Equilibration of Long Chain Polymer Melts in Computer Simulations

Several methods for preparing well equilibrated melts of long chains polymers are studied. We show that the standard method in which one starts with an ensemble of chains with the correct end-to-end distance arranged randomly in the simulation cell and introduces the excluded volume rapidly, leads to deformation on short length scales. This deformation is strongest for long chains and relaxes only after the chains have moved their own size. Two methods are shown to overcome this local deformation of the chains. One method is to first pre-pack the Gaussian chains, which reduces the density fluctuations in the system, followed by a gradual introduction of the excluded volume. The second method is a double-pivot algorithm in which new bonds are formed across a pair of chains, creating two new chains each substantially different from the original. We demonstrate the effectiveness of these methods for a linear bead spring polymer model with both zero and nonzero bending stiffness, however the methods are applicable to more complex architectures such as branched and star polymer.Comment: 12 pages, 9 figure

Noise-induced oscillatory shuttling of NF-{\kappa}B in a two compartment IKK-NF-{\kappa}B-I{\kappa}B-A20 signaling model

NF-{\kappa}B is a pleiotropic protein whose nucleo-cytoplasmic trafficking is tightly regulated by multiple negative feedback loops embedded in the NF-{\kappa}B signaling network and contributes to diverse gene expression profiles important in immune cell differentiation, cell apoptosis, and innate immunity. The intracellular signaling processes and their control mechanisms, however, are susceptible to both extrinsic and intrinsic noise. In this article, we present numerical evidence for a universal dynamic behavior of NF-{\kappa}B, namely oscillatory nucleo-cytoplasmic shuttling, due to the fundamentally stochastic nature of the NF-{\kappa}B signaling network. We simulated the effect of extrinsic noise with a deterministic ODE model, using a statistical ensemble approach, generating many copies of the signaling network with different kinetic rates sampled from a biologically feasible parameter space. We modeled the effect of intrinsic noise by simulating the same networks stochastically using the Gillespie algorithm. The results demonstrate that extrinsic noise diversifies the shuttling patterns of NF-{\kappa}B response, whereas intrinsic noise induces oscillatory behavior in many of the otherwise non-oscillatory patterns. We identify two key model parameters which significantly affect the NF-{\kappa}B dynamic response and deduce a two-dimensional phase-diagram of the NF-{\kappa}B response as a function of these parameters. We conclude that if single-cell experiments are performed, a rich variety of NF-{\kappa}B response will be observed, even if population-level experiments, which average response over large numbers of cells, do not evidence oscillatory behavior.Comment: 49 pages, 12 figure

Evaporation of Lennard-Jones Fluids

Evaporation and condensation at a liquid/vapor interface are ubiquitous interphase mass and energy transfer phenomena that are still not well understood. We have carried out large scale molecular dynamics simulations of Lennard-Jones (LJ) fluids composed of monomers, dimers, or trimers to investigate these processes with molecular detail. For LJ monomers in contact with a vacuum, the evaporation rate is found to be very high with significant evaporative cooling and an accompanying density gradient in the liquid domain near the liquid/vapor interface. Increasing the chain length to just dimers significantly reduces the evaporation rate. We confirm that mechanical equilibrium plays a key role in determining the evaporation rate and the density and temperature profiles across the liquid/vapor interface. The velocity distributions of evaporated molecules and the evaporation and condensation coefficients are measured and compared to the predictions of an existing model based on kinetic theory of gases. Our results indicate that for both monatomic and polyatomic molecules, the evaporation and condensation coefficients are equal when systems are not far from equilibrium and smaller than one, and decrease with increasing temperature. For the same reduced temperature $T/T_c$, where $T_c$ is the critical temperature, these two coefficients are higher for LJ dimers and trimers than for monomers, in contrast to the traditional viewpoint that they are close to unity for monatomic molecules and decrease for polyatomic molecules. Furthermore, data for the two coefficients collapse onto a master curve when plotted against a translational length ratio between the liquid and vapor phase.Comment: revised version, 15 pages, 15 figures, to appear in J. Chem. Phy

Confined granular packings: structure, stress, and forces

The structure and stresses of static granular packs in cylindrical containers are studied using large-scale discrete element molecular dynamics simulations in three dimensions. We generate packings by both pouring and sedimentation and examine how the final state depends on the method of construction. The vertical stress becomes depth-independent for deep piles and we compare these stress depth-profiles to the classical Janssen theory. The majority of the tangential forces for particle-wall contacts are found to be close to the Coulomb failure criterion, in agreement with the theory of Janssen, while particle-particle contacts in the bulk are far from the Coulomb criterion. In addition, we show that a linear hydrostatic-like region at the top of the packings unexplained by the Janssen theory arises because most of the particle-wall tangential forces in this region are far from the Coulomb yield criterion. The distributions of particle-particle and particle-wall contact forces $P(f)$ exhibit exponential-like decay at large forces in agreement with previous studies.Comment: 11 pages, 11 figures, submitted to PRE (v2) added new references, fixed typo

Granular Flow Down an Inclined Plane: Bagnold Scaling and Rheology

We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow vx(z) scales with height of the pile H, according to vx(z)∝Hα, with α=1.52±0.05. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations

Dynamical heterogeneities in a supercooled Lennard-Jones liquid

We present the results of a large scale molecular dynamics computer simulation study in which we investigate whether a supercooled Lennard-Jones liquid exhibits dynamical heterogeneities. We evaluate the non-Gaussian parameter for the self part of the van Hove correlation function and use it to identify ``mobile'' particles. We find that these particles form clusters whose size grows with decreasing temperature. We also find that the relaxation time of the mobile particles is significantly shorter than that of the bulk, and that this difference increases with decreasing temperature.Comment: 8 pages of RevTex, 4 ps figure