Biomedical subjects

D A Head

Publications and source records attributed to D A Head.

8 recordsLinked to original sources

PubMed2006

Modeling the elastic deformation of polymer crusts formed by sessile droplet evaporation.

Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapor interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by nonlinear quasistatic simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a nonuniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find that data collapse onto a master curve for both buckling pressure and deformation mode, thus allowing us to predict when the deformed shape is a dimple, Mexican hat, and so on. This master curve is parameterized by a dimensionless measure of the nonuniformity of the shell. We also speculate on how overlapping time scales for gelation and deformation may alter our findings.

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PubMed2005

Mechanical response of semiflexible networks to localized perturbations.

Previous research on semiflexible polymers including cytoskeletal networks in cells has suggested the existence of distinct regimes of elastic response, in which the strain field is either uniform (affine) or nonuniform (nonaffine) under external stress. Associated with these regimes, it has been further suggested that a mesoscopic length scale emerges, which characterizes the scale for the crossover from nonaffine to affine deformations. Here, we extend these studies by probing the response to localized forces and force dipoles. We show that the previously identified nonaffinity length [D. A. Head, Phys. Rev. E 68, 061907 (2003)] controls the mesoscopic response to point forces and the crossover to continuum elastic behavior at large distances.

Animals↗

PubMed2005

Mean-field description of jamming in noncohesive frictionless particulate systems.

A theory for kinetic arrest in isotropic systems of repulsive, radially interacting particles is presented that predicts exponents for the scaling of various macroscopic quantities near the rigidity transition that are in agreement with simulations, including the nontrivial shear exponent. Both statics and dynamics are treated in a simplified, one-particle level description and coupled via the assumption that kinetic arrest occurs on the boundary between mechanically stable and unstable regions of the static parameter diagram. This suggests that the arrested states observed in simulations are at (or near) an elastic buckling transition. Some additional numerical evidence to confirm the scaling of microscopic quantities is also provided.

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PubMed2003

Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks.

Semiflexible polymers such as filamentous actin (F-actin) play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominately affine and the filaments stretch and compress; and a second in which bending modes dominate. We identify a dimensionless scalar quantity, being a combination of the material length scales, that specifies to which regime a given network belongs. A scaling argument is presented that approximately agrees with this crossover variable. By a direct geometric measure, we also confirm that the degree of affinity under strain correlates with the distinct elastic regimes. We discuss the implications of our findings and suggest possible directions for future investigations.

Actins↗

PubMed2003

Nonuniversality of elastic exponents in random bond-bending networks.

We numerically investigate the rigidity percolation transition in two-dimensional flexible, random rod networks with freely rotating cross links. Near the transition, networks are dominated by bending modes and the elastic modulii vanish with an exponent f=3.0+/-0.2, in contrast with central force percolation which shares the same geometric exponents. This indicates that universality for geometric quantities does not imply universality for elastic ones. The implications of this result for actin-fiber networks is discussed.

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PubMed2002

Rheological chaos in a scalar shear-thickening model.

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress sigma is driven at a constant shear rate gamma; and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(sigma(1)) and a linear decay at rate lambda sigma(2). Here sigma(1,2)(t)= tau(-1)(1,2) integral (t)(0)sigma(t')exp[-(t-t')/tau(1,2)]dt' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when tau(2)>tau(1) and 0>R'(sigma)>-lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of the material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case tau(1)-->0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.

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PubMed2002

Universal persistence exponents in an extremally driven system.

The local persistence R(t), defined as the proportion of the system still in its initial state at time t, is measured for the Bak-Sneppen model. For one and two dimensions, it is found that the decay of R(t) depends on one of two classes of initial configuration. For a subcritical initial state, R(t) equivalent to t(-theta), where the persistence exponent theta can be expressed in terms of a known universal exponent. Hence theta is universal. Conversely, starting from a supercritical state, R(t) decays by the anomalous form 1-R(t) equivalent to t(tau(all)) until a finite time t(0), where tau(all) is also a known exponent. Finally, for the high dimensional model R(t) decays exponentially with a nonuniversal decay constant.

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PubMed2001

Jamming, hysteresis, and oscillation in scalar models for shear thickening.

We investigate shear thickening and jamming within the framework of a family of spatially homogeneous, scalar rheological models. These are based on the "soft glassy rheology" model of Sollich et al. [Phys. Rev. Lett. 78, 2020 (1997)], but with an effective temperature x that is a decreasing function of either the global stress sigma or the local strain l. For appropriate x=x(sigma), it is shown that the flow curves include a region of negative slope, around which the stress exhibits hysteresis under a cyclically varying imposed strain rate (.)gamma.A subclass of these x(sigma) have flow curves that touch the (.)gamma=0 axis for a finite range of stresses; imposing a stress from this range jams the system, in the sense that the strain gamma creeps only logarithmically with time t, gamma(t) approximately ln t. These same systems may produce a finite asymptotic yield stress under an imposed strain, in a manner that depends on the entire stress history of the sample, a phenomenon we refer to as history-dependent jamming. In contrast, when x=x(l) the flow curves are always monotonic, but we show that some x(l) generate an oscillatory strain response for a range of steady imposed stresses. Similar spontaneous oscillations are observed in a simplified model with fewer degrees of freedom. We discuss this result in relation to the temporal instabilities observed in rheological experiments and stick-slip behavior found in other contexts, and comment on the possible relationship with "delay differential equations" that are known to produce oscillations and chaos.

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