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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.

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., Comment: Includes main text with 4 figures and supplementary text with 10 supplementary figures

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., Comment: 33 pages, 8 figures

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., Comment: 11 pages, 10 figures

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., Comment: V5. Published version. 8 pages, 5 figures + SI

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 $\phi$. 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 $q(\phi)$, 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., Comment: 10 pages, 6 figures. v4 makes several small revisions for clarity

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., Comment: 60 pages, 17 figures. replaced preprint version with the version accepted for publication

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., Comment: 13 pages, 7 figures

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., Comment: 14 pages

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., Comment: 8 pages + appendices

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.

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., Comment: 13 pages, 5 figures, minor changes from v1 (to appear in Phys. Rev. E)

Conventional micelles, composed of simple amphiphiles, exhibit only a few standard morphologies, each characterized by its mean surface curvature set by the amphiphiles. Here we demonstrate a rational design scheme to construct micelles of more general shape from polymeric amphiphiles. We replace the many amphiphiles of a conventional micelle by a single flexible, linear, block copolymer chain containing two incompatible species arranged in multiple alternating segments. With suitable segment lengths, the chain exhibits a condensed spherical configuration in solution, similar to conventional micelles. Our design scheme posits that further shapes are attained by altering the segment lengths. To assess the power of this scheme, we exhibit stable micelles of horseshoe form using conventional bead-spring simulations in two dimensions. Modest changes in the segment lengths produce smooth changes in the micelle's shape and stability., Comment: 32 pages, 25 figures

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., Comment: 6 pages, 5 figures, 1 ancillary movie; to appear in Nature Physics

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., Comment: 12 pages (6 main text + 6 supplemental material); 3 figures

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., Comment: to be published in J. Phys. Cond. Mat

Colloidal bodies of irregular shape rotate as they descend under gravity in solution. This rotational response provides a means of bringing a dispersion of identical bodies into a synchronized rotation with the same orientation using programmed forcing. We use the notion of statistical entropy to derive bounds on the rate of synchronization. These bounds apply generally to dynamical systems with stable periodic motion with a phase $\phi(t)$, when subjected to an impulsive perturbation. The impulse causes a change of phase expressible as a phase map $\psi(\phi)$. We derive an upper limit on the average change of entropy $\left<\Delta H\right>$ in terms of this phase map; when this limit is negative, alignment must occur. For systems that have achieved a low entropy, the $\left<\Delta H\right>$ approaches this upper limit.

We discuss the response of thin cylindrical tubes to small indentations. The stretching-free embedding of these surfaces is completely determined by the embedding of one edge curve, thus reducing their bending response to an effectively one dimensional problem. We obtain that in general thin cylindrical tubes will bend non-uniformly in response to an indentation normal to their surface. As a consequence, their local bending stiffness, as measured by indenting at various locations along their axis, is predicted to peak at the center and decrease by a universal factor of 4 at either end of the tube. This characteristic spatial profile of the bending stiffness variation allows a direct determination of the bending modulus of very thin tubes that are shorter than their pinch persistence length, $l_{p}\propto R^{3/2}/t^{1/2}$, where $R$ is the tube diameter and $t$ its wall thickness. We compare our results with experiments performed on rolled-up stainless steel sheets.

The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation $h$ has a singular logarithmic dependence on $h$. We derive a general form for this energy in terms of the singular capacitance of two spheres in near contact $c(h)$, together with nonsingular geometric features of the cluster. Using this form, we determine the energies of various clusters, finding that more compact clusters are more stable. These energies are proposed to be significant for metal-semiconductor binary nanoparticle lattices found experimentally. We sketch how these effects should dictate the relative abundances of metal nanoparticle clusters in nonpolar solvents., Comment: 22 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1010.4488

We study the relative translation of two arbitrarily shaped objects, caused by their hydrodynamic interaction as they are forced through a viscous fluid in the limit of zero Reynolds number. It is well known that in the case of two rigid spheres in an unbounded fluid, the hydrodynamic interaction does not produce relative translation. More generally such an effective pair-interaction vanishes in configurations with spatial inversion symmetry; for example, an enantiomorphic pair in mirror image positions has no relative translation. We show that the breaking of inversion symmetry by boundaries of the system accounts for the interactions between two spheres in confined geometries, as observed in experiments. The same general principle also provides new predictions for interactions in other object configurations near obstacles. We examine the time-dependent relative translation of two self-aligning objects, extending the numerical analysis of our preceding publication [Goldfriend, Diamant and Witten, Phys. Fluids 27, 123303 (2015)]. The interplay between the orientational interaction and the translational one, in most cases, leads over time to repulsion between the two objects. The repulsion is qualitatively different for self-aligning objects compared to the more symmetric case of uniform prolate spheroids. The separation between the two objects increases with time $t$ as $t^{1/3}$ in the former case, and more strongly, as $t$, in the latter., Comment: 15 pages, 4 figures

