Nonequilibrium statistical mechanics of swarms of driven particles

As a rough model for the collective motions of cells and organisms we develop here the statistical mechanics of swarms of self-propelled particles. Our approach is closely related to the recently developed theory of active Brownian motion and the theory of canonical-dissipative systems. Free motion and motion of a swarms confined in an external field is studied. Briefly the case of particles confined on a ring and interacting by repulsive forces is studied. In more detail we investigate self-confinement by Morse-type attracting forces. We begin with pairs N = 2; the attractors and distribution functions are discussed, then the case N > 2 is discussed. Simulations for several dynamical modes of swarms of active Brownian particles interacting by Morse forces are presented. In particular we study rotations, drift, fluctuations of shape and cluster formation.Comment: 11 pages, 2 figure

Inverse coarse–graining methodologies to understand ion transport in block copolymer electrolytes

This research is focused on two fronts (i) developing multiscale simulation strategies for multicomponent polymers which can generate self assembled morphologies at both mesoscopic and atomistic length scales (ii) understanding the conformational attributes and dynamics of polymers in structured morphologies to understand the ion–transport mechanisms in block copolymer electrolytes. First part of the work is devoted in developing strategies to create equilibrated block copolymer morphologies below ODT with hard repulsive potentials. To this end, ordered morphologies with the help soft repulsive potentials are generated which possess equilibrated long range order within very short computational time. A rigorous mapping between the interaction parameters of the hard and soft potentials is then utilized to obtain the intermolecular interaction parameter of the soft potential corresponding to the target hard potential repulsion parameter. Subsequent to establishing the long range structure, short repulsive potential (within a coarse-grained framework) is reintroduced and equilibrated to generate ordered morphologies using hard repulsive potentials. Further to this, both topological and dynamic properties in ordered lamellar phases were characterized. The topological constraints are seen to increase with increasing degree of segregation. On characterizing the local dynamics of polymeric segments, we found that inhomogeneities exist in the spatially local dynamics and the length scale of perturbation of such inhomogeneities is controlled by the interfacial width of the block copolymer. The last part of the work involved the generation of ion–doped block copolymer melts at the atomistic level and to compare the results obtained therein with those for pure homopolymeric melts. To this end, we employed a multiscale simulation method to generate PS–PEO block copolymer doped with LiPF₆ ions. Our results demonstrate that the cation-anion radial distribution functions (RDF) display stronger coordination in the block copolymer melts compared to pure PEO homopolymer melts. Radial distribution functions isolated in the PEO and PS domains demonstrate that the stronger coordination seen in BCPs arise from the influence of both the higher fraction of ions segregated in the PS phase and the influence of interactions in the PS domain. Further, the cation-anion RDFs display spatial heterogeneity, with a stronger cation-anion binding in the interfacial region compared to bulk of the PEO domain. Investigations into the ion transport mechanisms in PS-PEO block copolymer melt reveal that ions exhibit slower dynamics in both the block copolymer (overall) and in the PEO phase of the BCP melt. Such results are shown to arise from the effects of slower polymer segmental dynamics in the BCP melt and the coordination characteristics of the ions. Polymer backbone-ion residence times analyzed as a function of distance from the interface indicate that ions have a larger residence time near the interface compared to that near the bulk of lamella, and demonstrates the influence of the glassy PS blocks and microphase segregation on the ion transport properties. Ion transport mechanisms in BCP melts reveal that there exist five distinct mechanisms for ion transport along the backbone of the chain and exhibit qualitative differences from the behavior in homopolymer melts.Chemical Engineerin

Theory of coherent two-dimensional vibrational spectroscopy

Two-dimensional (2D) vibrational spectroscopy has emerged as one of the most important experimental techniques useful to study the molecular structure and dynamics in condensed phases. Theory and computation have also played essential and integral roles in its development through the nonlinear optical response theory and computational methods such as molecular dynamics (MD) simulations and electronic structure calculations. In this article, we present the fundamental theory of coherent 2D vibrational spectroscopy and describe computational approaches to simulate the 2D vibrational spectra. The classical approximation to the quantum mechanical nonlinear response function is invoked from the outset. It is shown that the third-order response function can be evaluated in that classical limit by using equilibrium or non-equilibrium MD simulation trajectories. Another simulation method is based on the assumptions that the molecular vibrations can still be described quantum mechanically and that the relevant molecular response functions are evaluated by the numerical integration of the Schrodinger equation. A few application examples are presented to help the researchers in this and related areas to understand the fundamental principles and to use these methods for their studies with 2D vibrational spectroscopic techniques. In summary, this exposition provides an overview of current theoretical efforts to understand the 2D vibrational spectra and an outlook for future developments. c.Published under license by AIP Publishing

Making and Breaking of Chemical Bonds: Dynamics of elementary reactions from gas phase to condensed phase

The present thesis is concerned with the dynamics of elementary chemical reactions. In particular, the processes of bond formation (association) and of bond cleavage (dissociation) are studied. Both photo-induced and solvent-induced reaction mechanisms are elucidated. By embedding simple diatomic model systems in rare gas clusters and matrices, the transition of the dynamics of making and breaking of chemical bonds from the gas phase to the condensed phase is systematically investigated

Astrophysics in 2006

The fastest pulsar and the slowest nova; the oldest galaxies and the youngest stars; the weirdest life forms and the commonest dwarfs; the highest energy particles and the lowest energy photons. These were some of the extremes of Astrophysics 2006. We attempt also to bring you updates on things of which there is currently only one (habitable planets, the Sun, and the universe) and others of which there are always many, like meteors and molecules, black holes and binaries.Comment: 244 pages, no figure

Second International Workshop on Harmonic Oscillators

The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory