arXiv subjects

F. C. MacKintosh

Publications and source records attributed to F. C. MacKintosh.

53 records · Page 3Linked to original sources

arXiv2003

Velocity distributions in dissipative granular gases

Motivated by recent experiments reporting non-Gaussian velocity distributions in driven dilute granular materials, we study by numerical simulation the properties of 2D inelastic gases. We find theoretically that the form of the observed velocity distribution is governed primarily by the coefficient of restitution $η$ and $q=N_H/N_C$, the ratio between the average number of heatings and the average number of collisions in the gas. The differences in distributions we find between uniform and boundary heating can then be understood as different limits of $q$, for $q \gg 1$ and $q \lesssim 1$ respectively.

cond-mat.soft↗

arXiv2003

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

Semiflexible polymers such as filamentous 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 predominantly 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.

cond-mat.soft↗

arXiv2003

Collapse of a semiflexible polymer in poor solvent

We investigate the dynamics and the pathways of the collapse of a single, semiflexible polymer in a poor solvent via 3-D Brownian Dynamics simulations. Earlier work indicates that the condensation of semiflexible polymers generically proceeds via a cascade through metastable racquet-shaped, long-lived intermediates towards the stable torus state. We investigate the rate of decay of uncollapsed states, analyze the preferential pathways of condensation, and describe likelihood and lifespan of the different metastable states. The simulation are performed with a bead-stiff spring model with excluded volume interaction and exponentially decaying attractive potential. The semiflexible chain collapse is studied as functions of the three relevant length scales of the phenomenon, i.e., the total chain length $L$, the persistence length $L_p$ and the condensation length $L_0 = \sqrt{k_B T L_p/u_0}$, where $u_0$ is a measure of the attractive potential per unit length. Two dimensionless ratios, $L/L_p$ and $L_0/L_p$, suffice to describe the decay rate of uncollapsed states, which appears to scale as $(L/L_p)^{1/3} (L_0/L_p)$. The condensation sequence is described in terms of the time series of the well separated energy levels associated with each metastable collapsed state. The collapsed states are described quantitatively through the spatial correlation of tangent vectors along the chain. We also compare the results obtained with a locally inextensible bead-rod chain and with a phantom bead-spring model. Finally, we show preliminary results on the effects of steady shear flow on the kinetics of collapse.

cond-mat.soft↗

arXiv2003

Non-universality 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\pm0.2, 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.

cond-mat.stat-mech↗

arXiv2003

Deformation of crosslinked semiflexible polymer networks

Networks of filamentous proteins play a crucial role in cell mechanics. These cytoskeletal networks, together with various crosslinking and other associated proteins largely determine the (visco)elastic response of cells. In this letter we study a model system of crosslinked, stiff filaments in order to explore the connection between the microstructure under strain and the macroscopic response of cytoskeletal networks. We find two distinct regimes as a function primarily of crosslink density and filament rigidity: one characterized by affine deformation and one by non-affine deformation. We characterize the crossover between these two.

cond-mat.dis-nn↗

arXiv2003

Dynamics of rigid and flexible extended bodies in viscous films and membranes

We study the dynamics of extended rod-like bodies in (or associated with) membranes and films. We demonstrate a striking difference between the mobilities in films and bulk fluids, even when the dissipation is dominated by the fluid stress: for large inclusions we find that rotation and motion perpendicular to the rod axis exhibits purely local drag, in which the drag coefficient is algebraic in the rod dimensions. We also study the dynamics of the {\em internal} modes of a semiflexible inclusion and find two dynamical regimes in the relaxation spectrum.

cond-mat.soft↗

arXiv2003

On the mobility of extended bodies in viscous films and membranes

We develop general methods to calculate the mobilities of extended bodies in (or associated with) membranes and films. We demonstrate a striking difference between in-plane motion of rod-like inclusions and the corresponding case of bulk (three-dimensional) fluids: for rotations and motion perpendicular to the rod axis, we find purely local drag, in which the drag coefficient is purely algebraic in the rod dimensions. These results, as well as the calculational methods are applicable to such problems as the diffusion of objects in or associated with Langmuir films and lipid membranes. The methods can also be simply extended to treat viscoelastic systems.

