Phase Space Model Research Articles

Analysis of Observed Chaotic Data

Regular Dynamics: Newton to Poincare KAM Theorem | Bifurcations: Routes to Chaos, Stability and Instability | Reconstruction of Phase Space: Regular and Chaotic Motions Observed Chaos | Choosing Time Delays: Chaos as an Information Source Average Mutual Information. | Choosing the Dimension of Reconstructed Phase Space | Invariants of the Motion: Global & Local Lyapunov Exponents Lorenz Model | Modeling Chaos: Local & Global Models Phase Space Models | Signal Separation: Probabilistic Cleaning 'Blind' Signal Separation | Control and Chaos: Parametric Control Examples of Control (including magnetoelastic ribbon, electric circuits, cardiac tissue) | Synchronization of Chaotic Systems: Identical or Dissimilar Systems Chaotic Nonlinear Circuits | Other Example Systems: Laser Intensity Fluctuations Volume Fluctuations of the Great Salt Lake Motion in a Fluid Boundary Layer | Estimating in Chaos: Cramer-Rao Bounds | The Chaos Toolkit: Making 'Physics' out of Chaos

On the Dynamics of Planetary Flow Regimes. Part II: Results from a Hierarchy of Orographically Forced Models

The relationship between steady states of the large-scale flow regimes revealed by multimodality in phase space and quasi-resonant axes of a linearized atmospheric model (neutral vectors) is investigated by means of a hierarchy of three hemispheric quasigeostrophic(QG) models, in which the flow is relaxed toward a zonally symmetric equilibrium state and orography provides the only source of asymmetric forcing. Two of these models describe only the interaction between the mean zonal flow and planetary waves of zonal wavenumber 3, including one or two meridional wavenumbers. The third model also has a zonal wavenumber-3 symmetry, but includes waves up to total wavenumber 21, and therefore is able to properly represent the interactions between planetary waves and baroclinically unstable synoptic-scale waves. Three stationary solutions are found for the highly truncated models, two of which represent states with large wave amplitude but opposite phase. These two steady states produce two well-defined flow regimes in the higher-resolution hemispheric model. This result confirms that flow regimes found in highly truncated models are not merely an artifact of the excessive truncation and can still be found when a sufficiently large number of degrees of freedom is included. The agreement between large-scale steady states and regime centroids is improved if the average effect of high-frequency transients on the planetary-scale flow is parameterized by adjusting the sources of zonal available potential energy and kinetic energy in the highly truncated models. Using these hemispheric models, it is shown that the leading dynamical and generalized neutral vectors correctly identify the axis linking the centroids of the two regimes as the axis with the smallest linear time derivative. Although anomalies in transient eddies are important in determining the spatial pattern of these centroids, the ultimate source of the two regimes of the hemispheric QG model is the existence of multiple stationary solutions of the large-scale flow. There is no inconsistency between the energetically fundamental role played by high-frequency transients and the capacity of nonlinear large-scale dynamics to determine the multimodal structure of the model's phase space. The neutral vector analysis also confirms that tropical diabatic heating could effectively generate an extratropical response along an axis corresponding to the difference between opposite regime anomalies.

The contribution of 2N photon absorption in 12C(γ,2N) reactions for Eγ = 150–400 MeV

The 12C(γ,pn) and 12C(γ,pp) reactions have been studied using tagged photons of energy E γ = 150–400 MeV. Recoil momentum distributions are compared to the results of Monte Carlo calculations based on a two-nucleon photon absorption model and two different phase space models. The 12C(γ,pn) data at low missing energy are consistent with absorption on 1 p 2 and 1 s1 p nucleon pairs.

On the relationship of the scaled phase space and Skyrme-coherent state treatments of proton antiproton annihilation at rest

We discuss pion multiplicities and single pion momentum spectra from proton antiproton annihilation at rest. Both the scaled phase space model and the Skyrme-coherent state approach describe these observables well. In the coherent state approach the puzzling size of the scale parameter relating the phase space integrals for different multiplicities is replaced by a well defined weight function. The strength of this function is determined by the intensity of the classical pion field and its spatial extent is of order 1 fm.

Eight definitions of the slow manifold: seiches, pseudoseiches and exponential smallness

Abstract The slow manifold is the Holy Grail of initialization schemes for weather forecasting, a hypothetical subspace of the model's phase space which is free of high-frequency (and forecast-wrecking) gravity waves. Using new machinery, we analyze seven previous definitions of the slow manifold and one definition original to this work. One new tool is the mathematics of nonlocal solitary wave theory. The traditional definition of a slow manifold is too restrictive, but a generalization in the spirit of nonlocal soliton theory is computable. Another novelty is the conceptual distinction between ‘seiche’ and ‘pseudoseiche’. The former are free, unforced gravity waves, whereas pseudoseiches are forced gravity mode oscillations which mimic seiches over a finite time interval. We show through a linear model that it is possible to remove seiches by initialization, even though the usual algorithms are divergent. However, intermittent gravity waves, i.e. pseudoseiches, appears as inexorable as death and the tides.

