Single electron states in polyethylene

We report computer simulations of an excess electron in various structural motifs of polyethylene at room temperature, including lamellar and interfacial regions between amorphous and lamellae, as well as nanometre-sized voids. Electronic properties such as density of states, mobility edges, and mobilities are computed on the different phases using a block Lanczos algorithm. Our results suggest that the electronic density of states for a heterogeneous material can be approximated by summing the single phase density of states weighted by their corresponding volume fractions. Additionally, a quantitative connection between the localized states of the excess electron and the local atomic structure is presented.The US National Science Foundation under grant CHE-0911635 and from his Stokes Professorship in Nano Biophysics from Science Foundation Ireland thanks the Irish Centre for High End Computing (ICHEC) for computer resources and Science Foundation Ireland for support from grant 08-IN.1-I1869

Unfolding the prospects of computational (bio)materials modelling

Solid state NMR/Biophysical Organic Chemistr

On the Geometry and Entropy of Non-Hamiltonian Phase Space

We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation and phase space measure are clarified. In particular, we emphasize that a phase space measure should be defined by means of the Jacobian of the transformation between different types of coordinates since such a determinant is different from zero in the non-canonical case even if the phase space compressibility is null. Instead, the Jacobian determinant associated with phase space flows is unity whenever non-canonical coordinates lead to a vanishing compressibility, so that its use in order to define a measure may not be always correct. To better illustrate this point, we derive a mathematical condition for defining non-Hamiltonian phase space flows with zero compressibility. The Jacobian determinant associated with time evolution in phase space is altogether useful for analyzing time translation invariance. The proper definition of a phase space measure is particularly important when defining the entropy functional in the canonical, non-canonical, and non-Hamiltonian cases. We show how the use of relative entropies can circumvent some subtle problems that are encountered when dealing with continuous probability distributions and phase space measures. Finally, a maximum (relative) entropy principle is formulated for non-canonical and non-Hamiltonian phase space flows.Comment: revised introductio

Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Sequential short-time propagation of quantum-classical dynamics

An algorithm for the simulation of quantum-classical dynamics is presented. Quantum-classical evolution is effected by a propagator exp(i (L) over capt) involving the quantum classical Liouville operator (L) over cap that describes the evolution of a quantum subsystem coupled to a classical bath. Such a mixed description provides a means to study the dynamics of complex many-body systems where certain degrees of freedom are treated quantum mechanically. The algorithm is constructed by decomposing the time interval Deltat into small segments of length At and successively applying the propagator in the short time segments to obtain the evolution for long times. The algorithm is shown to be a discretization of the iterated Dyson form of the propagator whose direct solution is vexatious. The sequential short-time propagation algorithm is applied to the spin-boson model for a range of values of the Kondo parameter and shown to be effective

Probing the Structures of Hydrated Nafion in Different Morphologies Using Temperature-Accelerated Molecular Dynamics Simulations

We perform combined temperature-accelerated and standard molecular dynamics (MD) simulations to elucidate the atomistic structure of hydrated Nafion (hydration level lambda = 6.5) in the slab and cylinder morphologies. Our samples are initially made of elongated Nafion strands with a relatively small fraction of gauche defects. Our simulations show that even very long (>50 ns) "brute force" MD simulations are insufficient to reach equilibrated structures. In fact, similar to 30-40 ns long temperature-accelerated molecular dynamics (TAMD) simulations started from the same initial conditions explore more stable (lower potential energy) stationary structures. The effect of TAMD is to allow a rearrangement of the backbone consisting of an increase in gauche defects, which cannot be obtained by "brute force" MD because the trans-gauche transition is a rare event at room temperature. Associated with the backbone rearrangement, we observe a change in the structure of the water layers/tubes as measured by the size and number of bulk (four-fold coordinated water molecules) and surface-like water clusters. At equilibrium, the mean size of bulk-like water clusters is small, typically between 10 and 20 molecules, depending on the morphology. Larger clusters are also present in our samples, the largest being made of similar to 350 molecules, but even the latter is too small for percolation. This suggests that the proton transport through each morphology might be a two-step process: Grotthuss-like within bulk-like water clusters and of a different type (e.g., diffusive or even transport across fluctuatively opening necks) between clusters

Statistical approach to nonhyperbolic chaotic systems

info:eu-repo/semantics/publishe

Recurrence time statistics in chaotic dynamics: multiple recurrences in intermittent chaos

info:eu-repo/semantics/publishe