arXiv subjects

L. Mahadevan

Publications and source records attributed to L. Mahadevan.

At least 109 records · Page 6Linked to original sources

arXiv2015

Optimal switching strategies for stochastic geocentric/egocentric navigation

Animals use a combination of egocentric navigation driven by the internal integration of environmental cues, interspersed with geocentric course correction and reorientation, often with uncertainty in sensory acquisition of information, planning and execution. Inspired directly by observations of dung beetle navigational strategies that show switching between geocentric and egocentric strategies, we consider the question of optimal strategies for the navigation of an agent along a preferred direction in the presence of multiple sources of noise. We address this using a model that takes the form of a correlated random walk at short time scales that is interspersed with reorientation events that yields a biased random walks at long time scales. We identify optimal alternation schemes and characterize their robustness in the context of noisy sensory acquisition, and performance errors linked with variations in environmental conditions and agent-environment interactions.

physics.bio-ph↗

arXiv2015

The Organization and Control of an Evolving Interdependent Population

Starting with Darwin, biologists have asked how populations evolve from a low fitness state that is evolutionarily stable to a high fitness state that is not. Specifically of interest is the emergence of cooperation and multicellularity where the fitness of individuals often appears in conflict with that of the population. Theories of social evolution and evolutionary game theory have produced a number of fruitful results employing two-state two-body frameworks. In this study we depart from this tradition and instead consider a multi-player, multi-state evolutionary game, in which the fitness of an agent is determined by its relationship to an arbitrary number of other agents. We show that populations organize themselves in one of four distinct phases of interdependence depending on one parameter, selection strength. Some of these phases involve the formation of specialized large-scale structures. We then describe how the evolution of independence can be manipulated through various external perturbations.

q-bio.PE↗

arXiv2015

Elastohydrodynamics of contact in adherent sheets

Adhesive contact between a thin elastic sheet and a substrate in a liquid environment arises in a range of biological, physical and technological applications. By considering the dynamics of this process that naturally couples fluid flow, long wavelength elastic deformations and microscopic adhesion, and solving the resulting partial differential equation numerically, we uncover the short-time dynamics of the onset of adhesion and the long-time dynamics of a steady propagating adhesion front. Simple scaling laws corroborate our results for characteristic waiting-time for adhesive contact, as well as the speed of the adhesion front. A similarity analysis of the governing partial differential equation further allows us to determine the shape of a fluid filled bump ahead of the adhesion zone. Finally, our analysis yields the boundary conditions for the apparent elastohydrodynamic contact line, generalizing the well known conditions for static elastic contact while highlighting how microscale physics regularizes the dynamics of contact.

physics.flu-dyn↗

arXiv2015

Elastic Cheerios effect: self-assembly of cylinders on a soft solid

A rigid cylinder placed on a soft gel deforms its surface. When multiple cylinders are placed on the surface, they interact with each other via the topography of the deformed gel which serves as an energy landscape; as they move, the landscape changes which in turn changes their interaction. We use a combination of experiments, simple scaling estimates and numerical simulations to study the self-assembly of cylinders in this elastic analog of the Cheerios effect for capillary interactions on a fluid interface. Our results show that the effective two body interaction can be well described by an exponential attraction potential as a result of which the dynamics also show an exponential behavior with respect to the separation distance. When many cylinders are placed on the gel, the cylinders cluster together if they are not too far apart; otherwise their motion gets elastically arrested.

cond-mat.soft↗

arXiv2015

Elastohydrodynamics of a sliding, spinning and sedimenting cylinder near a soft wall

We consider the motion of a fluid-immersed negatively buoyant particle in the vicinity of a thin compressible elastic wall, a situation that arises in a variety of technological and natural settings. We use scaling arguments to establish different regimes of sliding, and complement these estimates using thin-film lubrication dynamics to determine an asymptotic theory for the sedimentation, sliding, and spinning motions of a cylinder. The resulting theory takes the form of three coupled nonlinear singular-differential equations. Numerical integration of the resulting equations confirms our scaling relations and further yields a range of unexpected behaviours. Despite the low-Reynolds feature of the flow, we demonstrate that the particle can spontaneously oscillate when sliding, can generate lift via a Magnus-like effect, can undergo a spin-induced reversal effect, and also shows an unusual sedimentation singularity. Our description also allows us to address a sedimentation-sliding transition that can lead to the particle coasting over very long distances, similar to certain geophysical phenomena. Finally, we show that a small modification of our theory allows to generalize the results to account for additional effects such as wall poroelasticity.

