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## Dynamic polarizability, Cauchy moments, and the optical absorption spectrum of liquid water: A sequential molecular dynamics/quantum mechanical approach

Fonte: AMER INST PHYSICS
Publicador: AMER INST PHYSICS

Tipo: Artigo de Revista Científica

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#coupled cluster calculations#density functional theory#electronic structure#infrared spectra#liquid theory#molecular dynamics method#permittivity#polarisability#ultraviolet spectra#visible spectra#water

The dynamic polarizability and optical absorption spectrum of liquid water in the 6-15 eV energy range are investigated by a sequential molecular dynamics (MD)/quantum mechanical approach. The MD simulations are based on a polarizable model for liquid water. Calculation of electronic properties relies on time-dependent density functional and equation-of-motion coupled-cluster theories. Results for the dynamic polarizability, Cauchy moments, S(-2), S(-4), S(-6), and dielectric properties of liquid water are reported. The theoretical predictions for the optical absorption spectrum of liquid water are in good agreement with experimental information.; FCT (Portugal)/CAPES (Brazil); FCT (Portugal)[SFRH/BPD/38447/2007]; Fundacao para a Ciencia e a Tecnologia (FCT), Portugal[POCI/MAT/55977/2004]; Fundacao para a Ciencia e a Tecnologia (FCT), Portugal[PTDC/QUI/68226/2006]

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## Molecular dynamics simulation of liquid trimethylphosphine

Fonte: AMER INST PHYSICS
Publicador: AMER INST PHYSICS

Tipo: Artigo de Revista Científica

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#SOLID-STATE NMR#PROBE MOLECULE#DIELECTRIC-PROPERTIES#ACID SITES#AB-INITIO#P-31 NMR#POTENTIALS#OXIDE#Physics, Atomic, Molecular & Chemical

Structural and dynamical properties of liquid trimethylphosphine (TMP), (CH(3))(3)P, as a function of temperature is investigated by molecular dynamics (MD) simulations. The force field used in the MD simulations, which has been proposed from molecular mechanics and quantum chemistry calculations, is able to reproduce the experimental density of liquid TMP at room temperature. Equilibrium structure is investigated by the usual radial distribution function, g(r), and also in the reciprocal space by the static structure factor, S(k). On the basis of center of mass distances, liquid TMP behaves like a simple liquid of almost spherical particles, but orientational correlation due to dipole-dipole interactions is revealed at short-range distances. Single particle and collective dynamics are investigated by several time correlation functions. At high temperatures, diffusion and reorientation occur at the same time range as relaxation of the liquid structure. Decoupling of these dynamic properties starts below ca. 220 K, when rattling dynamics of a given TMP molecules due to the cage effect of neighbouring molecules becomes important. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3624408]; FAPESP; CNPq

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## Polarization effects in molecular dynamics simulations of glass-formers Ca(NO(3))(2)center dot nH(2)O, n=4, 6, and 8

Fonte: AMER INST PHYSICS
Publicador: AMER INST PHYSICS

Tipo: Artigo de Revista Científica

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#calcium compounds#electrolytes#glass transition#inclusions#molecular dynamics method#polarisation#thermodynamics#viscosity#vitrification#CALCIUM NITRATE SOLUTIONS#INTERMEDIATE-RANGE ORDER

Thermodynamics, equilibrium structure, and dynamics of glass-forming liquids Ca(NO(3))(2)center dot nH(2)O, n=4, 6, and 8, have been investigated by molecular dynamics (MD) simulations. A polarizable model was considered for H(2)O and NO(3)- on the basis of previous fluctuating charge models for pure water and the molten salt 2Ca(NO(3))(2)center dot 3KNO(3). Similar thermodynamic properties have been obtained with nonpolarizable and polarizable models. The glass transition temperature, T(g), estimated from MD simulations was dependent on polarization, in particular the dependence of T(g) with electrolyte concentration. Significant polarization effects on equilibrium structure were observed in cation-cation, cation-anion, and water-water structures. Polarization increases the diffusion coefficient of H(2)O, but does not change significantly the diffusion coefficients of ions. Viscosity decreases upon inclusion of polarization, but the conductivity calculated with the polarizable model is smaller than the nonpolarizable model because polarization enhances anion-cation interactions.; CNPq; FAPESP