Randomly crumpled sheets have shape memory. In order to understand the basis of this form of memory, we simulate triangular lattices of springs whose lengths are altered to create a topography with multiple potential energy minima. We then deform these lattices into different shapes and investigate their ability to retain the imposed shape when the energy is relaxed. The lattices are able to retain a range of curvatures. Under moderate forcing from a state of local equilibrium, the lattices deform by several percent but return to their retained shape when the forces are removed. By increasing the forcing until an irreversible motion occurs, we find that the transitions between remembered shapes show co-operativity among several springs. For fixed lattice structures, the shape memory tends to decrease as the lattice is enlarged; we propose ways to counter this decrease by modifying the lattice geometry. We survey the energy landscape by displacing individual nodes. An extensive fraction of these nodes proves to be bistable; they retain their displaced position when the energy is relaxed. Bending the lattice to a stable curved state alters the pattern of bistable nodes. We discuss this shapeability in the context of other forms of material memory and contrast it with the shapeability of plastic deformation. We outline the prospects for making real materials based on these principles., Comment: 14 pages, 15 figures

We study the properties and symmetries governing the hydrodynamic interaction between two identical, arbitrarily shaped objects, driven through a viscous fluid. We treat analytically the leading (dipolar) terms of the pair-mobility matrix, affecting the instantaneous relative linear and angular velocities of the two objects at large separation. We prove that the instantaneous hydrodynamic interaction linearly degrades the alignment of asymmetric objects by an external time-dependent drive [Moths and Witten, Phys. Rev. Lett. 110, 028301 (2013)]. The time-dependent effects of hydrodynamic interactions are explicitly demonstrated through numerically calculated trajectories of model alignable objects composed of four stokeslets. In addition to the orientational effect, we find that the two objects usually repel each other. In this case the mutual degradation weakens as the two objects move away from each other, and full alignment is restored at long times., Comment: 31 pages, 8 figures

We examine the shape change of a thin disk with an inserted wedge of material when it is pushed against a plane, using analytical, numerical and experimental methods. Such sheets occur in packaging, surgery and nanotechnology. We approximate the sheet as having vanishing strain, so that it takes a conical form in which straight generators converge to a disclination singularity. Then its shape is that which minimizes elastic bending energy alone. Real sheets are expected to approach this limiting shape as their thickness approaches zero. The planar constraint forces a sector of the sheet to buckle into the third dimension. We find that the unbuckled sector is precisely semicircular, independent of the angle $\delta$ of the inserted wedge. We generalize the analysis to include conical as well as planar constraints and thereby establish a law of corresponding states for shallow cones of slope $\epsilon$ and thin wedges. In this regime the single parameter $\delta/\epsilon^2$ determines the shape. We discuss the singular limit in which the cone becomes a plane. We discuss the unexpected slow convergence to the semicircular buckling seen experimentally.

A connection between the dynamics of a sine-Gordon chain and a certain static membrane folding problem was recently found. The one-dimensional membrane profile is a cross-section of the position-time sine-Gordon amplitude profile. Here we show that when one system is embedded in a higher-dimensional system in this way, obvious symmetries in the larger system can lead to nontrivial symmetries in the embedded system. In particular, a thin buckled membrane on a fluid substrate has a continuous degeneracy that interpolates between a symmetric and an antisymmetric fold. We find the Hamiltonian generator of this symmetry and the corresponding conserved momentum by interpreting the simple translational symmetries of the sine-Gordon chain in terms of the embedded coordinates. We discuss possible extensions to other embedded dynamical systems., Comment: 8 pages

We re-examine previous observations of folding kinetics of compressed lipid monolayers in light of the accepted mechanical buckling mechanism recently proposed [L. Pocivavsek et al., Soft Matter, 2008, 4, 2019]. Using simple models, we set conservative limits on a) the energy released in the mechanical buckling process and b) the kinetic energy entailed by the observed folding motion. These limits imply a kinetic energy at least thirty times greater than the energy supplied by the buckling instability. We discuss possible extensions of the accepted picture that might resolve this discrepancy., Comment: 15 pages, 2 figures

