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 $200$ 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, $\rho$, 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 $\rho$ is fully determined. Finally, cell motility is shown to linearly decrease with increasing $\rho$, 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