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## Fragility and glassy dynamics of 2Ca(NO(3))(2)center dot 3KNO(3) under pressure: Molecular dynamics simulations

Fonte: AMER INST PHYSICS
Publicador: AMER INST PHYSICS

Tipo: Artigo de Revista Científica

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#FORMING LIQUIDS#NITRATE MELTS#TRANSITION#RELAXATION#CA0.4K0.6(NO3)(1.4)#TEMPERATURE#DEPENDENCE#TRANSPORT#Physics, Atomic, Molecular & Chemical

Molecular dynamics simulations of the glass-forming liquid 2Ca(NO(3))(2)center dot 3KNO(3) (CKN) were performed from high temperature liquid states down to low temperature glassy states at six different pressures from 10(-4) to 5.0 GPa. The temperature dependence of the structural relaxation time indicates that the fragility of liquid CKN changes with pressure. In line with recent proposal [Scopigno , Science 302, 849 (2003)], the change on liquid fragility is followed by a proportional change of the nonergodicity factor of the corresponding glass at low temperature. (c) 2008 American Institute of Physics.

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## Computer simulation study of collective dynamics in the glass former Ca(NO3)(2)center dot 4H(2)O

Fonte: AMER INST PHYSICS; MELVILLE
Publicador: AMER INST PHYSICS; MELVILLE

Tipo: Artigo de Revista Científica

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#CALCIUM NITRATE SOLUTIONS#HIGH-FREQUENCY DYNAMICS#LIQUID WATER#FORMING LIQUIDS#VIBRATIONAL DYNAMICS#SUPERCOOLED LIQUIDS#MOLECULAR-DYNAMICS#BOSON PEAK#RELAXATION#TRANSITION#PHYSICS, ATOMIC, MOLECULAR & CHEMICAL

Time correlation functions of current fluctuations were calculated by molecular dynamics (MD) simulations in order to investigate sound waves of high wavevectors in the glass-forming liquid Ca(NO3)(2)center dot 4H(2)O. Dispersion curves, omega(k), were obtained for longitudinal (LA) and transverse acoustic (TA) modes, and also for longitudinal optic (LO) modes. Spectra of LA modes calculated by MD simulations were modeled by a viscoelastic model within the memory function framework. The viscoelastic model is used to rationalize the change of slope taking place at k similar to 0.3 angstrom(-1) in the omega(k) curve of acoustic modes. For still larger wavevectors, mixing of acoustic and optic modes is observed. Partial time correlation functions of longitudinal mass currents were calculated separately for the ions and the water molecules. The wavevector dependence of excitation energies of the corresponding partial LA modes indicates the coexistence of a relatively stiff subsystem made of cations and anions, and a softer subsystem made of water molecules. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4751548]; FAPESP; FAPESP; CNPq; CNPq

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## Proton-driven spin diffusion in rotating solids via reversible and irreversible quantum dynamics

Fonte: American Institute of Physics
Publicador: American Institute of Physics

Tipo: Artigo de Revista Científica

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Proton-driven spin diffusion (PDSD) experiments in rotating solids have received a great deal of attention as a potential source of distance constraints in large biomolecules. However, the quantitative relationship between the molecular structure and observed spin diffusion has remained obscure due to the lack of an accurate theoretical description of the spin dynamics in these experiments. We start with presenting a detailed relaxation theory of PDSD in rotating solids that provides such a description. The theory applies to both conventional and radio-frequency-assisted PDSD experiments and extends to the non-Markovian regime to include such phenomena as rotational resonance (R2). The basic kinetic equation of the theory in the non-Markovian regime has the form of a memory function equation, with the role of the memory function played by the correlation function. The key assumption used in the derivation of this equation expresses the intuitive notion of the irreversible dissipation of coherences in macroscopic systems. Accurate expressions for the correlation functions and for the spin diffusion constants are given. The theory predicts that the spin diffusion constants governing the multi-site PDSD can be approximated by the constants observed in the two-site diffusion. Direct numerical simulations of PDSD dynamics via reversible Liouville-von Neumann equation are presented to support and compliment the theory. Remarkably...