The apparently intractable shape of a fold in a compressed elastic film lying on a fluid substrate is found to have an exact solution. Such systems buckle at a nonzero wavevector set by the bending stiffness of the film and the weight of the substrate fluid. Our solution describes the entire progression from a weakly displaced sinusoidal buckling to a single large fold that contacts itself. The pressure decrease is exactly quadratic in the lateral displacement. We identify a complex wavevector whose magnitude remains invariant with compression., Comment: 4 pages

The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation $h$ has a strong logarithmic dependence on $h$. We give a general law for the strength of this logarithmic correction in terms of a) the energy at contact ignoring the charge quantization effects and b) an adjacency matrix specifying which spheres of the cluster are in contact and which is charged. We verify the theory by comparing the predicted energies for a tetrahedral cluster with an explicit numerical calculation., Comment: 17 pages, 3 figures. Submitted to Phys Rev B

We analyze the buckling of a rigid thin membrane floating on a dense fluid substrate. The interplay of curvature and substrate energy is known to create wrinkling at a characteristic wavelength $\lambda$, which localizes into a fold at sufficient buckling displacement $\Delta$. By analyzing the regime $\Delta<<\lambda$, we show that wrinkles are unstable to localized folding for {\em arbitrarily small} $\Delta$. After observing that evanescent waves at the boundaries can be energetically favored over uniform wrinkles, we construct a localized Ansatz state far from boundaries that is also energetically favored. The resulting surface pressure $P$ in conventional units is $2-(\pi^2/4)(\Delta/\lambda)^2$, in entire agreement with previous numerical results. The decay length of the amplitude is $\kappa^{-1}=(2/\pi^2)\lambda^2/\Delta$. This case illustrates how a leading-order energy expression suggested by the infinitesimal displacement can give a qualitatively wrong configuration., Comment: 8 pages; important comment added at the beginning

We discuss the creeping motion of plugs of negligible viscosity in rough capillary tubes filled with carrier fluids. This extends Bretherton's research work on the infinite-length bubble motion in a cylindrical or smooth tube for small capillary numbers Ca. We first derive the asymptotic dependence of the plug speed on the finite length in the smooth tube case. This dependence on length is exponentially small, with a decay length much shorter than the tube radius R. Then we discuss the effect of azimuthal roughness of the tube on the plug speed. The tube roughness leads to an unbalanced capillary pressure and a carrier fluid flux in the azimuthal plane. This flux controls the relaxation of the plug shape to its infinite-length limit. For long-wavelength roughness, we find that the above decay length is much longer in the rough tube, and even becomes comparable to the tube radius R in some cases. This implies a much-enhanced dependence of the plug speed on the plug length. This mechanism may explain the catch-up effect seen experimentally., Comment: 39 pages, 7 figures. Submitted to Journal of Fluid Mechanics

We use computer simulations to study the glass transition of dense fluids made of polydisperse, repulsive spheres. For hard particles, we vary the volume fraction, phi, and use compressible particles to explore finite temperatures, T>0. In the hard sphere limit, our dynamic data show evidence of an avoided mode-coupling singularity near phi_{MCT} ~ 0.592, they are consistent with a divergence of equilibrium relaxation times occurring at phi_0 ~ 0.635, but they leave open the existence of a finite temperature singularity for compressible spheres at volume fraction phi > phi_0. Using direct measurements and a new scaling procedure, we estimate the equilibrium equation of state for the hard sphere metastable fluid up to phi_0, where pressure remains finite, suggesting that phi_0 corresponds to an ideal glass transition. We use non-equilibrium protocols to explore glassy states above phi_0 and establish the existence of multiple equations of state for the unequilibrated glass of hard spheres, all diverging at different densities in the range phi \in [0.642, 0.664]. Glassiness thus results in the existence of a continuum of densities where jamming transitions can occur., Comment: 16 pages; 7 figures

