A Continuum-Microscopic Algorithm for Modeling Fibrous, Heterogeneous Media with Dynamic Microstructures

Many materials undergo reconfiguration of microscopic structure in response to applied stress. Computing the mechanical behavior of such materials at the continuum level requires a locally valid stress-strain relation. Due to the dynamic microstructure reconfiguration, such relations are difficult to obtain analytically. Numerical simulation of the microscopic dynamics is an alternative, albeit one that is computationally expensive. Continuum-microscopic (CM) interaction algorithms seek to reduce computational cost by microscopic simulation over some small fraction of the continuum time step of interest, enough to determine the locally valid stress-strain relationship, assumed to hold over the entire continuum time step. One difficulty with this approach is the problem of recreating a valid microscopic configuration at the start of the next continuum time step. In most previous CM algorithms, the microscopic structure at the beginning of a new continuum time step is assumed to obey some predefined statistical distribution. This paper extends current CM methods by applying a probability distribution function (PDF) estimation procedure to describe local microscopic states within each continuum computational cell. The estimated PDFs are extrapolated forward over a continuum time step to recreate new microscopic configurations. This procedure captures local variability in the microscopic structure. The algorithm is applied to a generic fibrous material with randomly oriented, cross-linked fibers. Numerical results show that the procedure furnishes continuum stress and strain values to within 5-10% of those obtained from averaging a full microscopic simulation. The computational time is reduced by a factor of two in serial computation and by an order of magnitude when the PDF estimation procedures are computed in parallel

Continuum-kinetic-microscopic model of lung clearance due to core-annular fluid entrainment

The human lung is protected against aspirated infectious and toxic agents by a thin liquid layer lining the interior of the airways. This airway surface liquid is a bilayer composed of a viscoelastic mucus layer supported by a fluid film known as the periciliary liquid. The viscoelastic behavior of the mucus layer is principally due to long-chain polymers known as mucins. The airway surface liquid is cleared from the lung by ciliary transport, surface tension gradients, and airflow shear forces. This work presents a multiscale model of the effect of airflow shear forces, as exerted by tidal breathing and cough, upon clearance. The composition of the mucus layer is complex and variable in time. To avoid the restrictions imposed by adopting a viscoelastic flow model of limited validity, a multiscale computational model is introduced in which the continuum-level properties of the airway surface liquid are determined by microscopic simulation of long-chain polymers. A bridge between microscopic and continuum levels is constructed through a kinetic-level probability density function describing polymer chain configurations. The overall multiscale framework is especially suited to biological problems due to the flexibility afforded in specifying microscopic constituents, and examining the effects of various constituents upon overall mucus transport at the continuum scale

Metachronal wave formation in a model of pulmonary cilia

A three-dimensional simulation of the formation of metachronal waves in rows of pulmonary cilia is presented. The cilia move in a two-layer fluid model. The fluid layer adjacent to the cilia bases is purely viscous while the tips of the cilia move through a viscoelastic fluid. An overlapping fixed-moving grid formulation is employed to capture the effect of the cilia on the surrounding fluid. In contrast with immersed boundary methods, this technique allows a natural enforcement of boundary conditions without the need for smoothing of singular force distributions. The fluid domains are discretized using a finite volume method. The 9 + 2 internal microtubule structure of an individual cilium is modeled using large-deflection, curved, finite-element beams. The microtubule skeleton is cross-linked to itself and to the cilium membrane through spring elements which model nexin links. The cilium membrane itself is considered to be elastic and subject to fluid stresses computed from the moving grid formulation as well as internal forces transmitted from the microtubule skeleton. A cilium is set into motion by the action of dynein molecules exerting forces between adjacent microtubules. Realistic models of the forces exerted by dynein molecules are extracted from measurements of observed cilia shapes

A numerical model of cellular blebbing: A volume-conserving, fluid–structure interaction model of the entire cell