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## Neutron scattering studies of the magnetism and lattice dynamics in La₂âxÌ³SrxÌ³CuO₄

Fonte: Massachusetts Institute of Technology
Publicador: Massachusetts Institute of Technology

Tipo: Tese de Doutorado
Formato: 222 p.; 11181971 bytes; 11181724 bytes; application/pdf; application/pdf

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by Thomas Raymond Thurston.; Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1989.; Title as it appears in the M.I.T. Graduate List, Sept. 1989: Neutron scattering studies of the dynamics and magnetism and lattice dynamics in La₂âxÌ³SrxÌ³CuO₄. On t.p. double underscores indicate subscript.; Includes bibliographical references.

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## X-ray photon correlation spectroscopy studies of the dynamics of self-assembling block copolymer structures

Fonte: Massachusetts Institute of Technology
Publicador: Massachusetts Institute of Technology

Tipo: Tese de Doutorado
Formato: 240 p.; 8705789 bytes; 8705356 bytes; application/pdf; application/pdf

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Several improvements presented to the emerging technique of X-ray Photon Correlation Spectroscopy. These improvements enabled the study of polymer structures, in particular isotropic sponge phases of homo-polymer block copolymer mixtures. An analysis is presented on how to optimize the experimental beamline configuration for achieving the best possible signal-to-noise ratio (SNR) in x-ray photon correlation spectroscopy (XPCS) experiments. A new, fast x-ray detector system is developed for high-throughput, high-sensitivity, time-resolved, x-ray scattering and imaging experiments, most especially x-ray photon correlation spectroscopy (XPCS). The new detector is characterized in detail, and its performance is evaluated in terms of its signal to noise ratio. Data analysis and photon discrimination techniques are discussed in conjunction with the high data rates this detector produces. The improved detector is capable of collecting the same quality XPCS data in fifty times shorter time than previously available detectors. Detailed characterization of polystyrene ethylenebuthylene styrene sponge phase block copolymer samples is presented. Static X-ray scattering is employed to explore the structure of block copolymer sponge phase samples. The dynamics of the polymer samples is probed by X-ray Photon Correlation Spectroscopy...

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## Dynamics and evolution of dense stellar systems

Fonte: Massachusetts Institute of Technology
Publicador: Massachusetts Institute of Technology

Tipo: Tese de Doutorado
Formato: 175 p.; 8486098 bytes; 14929663 bytes; application/pdf; application/pdf

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The research presented in this thesis comprises a theoretical study of several aspects relating to the dynamics and evolution of dense stellar systems such as globular clusters. First, I present the results of a study of mass segregation in two-component star clusters, based on a large number of numerical N-body simulations using our Monte-Carlo code. Heavy objects, which could represent stellar remnants such as neutron stars or black holes, exhibit behavior that is in quantitative agreement with simple analytical arguments. Light objects, which could represent free-floating planets or brown dwarfs, are predominantly lost from the cluster, as expected from simple analytical arguments, but may remain in the halo in larger numbers than expected. Using a recent null detection of planetary-mass microlensing events in M22, I find an upper limit of 25% at the 63% confidence level for the current mass fraction of M22 in the form of very low-mass objects. Turning to more realistic clusters, I present a study of the evolution of clusters containing primordial binaries, based on an enhanced version of the Monte-Carlo code that treats binary interactions via cross sections and analytical prescriptions. All models exhibit a long-lived "binary burning" phase lasting many tens of relaxation times. The structural parameters of the models during this phase match well those of most observed Galactic globular clusters. At the end of this phase...

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## Low energy effective actions and tachyon dynamics from string field theory

Fonte: Massachusetts Institute of Technology
Publicador: Massachusetts Institute of Technology

Tipo: Tese de Doutorado
Formato: 144 p.; 7267719 bytes; 7275255 bytes; application/pdf; application/pdf

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In this thesis we show how to calculate off-shell low energy effective actions and how to study the dynamics of the tachyon from string field theory. We discuss how to obtain an effective action for the massless field and we explain how to relate it to well known results. We then study the tachyon dynamics both in cubic and in boundary string field theory.; by Erasmo Coletti.; Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.; Includes bibliographical references (p. 133-144).