cond-mat.soft↗

arXiv2015

Generalized Erdos Numbers for network analysis

In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erdős Numbers (GENs) satisfy a number of desirable properties as a measure of topological closeness when nodes share a finite resource between nodes as they are real-valued and non-local, and can be used to create an asymmetric matrix of connectivities. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to a new global measure of centrality and is highly correlated with Page Rank. The relative asymmetry of the GENs (due to their non-metric definition) is linked also to the asymmetry in the mean first passage time between nodes in a random walk, and we use a linearized form of the GENs to develop a continuum model for `closeness' in spatial networks. As an example of their practicality, we deploy them to characterize the structure of static networks and show how it relates to dynamics on networks in such situations as the spread of an epidemic.

physics.soc-ph↗

arXiv2015

Similarity and singularity in adhesive elastohydrodynamic touchdown

We consider the touchdown of an elastic sheet as it adheres to a wall, which has a dynamics that is limited by the viscous resistance provided by the squeeze flow of the intervening liquid trapped between the two solid surfaces. The dynamics of the sheet is described mathematically by elastohydrodynamic lubrication theory, coupling the elastic deformation of the sheet, the microscopic van der Waals adhesion and the viscous thin film flow. We use a combination of numerical simulations of the governing partial differential equation and a scaling analysis to describe the self-similar solution of the touchdown of the sheet as it approaches the wall. An analysis of the equation satisfied by the similarity variables in the vicinity of the touchdown event shows that an entire sequence of solutions are allowed. However, a comparison of these shows that only the fundamental similarity solution is observed in the time-dependent numerical simulations, consistent with the fact that it alone is stable. Our analysis generalizes similar approaches for rupture in capillary thin film hydrodynamics and suggests experimentally verifiable predictions for a new class of singular flows linking elasticity, hydrodynamics and adhesion.

physics.flu-dyn↗

arXiv2015

Elastohydrodynamics and kinetics of protein patterning in the immunological synapse

The cellular basis for the adaptive immune response during antigen recognition relies on a specialized protein interface known as the immunological synapse (IS). Understanding the biophysical basis for protein patterning by deciphering the quantitative rules for their formation and motion is an important aspect of characterizing immune cell recognition and thence the rules for immune system activation. We propose a minimal mathematical model for the physical basis of membrane protein patterning in the IS, which encompass membrane mechanics, protein binding kinetics and motion, and fluid flow in the synaptic cleft. Our theory leads to simple predictions for the spatial and temporal scales of protein cluster formation, growth and arrest as a function of membrane stiffness, rigidity and kinetics of the adhesive proteins, and the fluid in the synaptic cleft. Numerical simulations complement these scaling laws by quantifying the nucleation, growth and stabilization of proteins domains on the size of the cell. Direct comparison with experiment shows that passive elastohydrodynamics and kinetics of protein binding in the synaptic cleft can describe the short-time formation and organization of protein clusters, without evoking any active processes in the cytoskeleton. Despite the apparent complexity of the process, our analysis highlights the role of just two dimensionless parameters that characterize the spatial and temporal evolution of the protein pattern: a ratio of membrane elasticity to protein elasticity, and the ratio of a hydrodynamic time scale for fluid flow relative to the protein binding rate, and we present a simple phase diagram that encompasses the variety of patterns that can arise.

physics.bio-ph↗

arXiv2015

Gyrification from constrained cortical expansion

The exterior of the mammalian brain - the cerebral cortex - has a conserved layered structure whose thickness varies little across species. However, selection pressures over evolutionary time scales have led to cortices that have a large surface area to volume ratio in some organisms, with the result that the brain is strongly convoluted into sulci and gyri. Here we show that the gyrification can arise as a nonlinear consequence of a simple mechanical instability driven by tangential expansion of the gray matter constrained by the white matter. A physical mimic of the process using a layered swelling gel captures the essence of the mechanism, and numerical simulations of the brain treated as a soft solid lead to the formation of cusped sulci and smooth gyri similar to those in the brain. The resulting gyrification patterns are a function of relative cortical expansion and relative thickness (compared with brain size), and are consistent with observations of a wide range of brains, ranging from smooth to highly convoluted. Furthermore, this dependence on two simple geometric parameters that characterize the brain also allows us to qualitatively explain how variations in these parameters lead to anatomical anomalies in such situations as polymicrogyria, pachygyria, and lissencephalia.