In this paper we use the angular deficit scheme [V. Borrelli, F. Cazals, and J.-M. Morvan, {\sl Computer Aided Geometric Design} {\bf 20}, 319 (2003)] to determine the distribution of Gaussian curvature in developable cones (d-cones) [E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, {\sl Nature} {\bf 401}, 46 (1999)] numerically. These d-cones are formed by pushing a thin elastic sheet into a circular container. Negative Gaussian curvatures are identified at the rim where the sheet touches the container. Around the rim there are two narrow bands with positive Gaussian curvatures. The integral of the (negative) Gaussian curvature near the rim is almost completely compensated by that of the two adjacent bands. This suggests that the Gauss-Bonnet theorem which constrains the integral of Gaussian curvature globally does not explain the spontaneous curvature cancellation phenomenon [T. Liang and T. A. Witten, {\sl Phys. Rev. E} {\bf 73}, 046604 (2006)]. The locality of the compensation seems to increase for decreasing d-cone thickness. The angular deficit scheme also provides a new way to confirm the curvature cancellation phenomenon., Comment: 12 pages; 5 figures

We use molecular dynamics to investigate the glass transition occurring at large volume fraction, phi, and low temperature, T, in assemblies of soft repulsive particles. We find that equilibrium dynamics in the (phi, T) plane obey a form of dynamic scaling in the proximity of a critical point at T=0 and phi=phi_0, which should correspond to the ideal glass transition of hard spheres. This glass point, `point G', is distinct from athermal jamming thresholds. A remarkable consequence of scaling behaviour is that the dynamics at fixed phi passes smoothly from that of a strong glass to that of a very fragile glass as phi increases beyond phi_0. Correlations between fragility and various physical properties are explored., Comment: 5 pages, 3 figures; Version accepted at Europhys. Lett

We study theoretically the chirality of a generic rigid object's sedimentation in a fluid under gravity in the low Reynolds number regime. We represent the object as a collection of small Stokes spheres or stokeslets, and the gravitational force as a constant point force applied at an arbitrary point of the object. For a generic configuration of stokeslets and forcing point, the motion takes a simple form in the nearly free draining limit where the stokeslet radius is arbitrarily small. In this case, the internal hydrodynamic interactions between stokeslets are weak, and the object follows a helical path while rotating at a constant angular velocity $\omega$ about a fixed axis. This $\omega$ is independent of initial orientation, and thus constitutes a chiral response for the object. Even though there can be no such chiral response in the absence of hydrodynamic interactions between the stokeslets, the angular velocity obtains a fixed, nonzero limit as the stokeslet radius approaches zero. We characterize empirically how $\omega$ depends on the placement of the stokeslets, concentrating on three-stokeslet objects with the external force applied far from the stokeslets. Objects with the largest $\omega$ are aligned along the forcing direction. In this case, the limiting $\omega$ varies as the inverse square of the minimum distance between stokeslets. We illustrate the prevalence of this robust chiral motion with experiments on small macroscopic objects of arbitrary shape., Comment: 35 pages, 10 figures; Section VII.A redone and other edits made for clarity. Accepted by Phys. Rev. E

We discuss mechanical buckling instabilities of a rigid film under compression interacting repulsively with a substrate through a thin fluid layer. The buckling occurs at a characteristic wavelength that increases as the 1/4th power of the bending stiffness, like a gravitational instability studied previously by Milner et al. However, the potential can affect the characteristic buckling wavelength strongly, as predicted by Huang and Suo. If the potential changes sufficiently sharply with thickness, this instability is continuous, with an amplitude varying as the square root of overpressure. We discuss three forms of interaction important for the case of Langmuir monolayers transferred to a substrate: Casimir-van der Waals interaction, screened charged double-layer interaction and the Sharma potential. We verify these predictions numerically in the Van der Waals case., Comment: 12 pages, 6 figures. Accepted as a Regular Article in Physical Review E

We consider the feasibility of large-scale free-standing thin liquid film experiment in the space environment as a new realization to study two-dimensional hydrodynamics. We identify material and environmental criteria necessary to avoid freezing, evaporation, chemical degradation, and spontaneous collapse of the film. These criteria pose no obstacles to achieving films of kilometer scale and lifetime of many months, with attainable Reynolds number up to 10^7. However, impacts from meteoroids pose a serious threat to the film, and require substantial shielding or unproven self-healing properties in the film. Current theoretical and experimental studies of two-dimensional turbulence are briefly reviewed. We also describe a specific candidate liquid for the film., Comment: 13 pages