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## Aqueous systems from first-principles : structure, dynamics and electron-transfer reactions

Fonte: Massachusetts Institute of Technology
Publicador: Massachusetts Institute of Technology

Tipo: Tese de Doutorado
Formato: 141 p.

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In this thesis, we show for the first time how it is possible to calculated fully from first-principles the diabatic free-energy surfaces of electron-transfer reactions. The excitation energy corresponding to the transfer of an electron at any given ionic configuration (the Marcus energy gap) is accurately assessed within ground-state density-functional theory via a novel penalty functional for oxidation-reduction reactions that appropriately acts on the electronic degrees of freedom alone. The self-interaction error intrinsic to common exchange-correlation functionals is also corrected by the same penalty functional. The diabatic free-energy surfaces are then constructed from umbrella sampling on large ensembles of configurations. As a paradigmatic case study, the self-exchange reaction between ferrous and ferric ions in water is studied in detail. Since the solvent plays an central role in mediating the process, studying electron-transfer reactions requires us to first understand the structure and dynamics of the solvent molecules (water molecules in our case). Therefore, we have also studied the static and dynamical properties of (heavy) water at ambient conditions with extensive first-principles molecular-dynamics simulations in the canonical ensemble...

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## Obtaining 1D dynamics in a quasi-1D NMR spin system

Fonte: Massachusetts Institute of Technology
Publicador: Massachusetts Institute of Technology

Tipo: Tese de Doutorado
Formato: 62 p.

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In this thesis, I explored the evolution and dynamics of multiple quantum coherences in a quasi-iD crystal lattice, Fluorapatite (FAp), through the use of NMR. In particular I focused on the system with chains aligned with the magnetic field axis, and with the so-called "magic angle" of 54.7°. In addition, I created a new method of rotation and long RF pulses for NMR spectroscopy. The method cancels off-chain terms of the dipolar Hamiltonian in quasi-ID lattices, while preserving on-chain terms. This allows 1D dynamics to dominate for longer timescales. Finally, a framework is proposed by which one could generalize this method to other systems; similarly cancelling some set of "undesirable" dipolar couplings while preserving others. This method has applications in Quantum Information Processing (QIP), where it could lead to the experimental realization of a 1D spin chain, a system that has provoked much theoretical interest, and the framework has larger implications for simulation of other quantum systems.; by Brian Jeffrey Pepper.; Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.; Includes bibliographical references (p. 61-62).

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## Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Fonte: Brock University
Publicador: Brock University

Tipo: Electronic Thesis or Dissertation

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Molec ul ar dynamics calculations of the mean sq ua re
displacement have been carried out for the alkali metals Na, K
and Cs and for an fcc nearest neighbour Lennard-Jones model
applicable to rare gas solids. The computations for the alkalis
were done for several temperatures for
temperature vol ume a swell as for
the
the
ze r 0 pressure ze ro
zero pressure volume
corresponding to each temperature. In the fcc case, results were
obtained for a wide range of both the temperature and density.
Lattice dynamics calculations of the harmonic and the lowe s t
order anharmonic (cubic and quartic) contributions to the mean
square displacement were performed for the same potential models
as in the molecular dynamics calculations. The Brillouin zone
sums arising in the harmonic and the quartic terms were computed
for very large numbers of points in q-space, and were
extrapolated to obtain results ful converged with respect to
the number of points in the Brillouin zone.An excellent agreement between the
lattice dynamics results was observed
molecular dynamics and
in the case of all the
alkali metals, e~ept for the zero pressure case of CSt where the
difference is about 15 % near the melting temperature. It was
concluded that for the alkalis...

