. Cross sections for energies E = 1-7 eV as a function of final molecular angular momentum and scattering angle have been calculated using an ab initio SCF-potential hypersurface from Staemmler. Basic properties of the scattering process for a potential with a large attractive part and a strong anisotropy are discussed. The results are compared with experimental data from Boettner et al. In general the agreement is good. Minor differences can be attributed to small inaccuracies in the potential. (Auth.)
Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation
Energy Technology Data Exchange (ETDEWEB)
Zamstein, Noa; Tannor, David J. [Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)
2012-12-14
We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schroedinger equation, and the population exchange arises naturally from amplitude-transfer terms. In this paper the equations of motion are derived in the adiabatic representation to complement our work in the diabatic representation [N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517 (2012)]. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], and get very good agreement with converged quantum-mechanical calculations. Specifically, we show that decoherence (spatial separation of wavepackets on different surfaces) is already contained in the equations of motion and does not require ad hoc augmentation.
Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation
International Nuclear Information System (INIS)
We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schrödinger equation, and the population exchange arises naturally from amplitude-transfer terms. In this paper the equations of motion are derived in the adiabatic representation to complement our work in the diabatic representation [N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517 (2012)]. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], and get very good agreement with converged quantum-mechanical calculations. Specifically, we show that decoherence (spatial separation of wavepackets on different surfaces) is already contained in the equations of motion and does not require ad hoc augmentation.
An approximate method for classical scattering problems
International Nuclear Information System (INIS)
An approximate method of calculating scattering cross sections is presented. Newton's second law and the conservation of energy are used to relate the scattering angle to the impulse delivered to the projectile by the scatterer. In order to calculate the impulse, it is necessary to know the time dependence of the trajectory. We assume that the projectile travels the two asymptotes to the actual trajectory with constant velocity
Classical and semiclassical aspects of chemical dynamics
International Nuclear Information System (INIS)
Tunneling in the unimolecular reactions H2C2 → HC2H, HNC → HCN, and H2CO → H2 + 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
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.
Symmetry Properties of Optimal Relative Orbit Trajectories
Mauro Pontani
2015-01-01
The determination of minimum-fuel or minimum-time relative orbit trajectories represents a classical topic in astrodynamics. This work illustrates some symmetry properties that hold for optimal relative paths and can considerably simplify their determination. The existence of symmetry properties is demonstrated in the presence of certain boundary conditions for the problems of interest, described by the linear Euler-Hill-Clohessy-Wiltshire equations of relative motion. With regard to minimum-...
The Envelope of Projectile Trajectories in Midair
Chudinov, P
2005-01-01
A classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. Analytic approach is used for investigation. Simple analytical formulas are used for the constructing the envelope of the family of the point mass trajectories. The equation of envelope is applied for determination of maximum range of flight. The motion of a baseball is presented as an example.
Teaching Classical Mechanics using Smartphones
Chevrier, Joel; Ledenmat, Simon; Bsiesy, Ahmad
2012-01-01
Using a personal computer and a smartphone, iMecaProf is a software that provides a complete teaching environment for practicals associated to a Classical Mechanics course. iMecaProf proposes a visual, real time and interactive representation of data transmitted by a smartphone using the formalism of Classical Mechanics. Using smartphones is more than using a set of sensors. iMecaProf shows students that important concepts of physics they here learn, are necessary to control daily life smartphone operations. This is practical introduction to mechanical microsensors that are nowadays a key technology in advanced trajectory control. First version of iMecaProf can be freely downloaded. It will be tested this academic year in Universit\\'e Joseph Fourier (Grenoble, France)
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 theory of radiating strings
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.
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.
Trajectory tracking control for underactuated stratospheric airship
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.
Trajectory phases of a quantum dot model
International Nuclear Information System (INIS)
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)
Trajectory attractors of equations of mathematical physics
International Nuclear Information System (INIS)
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.
Applications of classical detonation theory
Energy Technology Data Exchange (ETDEWEB)
Davis, W.C.
1994-09-01
Classical detonation theory is the basis for almost all calculations of explosive systems. One common type of calculation is of the detailed behavior of inert parts driven by explosive, predicting pressures, velocities, positions, densities, energies, etc as functions of time. Another common application of the theory is predicting the detonation state and expansion isentrope of a new explosive or mixtures, perhaps an explosive that has not yet been made. Both types of calculations are discussed.
Trajectory versus probability density entropy
Bologna, Mauro; Grigolini, Paolo; Karagiorgis, Markos; Rosa, Angelo
2001-07-01
We show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. We adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the transport equation is built up for the purpose of affording a picture equivalent to that stemming from trajectory dynamics, no direct use of trajectory time evolution is allowed, once the transport equation is defined. With this definition in mind we prove that the detection of a time regime of increase of the density entropy with a rate identical to the KS entropy is possible only in a limited number of cases. The proposals made by some authors to establish a connection between the two entropies in general, violate our definition of density entropy and imply the concept of trajectory, which is foreign to that of density entropy.
