arXiv subjects

L. Mahadevan

Publications and source records attributed to L. Mahadevan.

At least 145 records · Page 8Linked to original sources

arXiv2012

Macroscopic magnetic frustration

Although geometrical frustration transcends scale, it has primarily been evoked in the micro and mesoscopic realm to characterize such phases as spin-ice liquids and glasses and to explain the behavior of such materials as multiferroics, high temperature superconductors, colloids and copolymers. Here we introduce a system of macroscopic ferromagnetic rotors arranged in a planar lattice capable of out-of-plane movement that exhibit the characteristic honeycomb spin ice rules studied and seen so far only in its mesoscopic manifestation. We find that a polarized initial state of this system settles into the honeycomb spin ice phase with relaxation on multiple time scales. We explain this relaxation process using a minimal classical mechanical model which includes Coulombic interactions between magnetic charges located at the ends of the magnets and viscous dissipation at the hinges. Our study shows how macroscopic frustration arises in a purely classical setting that is amenable to experiment, easy manipulation, theory and computation, and shows phenomena that are not visible in their microscopic counterparts.

cond-mat.mtrl-sci↗

arXiv2012

Geometric Mechanics of Curved Crease Origami

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations which allow us to generalize our analysis to study multiply folded structures.

cond-mat.soft↗

arXiv2012

The size, shape, and dynamics of cellular blebs

A cellular bleb grows when a portion of the cell membrane detaches from the underlying cortex under the influence of a cytoplasmic pressure. We develop a quantitative model for the growth and dynamics of these objects in a simple two-dimensional setting. In particular, we first find the minimum cytoplasmic pressure and minimum unsupported membrane length for a stationary bleb to nucleate and grow as a function of the membrane-cortex adhesion. We next show how a bleb may travel around the periphery of the cell when the cytoplasmic pressure varies in space and time in a prescribed way and find that the traveling speed is governed by the speed of the pressure change induced by local cortical contraction while the shape of the traveling bleb is governed by the speed of cortical healing. Finally, we relax the assumption that the pressure change is prescribed and couple it hydrodynamically to the cortical contraction and membrane deformation. By quantifying the phase space of bleb formation and dynamics, our framework serves to delineate the range and scope of bleb-associated cell motility and synthesizes a variety of experimental observations.

physics.bio-ph↗

arXiv2012

Minimal surfaces bounded by elastic lines

In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution to the Plateau problem. But what happens if a soap film spans a loop of inextensible but flexible wire? We consider this simple query that couples Plateau's problem to Euler's Elastica: a special class of twist-free curves of given length that minimize their total squared curvature energy. The natural marriage of two of the oldest geometrical problems linking physics and mathematics leads to a quest for the shape of a minimal surface bounded by an elastic line: the Euler-Plateau problem. We use a combination of simple physical experiments with soap films that span soft filaments, scaling concepts, exact and asymptotic analysis combined with numerical simulations to explore some of the richness of the shapes that result. Our study raises questions of intrinsic interest in geometry and its natural links to a range of disciplines including materials science, polymer physics, architecture and even art.

math.DG↗

arXiv2012

Twisting Graphene Nanoribbons into Carbon Nanotubes

Although carbon nanotubes consist of honeycomb carbon, they have never been fabricated from graphene directly. Here, it is shown by quantum molecular-dynamics simulations and classical continuum-elasticity modeling, that graphene nanoribbons can, indeed, be transformed into carbon nanotubes by means of twisting. The chiralities of the tubes thus fabricated can be not only predicted but also externally controlled. This twisting route is an opportunity for nanofabrication, and is easily generalizable to ribbons made of other planar nanomaterials.

cond-mat.mtrl-sci↗

arXiv2012

A simple model for nanofiber formation by rotary jet-spinning

Nanofibers are microstructured materials that span a broad range of applications from tissue engineering scaffolds to polymer transistors. An efficient method of nanofiber production is Rotary Jet-Spinning (RJS), consisting of a perforated reservoir rotating at high speeds along its axis of symmetry, which propels a liquid, polymeric jet out of the reservoir orifice. These jets undergo stretching and solidify forming nanoscale fibers. We report a minimal scaling framework complemented by a semi-analytic and numerical approach to characterize the regimes of nanofiber production using RJS. Our theoretical model is validated for the fiber radius as a function of experimentally tunable parameters. We summarize our findings in a phase diagram for the design space of continuous nanofibers as a function of process parameters, in good agreement with experiments and with natural implications for the production rates as well as in the morphological quality of fibers.

