arXiv subjects

T. A. Witten

Publications and source records attributed to T. A. Witten.

At least 19 recordsLinked to original sources

arXiv2017

Predicting tensorial electrophoretic effects in asymmetric colloids

We formulate a numerical method for predicting the tensorial linear response of a rigid, asymmetrically charged body to an applied electric field. This prediction requires calculating the response of the fluid to the Stokes drag forces on the moving body and on the countercharges near its surface. To determine the fluid's motion, we represent both the body and the countercharges using many point sources of drag known as stokeslets. Finding the correct flow field amounts to finding the set of drag forces on the stokeslets that is consistent with the relative velocities experienced by each stokeslet. The method rigorously satisfies the condition that the object moves with no transfer of momentum to the fluid. We demonstrate that a sphere represented by 1999 well-separated stokeslets on its surface produces flow and drag force like a solid sphere to one-percent accuracy. We show that a uniformly-charged sphere with 3998 body and countercharge stokeslets obeys the Smoluchowski prediction \cite{Morrison} for electrophoretic mobility when the countercharges lie close to the sphere. Spheres with dipolar and quadrupolar charge distributions rotate and translate as predicted analytically to four percent accuracy or better. We describe how the method can treat general asymmetric shapes and charge distributions. This method offers promise as a way to characterize and manipulate asymmetrically charged colloid-scale objects from biology (e.g. viruses) and technology (e.g. self-assembled clusters).

cond-mat.soft↗

arXiv2013

Orientational ordering of colloidal dispersions by application of time dependent external forces

We present a method of organizing incoherent motion of a colloidal suspension to produce synchronized, coherent motion. This method exploits general features of rotational response to time-dependent forcing, and it does not require interaction between the particles. We report two methods of achieving orientational alignment of an ensemble of identical colloids by means of a time-dependent, but spatially uniform forcing: a) a piecewise constant force alternating between two directions and b) a force uniformly rotating about an axis. The physical origin of the forcing may be e.g., sedimentation or electrophoresis. We will demonstrate that these forcing methods achieve alignment both by analyzing the equations of motion and by simulation. We find the conditions guaranteeing alignment, discuss the limitations of these methods, and suggest possible applications. Examples of such forcing include electrophoresis and sedimentation.

cond-mat.soft↗

arXiv2012

Full alignment of colloidal objects by programmed forcing

By analysis and simulation we demonstrate two methods for achieving complete orientational alignment of a set of identical, asymmetric colloidal objects dispersed randomly in a fluid. Sedimentation or electrophoresis in a constant field can lead to partial alignment, in which the objects rotate about a common body axis, but the phases of rotation for these objects are random. We show that this phase disorder can be removed by two forms of programmed forcing. First, simply alternating the forcing between two directions reduces the statistical entropy of the orientation arbitrarily. Second, addition of a small rotating component to the applied field in analogy to magnetic resonance can lead to phase locking of the objects' orientation. We identify conditions for alignment of a broad class of generic objects and discuss practical limitations.

cond-mat.soft↗

arXiv2010

Scientific interview

Four leading scientists in the field of the glass transition answer to a series of questions formulated by the Editors (L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, W. van Saarloos). No specific format has been imposed to their answers: the scientists were free to answer or not to any given question, using how much space they felt appropriate. After a first round of answers, each author was given the opportunity to read the answers by his colleagues and to adjust his own answers accordingly.

cond-mat.stat-mech↗

arXiv2009

Robust fadeout profile of an evaporation stain

We propose an explanation for the commonly-seen fading in the density of a stain remaining after a droplet has dried on a surface. The density decreases as a power $p$ of the distance from the edge. For thin, dilute drops of general shape this power is determined by a flow stagnation point in the distant interior of the drop. The power $p$ depends on the local evaporation rate J(0) at the stagnation point and the liquid depth $h(0)$ there: $p = 1 - 2 (h(0)/\bar h)(\bar J/J(0))$, where $\bar h$ and $\bar J$ are averages over the drop surface.

cond-mat.soft↗

arXiv2008

Spontaneous free-boundary structure in crumpled membranes

We investigate the strong curvature that appears at the boundaries of a thin crumpled elastic membrane. We account for these high-curvature regions in terms of the stretching-ridge singularity believed to dominate the structure of strongly deformed elastic membranes. Using a membrane fastened to itself to form a bag shape with a single stretching ridge, we show that the creation of points of high boundary curvature lowers the interior ridge's energy. In the limit of small thickness, the induced curvature becomes arbitrarily strong on the scale of the object size and results in sharp edges connecting interior vertices to the boundary. REVISED: We analyze these edges as conical sectors with no stretching. As the membrane size diverges, the edge energy grows as the square root of the central ridge energy. For comparison, we discuss the effect of truncating a stretching ridge at its ends. The effect of truncation becomes appreciable when the truncation length is comparable to the width of the untruncated ridge.

