arXiv subjects

Thomas A. Witten

Publications and source records attributed to Thomas A. Witten.

At least 19 recordsLinked to original sources

arXiv2026

STL-to-Stokeslet Computation of Mobility Tensors and Sedimentation Dynamics for Shaped Particles

Sedimentation is extremely common in nature, occurring throughout the atmosphere and oceans, and in every laboratory centrifuge. The shape and mass distribution of a particle uniquely determines its motion at low Reynolds number, and complex dynamics can emerge from even simple particle shapes. The dynamics are governed by the particle's hydrodynamic mobility tensor, which dictates the translational and rotational velocities given the forces and torques. However, to date the inference of the mobility tensor from the object shape has been cumbersome and tricky. Starting with an input file representing an object for a 3D printer, such as an STL file, here we present an efficient numerical framework to compute the mobility tensor by discretizing the particle surface into distributed point drag forces called stokeslets. We validate our results against analytical solutions of simple geometries and recent experimental measurements. With our calculated mobility tensors in hand, using standard transformation laws, we demonstrate the dramatic effect of shifting the center of mass from a center of symmetry: all initial orientations evolve into one, two, or three particular final motions dictated by the object. By providing a user-friendly and efficient framework to compute the mobility tensor and resulting particle dynamics, this work offers a broadly applicable tool for the soft-matter, fluid-mechanics, and biophysics communities, and facilitates the design of steerable particles under diverse external forces, with relevance to colloidal transport, biological locomotion, diffusion, and self-assembly.

cond-mat.soft↗

arXiv2026

Effective synchronization amid noise-induced chaos

Two remote agents with synchronized clocks may use them to act in concert and communicate. This necessitates some means of creating and maintaining synchrony. One method, not requiring any direct interaction between the agents, is to expose them to a common, environmental, stochastic forcing. This "noise-induced synchronization" only occurs under sufficiently mild forcing; stronger forcing disrupts synchronization. We investigate the regime of strong noise, where the clocks' relative phases evolve chaotically. Using a simple realization of disruptive noise, we demonstrate effective synchronization. First, although the relative phases of the two clocks varied erratically, we confirm that they became statistically independent of initial conditions and hence equivalent after a well-defined timescale. Second, we show that an agent can estimate an effective phase that closely agrees with the other's phase. Thus, synchronization is practically attainable beyond the regime of conventional noise-induced synchronization. We finally discuss how it might be used in living systems.

cond-mat.stat-mech↗

arXiv2025

Sub-singularities for shaping thin sheets

The principles behind the sharp, singular structures in a crumpled sheet are well understood. Here we discuss more general ways of exploiting such sharp structures to control the shape of a sheet by deforming or forcing it elsewhere. Often, the induced shape leads to further sharp structures -- ``sub-singularities". Though weaker and softer than the primary singularities, they nevertheless provide robust ways of shaping a sheet. In simple cases we understand the reason for these and their strength. This paper surveys a broad range of other sub-structure phenomena and reports recent progress in understanding some of them.

cond-mat.soft↗

arXiv2024

Trading particle shape with fluid symmetry: on the mobility matrix in 3D chiral fluids

Chiral fluids - such as fluids under rotation or a magnetic field as well as synthetic and biological active fluids - flow in a different way than ordinary ones. Due to symmetries broken at the microscopic level, chiral fluids may have asymmetric stress and viscosity tensors, for example giving rise to a hydrostatic torque or non-dissipative (odd) and parity-violating viscosities. In this article, we investigate the motion of rigid bodies in such an anisotropic fluid in the incompressible Stokes regime through the mobility matrix, which encodes the response of a solid body to forces and torques. We demonstrate how the form of the mobility matrix, which is usually determined by particle geometry, can be analogously controlled by the symmetries of the fluid. By computing the mobility matrix for simple shapes in a three-dimensional anisotropic chiral fluid, we predict counter-intuitive phenomena such as motion perpendicular to applied forces and spinning under the force of gravity.