cond-mat.mtrl-sci↗

arXiv2011

Multistability of free spontaneously-curved anisotropic strips

Multistable structures are objects with more than one stable conformation, exemplified by the simple switch. Continuum versions are often elastic composite plates or shells, such as the common measuring tape or the slap bracelet, both of which exhibit two stable configurations: rolled and unrolled. Here we consider the energy landscape of a general class of multistable anisotropic strips with spontaneous Gaussian curvature. We show that while strips with non-zero Gaussian curvature can be bistable, strips with positive spontaneous curvature are always bistable, independent of the elastic moduli, strips of spontaneous negative curvature are bistable only in the presence of spontaneous twist and when certain conditions on the relative stiffness of the strip in tension and shear are satisfied. Furthermore, anisotropic strips can become tristable when their bending rigidity is small. Our study complements and extends the theory of multistability in anisotropic shells and suggests new design criteria for these structures.

cond-mat.soft↗

arXiv2011

Reply to Comment on "Statistical mechanics of developable ribbons"

Starostin and van der Heijden [arXiv:1111.2029] question the validity of the results reported in our Letter [Phys. Rev. Lett. 104, 238104 (2010)] regarding the existence of spontaneous helical structure in finite-temperature developable ribbons. According to the authors of the Comment, our setting is affected by a systematic error in the calculation of the torsion τ that results in a bias of the Monte Carlo sampling toward helical configurations, and originates from the fact that the Frenet frame, used by us to describe the centerline of the ribbons, rotates by 180^{\circ} about the direction of the tangent vector every time an inflection point (i.e. a point where the curvature κ changes in sign) is encountered. While the rotation of the frame at infection points is a well known property of Frenet frame, the conclusions of Starostin and van der Heijden on how this phenomenon would affect the Monte Carlo sampling are incorrect, as are many of the other statements that they make.

cond-mat.soft↗

arXiv2011

Skating on a Film of Air: Drops Impacting on a Surface

Drops impacting on a surface are ubiquitous in our everyday experience. This impact is understood within a commonly accepted hydrodynamic picture: it is initiated by a rapid shock and a subsequent ejection of a sheet leading to beautiful splashing patterns. However, this picture ignores the essential role of the air that is trapped between the impacting drop and the surface. Here we describe a new imaging modality that is sensitive to the behavior right at the surface. We show that a very thin film of air, only a few tens of nanometers thick, remains trapped between the falling drop and the surface as the drop spreads. The thin film of air serves to lubricate the drop enabling the fluid to skate on the air film laterally outward at surprisingly high velocities, consistent with theoretical predictions. Eventually this thin film of air must break down as the fluid wets the surface. We suggest that this occurs in a spinodal-like fashion, and causes a very rapid spreading of a wetting front outwards; simultaneously the wetting fluid spreads inward much more slowly, trapping a bubble of air within the drop. Our results show that the dynamics of impacting drops are much more complex than previously thought and exhibit a rich array of unexpected phenomena that require rethinking classical paradigms.

physics.flu-dyn↗

arXiv2011

Banding, Excitability and Chaos in Active Nematic Suspensions

Motivated by the observation of highly unstable flowing states in suspensions of microtubules and kinesin, we analyze a model of mutually-propelled filaments suspended in a solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations when the nematic order parameter is allowed to vary in space and time. We analyze the model in two contexts: a quasi-one-dimensional channel with no-slip walls and a two-dimensional box with periodic boundaries. Using stability analysis and numerical calculations we show that the interplay between non-uniform nematic order, activity, and flow results in a variety of complex scenarios that include spontaneous banded laminar flow, relaxation oscillations, and chaos.

cond-mat.soft↗

arXiv2011

Shock driven jamming and periodic fracture of particulate rafts

A tenuous monolayer of hydrophobic particles at the air-water interface often forms a scum or raft. When such a monolayer is disturbed by the localized introduction of a surfactant droplet, a radially divergent surfactant shock front emanates from the surfactant origin and packs the particles into a jammed, compact, annular band with a packing fraction that saturates at a peak packing fraction $ϕ^*$. As the resulting two-dimensional, disordered elastic band grows with time and is driven radially outwards by the surfactant, it fractures to form periodic triangular cracks with robust geometrical features. We find the number of cracks $N$ and the compaction band radius $R^*$ at fracture onset vary monotonically with the initial packing fraction ($ϕ_{init}$). However, its width $W^*$ is constant for all $ϕ_{init}$. A simple geometric theory that treats the compaction band as an elastic annulus, and accounts for mass conservation allows us to deduce that $N \simeq 2πR^*/W^* \simeq 4πϕ_{RCP}/ϕ_{init}$, a result we verify both experimentally and numerically. We show the essential ingredients for this phenomenon are an initially low enough particulate packing fraction that allows surfactant driven advection to cause passive jamming and eventual fracture of the hydrophobic particulate interface.

cond-mat.soft↗

arXiv2011

Probability and dynamics in the toss of a non-bouncing thick coin

When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and precession and calculate the probability distribution of heads, tails, and sides for a thick coin as a function of its dimensions and the distribution of its initial conditions. Our theory yields a simple expression for the aspect ratio of homogeneous coins with a prescribed frequency of heads/tails compared to sides, which we validate by tossing experiments using coins of different aspect ratios.

