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...
Classical trajectory perspective of atomic ionization in strong laser fields. Semiclassical modeling
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.
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...
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.
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.
A model of carbon ion interactions in water using the classical trajectory Monte Carlo method
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)
Simulation of molecular transitions using classical trajectories
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
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 ...
Heavy-ion fusion: comparison of experimental data with classical trajectory models
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.)
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).
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
Effects of complex parameters on classical trajectories of Hamiltonian systems
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 $m \\mathbb{Z}$.
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
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.
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
Classical trajectory study of the photodissociation spectrum of H+3
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
Nonadiabatic nuclear dynamics of atomic collisions based on branching classical trajectories
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.
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
Classical trajectory study of rotational excitation in collisions of hydrogen molecules
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.)
Grassmannization of classical models
Pollet, Lode; Prokof'ev, Nikolay V; Svistunov, Boris V
2016-01-01
Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the perturbative diagrammatic expansion is generated by Wick's theorem, and (ii) the Dyson's collapse argument implying that the expansion in powers of coupling constant is divergent. We show that for arbitrary classical lattice models both problems can be solved/circumvented by reformulating the high-temperature expansion (more generally, any discrete representation of the model) in terms of Grassmann integrals. Discrete variables residing on either links, plaquettes, or sites of the lattice are associated with the Grassmann variables in such a way that the partition function (and correlations) of the original system and its Grassmann-field counterpart are identical. The expansion of the latter around its Gaussian point generates Feynman diagrams. A proof-of-principle implement...
Mechanical Systems, Classical Models
Teodorescu, Petre P
2009-01-01
This third volume completes the Work Mechanical Systems, Classical Models. The first two volumes dealt with particle dynamics and with discrete and continuous mechanical systems. The present volume studies analytical mechanics. Topics like Lagrangian and Hamiltonian mechanics, the Hamilton-Jacobi method, and a study of systems with separate variables are thoroughly discussed. Also included are variational principles and canonical transformations, integral invariants and exterior differential calculus, and particular attention is given to non-holonomic mechanical systems. The author explains in detail all important aspects of the science of mechanics, regarded as a natural science, and shows how they are useful in understanding important natural phenomena and solving problems of interest in applied and engineering sciences. Professor Teodorescu has spent more than fifty years as a Professor of Mechanics at the University of Bucharest and this book relies on the extensive literature on the subject as well as th...
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)
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...
Extending UML for trajectory data warehouses conceptual modelling
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
Mechanical Systems, Classical Models
Teodorescu, Petre P
2007-01-01
All phenomena in nature are characterized by motion; this is an essential property of matter, having infinitely many aspects. Motion can be mechanical, physical, chemical or biological, leading to various sciences of nature, mechanics being one of them. Mechanics deals with the objective laws of mechanical motion of bodies, the simplest form of motion. In the study of a science of nature mathematics plays an important role. Mechanics is the first science of nature which was expressed in terms of mathematics by considering various mathematical models, associated to phenomena of the surrounding nature. Thus, its development was influenced by the use of a strong mathematical tool; on the other hand, we must observe that mechanics also influenced the introduction and the development of many mathematical notions. In this respect, the guideline of the present book is precisely the mathematical model of mechanics. A special accent is put on the solving methodology as well as on the mathematical tools used; vectors, ...
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.
Regularized Finite Mixture Models for Probability Trajectories
Shedden, Kerby; Zucker, Robert A.
2008-01-01
Finite mixture models are widely used in the analysis of growth trajectory data to discover subgroups of individuals exhibiting similar patterns of behavior over time. In practice, trajectories are usually modeled as polynomials, which may fail to capture important features of the longitudinal pattern. Focusing on dichotomous response measures, we…
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.
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
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.
Classical Models of Subatomic Particles
Mann, R. B.; Morris, M. S.
1993-01-01
We look at the program of modelling a subatomic particle---one having mass, charge, and angular momentum---as an interior solution joined to a classical general-relativistic Kerr-Newman exterior spacetime. We find that the assumption of stationarity upon which the validity of the Kerr-Newman exterior solution depends is in fact violated quantum mechanically for all known subatomic particles. We conclude that the appropriate stationary spacetime matched to any known subatomic particle is flat ...
Classical models of subatomic particles
We look at the program of modelling a subatomic particle - one having mass, charge, and angular momentum - as an interior solution joined to a classical general-relativistic Kerr-Newman exterior spacetime. We find that the assumption of stationarity upon which the validity of the Kerr-Newman exterior solution depends is in fact violated quantum mechanically for all known subatomic particles. We conclude that the appropriate stationary spacetime matched to any known subatomic particle is flat space. (orig.)
The revision of classical stock model
叶柏青; 王洪利
2001-01-01
On the basis of the analysis of classical stock model, according to the limitation of the model, the article puts forward the revision of classical model and enforces the applicability of the stock model.
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.
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.
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)
The revision of classical stock model
YE Bai-qing; WANG Hong-li
2001-01-01
On the basis of the analysis of classical stock model, according to th e limitation of the model, the article puts forward the revision of classical mo del and enforces the applicability of the stock model.
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 simple model of quantum trajectories
Brun, Todd A.
2001-01-01
Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. In this paper I present a simple model, using two-level quantum systems (q-bits), to illustrate the essential physics of quantum trajectories and how different monitoring schemes correspond to different ``unravelings'' of a mixed state master equation. I also comment briefly on the relationship of t...
Trajectory phases of a quantum dot model
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)
Pseudoclassical fermionic model and classical solutions
We study classical limit of fermionic fields seen as Grassmann variables and deduce the proper quantization prescription using Dirac's method for constrained systems and investigate quantum meaning of classical solutions for the Thirring model. (author)
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
Empirical Model for Predicting Rockfall Trajectory Direction
Asteriou, Pavlos; Tsiambaos, George
2016-03-01
A methodology for the experimental investigation of rockfall in three-dimensional space is presented in this paper, aiming to assist on-going research of the complexity of a block's response to impact during a rockfall. An extended laboratory investigation was conducted, consisting of 590 tests with cubical and spherical blocks made of an artificial material. The effects of shape, slope angle and the deviation of the post-impact trajectory are examined as a function of the pre-impact trajectory direction. Additionally, an empirical model is proposed that estimates the deviation of the post-impact trajectory as a function of the pre-impact trajectory with respect to the slope surface and the slope angle. This empirical model is validated by 192 small-scale field tests, which are also presented in this paper. Some important aspects of the three-dimensional nature of rockfall phenomena are highlighted that have been hitherto neglected. The 3D space data provided in this study are suitable for the calibration and verification of rockfall analysis software that has become increasingly popular in design practice.
A Drosophila melanogaster model of classic galactosemia
Kushner, Rebekah F.; Ryan, Emily L.; Sefton, Jennifer M. I.; Rebecca D Sanders; Lucioni, Patricia Jumbo; Kenneth H Moberg; Fridovich-Keil, Judith L.
2010-01-01
Classic galactosemia is a potentially lethal disorder that results from profound impairment of galactose-1-phosphate uridylyltransferase (GALT). Despite decades of research, the underlying pathophysiology of classic galactosemia remains unclear, in part owing to the lack of an appropriate animal model. Here, we report the establishment of a Drosophila melanogaster model of classic galactosemia; this is the first whole-animal genetic model to mimic aspects of the patient phenotype. Analogous t...
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 ...
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.
Lagrangian Trajectory Modeling of Lunar Dust Particles
Lane, John E.; Metzger, Philip T.; Immer, Christopher D.
2008-01-01
Apollo landing videos shot from inside the right LEM window, provide a quantitative measure of the characteristics and dynamics of the ejecta spray of lunar regolith particles beneath the Lander during the final 10 [m] or so of descent. Photogrammetry analysis gives an estimate of the thickness of the dust layer and angle of trajectory. In addition, Apollo landing video analysis divulges valuable information on the regolith ejecta interactions with lunar surface topography. For example, dense dust streaks are seen to originate at the outer rims of craters within a critical radius of the Lander during descent. The primary intent of this work was to develop a mathematical model and software implementation for the trajectory simulation of lunar dust particles acted on by gas jets originating from the nozzle of a lunar Lander, where the particle sizes typically range from 10 micron to 500 micron. The high temperature, supersonic jet of gas that is exhausted from a rocket engine can propel dust, soil, gravel, as well as small rocks to high velocities. The lunar vacuum allows ejected particles to travel great distances unimpeded, and in the case of smaller particles, escape velocities may be reached. The particle size distributions and kinetic energies of ejected particles can lead to damage to the landing spacecraft or to other hardware that has previously been deployed in the vicinity. Thus the primary motivation behind this work is to seek a better understanding for the purpose of modeling and predicting the behavior of regolith dust particle trajectories during powered rocket descent and ascent.
Regularities in hadron systematics, Regge trajectories and a string quark model
An empirical principle for the construction of a linear relationship between the total angular momentum and squared-mass of baryons is proposed. In order to examine linearity of the trajectories, a rigorous least-squares regression analysis was performed. Unlike the standard Regge-Chew-Frautschi approach, the constructed trajectories do not have non-linear behaviour. A similar regularity may exist for lowest-mass mesons. The linear baryonic trajectories are well described by a semi-classical picture based on a spinning relativistic string with tension. The obtained numerical solution of this model was used to extract the (di)quark masses. (orig.)
Solar sails: Modeling, estimation, and trajectory control
Rios-Reyes, Leonel
There has been great interest in developing solar sail technology and missions by several international space agencies in recent years. However, at present there is no consensus on how one can mathematically model forces and moments acting on a solar sail. Traditional analytical models and finite element methods are not feasible for integration into a precise navigation system. This dissertation takes a step toward resolving this issue by developing tools and concepts that can be integrated into a precise solar sail navigation system. These steps are the derivation of a generalized sail model, a linear estimation method for estimating and predicting forces and moments acting on a solar sail, and a new trajectory control methodology for tracking a nominal trajectory when the sail performance exceeds the nominal design performance. The main contributions of this dissertation follow. First, the generalized sail model (GSM) is defined to analytically describe the forces and moments acting on a solar sail of arbitrary shape. The GSM is derived by performing an integration, of all the differential forces and moments acting on the sail, over the sail surface. Next, the GSM is applied to several examples to illustrate the use of the GSM's analytic equations. These examples allow comparisons of forces and moments generated by different solar sails, the computation of force derivatives, and the application of the model to orbital mechanics problems. Since it is difficult to model the sail geometry based on ground measurements; errors in the sail model are expected once the sail is deployed in space. Due to this difficulty; a least-squares estimation method for the force and moment coefficients of the GSM is derived. For realistic implementation of a sail trajectory, the deployed sail must have an excess thrust capacity. We develop and implement a control methodology for flying a nominal mission profile with such an excess capacity. Control laws for maintaining a flat, ideal
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...
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.
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
CLASSICAL RISK MODEL WITH THRESHOLD DIVIDEND STRATEGY
Zhou Ming; Guo Junyi
2008-01-01
In this article, a threshold dividend strategy is used for classical risk model.Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen(2000, P195, Proposition 1.10). The occupation time of non-dividend of this model is also discussed by means of Martingale method.
Reduced parameter model on trajectory tracking data with applications
王正明; 朱炬波
1999-01-01
The data fusion in tracking the same trajectory by multi-measurernent unit (MMU) is considered. Firstly, the reduced parameter model (RPM) of trajectory parameter (TP), system error and random error are presented,and then the RPM on trajectory tracking data (TTD) is obtained, a weighted method on measuring elements (ME) is studied and criteria on selection of ME based on residual and accuracy estimation are put forward. According to RPM,the problem about selection of ME and self-calibration of TTD is thoroughly investigated. The method improves data accuracy in trajectory tracking obviously and gives accuracy evaluation of trajectory tracking system simultaneously.
Trajectories and models of individual growth
Arseniy Karkach
2006-11-01
Full Text Available It has long been recognized that the patterns of growth play an important role in the evolution of age trajectories of fertility and mortality (Williams, 1957. Life history studies would benefit from a better understanding of strategies and mechanisms of growth, but still no comparative research on individual growth strategies has been conducted. Growth patterns and methods have been shaped by evolution and a great variety of them are observed. Two distinct patterns - determinate and indeterminate growth - are of a special interest for these studies since they present qualitatively different outcomes of evolution. We attempt to draw together studies covering growth in plant and animal species across a wide range of phyla focusing primarily on the noted qualitative features. We also review mathematical descriptions of growth, namely empirical growth curves and growth models, and discuss the directions of future research.
Two simple models of classical heat pumps
Marathe, Rahul; Jayannavar, A. M.; Dhar, Abhishek
2006-01-01
Motivated by recent studies on models of particle and heat quantum pumps, we study similar simple classical models and examine the possibility of heat pumping. Unlike many of the usual ratchet models of molecular engines, the models we study do not have particle transport. We consider a two-spin system and a coupled oscillator system which exchange heat with multiple heat reservoirs and which are acted upon by periodic forces. The simplicity of our models allows accurate numerical and exact s...
A Trajectory UML profile For Modeling Trajectory Data: A Mobile Hospital Use Case
Oueslati, Wided
2011-01-01
A large amount of data resulting from trajectories of moving objects activities are collected thanks to localization based services and some associated automated processes. Trajectories data can be used either for transactional and analysis purposes in various domains (heath care, commerce, environment, etc.). For this reason, modeling trajectory data at the conceptual level is an important stair leading to global vision and successful implementations. However, current modeling tools fail to fulfill specific moving objects activities requirements. In this paper, we propose a new profile based on UML in order to enhance the conceptual modeling of trajectory data related to mobile objects by new stereotypes and icons. As illustration, we present a mobile hospital use case.
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
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.
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
Modeling Pulsar Trajectories to Determine Birth Locations
Shapiro-Albert, Brent; Chatterjee, Shami; Cordes, James M.; Hallenbeck, Gregory L.; Vlemmings, Wouter
2016-01-01
Neutron stars are the remnants of massive stars after their deaths in supernova explosions. They typically have higher velocities than their progenitor stellar population due to either kicks from supernova asymmetries or from remnant velocities of compact binaries after they are disrupted by explosions. Velocities are large enough that pulsars will typically move large distances from their birth sites. By determining the present day location and velocity, we project back to twice the pulsars characteristic age to constrain the location of the progenitor star (within the uncertainty of the unknown line-of-sight velocity component). We use precision measurements of the proper motion and parallax determined with the Very Long Baseline Array as input to trajectory modeling that includes deceleration in the Galactic potential. Using a python implementation utilizing astropy and galpy, we verify the results of Vlemmings et al. (2004, ApJ, 610, 402) on two pulsars, B2020+28 and B2012+51, which found that the two objects very likely originated in the same star cluster and whose progenitor stars could have been in the same binary system. We have applied the trace back algorithm to other pulsars using the most recent astrometric measurements to identify their birth locations. Results on these objects will be reported.
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.
Model predictive control classical, robust and stochastic
Kouvaritakis, Basil
2016-01-01
For the first time, a textbook that brings together classical predictive control with treatment of up-to-date robust and stochastic techniques. Model Predictive Control describes the development of tractable algorithms for uncertain, stochastic, constrained systems. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closed-loop stability and performance. Moving on to robust predictive control, the text explains how similar guarantees may be obtained for cases in which the model describing the system dynamics is subject to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are considered and the state of the art in computationally tractable methods based on uncertainty tubes presented for systems with additive model uncertainty. Finally, the tube framework is also applied to model predictive control problems involving hard or probabilistic constraints for the cases of multiplic...
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.
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.)
Developmental Trajectories of Adolescent Popularity: A Growth Curve Modelling Analysis
Cillessen, Antonius H. N.; Borch, Casey
2006-01-01
Growth curve modelling was used to examine developmental trajectories of sociometric and perceived popularity across eight years in adolescence, and the effects of gender, overt aggression, and relational aggression on these trajectories. Participants were 303 initially popular students (167 girls, 136 boys) for whom sociometric data were…
A Classical Probabilistic Computer Model of Consciousness
Blaha, Stephen
2002-01-01
We show that human consciousness can be modeled as a classical (not quantum) probabilistic computer. A quantum computer representation does not appear to be indicated because no known feature of consciousness depends on Planck's constant h, the telltale sign of quantum phenomena. It is argued that the facets of consciousness are describable by an object-oriented design with dynamically defined classes and objects. A comparison to economic theory is also made. We argue consciousness may also h...
