5,419 research outputs found
Evidence for a continuum limit in causal set dynamics
We find evidence for a continuum limit of a particular causal set dynamics
which depends on only a single ``coupling constant'' and is easy to
simulate on a computer. The model in question is a stochastic process that can
also be interpreted as 1-dimensional directed percolation, or in terms of
random graphs.Comment: 24 pages, 19 figures, LaTeX, adjusted terminolog
Influence of pH and sequence in peptide aggregation via molecular simulation
We employ a recently developed coarse-grained model for peptides and proteins
where the effect of pH is automatically included. We explore the effect of pH
in the aggregation process of the amyloidogenic peptide KTVIIE and two related
sequences, using three different pH environments. Simulations using large
systems (24 peptides chains per box) allow us to correctly account for the
formation of realistic peptide aggregates. We evaluate the thermodynamic and
kinetic implications of changes in sequence and pH upon peptide aggregation,
and we discuss how a minimalistic coarse-grained model can account for these
details.Comment: 21 pages, 4 figure
Multilevel coarse graining and nano--pattern discovery in many particle stochastic systems
In this work we propose a hierarchy of Monte Carlo methods for sampling
equilibrium properties of stochastic lattice systems with competing short and
long range interactions. Each Monte Carlo step is composed by two or more sub -
steps efficiently coupling coarse and microscopic state spaces. The method can
be designed to sample the exact or controlled-error approximations of the
target distribution, providing information on levels of different resolutions,
as well as at the microscopic level. In both strategies the method achieves
significant reduction of the computational cost compared to conventional Markov
Chain Monte Carlo methods. Applications in phase transition and pattern
formation problems confirm the efficiency of the proposed methods.Comment: 37 page
Coupled coarse graining and Markov Chain Monte Carlo for lattice systems
We propose an efficient Markov Chain Monte Carlo method for sampling
equilibrium distributions for stochastic lattice models, capable of handling
correctly long and short-range particle interactions. The proposed method is a
Metropolis-type algorithm with the proposal probability transition matrix based
on the coarse-grained approximating measures introduced in a series of works of
M. Katsoulakis, A. Majda, D. Vlachos and P. Plechac, L. Rey-Bellet and
D.Tsagkarogiannis,. We prove that the proposed algorithm reduces the
computational cost due to energy differences and has comparable mixing
properties with the classical microscopic Metropolis algorithm, controlled by
the level of coarsening and reconstruction procedure. The properties and
effectiveness of the algorithm are demonstrated with an exactly solvable
example of a one dimensional Ising-type model, comparing efficiency of the
single spin-flip Metropolis dynamics and the proposed coupled Metropolis
algorithm.Comment: 20 pages, 4 figure
Coarse-grained simulations of flow-induced nucleation in semi-crystalline polymers
We perform kinetic Monte Carlo simulations of flow-induced nucleation in
polymer melts with an algorithm that is tractable even at low undercooling. The
configuration of the non-crystallized chains under flow is computed with a
recent non-linear tube model. Our simulations predict both enhanced nucleation
and the growth of shish-like elongated nuclei for sufficiently fast flows. The
simulations predict several experimental phenomena and theoretically justify a
previously empirical result for the flow-enhanced nucleation rate. The
simulations are highly pertinent to both the fundamental understanding and
process modeling of flow-induced crystallization in polymer melts.Comment: 17 pages, 6 eps figure
Self-Assembly of Nanocomponents into Composite Structures: Derivation and Simulation of Langevin Equations
The kinetics of the self-assembly of nanocomponents into a virus,
nanocapsule, or other composite structure is analyzed via a multiscale
approach. The objective is to achieve predictability and to preserve key
atomic-scale features that underlie the formation and stability of the
composite structures. We start with an all-atom description, the Liouville
equation, and the order parameters characterizing nanoscale features of the
system. An equation of Smoluchowski type for the stochastic dynamics of the
order parameters is derived from the Liouville equation via a multiscale
perturbation technique. The self-assembly of composite structures from
nanocomponents with internal atomic structure is analyzed and growth rates are
derived. Applications include the assembly of a viral capsid from capsomers, a
ribosome from its major subunits, and composite materials from fibers and
nanoparticles. Our approach overcomes errors in other coarse-graining methods
which neglect the influence of the nanoscale configuration on the atomistic
fluctuations. We account for the effect of order parameters on the statistics
of the atomistic fluctuations which contribute to the entropic and average
forces driving order parameter evolution. This approach enables an efficient
algorithm for computer simulation of self-assembly, whereas other methods
severely limit the timestep due to the separation of diffusional and complexing
characteristic times. Given that our approach does not require recalibration
with each new application, it provides a way to estimate assembly rates and
thereby facilitate the discovery of self-assembly pathways and kinetic dead-end
structures.Comment: 34 pages, 11 figure
Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms
We present a mathematical framework for constructing and analyzing parallel
algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting
algorithms have the capacity to simulate a wide range of spatio-temporal scales
in spatially distributed, non-equilibrium physiochemical processes with complex
chemistry and transport micro-mechanisms. The algorithms can be tailored to
specific hierarchical parallel architectures such as multi-core processors or
clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms
are controlled-error approximations of kinetic Monte Carlo algorithms,
departing from the predominant paradigm of creating parallel KMC algorithms
with exactly the same master equation as the serial one.
Our methodology relies on a spatial decomposition of the Markov operator
underlying the KMC algorithm into a hierarchy of operators corresponding to the
processors' structure in the parallel architecture. Based on this operator
decomposition, we formulate Fractional Step Approximation schemes by employing
the Trotter Theorem and its random variants; these schemes, (a) determine the
communication schedule} between processors, and (b) are run independently on
each processor through a serial KMC simulation, called a kernel, on each
fractional step time-window.
Furthermore, the proposed mathematical framework allows us to rigorously
justify the numerical and statistical consistency of the proposed algorithms,
showing the convergence of our approximating schemes to the original serial
KMC. The approach also provides a systematic evaluation of different processor
communicating schedules.Comment: 34 pages, 9 figure
Micellar Crystals in Solution from Molecular Dynamics Simulations
Polymers with both soluble and insoluble blocks typically self-assemble into
micelles, aggregates of a finite number of polymers where the soluble blocks
shield the insoluble ones from contact with the solvent. Upon increasing
concentration, these micelles often form gels that exhibit crystalline order in
many systems. In this paper, we present a study of both the dynamics and the
equilibrium properties of micellar crystals of triblock polymers using
molecular dynamics simulations. Our results show that equilibration of single
micelle degrees of freedom and crystal formation occurs by polymer transfer
between micelles, a process that is described by transition state theory. Near
the disorder (or melting) transition, bcc lattices are favored for all
triblocks studied. Lattices with fcc ordering are also found, but only at lower
kinetic temperatures and for triblocks with short hydrophilic blocks. Our
results lead to a number of theoretical considerations and suggest a range of
implications to experimental systems with a particular emphasis on Pluronic
polymers.Comment: 12 pages, 11 figures. Note that some figures are extremely low
quality to meet arXiv's file size limit
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