physics.class-ph↗

arXiv2011

Dynamic instability of a growing adsorbed polymorphic filament

The intermittent transition between slow growth and rapid shrinkage in polymeric assemblies is termed dynamic instability, a feature observed in a variety of biochemically distinct assemblies including microtubules, actin and their bacterial analogs. The existence of this labile phase of a polymer has many functional consequences in cytoskeletal dynamics, and its repeated appearance suggests that it is relatively easy to evolve. Here, we consider the minimal ingredients for the existence of dynamic instability by considering a single polymorphic filament that grows by binding to a substrate, undergoes a conformation change, and may unbind as a consequence of the residual strains induced by this change. We identify two parameters that control the phase space of possibilities for the filament: a structural mechanical parameter that characterizes the ratio of the bond strengths along the filament to those with the substrate (or equivalently the ratio of longitudinal to lateral interactions in an assembly), and a kinetic parameter that characterizes the ratio of time scales for growth and conformation change. In the deterministic limit, these parameters serve to demarcate a region of uninterrupted growth from that of collapse. However, in the presence of disorder in either the structural or the kinetic parameter the growth and collapse phases can coexist where the filament can grow slowly, shrink rapidly, and transition between these phases, thus exhibiting dynamic instability. We exhibit the window for the existence of dynamic instability in a phase diagram that allows us to quantify the evolvability of this labile phase.

cond-mat.soft↗

arXiv2011

Unfolding the Sulcus

Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for sulcfication showing that it is a scale-free, sub-critical {\em nonlinear} instability. In contrast with classical nucleation, sulcification is {\em continuous}, occurs in purely elastic continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On unloading, it quasi-statically shrinks to a point with a lower critical strain, explained by breaking of scale symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with {\em no} energy barrier. Simple experiments confirm the existence of these two critical strains.

cond-mat.soft↗

arXiv2011

Buckling instability of a thin-layer rectilinear Couette flow

We analyse the buckling stability of a thin, viscous sheet when subject to simple shear, providing conditions for the onset of the dominant out-of-plane modes using two models: (i) an asymptotic theory for the dynamics of a viscous plate and (ii) the full Stokes equations. In either case, the plate is stabilised by a combination of viscous resistance, surface tension and buoyancy relative to an underlying denser fluid. In the limit of vanishing thickness, plates buckle at a shear rate $γ/(μd)$ independent of buoyancy, where 2d is the plate thickness, $γ$ is the average surface tension between the upper and lower surfaces and $μ$ is the fluid viscosity. For thicker plates stabilised by an equal surface tension at the upper and lower surfaces, at and above onset, the most unstable mode has moderate wavelength, is stationary in the frame of the centre-line, spans the width of the plate with crests and troughs aligned at approximately $45^\circ$ to the walls and closely resembles elastic shear modes. The thickest plates that can buckle have an aspect ratio (thickness/width) approximately $\EC$ and are stabilised only by internal viscous resistance. We show that the viscous plate model can only accurately describe the onset of buckling for vanishingly thin plates but provides an excellent description of the most unstable mode above onset. Finally, we show that by modifying the plate model to incorporate advection and make the model material frame-invariant, it is possible to extend its predictive power to describe relatively short, travelling waves.

physics.flu-dyn↗

arXiv2010

Excitable Patterns in Active Nematics

We analyze a model of mutually-propelled filaments suspended in a two-dimensional solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations and the nematic order parameter is allowed to vary in space and time. We show that the interplay between non-uniform nematic order, activity and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media. In this regime the dynamics consists of nearly stationary periods separated by "bursts" of activity in which the system is elastically distorted and solvent is pumped throughout. At even higher activity the dynamics becomes chaotic.

cond-mat.soft↗

arXiv2010

Generalized Erdos Numbers

We propose a simple real-valued generalization of the well known integer-valued Erdos number as a topological, non-metric measure of the `closeness' felt between two nodes in an undirected, weighted graph. These real-valued Erdos numbers are asymmetric and are able to distinguish between network topologies that standard distance metrics view as identical. We use this measure to study some simple analytically tractable networks, and show the utility of our measure to devise a ratings scheme based on the generalized Erdos number that we deploy on the data from the NetFlix prize, and find a significant improvement in our ratings prediction over a baseline.

physics.soc-ph↗

arXiv2010

Flow-induced channelization in a porous medium

We propose a theory for erosional channelization induced by fluid flow in a saturated granular porous medium. When the local fluid flow-induced stress is larger than a critical threshold, grains are dislodged and carried away so that the porosity of the medium is altered by erosion. This in turn affects the local hydraulic conductivity and pressure in the medium and results in the growth and development of channels that preferentially conduct the flow. Our multiphase model involves a dynamical porosity field that evolves along with the volume fraction of the mobile and immobile grains in response to fluid flow that couples the spatiotemporal dynamics of the three phases. Numerical solutions of the resulting initial boundary value problem show how channels form in porous media and highlights how heterogeneity in the erosion threshold dictates the form of the patterns and thus the ability to control them.

nlin.PS↗