The stiffness of cells is commonly assumed to depend on the stiffness of their surrounding: bone cells are much stiffer than neurons, and each exists in surrounding tissue that matches the cell stiffness. In this talk, I will discuss new measurements of cell stiffness, and show that that cell stiffness is strongly correlated to cell volume. This affects both the mechanics and the gene expression in the cell, and even impacts on the differentiation of stem cells.

A consensus is emerging that discontinuous shear thickening (DST) in dense suspensions marks a transition from a flow state where particles remain well separated by lubrication layers, to one dominated by frictional contacts. We show here that reasonable assumptions about contact proliferation predict two distinct types of DST in the absence of inertia. The first occurs at densities above the jamming point of frictional particles; here the thickened state is completely jammed and (unless particles deform) cannot flow without inhomogeneity or fracture. The second regime shows strain-rate hysteresis and arises at somewhat lower densities where the thickened phase flows smoothly. DST is predicted to arise when finite-range repulsions defer contact formation until a characteristic stress level is exceeded.

The deformation of many solid and granular materials is not continuous, but discrete, with intermittent slips similar to earthquakes. A simple model suggests that the statistical distributions of the slips, such as the slip-size distributions, reflect tuned criticality, with approximately the same regular (power-law) functions, and the same tunable exponential cutoffs, for systems spanning 13 decades in length, from tens of nanometers to hundreds of kilometers; for compressed nano-crystals, amorphous materials, possibly sheared granular materials, lab-sized rocks, and earthquakes. The similarities are explained by a simple analytic model, which suggests that results are transferable across scales. This study provides a unified understanding of fundamental properties of shear-induced deformation in systems ranging from nanocrystals to earthquakes. It also provides many new predictions for future experiments and simulations. The studies draw on methods from the theory of phase transitions, the renormalization group, and numerical simulations. Connections to other systems with avalanches, such as magnets and neuron firing avalanches in the brain are also discussed.

The problem of reforestation is studied by solving a vegetation model in drylands. The "shikim" water harvesting method is seen as a parametric periodic forcing of a pattern forming system, where the resulting stripes and spots patterns are 1:1 and 2:1 resonant solutions. A modified Swift-Hohenberg equation helps us understand the dynamics of collapse and expansion of patterned states. I conclude by addressing preventive measures that make the vegetation system more resilient to climatic changes, and help avoid catastrophic regime shifts.

Despite an enormous range of applications and centuries of scientific study, understanding and predicting the flow of fluids remains a tremendous challenge, particularly when the flow is chaotic or turbulent. Turbulent flows tend to be characterized by violent fluctuations, enormous numbers of strongly coupled degrees of freedom, and significant variability in space and time. But despite all this complexity, turbulence is not random. Rather, it tends to self-organize into striking but transient patterns and features that arise from nonlinear interactions. Some of these "coherent structures," such as strong vortices, are readily apparent; others are more subtle. But how much can we learn or predict about the flow from studying coherent structures? The answer may lie in the energetics of the flow, since these same nonlinearities couple dynamics on different scales and, in turbulence, drive a net transfer of energy from the scales at which it is injected into the flow to the scales at which it is dissipated. To begin to make quantitative links between the nonlinear dynamics of the flow and the spontaneous generation of spatiotemporal order, I will discuss experimental results from a quasi-two-dimensional turbulent flow. Using a filtering technique, we extract the spatially localized scale-to-scale flux of energy, and show that it is linked to suitably defined coherent structures. I will also discuss the self-organization of the turbulent stress that drives this energy transfer.

Cardiac cells, like toilets, are excitable: Giving a sufficiently strong push to the handle of a quiescent toilet elicits a dramatic response (flush) followed by a gradual return to the resting state. Likewise, supplying a sufficiently strong electrical stimulus to a quiescent cardiac cell elicits a prolonged elevation of the membrane potential (an action potential).

Suppose that one end of an excitable fiber of cardiac cells is paced periodically. If the period is large, the generic response is a stable periodic wave train of the sort associated with normal, coordinated contraction of heart muscle tissue. Reducing the period (think "speeding up the heart rate") can cause the onset of an instability which can have devastating physiological consequences. Echebarria and Karma (Chaos, 2002) argued that if one attempts to stabilize the periodic wave train by using feedback control to perturb the pacing period, success can be achieved only within some small radius of the stimulus site. Those authors used a special case of the ETDAS control method that Dan Gauthier and Josh Socolar devised.

Here, I will offer an explanation as to WHY algorithms like ETDAS, applied locally, cannot achieve global results in this context. Then, I'll argue that it actually IS possible to stabilize the periodic wave train if the perturbations are chosen more carefully. While these findings may seem encouraging from an experimental or clinical standpoint, I will close by describing some recent work of Flavio Fenton which I believe is even more promising.

