The idea that glasses can become marginally stable at a Gardner transition has attracted significant interest among the glass community. Yet, the situation is confusing: even at the theoretical level, renormalization group approaches provide contradictory results on whether the transition can exist in three dimensions. The Gardner transition was searched in only two experimental studies and few specific numerical models. These works lead to different conclusions for the existence of the transition, resulting in a poor understanding of the conditions under which a marginally stable phase can be observed. The very relevance of the Gardner transition for experimental glasses is at stake.

We study analytically and numerically the Weeks-Chandler-Andersen model. By changing external parameters, we continuously explore the phase diagram and regimes relevant to granular, colloidal, and molecular glasses. We revisit previous numerical studies and confirm their conclusions. We reconcile previous results and rationalise under which conditions a Gardner phase can be observed. We find that systems in the vicinity of a jamming transition possess a Gardner phase. Our findings confirm the relevance of a Gardner transition for colloidal and granular glasses, and encourage future experimental work in this direction. For molecular glasses, we find that no Gardner phase is present, but our studies reveal instead the presence of localised excitations presumably relevant for mechanical and vibrational properties of glasses.

Under shear, a jammed packing of particles will break in characteristic ways and transition between mechanically stable states. One can then ask whether the signatures of failure are specific to shear, or whether they are the same in more generic perturbations. Interestingly, recent mean-field calculations suggest that in infinite dimensions, the response of a system to global shear and random forces may be equivalent. Whether or not this is true in 2D or 3D systems remains an open question. Therefore, I've developed a method for driving 2D jammed packings of disks by quasti-static persistent random forces to demonstrate that the response is similar to what is observed in athermal quasi-static shear simulations. I will also comment on how we expect the similarities to break in finite dimensions and what these results might imply for active matter systems.

We review recent developments in the control of deterministic and stochastic nonlinear dynamics by time-delayed feedback methods [1]. We point out how to overcome the alleged odd number limitation for unstable periodic orbits, and discuss the control of complex chaotic or noise-induced space-time patterns. Our findings are applied to a selection of models ranging from semiconductor nanostructures, like resonant-tunneling diodes [2], to neural systems. [1] E. Sch{\"o}ll and H.G. Schuster (Eds.): Handbook of Chaos Control (Wiley-VCH, Weinheim, 2008), second completely revised and enlarged edition. [2] E. Sch{\"o}ll, Nonlinear spatio-temporal dynamics and chaos in semiconductors (Cambridge University Press, Cambridge, 2001).

Developing descriptive and predictive models of human behavior and decision making in complex sociotechnical systems is critical for system design and evaluation. However, developing such models is difficult due to individual variability, brittle assumptions, and the need to often integrate qualitative and quantitative data. This talk will discuss various human-systems modeling techniques developed in the Humans and Autonomy Laboratory.

Simple models of classical particles, interacting via soft- or hard-core repulsive contact interactions, have been used to model a wide variety of granular and soft-matter materials, such as dry granular particles, foams, emulsions, non-Brownian suspensions, and colloids. Such materials display a variety of complex behaviors when in a state of steady shear driven flow. These include (i) Jamming: where the system transitions from a flowing liquid to a rigid but disordered solid as the particle packing increases; (ii) Shear Banding: where the system becomes spatially inhomogeneous, separating into distinct bands flowing at different sh ear strain rates; (iii) Discontinuous Shear Thickening: where the shear stress jumps discontinuously as the shear strain rate is increased. In this talk we will consider a simple numerical model of athermal soft-core interacting frictionless disks in steady state shear flow. We will show that the mechanism by which energy is dissipated plays a key role in determining the rheology of the system. For a model with a tangential viscous collisional dissipation, but no elastic friction, we will show that as the particle packing increases there is a sharp first order phase transition from a region of Bagnoldian rheology (stress ~ strain-rate^2) to a region of Newtonian rheology (stress ~ strain-rate), that takes place below the jamming transition. In a phase diagram of varying strain-rate and packing fraction (or strain-rate and pressure) this first order rheological phase transition manifests itself as a coexistence region, consisting of coexisting bands of Bagnoldian and Newtonian rheology in mechanical equilibrium with each other. Crossing this coexistence region by increasing the strain-rate at fixed packing, we find that discontinuous shear thickening can result if the strain-rate is varied too rapidly for the system to relax to the true shear-banded steady state. We thus demonstrate that the rheology of simply interacting sheared disks can be considerably more complex than previously realized, and our model suggests a simple mechanism for both the phenomena of shear banding and discontinuous shear thickening in spatially homogeneous systems, without the need to introduce elastic friction.

Upon approaching the glass transition a liquid gets extremely sluggish without obvious structural changes. Despite decades of work, the physical origin of this glassy slowdown remains controversial. A common explanation relies on the increasing roughness of the underlying free-energy landscape, but the theoretical and experimental underpinnings of this scenario are still lacking. In this talk, I will survey recent advances that let us unambiguously identify and track the growing amorphous order, a manifestation of the rarefaction of metastable states in the rugged landscape. I will further explore the crucial role this order plays in driving the glassy slowdown.

Diffusion over a network depends crucially on the pattern and timing of relations. This is particularly important for diseases carried over networks with relatively low volume and turnover. Here we explore both aspects using simulation tools. First, we ask how the shape of the distribution of number of partners affects multiple connectivity, and second we measure the exposure potential in dynamic networks across a wide array of structural patterns to identify the influence of "concurrency," the overlap in time of interactions among network nodes. We find that concurrency in low-volume settings has the same effect on epidemic spreading as a structural increase in the average degree. 

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.

