Reaction rate calculation with time-dependent invariant manifolds

The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in particular if the reactive system is exposed to the influence of a heat bath. As an efficient alternative, we propose here to compute invariant surfaces in the phase space of the reactive system that separate reactive from nonreactive trajectories. The location of these invariant manifolds depends both on time and on the realization of the driving force exerted by the bath. These manifolds allow the identification of reactive trajectories simply from their initial conditions, without the need of any further simulation. In this paper, we show how these invariant manifolds can be calculated, and used in a formally exact reaction rate calculation based on perturbation theory for any multidimensional potential coupled to a noisy environment

The reconstruction of causal networks in physiology

We systematically compare strengths and weaknesses of two methods that can be used to quantify causal links between time series: Granger-causality and Bivariate Phase Rectified Signal Averaging (BPRSA). While a statistical test method for Granger-causality has already been established, we show that BPRSA causality can also be probed with existing statistical tests. Our results indicate that more data or stronger interactions are required for the BPRSA method than for the Granger-causality method to detect an existing link. Furthermore, the Granger-causality method can distinguish direct causal links from indirect links as well as links that arise from a common source, while BPRSA cannot. However, in contrast to Granger-causality, BPRSA is suited for the analysis of non-stationary data. We demonstrate the practicability of the Granger-causality method by applying it to polysomnography data from sleep laboratories. An algorithm is presented, which addresses the stationarity condition of Granger-causality by splitting non-stationary data into shorter segments until they pass a stationarity test. We reconstruct causal networks of heart rate, breathing rate, and EEG amplitude from young healthy subjects, elderly healthy subjects, and subjects with obstructive sleep apnea, a condition that leads to disruption of normal respiration during sleep. These networks exhibit differences not only between different sleep stages, but also between young and elderly healthy subjects on the one hand and subjects with sleep apnea on the other hand. Among these differences are 1) weaker interactions in all groups between heart rate, breathing rate and EEG amplitude during deep sleep, compared to light and REM sleep, 2) a stronger causal link from heart rate to breathing rate but disturbances in respiratory sinus arrhythmia (breathing to heart rate coupling) in subjects with sleep apnea, 3) a stronger causal link from EEG amplitude to breathing rate during REM sleep in subjects with sleep apnea. The Granger-causality method, although initially developed for econometric purposes, can provide a quantitative, testable measure for causality in physiological networks

Finite size effects on transport coefficients for models of atomic wires coupled to phonons

We consider models of quasi-1-d, planar atomic wires consisting of several, laterally coupled rows of atoms, with mutually non-interacting electrons. This electronic wire system is coupled to phonons, corresponding, e.g., to some substrate. We aim at computing diffusion coefficients in dependence on the wire widths and the lateral coupling. To this end we firstly construct a numerically manageable linear collision term for the dynamics of the electronic occupation numbers by following a certain projection operator approach. By means of this collision term we set up a linear Boltzmann equation. A formula for extracting diffusion coefficients from such Boltzmann equations is given. We find in the regime of a few atomic rows and intermediate lateral coupling a significant and non-trivial dependence of the diffusion coefficient on both, the width and the lateral coupling. These results, in principle, suggest the possible applicability of such atomic wires as electronic devices, such as, e.g., switches.Comment: 9 pages, 5 figures, accepted for publication in Eur. Phys. J.

Heparin and air filters reduce embolic events caused by intra-arterial cerebral angiography - A prospective, randomized trial

Background-Intra-arterial cerebral angiography is associated with a low risk for neurological complications, but clinically silent ischemic events after angiography have been seen in a substantial number of patients.Methods and Results-In a prospective study, diffusion-weighted magnetic resonance imaging (DW-MRI) before and after intra-arterial cerebral angiography and transcranial Doppler sonography during angiography were used to evaluate the frequency of cerebral embolism. One hundred fifty diagnostic cerebral angiographies were randomized into 50 procedures, each using conventional angiographic technique, or systemic heparin treatment throughout the procedure, or air filters between the catheter and both the contrast medium syringe and the catheter flushing. There was no neurological complication during or after angiography. Overall, DW-MRI revealed 26 new ischemic lesions in 17 patients (11%). In the control group, 11 patients showed a total of 18 lesions. In the heparin group, 3 patients showed a total of 4 lesions. In the air filter group, 3 patients exhibited a total of 4 lesions. The reduced incidence of ischemic events in the heparin and air filter groups compared with the control group was significantly different (P=0.002). Transcranial Doppler sonography demonstrated a large number of microembolic signals that was significantly lower in the air filter group compared with the heparin and control groups (P=0.01), which did not differ from each other.Conclusions-Air filters and heparin both reduce the incidence of silent ischemic events detected by DW-MRI after intra-arterial cerebral angiography and can potentially lower clinically overt ischemic complications. This may apply to any intra-arterial angiographic procedure