cond-mat.soft↗

arXiv2024

Shear thickening in suspensions of particles with dynamic brush layers

Control of frictional interactions among liquid-suspended particles has led to tunable, strikingly non-Newtonian rheology via the formation of strong flow constraints as particles come into close proximity under shear. Typically, these frictional interactions have been in the form of physical contact, controllable via particle shape and surface roughness. We investigate a different route, where molecular bridging between nearby particle surfaces generates a controllable "sticky" friction. This is achieved with surface-functionalized colloidal particles capable of forming dynamic covalent bonds with telechelic polymers that comprise the suspending fluid. At low shear stress this results in particles coated with a uniform polymer brush layer. Beyond an onset stress the telechelic polymers become capable of bridging and generate shear thickening. Over the size range investigated, we find that the dynamic brush layer leads to dependence of the onset stress on particle diameter that closely follows a power law with exponent -1.76. In the shear thickening regime, we observe an enhanced dilation in measurements of the first normal stress difference and reduction in the extrapolated volume fraction required for jamming, both consistent with an effective particle friction that increases with decreasing particle diameter. These results are discussed in light of predictions for suspensions of hard spheres and of polymer-grafted particles.

cond-mat.soft↗

arXiv2024

Faceted wrinkling by contracting a curved boundary

Single-mode deformations of two-dimensional materials, such as the Miura-ori zig-zag fold, are important to the design of deployable structures because of their robustness; these usually require careful pre-patterning of the material. Here we show that inward contraction of a curved boundary produces a fine wrinkle pattern with a novel structure that suggests similar single-mode characteristics, but with minimal pre-patterning. Using finite-element representation of the contraction of a thin circular annular sheet, we show that these sheets wrinkle into a structure well approximated by an isometric structure composed of conical sectors and flat, triangular facets. Isometry favours the restriction of such deformations to a robust low-bending energy channel that avoids stretching. This class of buckling offers a novel way to manipulate sheet morphology via boundary forces.

cond-mat.soft↗

arXiv2023

Universal wrinkling of freestanding atomically thin films

Atomically thin films, like transition metal dichalcogenides, can now be synthesized at wafer scale, achieving the same extreme aspect ratio (~10^8) that a sheet of paper would have if it covered an entire city. Yet, the intrinsic (i.e. unconfined) three-dimensional shape of these extreme membranes remains a mystery because of the very fundamentals of mechanical measurements: to measure such an ultra-thin film, one first needs to simultaneously free it and stabilize it without introducing confining boundaries. Here, we introduce a counter-intuitive solution to this problem: place atomically thin films on water. Using atomic force microscopy (AFM) and Raman spectroscopy adapted to water's surface, we reveal that large-scale freestanding membranes spontaneously self-wrinkle into a universal mechanical state with long emergent length scales that follow robust scaling trends. Our analytical and numerical models suggest that these universal trends are controlled by mesoscopic parameters of the polycrystalline domains instead of atomistic details. Moreover, we demonstrate experimentally that the wrinkles result in a large and tunable reduction of elastic stiffness by up to 2 orders of magnitude. The present work illuminates the physical properties of the world's thinnest materials at length scales never probed before and highlights their potential for tunable strain-controlled nanomechanical devices.

cond-mat.mes-hall↗

arXiv2023

Granular convergence as an iterated local map

Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations encountered converges to a periodic sequence after sufficient shear cycles. Prior work modeled this evolution as the iteration of a pre-determined, random map from a set of discrete configurations into itself. Iterating such a map from a random starting point leads to similar periodic repetition. This work explores the effect of restricting the randomness of such maps in order to account for the local nature of the discrete events. The number of cycles needed for convergence shows similar statistical behavior to that of numerical granular experiments. The number of cycles in a repeating period behaves only qualitatively like these granular studies.

cond-mat.soft↗

arXiv2022

Stochastic synchronization induced by noise

Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture. The copies differ only in their arbitrary phases $ϕ$. Weak, randomly-timed external impulses applied to all the copies can synchronize these phases over time. Beyond a threshold strength there is no such convergence to a common phase. Instead, the synchronization becomes erratic: successive impulses produce stochastic fluctuations in the phase distribution $q(ϕ)$, ranging from near-perfect to near-random synchronization. Here we show that the sampled entropies of these phase distributions themselves form a steady-state ensemble, whose average can be made arbitrarily negative by tuning the impulse strength. A random-walk description of the entropy's evolution accounts for the observed exponential distribution of entropies and for the stochastic synchronization phenomenon.