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## Combinatorial-topological framework for the analysis of global dynamics

Fonte: American Institute of Physics - AIP; College Park
Publicador: American Institute of Physics - AIP; College Park

Tipo: Artigo de Revista Científica

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#CONLEY INDEX#SYSTEMS#EQUAÇÕES DIFERENCIAIS#EQUAÇÕES DIFERENCIAIS PARCIAIS#MATHEMATICS, APPLIED#PHYSICS, MATHEMATICAL

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]; Fapesp [2010/00875-9]; CNPq [306453/2009-6]; Ministry of Education, Culture, Sports, Science, and Technology (Japan); Ministry of Education, Science, Technology, Culture and Sports, Japan [21340035]; NSF [DMS-0915019, CBI-0835621]; DARPA; AFOSR; E.U.; Fundação para a Ciência e a Tecnologia (FCT) [FCOMP-01-0124-FEDER-010645, FCT PTDC/MAT/098871/2008, Est-C/MAT/UI0013/2011]; Fundação para a Ciência e Tecnologia (FCT)

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## Measurements of dynamics in an orientationally anisotropic system

Fonte: Massachusetts Institute of Technology
Publicador: Massachusetts Institute of Technology

Tipo: Tese de Doutorado
Formato: 148 p.; 8551078 bytes; 8570799 bytes; application/pdf; application/pdf

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(cont.) coefficients, and these were compared to the "effective" coefficients yielded by the former. Because scattering from a nematic domain is limited to a narrow azimuthal range, while an isotropic domain scatters uniformly to all azimuthal angles, separate but simultaneous , measurements of dynamics in coexisting isotropic and orientationally ordered domains were possible. The observed correlation functions indicated that the flow-aligned, equilibrium nematic phase predominant just above the ordering transition was supplanted by a surface-aligned, nonequilibrium, "jammed" phase as the concentration of rods was further increased.; We present X-ray photon correlation spectroscopy and small-angle X-ray scattering studies of charge-stabilized, rodlike boehmite (AlOOH) particles in semidilute and concentrated suspensions in glycerol, both in an isotropic phase and an orientationally ordered, lyotropic liquid crystalline phase. Using an array detector, simultaneous measurements were made along both the radial and azimuthal directions of the scattering vector. The measured scattering was compared to the isotropic, polydisperse rod form factor, and an electrical double-layer was included in the model. Two distinct sets of nematic ordering were seen in each sample: one...

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## Shock convergence and mix dynamics in inertial confinement fusion

Fonte: Massachusetts Institute of Technology
Publicador: Massachusetts Institute of Technology

Tipo: Tese de Doutorado
Formato: 124 p.

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Understanding the phenomena of shock propagation and of turbulent mix induced by Rayleigh-Taylor (RT) instability growth is of critical importance for ignition and high gain in inertial confinement fusion (ICF). Capsule assembly and hot-spot formation require careful timing of multiple shocks to maximize hot-spot heating while minimizing heating of the main fuel. Unmitigated mixing of the main fuel with the hot-spot can quench hot-spot heating, resulting in reduced gain or failed ignition. Nuclear measurements of direct-drive implosions at the OMEGA laser facility were performed to study shock convergence and mix dynamics in ICF. During these studies, an unexpected scaling of experimental nuclear yields was observed in implosions of capsules filled with different mixtures of D2 and 3He. A number of possible mechanisms to cause the scaling were considered, but no dominant mechanism has been identified. Mix dynamics were studied using a novel capsule configuration that only emits D3He protons when the fuel and shell are atomically mixed. Temporal and spectral measurements of protons emitted from such capsules were used to investigate the extent and evolution of mix, and demonstrate that the time necessary for RT instabilities to induce mix results in a delay of the peak D3He reaction rate in these special capsules compared to standard capsules.; (cont.) The collapse of a converging spherical shock launched by the onset of the laser pulse induces nuclear production several hundred picoseconds before deceleration and stagnation of the imploding shell. The time...