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.
VOTERS DECIDE. CLASSICAL MODELS OF ELECTORAL BEHAVIOR.
Constantin SASU
2015-04-01
Full Text Available The decision to vote and choosing among the candidates is a extremely important one with repercussions on everyday life by determining, in global mode, its quality for the whole society. Therefore the whole process by which the voter decide becomes a central concern. In this paper we intend to locate the determinants of the vote decision in the electoral behavior classical theoretical models developed over time. After doing synthesis of classical schools of thought on electoral behavior we conclude that it has been made a journey through the mind, soul and cheek, as follows: the mind as reason in theory developed by Downs, soul as preferably for an actor in Campbell's theory, etc. and cheek as an expression of the impossibility of detachment from social groups to which we belong in Lazarsfeld's theory.
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
Classical model for bulk-ensemble NMR quantum computation
Schack, R.; Caves, C. M.
1999-01-01
We present a classical model for bulk-ensemble NMR quantum computation: the quantum state of the NMR sample is described by a probability distribution over the orientations of classical tops, and quantum gates are described by classical transition probabilities. All NMR quantum computing experiments performed so far with three quantum bits can be accounted for in this classical model. After a few entangling gates, the classical model suffers an exponential decrease of the measured signal, whe...
RETADD: a Regional Trajectory And Diffusion-Deposition model
Begovich, C. L.; Murphy, B. D.; Nappo, Jr., C. J.
1978-06-01
The Regional Trajectory and Diffusion-Deposition Model (RETADD) is based upon a version of the National Oceanic and Atmospheric Administration Air Resources Laboratory's Regional-Continental Scale Transport, Diffusion, and Deposition Model. The FORTRAN IV computer model uses a trajectory analysis technique for estimating the transport and long-range diffusion of material emitted from a point source. The wind trajectory portion of the code uses observed upper air winds to compute the transport of the material. Ground level concentrations and depositions are computed by using the Gaussian plume equation for wind trajectories projected forward in time. Options are included to specify an upper bound for the mixed layer and a chemical decomposition rate for the effluent. The limitations to the technique are discussed, the equations and model are described, and listings of the program, input, and output are included.
Classical trajectory calculations for anisotropy-dependent cross sections for He-N2 mixtures
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)
Semiclassical approach to mesoscopic systems. Classical trajectory correlations and wave interface
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.)
Probabilistic Modeling of Aircraft Trajectories for Dynamic Separation Volumes
Lewis, Timothy A.
2016-01-01
With a proliferation of new and unconventional vehicles and operations expected in the future, the ab initio airspace design will require new approaches to trajectory prediction for separation assurance and other air traffic management functions. This paper presents an approach to probabilistic modeling of the trajectory of an aircraft when its intent is unknown. The approach uses a set of feature functions to constrain a maximum entropy probability distribution based on a set of observed aircraft trajectories. This model can be used to sample new aircraft trajectories to form an ensemble reflecting the variability in an aircraft's intent. The model learning process ensures that the variability in this ensemble reflects the behavior observed in the original data set. Computational examples are presented.
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
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
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.
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.)
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
Zipf exponent of trajectory distribution in the hidden Markov model
Bochkarev, V. V.; Lerner, E. Yu
2014-03-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.
Zipf exponent of trajectory distribution in the hidden Markov model
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different
Wind field and trajectory models for tornado-propelled objects
This report contains the results of the second phase of a research program which has as its objective the development of a mathematical model to predict the trajectory of tornado-borne objects postulated to be in the vicinity of nuclear power plants. An improved tornado wind field model satisfies the no-slip ground boundary condition of fluid mechanics and includes the functional dependence of eddy viscosity with altitude. Sub-scale wind tunnel data are obtained for all of the missiles currently specified for nuclear plant design. Confirmatory full-scale data are obtained for a 12-inch pipe and automobile. The original six-degree-of-freedom trajectory model is modified to include the improved wind field and increased capability as to body shapes and inertial characteristics that can be handled. The improved trajectory model is used to calculate maximum credible speeds, which for all of the heavy missiles are considerably less than those currently specified for design. Equivalent coefficients for use in three-degree-of-freedom models are developed and the sensitivity of range and speed to various trajectory parameters for the 12-inch diameter pipe is examined
Quasi-classical trajectory approach to the stereo-dynamics of the reaction F+HO→HF+O
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
Crack trajectory near a weld: Modeling and simulation
Rashid, M.M.; Tvergaard, Viggo
2008-01-01
A 2D computational model of ductile fracture, in which arbitrary crack extension through the mesh is accommodated without mesh bias, is used to study ductile fracture near the weld line in welded aluminum plates. Comparisons of the calculated toughness behavior and crack trajectory are made with...
Lagrangian Time Series Models for Ocean Surface Drifter Trajectories
Sykulski, Adam M; Lilly, Jonathan M; Danioux, Eric
2016-01-01
This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer important physical parameters of inertial oscillations and other ocean processes. Nonstationary time series methods are employed to account for the spatiotemporal variability of each trajectory. Because the datasets are large, we construct computationally efficient methods through the use of frequency-domain modelling and estimation, with the data expressed as complex-valued time series. We detail how practical issues related to sampling and model misspecification may be addressed using semi-parametric techniques for time series, and we demonstrate the effectiveness of our stochastic models through application to both real-world data and to numerical model output.
Trajectory based models. Evaluation of minmax pricing bounds
Degano, Ivan; Ferrando, Sebastian; Gonzalez, Alfredo
2015-01-01
The paper studies market models based on trajectory spaces, properties of such models are obtained without recourse to probabilistic assumptions. For a given European option, an interval of rational prices exists under a more general condition than the usual no-arbitrage requirement. The paper develops computational results in order to evaluate the option bounds; the global minmax optimization, defining the price interval, is reduced to a local minmax optimization via dynamic programming. A g...
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.
An hydrodynamic model for the calculation of oil spills trajectories
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)
A Multi-billion Parcel Atmospheric Trajectory Model
Cruz, C.; Clune, T. L.; Lait, L. R.; Ranawake, U.; Burns, R. W.
2009-12-01
We present a new parallel implementation of an atmospheric trajectory modelling framework which provides improved numerical accuracy, greater flexibility for specifying experiments, and sufficient raw performance to simultaneously simulate billions of parcel trajectories on suitable computing platforms. The application is parallelized using the Message Passing Interface (MPI) library and can scale efficiently on a wide variety of modern computing platforms. The ability to treat such large numbers of parcels is expected to enable a new generation of experiments to explore questions related to global stratosphere-troposphere exchange, age-of-air spectra, and transport of trace gases and aerosols. The modelling framework is written in C++ for easy integration with other computing technologies. It also provides a great deal of flexibility by allowing users to select from (or add to) alternative subclasses for vertical coordinates (pressure, potential temperature), integration schemes (Runge-Kutta, Euler), meteorological data sources (NCEP/NCAR Reanalsyis, MERRA), data interpolation methods (linear, log-linear, splines), and output (parcel histories, summary statistics, min/max quantities encountered). Significantly improved numerical accuracy, especially near the poles, is provided by expressing integration in terms of purely geometric constructs which avoid various complications associated with spherical coordinates near the poles. The entire package has been rigorously developed using Test-Driven Development (TDD) which both provides confidence in the implementation and should also assist other developers that wish to extend the framework. Several tests are performed to demonstrate the fourth-order Runge-Kutta integration scheme with our spherical geometric constructs. Tilted solid body rotation provides a baseline synthetic wind field for assessing model performance, and a time-varying case is used to examine the errors introduced by interpolating linearly in time
Photochemical trajectory modeling of ozone concentrations in Hong Kong
In this study, tropical cyclones over the East and South China Seas were found to be the most predominant weather conditions associated with the occurrence of high ozone (O3) episodes in Hong Kong in 2005–2009. A photochemical trajectory model coupled with Master Chemical Mechanism (MCM) was adapted to simulate the O3 concentrations during two O3 pollution episodes. The results agreed well with the observed data. A representative backward air mass trajectory was used to determine the contribution of each volatile organic compound (VOC) to the O3 levels. After taking into account both reactivity and mass emission of each VOC, 10 species were found to be the key O3 precursors in Hong Kong. Further analysis identified solvent related products accounting for 70% of the modeled O3 concentration in Hong Kong. The results highlight the importance of considering together reactivity and source sector emissions in developing targeted VOC reduction for O3 abatement strategies. -- Highlights: •A photochemical trajectory model was developed to simulate the O3 formation in Hong Kong. •Isoprene, ethene, and toluene were the key precursors to photochemical O3 formation in Hong Kong. •Solvent-related products accounted for 70% of the modeled ozone concentration in Hong Kong. -- Isoprene, ethene, toluene, formaldehyde, and m,p-xylene were the key O3 precursors in Hong Kong
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.
Modeling the trajectory of a microparticle in a dielectrophoresis device.
Kharboutly, Mohamed; Gauthier, Michaël; Chaillet, Nicolas
2009-01-01
Micro- and nanoparticles can be trapped by a nonuniform electric field through the effect of the dielectrophoretic principle. Dielectrophoresis DEP is used to separate, manipulate, and detect microparticles in several domains, such as in biological or carbon nanotube manipulations. Current methods to simulate the trajectory of microparticles under a DEP force field are based on finite element model FEM, which requires new simulations when electrode potential is changed, or on analytic equatio...
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
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
Mathematical Model to Simulate the Trajectory Elements ofan Artillery Projectile Proof Shot
K.K. Chand; H.S. Panda
2007-01-01
In external ballistics of a conventional spin-stabilised artillery projectile, there are a numberof trajectory models developed for computing trajectory elements having varying degrees ofcomplexity. The present study attempts to propose a single mathematical model, viz., simplifiedpoint-mass/simple particle trajectory model to simulate the trajectory elements of a typical spin-stabilised flat-head artillery projectile proof shot. Due to difficulties in the projectile shape andsize, and the co...
A Model of Classical and Quantum Measurement
Francis, C
1999-01-01
We take the view that physical quantities are values generated by processes in measurement, not pre-existent objective quantities, and that a measurement result is strictly a product of the apparatus and the subject of the measurement. We habitually make an inaccurate statements when we speak of the measurement of a quantity by an apparatus. These statements can be formalised as a many valued logic with the structure of a vector space with a hermitian form in such a way as to generate probabilities in the results of measurement. The difference between this and classical probability theory is that we are not finding probabilities generated by unknown variables, but probabilities generated by unknown structure. We thus interpret quantum logic as the application of complex truth values to statements in an inaccurate language, and find that the properties of vector space hold for approximate measurement as well as for measurement of optimal accuracy, suggesting that Planck's constant governs the scale of the fund...
Pomeron and odderon Regge trajectories from a dynamical holographic model
Capossoli, Eduardo Folco; Li, Danning; Boschi-Filho, Henrique
2016-09-01
In this work we use gauge/string dualities and a dynamical model that takes into account dynamical corrections to the metric of the anti de Sitter space due to a quadratic dilaton field and calculate the masses of even and odd spin glueball states with P = C = + 1, and P = C = - 1, respectively. Then we construct the corresponding Regge trajectories which are associated with the pomeron for even states with P = C = + 1, and with the odderon for odd states with P = C = - 1. We compare our results with those coming from experimental data as well as other models.
Simple universal models capture all classical spin physics.
De las Cuevas, Gemma; Cubitt, Toby S
2016-03-11
Spin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. Here, we prove that all the physics of every classical spin model is reproduced in the low-energy sector of certain "universal models," with at most polynomial overhead. This holds for classical models with discrete or continuous degrees of freedom. We prove necessary and sufficient conditions for a spin model to be universal and show that one of the simplest and most widely studied spin models, the two-dimensional Ising model with fields, is universal. Our results may facilitate physical simulations of Hamiltonians with complex interactions. PMID:26965624
Classical conformality in the Standard Model from Coleman's theory
Kawana, Kiyoharu
2016-01-01
The classical conformality is one of the possible candidates for explaining the gauge hierarchy of the Standard Model. We show that it is naturally obtained from the Coleman's theory on baby universe.
Classical analogous of quantum cosmological perfect fluid models
Batista, A B; Gonçalves, S V B; Tossa, J
2001-01-01
Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state $p_Q = \\rho_Q$ is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classical system reveals the condition for the stability of the classical system in terms of the existence of an anti-gravity phase.
A finite mixture latent trajectory model for modeling ultrarunners' behavior in a 24-hour race
Bartolucci, Francesco; Murphy, Thomas Brendan
2015-01-01
A finite mixture latent trajectory model is developed to study the performance and strategy of runners in a 24-h long ultra running race. The model facilitates clustering of runners based on their speed and propensity to rest and thus reveals the strategies used in the race. Inference for the adopted latent trajectory model is achieved using an expectation-maximization algorithm. Fitting the model to data from the 2013 World Championships reveals three clearly separated clusters of runners wh...
Classical limits of an extended unitary model
The paper studies the limiting cases of an extended unitary model and it is shown that rotational, vibrational and transition excitation spectra are generated depending on the parameters ratio. The limits concerned resemble, by some properties, the analogous limits of an interacting boson model, however, the physical nature of the two models is different. Their generality is caused by the group structure similarity. 31 refs.; 5 figs.; 6 tabs
Modeling the Classic Meselson and Stahl Experiment.
D'Agostino, JoBeth
2001-01-01
Points out the importance of molecular models in biology and chemistry. Presents a laboratory activity on DNA. Uses different colored wax strips to represent "heavy" and "light" DNA, cesium chloride for identification of small density differences, and three different liquids with varying densities to model gradient centrifugation. (YDS)
Rock shape, restitution coefficients and rockfall trajectory modelling
Glover, James; Christen, Marc; Bühler, Yves; Bartelt, Perry
2014-05-01
Restitution coefficients are used in rockfall trajectory modelling to describe the ratio between incident and rebound velocities during ground impact. They are central to the problem of rockfall hazard analysis as they link rock mass characteristics to terrain properties. Using laboratory experiments as a guide, we first show that restitution coefficients exhibit a wide range of scatter, although the material properties of the rock and ground are constant. This leads us to the conclusion that restitution coefficients are poor descriptors of rock-ground interaction. The primary problem is that "apparent" restitution coefficients are applied at the rock's centre-of-mass and do not account for rock shape. An accurate description of the rock-ground interaction requires the contact forces to be applied at the rock surface with consideration of the momentary rock position and spin. This leads to a variety of rock motions including bouncing, sliding, skipping and rolling. Depending on the impact configuration a wide range of motions is possible. This explains the large scatter of apparent restitution coefficients. We present a rockfall model based on newly developed hard-contact algorithms which includes the effects of rock shape and therefore is able to reproduce the results of different impact configurations. We simulate the laboratory experiments to show that it is possible to reproduce run-out and dispersion of different rock shapes using parameters obtained from independent tests. Although this is a step forward in rockfall trajectory modelling, the problem of parametersing real terrain remains.
The Jackiw–Pi model: Classical theory
The massive even-parity non-Abelian gauge model in three space–time dimensions proposed by Jackiw and Pi is studied at the tree-level. The propagators are computed and the spectrum consistency is analyzed, besides, the symmetries of the model are collected and established through BRS invariance and Slavnov–Taylor identity. In the Landau gauge, thanks to the antighost equations and the Slavnov–Taylor identity, two rigid symmetries are identified by means of Ward identities. It is presented here a promising path for perturbatively quantization of the Jackiw–Pi model and a hint concerning its possible quantum scale invariance is also pointed out
Classical models of the spin 1/2 system
Salazar-Lazaro, Carlos H.
We proposed a Quaternionic mechanical system motivated by the Foucault pendulum as a classical model for the dynamics of the spin ½ system. We showed that this mechanical system contains the dynamics of the spin state of the electron under a uniform magnetic field as it is given by the Schrodinger-Pauli-Equation (SPE). We closed with a characterization of the dynamics of this generalized classical system by showing that it is equivalent with the dynamics of the Schrodinger Pauli Equation as long as the solutions to the generalized classical system are roots of the Lagrangian, that is the condition L = 0 holds.