cond-mat.stat-mech↗

arXiv2020

Excess Semiannual Variation in Historic Temperature Records

The annual temperature cycle of the earth closely follows the annual cycle of solar flux. At temperate latitudes, both driving and response cycles are well described by a strong annual sinusoidal component and a non-vanishing semiannual component. A new analysis of historical weather station records in the United States determines persistent annual and semiannual variation with high precision. Historical annual temperature ranges are consistent with prior studies. Semiannual temperature cycles were much stronger than expected based on the semiannual solar driving. Instead, these cycles were consistent with multiplicative effects of two annual cycles. Our methods provide a quantitative window into the climate's nonlinear response to solar driving, which is of potential value in testing climate models.

physics.ao-ph↗

arXiv2020

A review of shaped colloidal particles in fluids: Anisotropy and chirality

This review treats asymmetric colloidal particles moving through their host fluid under the action of some form of propulsion. The propulsion can come from an external body force or from external shear flow. It may also come from externally-induced stresses at the surface, arising from imposed chemical, thermal or electrical gradients. The resulting motion arises jointly from the driven particle and the displaced fluid. If the objects are asymmetric, every aspect of their motion and interaction depends on the orientation of the objects. This orientation in turn changes in response to the driving. The objects' shape can thus lead to a range of emergent anisotropic and chiral motion not possible with isotropic spherical particles. We first consider what aspects of a body's asymmetry can affect its drift through a fluid, especially chiral motion. We next discuss driving by injecting external force or torque into the particles. Then we consider driving without injecting force or torque. This includes driving by shear flow and driving by surface stresses, such as electrophoresis. We consider how time-dependent driving can induce collective orientational order and coherent motion. We show how a given particle shape can be represented using an assembly of point forces called a Stokeslet object. We next consider the interactions between anisotropic propelled particles, the symmetries governing the interactions, and the possibility of bound pairs of particles. Finally we show how the collective hydrodynamics of a suspension can be qualitatively altered by the particles' shapes. The asymmetric responses discussed here are broadly relevant also for swimming propulsion of active micron-scale objects such as microorganisms.

physics.flu-dyn↗

arXiv2019

Chiral motion in colloidal electrophoresis

Asymmetrically charged, nonspherical colloidal particles in general perform complex rotations and oblique motions under an electric field. The interplay of electrostatic and hydrodynamic forces complicate the prediction of these motions. We demonstrate a method of calculating the body tensors that dictate translational and rotational velocity vectors arising from an external electric field. We treat insulating, rigid bodies in the linear-response regime, with indefinitely small electrostatic screening length. The method represents the body as an assembly of point sources of both hydrodynamic drag and surface electric field. We demonstrate agreement with predicted electrophoretic mobility to within a few percent for several shapes with uniform and nonuniform charge. We demonstrate strong chiral twisting motions for colloidal bodies of symmetrical realistic shapes. The method applies more generally to active colloidal swimmers.

cond-mat.soft↗

arXiv2019

Nucleation and shape dynamics of model nematic tactoids around adhesive colloids

Recent experiments have shown how nematically-ordered tactoid shaped actin droplets can be reorganized and divided by the action of myosin molecular motors. In this paper, we consider how similar morphological changes can potentially be achieved under equilibrium conditions. Using simulations, both atomistic and continuum, and a phenomenological model, we explore how the nucleation dynamics, shape changes, and the final steady state of a nematic tactoid droplet can be modified by interactions with model adhesive colloids that mimic a myosin motor cluster. Our results provide a prescription for the minimal conditions required to stabilize tactoid reorganization and division in an equilibrium colloidal-nematic setting.