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## MCMC using Hamiltonian dynamics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/06/2012
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Hamiltonian dynamics can be used to produce distant proposals for the
Metropolis algorithm, thereby avoiding the slow exploration of the state space
that results from the diffusive behaviour of simple random-walk proposals.
Though originating in physics, Hamiltonian dynamics can be applied to most
problems with continuous state spaces by simply introducing fictitious
"momentum" variables. A key to its usefulness is that Hamiltonian dynamics
preserves volume, and its trajectories can thus be used to define complex
mappings without the need to account for a hard-to-compute Jacobian factor - a
property that can be exactly maintained even when the dynamics is approximated
by discretizing time. In this review, I discuss theoretical and practical
aspects of Hamiltonian Monte Carlo, and present some of its variations,
including using windows of states for deciding on acceptance or rejection,
computing trajectories using fast approximations, tempering during the course
of a trajectory to handle isolated modes, and short-cut methods that prevent
useless trajectories from taking much computation time.

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## Atomic motions in the ab-merging region of 1,4-polybutadiene: A molecular dynamics simulation study

Fonte: American Institute of Physics
Publicador: American Institute of Physics

Tipo: Artículo
Formato: 533 bytes; text/plain

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17 pp.-- PACS nrs.: 36.20.Ey, 36.20.Hb, 31.15.xv.; We present fully atomistic molecular dynamics simulations on 1,4-polybutadiene in a wide temperature range from 200 to 280 K, i.e., in the region where the α- and β-relaxations merge and above. A big computational effort has been performed —especially for the lowest temperatures investigated — to extend the simulation runs to very long times (up to 1 µs for 200 K). The simulated sample has been carefully validated by using previous neutron scattering data on the real sample with similar microstructure. Inspecting the trajectories of the different hydrogens in real space, we have observed a heterogeneous dynamical behavior (each kind of hydrogen moves in a different way) with signatures of combined hopping and diffusive motions in the whole range investigated. The application of a previously proposed model [Colmenero et al., Europhys. Lett. 71, 262 (2005)] is successful and a characterization of the local motions and diffusion is possible. The comparison of our results to those reported in the literature provides a consistent scenario for polybutadiene dynamics and puts into a context the different experimental observations. We also discuss the impact of the hopping processes on the observation and interpretation of experimentally accessible magnitudes and the origin of the deviations from Gaussian behavior in this system.; This research project has been supported by the European Commission NoE SoftComp...

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## Dynamics on Complex Networks and Applications (Preface)

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artículo
Formato: 2373 bytes; 125365 bytes; text/plain; application/pdf

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Preface to Volume 224, Issues 1-2, Pages 1-214 (December 2006) of Physica D: Nonlinear Phenomena: "Dynamics on Complex Networks and Applications", edited by Adilson E. Motter, Manuel A. Matías, Jürgen Kurths and Edward Ott, URL http://www.sciencedirect.com/science/journal/01672789.; 2 pages.-- Texto completo arXiv:cond-mat/0612068v1; At the eight-year anniversary of Watts & Strogatz's work on the collective dynamics of small-world networks and seven years after Barabási & Albert's discovery of scale-free networks, the area of dynamical processes on complex networks is at the forefront of the current research on nonlinear dynamics and complex systems. This volume brings together a selection of original contributions in complementary topics of statistical physics, nonlinear dynamics and biological sciences, and is expected to provide the reader with a comprehensive up-to-date representation of this rapidly developing area.; We would like to thank the MPIPKS for sponsoring the conference that culminated with this publication.

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## Non-integrable galactic dynamics

Fonte: Taylor and Francis: Institute of Physics
Publicador: Taylor and Francis: Institute of Physics

Tipo: Proceedings
Formato: 2293603 bytes; application/pdf

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Orbital and self-consistent dynamics of non-integrable galaxy models are reviewed. Topics covered include torus construction; resonances; triaxial systems with central singularities; mixing and collisionless relaxation; and chaos in collisional systems.; "The Restless Universe: Applications of Gravitational N-Body Dynamics to Planetary, Stellar and Galactic Systems." Proceedings of the 54th Scottish Universities Summer School in Physics. Blair Atholl, Scotland, UK: 23 July - 5 August 2000.; Also archived in: arXiv:astro-ph/0106082 v1 5 Jun 2001 AND Rutgers Astrophysics Preprint Series No. 262; RIT community members may access full-text via RIT Libraries licensed databases: http://library.rit.edu/databases/; The preparation of this review was supported by NSF grant AST-0071099 and by NASA grants NAG 5-2803 and NAG 5-9046.

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