physics.bio-ph↗

arXiv2015

Solid friction between soft filaments

Any macroscopic deformation of a filamentous bundle is necessarily accompanied by local sliding and/or stretching of the constituent filaments. Yet the nature of the sliding friction between two aligned filaments interacting through multiple contacts remains largely unexplored. Here, by directly measuring the sliding forces between two bundled F-actin filaments, we show that these frictional forces are unexpectedly large, scale logarithmically with sliding velocity as in solid-like friction, and exhibit complex dependence on the filaments' overlap length. We also show that a reduction of the frictional force by orders of magnitude, associated with a transition from solid-like friction to Stokes' drag, can be induced by coating F-actin with polymeric brushes. Furthermore, we observe similar transitions in filamentous microtubules and bacterial flagella. Our findings demonstrate how altering a filament's elasticity, structure and interactions can be used to engineer interfilament friction and thus tune the properties of fibrous composite materials.

physics.bio-ph↗

arXiv2015

Persistence of activity in noisy motor-filament assemblies

Long, elastic filaments cross-linked and deformed by active molecular motors occur in various natural settings. The overall macroscopic mechanical response of such a composite network depends on the coupling between the active and the passive properties of the underlying constituents and nonlocal interactions between different parts of the composite. In a simple one dimensional system, using a mean field model, it has been shown that the combination of motor activity and finite filament extensibility yields a persistence length scale over which strain decays. Here we study a similar system, in the complementary limit of strong noise and moderate extensibility, using Brownian multi-particle collision dynamics-based numerical simulations that includes the coupling between motor kinetics and local filament extensibility. While the numerical model shows deviations from the mean field predictions due to the presence of strong active noise caused by the variations in individual motor activity, several qualitative features are still retained. Specifically, for fixed motor attachment and detachment rates, the decay is length is set by the ratio of the passive elasticity to the active shear resistance generated by attached motors. Our study generalizes the notion of persistence in passive thermal systems to actively driven systems with testable predictions.

physics.bio-ph↗

arXiv2014

Optimal control of plate shape with incompatible strain fields

A flat plate can bend into a curved surface if it experiences an inhomogeneous growth field. In this article a method is described that numerically determines the optimal growth field giving rise to an arbitrary target shape, optimizing for closeness to the target shape and for growth field smoothness. Numerical solutions are presented, for the full non-symmetric case as well as for simplified one-dimensional and axisymmetric geometries. This system can also be solved semi-analytically by positing an ansatz for the deformation and growth fields in a circular disk with given thickness profile. Paraboloidal, cylindrical and saddle-shaped target shapes are presented as examples, of which the last two exemplify a soft mode arising from a non-axisymmetric deformation of a structure with axisymmetric material properties.

cond-mat.soft↗

arXiv2014

Dynamics of evaporative colloidal patterning

Drying suspensions often leave behind complex patterns of particulates, as might be seen in the coffee stains on a table. Here we consider the dynamics of periodic band or uniform solid film formation on a vertical plate suspended partially in a drying colloidal solution. Direct observations allow us to visualize the dynamics of the band and film deposition, and the transition in between when the colloidal concentration is varied. A minimal theory of the liquid meniscus motion along the plate reveals the dynamics of the banding and its transition to the filming as a function of the ratio of deposition and evaporation rates. We also provide a complementary multiphase model of colloids dissolved in the liquid, which couples the inhomogeneous evaporation at the evolving meniscus to the fluid and particulate flows and the transition from a dilute suspension to a porous plug. This allows us to determine the concentration dependence of the bandwidth and the deposition rate. Together, our findings allow for the control of drying-induced patterning as a function of the colloidal concentration and evaporation rate.

cond-mat.soft↗

arXiv2014

Evaporation-driven ring and film deposition from colloidal droplets

Evaporating suspensions of colloidal particles lead to the formation of a variety of patterns, ranging from a left-over ring of a dried coffee drop to uniformly distributed solid pigments left behind wet paint. To characterize the transition between single rings, multiple concentric rings, broad bands, and uniform deposits, we investigate the dynamics of a drying droplet via a multiphase model of colloidal particles in a solvent. Our theory couples the inhomogeneous evaporation at the evolving droplet interface to the dynamics inside the drop, i.e. the liquid flow, local variations of the particle concentration, and the propagation of the deposition front where the solute forms an incompressible porous medium at high concentrations. A dimensionless parameter combining the capillary number and the droplet aspect ratio captures the formation conditions of different pattern types.