The characterization of chaos as a random-like response from a deterministic dynamical system with an extreme sensitivity to initial conditions is well-established, and has provided a stimulus to research in nonlinear dynamical systems in general. In a formal sense, the computation of the Lyapunov Exponent (LE) spectrum establishes a quantitative measure, with at least one positive LE (and generally bounded motion) indicating a local exponential divergence of adjacent trajectories. Other measures are associated with certain geometric features of a chaotic attractor, e.g., the fractal dimension, and broadband frequency content. However, although the extraction of LE's can be accomplished with (necessarily noisy) experimental data, this is still a relatively data-intensive, sensitive (and frustrating) endeavor.
We present here an alternative, pragmatic approach to identifying chaos as a function of system parameters, based on frequency content and extending the concept of the spectrogram. This talk will describe this approach applied to systems of increasing complexity, ranging from direct numerical simulations of familiar archetypal systems like Lorenz and the pendulum to experimental data generated from mechanical systems. The accuracy and utility of the approach, including the effect of noise, is tested relative to the standard (LE) approach.

Active motion of microorganisms or artificial microswimmers in a fluid at low Reynolds number is an appealing subject which has attracted much attention recently. Since these swimmers move constantly in nonequilibrium, they give rise to novel phenomena which, in particular, occur when external fields are applied or when they move collectively.

The talk reviews three situations where active motion manifests itself. First, a swimmer under Poiseuille flow shows nonlinear dynamics reminiscent of the nonlinear pendulum. Bounding walls introduce "dissipation" [1] and an elliptical crosssection of the microchannel leads to chaotic motion. Secondly, I discuss the collective motion of model swimmers, so-called squirmers, in a quasi 2D geometry by means of multi-particle collision dynamics. This is a particle based method to solve the Navier-Stokes equations and helps to elucidate the role of hydrodynamics in collective phenomena. Indeed, we find gas-like and cluster phases as well as phase separation which is strongly influenced by hydrodynamic near-field interactions and the swimmer type. Thirdly, I discuss dynamic clustering of active or self-propelling colloids that interact by diffusiophoresis reminiscent of chemotaxis in bacterial systems.

Several geometric and probabilistic methods for studying chaotic phase space transport have been developed and fruitfully applied to diverse areas from orbital mechanics to fluid mechanics and beyond. Increasingly, systems of interest are determined not by analytically defined model systems, but by data from experiments or large-scale simulations. This emphasis on real-world systems sharpens our focus on those features of phase space transport in finite-time systems which seem robust, leading to the consideration of not only invariant manifolds and invariant manifold-like objects, but also their connection with concepts such as symbolic dynamics, chaos, coherent sets, and optimal control. We will highlight some recent applications to areas such as spacecraft trajectories, microfluidic mixing, ship capsize prediction, and biological invasions.

The physics of granular flow is of widespread practical and fundamental interest, and is also important in geology and astrophysics. One challenge to understanding and controlling behavior is that the mechanical response is nonlinear, with a forcing threshold below which the medium is static and above which it flows freely. Furthermore, just above threshold the response may be intermittent even though the forcing is steady. Two familiar examples are avalanches on a heap and clogging in a silo. Another example is dynamical heterogeneities for systems brought close to jamming, where intermediate-time motion is correlated in the form of intermitted string-like swirls. This will be reviewed in the context of glassy liquids and colloids, and more deeply illustrated with experiments on three different granular systems. This includes air-fluidized beads, where jamming is approached by density and airspeed; granular heap flow, where jamming is approached by depth from the free surface; and dense suspensions of NIPA beads, where jamming is approached by both density and shear rate. Emphasis will be given to measurement and analysis methods for quantifying heterogeneities, as well as the scaling of the size of heterogeneities with distance to jamming.

The challenge of predicting velocity and stress fields in any flowing granular material has proven to be a difficult one, from both computational and theoretical perspectives. Indeed, researchers are still in search of the ``Navier-Stokes''-equivalent for flowing granular materials. Granular flows can be adequately predicted using grain-by-grain discrete element methods (DEM), but these approaches become computationally unrealistic for large bodies of material and long times. A robust continuum model, once identified, would have the practical benefit that it could be implemented at a meso-scale saving many orders of magnitude in computation time compared to DEM.

Here, we begin by synthesizing a 3D elasto-viscoplastic law for steady granular flow, merging an existing "frictional fluid" relation with a nonlinear granular elasticity relation to close the system. The flow rate vanishes within a frictional (Drucker-Prager) yield surface and the elastic response is based on a mean-field model generalizing Hertz's contact law. The resulting form is general, able to produce flow and stress predictions in any well-posed boundary value problem. We implement it using ABAQUS/Explicit finite-element package and run test simulations in multiple geometries. The solutions are shown to compare favorably against a number of experiments and DEM simulations.