Transient fluctuation theorem in closed quantum systems

Our point of departure are the unitary dynamics of closed quantum systems as generated from the Schr\"odinger equation. We focus on a class of quantum models that typically exhibit roughly exponential relaxation of some observable within this framework. Furthermore, we focus on pure state evolutions. An entropy in accord with Jaynes principle is defined on the basis of the quantum expectation value of the above observable. It is demonstrated that the resulting deterministic entropy dynamics are in a sense in accord with a transient fluctuation theorem. Moreover, we demonstrate that the dynamics of the expectation value are describable in terms of an Ornstein-Uhlenbeck process. These findings are demonstrated numerically and supported by analytical considerations based on quantum typicality.Comment: 5 pages, 6 figure

Stochastic Transition States: Reaction Geometry amidst Noise

Classical transition state theory (TST) is the cornerstone of reaction rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface. This no-recrossing rule is difficult (and sometimes impossible) to enforce, however, when a chemical reaction takes place in a fluctuating environment such as a liquid. High-accuracy approximations to the rate are well known when the solvent forces are treated using stochastic representations, though again, exact no-recrossing surfaces have not been available. To generalize the exact limit of TST to reactive systems driven by noise, we introduce a time-dependent dividing surface that is stochastically moving in phase space such that it is crossed once and only once by each transition path

Cyclotron-resonant exciton transfer between the nearly free and strongly localized radiative states of a two-dimensional hole gas in a high magnetic field

Avoided crossing of the emission lines of a nearly free positive trion and a cyclotron replica of an exciton bound to an interface acceptor has been observed in the magneto-photoluminescence spectra of p-doped GaAs quantum wells. Identification of the localized state depended on the precise mapping of the anti-crossing pattern. The underlying coupling is caused by an exciton transfer combined with a resonant cyclotron excitation of an additional hole. The emission spectrum of the resulting magnetically tunable coherent state probes weak localization in the quantum well.Comment: 5 pages, 5 figure

Plasmas and Controlled Nuclear Fusion

Contsins reports on four research projects split into two sections.National Science Foundation (Grant GK-1165)National Science Foundation (Grant GK-57

Properties of cage rearrangements observed near the colloidal glass transition

We use confocal microscopy to study the motions of particles in concentrated colloidal systems. Near the glass transition, diffusive motion is inhibited, as particles spend time trapped in transient ``cages'' formed by neighboring particles. We measure the cage sizes and lifetimes, which respectively shrink and grow as the glass transition approaches. Cage rearrangements are more prevalent in regions with lower local concentrations and higher disorder. Neighboring rearranging particles typically move in parallel directions, although a nontrivial fraction move in anti-parallel directions, usually from pairs of particles with initial separations corresponding to the local maxima and minima of the pair correlation function $g(r)$, respectively.Comment: 5 pages, 4 figures; text & figures revised in v

Dielectronic Recombination in Photoionized Gas. II. Laboratory Measurements for Fe XVIII and Fe XIX

In photoionized gases with cosmic abundances, dielectronic recombination (DR) proceeds primarily via nlj --> nl'j' core excitations (Dn=0 DR). We have measured the resonance strengths and energies for Fe XVIII to Fe XVII and Fe XIX to Fe XVIII Dn=0 DR. Using our measurements, we have calculated the Fe XVIII and Fe XIX Dn=0 DR DR rate coefficients. Significant discrepancies exist between our inferred rates and those of published calculations. These calculations overestimate the DR rates by factors of ~2 or underestimate it by factors of ~2 to orders of magnitude, but none are in good agreement with our results. Almost all published DR rates for modeling cosmic plasmas are computed using the same theoretical techniques as the above-mentioned calculations. Hence, our measurements call into question all theoretical Dn=0 DR rates used for ionization balance calculations of cosmic plasmas. At temperatures where the Fe XVIII and Fe XIX fractional abundances are predicted to peak in photoionized gases of cosmic abundances, the theoretical rates underestimate the Fe XVIII DR rate by a factor of ~2 and overestimate the Fe XIX DR rate by a factor of ~1.6. We have carried out new multiconfiguration Dirac-Fock and multiconfiguration Breit-Pauli calculations which agree with our measured resonance strengths and rate coefficients to within typically better than <~30%. We provide a fit to our inferred rate coefficients for use in plasma modeling. Using our DR measurements, we infer a factor of ~2 error in the Fe XX through Fe XXIV Dn=0 DR rates. We investigate the effects of this estimated error for the well-known thermal instability of photoionized gas. We find that errors in these rates cannot remove the instability, but they do dramatically affect the range in parameter space over which it forms.Comment: To appear in ApJS, 44 pages with 13 figures, AASTeX with postsript figure