Atomistic models of three fluorinated polyimides in the amorphous state

Molecular models of three fluorinated polyimides based on the 4,4′‐(hexafluoroisopropylidene)diphthalic dianhydride (6FDA) have been studied using molecular dynamics (MD) simulations. The respective diamines were 4,4′‐hexafluoroisopropylidene dianiline (6FpDA), 3,3′‐hexafluoroisopropylidene dianiline (6FmDA), and 2,4,6‐trimethyl‐1,3phenylenediamine (DAM). Thirty independent samples were prepared using a hybrid pivot Monte Carlo‐MD generation technique and average densities were found to be in very good agreement with experiment. Model structures also agreed with available wide‐angle X‐ray scattering data. Cohesive energies, Hildebrand solubility parameters, fractional free volumes (FFV), void space distributions and intermolecular as well as intramolecular interactions were analyzed. The differences in bulk properties between both 6FDA‐6FpDA and 6FDA‐6FmDA isomers remain fairly small, although the configurations of the former are more extended. 6FDA‐DAM has a lower density, larger intermolecular distances, and higher free volume than the other two polyimides. Results are discussed with respect to their use as matrices for gas separation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1166–1180, 2009     

Operator Correlations and Quantum Regression Theorem in Non-Markovian Lindblad Rate Equations

Non-Markovian Lindblad rate equations arise from alternative microscopic interactions such as quantum systems coupled to composite reservoirs, where extra degrees of freedom mediate the interaction between the system and a Markovian reservoir, as well as from systems coupled to complex structured reservoirs whose action can be well approximated by a direct sum of Markovian sub-reservoirs (Budini in Phys. Rev. A 74:053815 [2006]). The purpose of this paper is two fold. First, for both kinds of interactions we find general expressions for the system operator correlations written in terms of the Lindblad rate propagator. Secondly, we find the conditions under which a quantum regression hypothesis is valid. We show that a non-Markovian quantum regression theorem can only be granted in a stationary regime, being a necessary condition the fulfillment of a detailed balance condition. This result is independent of the underlying microscopic interaction, providing a criterion for the validity of the regression hypothesis in non-Markovian Lindblad-like master equations. As an example, we study the correlations of a two-level system coupled to different kind of reservoirs.     

Quantum simulations of toroidal electric ring currents and magnetic fields in linear molecules induced by circularly polarized laser pulses

Circularly polarized laser pulses may excite state selective unidirectional toroidal electric ring currents around the axis of oriented linear molecules. These in turn induce state selective magnetic fields. Quantum simulations for AlCl show that these effects are about one or even more than three orders of magnitudes larger than those which may be prepared in oriented planar molecules such as Mg-porphyrin, by means of either circularly polarized laser pulses, or by traditional magnetic fields, respectively.     

Solid‐State NMR investigations of anhydrous proton‐conducting acid–base poly(acrylic acid)– poly(4‐vinyl pyridine) polymer blend system: A study of hydrogen bonding and proton conduction

NMR studies of the structure and dynamics of a system composed of the acidic polymer poly(acrylic acid) (PAA) and the basic polymer poly(4‐vinyl pyridine) (P4VP) are presented. This system aims at the application of anhydrous proton‐conducting membranes that can be used at elevated temperatures at which the proton conduction of hydrated membranes breaks down. The ¹H NMR measurements have been preformed under fast magic angle spinning (MAS) conditions to achieve sufficient resolution and the applied ¹H NMR methods vary from simple ¹H MAS to double‐quantum filtered methods and two‐dimensional ¹H double‐quantum spectroscopy. The dynamic behavior of the systems has been investigated via variable temperature ¹H MAS NMR. ¹³C cross‐polarization MAS NMR provides additional aspects of dynamic and structural features to complete the picture. Different types of acidic protons have been identified in the studied PAA‐P4VP systems that are nonhydrogen‐bonded free acidic protons, hydrogen‐bonded dicarboxylic dimers, and protons forming hydrogen bonds between carboxylic protons and ring nitrogens. The conversion of dimer structures in dried PAA to free carboxylic acid groups is accomplished at temperatures above 380 K. However, the stability of hydrogen‐bonding strongly depends on the hydration level of the polymer systems. The effect of hydration becomes less apparent in the complexes. An inverse proportionality between hydrogen‐bonding strength and proton conduction in the PAA‐P4VP acid–base polymer blend systems was established. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 138–155, 2009     

Optimal Control of Non-stationary Differential Linear Repetitive Processes

Differential repetitive processes are a distinct class of continuous-discrete 2D linear systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is the fact that information propagation in one of the two independent directions only occurs over a finite interval. Applications areas include iterative learning control and iterative solution algorithms for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modelling of numerous industrial processes such as metal rolling, and long-wall cutting etc. The new results in is paper solve a general optimal problem in the presence of non-stationary dynamics.     

Phase space density representations in fluid dynamics

Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable.     

The time-local view of nonequilibrium statistical mechanics. II. Generalized Langevin equations

On a semiphenomenological level, generalized Langevin equations are usually obtained by adding a random force (RF) term to macroscopic deterministic equations assumed to be known. Here this procedure is made rigorous by conveniently redefining the RF, which is shown to be colored noise weakly correlated with the observables at earlier times due to the finite lifetime of microscopic events. Corresponding fluctuation-dissipation theorems are derived. Explicit expressions for the spectral density of the fluctuations are obtained in a particularly simple form, with the deviation of the line shape from the Lorentzian being related most explicitly to the spectral density of the RF. Well-known low-frequency expressions and the Einstein relation of (generalized) Brownian motion theory are modified so as to include lifetime effects. New sum rules are obtained relating dissipative quantities to contour integrals (in the complex frequency domain) over spectral densities or corresponding response functions. The Heisenberg dynamics of a complete set of macroobservables is shown to be equivalent to a generalized Orstein-Uhlenbeck stochastic process which is a non-Markovian process due to the lifetime effects.     

Moment equations for a spatially extended system of two competing species

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulations of the time discrete version of LV equations, that is coupled map lattice (CML) model, we conclude that the anticorrelated oscillations of the species densities are strictly related to non-overlapping spatial patterns.     

Open dynamic behaviour of financial markets

Open dynamic behaviour of financial markets with internal interactions between agents and with external “fields” from other systems are investigated using the approach of Grossman and Stiglitz for inefficient markets, and Keynes for interference of the market using physics of finance (referred to hereafter as phynance). The simulation results indicate that the NYSE data analyzed in Plerou, V. et al., Nature 421, 130 (2003) can be fitted by an equation of order parameter Φ and local deviation R of type: -(R+0.03) Φ+ 0.6 Φ³ + 0.02 = 0, which is shown to be in remarkable agreement with Plerou's data.