Study of a soft quadrupole excitation in the nucleus 11Li: A phase space model of neutron halo nuclei.

Quadrupole excitations in the nucleus $^{11}\mathrm{Li}$ have been studied in a semiclassical framework using the nuclear Vlasov equation solved with the test particle method. A soft mode of quadrupole excitation located around 2 MeV is found. The strength (in percentage of the energy-weighted sum rule) exhausted in such a soft quadrupole excitation region is very sensitive to the extension of the neutron halo in the nucleus $^{11}\mathrm{Li}$. The results are discussed in comparison with other recent calculations. The use of the collective response to tune phase-space models of neutron excess nuclei to be used in collision dynamics is finally stressed.

Antiproton production inp+A andd+A reactions at subthreshold energies

The production of antiprotons in proton-nucleus and deuteron-nucleus collisions is analyzed with respect to one-step nucleon-nucleon (NN → NNp¯ p) and secondary Δ-nucleon (ΔN → NNN¯ p) production channels within a phase-space model incorporating the selfenergies of the baryons. It is found that contrary to nucleus-nucleus collisions the Δ induced reaction channels are of minor importance except at very low bombarding energies. The data from KEK are approximately reproduced when accounting for the internal momentum distribution of the deuteron which provides a natural explanation for the large enhancement of the ¯p cross section ind+A as compared top+A.

State-selective electron capture in He2+-H2 collisions

A classical phase-space model of the hydrogen molecule which includes both electrons and nuclear centers is utilized to study state selective electron capture for collisions with alpha particles at intermediate impact energies (30-200 keV amu-1). The calculations are performed within the framework of the classical trajectory Monte Carlo method. The direct one-electron transfer process and the transfer ionization reaction which becomes increasingly important at the higher impact energies are directly included to obtain line emission cross sections for capture to the He+(np) states, n=2-5, for energies from 16 to 60 keV amu-1. Agreement between theory and available experimental data is good at energies above 40 keV amu-1.

Dynamics of information and uncertainty

The question of what information might be inferred from a set of data is posed in terms of the uncertainties of model variables determined by a least-squares fit. When a dynamical model is fitted to asynoptic data, the uncertainty can be characterized by a region in the model's phase space surrounding the point associated with the best fit. Changes in the shape and orientation of this region as it evolves indicate how information is redistributed dynamically among the model variables, much as kinetic and potential energy might be redistributed. These ideas are illustrated within the context of single and double oscillator systems. Information about the state of a shallow-water model is shown to depend sensitively on the sampling interval of fictitious altimetric data. DOI: 10.1034/j.1600-0870.1994.t01-3-00007.x

Laser-induced flourescence studies of C 3 formation and isomerization in the 193 nm photolysis of allene and propyne

The quantum state distributions of the C 3 radical from the UV multiphoton dissociation of allene and propyne in a pulsed molecular beam have been measured. The observed distributions for both molecules are identical and are much colder than a phase space model would predict, implying that direct dissociation is occurring in one step and isomerization in another. It is concluded that both allene and propyne undergo internal conversion from the S 1 state to the vibrationally excited S 0 ground state of allene followed by molecular elimination of H 2. The observed C 3 is then produced by molecular elimination of H 2 from the secondary photolysis of C 3H 2.

Hole burning and pressure phenomena in chromoproteins

We investigated the behavior of spectral holes under pressure at various frequencies within the inhomogeneous band for two proteins, namely myoglobin and horseradish peroxidase. In order to achieve narrow bandwidth hole burning, the heme chromophore was replaced by protoporphyrin IX and mesoporphyrin IX, respectively. In myoglobin, we found that the pressure induced shift of the holes varied in a strongly non-linear fashion, when the burn-frequency was tuned across the absorption band. In horseradish peroxidase the pressure shift was linear with burn-frequency but changed in a dramatic fashion upon complex formation with a substrate molecule. These observations are interpreted within the frame of the so-called correlated phase space model.

Meson production in proton-nucleus and nucleus-nucleus collisions

The production of K+ or η mesons in proton-nucleus reactions is analysed with respect to primary nucleon-nucleon (NN → NΛK+ or NNη) and secondary pion-nucleon (πN → K+Λ or ηN) production channels on the basis of a phase-space model employing Hartree-Fock groundstate momentum distributions and free on-shell production processes. The phase-space model adopted here compares well for meson production with more involved simulations based on VUU transport equations. Whereas for K+ production in proton-nucleus reactions the secondary channel clearly dominates at subthreshold energies, η mesons arise from primary and secondary processes with roughly the same order of magnitude. Detailed VUU calculations show that the relative weight of the various channels for nucleus-nucleus reactions is quite different as compared to the proton-nucleus case since Δ-resonance excitation and inelastic Δ-nucleon collisions are much more frequent.