In this paper we report numerically observed spontaneous vanishing of mean curvature on a developable cone made by pushing a thin elastic sheet into a circular container. We show that this feature is independent of thickness of the sheet, the supporting radius and the amount of deflection. Several variants of developable cone are studied to examine the necessary conditions that lead to the vanishing of mean curvature. It is found that the presence of appropriate amount of radial stress is necessary. The developable cone geometry somehow produces the right amount of radial stress to induce just enough radial curvature to cancel the conical azimuthal curvature. In addition, the circular symmetry of supporting container edge plays an important role. With an elliptical supporting edge, the radial curvature overcompensates the azimuthal curvature near the minor axis and undercompensates near the major axis. Our numerical finding is verified by a crude experiment using a reflective plastic sheet. We expect this finding to have broad importance in describing the general geometrical properties of forced crumpling of thin sheets., Comment: 13 pages, 12 figures, revtex4

Glasses have a large excess of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature is a necessary consequence of the weak connectivity of the solid, and that the frequency of modes in excess is very sensitive to the pressure. We analyze in particular two systems whose density D(w) of vibrational modes of angular frequency w display scaling behaviors with the packing fraction: (i) simulations of jammed packings of particles interacting through finite-range, purely repulsive potentials, comprised of weakly compressed spheres at zero temperature and (ii) a system with the same network of contacts, but where the force between any particles in contact (and therefore the total pressure) is set to zero. We account in the two cases for the observed a) convergence of D(w) toward a non-zero constant as w goes to 0, b) appearance of a low-frequency cutoff w*, and c) power-law increase of w* with compression. Differences between these two systems occur at lower frequency. The density of states of the modified system displays an abrupt plateau that appears at w*, below which we expect the system to behave as a normal, continuous, elastic body. In the unmodified system, the pressure lowers the frequency of the modes in excess. The requirement of stability despite the destabilizing effect of pressure yields a lower bound on the number of extra contact per particle dz: dz > p^(1/2), which generalizes the Maxwell criterion for rigidity when pressure is present. This scaling behavior is observed in the simulations. We finally discuss how the cooling procedure can affect the microscopic structure and the density of normal modes., Comment: 13 pages, 8 figures

By evaporating a drop of lipid dispersion we generate the myelin morphology often seen in dissolving surfactant powders. We explain these puzzling nonequilibrium structures using a geometric argument: The bilayer repeat spacing increases and thus the repulsion between bilayers decreases when a multilamellar disk is converted into a myelin without gain or loss of material and with number of bilayers unchanged. Sufficient reduction in bilayer repulsion can compensate for the cost in curvature energy, leading to a net stability of the myelin structure. A numerical estimate predicts the degree of dehydration required to favor myelin structures over flat lamellae., Comment: 6 pages, 3 figures, submitted to Euro. Phys. J. E

Solvent loss due to evaporation in a drying drop can drive capillary flows and solute migration. The flow is controlled by the evaporation profile and the geometry of the drop. We predict the flow and solute migration near a sharp corner of the perimeter under the conditions of uniform evaporation. This extends the study of Ref. 6, which considered a singular evaporation profile, characteristic of a dry surrounding surface. We find the rate of the deposit growth along contact lines in early and intermediate time regimes. Compared to the dry-surface evaporation profile of Ref. 6, uniform evaporation yields more singular deposition in the early time regime, and nearly uniform deposition profile is obtained for a wide range of opening angles in the intermediate time regime. Uniform evaporation also shows a more pronounced contrast between acute opening angles and obtuse opening angles., Comment: 12 figures, submitted to Physical Review E

We examine the crescent singularity of a developable cone in a setting similar to that studied by Cerda et al [Nature 401, 46 (1999)]. Stretching is localized in a core region near the pushing tip and bending dominates the outer region. Two types of stresses in the outer region are identified and shown to scale differently with the distance to the tip. Energies of the d-cone are estimated and the conditions for the scaling of core region size R_c are discussed. Tests of the pushing force equation and direct geometrical measurements provide numerical evidence that core size scales as R_c ~ h^{1/3} R^{2/3}, where h is the thickness of sheet and R is the supporting container radius, in agreement with the proposition of Cerda et al. We give arguments that this observed scaling law should not represent the asymptotic behavior. Other properties are also studied and tested numerically, consistent with our analysis., Comment: 13 pages with 8 figures, revtex. To appear in PRE