cond-mat.soft↗

arXiv2002

Metastable Intermediates in the Condensation of Semiflexible Polymers

Motivated by results from an earlier Brownian Dynamics (BD) simulation for the collapse of a single, stiff polymer in a poor solvent [B. Schnurr, F. C. MacKintosh, and D. R. M. Williams, Europhys. Lett. 51 (3), 279 (2000)] we calculate the conformational energies of the intermediate (racquet) states suggested by the simulations. In the absence of thermal fluctuations (at zero temperature) the annealed shapes of these intermediates are well-defined in certain limits, with their major structural elements given by a particular case of Euler's elastica. In appropriate units, a diagram emerges which displays the relative stability of all states, tori and racquets. We conclude that, in marked contrast to the collapse of flexible polymers, the condensation of semiflexible or stiff polymers generically proceeds via a cascade through metastable intermediates, the racquets, towards a ground state, the torus or ring, as seen in the dynamical simulations.

cond-mat.soft↗

arXiv2001

Dynamics of viscoelastic membranes

We determine both the in-plane and out-of-plane dynamics of viscoelastic membranes separating two viscous fluids in order to understand microrheological studies of such membranes. We demonstrate the general viscoelastic signatures in the dynamics of shear, bending, and compression modes. We also find a screening of the otherwise two-dimensional character of the response to point forces due to the presence of solvent. Finally, we show that there is a linear, hydrodynamic coupling between the in-plane compression modes of the membrane and the out-of-plane bending modes in the case where the membrane separates two different fluids or environments.

cond-mat.soft↗

arXiv2001

Instability of Myelin Tubes under Dehydration: deswelling of layered cylindrical structures

We report experimental observations of an undulational instability of myelin figures. Motivated by this, we examine theoretically the deformation and possible instability of concentric, cylindrical, multi-lamellar membrane structures. Under conditions of osmotic stress (swelling or dehydration), we find a stable, deformed state in which the layer deformation is given by δR ~ r^{\sqrt{B_A/(hB)}}, where B_A is the area compression modulus, B is the inter-layer compression modulus, and h is the repeat distance of layers. Also, above a finite threshold of dehydration (or osmotic stress), we find that the system becomes unstable to undulations, first with a characteristic wavelength of order \sqrt{xi d_0}, where xi is the standard smectic penetration depth and d_0 is the thickness of dehydrated region.

cond-mat.soft↗

arXiv1997

Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations

We have developed a new technique to measure viscoelasticity in soft materials such as polymer solutions, by monitoring thermal fluctuations of embedded probe particles using laser interferometry in a microscope. Interferometry allows us to obtain power spectra of fluctuating beads from 0.1 Hz to 20 kHz, and with sub-nanometer spatial resolution. Using linear response theory, we determined the frequency-dependent loss and storage shear moduli up to frequencies on the order of a kHz. Our technique measures local values of the viscoelastic response, without actively straining the system, and is especially suited to soft biopolymer networks. We studied semiflexible F-actin solutions and, as a control, flexible polyacrylamide (PAAm) gels, the latter close to their gelation threshold. With small particles, we could probe the transition from macroscopic viscoelasticity to more complex microscopic dynamics. In the macroscopic limit we find shear moduli at 0.1 Hz of G'=0.11 +/- 0.03 Pa and 0.17 +/- 0.07 Pa for 1 and 2 mg/ml actin solutions, close to the onset of the elastic plateau, and scaling behavior consistent with G(omega) as omega^(3/4) at higher frequencies. For polyacrylamide we measured plateau moduli of 2.0, 24, 100 and 280 Pa for crosslinked gels of 2, 2.5, 3 and 5% concentration (weight/volume) respectively, in agreement to within a factor of two with values obtained from conventional rheology. We also found evidence for scaling of G(omega) as ω^(1/2), consistent with the predictions of the Rouse model for flexible polymers.

cond-mat.soft↗

arXiv1997

Microscopic Viscoelasticity: Shear Moduli of Soft Materials Determined from Thermal Fluctuations