In animal cells, blebs are smooth, quasi-hemispherical protrusions of the plasma membrane that form when a section of the membrane detaches from the underlying actin cytoskeleton and is inflated by flowing cytosol. The mechanics behind this common cellular activity are not yet clear. As a first step in the development of a full computational framework, we present a numerical model of overall cell behavior based upon the interaction between a background Newtonian-fluid cytosol and elastic structures modeling the membrane and filaments. The detailed micromechanics of the cytoskeletal network are the subject of future work. Here, the myosin-driven contraction of the actin network is modeled through stressed elastic filaments. Quantitative models of cytoskeletal micromechanics and biochemistry require accurate estimates of local stress and flow conditions. The main contribution of this paper is the development of a computationally efficient fluid-structure interaction model based on operator splitting, to furnish this data. Cytosol volume conservation, (as supported by experimental evidence), is enforced through an intermediate energy minimization step. Realistic bleb formation and retraction is observed from this model, offering an alternative formulation to positing complex continuum behavior of the cytoplasm (e.g. poroelastic model of [Charras et al., 2008])

Proto–Planetary Nebulae as Explosions: Bullets versus Jets and Nebular Shaping

Many proto-planetary nebulae (PPNs) appear as narrow collimated structures sometimes showing multiple, roughly aligned lobes. In addition, many PPN flows have been shown to have short acceleration times. In this paper we explore whether jet or "bullet" (a massive clump) models fit the observations of individual collimated lobes adequately by comparing simulations of both radiatively cooled (stable) jets and bullets. We find that the clump model is favored over jets because (1) it leads to greater collimation of outflows, (2) it accounts better and more naturally for ringlike structures observed in the PPN CRL 618, and (3) it is more successful in reproducing the Hubble-flow character of observed kinematics in some PPNs. In addition, bullets naturally account for observed multipolar flows, since the likely MHD launch mechanisms required to drive outflows make multiple nonaligned jets unlikely. We also find that the bow shock heads of bullets take on a -shaped configuration, whereas bow shock heads of jets are more -shaped. The differences in these configurations occur on a linear scale corresponding to an angular size of the order of ~3''—sufficiently large to suggest a viable means of distinguishing bullets from jets in observations. We argue that PPN outflows may be driven by explosive MHD launch mechanisms such as those discussed in the context of supernovae (SNe) and gamma-ray bursts (GRBs)

A consistent hierarchy of generalized kinetic equation approximations to the chemical master equation applied to surface catalysis

We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations, are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models

Effects of Stone Size on the Comminution Process and Efficiency in Shock Wave Lithotripsy

The effects of stone size on the process and comminution efficiency in shock wave lithotripsy (SWL) are investigated by experiments, numerical simulations, and scale analysis. Cylindrical BegoStone phantoms with approximately equal height and diameter of either 4-, or 7- or 10-mm, in a total aggregated mass of about 1.5 g, were treated in an electromagnetic shock wave lithotripter field. The resultant stone comminution (SC) was found to correlate closely with the average peak pressure, P+(avg), incident on the stones. The P+(avg) threshold to initiate stone fragmentation in water increased from 7.9 to 8.8 to 12.7 MPa, respectively, when the stone size decreased from 10 to 7 to 4 mm. Similar changes in the P+(avg) threshold were observed for the 7- and 10-mm stones treated in 1,3-butanediol where cavitation is suppressed, suggesting that the observed size dependency is due to changes in stress distribution within different size stones. Moreover, the slope of the correlation curve between SC and ln(P‒+(avg)) in water increased with decreasing stone size, while the opposite trend was observed in 1,3-butanediol. The progression of stone comminution in SWL showed a size-dependency with the 7- and 10-mm stones fragmented into progressively smaller pieces while a significant portion (> 30%) of the 4-mm stones were stalemated within the size range of 2.8 ~ 4 mm even after 1,000 shocks. Analytical scaling considerations suggest size-dependent fragmentation behaviour, a hypothesis further supported by numerical model calculations that exhibit changing patterns of constructive and destructive wave interference, and thus variations in the maximum tensile stress or stress integral produced in cylindrical and spherical stone of different sizes