We investigate spreading of phase separated copolymer films, where domain walls and thickness steps influence polymer flow. We show that at early stages of spreading its rate is determined by slow activated flow at terrace steps (i.e. thickness steps). At late stages of spreading, on the other hand, the rate is determined by the flow along terraces, with diffusion-like time dependence $t^{-1/2}$. This dependence is similar to de Gennes and Cazabat's prediction for generic layered liquids, as opposed to the classical Tanner's law of drop spreading. We also argue that chain hopping at the spreading terrace steps should lead to the formation of aligned, defect-free domain patterns on the growing terraces., Comment: 11 pages, 7 figures, submitted to J. Chem. Phys

As was shown in an earlier paper [1], solids dispersed in a drying drop migrate to the (pinned) contact line. This migration is caused by outward flows driven by the loss of the solvent due to evaporation and by geometrical constraint that the drop maintains an equilibrium surface shape with a fixed boundary. Here, in continuation of our earlier paper [2], we theoretically investigate the evaporation rate, the flow field and the rate of growth of the deposit patterns in a drop over an angular sector on a plane substrate. Asymptotic power laws near the vertex (as distance to the vertex goes to zero) are obtained. A hydrodynamic model of fluid flow near the singularity of the vertex is developed and the velocity field is obtained. The rate of the deposit growth near the contact line is found in two time regimes. The deposited mass falls off as a weak power Gamma of distance close to the vertex and as a stronger power Beta of distance further from the vertex. The power Gamma depends only slightly on the opening angle Alpha and stays between roughly -1/3 and 0. The power Beta varies from -1 to 0 as the opening angle increases from 0 to 180 degrees. At a given distance from the vertex, the deposited mass grows faster and faster with time, with the greatest increase in the growth rate occurring at the early stages of the drying process., Comment: v1: 36 pages, 21 figures, LaTeX; submitted to Physical Review E; v2: minor additions to Abstract and Introduction

Crumpled sheets have a surprisingly large resistance to further compression. We have studied the crumpling of thin sheets of Mylar under different loading conditions. When placed under a fixed compressive force, the size of a crumpled material decreases logarithmically in time for periods up to three weeks. We also find hysteretic behavior when measuring the compression as a function of applied force. By using a pre-treating protocol, we control this hysteresis and find reproducible scaling behavior for the size of the crumpled material as a function of the applied force., Comment: revtex 4 pages, 6 eps figures submitted to Phys Rev. lett

We study stress relaxation in a strongly segregated lamellar mesophase of diblock copolymers. We consider the extreme limit in which chains are highly stretched and with their junction points confined to narrow interfaces. A lamella can be divided into "stress blobs" at some distance $z$ from the interface, with well defined local modulus $G(z,\omega)$ at frequency $\omega$. For sliding (compressional) stress the total modulus is transmitted in series (parallel) across the layer. We evaluate the local $G(z,t)$ which shows, for a given height, a very broad spectrum of relaxation times.

The shape of a liquid surface bounded by an acute or obtuse planar angular sector is considered by using classical analysis methods. For acute angular sectors the two principal curvatures are of the order of the (fixed) mean curvature. But for obtuse sectors, the principal curvatures both diverge as the vertex is approached. The power-law divergence becomes stronger with increasing opening angle. Possible implications of this contrasting behavior are suggested., Comment: 19 pages, 9 figures, LaTeX; submitted to The European Physics Journal E; v2: Introduction was revised (a number of references added), minor changes to the main part (mostly typos), former Implications subsection was almost entirely rewritten and is now called Experimental Realizations (experimental results and two figures added); v3: Introduction was slightly modified, four references added; v4: Title was modified, section Calculation was significantly modified (subsections Bounary Problem and Horizontal Solution almost entirely rewritten, minor changes to the other subsections), subsection Curvature in section Discussion was revised, one reference added

We present a minimalistic approach to simulations of force transmission through granular systems. We start from a configuration containing cohesive (tensile) contact forces and use an adaptive procedure to find the stable configuration with no tensile contact forces. The procedure works by sequentially removing and adding individual contacts between adjacent beads, while the bead positions are not modified. In a series of two-dimensional realizations, the resulting force networks are shown to satisfy a linear constraint among the three components of average stress, as anticipated by recent theories. The coefficients in the linear constraint remain nearly constant for a range of shear loadings up to about .6 of the normal loading. The spatial distribution of contact forces shows strong concentration along ``force chains". The probability of contact forces of magnitude f shows an exponential falloff with f. The response to a local perturbing force is concentrated along two characteristic rays directed downward and laterally., Comment: 8 pages, 8 figures