Lyapunov exponents from geodesic spread in configuration space

The exact form of the Jacobi–Levi-Civita (JLC) equation for geodesic spread is here explicitly worked out at arbitrary dimension for the configuration space manifold [Formula Presented] of a standard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric [Formula Presented] As the Hamiltonian flow corresponds to a geodesic flow on [Formula Presented] the JLC equation can be used to study the degree of instability of the Hamiltonian flow. It is found that the solutions of the JLC equation are closely resembling the solutions of the standard tangent dynamics equation which is used to compute Lyapunov exponents. Therefore the instability exponents obtained through the JLC equation are in perfect quantitative agreement with usual Lyapunov exponents. This work completes a previous investigation that was limited only to two degrees of freedom systems. © 1997 The American Physical Society

Evaluating Spiders for their Potential to Control Cabbage White Butterflies (Pieris rapae)

Field experiments revealed that presence of spiders increased mortality of butterfly eggs and improved brocolli yield

Analyzing intramolecular vibrational energy redistribution via the overlap intensity-level velocity correlator

Numerous experimental and theoretical studies have established that intramolecular vibrational energy redistribution (IVR) in isolated molecules has a heirarchical tier structure. The tier structure implies strong correlations between the energy level motions of a quantum system and its intensity-weighted spectrum. A measure, which explicitly accounts for this correaltion, was first introduced by one of us as a sensitive probe of phase space localization. It correlates eigenlevel velocities with the overlap intensities between the eigenstates and some localized state of interest. A semiclassical theory for the correlation is developed for systems that are classically integrable and complements earlier work focusing exclusively on the chaotic case. Application to a model two dimensional effective spectroscopic Hamiltonian shows that the correlation measure can provide information about the terms in the molecular Hamiltonian which play an important role in an energy range of interest and the character of the dynamics. Moreover, the correlation function is capable of highlighting relevant phase space structures including the local resonance features associated with a specific bright state. In addition to being ideally suited for multidimensional systems with a large density of states, the measure can also be used to gain insights into the phase space transport and localization. It is argued that the overlap intensity-level velocity correlation function provides a novel way of studying vibrational energy redistribution in isolated molecules. The correlation function is ideally suited to analyzing the parametric spectra of molecules in external fields.Comment: 16 pages, 13 figures (low resolution

Examinations of Fusarium sambucinum on Humulus lupulus and co-infection with hop stunt viroid in commercial hop fields

After an unusually high incidence of Fusarium canker was observed in commercial hop fields of the Pacific Northwest, field surveys were conducted and revealed that canker incidence ranged from 20 to 60% of bines sampled in six commercial fields, as well as wide-spread Hop stunt viroid infection in these six fields. A variety of inoculation techniques and incubation conditions were evaluated in laboratory and greenhouse studies to determine whether Fusarium sambucinum incites girdling symptoms on hop bines, which is characteristic of later stage Fusarium canker infection in commercial hop fields. Koch's postulates were fulfilled, confirming that F. sambucinum incites Fusarium canker and produces girdling, killing the bine. Colonization of detached hop stems with green fluorescent protein-labeled F. sambucinum or F. verticillioides were observed microscopically, but F. sambucinum colonized more aggressively and to a greater extent. Investigation into the effect of relative humidity on colonization of hop stems demonstrated that relative humidities greater than 88% are required for F. sambucinum to colonize green hop stems. Hilling of commercial hop plants was explored as a management strategy to ameliorate canker symptoms or improve yields in commercial fields with wide-spread Hop stunt viroid infection and results indicate that hilling can improve cone yields in commercial hop plantings co-infected with HpSVd and F. sambucinum

Absolute properties of the binary system BB Pegasi

We present a ground based photometry of the low-temperature contact binary BB Peg. We collected all times of mid-eclipses available in literature and combined them with those obtained in this study. Analyses of the data indicate a period increase of 3.0(1) x 10^{-8} days/yr. This period increase of BB Peg can be interpreted in terms of the mass transfer 2.4 x 10^{-8} Ms yr^{-1} from the less massive to the more massive component. The physical parameters have been determined as Mc = 1.42 Ms, Mh = 0.53 Ms, Rc = 1.29 Rs, Rh = 0.83 Rs, Lc = 1.86 Ls, and Lh = 0.94 Ls through simultaneous solution of light and of the radial velocity curves. The orbital parameters of the third body, that orbits the contact system in an eccentric orbit, were obtained from the period variation analysis. The system is compared to the similar binaries in the Hertzsprung-Russell and Mass-Radius diagram.Comment: 17 pages, 3 figures, accepted for Astronomical Journa

A trivial observation on time reversal in random matrix theory

It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonians is time reversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models.Comment: 7 pages 3 figure

Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics

We re-examine the problem of the "Loschmidt echo", which measures the sensitivity to perturbation of quantum chaotic dynamics. The overlap squared $M(t)$ of two wave packets evolving under slightly different Hamiltonians is shown to have the double-exponential initial decay $\propto \exp(-{\rm constant}\times e^{2\lambda_0 t})$ in the main part of phase space. The coefficient $\lambda_0$ is the self-averaging Lyapunov exponent. The average decay $\bar{M}\propto e^{-\lambda_1 t}$ is single exponential with a different coefficient $\lambda_1$. The volume of phase space that contributes to $\bar{M}$ vanishes in the classical limit $\hbar\to 0$ for times less than the Ehrenfest time $\tau_E=\frac{1}{2}\lambda_0^{-1}|\ln \hbar|$. It is only after the Ehrenfest time that the average decay is representative for a typical initial condition.Comment: 4 pages, 4 figures, [2017: fixed broken postscript figures

Weak and strong chaos in Fermi-Pasta-Ulam models and beyond

We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions. (C) 2005 American Institute of Physics

The gas turbulence in planetary nebulae: quantification and multi-D maps from long-slit, wide-spectral range echellogram

This methodological paper is part of a short series dedicated to the long-standing astronomical problem of de-projecting the bi-dimensional, apparent morphology of a three-dimensional distribution of gas. We focus on the quantification and spatial recovery of turbulent motions in planetary nebulae (and other classes of expanding nebulae) by means of long-slit echellograms over a wide spectral range. We introduce some basic theoretical notions, discuss the observational methodology, and develop an accurate procedure disentangling all broadening components of the velocity profile in all spatial positions of each spectral image. This allows us to extract random, non-thermal motions at unprecedented accuracy, and to map them in 1-, 2- and 3-dimensions. We present the solution to practical problems in the multi-dimensional turbulence-analysis of a testing-planetary nebula (NGC 7009), using the three-step procedure (spatio-kinematics, tomography, and 3-D rendering) developed at the Astronomical Observatory of Padua. In addition, we introduce an observational paradigm valid for all spectroscopic parameters in all classes of expanding nebulae. Unsteady, chaotic motions at a local scale constitute a fundamental (although elusive) kinematical parameter of each planetary nebula, providing deep insights on its different shaping agents and mechanisms, and on their mutual interaction. The detailed study of turbulence, its stratification within a target and (possible) systematic variation among different sub-classes of planetary nebulae deserve long-slit, multi-position angle, wide-spectral range echellograms containing emissions at low-, medium-, and high-ionization, to be analyzed pixel-to-pixel with a straightforward and versatile methodology, extracting all the physical information stored in each frame at best.Comment: 11 page, 10 figures, A&A in pres