Dynamic Modeling of Trajectory Patterns using Data Mining and Reverse Engineering
Alvares, Luis Otavio; Bogorny, Vania; FERNANDES de MACEDO, J.A.; Moelans, Bart; Spaccapietra, Stefano
2007-01-01
The constant increase of moving object data imposes the need for modeling, processing, and mining trajectories, in order to find and understand the patterns behind these data. Existing works have mainly focused on the geometric properties of trajectories, while the semantics and the background geographic information has rarely been addressed. We claim that meaningful patterns can only be extracted from trajectories if the geographic space where trajectories are located is considered. In this ...
Plasma sheath studies using the kinetic trajectory simulation model
Plasma sheath formed in front of a material wall for different cases have been studied. For given electron and ion distributions at the sheath entrance we use Kinetic Trajectory Simulation (KTS) model to obtain the solution to a non-neutral, time-independent, collisionless plasma sheath. The characteristic feature of the KTS method is that the distribution functions of the particle species involved are calculated directly by solving the related kinetic equations along the respective collisionless particle trajectories. For a given potential distribution, we calculate the exact ion distribution function by integrating Vlasov's equation along its characteristics and taking into account the scraping-off effect at the wall. The electron distribution, on the other hand, is calculated analytically, however taking into account the cut-off introduced by electron absorption at the wall.We also present a scheme for coupling a quasineutral two-fluid (electron-ion) presheath solution to a non-neutral, collisionless kinetic sheath solution for a 1d1v case. It has been observed that the sheath structure is highly influenced by the magnitude of potential applied to the wall. The applied kinetic model is thus expected to give better insight to the sheath phenomena. (author)
Classical solutions of some field theoretic models
In recent years much attention has been paid to simpler fields theories, so chosen that they possess several properties of nonabelian gauge theories. They preserve the conformal invariance of the action and one can define the topological charge for them. They possess nontrivial solutions to the equations of motion. The perturbation theory based on the fluctuations around each solution is characterized by asymptotic freedom. A model called CP sup(n-1) is presented and some models which are its natural generalizations are discussed. (M.F.W.)
Application of particle trajectory model in 1D planar ejection
刘坤; 柏劲松; 李平
2008-01-01
A simple one-dimensional planar model for ejection was set up based on experiments.And numerical simulation was performed on this model with particle trajectory model method.An Eulerian finite volume method was conducted to resolve gas field.And Lagrangian method was imposed to track each particle.The interaction between gas and particles was responded as source terms in governing equations which were induced by forces.The effects of total spraying mass,particle size and other factors on the mixture of particles and gas were investigated.The spatial distributions of particle mass and velocity at different time were presented.The result shows that the numerical results are qualitatively consistent to those of experiments.
The Jackiw-Pi model: Classical theory
Full text: One of the central problems in the framework of gauge field theories is the issue of gauge field mass. Gauge symmetry is not, in principle, conflicting with the presence of a massive gauge boson. In two space-time dimensions, the well-known Schwinger model puts in evidence the presence of a massive photon without the breaking of gauge symmetry. Another evidence for the compatibility between gauge symmetry and massive vector fields comes from the study of three-dimensional gauge theories. A topological mass term referred to as the Chern-Simons Lagrangian, once added to the Yang-Mills term, shifts the photon mass to a non-vanishing value without breaking gauge invariance, however parity symmetry is lost. In 1997, a massive even-parity non- Abelian gauge model in three space-time dimensions has been proposed by Jackiw and Pi, which is studied, at the tree-level, in this work. The propagators are computed and the spectrum consistency is analyzed, besides, the symmetries of the model are collected and established through BRS invariance and Slavnov-Taylor identity. In the Landau gauge, thanks to the antighost equations and the Slavnov-Taylor identity, two rigid symmetries are identified by means of Ward identities. It is presented here a promising path for perturbatively quantization of the Jackiw-Pi model and a hint concerning its possible quantum scale invariance is also pointed out. (author)
Classical solutions of a flag manifold sigma-model
Bykov, Dmitri
2015-01-01
We study a sigma-model with target space the flag manifold U(3)/U(1)^3. A peculiarity of the model is that the complex structure on the target space enters explicitly in the action. We describe the classical solutions of the model for the case when the worldsheet is a sphere CP^1.
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
Historical forest biomass dynamics modelled with Landsat spectral trajectories
Gómez, Cristina; White, Joanne C.; Wulder, Michael A.; Alejandro, Pablo
2014-07-01
Estimation of forest aboveground biomass (AGB) is informative of the role of forest ecosystems in local and global carbon budgets. There is a need to retrospectively estimate biomass in order to establish a historical baseline and enable reporting of change. In this research, we used temporal spectral trajectories to inform on forest successional development status in support of modelling and mapping of historic AGB for Mediterranean pines in central Spain. AGB generated with ground plot data from the Spanish National Forest Inventory (NFI), representing two collection periods (1990 and 2000), are linked with static and dynamic spectral data as captured by Landsat Thematic Mapper (TM) and Enhanced Thematic Mapper Plus (ETM+) sensors over a 25 year period (1984-2009). The importance of forest structural complexity on the relationship between AGB and spectral vegetation indices is revealed by the analysis of wavelet transforms. Two-dimensional (2D) wavelet transforms support the identification of spectral trajectory patterns of forest stands that in turn, are associated with traits of individual NFI plots, using a flexible algorithm sensitive to capturing time series similarity. Single-date spectral indices, temporal trajectories, and temporal derivatives associated with succession are used as input variables to non-parametric decision trees for modelling, estimation, and mapping of AGB and carbon sinks over the entire study area. Results indicate that patterns of change found in Normalized Difference Vegetation Index (NDVI) values are associated and relate well to classes of forest AGB. The Tasseled Cap Angle (TCA) index was found to be strongly related with forest density, although the related patterns of change had little relation with variability in historic AGB. By scaling biomass models through small (∼2.5 ha) spatial objects defined by spectral homogeneity, the AGB dynamics in the period 1990-2000 are mapped (70% accuracy when validated with plot values of
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
Mathematical Models for Aircraft Trajectory Design : A Survey
Delahaye, Daniel; Puechmorel, Stéphane; Tsiotras, Panagiotis; Féron, Éric
2014-01-01
Air traffic management ensures the safety of flight by optimizing flows and maintaining separation between aircraft. After giving some definitions, some typical feature of aircraft trajectories are presented. Trajectories are objects belonging to spaces with infinite dimensions. The naive way to address such problem is to sample trajectories at some regular points and to create a big vector of positions (and or speeds). In order to manipulate such objects with algorithms, one must reduce the ...
Ising models and topological codes: classical algorithms and quantum simulation
Nest, M Van den
2014-01-01
We present an algorithm to approximate partition functions of 3-body classical Ising models on two-dimensional lattices of arbitrary genus, in the real-temperature regime. Even though our algorithm is purely classical, it is designed by exploiting a connection to topological quantum systems, namely the color codes. The algorithm performance is exponentially better than other approaches which employ mappings between partition functions and quantum state overlaps. In addition, our approach gives rise to a protocol for quantum simulation of such Ising models by simply measuring local observables on color codes.
Classical analogous of quantum cosmological perfect fluid models
Batista, A. B.; Fabris, J. C.; Goncalves, S. V. B.; Tossa, J.
2000-01-01
Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state $p_Q = \\rho_Q$ is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classic...
THE NEW CLASSICAL THEORY AND THE REAL BUSINESS CYCLE MODEL
Oana Simona HUDEA (CARAMAN
2014-11-01
Full Text Available The present paper aims at describing some key elements of the new classical theory-related model, namely the Real Business Cycle, mainly describing the economy from the perspective of a perfectly competitive market, characterised by price, wage and interest rate flexibility. The rendered impulse-response functions, that help us in revealing the capacity of the model variables to return to their steady state under the impact of a structural shock, be it technology or monetary policy oriented, give points to the neutrality of the monetary entity decisions, therefore confirming the well-known classical dichotomy existing between the nominal and the real factors of the economy.
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
Autoparallel vs. Geodesic Trajectories in a Model of Torsion Gravity
Luis Acedo
2015-11-01
Full Text Available We consider a parametrized torsion gravity model for Riemann–Cartan geometry around a rotating axisymmetric massive body. In this model, the source of torsion is given by a circulating vector potential following the celestial parallels around the rotating object. Ours is a variant of the Mao, Tegmark, Guth and Cabi (MTGC model in which the total angular momentum is proposed as a source of torsion. We study the motion of bodies around the rotating object in terms of autoparallel trajectories and determine the leading perturbations of the orbital elements by using standard celestial mechanics techniques. We find that this torsion model implies new gravitational physical consequences in the Solar system and, in particular, secular variations of the semi-major axis of the planetary orbits. Perturbations on the longitude of the ascending node and the perihelion of the planets are already under discussion in the astronomical community, and if confirmed as truly non-zero effects at a statistically significant level, we might be at the dawn of an era of torsion phenomenology in the Solar system.
"Finance in a Classical and Harrodian Cyclical Growth Model"
Jamee K. Moudud
1999-01-01
This paper is an extension of an earlier working paper ("Finance and the Macroeconomic Process in a Classical Growth and Cycles Model," Levy Institute Working Paper No. 253). The basic structure of the model remains unchanged in that it is based on a social accounting matrix (SAM) with endogenous money. Investment in circulating capital adds to output and investment in fixed capital adds to potential output. Driving the model's fast adjustment process, which describes the disequilibrium adjus...
Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com [Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2015-04-07
It is noted that the recently developed symmetrical quasi-classical (SQC) treatment of the Meyer-Miller (MM) model for the simulation of electronically non-adiabatic dynamics provides a good description of detailed balance, even though the dynamics which results from the classical MM Hamiltonian is “Ehrenfest dynamics” (i.e., the force on the nuclei is an instantaneous coherent average over all electronic states). This is seen to be a consequence of the SQC windowing methodology for “processing” the results of the trajectory calculation. For a particularly simple model discussed here, this is shown to be true regardless of the choice of windowing function employed in the SQC model, and for a more realistic full classical molecular dynamics simulation, it is seen to be maintained correctly for very long time.
It is noted that the recently developed symmetrical quasi-classical (SQC) treatment of the Meyer-Miller (MM) model for the simulation of electronically non-adiabatic dynamics provides a good description of detailed balance, even though the dynamics which results from the classical MM Hamiltonian is “Ehrenfest dynamics” (i.e., the force on the nuclei is an instantaneous coherent average over all electronic states). This is seen to be a consequence of the SQC windowing methodology for “processing” the results of the trajectory calculation. For a particularly simple model discussed here, this is shown to be true regardless of the choice of windowing function employed in the SQC model, and for a more realistic full classical molecular dynamics simulation, it is seen to be maintained correctly for very long time
General classical solutions in the noncommutative CPN-1 model
We give an explicit construction of general classical solutions for the noncommutative CPN-1 model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied
Classical solutions for Hele-Shaw models with surface tension
Escher, Joachim; Simonett, Gieri
1997-01-01
It is shown that surface tension effects on the free boundary are regularizing for Hele-Shaw models. This implies, in particular, existence and uniqueness of classical solutions for a large class of initial data. As a consequence, we give a rigorous proof of the fact that homogeneous Hele-Shaw flows with positive surface tension are volume preserving and area shrinking.
General classical solutions in the CPsup(n-1) model
We study the classical solutions with finite action of the CPsup(n-1) non-linear sigma model in two dimensions. The general solution can be expressed explicitly in terms of n rational analytic functions. All solutions which are neither instantons nor anti-instantons turn out to be saddle points of the action
Research on Three-dimensional Modeling and Visualization for Well Trajectory of Drilling
Gao Xiaorong
2013-09-01
Full Text Available This study aims to realize 3D visualization of well trajectory more efficiently by use of a new method. In view of the shortcomings of traditional three-dimensional (3D modeling methods for well trajectory, a new method of slice-based 3D modeling for the tubular well trajectory was put forward, by which a 3D well trajectory model was established. The method can realize the 3D tubular well trajectory seamless connection efficiently and conveniently without interpolation smoothing treatment of the well trajectory’s crook. In order to provide a convenience to observe and analyze intuitively as well as control the well trajectory effectively in drilling for the drilling staff, realized 3D visualization of the well trajectory based on virtual reality technology and provided flexible human-computer interaction functions with which the drilling staff can make interactive operation such as zooming, translating and rotating, etc., for the 3D well trajectory. Consequently, the well trajectory can be observed from multi-azimuth and multi-angle, improving the oil reservoir encountering rate. Finally, an application example of 3D visualization for well trajectory in Dagang Oilfield was given.
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
THE NEW CLASSICAL THEORY AND THE REAL BUSINESS CYCLE MODEL
Oana Simona HUDEA (CARAMAN); Sorin George TOMA; Marin BURCEA
2014-01-01
The present paper aims at describing some key elements of the new classical theory-related model, namely the Real Business Cycle, mainly describing the economy from the perspective of a perfectly competitive market, characterised by price, wage and interest rate flexibility. The rendered impulse-response functions, that help us in revealing the capacity of the model variables to return to their steady state under the impact of a structural shock, be it technology or monetary policy oriented, ...
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.
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.
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)
Quasi-classical Trajectory Study of Reaction O (3P) + HCl (v = 2; j = 1,6,9) → OH + Cl
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)
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.
Modelling BMI trajectories in children for genetic association studies.
Nicole M Warrington
Full Text Available BACKGROUND: The timing of associations between common genetic variants and changes in growth patterns over childhood may provide insight into the development of obesity in later life. To address this question, it is important to define appropriate statistical models to allow for the detection of genetic effects influencing longitudinal childhood growth. METHODS AND RESULTS: Children from The Western Australian Pregnancy Cohort (Raine; n=1,506 Study were genotyped at 17 genetic loci shown to be associated with childhood obesity (FTO, MC4R, TMEM18, GNPDA2, KCTD15, NEGR1, BDNF, ETV5, SEC16B, LYPLAL1, TFAP2B, MTCH2, BCDIN3D, NRXN3, SH2B1, MRSA and an obesity-risk-allele-score was calculated as the total number of 'risk alleles' possessed by each individual. To determine the statistical method that fits these data and has the ability to detect genetic differences in BMI growth profile, four methods were investigated: linear mixed effects model, linear mixed effects model with skew-t random errors, semi-parametric linear mixed models and a non-linear mixed effects model. Of the four methods, the semi-parametric linear mixed model method was the most efficient for modelling childhood growth to detect modest genetic effects in this cohort. Using this method, three of the 17 loci were significantly associated with BMI intercept or trajectory in females and four in males. Additionally, the obesity-risk-allele score was associated with increased average BMI (female: β=0.0049, P=0.0181; male: β=0.0071, P=0.0001 and rate of growth (female: β=0.0012, P=0.0006; male: β=0.0008, P=0.0068 throughout childhood. CONCLUSIONS: Using statistical models appropriate to detect genetic variants, variations in adult obesity genes were associated with childhood growth. There were also differences between males and females. This study provides evidence of genetic effects that may identify individuals early in life that are more likely to rapidly increase their BMI
Windfield and trajectory models for tornado-propelled objects. Final report
This is the final report of a three-phased research project to develop a six-degree-of-freedom mathematical model to predict the trajectories of tornado-propelled objects. The model is based on the meteorological, aerodynamic, and dynamic processes that govern the trajectories of missiles in a tornadic windfield. The aerodynamic coefficients for the postulated missiles were obtained from full-scale wind tunnel tests on a 12-inch pipe and car and from drop tests. Rocket sled tests were run whereby the 12-inch pipe and car were injected into a worst-case tornado windfield in order to verify the trajectory model. To simplify and facilitate the use of the trajectory model for design applications without having to run the computer program, this report gives the trajectory data for NRC-postulated missiles in tables based on given variables of initial conditions of injection and tornado windfield. Complete descriptions of the tornado windfield and trajectory models are presented. The trajectory model computer program is also included for those desiring to perform trajectory or sensitivity analyses beyond those included in the report or for those wishing to examine other missiles and use other variables
Quantum cosmological perfect fluid model and its classical analogue
Batista, A B; Gonçalves, S V B; Tossa, J; Tossa, Joel
2002-01-01
The quantization of gravity coupled to a perfect fluid model leads to a Schr\\"odinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state $p = \\alpha\\rho$; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. We show that such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition, to the ordinary classical model, of a repulsive stiff matter fluid. The meaning of the existence of this universal classical analogue is discussed. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of $\\alpha$, while the radiative non-flat case is equivalent to the harmonic osci...