cond-mat.soft↗

arXiv2014

Neuromimetic Circuits with Synaptic Devices based on Strongly Correlated Electron Systems

Strongly correlated electron systems such as the rare-earth nickelates (RNiO3, R = rare-earth element) can exhibit synapse-like continuous long term potentiation and depression when gated with ionic liquids; exploiting the extreme sensitivity of coupled charge, spin, orbital, and lattice degrees of freedom to stoichiometry. We present experimental real-time, device-level classical conditioning and unlearning using nickelate-based synaptic devices in an electronic circuit compatible with both excitatory and inhibitory neurons. We establish a physical model for the device behavior based on electric-field driven coupled ionic-electronic diffusion that can be utilized for design of more complex systems. We use the model to simulate a variety of associate and non-associative learning mechanisms, as well as a feedforward recurrent network for storing memory. Our circuit intuitively parallels biological neural architectures, and it can be readily generalized to other forms of cellular learning and extinction. The simulation of neural function with electronic device analogues may provide insight into biological processes such as decision making, learning and adaptation, while facilitating advanced parallel information processing in hardware.

cond-mat.str-el↗

arXiv2014

How the velvet worm squirts slime

The rapid squirt of a proteinaceous slime jet endows the ancient velvet worms (Onychophora) with a unique mechanism for defense from predators and for capturing prey by entangling them in a disordered web that immobilizes their target. However, to date neither qualitative nor quantitative descriptions have been provided for this unique adaptation. Here we investigate the fast oscillatory motion of the oral papillae and the exiting liquid jet that oscillates with frequencies $f\sim 30-60$ Hz. Using anatomical images, high speed videography, theoretical analysis and a physical simulacrum we show that this fast oscillatory motion is the result of an elastohydrodynamic instability driven by the interplay between the elasticity of oral papillae and the fast unsteady flow during squirting. Our results demonstrate how passive strategies can be cleverly harnessed by organisms, while suggesting future oscillating micro-fluidic devices as well as novel ways for micro and nano fiber production using bioinspired strategies.

physics.flu-dyn↗

arXiv2014

Elastocapillary coalescence of plates and pillars

When a fluid-immersed array of lamellae or filaments that is attached to a substrate is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together. Similarly, when hair dries it clumps together due to capillary forces induced by the liquid menisci between the flexible hairs. Building on prior experimental observations, we use a combination of theory and computation to understand the nature of this instability and its evolution in both the two-dimensional and three-dimensional setting of the problem. For the case of lamellae, we explicitly derive the interaction torques based on the relevant physical parameters. A Bloch-wave analysis for our periodic mechanical system captures the critical volume of the liquid and the 2-plate-collapse eigenmode at the onset of instability. We study the evolution of clusters and their arrest using numerical simulations to explain the hierarchical cluster formation and characterize the sensitive dependence of the final structures on the initial perturbations. We then generalize our analysis to treat the problem of pillar collapse in 3D, where the fluid domain is completely connected and the interface is a surface with the uniform mean curvature. Our theory and simulations capture the salient features of both previous experimental observations and our own in terms of the key parameters that can be used to control the kinetics of the process.

cond-mat.soft↗

arXiv2014

Fluid driven fingering instability of a confined elastic meniscus

When a fluid is pumped into a cavity in a confined elastic layer, at a critical pressure, destabilizing fingers of fluid invade the elastic solid along its meniscus (Saintyves, Dauchot, and Bouchaud, 2013). These fingers occur without fracture or loss of adhesion and are reversible, disappearing when the pressure is decreased. We develop an asymptotic theory of pressurized highly elastic layers trapped between rigid bodies to explain these observations, with predictions for the critical fluid pressure for fingering, and the finger wavelength. We also show that the theory links this fluid-driven fingering with a similar transition driven instead by transverse stretching of the elastic layer. We further verify these predictions by using finite-element simulations on the two systems which show that, in both cases, the fingering transition is first-order (sudden) and hence has a region of bistability. Our predictions are in good agreement with recent observations of this elastic analog of the classical Saffman-Taylor interfacial instability in hydrodynamics.

cond-mat.soft↗