The tracking of small, colloidal particles is a common technique for measuring fluid velocities, highly successful at the micro-scale and recently extended to measurements at nano-scales. The Brownian fluctuations of the colloidal tracers are typically isotropic in the bulk; but in the near-wall region, these fluctuations are strongly affected by the hydrodynamic interaction with the wall and by the no-flux condition imposed there. Such wall effects can, under appropriate conditions, bias particle image velocimetry (PIV) measurements based on colloidal tracers, potentially leading to significant overestimation of near-wall velocities. The quantification of the resulting bias is presented in terms of the size of the imaged region and the measurement interval between PIV images. The effect of the steady state particle distribution is additionally explored, and implications for near-wall velocimetry measurements are briefly discussed.

This talk represents collaborative work with Christel Hohenegger, Minami Yoda, Reza Sadr, and Haifeng Li.

We discuss the characterization of chaos displayed by continuous time digital circuits, both numerically and experimentally. Continuous models for physical systems with switch-like behavior are used to simulate those circuits and their coupling. The effect of perturbations in the coupling and synchronization is also studied experimentally and numerically.

For many biological systems, the timescale at which ecological interactions occur is much shorter than the timescale at which evolutionary changes occur. For rapidly evolving pathogens such as influenza, however, this is not the case; influenza researchers therefore need to understand both the ecological interactions between the host and the pathogen and the virus?s evolutionary changes in order to ultimately control the disease in humans. Recently, a study looking at the evolutionary patterns of influenza showed that, while the virus?s genetic evolution occurred gradually, its antigenic evolution occurred in a punctuated manner. (Genetic evolution refers to how the virus?s nucleotides change over time; antigenic evolution refers to how the virus changes over time with respect to how our immune system recognizes it.) Previous research from our group hypothesized that these differences in evolutionary patterns could be explained by the presence of /neutral networks/ in the virus?s genotype space: networks of sequences that differ genetically from one another but fold into the same protein conformation and thereby share antigenic properties. Here, I will present a simple epidemiological model that implicitly incorporates these neutral networks. I show that this model can reproduce (1) the seasonal and interannual outbreak patterns of influenza, (2) the quantitative patterns of influenza?s antigenic evolution, and (3) the patterns of the virus?s genetic evolution, including its characteristic phylogenetic tree. I end with how this model may be useful in understanding patterns of viral diversity in other host species (e.g., avian and equine hosts).

Transonic flows over airfoils at certain combinations of Mach numbers and steady mean angle of attack exhibit buffet; a phenomenon of large shock-wave oscillations due to flow separation and vortex shedding at a characteristic flow frequency. Buffet may occur even when the airfoil does not move. The seminar will present two recent studies of numerical simulations of an airfoil that a) undergoes prescribed harmonic oscillations, and b) is suspended by a spring in transonic buffeting flows. Both studies focus on the nonlinear interaction between the two oscillatory systems, namely the buffeting flow and the oscillating airfoil. Flow simulations of prescribed airfoil motions (using a Navier-Stokes turbulent flow solver) reveal a lock-in phenomenon. Certain combinations of amplitude and frequency of a prescribed airfoil oscillatory motion caused the buffet flow oscillations to lock into the prescribed frequency. The combinations of prescribed frequencies and amplitudes that cause lock-in present an .Arnold tongue. structure. There is a broad analogy between this flow phenomenon and the flow field of the Von Karman vortex street found behind a cylinder with the cylinder undergoing a prescribed oscillation. Flow simulations of an airfoil that is suspended on a spring reveal three distinct response characteristics, depending on the relationship of the elastic system.s natural frequency to the buffet frequency, and on the system.s mass ratio (the structural to fluid mass ratio). Elastic systems with natural frequencies that are lower than the buffet frequency exhibit a single-frequency response, with a frequency that is shifted form the buffet frequency towards the elastic natural frequency as the mass ratio is decreased (and the magnitude of the elastic response increases). On the other hand, an elastic system with a natural frequency that is the same as the buffet frequency exhibits resonance. Finally, elastic systems with natural frequencies that are higher than the buffet frequency exhibit a response with two distinct frequencies, that of the buffet and that of the elastic natural frequency. As long as the pitch amplitudes are small, the response is mostly at the buffet frequency. As the pitch amplitudes increase there is more power in the elastic natural frequency, and less in the buffet frequency. As the pitch amplitudes further grow, the response is in the elastic natural frequency solely, and the buffet frequency vanishes. To the best of the authors. knowledge the nonlinear dynamics of elastic systems in buffeting flows has not been reported previously. The authors are interested to learn whether similar phenomena are known in other research communities.

Qualitatively new behavior often emerges when large numbers of similar entities are interacting at high densities, no matter how simple the individual components. One prototypical example is granular matter such as fine dry sand, where individual grains are solids. In this talk I will discuss several striking phenomena, including the formation of jets and their break-up into droplets, where large ensembles of grains behave very much like a liquid, except that they do so without apparent surface tension.

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.

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 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.

A drop translating in the presence of an electric field is studied using a combination of experiments and numerical analysis to determine the underly- ing mechanism that leads to chaotic advection. The flow is a combination of a Hadamard-Rybczynski, and a Taylor circulation due to the translation and electric field, respectively. Two cases for generating chaotic advection by, (i) tilting the electric field relative to the drops translation motion and (ii) time-dependent modulation of the electric field, will be considered. The numerical analysis includes qualitative analysis of the degree of mixing by Poincare mapping and quantitative estimates of the largest percentage of drop volume mixed by a single streamline as well as the rate of mixing by calculating the largest Lyapunov exponent. Experiments are performed using a castor oil/silicone oil system for the continuous and dispersed phases respectively.

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.