Mathematical Model to Simulate the Trajectory Elements ofan Artillery Projectile Proof Shot
K.K. Chand
2007-01-01
Full Text Available In external ballistics of a conventional spin-stabilised artillery projectile, there are a numberof trajectory models developed for computing trajectory elements having varying degrees ofcomplexity. The present study attempts to propose a single mathematical model, viz., simplifiedpoint-mass/simple particle trajectory model to simulate the trajectory elements of a typical spin-stabilised flat-head artillery projectile proof shot. Due to difficulties in the projectile shape andsize, and the complicated nature of air resistance, an accurate mathematical prediction of thetrajectory is difficult. To simplify the computations, the governing equations of motion of theprojectile have been simplified and assumed that the projectile is a particle and the only forcesacting on the projectile are drag and gravity. With this model, trajectory elements have beengenerated and compared with experimental results obtained in the field test. The measuringinstrument used in this case is a Doppler radar.
Modelling Of Flotation Processes By Classical Mathematical Methods - A Review
Jovanović, Ivana; Miljanović, Igor
2015-12-01
Flotation process modelling is not a simple task, mostly because of the process complexity, i.e. the presence of a large number of variables that (to a lesser or a greater extent) affect the final outcome of the mineral particles separation based on the differences in their surface properties. The attempts toward the development of the quantitative predictive model that would fully describe the operation of an industrial flotation plant started in the middle of past century and it lasts to this day. This paper gives a review of published research activities directed toward the development of flotation models based on the classical mathematical rules. The description and systematization of classical flotation models were performed according to the available references, with emphasize exclusively given to the flotation process modelling, regardless of the model application in a certain control system. In accordance with the contemporary considerations, models were classified as the empirical, probabilistic, kinetic and population balance types. Each model type is presented through the aspects of flotation modelling at the macro and micro process levels.
Simulating the classical XY model with a laser network
Tamate, Shuhei; Marandi, Alireza; McMahon, Peter; Utsunomiya, Shoko
2016-01-01
Drawing fair samples from the Boltzmann distribution of a statistical model is a challenging task for modern digital computers. We propose a physical implementation of a Boltzmann sampler for the classical XY model by using a laser network. The XY spins are mapped onto the phases of multiple laser pulses in a fiber ring cavity and the steady-state distribution of phases naturally realizes the Boltzmann distribution of the corresponding XY model. We experimentally implement the laser network by using an actively mode-locked fiber laser with optical delay lines, and demonstrate Boltzmann sampling for a one-dimensional XY ring.
Classical mutual information in mean-field spin glass models
Alba, Vincenzo; Inglis, Stephen; Pollet, Lode
2016-03-01
We investigate the classical Rényi entropy Sn and the associated mutual information In in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and analytical tools we investigate the S-K model in the n -sheet booklet. This is achieved by gluing together n independent copies of the model, and it is the main ingredient for constructing the Rényi entanglement-related quantities. We find a glassy phase at low temperatures, whereas at high temperatures the model exhibits paramagnetic behavior, consistent with the regular S-K model. The temperature of the paramagnetic-glassy transition depends nontrivially on the geometry of the booklet. At high temperatures we provide the exact solution of the model by exploiting the replica symmetry. This is the permutation symmetry among the fictitious replicas that are used to perform disorder averages (via the replica trick). In the glassy phase the replica symmetry has to be broken. Using a generalization of the Parisi solution, we provide analytical results for Sn and In and for standard thermodynamic quantities. Both Sn and In exhibit a volume law in the whole phase diagram. We characterize the behavior of the corresponding densities, Sn/N and In/N , in the thermodynamic limit. Interestingly, at the critical point the mutual information does not exhibit any crossing for different system sizes, in contrast with local spin models.
Macroeconomic Forecasts in Models with Bayesian Averaging of Classical Estimates
Piotr Białowolski
2012-03-01
Full Text Available The aim of this paper is to construct a forecasting model oriented on predicting basic macroeconomic variables, namely: the GDP growth rate, the unemployment rate, and the consumer price inflation. In order to select the set of the best regressors, Bayesian Averaging of Classical Estimators (BACE is employed. The models are atheoretical (i.e. they do not reflect causal relationships postulated by the macroeconomic theory and the role of regressors is played by business and consumer tendency survey-based indicators. Additionally, survey-based indicators are included with a lag that enables to forecast the variables of interest (GDP, unemployment, and inflation for the four forthcoming quarters without the need to make any additional assumptions concerning the values of predictor variables in the forecast period. Bayesian Averaging of Classical Estimators is a method allowing for full and controlled overview of all econometric models which can be obtained out of a particular set of regressors. In this paper authors describe the method of generating a family of econometric models and the procedure for selection of a final forecasting model. Verification of the procedure is performed by means of out-of-sample forecasts of main economic variables for the quarters of 2011. The accuracy of the forecasts implies that there is still a need to search for new solutions in the atheoretical modelling.
Completeness of classical spin models and universal quantum computation
We study mappings between different classical spin systems that leave the partition function invariant. As recently shown in Van den Nest et al (2008 Phys. Rev. Lett. 100 110501), the partition function of the 2D square lattice Ising model in the presence of an inhomogeneous magnetic field can specialize to the partition function of any Ising system on an arbitrary graph. In this sense the 2D Ising model is said to be 'complete'. However, in order to obtain the above result, the coupling strengths on the 2D lattice must assume complex values, and thus do not allow for a physical interpretation. Here we show how a complete model with real—and, hence, 'physical'—couplings can be obtained if the 3D Ising model is considered. We furthermore show how to map general q-state systems with possibly many-body interactions to the 2D Ising model with complex parameters, and give completeness results for these models with real parameters. We also demonstrate that the computational overhead in these constructions is in all relevant cases polynomial. These results are proved by invoking a recently found cross-connection between statistical mechanics and quantum information theory, where partition functions are expressed as quantum mechanical amplitudes. Within this framework, there exists a natural correspondence between many-body quantum states that allow for universal quantum computation via local measurements only, and complete classical spin systems
Classically conformal radiative neutrino model with gauged B - L symmetry
Okada, Hiroshi; Orikasa, Yuta
2016-09-01
We propose a classically conformal model in a minimal radiative seesaw, in which we employ a gauged B - L symmetry in the standard model that is essential in order to work the Coleman-Weinberg mechanism well that induces the B - L symmetry breaking. As a result, nonzero Majorana mass term and electroweak symmetry breaking simultaneously occur. In this framework, we show a benchmark point to satisfy several theoretical and experimental constraints. Here theoretical constraints represent inert conditions and Coleman-Weinberg condition. Experimental bounds come from lepton flavor violations (especially μ → eγ), the current bound on the Z‧ mass at the CERN Large Hadron Collider, and neutrino oscillations.
Meng, Deyuan; Tao, Guoliang; Liu, Hao; Zhu, Xiaocong
2014-07-01
Friction compensation is particularly important for motion trajectory tracking control of pneumatic cylinders at low speed movement. However, most of the existing model-based friction compensation schemes use simple classical models, which are not enough to address applications with high-accuracy position requirements. Furthermore, the friction force in the cylinder is time-varying, and there exist rather severe unmodelled dynamics and unknown disturbances in the pneumatic system. To deal with these problems effectively, an adaptive robust controller with LuGre model-based dynamic friction compensation is constructed. The proposed controller employs on-line recursive least squares estimation (RLSE) to reduce the extent of parametric uncertainties, and utilizes the sliding mode control method to attenuate the effects of parameter estimation errors, unmodelled dynamics and disturbances. In addition, in order to realize LuGre model-based friction compensation, the modified dual-observer structure for estimating immeasurable friction internal state is developed. Therefore, a prescribed motion tracking transient performance and final tracking accuracy can be guaranteed. Since the system model uncertainties are unmatched, the recursive backstepping design technology is applied. In order to solve the conflicts between the sliding mode control design and the adaptive control design, the projection mapping is used to condition the RLSE algorithm so that the parameter estimates are kept within a known bounded convex set. Finally, the proposed controller is tested for tracking sinusoidal trajectories and smooth square trajectory under different loads and sudden disturbance. The testing results demonstrate that the achievable performance of the proposed controller is excellent and is much better than most other studies in literature. Especially when a 0.5 Hz sinusoidal trajectory is tracked, the maximum tracking error is 0.96 mm and the average tracking error is 0.45 mm. This
A Trajectory-Oriented Carriageway-Based Road Network Data Model, Part 1: Background
无
2006-01-01
This is the first of a three-part series of papers which introduces a general background of building trajectory-oriented road network data models, including motivation, related works, and basic concepts. The purpose of the series is to develop a trajectory-oriented road network data model, namely carriageway-based road network data model (CRNM). Part 1 deals with the modeling background. Part 2 proposes the principle and architecture of the CRNM. Part 3 investigates the implementation of the CRNM in a case study. In the present paper, the challenges of managing trajectory data are discussed. Then, developing trajectory-oriented road network data models is proposed as a solution and existing road network data models are reviewed. Basic representation approaches of a road network are introduced as well as its constitution.
A Classical Realizability Model arising from a Stable Model of Untyped Lambda Calculus
Streicher, Thomas
2014-01-01
We study a classical realizability model (in the sense of J.-L. Krivine) arising from a model of untyped lambda calculus in coherence spaces. We show that this model validates countable choice using bar recursion and bar induction.
Matamoros Cid, Ismael
2015-01-01
The Air Traffic Management (ATM) paradigm is shifting towards a scenario where Trajectory Predictors (TP) play a key role. They rely on Aircraft Performance Models (APM), mathematical models of the performance related characteristics of aircraft. The widespread use of non-coventional take-off procedures, such as the flexible thrust method, has arose the necessity of modelling them to keep fidelity in take-off trajectory predictions. This project, carried out with Boeing Research & Technology ...
Abbaszadeh, Masoud
2015-01-01
A sequential trajectory linearized adaptive model based predictive controller is designed using the DMC algorithm to control the temperature of a batch MMA polymerization process. Using the mechanistic model of the polymerization, a parametric transfer function is derived to relate the reactor temperature to the power of the heaters. Then, a multiple model predictive control approach is taken in to track a desired temperature trajectory.The coefficients of the multiple transfer functions are ...
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
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.
Model-based control versus classical control for parallel robots
Belda, Květoslav
Praha : ÚTIA AV ČR, 2004 - ( And rýsek, J.; Kárný, M.; Kracík, J.), s. 1-9 [Computer-Intensive Methods in Control and Data Processing. CMP'04: Towards Electronic Democracy. Praha (CZ), 12.05.2004-14.05.2004] R&D Projects: GA ČR GA101/03/0620 Institutional research plan: CEZ:AV0Z1075907 Keywords : model based control * classical PSD control * global and local levels of control Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/historie/belda-0106263.pdf
Modeling and Characterization of Charged Particle Trajectories in an Oscillating Magnetic Field
Irawan, Dani; Khotimah, Siti Nurul; Latief, Fourier Dzar Eljabbar; Novitrian,
2015-01-01
A constant magnetic field has frequently been discussed and has been known that it can cause a charged particle to form interesting trajectories such as cycloid and helix in presence of electric field, but a changing magnetic field is rarely discussed. In this work, modeling and characterization of charged particle trajectories in oscillating magnetic field is reported. The modeling is performed using Euler method with speed corrector. The result shows that there are two types of trajectory patterns that will recur for every $180 n T_0$ ($n = 0, 1, 2, ..$) in increasing of magnetic field oscillation period, where $T_0$ is about $6.25\\times10^{-7}$ s.
Trajectory Stability Modeling And Tolerances in the LCLS
To maintain stable performance of the Linac Coherent Light Source (LCLS) x-ray free-electron laser, one must control the electron trajectory stability through the undulator to a small fraction of the beam size. BPM-based feedback loops running at 120 Hz will be effective in controlling jitter at low frequencies less than a few Hz. On the other hand, linac and injector stability tolerances must be chosen to limit jitter at higher frequencies. In this paper we study possible sources of high frequency jitter, including: (1) steering coil current regulation; (2) quadrupole magnet transverse vibrations; (3) quadrupole current regulation with transverse misalignments; (4) charge variations coupled to jitter through transverse wakefields of misaligned RF structures; and (5) bunch length variations coupled through coherent synchrotron radiation in the bunch compressor chicanes. Based on this study, we set component tolerances and estimate expected trajectory stability in the LCLS
Characterizing long-term patterns of weight change in China using latent class trajectory modeling.
Lauren Paynter
Full Text Available Over the past three decades, obesity-related diseases have increased tremendously in China, and are now the leading causes of morbidity and mortality. Patterns of weight change can be used to predict risk of obesity-related diseases, increase understanding of etiology of disease risk, identify groups at particularly high risk, and shape prevention strategies.Latent class trajectory modeling was used to compute weight change trajectories for adults aged 18 to 66 using the China Health and Nutrition Survey (CHNS data (n = 12,611. Weight change trajectories were computed separately for males and females by age group at baseline due to differential age-related patterns of weight gain in China with urbanization. Generalized linear mixed effects models examined the association between weight change trajectories and baseline characteristics including urbanicity, BMI category, age, and year of study entry.Trajectory classes were identified for each of six age-sex subgroups corresponding to various degrees of weight loss, maintenance and weight gain. Baseline BMI status was a significant predictor of trajectory membership for all age-sex subgroups. Baseline overweight/obesity increased odds of following 'initial loss with maintenance' trajectories. We found no significant association between baseline urbanization and trajectory membership after controlling for other covariates.Trajectory analysis identified patterns of weight change for age by gender groups. Lack of association between baseline urbanization status and trajectory membership suggests that living in a rural environment at baseline was not protective. Analyses identified age-specific nuances in weight change patterns, pointing to the importance of subgroup analyses in future research.
Group-Based Trajectory Modeling of Caregiver Psychological Distress Over Time
Stone, Roslyn A.; Kim, Kevin H.; Ren, Dianxu; Schulz, Richard; Given, Charles W.; Given, Barbara A.; Sherwood, Paula R.
2013-01-01
Background Competing theories of adaptation and wear-and-tear describe psychological distress patterns among family caregivers. Purpose This study seeks to characterize psychological distress patterns in family caregivers and identify predictors. Methods One hundred three caregivers of care recipients with primary malignant brain tumors were interviewed within 1, 4, 8, and 12 months post-diagnosis regarding psychological distress; care recipients were interviewed regarding clinical/functional characteristics. Group-based trajectory modeling identified longitudinal distress patterns, and weighted logistic/multinomial regression models identified predictors of distress trajectories. Results Group-based trajectory modeling identified high-decreasing (51.1 % of caregivers) and consistently low (48.9 %) depressive symptom trajectories, high-decreasing (75.5 %) and low-decreasing (24.5 %) anxiety trajectories, and high (37.5 %), moderate (40.9 %), and low-decreasing (21.6 %) caregiver burden trajectories. High depressive symptoms were associated with high trajectories for both anxiety and burden, lower caregivers age, income, and social support, and lower care recipient functioning. Conclusions Our data support the adaptation hypothesis; interventions should target those at risk for persistent distress. PMID:22585179
Improvements on Semi-Classical Distorted-Wave model
Sun Weili; Watanabe, Y.; Kuwata, R. [Kyushu Univ., Fukuoka (Japan); Kohno, M.; Ogata, K.; Kawai, M.
1998-03-01
A method of improving the Semi-Classical Distorted Wave (SCDW) model in terms of the Wigner transform of the one-body density matrix is presented. Finite size effect of atomic nuclei can be taken into account by using the single particle wave functions for harmonic oscillator or Wood-Saxon potential, instead of those based on the local Fermi-gas model which were incorporated into previous SCDW model. We carried out a preliminary SCDW calculation of 160 MeV (p,p`x) reaction on {sup 90}Zr with the Wigner transform of harmonic oscillator wave functions. It is shown that the present calculation of angular distributions increase remarkably at backward angles than the previous ones and the agreement with the experimental data is improved. (author)
Using Markov models to simulate electron spin resonance spectra from molecular dynamics trajectories
Sezer, Deniz; Freed, Jack H.; Roux, Benoît
2008-01-01
Simulating electron spin resonance (ESR) spectra directly from molecular dynamics simulations of a spin labeled protein necessitates a large number (hundreds or thousands) of relatively long (hundreds of ns) trajectories. To meet this challenge, we explore the possibility of constructing accurate stochastic models of the spin label dynamics from atomistic trajectories. A systematic, two-step procedure, based on the probabilistic framework of hidden Markov models, is developed to build a discr...
