arXiv subjects

L. Mahadevan

Publications and source records attributed to L. Mahadevan.

At least 91 records · Page 5Linked to original sources

arXiv2020

Deterministic and stochastic control of kirigami topology

Kirigami, the creative art of paper cutting, is a promising paradigm for mechanical metamaterials. However, to make kirigami-inspired structures a reality requires controlling the topology of kirigami to achieve connectivity and rigidity. We address this question by deriving the maximum number of cuts (minimum number of links) that still allow us to preserve global rigidity and connectivity of the kirigami. A deterministic hierarchical construction method yields an efficient topological way to control both the number of connected pieces and the total degrees of freedom. A statistical approach to the control of rigidity and connectivity in kirigami with random cuts complements the deterministic pathway, and shows that both the number of connected pieces and the degrees of freedom show percolation transitions as a function of the density of cuts (links). Together this provides a general framework for the control of rigidity and connectivity in planar kirigami.

cond-mat.soft↗

arXiv2019

Rotation of a submerged finite cylinder moving down a soft incline

A submerged finite cylinder moving under its own weight along a soft incline lifts off and slides at a steady velocity while also spinning. Here, we experimentally quantify the steady spinning of the cylinder and show theoretically that it is due to a combination of an elastohydrodynamic torque generated by flow in the variable gap, and the viscous friction on the edges of the finite-length cylinder. The relative influence of the latter depends on the aspect ratio of the cylinder as well as the deformability of the substrate, which we express in term of a single scaled compliance parameter. By varying this compliance parameter, we show that our experimental results are consistent with a transition from an edge-effect dominated regime for short cylinders to a gap-dominated elastohydrodynamic regime when the cylinder is very long.

cond-mat.soft↗

arXiv2019

Optimal control of aging in complex networks

Many complex systems experience damage accumulation which leads to aging, manifest as an increasing probability of system collapse with time. This naturally raises the question of how to maximize health and longevity in an aging system at minimal cost of maintenance and intervention. Here, we pose this question in the context of a simple interdependent network model of aging in complex systems, and use both optimal control theory and reinforcement learning alongside a combination of analysis and simulation to determine optimal maintenance protocols. These protocols may motivate the rational design of strategies for promoting longevity in aging complex systems with potential applications in therapeutic schedules and engineered system maintenance.

q-bio.PE↗

arXiv2019

Random sequential adsorption of spheres on a cylinder

Inspired by observations of beads packed on a thin string in such systems as sea-grapes and dental plaque, we study the random sequential adsorption of spheres on a cylinder. We determine the asymptotic fractional coverage of the cylinder as a function of the sole parameter in the problem, the ratio of the sphere radius to the cylinder radius (for a very long cylinder) using a combination of analysis and numerical simulations. Examining the asymptotic structures, we find weak chiral ordering on sufficiently small spatial scales. Experiments involving colloidal microspheres that can attach irreversibly to a silica wire via electrostatic forces or DNA hybridization allow us to verify our predictions for the asymptotic coverage.

cond-mat.soft↗

arXiv2019

Dynamics of growth and form in prebiotic vesicles

The growth, form, and division of prebiotic vesicles, membraneous bags of fluid of varying components and shapes is hypothesized to have served as the substrate for the origin of life. The dynamics of these out-of-equilibrium structures is controlled by physicochemical processes that include the intercalation of amphiphiles into the membrane, fluid flow across the membrane, and elastic deformations of the membrane. To understand prebiotic vesicular forms and their dynamics, we construct a minimal model that couples membrane growth, deformation, and fluid permeation, ultimately couched in terms of two dimensionless parameters that characterize the relative rate of membrane growth and the membrane permeability. Numerical simulations show that our model captures the morphological diversity seen in extant precursor mimics of cellular life, and might provide simple guidelines for the synthesis of these complex shapes from simple ingredients.