We describe a high-resolution, high-bandwidth technique for determining the local viscoelasticity of soft materials such as polymer gels. Loss and storage shear moduli are determined from the power spectra of thermal fluctuations of embedded micron-sized probe particles, observed with an interferometric microscope. This provides a passive, small-amplitude measurement of rheological properties over a much broader frequency range than previously accessible to microrheology. We study both F-actin biopolymer solutions and polyacrylamide (PAAm) gels, as model semiflexible and flexible systems, respectively. We observe high-frequency omega^(3/4) scaling of the shear modulus in F-actin solutions, in contrast to omega^(1/2) scaling for PAAm.

cond-mat.soft↗

arXiv1996

Instability and front propagation in laser-tweezed lipid bilayer tubules

We study the mechanism of the `pearling' instability seen recently in experiments on lipid tubules under a local applied laser intensity. We argue that the correct boundary conditions are fixed chemical potentials, or surface tensions Σ, at the laser spot and the reservoir in contact with the tubule. We support this with a microscopic picture which includes the intensity profile of the laser beam, and show how this leads to a steady-state flow of lipid along the surface and gradients in the local lipid concentration and surface tension (or chemical potential). This leads to a natural explanation for front propagation and makes several predictions based on the tubule length. While most of the qualitative conclusions of previous studies remain the same, the `ramped' control parameter (surface tension) implies several new qualitative results. We also explore some of the consequences of front propagation into a noisy (due to pre-existing thermal fluctuations) unstable medium.

cond-mat.soft↗

arXiv1996

n-atic Order and Continuous Shape Changes of Deformable Surfaces of Genus Zero

We consider in mean-field theory the continuous development below a second-order phase transition of $n$-atic tangent plane order on a deformable surface of genus zero with order parameter $ψ= \langle e^{i n θ} \rangle$. Tangent plane order expels Gaussian curvature. In addition, the total vorticity of orientational order on a surface of genus zero is two. Thus, the ordered phase of an $n$-atic on such a surface will have $2n$ vortices of strength $1/n$, $2n$ zeros in its order parameter, and a nonspherical equilibrium shape. Our calculations are based on a phenomenological model with a gauge-like coupling between $ψ$ and curvature, and our analysis follows closely the Abrikosov treatment of a type II superconductor just below $H_{c2}$.

cond-mat↗

arXiv1995

Theory of Cylindrical Tubules and Helical Ribbons of Chiral Lipid Membranes

We present a general theory for the equilibrium structure of cylindrical tubules and helical ribbons of chiral lipid membranes. This theory is based on a continuum elastic free energy that permits variations in the direction of molecular tilt and in the curvature of the membrane. The theory shows that the formation of tubules and helical ribbons is driven by the chirality of the membrane. Tubules have a first-order transition from a uniform state to a helically modulated state, with periodic stripes in the tilt direction and ripples in the curvature. Helical ribbons can be stable structures, or they can be unstable intermediate states in the formation of tubules.

cond-mat↗

arXiv1995

Elasticity of Semiflexible Biopolymer Networks

We develop a model for gels and entangled solutions of semiflexible biopolymers such as F-actin. Such networks play a crucial structural role in the cytoskeleton of cells. We show that the rheologic properties of these networks can result from nonclassical rubber elasticity. This model can explain a number of elastic properties of such networks {\em in vitro}, including the concentration dependence of the storage modulus and yield strain.

cond-mat↗

arXiv1995

Swelling Kinetics of Layered Structures: Triblock Copolymer Mesogels

We consider the swelling kinetics of layered structures. We focus on the case of triblock copolymer mesogels, although our results are applicable to other layered structures including clays. We assume the mesogels are swollen by a solvent that is good for the bridging block but poor for the non-bridging block. At long times the penetration front moves as in ordinary diffusion, i.e., as $t^{1/2}$. At short times, however, the bending elasticity of the non-bridging layers becomes important. This bending elasticity leads to a $t^{1/6}$ relaxation of the penetration front at early times. The crossover length between these two regimes is approximately the width of a single layer. However, for a large number of lamellae there is a cooperative effect which leads to a large enhancement of this crossover length.

cond-mat↗