Description of Entanglement Dynamics of Flexible Polymers: Self-Consistent Coarse-Graining in Length and Time Scales

2006 ◽  
Author(s):  
Hiroshi Watanabe
Keyword(s):  
Time Scales ◽  
Coarse Graining ◽  
Entanglement Dynamics ◽  
Flexible Polymers ◽  
Self Consistent

scholarly journals Dancing to changa: a self-consistent prediction for close SMBH pair formation time-scales following galaxy mergers

2018 ◽  
Vol 475 (4) ◽  
pp. 4967-4977 ◽  
Author(s):  
M Tremmel ◽  
F Governato ◽  
M Volonteri ◽  
T R Quinn ◽  
A Pontzen
Keyword(s):  
Time Scales ◽  
Pair Formation ◽  
Formation Time ◽  
Galaxy Mergers ◽  
Self Consistent

SYMBOLIC DYNAMICS, COARSE GRAINING AND THE MONITORING OF COMPLEX SYSTEMS

2011 ◽  
Vol 21 (12) ◽  
pp. 3465-3475 ◽  
Author(s):  
VASILEIOS BASIOS ◽  
DÓNAL MAC KERNAN
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Complex Systems ◽  
Error Estimates ◽  
Time Scales ◽  
Symbolic Dynamics ◽  
Prediction Error ◽  
Probabilistic Approach ◽  
Coarse Graining ◽  
Complex Nonlinear Systems

Coarse graining techniques and their associated symbolic dynamics are reviewed with a focus on probabilistic aspects of complex dynamical systems. The probabilistic approach initiated by Nicolis and coworkers has been elaborated. One of the major issues when dealing with the dynamics of complex nonlinear systems, the fact that the inherent time-scales of the unfolding phenomena are not well separated, is brought into focus. Recent results related to this interdependence, which is one of the most characteristic aspects of complexity and a major challenge in prediction, error estimates and monitoring of nonlinear complex systems, are discussed.

Systematic Coarse-graining and Multiscale Modeling of Soft Matter [PowerPoint Submission]

2006 ◽  
Vol 978 ◽  
Author(s):  
Gregory A. Voth
Keyword(s):  
Multiscale Modeling ◽  
Time Scales ◽  
Continuum Mechanics ◽  
Liquid State ◽  
Soft Matter ◽  
Coarse Graining ◽  
Mesoscale Dynamics ◽  
Computational Methodology ◽  
Primary Focus ◽  
Mesoscale Simulations

AbstractA multiscale theoretical and computational methodology will be presented for describing liquid state, biomolecular, and nanoparticle systems across multiple length- and time-scales. The approach provides an interface between atomistic molecular simulations, mesoscale dynamics, and continuum mechanics. The underlying methodology couples atomistic-level simulations with mesoscale simulations which, in turn, can be bridged to continuum-level modeling where necessary. A new and systematic multiscale coarse-graining strategy for linking the atomistic-scale interactions to the mesoscale will be the primary focus of the presentation. Applications of the overall methodology will be given.

RENORMALIZATION OF ATOMISTIC GROWTH MODELS

2008 ◽  
Vol 22 (22) ◽  
pp. 3721-3755 ◽  
Author(s):  
CHRISTOPH A. HASELWANDTER ◽  
DIMITRI D. VVEDENSKY
Keyword(s):  
Time Scales ◽  
Initial Conditions ◽  
Growth Models ◽  
Kinetic Monte Carlo ◽  
General Procedure ◽  
Lattice Models ◽  
Coarse Graining ◽  
General Terms ◽  
Kinetic Monte Carlo Simulations ◽  
Transition Rules

We review a general procedure for the multiscale analysis of atomistic lattice models of fluctuating interfaces driven by the deposition of new material. Beginning with a lattice Langevin formulation of site fluctuations, stochastic differential equations are derived by regularizing the lattice transition rules. Subsequent coarse graining is accomplished by applying the renormalization group, which yields trajectories from initial conditions determined by the regularized atomistic models. These trajectories correspond to hierarchies of continuum equations that describe the original lattice models over expanding length and time scales as the extent of coarse graining increases. This provides a systematic method for the derivation of continuum equations from the transition rules of lattice models appropriate for any length and time scales, and thereby establishes a quantitative link between atomistic transition rules and the collective behavior of the system. The results obtained with this method are confirmed by all available kinetic Monte Carlo simulations and, in some cases, have provided new interpretations of previous experimental observations. In this review, we first discuss the elements of our multiscale method in general terms, and then illustrate their implementation for specific growth models.

scholarly journals Time scales for dynamical relaxation to the Born rule

2011 ◽  
Vol 468 (2140) ◽  
pp. 990-1013 ◽  
Author(s):  
M. D. Towler ◽  
N. J. Russell ◽  
Antony Valentini
Keyword(s):  
Wave Function ◽  
Time Scales ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Relativistic Quantum Mechanics ◽  
Inflationary Cosmology ◽  
Electron Trajectory ◽  
Born Rule ◽  
Pilot Wave ◽  
De Broglie Bohm

We illustrate through explicit numerical calculations how the Born rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie–Bohm pilot-wave theory. The time evolution of a particle distribution initially not equal to the absolute square of the wave function is calculated for a particle in a two-dimensional infinite potential square well. Under the de Broglie–Bohm ontology, the box contains an objectively existing ‘pilot wave’ which guides the electron trajectory, and this is represented mathematically by a Schrödinger wave function composed of a finite out-of-phase superposition of M energy eigenstates (with M ranging from 4 to 64). The electron density distributions are found to evolve naturally into the Born rule ones and stay there; in analogy with the classical case this represents a decay to ‘quantum equilibrium’. The proximity to equilibrium is characterized by the coarse-grained subquantum H -function which is found to decrease roughly exponentially towards zero over the course of time. The time scale τ for this relaxation is calculated for various values of M and the coarse-graining length ε . Its dependence on M is found to disagree with an earlier theoretical prediction. A power law, τ ∝ M −1 , is found to be fairly robust for all coarse-graining lengths and, although a weak dependence of τ on ε is observed, it does not appear to follow any straightforward scaling. A theoretical analysis is presented to explain these results. This improvement in our understanding of time scales for relaxation to quantum equilibrium is likely to be of use in the development of models of relaxation in the early Universe, with a view to constraining possible violations of the Born rule in inflationary cosmology.

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