cond-mat.stat-mech↗

arXiv2019

Adapting the Teubner reciprocal relations for stokeslet objects

Self-propelled colloidal swimmers move by pushing the adjacent fluid backwards. The resulting motion of an asymmetric body depends on the profile of pushing velocity over its surface. We describe a method of predicting the motion arising from arbitrary velocity profiles over a given body shape, using a discrete-source "stokeslet" representation. The net velocity and angular velocity is a sum of contributions from each point on the surface. The contributions from a given point depend only on the shape. We give a numerical method to find these contributions in terms of the stokeslet positions defining the shape. Each contribution is determined by linear operations on the Oseen interaction matrix between pairs of stokeslets. We first adapt the Lorentz Reciprocal Theorem to discrete sources. We then use the theorem to implement the method of Teubner[1] to determine electrophoretic mobilities of nonuniformly charged bodies.

cond-mat.soft↗

arXiv2019

Cyclic annealing as an iterated random map

Disordered magnets, martensitic mixed crystals, and glassy solids can be irreversibly deformed by subjecting them to external deformation. The deformation produces a smooth, reversible response punctuated by abrupt relaxation "glitches". Under appropriate repeated forward and reverse deformation producing multiple glitches, a strict repetition of a single sequence of microscopic configurations often emerges. We exhibit these features by describing the evolution of the system configuration from glitch to glitch as a mapping of $\mathcal{N}$ states into one-another. A map $\mathbf{U}$ controls forward deformation; a second map $\mathbf{D}$ controls reverse deformation. Iteration of a given sequence of forward and reverse maps, e.g. $\mathbf{DDDDUUU}$ necessarily produces a convergence to a fixed cyclic repetition of states covering multiple glitches. The repetition may have a period of more than one strain cycle, as recently observed in simulations. Using numerical sampling, we characterize the convergence properties of four types of random maps implementing successive physical restrictions. The most restrictive is the much-studied Preisach model. These maps show only the most qualitative resemblance to annealing simulations. However, they suggest further properties needed for a realistic mapping scheme.

cond-mat.soft↗

arXiv2017

Geometrical frustration yields fiber formation in self-assembly

Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales. Nevertheless, even particles without optimized shapes can robustly form well-defined morphologies. This is the case in numerous medical conditions where normally soluble proteins aggregate into fibers. Beyond the diversity of molecular mechanisms involved, we propose that fibers generically arise from the aggregation of irregular particles with short-range interactions. Using a minimal model of ill-fitting, sticky particles, we demonstrate robust fiber formation for a variety of particle shapes and aggregation conditions. Geometrical frustration plays a crucial role in this process, and accounts for the range of parameters in which fibers form as well as for their metastable character.

cond-mat.soft↗

arXiv2017

Screening, Hyperuniformity, and Instability in the Sedimentation of Irregular Objects

We study the overdamped sedimentation of non-Brownian objects of irregular shape using fluctuating hydrodynamics. The anisotropic response of the objects to flow, caused by their tendency to align with gravity, directly suppresses concentration and velocity fluctuations. This allows the suspension to avoid the anomalous fluctuations predicted for suspensions of symmetric spheroids. The suppression of concentration fluctuations leads to a correlated, hyperuniform structure. For certain object shapes, the anisotropic response may act in the opposite direction, destabilizing uniform sedimentation.

cond-mat.soft↗

arXiv2016

Signal Transmissibility in Marginal Granular Materials

We examine the "transmissibility" of a simulated two-dimensional pack of frictionless disks formed by confining dilute disks in a shrinking, periodic box to the point of mechanical stability. Two opposite boundaries are then removed, thus allowing a set of free motions. Small free displacements on one boundary then induce proportional displacements on the opposite boundary. Transmissibility is the ability to distinguish different perturbations by their distant responses. We assess transmissibility by successively identifying free orthonormal modes of motion that have the {\em smallest} distant responses. The last modes to be identified in this "pessimistic" basis are the most transmissive. The transmitted amplitudes of these most transmissive modes fall off exponentially with mode number. Similar exponential falloff is seen in a simple elastic medium, though the responsible modes differ greatly in structure in the two systems. Thus the marginal pack's transmissibility is qualitatively similar to that of a simple elastic medium. We compare our results with recent findings based on the projection of the space of free motion onto interior sites.

cond-mat.soft↗