cond-mat.soft↗

arXiv2008

Force focusing in confined fibers and sheets

A thin fiber or sheet curled into a circular container has a detached region whose shape and force ratios are independent of material properties and container radius. We compute this shape and compare it with experiments. The discrete forces acting at either end of the detached region have a ratio that depends only on the length of the fiber or sheet relative to the circle radius. We calculate this force ratio in three regimes of circle radius.

cond-mat.mtrl-sci↗

arXiv2005

Geometric origin of excess low-frequency vibrational modes in amorphous solids

Glasses have a large excess of low-frequency vibrational modes in comparison with crystalline solids. We show that such a feature is a necessary consequence of the geometry generic to weakly connected solids. In particular, we analyze the density of states of a recently simulated system, comprised of weakly compressed spheres at zero temperature. We account for the observed a) constancy of the density of modes with frequency, b) appearance of a low-frequency cutoff, and c) power-law increase of this cutoff with compression. We predict a length scale below which vibrations are very different from those of a continuous elastic body.

cond-mat.soft↗

arXiv2004

Chain-reaction cascades in surfactant monolayer buckling

Certain surfactant monolayers at the water-air interface have been found to undergo, at a critical surface pressure, a dynamic instability involving multiple long folds of micron width. We exploit the sharp monolayer translations accompanying folding events to acquire, using a combination of fluorescence microscopy and digital image analysis, detailed statistics concerning the folding dynamics. The motions have a broad distribution of magnitudes and narrow, non-Gaussian distributions of angles and durations. The statistics are consistent with the occurrence of cooperative cascades of folds, implying an autocatalytic process uncommon in the context of mechanical instability.

cond-mat.soft↗

arXiv2004

Surface charge relaxation and the pearling instability of charged surfactant tubes

The pearling instability of bilayer surfactant tubes was recently observed during the collapse of fluid monolayers of binary mixtures of DMPC$-$POPG and DPPC$-$POPG surfactants. We suggested it has the same physics as the well-known Raleigh instability under the action of the bilayer surface tension whose magnitude is dictated by the electrostatic interaction between charged surfactants. In this paper, we calculate the relaxation of charge molecules during the deformation of the tubes into pearling structure. We find the functional dependence of the relaxation energy on the screening length $κ^{-1}$ explicitly. Relaxation effect lowers the cost of bending a tube into pearls making the cylindrical tube even more unstable. It is known that for weak screening case where the tube radius is smaller than the screening length of the solution, this relaxation effect is important. However, for the case of strong screening it is negligible. For the experiments mentioned, the situation is marginal. In this case, we show this relaxation effect remains small. It gives less than 20% contribution to the total electrostatic energy.

cond-mat.soft↗

arXiv2003

Defect Formation and Kinetics of Atomic Terrace Merging

Pairs of atomic scale terraces on a single crystal metal surface can be made to merge controllably under suitable conditions to yield steps of double height and width. We study the effect of various physical parameters on the formation of defects in a kinetic model of step doubling. We treat this manifestly non- equilibrium problem by mapping the model onto a 1-D random sequential adsorption problem and solving this analytically. We also do simulations to check the validity of our treatment. We find that our treatment effectively captures the dynamic evolution and the final state of the surface morphology. We show that the number and nature of the defects formed is controlled by a single dimensionless parameter $q$. For $q$ close to one we show that the fraction of defects rises linearly with $ε\equiv 1-q$ as $0.284 \times ε$. We also show that one can arrive at the final state faster and with fewer defects by changing the parameter with time.

cond-mat.mtrl-sci↗

arXiv2002

Universal Ratios of Characteristic Lengths in Semidilute Polymer Solutions

We use experimental and simulation data from the literature to infer five characteristic lengths, denoted $ξ_s$, $ξ_f$, $ξ_Π$, $ξ_ϕ$, and $ξ_D$ of a semidilute polymer solution. The first two of these are defined in terms of scattering from the solution, the third is defined in terms of osmotic pressure, the fourth by the spatial monomer concentration profile, and the last by co-operative diffusion. In a given solution the ratios of any of these five lengths are expected to be universal constants. Knowing these constants thus allows one to use one measured property of a solution as a means of inferring others. We calculate these ratios and estimate their uncertainties for solutions in theta as well as good-solvent conditions. The analysis is strengthened by use of scattering properties of isolated polymers inferred from computer simulations.

