13,501 research outputs found
Lattice Boltzmann method for viscoelastic fluids
Lattice Boltzmann model for viscoelastic flow simulation is proposed; elastic
effects are taken into account in the framework of Maxwell model. The following
three examples are studied using the proposed approach: a transverse velocity
autocorrelation function for free evolving system with random initial
velocities, a boundary-driven propagating shear waves, and a resonant
enhancement of oscillations in a periodically driven fluid in a capillary. The
measured shear wave dispersion relation is found to be in a good agreement with
the theoretical one derived for the Navier-Stokes equation with the Maxwell
viscoelastic term.Comment: 4 pages, 5 figure
Unfolding designable structures
Among an infinite number of possible folds, nature has chosen only about 1000
distinct folds to form protein structures. Theoretical studies suggest that
selected folds are intrinsically more designable than others; these selected
folds are unusually stable, a property called the designability principle. In
this paper we use the 2D hydrophobic-polar lattice model to classify structures
according to their designability, and Langevin dynamics to account for their
time evolution. We demonstrate that, among all possible folds, the more
designable ones are easier to unfold due to their large number of surface-core
bonds.Comment: 10 pages, 4 figures, Proceeding of the 3rd International Conference
NEXT-SigmaPh
Phase Field Crystals as a Coarse-Graining in Time of Molecular Dynamics
Phase field crystals (PFC) are a tool for simulating materials at the atomic
level. They combine the small length-scale resolution of molecular dynamics
(MD) with the ability to simulate dynamics on mesoscopic time scales. We show
how PFC can be interpreted as the result of applying coarse-graining in time to
the microscopic density field of molecular dynamics simulations. We take the
form of the free energy for the phase field from the classical density
functional theory of inhomogeneous liquids and then choose coefficients to
match the structure factor of the time coarse-grained microscopic density
field. As an example, we show how to construct a PFC free energy for Weber and
Stillinger's two-dimensional square crystal potential which models a system of
proteins suspended in a membrane.Comment: 5 pages, 4 figures, typos corrected, more explanation in parts,
equilib vs non-equilib clarifie
Effects of cell elasticity on the migration behavior of a monolayer of motile cells: Sharp Interface Model
In order to study the effect of cell elastic properties on the behavior of
assemblies of motile cells, this paper describes an alternative to the cell
phase field (CPF) \cite{Palmieri2015} we have previously proposed. The CPF is a
multi-scale approach to simulating many cells which tracked individual cells
and allowed for large deformations. Though results were largely in agreement
with experiment that focus on the migration of a soft cancer cell in a
confluent layer of normal cells \cite{Lee2012}, simulations required large
computing resources, making more detailed study unfeasible. In this work we
derive a sharp interface limit of CPF, including all interactions and
parameters. This new model offers over fold speedup when compared to our
original CPF implementation. We demonstrate that this model captures similar
behavior and allows us to obtain new results that were previously intractable.
We obtain the full velocity distribution for a large range of degrees of
confluence, , and show regimes where its tail is heavier and lighter than
a normal distribution. Furthermore, we fully characterize the velocity
distribution with a single parameter, and its dependence on is fully
determined. Finally, cell motility is shown to linearly decrease with
increasing , consistent with previous theoretical results
Modeling multiple time scales during glass formation with phase-field crystals
The dynamics of glass formation in monatomic and binary liquids are studied
numerically using a microscopic field theory for the evolution of the
time-averaged atomic number density. A stochastic framework combining phase
field crystal free energies and dynamic density functional theory is shown to
successfully describe several aspects of glass formation over multiple time
scales. Agreement with mode coupling theory is demonstrated for underdamped
liquids at moderate supercoolings, and a rapidly growing dynamic correlation
length is found to be associated with fragile behavior.Comment: 4+ pages, 4 figures, to appear in Physical Review Letter
Characterizing Strategic Cascades on Networks
Transmission of disease, spread of information and rumors, adoption of new
products, and many other network phenomena can be fruitfully modeled as
cascading processes, where actions chosen by nodes influence the subsequent
behavior of neighbors in the network graph. Current literature on cascades
tends to assume nodes choose myopically based on the state of choices already
taken by other nodes. We examine the possibility of strategic choice, where
agents representing nodes anticipate the choices of others who have not yet
decided, and take into account their own influence on such choices. Our study
employs the framework of Chierichetti et al. [2012], who (under assumption of
myopic node behavior) investigate the scheduling of node decisions to promote
cascades of product adoptions preferred by the scheduler. We show that when
nodes behave strategically, outcomes can be extremely different. We exhibit
cases where in the strategic setting 100% of agents adopt, but in the myopic
setting only an arbitrarily small epsilon % do. Conversely, we present cases
where in the strategic setting 0% of agents adopt, but in the myopic setting
(100-epsilon)% do, for any constant epsilon > 0. Additionally, we prove some
properties of cascade processes with strategic agents, both in general and for
particular classes of graphs.Comment: To appear in EC 201
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