Penalized Spline: a General Robust Trajectory Model for ZIYUAN-3 Satellite
Pan, H.; Zou, Z.
2016-06-01
Owing to the dynamic imaging system, the trajectory model plays a very important role in the geometric processing of high resolution satellite imagery. However, establishing a trajectory model is difficult when only discrete and noisy data are available. In this manuscript, we proposed a general robust trajectory model, the penalized spline model, which could fit trajectory data well and smooth noise. The penalized parameter λ controlling the smooth and fitting accuracy could be estimated by generalized cross-validation. Five other trajectory models, including third-order polynomials, Chebyshev polynomials, linear interpolation, Lagrange interpolation and cubic spline, are compared with the penalized spline model. Both the sophisticated ephemeris and on-board ephemeris are used to compare the orbit models. The penalized spline model could smooth part of noise, and accuracy would decrease as the orbit length increases. The band-to-band misregistration of ZiYuan-3 Dengfeng and Faizabad multispectral images is used to evaluate the proposed method. With the Dengfeng dataset, the third-order polynomials and Chebyshev approximation could not model the oscillation, and introduce misregistration of 0.57 pixels misregistration in across-track direction and 0.33 pixels in along-track direction. With the Faizabad dataset, the linear interpolation, Lagrange interpolation and cubic spline model suffer from noise, introducing larger misregistration than the approximation models. Experimental results suggest the penalized spline model could model the oscillation and smooth noise.
Three-dimensional classical-ensemble modeling of non-sequential double ionization
Full text: We have been using 1d ensembles of classical two-electron atoms to simulate helium atoms that are exposed to pulses of intense laser radiation. In this talk we discuss the challenges in setting up a 3d classical ensemble that can mimic the quantum ground state of helium. We then report studies in which each one of 500,000 two-electron trajectories is followed in 3d through a ten-cycle (25 fs) 780 nm laser pulse. We examine double-ionization yield for various intensities, finding the familiar knee structure. We consider the momentum spread of outcoming electrons in directions both parallel and perpendicular to the direction of laser polarization, and find results that are consistent with experiment. We examine individual trajectories and recollision processes that lead to double ionization, considering the best phases of the laser cycle for recollision events and looking at the possible time delay between recollision and emergence. We consider also the number of recollision events, and find that multiple recollisions are common in the classical ensemble. We investigate which collisional processes lead to various final electron momenta. We conclude with comments regarding the ability of classical mechanics to describe non-sequential double ionization, and a quick summary of similarities and differences between 1d and 3d classical double ionization using energy-trajectory comparisons. Refs. 3 (author)
Probing classically conformal $B-L$ model with gravitational waves
Jinno, Ryusuke
2016-01-01
We study the cosmological history of the classical conformal $B-L$ gauge extension of the standard model, in which the physical scales are generated via the Coleman-Weinberg-type symmetry breaking. Especially, we consider the thermal phase transition of the U$(1)_{B-L}$ symmetry in the early universe and resulting gravitational-wave production. Due to the classical conformal invariance, the phase transition tends to be a first-order one with ultra-supercooling, which enhances the strength of the produced gravitational waves. We show that, requiring (1) U$(1)_{B-L}$ is broken after the reheating, (2) the $B-L$ gauge coupling does not blow up below the Planck scale, (3) the thermal phase transition completes in almost all the patches in the universe, the gravitational wave spectrum can be as large as $\\Omega_{\\rm GW} \\sim 10^{-8}$ at the frequency $f \\sim 0.01$-$1$Hz for some model parameters, and a vast parameter region can be tested by future interferometer experiments such as eLISA, LISA, BBO and DECIGO.
Three-stage classical molecular dynamics model for simulation of heavy-ion fusion
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.
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.
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
Classical symmetries of some two-dimensional models
It is well-known that principal chiral models and symmetric space models in two-dimensional Minkowski space have an infinite-dimensional algebra of hidden symmetries. Because of the relevance of symmetric space models to duality symmetries in string theory, the hidden symmetries of these models are explored in some detail. The string theory application requires including coupling to gravity, supersymmetrization, and quantum effects. However, as a first step, this paper only considers classical bosonic theories in flat space-time. Even though the algebra of hidden symmetries of principal chiral models is confirmed to include a Kac-Moody algebra (or a current algebra on a circle), it is argued that a better interpretation is provided by a doubled current algebra on a semi-circle (or line segment). Neither the circle nor the semi-circle bears any apparent relationship to the physical space. For symmetric space models the line segment viewpoint is shown to be essential, and special boundary conditions need to be imposed at the ends. The algebra of hidden symmetries also includes Virasoro-like generators. For both principal chiral models and symmetric space models, the hidden symmetry stress tensor is singular at the ends of the line segment. (orig.)
Modeling of aerodynamic Space-to-Surface flight with optimal trajectory for targeting
Gornev, Serge
2003-01-01
Modeling has been created for a Space-to-Surface system defined for an optimal trajectory for targeting in terminal phase. The modeling includes models for simulation atmosphere, speed of sound, aerodynamic flight and navigation by an infrared system. The modeling simulation includes statistical analysis of the modeling results.
Gornev, Serge
2006-01-01
Modeling has been created for a Space-to-Surface system defined for an optimal trajectory for targeting in terminal phase with avoids an intercepting process. The modeling includes models for simulation atmosphere, speed of sound, aerodynamic flight and navigation by an infrared system. The modeling and simulation includes statistical analysis of the modeling results.
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...
Intermediate time scaling in classical continuous-spin models
Oh, S K; Chung, J S
1999-01-01
The time-dependent total spin correlation functions of the two- and the three-dimensional classical XY models seem to have a very narrow first dynamic scaling interval and, after this interval, a much broader anomalous second dynamic scaling interval appears. In this paper, this intriguing feature found in our previous work is re-examined. By introducing a phenomenological characteristic time for this intermediate time interval, the second dynamic scaling behavior can be explained. Moreover, the dynamic critical exponent found from this novel characteristic time is found to be identical to that found from the usual dynamic scaling theory developed in the wave vector and frequency domain. For continuous spin models, in which the spin variable related to a long-range order parameter is not a constant of motion, our method yielded the dynamic critical exponent with less computational efforts.
Mixed Membership Trajectory Models of Cognitive Impairment in the Multicenter AIDS Cohort Study
Molsberry, Samantha A.; Lecci, Fabrizio; Kingsley, Lawrence; Junker, Brian; Reynolds, Sandra; Goodkin, Karl; Levine, Andrew J.; Martin, Eileen; Miller, Eric N.; Munro, Cynthia A.; Ragin, Ann; Sacktor, Ned; Becker, James T.
2016-01-01
Objective The longitudinal trajectories that individuals may take from a state of normal cognition to HIV-associated dementia are unknown. We applied a novel statistical methodology to identify trajectories to cognitive impairment, and factors that affected the “closeness” of an individual to one of the canonical trajectories. Design The Multicenter AIDS Cohort Study (MACS) is a four-site longitudinal study of the natural and treated history of HIV Disease among gay and bisexual men. Methods Using data from 3,892 men (both HIV-infected and uninfected) enrolled in the neuropsychology substudy of the MACS, a Mixed Membership Trajectory Model (MMTM) was applied to capture the pathways from normal cognitive function to mild impairment to severe impairment. MMTMs allow the data to identify canonical pathways and to model the effects of risk factors on an individual’s “closeness” to these trajectories. Results We identified three distinct trajectories to cognitive impairment – one “normal aging” (low probability of mild impairment until age 60), one “premature aging” (mild impairment starting at age 45–50), and one “unhealthy” (mild impairment in 20s and 30s) profile. Second, clinically defined AIDS and not simply HIV Disease, was associated with closeness to the premature aging trajectory. And, third, Hepatitis-C infection, Depression, Race, Recruitment Cohort and Confounding Conditions all affected individual’s closeness to these trajectories. Conclusions These results provide new insight into the natural history of cognitive dysfunction in HIV disease and provide evidence for a potential difference in the pathophysiology of the development of cognitive impairment based on trajectories to impairment. PMID:25565498
Chuen-An Tang
2014-01-01
Full Text Available The purposes of this study are to test reliabilities and validities of classics-reading curriculum (CRC scale, classics-reading promotion (CRP scale, and classics-reading effect (CRE scale and to examine the relationships between CRC, CRP, and CRE in elementary schools through applying CORPS framework. The pilot sample and formal sample contain 141 and 500 participants from elementary school faculties and classics-reading volunteers in the north, central, south, and east regions of Taiwan. The findings indicate that Cronbach α coefficients of curriculum cognition (CC, curriculum teaching (CT, inside-school promotion (IP, outside-school promotion (EP, learning effect (LE, and class management effect (CME subscales are .88, .85, .93, .91, .91, .94, respectively, through exploratory factor analysis and they have good internal reliabilities and construct validities, respectively, through confirmatory factor analysis. Moreover, CC, CT, IP, and EP have positive influences on LE (standardized coefficients .34, .25, .14, and .22 and on CME (standardized coefficients .41, .14, .14, and .20, respectively. CC, CT, IP, and EP can explain 69% of LE and 61% of CME. The model is supported by the data. Lastly, this study proposes some suggestions regarding the classics-reading education for elementary schools.
Lebiedz, Dirk; Siehr, Jochen
2009-01-01
In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into fast and slow modes. The aim is to approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones via computation of a slow attracting manifold. We present a novel method for computing approximations of such manifolds using trajectory-based optimization. We discuss Riemannian geometry concepts as a basis for suitable optimization criteria characterizing trajectories near slow attracting manifolds and thus provide insight into fundamental geometric properties of multiple time scale chemical kinetics. The optimization criteria correspond to a suitable mathematical formulation of "minimal relaxation" of chemical forces along reaction trajectories under given constraints. We present various geometri...
Modelling of bubble trajectories in a pump impeller
Dupoiron, Marine; Linden, Paul
2015-11-01
A vertical rotating flow in an annulus gap with an increasing diameter is used to approximate the flow in a pump impeller. We study a spherical gas bubble released at the flow inlet, subject to turbulent drag and added mass forces. Bubbles trajectories have been computed for different geometries, rotation speeds and bubble size, showing a deviation from the liquid streamlines in the angular and radial directions. This effect is related to the pump performance in multiphase conditions: the velocity difference between the gas and the liquid phases changes the final pressure rise produced by the impeller. In some extreme cases, the centrifugal force can be large enough to prevent bubbles from exiting the impeller at all, leading to an unwanted gas accumulation and the blockage of the pump. We eventually quantify the effects of geometrical and operational parameters on the pump behaviour. Work done in collaboration with Schlumberger Gould Research, Cambridge.
Mathematical modeling and numerical simulation of oil spill trajectories on the sea
Paladino, Emilio Ernesto; Maliska, Clovis Raimundo [Santa Catarina Univ., Florianopolis, MG (Brazil). Lab. Computacional de Dinamica dos Fluidos]. 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 and in combating the pollution using floating barriers, detergents, etc. In order to estimate these slicks trajectories a new model, based on mass and momentum conservation equations, is presented. This model considers the spreading in the regime when the inertial and viscous forces counterbalance gravity and takes into account the effects of winds and water currents. The mass loss caused by oil evaporation is also considered. The numerical model is developed in generalized coordinates, making the model easily applicable to complex coastal geographies. (author)
Preduction of transport properties of gases using classical nonspherical models
The general formulation of the classical kinetic theory, which is needed to predict transport properties of gases in situations where the hydrodynamic equations are valid, is reviewed. A rigid convex model of tetrahedral symmetry is used to predict the Senftleben-Beenakker effect of a static magnetic field on the thermal conductivity and viscosity of pure CH4, CD4 and CF4. The parameters of the model are optimized and are found to assume physically reasonable values. The calculations agree with experiment to a degree comparable to that of similar work on diatomic molecules. A generalized scattering cross section, γ, is defined which can be evaluated exactly for the limiting cases of a spherical soft potential and rigid ovaloids. For a general soft nonspherical interaction of the Kihara type, a suitable approximation for the momentum dependence is made with the following attributes: γ reduces to the form for soft sphere and rigid ovaloid in the limits and the resulting matrix elements of the collision operator can be written in terms of the familiar Ω* integrals. This formulation is used to investigate thermal diffusion in binary isotopic mixtures of CO. Calculations are made in an 800K to 3000K range which includes the inversion temperatures for all mixtures studied. Thermal conductivity and diffusion coefficients of CO are also calculated. The parameters of the model can be adjusted to account for the major features of the experimental data. The physical significance of the parameters is discussed
Classical and Quantum Consistency of the DGP Model
Nicolis, A; Nicolis, Alberto; Rattazzi, Riccardo
2004-01-01
We study the Dvali-Gabadadze-Porrati model by the method of the boundary effective action. The truncation of this action to the bending mode \\pi consistently describes physics in a wide range of regimes both at the classical and at the quantum level. The Vainshtein effect, which restores agreement with precise tests of general relativity, follows straightforwardly. We give a simple and general proof of stability, i.e. absence of ghosts in the fluctuations, valid for most of the relevant cases, like for instance the spherical source in asymptotically flat space. However we confirm that around certain interesting self-accelerating cosmological solutions there is a ghost. We consider the issue of quantum corrections. Around flat space \\pi becomes strongly coupled below a macroscopic length of 1000 km, thus impairing the predictivity of the model. Indeed the tower of higher dimensional operators which is expected by a generic UV completion of the model limits predictivity at even larger length scales. We outline ...
Classical scale invariance in the inert doublet model
Plascencia, Alexis D
2015-01-01
The inert doublet model (IDM) is a minimal extension of the Standard Model (SM) that can account for the dark matter in the universe. Naturalness arguments motivate us to study whether the model can be embedded into a theory with dynamically generated scales. In this work we study a classically scale invariant version of the IDM with a minimal hidden sector, which has a $U(1)_{\\text{CW}}$ gauge symmetry and a complex scalar $\\Phi$. The mass scale is generated in the hidden sector via the Coleman-Weinberg (CW) mechanism and communicated to the two Higgs doublets via portal couplings. Since the CW scalar remains light, acquires a vacuum expectation value and mixes with the SM Higgs boson, the phenomenology of this construction can be modified with respect to the traditional IDM. We analyze the impact of adding this CW scalar and the $Z'$ gauge boson on the calculation of the dark matter relic density and on the spin-independent nucleon cross section for direct detection experiments. Finally, by studying the RG ...
Modelling individual routines and spatio-temporal trajectories in human mobility
Pappalardo, Luca
2016-01-01
Human mobility modelling is of fundamental importance in a wide range of applications, such as the developing of protocols for mobile ad hoc networks or for what-if analysis and simulation in urban ecosystems. Current generative models generally fail in accurately reproducing the individuals' recurrent daily schedules and at the same time in accounting for the possibility that individuals may break the routine and modify their habits during periods of unpredictability of variable duration. In this article we present DITRAS (DIary-based TRAjectory Simulator), a framework to simulate the spatio-temporal patterns of human mobility in a realistic way. DITRAS operates in two steps: the generation of a mobility diary and the translation of the mobility diary into a mobility trajectory. The mobility diary is constructed by a Markov model which captures the tendency of individuals to follow or break their routine. The mobility trajectory is produced by a model based on the concept of preferential exploration and pref...
Classical Wave Model of Quantum-Like Processing in Brain
Khrennikov, A.
2011-01-01
We discuss the conjecture on quantum-like (QL) processing of information in the brain. It is not based on the physical quantum brain (e.g., Penrose) - quantum physical carriers of information. In our approach the brain created the QL representation (QLR) of information in Hilbert space. It uses quantum information rules in decision making. The existence of such QLR was (at least preliminary) confirmed by experimental data from cognitive psychology. The violation of the law of total probability in these experiments is an important sign of nonclassicality of data. In so called "constructive wave function approach" such data can be represented by complex amplitudes. We presented 1,2 the QL model of decision making. In this paper we speculate on a possible physical realization of QLR in the brain: a classical wave model producing QLR . It is based on variety of time scales in the brain. Each pair of scales (fine - the background fluctuations of electromagnetic field and rough - the cognitive image scale) induces the QL representation. The background field plays the crucial role in creation of "superstrong QL correlations" in the brain.