cond-mat.soft↗

arXiv2019

Geometric localization in supported elastic struts

Localized deformation patterns are a common motif in morphogenesis and are increasingly finding widespread applications in materials science, for instance as memory devices. Here we describe the emergence of spatially localized deformations in a minimal mechanical system by exploring the impact of growth and shear on the conformation of a semi-flexible filament connected to a pliable shearable substrate. We combine numerical simulations of a discrete rod model with theoretical analysis of the differential equations recovered in the continuum limit to quantify (in the form of scaling laws) how geometry, mechanics, and growth act together to give rise to such localized structures in this system. We find that spatially localized deformations along the filament emerge for intermediate shear modulus and increasing growth. Finally, we use experiments on a 3D printed multi-material model system to demonstrate that external control of the amount of shear and growth regulates the spatial extent of the localized strain texture.

cond-mat.soft↗

arXiv2019

Topology, geometry and mechanics of strongly stretched and twisted filaments

Soft elastic filaments that can be stretched, bent and twisted exhibit a range of topologically and geometrically complex morphologies that include plectonemes, solenoids, knot-like and braid-like structures. We combine numerical simulations of soft elastic filaments that account for geometric nonlinearities and self-contact to map out these structures in a phase diagram that is a function of extension and twist density, consistent with previous experimental observations. By using ideas from computational topology, we also track the interconversion of link, twist and writhe in these geometrically complex physical structures. This allows us to explain recent experiments on fiber-based artificial muscles that use the conversion of writhe to extension or contraction, exposing the connection between topology, geometry and mechanics in an everyday practical setting.

cond-mat.soft↗

arXiv2018

Programming Curvature using Origami Tessellations

Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one degree-of-freedom collapsible structures, we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, and quantify the energetic and material cost of doing so.

cond-mat.soft↗

arXiv2018

Programming shape using kirigami tessellations

Kirigami tessellations, regular planar patterns formed by cutting flat, thin sheets, have attracted recent scientific interest for their rich geometries, surprising material properties and promise for technologies. Here we pose and solve the inverse problem of designing the number, size, and orientation of cuts that allows us to convert a closed, compact regular kirigami tessellation of the plane into a deployment that conforms approximately to any prescribed target shape in two and three dimensions. We do this by first identifying the constraints on the lengths and angles of generalized kirigami tessellations which guarantee that their reconfigured face geometries can be contracted from a non-trivial deployed shape to a novel planar cut pattern. We encode these conditions in a flexible constrained optimization framework which allows us to deform the geometry of periodic kirigami tesselations with three, four, and sixfold symmetry, among others, into generalized kirigami patterns that deploy to a wide variety of prescribed boundary target shapes. Physically fabricated models verify our inverse design approach and allow us to determine the tunable material response of the resulting structures. We then extend our framework to create generalized kirigami patterns that deploy to approximate curved surfaces in $\mathbb{R}^3$. Altogether, this work illustrates a novel framework for designing complex, shape-changing sheets from simple cuts showing the power of kirigami tessellations as flexible mechanical metamaterials.

cond-mat.soft↗

arXiv2018

Persistence of strain in motor-filament assemblies

Crosslinked semi-flexible and flexible filaments that are actively deformed by molecular motors occur in various natural settings, such as the ordered eukaryotic flagellum, and the disordered cytoskeleton. The deformation of these composite systems is driven by active motor forces and resisted by passive filament elasticity, and structural constraints due to permanent cross-links. Using a mean field theory for a one-dimensional ordered system, we show that the combination of motor activity and finite filament extensibility yields a characteristic persistence length scale over which active strain decays. This decay length is set by the ability of motors to respond to combination of the weak extensional elasticity, passive shear resistance and the viscoelastic properties of the motor assembly, and generalizes the notion of persistence in purely thermal filaments to active systems.

