Shear stress in lattice Boltzmann simulations

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also investigated which value of the relaxation parameter minimizes the error. Furthermore, for simulations using velocity boundary conditions, an artificial mass increase is often observed. This is a consequence of the compressibility of the lattice Boltzmann fluid. We investigate this issue and derive an analytic expression for the time-dependence of the fluid density in terms of the Reynolds number, Mach number and a geometric factor for the case of a Poiseuille flow through a rectangular channel in three dimensions. Comparison of the analytic expression with results of lattice Boltzmann simulations shows excellent agreement.Comment: 15 pages, 4 figures, 2 table

Modeling and Analysis of Resource Sharing Approach in Common Platform Strategy Using Petri Net Theory

The most competitive advantages in business and manufacturing is resource-sharing.We must share common resources to produce a group of product family with using common platform strategy. This strategy helps us to increase profit and value in business. It is necessary to apply this strategy to model and analyze resource achievability in different situations. In this paper we try to develop a practical model for analyzing common resource behavioral in platform area with using Petri net theory. Petri Nets have been successfully used for modeling and control the dynamics of flexible manufacturing systems.This paper presents some important concepts about common platform and petri net theory and then presents numerical examples to show how to use Petri net for modeling and analysis in common platform. This model is very useful for common platform strategy and can be used to determine reliability of common platform systems in an effective way

Multiple character of non-monotonic size-dependence for relaxation dynamics in polymer-particle and binary mixtures

Adding plasticizers is a well-known procedure to reduce the glass transition temperature in polymers. It has been recently shown that this effect shows a non-monotonic dependence on the size of additive molecules [The Journal of Chemical Physics 150 (2019) 024903]. In this work, we demonstrate that, as the size of the additive molecules is changed at fixed concentration, multiple extrema emerge in the dependence of the system's relaxation time on the size ratio. The effect occurs on all relevant length scales including single monomer dynamics, decay of Rouse modes and relaxation of the chain's end-to-end vector. A qualitatively similar trend is found within mode-coupling theoretical results for a binary hard-sphere (HS) mixture. An interpretation of the effect in terms of local packing efficiency and coupling between the dynamics of minority and majority species is provided.Comment: 16 pages, 7 figure

Leucine-rich amelogenin peptide (LRAP) as a surface primer for biomimetic remineralization of superficial enamel defects: An in vitro study

This study was carried out to obtain more information about the assembly of hydroxyapatite bundles formed in the presence of Leucine-Rich Amelogenin Peptide (LRAP) and to evaluate its effect on the remineralization of enamel defects through a biomimetic approach. One or 2 mg/mL LRAP solutions containing 2.5 mM of Ca+2 and 1.5 mM phosphate were prepared (pH = 7.2) and stored at 37 °C for 24 h. The products of the reaction were studied using atomic force microscopy (AFM), transmission electron microscopy (TEM), and selected area electron diffraction (SAED). Vickers surface microhardness recovery (SMR) of acid-etched bovine enamel, with or without LRAP surface treatment, were calculated to evaluate the influence of peptide on the lesion remineralization. Distilled water and 1 or 2 mg/mL LRAP solution (pH = 7.2) were applied on the lesions and the specimens were incubated in mineralization solution (2.5mM Ca+2, 1.5mM PO4 -3, pH = 7.2) for 24 h. One-way ANOVA and Tukey's multi-comparison tests were used for statistical analysis. The pattern of enamel surface repair was studied using FE-SEM. AFM showed the formation of highly organized hierarchical structures, composed of hydroxyapatite (HA) crystals, similar to the dental enamel microstructure. ANOVA procedure showed significant effect of peptide treatment on the calculated SMR (p < 0.001). Tukey's test revealed that peptide treated groups had significantly higher values of SMR. In conclusion, LRAP is able to regulate the formation of HA and enhances the remineralization of acid-etched enamel as a surface treatment agent. © 2015 Wiley Periodicals, Inc

Long-range strain correlations in 3D quiescent glass forming liquids

We present a quantitative study of strain correlations in quiescent supercooled liquids and glasses. Recent two-dimensional computer simulations and experiments indicate that even supercooled liquids exhibit long-lived, long-range strain correlations. Here we investigate this issue in three dimensions via experiments on hard sphere colloids and molecular dynamics simulations of a glass forming binary Lennard Jones mixture. Both in the glassy state and in the supercooled regime, strain correlations are found to decay with a $1/r^{3}$ power-law behavior, reminiscent of elastic fields around an inclusion. Moreover, theoretical predictions on the time dependence of the correlation amplitude are in line with the results obtained from experiments and simulations. It is argued that the size of the domain, which exhibits a "solid-like" cooperative strain pattern in a supercooled liquid, is determined by the product of the speed of sound with the structural relaxation time. While this length is of the order of nanometers in the normal liquid state, it grows to macroscale when approaching the glass transition

Critical dynamics of an isothermal compressible non-ideal fluid

A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible non-ideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.Comment: 19 pages, 7 figures; v3: minor corrections and clarifications; as published in Phys. Rev.

Fluctuations and diffusion in sheared athermal suspensions of deformable particles

We analyze fluctuations of particle displacements and stresses in a sheared athermal suspension of elastic capsules (red blood cells). Upon variation of the volume fraction from the dilute up to the highly concentrated regime, our numerical simulations reveal different characteristic power-law regimes of the fluctuation variances and relaxation times. In the jammed phase and at high shear rates, anomalous scaling exponents are found that deviate from pure dimensional predictions. The observed behavior is rationalized via kinetic arguments and a dissipation balance model that takes into account the local fluid flows between the particles. Our findings support the view that the rheology of dense suspensions is essentially governed by the non-affine displacements.Comment: 6 pages, 6 figure

Molecular Dynamics Simulations

A tutorial introduction to the technique of Molecular Dynamics (MD) is given, and some characteristic examples of applications are described. The purpose and scope of these simulations and the relation to other simulation methods is discussed, and the basic MD algorithms are described. The sampling of intensive variables (temperature T, pressure p) in runs carried out in the microcanonical (NVE) ensemble (N= particle number, V = volume, E = energy) is discussed, as well as the realization of other ensembles (e.g. the NVT ensemble). For a typical application example, molten SiO2, the estimation of various transport coefficients (self-diffusion constants, viscosity, thermal conductivity) is discussed. As an example of Non-Equilibrium Molecular Dynamics (NEMD), a study of a glass-forming polymer melt under shear is mentioned.Comment: 38 pages, 11 figures, to appear in J. Phys.: Condens. Matte