A modelling and experimental study of the bubble trajectory in a non-Newtonian crystal suspension
Hassan, N M S [Process Engineering and Light Metals (PELM) Centre, Faculty of Sciences, Engineering and Health, CQUniversity, Rockhampton, QLD 4702 (Australia); Khan, M M K; Rasul, M G, E-mail: m.rasul@cqu.edu.a [School of Engineering and Built Environment, Faculty of Sciences, Engineering and Health, CQUniversity, Rockhampton, QLD 4702 (Australia)
2010-12-15
This paper presents an experimental and computational study of air bubbles rising in a massecuite-equivalent non-Newtonian crystal suspension. The bubble trajectory inside the stagnant liquid of a 0.05% xanthan gum crystal suspension was investigated and modelled using the computational fluid dynamics (CFD) model to gain an insight into the bubble flow characteristics. The CFD code FLUENT was used for numerical simulation, and the bubble trajectory calculations were performed through a volume of fluid (VOF) model. The influences of the Reynolds number (Re), the Weber number (We) and the bubble aspect ratio (E) on the bubble trajectory are discussed. The conditions for the bubbles' path oscillations are identified. The experimental results showed that the path instability for the crystal suspension was less rapid than in water. The trajectory analysis indicated that 5.76 mm diameter bubbles followed a zigzag motion in the crystal suspension. Conversely, the smaller bubbles (5.76 mm) followed a path of least horizontal movement and larger bubbles (21.21 mm) produced more spiral motion within the crystal suspension. Path instability occurred for bubbles of 15.63 and 21.21 mm diameter, and they induced both zigzag and spiral trajectories within the crystal suspension. At low Re and We, smaller bubbles (5.76 mm) produced a zigzag trajectory, whereas larger bubbles (15.63 and 21.21 mm) showed both zigzag and spiral trajectories at intermediate and moderately high Re and We in the crystal suspension. The simulation results illustrated that a repeating pattern of swirling vortices was created for smaller bubbles due to the unstable wake and unsteady flow of these bubbles. This is the cause of the smaller bubbles moving in a zigzag way. Larger bubbles showed two counter-rotating trailing vortices at the back of the bubble. These vortices induced a velocity component to the gas-liquid interface and caused a deformation. Hence, the larger bubbles produced a path
A modelling and experimental study of the bubble trajectory in a non-Newtonian crystal suspension
This paper presents an experimental and computational study of air bubbles rising in a massecuite-equivalent non-Newtonian crystal suspension. The bubble trajectory inside the stagnant liquid of a 0.05% xanthan gum crystal suspension was investigated and modelled using the computational fluid dynamics (CFD) model to gain an insight into the bubble flow characteristics. The CFD code FLUENT was used for numerical simulation, and the bubble trajectory calculations were performed through a volume of fluid (VOF) model. The influences of the Reynolds number (Re), the Weber number (We) and the bubble aspect ratio (E) on the bubble trajectory are discussed. The conditions for the bubbles' path oscillations are identified. The experimental results showed that the path instability for the crystal suspension was less rapid than in water. The trajectory analysis indicated that 5.76 mm diameter bubbles followed a zigzag motion in the crystal suspension. Conversely, the smaller bubbles (5.76 mm) followed a path of least horizontal movement and larger bubbles (21.21 mm) produced more spiral motion within the crystal suspension. Path instability occurred for bubbles of 15.63 and 21.21 mm diameter, and they induced both zigzag and spiral trajectories within the crystal suspension. At low Re and We, smaller bubbles (5.76 mm) produced a zigzag trajectory, whereas larger bubbles (15.63 and 21.21 mm) showed both zigzag and spiral trajectories at intermediate and moderately high Re and We in the crystal suspension. The simulation results illustrated that a repeating pattern of swirling vortices was created for smaller bubbles due to the unstable wake and unsteady flow of these bubbles. This is the cause of the smaller bubbles moving in a zigzag way. Larger bubbles showed two counter-rotating trailing vortices at the back of the bubble. These vortices induced a velocity component to the gas-liquid interface and caused a deformation. Hence, the larger bubbles produced a path transition.
Isogeometric shell formulation based on a classical shell model
Niemi, Antti
2012-09-04
This paper constitutes the first steps in our work concerning isogeometric shell analysis. An isogeometric shell model of the Reissner-Mindlin type is introduced and a study of its accuracy in the classical pinched cylinder benchmark problem presented. In contrast to earlier works [1,2,3,4], the formulation is based on a shell model where the displacement, strain and stress fields are defined in terms of a curvilinear coordinate system arising from the NURBS description of the shell middle surface. The isogeometric shell formulation is implemented using the PetIGA and igakit software packages developed by the authors. The igakit package is a Python package used to generate NURBS representations of geometries that can be utilised by the PetIGA finite element framework. The latter utilises data structures and routines of the portable, extensible toolkit for scientific computation (PETSc), [5,6]. The current shell implementation is valid for static, linear problems only, but the software package is well suited for future extensions to geometrically and materially nonlinear regime as well as to dynamic problems. The accuracy of the approach in the pinched cylinder benchmark problem and present comparisons against the h-version of the finite element method with bilinear elements. Quadratic, cubic and quartic NURBS discretizations are compared against the isoparametric bilinear discretization introduced in [7]. The results show that the quadratic and cubic NURBS approximations exhibit notably slower convergence under uniform mesh refinement as the thickness decreases but the quartic approximation converges relatively quickly within the standard variational framework. The authors future work is concerned with building an isogeometric finite element method for modelling nonlinear structural response of thin-walled shells undergoing large rigid-body motions. The aim is to use the model in a aeroelastic framework for the simulation of flapping wings.
Equality conditions for internal entropies of certain classical and quantum models
Gmeiner, Peter
2011-01-01
Mathematical models use information from past observations to generate predictions about the future. If two models make identical predictions the one that needs less information from the past to do this is preferred. It is already known that certain classical models (certain Hidden Markov Models called \\epsilon-machines which are often optimal classical models) are not in general the preferred ones. We extend this result and show that even optimal classical models (models with minimal internal entropy) in general are not the best possible models (called ideal models). Instead of optimal classical models we can construct quantum models which are significantly better but not yet the best possible ones (i.e. they have a strictly smaller internal entropy). In this paper we show conditions when the internal entropies between classical models and specific quantum models coincide. Furthermore it turns out that this situation appears very rarely. An example shows that our results hold only for the specific quantum mo...
Preduction of transport properties of gases using classical nonspherical models
Verlin, J.D.
1976-01-01
The general formulation of the classical kinetic theory, which is needed to predict transport properties of gases in situations where the hydrodynamic equations are valid, is reviewed. A rigid convex model of tetrahedral symmetry is used to predict the Senftleben-Beenakker effect of a static magnetic field on the thermal conductivity and viscosity of pure CH/sub 4/, CD/sub 4/ and CF/sub 4/. The parameters of the model are optimized and are found to assume physically reasonable values. The calculations agree with experiment to a degree comparable to that of similar work on diatomic molecules. A generalized scattering cross section, ..gamma.., is defined which can be evaluated exactly for the limiting cases of a spherical soft potential and rigid ovaloids. For a general soft nonspherical interaction of the Kihara type, a suitable approximation for the momentum dependence is made with the following attributes: ..gamma.. reduces to the form for soft sphere and rigid ovaloid in the limits and the resulting matrix elements of the collision operator can be written in terms of the familiar ..cap omega..* integrals. This formulation is used to investigate thermal diffusion in binary isotopic mixtures of CO. Calculations are made in an 80/sup 0/K to 300/sup 0/K range which includes the inversion temperatures for all mixtures studied. Thermal conductivity and diffusion coefficients of CO are also calculated. The parameters of the model can be adjusted to account for the major features of the experimental data. The physical significance of the parameters is discussed. (auth)
Review of oil spill trajectory modelling in the presence of ice
This study report addresses marine oil spill trajectory modeling, an essential tool for risk assessment, with a focus on the Arctic environment. The first goal is a synthesis of the results into a state-of-knowledge report on oil spill trajectory modeling and its various components. Physical components (i.e. atmospheric forcing, currents, ice and waves), their nature and the way they affect the model are discussed. The mechanics of the internal workings of the model itself are also presented, as well as a brief review of real time data, such as that available from satellite-based remote sensing, and of how emerging technology in this field could enhance the trajectory prediction. A review of existing models and their potential application to the Arctic environment provides information on the scientists and laboratories that are actively engaged in ice-ocean modeling and the tools that could be used. The second goal is the identification of the key gaps that exist in the knowledge of modeling oil spill trajectories.
An analytic model for tool trajectory error in 5-axis machining
B.S. So
2008-12-01
Full Text Available Purpose: This paper proposes an analytical method of evaluating the maximum error by modeling the exact toolpath when the tool traverses singular region in five-axis machining.Design/methodology/approach: It is known that the Numerical Control (NC data obtained from the inversekinematic transformation can generate singular positions, which have incoherent movements on the rotary axes.Such movements cause unexpected errors and abrupt operations, resulting in scoring on the machined surface.To resolve this problem, previous methods have calculated several tool positions during a singular operation,using inverse kinematic equations to predict tool trajectory and approximate the maximum error. This type ofnumerical approach, configuring the tool trajectory, requires a lot of computational time to obtain a sufficientnumber of tool positions in the singular region. We have derived an analytical equation for the tool trajectoryin the singular area by modeling the tool operation, by considering linear and nonlinear parts that are a generalform of the tool trajectory in the singular area and that are suitable for all types of five-axis machine tools. Inaddition, evaluation of the maximum tool-path error shows high accuracy, using our analytical model.Findings: : In this study, we have separated the linear components of the tool trajectory from the nonlinear ones,to propose a tool trajectory model that is applicable to any kind of 5-axis machine. We have also proposed amethod to calculate the maximum deviation error based on the proposed tool trajectory model.Practical implications: The algorithms proposed in this work can be used for evaluating NC data and forlinearization of NC data with singularity.Originality/value: Our algorithm can be used to modify NC data, making the operation smoother and reducingany errors within tolerance.
Failure of the classical field model of Moessbauer spectroscopy
The conventional classical treatment of the field emitted by a Moessbauer nucleus predicts an enhanced counting rate in a two-detector coincidence scheme, whereas quantum electrodynamics does not. Our experiment agrees with QED
Flora-Writing Exemplified by Classical, Conservational and Unconventional Models
Tan, Kit
2004-01-01
There are many ways to compile a Flora. The Flora of Turkey is a remarkable 10-volume work completed within a quarter-century of its inception. A review of the factors contributing to the Flora's success is provided. The Flora of Turkey is a classical Flora with an additional supplement recently produced by Turkish botanists. Flora Hellenica is another example of a classical Flora. Some aspects of its background and production are briefly mentioned. Conservationists consider the endemic ...
The shape of the renormalized trajectory in the two-dimensional O(n) non-linear sigma model
Kuti, Julius; Kuti, Julius; Bock, Wolfgang
1995-01-01
The renormalized trajectory in the multi-dimensional coupling parameter space of the two-dimensional O(3) non-linear sigma model is determined numerically under delta-function block spin transformations using two different Monte Carlo renormalization group techniques. The renormalized trajectory is compared with the straight line of the fixed point trajectory (fixed point action) which leaves the asymptotically free ultraviolet fixed point of the critical surface in the orthogonal direction. Our results show that the renormalized trajectory breaks away from the fixed point trajectory at a correlation length of approximately 3-5, flowing into the high temperature fixed point at zero correlation length. The analytic large N calculation of the renormalized trajectory is also presented in the coupling parameter space of the most general bilinear Hamiltonians. The renormalized trajectory in the large N approximation exhibits a similar shape as in the N=3 case, with the sharp break occurring at a somewhat smaller c...
Wind field and trajectory models for tornado-propelled objects. Final report 2
The report contains the results of the second phase of a research program which has as its objective the development of a mathematical model to predict the trajectory of tornado-borne objects postulated to be in the vicinity of nuclear power plants. An improved tornado wind field model satisfies the no-slip ground boundary condition of fluid mechanics and includes the functional dependence of eddy viscosity with altitude. Sub-scale wind tunnel data are obtained for all of the missiles currently specified for nuclear plant design. Confirmatory full-scale data are obtained for a 12-inch pipe and automobile. The original six-degree-of-freedom trajectory model is modified to include the improved wind field and increased capability as to body shapes and inertial characteristics that can be handled. The improved trajectory model is used to calculate maximum credible speeds, which for all of the heavy missiles are considerably less than those currently specified for design. Equivalent coefficients for use in three-degree-of-freedom models are developed and the sensitivity of range and speed to various trajectory parameters for the 12-inch diameter pipe is examined
Application of Back Trajectory Model to Predict Long Range Transport of Pollutant
Trans-boundary haze pollution in Malaysia has become an issue that created a public attention over the past several years. The presence of haze not only caused by internal and external sources but it sometime coincided with the El Nino phenomenon which prolonged the dry season during the southwest monsoon in May to September. In this study fine particulate data (PM 2.5) of Klang Valley region covering the period from 1997 to 2008 were used to investigate the source location that responsible for the long range transport of pollutant. Back trajectory model the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) was used to calculate the air mass backward trajectories up to 120 hours (5 days) for the days when fine particle were sampled. (author)
Lock-in and break-out from technological trajectories : Modeling and policy implications
Dolfsma, W.A.; Leydesdorff, L.
2009-01-01
The prevailing models explaining how technologies develop along a specific trajectory largely focus on the circumstances that lead to technological lock-in. We contribute substantially to this area of research by investigating the circumstances under which technological development may break-out of
Trajectories of Attentional Development: An Exploration with the Master Activation Map Model
Michael, George A.; Lete, Bernard; Ducrot, Stephanie
2013-01-01
The developmental trajectories of several attention components, such as orienting, inhibition, and the guidance of selection by relevance (i.e., advance knowledge relevant to the task) were investigated in 498 participants (ages 7, 8, 9, 10, 11, and 20). The paradigm was based on Michael et al.'s (2006) master activation map model and consisted of…
Modelling cosmic ray intensities along the Ulysses trajectory
Ndiitwani, D. C.; Ferreira, S. E. S.; Potgieter, M. S.; Heber, B.
2005-01-01
International audience Time dependent cosmic ray modulation in the inner heliosphere is studied by comparing results from a 2-D, time-dependent cosmic ray transport model with Ulysses observations. A compound approach, which combines the effects of the global changes in the heliospheric magnetic field magnitude with drifts to establish a realistic time-dependence, in the diffusion and drift coefficients, are used. We show that this model results in realistic cosmic ray modulation from the ...
Modeling of Human Arm Energy Expenditure for Predicting Energy Optimal Trajectories
L. Zhou
2011-07-01
Full Text Available Human arm motion can inspire the trajectory planning of anthropomorphic robotic arms to achieve energy-efficient movements. An approach for predicting metabolic cost in the planar human arm motion by means of the biomechanical simulation is proposed in this work. Two biomechanical models, including an analytical model and a musculoskeletal model, are developed to implement the proposed approach. The analytical model is developed by modifying a human muscle expenditure model, in which the muscles are grouped as torque providers for computation efficiency. In the musculoskeletal model, the predication of metabolic cost is conducted on the basis of individual muscles. With the proposed approach, metabolic costs for parameterized target-reaching arm motions are calculated and utilized to identify optimal arm trajectories.
Modeling Classical Swine Fever Outbreak-Related Outcomes.