physics.bio-ph↗

arXiv2018

Spatial control of irreversible protein aggregation

Liquid cellular compartments spatially segregate from the cytoplasm and can regulate aberrant protein aggregation, a process linked to several medical conditions, including Alzheimer's and Parkinson's diseases. Yet the mechanisms by which these droplet-like compartments affect protein aggregation remain unknown. Here, we combine kinetic theory of protein aggregation and liquid-liquid phase separation to study the spatial control of irreversible protein aggregation in the presence of liquid compartments. We find that, even for weak interactions between the compartment constituents and the aggregating monomers, aggregates are strongly enriched inside the liquid compartment relative to the surrounding cytoplasm. We show that this enrichment is caused by a positive feedback mechanism of aggregate nucleation and growth which is mediated by a flux maintaining the phase equilibrium between the compartment and the cytoplasm. Our model predicts that the compartment volume that maximizes aggregate enrichment in the compartment is determined by the reaction orders of aggregate nucleation. The underlying mechanism of aggregate enrichment could be used to confine cytotoxic protein aggregates inside droplet-like compartments suggesting potential new avenues against aberrant protein aggregation. Our findings could also represent a common mechanism for the spatial control of irreversible chemical reactions in general.

physics.bio-ph↗

arXiv2017

Active elastohydrodynamics of vesicles in narrow, blind constrictions

Fluid-resistance limited transport of vesicles through narrow constrictions is a recurring theme in many biological and engineering applications. Inspired by the motor-driven movement of soft membrane-bound vesicles into closed neuronal dendritic spines, here we study this problem using a combination of passive three-dimensional simulations and a simplified semi-analytical theory for active transport of vesicles that are forced through such constrictions by molecular motors. We show that the motion of these objects is characterized by two dimensionless quantities related to the geometry and the strength of forcing relative to the vesicle elasticity. We use numerical simulations to characterize the transit time for a vesicle forced by fluid pressure through a constriction in a channel, and find that relative to an open channel, transport into a blind end leads to the formation of an effective lubrication layer that strongly impedes motion. When the fluid pressure forcing is complemented by forces due to molecular motors that are responsible for vesicle trafficking into dendritic spines, we find that the competition between motor forcing and fluid drag results in multistable dynamics reminiscent of the real system. Our study highlights the role of non-local hydrodynamic effects in determining the kinetics of vesicular transport in constricted geometries.

cond-mat.soft↗

arXiv2017

Differential-activity driven instabilities in biphasic active matter

Active stresses can cause instabilities in contractile gels and living tissues. Here we describe a generic hydrodynamic theory that treats these systems as a mixture of two phases of varying activity and different mechanical properties. We find that differential activity between the phases provides a mechanism causing a demixing instability. We follow the nonlinear evolution of the instability and characterize a phase diagram of the resulting patterns. Our study complements other instability mechanisms in mixtures such as differential growth, shape, motion or adhesion.

physics.bio-ph↗

arXiv2017

Computational mechanics of soft filaments

Soft slender structures are ubiquitous in natural and artificial systems and can be observed at scales that range from the nanometric to the kilometric, from polymers to space tethers. We present a practical numerical approach to simulate the dynamics of filaments that, at every cross-section, can undergo all six possible modes of deformation, allowing the filament to bend, twist, stretch and shear, while interacting with complex environments via muscular activity, surface contact, friction and hydrodynamics. We examine the accuracy of our method by means of several benchmark problems with known analytic solutions. We then demonstrate the capabilities and robustness of our approach to solve forward problems in physics and mechanics related to solenoid and plectoneme formation in twisted, stretched filaments, and inverse problems related to active biophysics of limbless locomotion on solid surfaces and in bulk liquids. All together, our approach provides a robust computational framework to characterize the mechanical response and design of soft active slender structures.