Comparisons of classical and quantum dynamics for initially localized states
International Nuclear Information System (INIS)
We compare the dynamics of quantum wave packets with the dynamics of classical trajectory ensembles. The wave packets are Gaussian with expectation values of position and momenta which centers them in phase space. The classical trajectory ensembles are generated directly from the quantum wave packets via the Wigner transform. Quantum and classical dynamics are then compared using several quantum measures and the analogous classical ones derived from the Wigner equivalent formalism. Comparisons are made for several model potentials and it is found that there is generally excellent classical--quantum correspondence except for certain specific cases of tunneling and interference. In general, this correspondence is also very good in regions of phase space where there is classical chaos
Some Characterizations of Optimal Trajectories in Control Theory
Cannarsa, P.; Frankowska, H.
1989-01-01
The authors provide several characterizations of optimal trajectories for the classical Meyer problem arising in optimal control. For this purpose they study the regularity of directional derivatives of the value function: for instance it is shown that for smooth control systems the value function V is continuously differentiable along an optimal trajectory x. Then they deduce the upper semicontinuity of the optimal feedback map and address the problem of optimal design, obtaining sufficient ...
Optimum Inter terminal Transfer Trajectories
Directory of Open Access Journals (Sweden)
T. N. Srivastava
1968-01-01
Full Text Available Rocket trajectories in a gravitational field between two terminals with specified velocities at each terminal are investigated with a view to total velocity increment required in initiating the rocket along the transfer path at the first terminal and in the attainment of the given final velocity at the final terminal. The equations are transformed for transfer between circular orbits and numerical results for Earth-Mars transfer are calculated. Finally particular cases of the above problem are discussed and Stark's results is drived therefrom.
International Nuclear Information System (INIS)
A condition for the existence of a periodic TDHF trajectory of period T is derived. It takes a from very similar to the static H.F. equation and shows that associated to a periodic trajectory there is a static single particle hamiltonian which is a complicated functional of the time dependent density matrix. An explicit expansion for this functional is derived. It is shown that many properties of the static H.F. rest point are shared by periodic solutions. (Author)
Extending UML for trajectory data warehouses conceptual modelling
Directory of Open Access Journals (Sweden)
Wided Oueslati
2012-12-01
Full Text Available The new positioning and information capture technologies are able to treat data related to moving objects taking place in targeted phenomena. This gave birth to a new data source type called trajectory data (TD which handle information related to moving objects. Trajectory Data must be integrated in a new data warehouse type called trajectory data warehouse (TDW that is essential to model and to implement in order to analyze and understand the nature and the behavior of movements of objects in various contexts. However, classical conceptual modeling does not incorporate the specificity of trajectory data due to the complexity of their components that are spatial, temporal and thematic (semantic. For this reason, we focus in this paper on presenting the conceptual modeling of the trajectory data warehouse by defining a new profile using the StarUML extensibility mechanism
Above-threshold ionization photoelectron spectrum from quantum trajectory
Lai, X Y; Zhan, M S
2009-01-01
Many nonlinear quantum phenomena of intense laser-atom physics can be intuitively explained with the concept of trajectory. In this paper, Bohmian mechanics (BM) is introduced to study a multiphoton process of atoms interacting with the intense laser field: above-threshold ionization (ATI). Quantum trajectory of an atomic electron in intense laser field is obtained from the Bohm-Newton equation first and then the energy of the photoelectron is gained from its trajectory. With energies of an ensemble of photoelectrons, we obtain the ATI spectrum which is consistent with the previous theoretical and experimental results. Comparing BM with the classical trajectory Monte-Carlo method, we conclude that quantum potential may play a key role to reproduce the spectrum of ATI. Our work may present a new approach to understanding quantum phenomena in intense laser-atom physics with the image of trajectory.
Direct trajectory method for semiclassical wave functions
International Nuclear Information System (INIS)
This paper reports a method to build a semiclassical wave function corresponding to an invariant torus satisfying Einstein-Brillouin-Keller quantization conditions. Instead of calculating the stability matrix of the trajectory at each step, as in the standard method of Keller [Ann. Phys. (N.Y.) 4, 180 (1958)] or the modification of Maslov and Fedoriuk [Semiclassical Approximations in Quantum Mechanics (Reidel, Dordrecht, 1981)], we use the actual density of the trajectory, calculated by running the trajectory and counting passages through cells in coordinate space. The method is tested for a system of coupled Morse oscillators, and found to be comparable in accuracy to the standard method. It may be more useful than the standard method for testing ideas for semiclassical quantization in the chaotic regime. (c) 2000 The American Physical Society