Yadav, Shankar; Olynk Widmar, Nicole J; Weng, Hsin-Yi
2016-01-01
The study was carried out to estimate classical swine fever (CSF) outbreak-related outcomes, such as epidemic duration and number of infected, vaccinated, and depopulated premises, using defined most likely CSF outbreak scenarios. Risk metrics were established using empirical data to select the most likely CSF outbreak scenarios in Indiana. These scenarios were simulated using a stochastic between-premises disease spread model to estimate outbreak-related outcomes. A total of 19 single-site (i.e., with one index premises at the onset of an outbreak) and 15 multiple-site (i.e., with more than one index premises at the onset of an outbreak) outbreak scenarios of CSF were selected using the risk metrics. The number of index premises in the multiple-site outbreak scenarios ranged from 4 to 32. The multiple-site outbreak scenarios were further classified into clustered (N = 6) and non-clustered (N = 9) groups. The estimated median (5th, 95th percentiles) epidemic duration (days) was 224 (24, 343) in the single-site and was 190 (157, 251) and 210 (167, 302) in the clustered and non-clustered multiple-site outbreak scenarios, respectively. The median (5th, 95th percentiles) number of infected premises was 323 (0, 488) in the single-site outbreak scenarios and was 529 (395, 662) and 465 (295, 640) in the clustered and non-clustered multiple-site outbreak scenarios, respectively. Both the number and spatial distributions of the index premises affected the outcome estimates. The results also showed the importance of implementing vaccinations to accommodate depopulation in the CSF outbreak controls. The use of routinely collected surveillance data in the risk metrics and disease spread model allows end users to generate timely outbreak-related information based on the initial outbreak's characteristics. Swine producers can use this information to make an informed decision on the management of swine operations and continuity of business, so that potential losses could
Modeling classical swine fever outbreak-related outcomes
Shankar eYadav
2016-02-01
Full Text Available The study was carried out to estimate classical swine fever (CSF outbreak-related outcomes such as epidemic duration and number of infected, vaccinated, and depopulated premises, using defined most likely CSF outbreak scenarios. Risk metrics were established using empirical data to select the most likely CSF outbreak scenarios in Indiana. The scenarios were simulated using a stochastic between-premises disease spread model to estimate outbreak-related outcomes. A total of 19 single-site (i.e., with a single-index premises at the onset of an outbreak and 15 multiple-site (i.e., with more than one index premises at the onset of an outbreak outbreak scenarios of CSF were selected using the risk metrics. The number of index premises in the multiple-site outbreak scenarios ranged from 4 to 32. The multiple-site outbreak scenarios were further classified into clustered (N=6 and non-clustered (N=9 groups. The estimated median (5th, 95th percentiles epidemic duration (days was 224 (24, 343 in the single-site and was 190 (157, 251 and 210 (167, 302 in the clustered and non-clustered multiple-site outbreak scenarios, respectively. The median (5th, 95th percentiles number of infected premises was 323 (0, 488 in the single-site outbreak scenarios and was 529 (395, 662 and 465 (295, 640 in the clustered and non-clustered multiple-site outbreak scenarios, respectively. Both the number and spatial distribution of the index premises affected the outcome estimates. The results also showed the importance of implementing vaccinations to accommodate depopulation in the CSF outbreak controls. The use of routinely collected surveillance data in the risk metrics and disease spread model allows end users to generate timely outbreak-related information based on the initial outbreak’s characteristics. Swine producers can use this information to make an informed decision on management of swine operations and continuity of business so that potential losses could be
Trajectory Tracking Control of Mobile Robot by Fluid Model
Miyata, Junichi; Murakami, Toshiyuki
This paper describes a fluid model based path planning of mobile robot. In the previous research, the authors have already proposed TBSA (Time Based Spline Approach) for smooth motion of industrial robots(1). The TBSA is a powerful method in industrial applications, but the future position and velocity commands must be known to use it. In the general applications of repeat motion, this assumption is acceptable. In the path planning of mobile robot, however, the future position and velocity commands are unknown. To address the above issue, a strategy to generate the path of mobile robot based on fluid model is proposed in this paper. The combination of the TBSA and the generated path by fluid model brings a smooth motion of mobile robots.
Maldonado-Molina, Mildred M.; Jennings, Wesley G.; Komro, Kelli A.
2010-01-01
Several studies have investigated factors associated with physical aggression during adolescence. Yet, little is known about the longitudinal relationship between drug use, particularly alcohol use, and physical aggression among minority youth. The present study examined the effects of alcohol and substance use at age 11 on trajectories of…
A Non-Classical Linear Xenomorph as a Model for Quantum Causal Space
Raptis, Ioannis
1999-01-01
A quantum picture of the causal structure of Minkowski space M is presented. The mathematical model employed to this end is a non-classical version of the classical topos {H} of real quaternion algebras used elsewhere to organize the perceptions of spacetime events of a Boolean observer into M. Certain key properties of this new quantum topos are highlighted by contrast against the corresponding ones of its classical counterpart {H} modelling M and are seen to accord with some key features of...
Corrections to TDHF trajectories in a simple model
Expectation values of one and two body operators are compared in the exact and TDHF wave function in the Lipkin model. A ''linear response'' correction to the evolution of two body operators, in particular dispersions, is proposed. The correction is not small and it improves substantially the agreement of two body quantities with exact results. (Auth.)
Modelling cosmic ray intensities along the Ulysses trajectory
D. C. Ndiitwani
2005-03-01
Full Text Available Time dependent cosmic ray modulation in the inner heliosphere is studied by comparing results from a 2-D, time-dependent cosmic ray transport model with Ulysses observations. A compound approach, which combines the effects of the global changes in the heliospheric magnetic field magnitude with drifts to establish a realistic time-dependence, in the diffusion and drift coefficients, are used. We show that this model results in realistic cosmic ray modulation from the Ulysses launch (1990 until recently (2004 when compared to 2.5-GV electron and proton and 1.2-GV electron and Helium observations from this spacecraft. This approach is also applied to compute radial gradients present in 2.5-GV cosmic ray electron and protons in the inner heliosphere. The observed latitude dependence for both positive and negative charged particles during both the fast latitude scan periods, corresponding to different solar activity conditions, could also be realistically computed. For this an additional reduction in particle drifts (compared to diffusion toward solar maximum is needed. This results in a realistic charge-sign dependent modulation at solar maximum and the model is also applied to predict charge-sign dependent modulation up to the next expected solar minimum.
Construction of classical and quantum integrable field models unravelling hidden possibilities
Anjan Kundu
2015-11-01
Reviewing briefly the concept of classical and quantum integrable systems, we propose an alternative Lax operator approach, leading to quasi-higher-dimensional integrable model, unravelling some hidden dimensions in integrable systems. As an example, we construct a novel integrable quasi-two-dimensional NLS equation at the classical and the quantum levels with intriguing application in rogue wave modelling.
Determining Trajectory of Triboelectrically Charged Particles, Using Discrete Element Modeling
2008-01-01
The Kennedy Space Center (KSC) Electrostatics and Surface Physics Laboratory is participating in an Innovative Partnership Program (IPP) project with an industry partner to modify a commercial off-the-shelf simulation software product to treat the electrodynamics of particulate systems. Discrete element modeling (DEM) is a numerical technique that can track the dynamics of particle systems. This technique, which was introduced in 1979 for analysis of rock mechanics, was recently refined to include the contact force interaction of particles with arbitrary surfaces and moving machinery. In our work, we endeavor to incorporate electrostatic forces into the DEM calculations to enhance the fidelity of the software and its applicability to (1) particle processes, such as electrophotography, that are greatly affected by electrostatic forces, (2) grain and dust transport, and (3) the study of lunar and Martian regoliths.
Modeling and Robust Trajectory Tracking Control for a Novel Six-Rotor Unmanned Aerial Vehicle
Chengshun Yang; Zhong Yang; Xiaoning Huang; Shaobin Li; Qiang Zhang
2013-01-01
Modeling and trajectory tracking control of a novel six-rotor unmanned aerial vehicle (UAV) is concerned to solve problems such as smaller payload capacity and lack of both hardware redundancy and anticrosswind capability for quad-rotor. The mathematical modeling for the six-rotor UAV is developed on the basis of the Newton-Euler formalism, and a second-order sliding-mode disturbance observer (SOSMDO) is proposed to reconstruct the disturbances of the rotational dynamics. In consideration of ...
A model for estimating radiation doses resulting from long range atmospheric transport of released radionuclides in accidents is precented. The model (TRADOS) is able to treat changing diffusion conditions. For example the plume can be exposed to temporary rain, changes in turbulence and mixing depth. This can result in considerable changes in individual doses. The method is applied to an example trajectory and the doses caused by a serious reactor accident are calculated
The classical Stefan problem basic concepts, modelling and analysis
Gupta, SC
2003-01-01
This volume emphasises studies related toclassical Stefan problems. The term "Stefan problem" isgenerally used for heat transfer problems with phase-changes suchas from the liquid to the solid. Stefan problems have somecharacteristics that are typical of them, but certain problemsarising in fields such as mathematical physics and engineeringalso exhibit characteristics similar to them. The term``classical" distinguishes the formulation of these problems fromtheir weak formulation, in which the solution need not possessclassical derivatives. Under suitable assumptions, a weak solutioncould be as good as a classical solution. In hyperbolic Stefanproblems, the characteristic features of Stefan problems arepresent but unlike in Stefan problems, discontinuous solutions areallowed because of the hyperbolic nature of the heat equation. Thenumerical solutions of inverse Stefan problems, and the analysis ofdirect Stefan problems are so integrated that it is difficult todiscuss one without referring to the other. So no...
On q-deformed supersymmetric classical mechanical models
Based on the idea of quantum groups and paragrassmann variables, we present a generalization of supersymmetric classical mechanics with a deformation parameter q=exp 2πi/k dealing with the k=3 case. The coordinates of the q-superspace are a commuting parameter t and a paragrassmann variable θ, where θ3=0. The generator and covariant derivative are obtained, as well as the action for some possible superfields. (author). 13 refs
Comment on "Simple improvements to classical bubble nucleation models"
Schmelzer, Jürn W. P.; Baidakov, Vladimir G.
2016-08-01
A critical analysis of several statements concerning experimental studies, molecular dynamics simulations, and the theoretical interpretation of bubble nucleation processes is performed. In particular, it is shown that the Tolman equation does not supply us, in general, with a satisfactory theoretically founded description of the curvature dependence of the surface tension and the dependence of the steady-state nucleation rate of bubbles and droplets on supersaturation in the framework of classical nucleation theory.
Maldonado-Molina, Mildred M.; Jennings, Wesley G.; Komro, Kelli A.
2009-01-01
Several studies have investigated factors associated with physical aggression during adolescence. Yet, little is known about the longitudinal relationship between drug use, particularly alcohol use, and physical aggression among minority youth. The present study examined the effects of alcohol and substance use at age 11 on trajectories of physical aggression over time (ages 12–14) among urban adolescents from Chicago, IL. Data from the Project Northland Chicago (n = 3038, 49.4% female) was u...
Characterization of bead trajectories through the draft tube of a turbine physical model
Weiland, M. A. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Mueller, R. P. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Carlson, T. J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Deng, Z. D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); McKinstry, C. A. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2005-02-01
The U.S. Army Corps of Engineers (USACE) makes extensive use of 1:25 scale Plexiglass models of hydroelectric turbines along the Columbia River to study turbine hydraulic performance and to identify potential hazards for fish passing through the turbines. Plastic beads are sent through the models and imaging has been done with laser Doppler velocimetry and high-speed videography to measure flow field variables and to study the probable paths of fish through the turbine units. Understanding has been limited by the lack of data showing actual bead trajectories in three dimensions (3-D) and the lack of quantified velocity, acceleration, and other kinematics describing the trajectories of beads as they pass through the physical models.
Aspects of integrability in a classical model for non-interacting fermionic fields
Grosse-Holz, Simon; Richter, Klaus; Urbina, Juan Diego
2015-01-01
In this work we investigate the issue of integrability in a classical model for noninteracting fermionic fields. This model is constructed via classical-quantum correspondence obtained from the semiclassical treatment of the quantum system. Our main finding is that the classical system, contrary to the quantum system, is not integrablein general. Regarding this contrast it is clear that in general classical models for fermionic quantum systems have to be handled with care. Further numerical investigation of the system showed that there may be islands of stability in the phase space. We also investigated a similar model that is used in theoretical chemistry and found this one to be most probably integrable, although also here the integrability is not assured by the quantum-classical correspondence principle.
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)
S.E. Baumgartner; L. Leydesdorff
2013-01-01
Group-based trajectory modeling (GBTM) is applied to the citation curves of articles in six journals and to all citable items in a single field of science (virology, 24 journals) to distinguish among the developmental trajectories in subpopulations. Can citation patterns of highly-cited papers be di
SONG Zhen-duo; XU Wen-xu; DIAO Qing
2006-01-01
Puts forward a design project of light anti-tank missile controlled by gesture replication at the terminal trajectory, and it can hit the top of tank. The paper studies the closed-loop control rigid ballistic model and simulation for the straight and fleeting flight and terminal replication trajectory for both fixed and moving targets. Simulation results show the program to be practicable.
Classical Anthropic Everett model: indeterminacy in a preordained multiverse
Carter, Brandon
2012-01-01
Although ultimately motivated by quantum theoretical considerations, Everett's many-world idea remains valid, as an approximation, in the classical limit. However to be applicable it must in any case be applied in conjunction with an appropriate anthropic principle, whose precise formulation involves an anthropic quotient that can be normalised to unity for adult humans but that would be lower for infants and other animals. The outcome is a deterministic multiverse in which the only function of chance is the specification of one's particular identity.
A Trajectory-Oriented, Carriageway-Based Road Network Data Model, Part 2: Methodology
LI Xiang; LIN Hui
2006-01-01
This is the second of a three-part series of papers which presents the principle and architecture of the CRNM, a trajectory-oriented, carriageway-based road network data model. The first part of the series has introduced a general background of building trajectory-oriented road network data models, including motivation, related works, and basic concepts. Based on it, this paper describs the CRNM in detail. At first, the notion of basic roadway entity is proposed and discussed. Secondly, carriageway is selected as the basic roadway entity after compared with other kinds of roadway, and approaches to representing other roadways with carriageways are introduced. At last, an overall architecture of the CRNM is proposed.
H. Riede; Jöckel, P.; Sander, R.
2009-01-01
We present a novel method for the quantification of transport, chemistry, and mixing along atmospheric trajectories based on a consistent model hierarchy. The hierarchy consists of the new atmospheric-chemistry trajectory-box model CAABA/MJT and the three-dimensional (3-D) global ECHAM/MESSy atmospheric-chemistry (EMAC) general circulation model. CAABA/MJT employs the atmospheric box model CAABA in a configuration using the atmospheric-chemistry submodel MECCA (M), the photochemistry submodel...
Satellite observations and modeling of oil spill trajectories in the Bohai Sea
Xu, Qing; Li, Xiaofeng; Wei, Yongliang;
2013-01-01
On June 4 and 17, 2011, separate oil spill accidents occurred at two oil platforms in the Bohai Sea, China. The oil spills were subsequently observed on different types of satellite images including SAR (Synthetic Aperture Radar), Chinese HJ-1-B CCD and NASA MODIS. To illustrate the fate of the oil...... spills, we performed two numerical simulations to simulate the trajectories of the oil spills with the GNOME (General NOAA Operational Modeling Environment) model. For the first time, we drive the GNOME with currents obtained from an operational ocean model (NCOM, Navy Coastal Ocean Model) and surface...
Modeling the trajectory of a micro particle in a dielectrophoresis device.
Kharboutly, Mohamed; Gauthier, Michaël; Chaillet, Nicolas
2010-01-01
Micro and nano-particles can be trapped by a non uniform electric field through the effect of dielectrophoretic principle. Dielectrophoresis (DEP) is used to separate, manipulate and detect micro particles in several domains, such as in biological or Carbon Nano-Tubes (CNTs) manipulations. Current methods to simulate the trajectory of micro-particles under a DEP force field are based on Finite Elements Modeling (FEM) which requires new simulations when the electrodes potentials are changed, o...
Macek, Karel; Rojíček, J.; Bičík, V.