cond-mat.soft↗

arXiv2002

The polymer mat: Arrested rebound of a compressed polymer layer

Compression of an adsorbed polymer layer distorts its relaxed structure. Surface force measurements from different laboratories show that the return to this relaxed structure after the compression is released can be slowed to the scale of tens of minutes and that the recovery time grows rapidly with molecular weight. We argue that the arrested state of the free layer before relaxation can be described as a Guiselin brush structure1, in which the surface excess lies at heights of the order of the layer thickness, unlike an adsorbed layer. This brush structure predicts an exponential falloff of the force at large distance with a decay length that varies as the initial compression distance to the 6/5 power. This exponential falloff is consistent with surface force measurements. We propose a relaxation mechanism that accounts for the increase in relaxation time with chain length.

physics.chem-ph↗

arXiv2001

Robust propagation direction of stresses in a minimal granular packing

By employing the adaptive network simulation method, we demonstrate that the ensemble-averaged stress caused by a local force for packings of frictionless rigid beads is concentrated along rays whose slope is consistent with unity: forces propagate along lines at 45 degrees to the horizontal or vertical. This slope is shown to be independent of polydispersity or the degree to which the system is sheared. Further confirmation of this result comes from fitting the components of the stress tensor to the null stress constitutive equation. The magnitude of the response is also shown to fall off with the -1/2 power of distance. We argue that our findings are a natural consequence of a system that preserves its volume under small perturbations.

cond-mat.stat-mech↗

arXiv2001

Trapping of Vibrational Energy in Crumpled Sheets

We investigate the propagation of transverse elastic waves in crumpled media. We set up the wave equation for transverse waves on a generic curved, strained surface via a Langrangian formalism and use this to study the scaling behaviour of the dispersion curves near the ridges and on the flat facets. This analysis suggests that ridges act as barriers to wave propagation and that modes in a certain frequency regime could be trapped in the facets. A simulation study of the wave propagation qualitatively supported our analysis and showed interesting effects of the ridges on wave propagation.

cond-mat.mtrl-sci↗

arXiv2001

Anomalous strength of membranes with elastic ridges

We report on a simulational study of the compression and buckling of elastic ridges formed by joining the boundary of a flat sheet to itself. Such ridges store energy anomalously: their resting energy scales as the linear size of the sheet to the 1/3 power. We find that the energy required to buckle such a ridge is a fixed multiple of the resting energy. Thus thin sheets with elastic ridges such as crumpled sheets are qualitatively stronger than smoothly bent sheets.

cond-mat↗

arXiv2001

Topography and instability of monolayers near domain boundaries

We theoretically study the topography of a biphasic surfactant monolayer in the vicinity of domain boundaries. The differing elastic properties of the two phases generally lead to a nonflat topography of ``mesas'', where domains of one phase are elevated with respect to the other phase. The mesas are steep but low, having heights of up to 10 nm. As the monolayer is laterally compressed, the mesas develop overhangs and eventually become unstable at a surface tension of about K(dc)^2 (dc being the difference in spontaneous curvature and K a bending modulus). In addition, the boundary is found to undergo a topography-induced rippling instability upon compression, if its line tension is smaller than about K(dc). The effect of diffuse boundaries on these features and the topographic behavior near a critical point are also examined. We discuss the relevance of our findings to several experimental observations related to surfactant monolayers: (i) small topographic features recently found near domain boundaries; (ii) folding behavior observed in mixed phospholipid monolayers and model lung surfactants; (iii) roughening of domain boundaries seen under lateral compression; (iv) the absence of biphasic structures in tensionless surfactant films.

cond-mat.soft↗

arXiv2001

Singularities, Structures and Scaling in Deformed Elastic m-Sheets

The crumpling of a thin sheet can be understood as the condensation of elastic energy into a network of ridges which meet in vertices. Elastic energy condensation should occur in response to compressive strain in elastic objects of any dimension greater than 1. We study elastic energy condensation numerically in 2-dimensional elastic sheets embedded in spatial dimensions 3 or 4 and 3-dimensional elastic sheets embedded in spatial dimensions 4 and higher. We represent a sheet as a lattice of nodes with an appropriate energy functional to impart stretching and bending rigidity. Minimum energy configurations are found for several different sets of boundary conditions. We observe two distinct behaviors of local energy density fall-off away from singular points, which we identify as cone scaling or ridge scaling. Using this analysis we demonstrate that there are marked differences in the forms of energy condensation depending on the embedding dimension.

math-ph↗