An approach to the refractive guiding in FEL through the beam phase space model

Refractive guiding in the FEL is investigated with a new approach, the beam phase space model, in which the optical beam is regarded as a bundle of rays which is assumed to be an ellipse in optical phase. In this nonwave optical model the area of the ellipse acts like the wavelength resulting from wave theory. A beam envelope equation is deduced from the model to describe the propagation behavior of a Gaussian beam through free space and various optical devices. This equation is applied to an FEL with the effective refractive index derived from 1-D FEL theory to study the refractive guiding effect in the FEL. As an example the effect in an FEL oscillator is modeled by means of the theory.

Improved microscopic calculation of initial exciton number.

An improved microscopic calculation of the initial exciton number has been carried out on the basis of the original microscopic model---the so-called phase-space model. In our calculation the Vlasov or Boltzmann-Uehling--Uhlenbeck dynamics is used during the nucleus-nucleus collision instead of a simple dynamical process without friction. Our calculation reproduces the experimental results better than the original microscopic model.

Multiple electron emission characteristics in heavy ion collisions

A semiclassical ( h ̵ = 0 ) independent particle model in phase space based on the Vlasov equation is used to describe the electron motion in fast bare ion-rare gas atom collisions. The phase space density is discretized by an ensemble of test particles that are propagated simultaneously in order to account for the electron-electron interaction in the mean field approximation. The ejected particle distribution provides information about multiple electron emission as a function of electron scattering angle and energy. Some results are given for the C 6+-Ne and F 8+-Ne systems at 10 MeV impact energy.

Classical frames for a quantum theory ? A bird's-eye view

All proposals of phase-space models for quantum mechanics are classified into two well-defined classes and then described in terms of operational statistical theories. The extreme generality of the description, devoid of unessential details, leads to almost trivial proofs of many facts discovered elsewhere with great effort. A new proposal of quantization is briefly sketched.

Light-particle emission versus evaporation residue formation in collisions of40Ar onnatCa at 30 MeV/u

The closely associated phenomena of preequilibrium emission and evaporation residue formation in fusion-like reactions were studied in central collisions between40Ar andnatCa at 30 MeV/u. Heavy reaction products were taken in coincidence with neutrons and light charged particles. The preequilibrium neutron data agree very well with predictions of a quantal phase-space model which, in addition to the mean field, takes two-body collisions properly into account. Preequilibrium emission ends in thermally equilibrated hot nuclei with an average excitation energy of about 6 MeV/u. The combined results show a striking interrelation between the ‘missing mass’ and light-particle multiplicities: the mass difference between the full compound mass and the observed residues can be explained quantitatively by the emission of only neutrons and light charged particles withZ≦2 during the entire course of energy dissipation.

Hadron-nucleon interactions in view of a multi-peripheral model

A dynamical phase space model is proposed to describe the hadron-hadron interactions at few GeV incident energy. A matrix element of a multiperipheral nature is used whose parameters are strongly correlated to the final-state multiplicity. A simplified quark-quark interaction picture is considered to improve the results. The multiplicity distribution, the inclusive rapidity and longitudinal-momentum distributions are reproduced for the\(\pi ^ - p\) interactions at 6.1 GeV.

An Improved Microscopic Method for Calculating Initial Exciton Number

An improved microscopic model to calculate the initial exciton number has been developed on the basis of original microscopic model–so-called phase-space model. In our model the particle number p0 and hole number h0 are treated separately and the Vlasov or BUU dynamics is used during the nucleus-nucleus collision instead of simple dynamical process without friction. This model reproduces the experimental results rather well.

Light-particle emission and heavy-residue formation in the fusion-like reactions 40Ar+ 40Ca at 15 MeV/u and 28Si+ 28Si at 20 MeV/u

Heavy reaction products coincident with neutrons and light charged particles were studied in central collisions in the mass-symmetric systems 40Ar+ 40Ca and 28Si+ 28Si at incident energies of 15 respectively 20 MeV/u. The results demonstrate quantitatively an interrelation between heavy-residue mass and element distributions and light-particle multipicities: the mass difference between the observed fragments and the compound nuclei can be explained entirely by the emission of light particles with Z ⩽ 2. All neutron data are very well reproduced within the framework of a quantal phase-space model, stressing the importance of two-body collisions in the reaction dynamics already at these energies. Trends in the deduced nultiplicities and nuclear temperatures indicate evidence for a limiting excitation energy for residue formation.