While this relation appears to function well for rapid flows, experimental results can often differ from the predictions in regions of slower flows. We have been able to attribute many of these phenomena to nonlocal effects stemming from the finite-ness of the grain size. To correct this, we consider the addition of a simple nonlocal term to the rheology in a fashion similar to recent nonlocal flow models in the emulsions community. The results of this extended model are compared against many DEM steady-flow simulations in three different 2D geometries. Quantitative agreement is found for all geometries and over various geometrical/loading parameters. By natural extension, the nonlocal model is then converted to three dimensions with minimal changes, and is implemented numerically as a User-Element in the ABAQUS package. We show that a single calibration of the 3D model quantitatively predicts hundreds of experimental flows in different geometries, including, for the first time, the wide-shear zones observed in split-bottom cells, a geometry made infamous for resisting a theoretical treatment for almost a decade.

We apply super-resolution imaging and single-molecule tracking to gain insight into how proteins assemble to form organized structures in cells. We describe several new tools that were developed to study diverse systems, from viruses to chromatin. The HIV structural protein Gag assembles to form spherical particles of radius ~70 nm. During the assembly process, the number of Gag proteins increases over several orders of magnitude, from a few at nucleation to thousands at completion. We demonstrated an approach that permits quantitative morphological and molecular counting analysis of hundreds of HIV-Gag clusters at the cellular plasma membrane, thus elucidating how different fluorescent labels can change the assembly of virions. Higher-order chromatin structure determines the degree of local DNA condensation, which in turn influences gene accessibility and therefore the expression of particular genes. We present two complementary approaches to address this limitation: super-resolution imaging of directly labeled DNA, and singlemolecule high density tracking of proteins participating in DNA packaging. For STORM imaging of DNA, we stained cells with the DNA-specific dye Picogreen, and obtained a ~5-fold improvement in resolution, resolving the sub-diffraction organization of chromatin structures in living cells. For single molecule tracking (sptPALM), we used small chemical tags to target synthetic dyes to specific protein targets, and visualized their dynamics3. The combination of DNA and protein superresolution imaging and single particle tracking will allow us to study chromatin organization in living cells, and rearrangements in response to exogenous signals.

I will describe two simple models that incorporate only hard-sphere and geometrical constraints, yet provide quantitatively accurate predictions for the structural and mechanical properties of frictional packings of granular media and proteins. We first model static friction between grains by considering nominally spherical particles with periodically spaced asperities on the surface of the grains. This model captures the dependence of the average packing fraction and number of interparticle contacts on the static friction coefficient obtained from experiments, and has significant advantages over other models. Second, in the spirit of the Ramachandran map for the backbone dihedral angles of proteins, we develop a model for nonpolar amino acids that allows us to predict the allowed conformations of sidechain dihedral angles. Our predictions are quantitatively similar to the sidechain dihedral angle distributions obtained from known crystal structures. These two examples emphasize the power of simple physical models, which are able to predict important properties of soft and biological materials.

A certain 2D lattice model with nearest and next-nearest neighbor interactions is known to have a nonperiodic ground state. We show that during a slow quench from the high temperature, disordered phase, the ground state emerges through an infinite sequence of phase transitions. We define appropriate order parameters and show that the transitions are related by renormalizations of the temperature scale. As the temperature is decreased, sublattices with increasingly large lattice constants become ordered. A rapid quench results in glass-like state due to kinetic barriers created by simultaneous freezing on sublattices with different lattice constants.

The ability to effectively control a fluid would enable many exciting technological advances, such as the design of quieter, more efficient aircraft. Model-based feedback control is a particularly attractive approach, but the equations governing the fluid, although known, are typically too complex to apply standard tools for dynamical systems analysis or control synthesis. This talk addresses model reduction techniques, which are used to simplify existing models, to obtain low-order models tractable enough to be used for analysis and control, while retaining the essential physics. In particular, we will discuss two techniques: balanced truncation and Koopman modes. Balanced truncation is a well-known technique for model reduction of linear systems, with provable error bounds, but it is not computationally tractable for very large systems. We present an approximate version, called Balanced POD, that is computationally tractable, and produces much better models than traditional Proper Orthogonal Decomposition (POD), at least for the examples studied. Koopman modes are based on spectral analysis of the Koopman operator, an infinite-dimensional linear operator that describes the full nonlinear dynamics of a nonlinear system, and we show how the associated modes can elucidate coherent structures in examples including a jet in crossflow and the wake of a flat plate.

Surface energy can be harnessed to introduce new features essential to a variety of engineering systems, such as large-area scalability for phase-change thermal diodes and non-clogging apertures for resistive Coulter counting. In the first case, surface energy drives dropwise condensate to spontaneously jump on a superhydrophobic surface, and the self-propelled motion is exploited to create a planar and orientation-independent thermal diode. In the second case, surface tension is manipulated electrohydrodynamically to produce a cone-jet liquid bridge, which serves as a tunable and deformable aperture for resistive pulse sensing. This presentation will cover both fundamental interfacial phenomena and practical engineering applications.

Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static replica theory, but disagree with the dynamic mode- coupling theory, indicating that key ingredients of high-dimensional physics are missing from the latter. We also obtain numerical estimates of the random close packing density, which provides new insights into the mathematical problem of packing spheres in large dimension.

As a voltage is applied on a layer of an electroactive polymer, the polymer can reduce in thickness and expand in area, giving an actuation strain over 100%. This talk will discuss the large deformation, instabilities, and energy conversion of electroactive polymers. We will particularly focus on new phenomena of electroactive polymers recently observed at Duke Soft Active Materials Laboratory. Interestingly, these phenomena are closely related to daily-life issues such as skin wrinkling and creasing, physical topics such as the Taylor-Cone instability, and engineering applications such as high-energy-density capacitors and anti-biofouling.

We will discuss the application of multi-scale graph theory based methods to the detection of general structures in networks, lattices, and amorphous physical systems. These methods enable the detection of the "natural" system structures on all scales. We specifically analyze lattices and spin systems with defects and various glass formers (including an analysis based on experimental data) to ascertain dominant structures at different temperatures. We will discuss general features of the phase diagram related to this analysis.

My group studies colloidal suspensions, which are solid micron-sized particles in a liquid. We use an optical confocal microscope to view the motion of these colloidal particles in three dimensions. In some experiments, these particles arrange into a crystalline lattice, and thus the sample is analogous to a traditional solid. We study the interface between colloidal crystals and colloidal liquids, and find that this interface is quite sharply defined. In other experiments, the sample is analogous to a glass, with particles randomly packed together. The particles correspond to individual molecules in a traditional glass, and the sample exhibits glassy behavior when the particle concentration is high. This allows us to directly study the microscopic behavior responsible for the macroscopic viscosity divergence of glasses.

Buoyancy-driven flows, which are fluid flows driven by spatial variations of fluid density, play many key roles in the environment. Examples include winds in valleys and over glaciers, mineral transport in rock fissures, and ocean boundary mixing. To date, however, all investigations of buoyancy-driven flow have considered flow induced by a fixed boundary that influences fluid density (e.g. by heating or cooling). We have discovered that buoyancy-driven flows provide a previously unrecognized means of propulsion for freely-floating objects, and we demonstrate this new concept to surprising effect in a series of laboratory experiments.

Motivated by the dewetting of viscous thin films on hydrophobic substrates, we study models for the coarsening dynamics of interacting localized structures in one dimension. For the thin films problem, lubrication theory yields a Cahn-Hilliard-type governing PDE which describes spinodal dewetting and the subsequent formation of arrays of metastable fluid droplets. The evolution for the masses and positions of the droplets can be reduced to a coarsening dynamical system (CDS) consisting of a set of coupled ODEs and deletion rules. Previous studies have established that the number of drops will follow a statistical scaling law, N(t)=O(t^{-2/5}). We derive a Lifshitz-Slyozov-Wagner-type (LSW) continuous model for the drop size distribution and compare it with discrete models derived from the CDS. Large deviations from self-similar LSW dynamics are examined on short- to moderate-times and are shown to conform to bounds given by Kohn and Otto. Insight can be applied to similar models in image processing and other problems in materials science. Joint work with M.B. Gratton (Northwestern Applied Math).

Fluidized granular systems with inelastic inter-particle collisions exhibit distinguishing behavior from it's elastic counterpart. Two species of particles in a binary granular system typically do not have the same mean kinetic energy, in contrast to the equipartition of energy required in equilibrium. It is found that not only the mechanical properties of these two types of particles, but also the heating mechanism plays an important role in affecting the extent of nonequipartition of kinetic energy, even in the bulk of the system. An experimental measurement of the velocity distribution of a 3D vibration fluidized granular medium by spatial resolved high speed video particle tracking is also reported. It is found that the distribution is wider than a Gaussian and broadens continuously with increasing volume fraction.

Friction plays a key role in controlling the rheology of dense granular flows. Ertas and Halsey, among others, have proposed that friction and inelasticity-enabled structures with a characteristic length scale in such flows can be directly linked to such rheologies, particularly that summarized in the “Pouliquen flow rule.” In dense flows, “gear” states in which all contacts roll without frictional sliding are naively possible below critical coordination numbers. We construct an explicit example of such a state in D=2; and show that organized shear can exist in this state only on scales l < d/I, where d is the grain size and I is the Inertial Number, characterizing the balance between inertial and pressure forces in the flow. Above this scale the packing is destabilized by centrifugal forces. Similar conclusions can be drawn in disordered packings of grains. We comment on the possible relationship between this length scale l and that which has been hypothesized to control the rheology.