physics.flu-dyn↗

arXiv2017

Rotation of an immersed cylinder sliding near a thin elastic coating

It is known that an object translating parallel to a soft wall in a viscous fluid produces hydro- dynamic stresses that deform the wall, which, in turn, results in a lift force on the object. Recent experiments with cylinders sliding under gravity near a soft incline, which confirmed theoretical arguments for the lift force, also reported an unexplained steady-state rotation of the cylinders [Saintyves et al. PNAS 113(21), 2016]. Motivated by these observations, we show, in the lubrication limit, that an infinite cylinder that translates in a viscous fluid parallel to a soft wall at constant speed and separation distance must also rotate in order to remain free of torque. Using the Lorentz reciprocal theorem, we show analytically that for small deformations of the elastic layer, the angular velocity of the cylinder scales with the cube of the sliding speed. These predictions are confirmed numerically. We then apply the theory to the gravity-driven motion of a cylinder near a soft incline and find qualitative agreement with the experimental observations, namely that a softer elastic layer results in a greater angular speed of the cylinder.

physics.flu-dyn↗

arXiv2017

Wrinkling instability of an inhomogeneously stretched viscous sheet

Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed non-uniform temperature field. We first determine the associated base flow by solving the long-timescale stretching flow of a flat sheet as a function of two dimensionless parameters: the normalized stretching velocity $α$, and a dimensionless width of the heating zone $β$. This allows us to determine the conditions for the onset of an out-of-plane wrinkling instability stated in terms of an eigenvalue problem for a linear partial differential equation governing the displacement of the midsurface of the sheet. We show the sheet can become unstable in two regions that are upstream and downstream of the heating zone where the minimum in-plane stress is negative. This yields the shape and growth rates of the most unstable buckling mode in both regions for various values of the stretching velocity and heating zone width. A transition from stationary to oscillatory unstable modes is found in the upstream region with increasing $β$ while the downstream region is always stationary. We show that the wrinkling instability can be entirely suppressed when the surface tension is large enough relative to the magnitude of the in-plane stress. Finally, we present an operating diagram that indicates regions of the parameter space that result in a required outlet sheet thickness upon stretching, while simultaneously minimizing or suppressing the out-of-plane buckling; a result that is relevant for the glass redraw method used to create ultrathin glass sheets.

physics.flu-dyn↗

arXiv2017

Termite mounds harness diurnal temperature oscillations for ventilation

Many species of millimetric fungus-harvesting termites collectively build uninhabited, massive mound structures enclosing a network of broad tunnels which protrude from the ground meters above their subterranean nests. It is widely accepted that the purpose of these mounds is to give the colony a controlled micro-climate in which to raise fungus and brood by managing heat, humidity, and respiratory gas exchange. While different hypotheses such as steady and fluctuating external wind and internal metabolic heating have been proposed for ventilating the mound, the absence of direct in-situ measurement of internal air flows has precluded a definitive mechanism for this critical physiological function. By measuring diurnal variations in flow through the surface conduits of the mounds of the species Odontotermes obesus, we show that a simple combination of geometry, heterogeneous thermal mass and porosity allows the mounds to use diurnal ambient temperature oscillations for ventilation. In particular, the thin outer flute-like conduits heat up rapidly during the day relative to the deeper chimneys, pushing air up the flutes and down the chimney in a closed convection cell, with the converse situation at night. These cyclic flows in the mound flush out $\text{CO}_2$ from the nest and ventilate the colony, in a novel example of deriving useful work from thermal oscillations.

physics.bio-ph↗

arXiv2016

Self-sustained lift and low friction via soft lubrication

Relative motion between soft wet solids arises in a number of applications in natural and artificial settings, and invariably couples elastic deformation and fluid flow. We explore this in a minimal setting by considering a fluid-immersed negatively-buoyant cylinder moving along a soft inclined wall. Our experiments show that there is an emergent robust steady-state sliding regime of the cylinder with an effective friction that is significantly reduced relative to that of rigid fluid-lubricated contacts. A simple scaling approach that couples the cylinder-induced flow to substrate deformation allows us to explain the emergence of an elastohydrodynamic lift that underlies the self-sustained lubricated motion of the cylinder, consistent with recent theoretical predictions. Our results suggest an explanation for a range of effects such as reduced wear in animal joints and long-runout landslides, and can be couched as a design principle for low-friction interfaces.

cond-mat.soft↗