Vol. XVIII. Cham: Springer, 2013, s. 267-274. (XVIII. 217). ISBN 978-3-319-00550-8. [10th International Symposium on Distributed Computing and Artificial Intelligence . Salamanca (ES), 22.05.2013-24.05.2013] Institutional support: RVO:67985556 Keywords : Empirical function minimization * black-box modeling * simplification * refining * dynamic building control Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2013/AS/macek-trajectory optimization under changing.pdf
A pre-quantum classical statistical model with infinite-dimensional phase space
We study the problem of correspondence between classical and quantum statistical models. We show that (contrary to a rather common opinion) it is possible to construct a natural pre-quantum classical statistical model. The crucial point is that such a pre-quantum classical statistical model is not the conventional classical statistical mechanics on the phase space R2n, but its infinite-dimensional analogue. Here the phase space Ω = H x H, where H is the (real separable) Hilbert space. The classical → quantum correspondence is based on the Taylor expansion of classical physical variables-maps f:Ω → R. The space of classical statistical states consists of Gaussian measures on Ω having zero mean value and dispersion ∼h. The quantum statistical model is obtained as the limh→0 of the classical one. All quantum states including so-called 'pure states' (wavefunctions) are simply Gaussian fluctuations of the 'vacuum field', ω = 0 element of Ω, having dispersions of the Planck magnitude
Cotton, Stephen J; Miller, William H
2016-03-01
In a recent series of papers, it has been illustrated that a symmetrical quasi-classical (SQC) windowing model applied to the Meyer-Miller (MM) classical vibronic Hamiltonian provides an excellent description of a variety of electronically non-adiabatic benchmark model systems for which exact quantum results are available for comparison. In this paper, the SQC/MM approach is used to treat energy transfer dynamics in site-exciton models of light-harvesting complexes, and in particular, the well-known 7-state Fenna-Mathews-Olson (FMO) complex. Again, numerically "exact" results are available for comparison, here via the hierarchical equation of motion (HEOM) approach of Ishizaki and Fleming, and it is seen that the simple SQC/MM approach provides very reasonable agreement with the previous HEOM results. It is noted, however, that unlike most (if not all) simple approaches for treating these systems, because the SQC/MM approach presents a fully atomistic simulation based on classical trajectory simulation, it places no restrictions on the characteristics of the thermal baths coupled to each two-level site, e.g., bath spectral densities (SD) of any analytic functional form may be employed as well as discrete SD determined experimentally or from MD simulation (nor is there any restriction that the baths be harmonic), opening up the possibility of simulating more realistic variations on the basic site-exciton framework for describing the non-adiabatic dynamics of photosynthetic pigment complexes. PMID:26761191
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Kamenshchik, Alexander Y.; Manti, Serena
2012-01-01
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical ...
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Kamenshchik, A.; Manti, S.
2013-01-01
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical ...
Pre-equilibrium nuclear reactions: An introduction to classical and quantum-mechanical models
In studies of light-ion induced nuclear reactions one distinguishes three different mechanisms: direct, compound and pre-equilibrium nuclear reactions. These reaction processes can be subdivided according to time scales or, equivalently, the number of intranuclear collisions taking place before emission. Furthermore, each mechanism preferably excites certain parts of the nuclear level spectrum and is characterized by different types of angular distributions. This presentation includes description of the classical, exciton model, semi-classical models, with some selected results, and quantum mechanical models. A survey of classical versus quantum-mechanical pre-equilibrium reaction theory is presented including practical applications
A generalization of a classical model in contract theory: The agent behavior
Gutiérrez, Francisco; Moreno, Stefany
2011-01-01
We present a first approximation of agent behaviour in a generalized model in contract theory. This model relaxes some of the the assumptions of one of the classical models allowing to include a broader range of agents. We introduce the motivation for the agent and reinterpret the classical definition of risk perception. Besides, we analyze different scenarios for the relation between the effort exerted by the agent and the probability that he gets an especfic result.
Bogolubov, N.N.; Prykarpatsky, A. K.
2009-01-01
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry approach developed in [6,7,9], the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. The Dirac-type quantization procedure for the considered alternative electrodynamics models, based on the obtained cano...
H. Riede
2009-12-01
Full Text Available We present a novel method for the quantification of transport, chemistry, and mixing along atmospheric trajectories based on a consistent model hierarchy. The hierarchy consists of the new atmospheric-chemistry trajectory-box model CAABA/MJT and the three-dimensional (3-D global ECHAM/MESSy atmospheric-chemistry (EMAC general circulation model. CAABA/MJT employs the atmospheric box model CAABA in a configuration using the atmospheric-chemistry submodel MECCA (M, the photochemistry submodel JVAL (J, and the new trajectory submodel TRAJECT (T, to simulate chemistry along atmospheric trajectories, which are provided offline. With the same chemistry submodels coupled to the 3-D EMAC model and consistent initial conditions and physical parameters, a unique consistency between the two models is achieved. Since only mixing processes within the 3-D model are excluded from the model consistency, comparisons of results from the two models allow to separate and quantify contributions of transport, chemistry, and mixing along the trajectory pathways. Consistency of transport between the trajectory-box model CAABA/MJT and the 3-D EMAC model is achieved via calculation of kinematic trajectories based on 3-D wind fields from EMAC using the trajectory model LAGRANTO. The combination of the trajectory-box model CAABA/MJT and the trajectory model LAGRANTO can be considered as a Lagrangian chemistry-transport model (CTM moving isolated air parcels. The procedure for obtaining the necessary statistical basis for the quantification method is described as well as the comprehensive diagnostics with respect to chemistry.
The quantification method presented here allows to investigate the characteristics of transport, chemistry, and mixing in a grid-based 3-D model. The analysis of chemical processes within the trajectory-box model CAABA/MJT is easily extendable to include, for example, the impact of different transport pathways or of mixing processes onto
Study of Mechanical Model of Sports Ball’S Flight Trajectory and Its Application
Xiaoyan Yu
2013-05-01
Full Text Available In order to resolve the controversy of ball games the placement problem fined on the other hand, to promote the teaching and training ball flight trajectory. Tennis is the main object of study, use of literature, mathematical statistics and experimental research methods and to establish an appropriate mathematical model, using MATLAB software to accurately determine the trajectory and impact point of the ball's flight, used in teaching, training and competition in. The conclusions show that the law, accurate data analysis using MATLAB software can simulate the flight of the ball moving on sports development has a very good help provide a new way of thinking for the in-depth study the pattern of winning ball games and similar sports teaching, training and selection of athletes is an important complementary and valuable.
Trajectory attractors for the Sun–Liu model for nematic liquid crystals in 3D
In this paper we prove the existence of a trajectory attractor (in the sense of Chepyzhov and Vishik) for a nonlinear PDE system obtained from a 3D liquid crystal model accounting for stretching effects. The system couples a nonlinear evolution equation for the director d (introduced in order to describe the preferred orientation of the molecules) with an incompressible Navier–Stokes equation for the evolution of the velocity field u. The technique is based on the introduction of a suitable trajectory space and of a metric accounting for the double-well type nonlinearity contained in the director equation. Finally, a dissipative estimate is obtained by using a proper integrated energy inequality. Both the cases of (homogeneous) Neumann and (non-homogeneous) Dirichlet boundary conditions for d are considered. (paper)
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.
Modeling and Robust Trajectory Tracking Control for a Novel Six-Rotor Unmanned Aerial Vehicle
Chengshun Yang
2013-01-01
Full Text Available Modeling and trajectory tracking control of a novel six-rotor unmanned aerial vehicle (UAV is concerned to solve problems such as smaller payload capacity and lack of both hardware redundancy and anticrosswind capability for quad-rotor. The mathematical modeling for the six-rotor UAV is developed on the basis of the Newton-Euler formalism, and a second-order sliding-mode disturbance observer (SOSMDO is proposed to reconstruct the disturbances of the rotational dynamics. In consideration of the under-actuated and strong coupling properties of the six-rotor UAV, a nested double loops trajectory tracking control strategy is adopted. In the outer loop, a position error PID controller is designed, of which the task is to compare the desired trajectory with real position of the six-rotor UAV and export the desired attitude angles to the inner loop. In the inner loop, a rapid-convergent nonlinear differentiator (RCND is proposed to calculate the derivatives of the virtual control signal, instead of using the analytical differentiation, to avoid “differential expansion” in the procedure of the attitude controller design. Finally, the validity and effectiveness of the proposed technique are demonstrated by the simulation results.
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
Alexis, Nutz; Pierre, Dietrich; Vafe, Soumahoro; Mathieu, Schuster; Jean-François, Ghienne
2016-04-01
Deltas simultaneously respond to modifications in parameters such as water discharge, sediment supply and base-level change. Those parameters are driven by a number of potential external forcing processes, nevertheless mainly corresponding to tectonism and climate. In this study, geomorphology and numerical modeling are coupled in order to provide analysis of the delta complex of the Turkwel River (Lake Turkana, Kenya). The Turkwel delta complex is 35 km long, forming one of the major deltaic systems that has fringed Lake Turkana during the Holocene. It developed during the lake level regression at the end of the holocene African Humid Period and correspond to a typical forced-regressive delta. Trajectory analysis was performed on three transects cross-cutting the deltaic complex. Transects consistently display five slightly descending (slope gradient: >0° to 0.4°) plateaus separated by four abrupt steps of higher slope gradients (1° to 3.8°). Conventional interpretations presume that the deltaic trajectory results from either (1) four abrupt accelerations in lake level fall during the continuous regression, (2) four abrupt declines in sediment supply and/or water discharge during a steady lake level fall or (3) a combination of both. We used numerical stratigraphic modeling (Dionisos) in order to test the aforementioned hypotheses as the origin of observed trajectories. We concluded that causal relationships between sediment supply, lake level change and progradation trajectory are not as straightforward as recurrently envisioned. We think that this contribution brings new lights on the relationships between deltaic architectures and controlling factors.
The impact of temperature resolution on trajectory modeling of stratospheric water vapour
T. Wang
2014-11-01
Full Text Available Lagrangian trajectories driven by reanalysis meteorological fields are frequently used to study water vapour (H2O in the stratosphere, in which the tropical cold-point temperatures regulate H2O amount entering the stratosphere. Therefore, the accuracy of temperatures in the tropical tropopause layer (TTL is of great importance for trajectory studies. Currently, most reanalyses, such as the NASA MERRA (Modern Era Retrospective-Analysis for Research and Applications, only provide temperatures with ~1.2 km vertical resolution in the TTL, which has been argued to introduce uncertainties in the simulations. In this paper, we quantify this uncertainty by comparing the trajectory results using MERRA temperatures on model levels (traj.MER-T to those using temperatures in finite resolutions, including GPS temperatures (traj.GPS-T and MERRA temperatures adjusted to recover wave-induced variability underrepresented by the current ~1.2 km vertical resolution (traj.MER-Twave. Comparing with traj.MER-T, traj.GPS-T has little impact on simulated stratospheric H2O (changes ~0.1 ppmv, whereas traj.MER-Twave tends to dry air by 0.2–0.3 ppmv. The bimodal dehydration peaks in traj.MER-T due to limited vertical resolution disappear in traj.GPS-T and traj.MER-Twave by allowing the cold-point tropopause to be found at finer vertical levels. Despite these differences in absolute values of predicted H2O and vertical dehydration patterns, there is virtually no difference in the interannual variability in different runs. Overall, we find that the finite resolution of temperature has limited impact on predicted H2O in the trajectory model.
A Non-Classical Linear Xenomorph as a Model for Quantum Causal Space
Raptis, I
1999-01-01
A quantum picture of the causal structure of Minkowski space M is presented. The mathematical model employed to this end is a non-classical version of the classical topos {H} of real quaternion algebras used elsewhere to organize the perceptions of spacetime events of a Boolean observer into M. Certain key properties of this new quantum topos are highlighted by contrast against the corresponding ones of its classical counterpart {H} modelling M and are seen to accord with some key features of the algebraically quantized causal set structure.
Models of measurement for quantum fields and for classical continuous random fields
Morgan, Peter
2006-01-01
A quantum field model for an experiment describes thermal fluctuations explicitly and quantum fluctuations implicitly, whereas a comparable continuous random field model would describe both thermal and quantum fluctuations explicitly. An ideal classical measurement does not affect the results of later measurements, in contrast to ideal quantum measurements, but we can describe the consequences of the thermal and quantum fluctuations of classically non-ideal measurement apparatuses explicitly....
Optimum Trajectory of Dynamic Input-Output Balance Model for Open Economy
Lyashenko, Igor; Lyashenko, Olena
2006-01-01
When export and import is connected with output of basic production, and criterion functional represents a final state of economy, the generalization of classical qualitative results of the main-line theory on a case of dynamic input-output balance optimization model for open economy is given.
Generalized continua as models for classical and advanced materials
Forest, Samuel
2016-01-01
This volume is devoted to an actual topic which is the focus world-wide of various research groups. It contains contributions describing the material behavior on different scales, new existence and uniqueness theorems, the formulation of constitutive equations for advanced materials. The main emphasis of the contributions is directed on the following items - Modelling and simulation of natural and artificial materials with significant microstructure, - Generalized continua as a result of multi-scale models, - Multi-field actions on materials resulting in generalized material models, - Theories including higher gradients, and - Comparison with discrete modelling approaches.
Samuels, Marina A; Reed, Matthew P; Arbogast, Kristy B; Seacrist, Thomas
2016-08-01
Designing motor vehicle safety systems requires knowledge of whole body kinematics during dynamic loading for occupants of varying size and age, often obtained from sled tests with postmortem human subjects and human volunteers. Recently, we reported pediatric and adult responses in low-speed (shape is also relevant for restraint design, this study quantified the time-series trajectories using basis splines and developed a statistical model for predicting trajectories as a function of body dimension or age. Previously collected trajectories of the head, spine, and pelvis were modeled using cubic basis splines with eight control points. A principal component analysis was conducted on the control points and related to erect seated height using a linear regression model. The resulting statistical model quantified how trajectories became shorter and flatter with increasing body size, corresponding to the validation data-set. Trajectories were then predicted for erect seated heights corresponding to pediatric and adult anthropomorphic test devices (ATDs), thus generating performance criteria for the ATDs based on human response. This statistical model can be used to predict trajectories for a subject of specified anthropometry and utilized in subject-specific computational models of occupant response. PMID:26428257
On convergence of trajectory attractors of the 3D Navier-Stokes-α model as α approaches 0
We study the relations between the long-time dynamics of the Navier-Stokes-α model and the exact 3D Navier-Stokes system. We prove that bounded sets of solutions of the Navier-Stokes-α model converge to the trajectory attractor A0 of the 3D Navier-Stokes system as the time approaches infinity and α approaches zero. In particular, we show that the trajectory attractor Aα of the Navier-Stokes-α model converges to the trajectory attractor A0 of the 3D Navier-Stokes system as α→0+. We also construct the minimal limit Amin(subset or equal A0) of the trajectory attractor Aα as α→0+ and prove that the set Amin is connected and strictly invariant. Bibliography: 35 titles.
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...
Comparisons of classical and quantum dynamics for initially localized states
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
Trajectory prediction of saccadic eye movements using a compressed exponential model
Han, Peng; Saunders, Daniel R.; Woods, Russell L.; Luo, Gang
2013-01-01
Gaze-contingent display paradigms play an important role in vision research. The time delay due to data transmission from eye tracker to monitor may lead to a misalignment between the gaze direction and image manipulation during eye movements, and therefore compromise the contingency. We present a method to reduce this misalignment by using a compressed exponential function to model the trajectories of saccadic eye movements. Our algorithm was evaluated using experimental data from 1,212 saccades ranging from 3° to 30°, which were collected with an EyeLink 1000 and a Dual-Purkinje Image (DPI) eye tracker. The model fits eye displacement with a high agreement (R2 > 0.96). When assuming a 10-millisecond time delay, prediction of 2D saccade trajectories using our model could reduce the misalignment by 30% to 60% with the EyeLink tracker and 20% to 40% with the DPI tracker for saccades larger than 8°. Because a certain number of samples are required for model fitting, the prediction did not offer improvement for most small saccades and the early stages of large saccades. Evaluation was also performed for a simulated 100-Hz gaze-contingent display using the prerecorded saccade data. With prediction, the percentage of misalignment larger than 2° dropped from 45% to 20% for EyeLink and 42% to 26% for DPI data. These results suggest that the saccade-prediction algorithm may help create more accurate gaze-contingent displays. PMID:23902753
Quantum integrable models of interacting bosons and classical r-matrices with spectral parameters
Skrypnyk, T.
2015-11-01
Using the technique of classical r-matrices with spectral parameters we construct a general form of quantum Lax operators of interacting boson systems corresponding to an arbitrary simple (or reductive) Lie algebra. We prove quantum integrability of these models in the physically important case of g = gl(n) and "diagonal" in the root basis classical r-matrices. We consider in detail two classes of non-skew-symmetric classical r-matrices with spectral parameters and obtain the corresponding quantum Lax operators and quantum integrable many-boson hamiltonians that generalize Bose-Hubbard dimer hamiltonians.