Granular materials exist all around us, from avalanches in nature to the mixing of pharmaceuticals, yet the behavior of these ``fluids'' is poorly understood. Their flow can be characterized by the continuous forming and breaking of a strong force network resisting flow. This jamming/unjamming behavior is typical of a variety of systems, including granular flows, and is influenced by factors such as grain packing fraction, applied shear stress, and the random kinetic energy of the particles. I'll present experiments on quasi-static shear and free-surface granular flows under the influence of external vibrations. By using photoelastic grains, we are able to measure both particle trajectories and the local force network in these 2D flows. We find through particle tracking that dense granular flow is composed of comparable contributions from the mean flow, affine, and non-affine deformations. During shear, sufficient external vibration weakens the strong force network and reduces the amount of flow driven by sidewalls. In a rotating drum geometry, large vibrations induce failure as might be expected, while small vibration leads to strengthening of the pile. The avalanching behavior is also strongly history dependent, as evident when the rotating drum is driven in an oscillatory motion, and we find that sufficient vibration erases the memory of the pile. These results point to the central role of the mobilization of friction in quasi-static granular flow.

Numerical continuation is a tool for investigating the bifurcation structure of a nonlinear dynamical system with respect to the system parameters. It is most often used to "carve up" parameter space into regions of qualitatively different behaviour by finding and tracking bifurcations (e.g., Hopf bifurcations) as the system parameters change. This talk will give an introduction to the theory behind numerical continuation and go on to discuss recent developments in the field.

Particular attention will be paid to numerical continuation of systems with non-smoothness, motivated by the example of intermittent contacts in a model of orthogonal cutting (turning). Rich dynamical behaviour is present in this model due to the presence of a grazing bifurcation which denotes the transition point from constant contact of the cutting tool with the workpiece to intermittent contact. Using numerical continuation it is possible to elucidate the full bifurcation structure of the system, something that would be extremely difficult with other methods.

Finally, numerical continuation will be demonstrated as applied to a physical experiment (so-called control-based continuation): a nonlinear energy harvesting device. Numerical continuation in this context allows the investigation of a physical device without prior knowledge of a model. Both stable and unstable motions can be investigated and bifurcations found directly. As such these investigations may aid in establishing what an appropriate mathematical model could be.

Gas-solids chemically reacting flows are omnipresent in many multiphase flow reactors in various industries like Chemical, Fossil and Nuclear. The challenging aspect of modeling these reacting flows are the wide range of both temporal and spatial scales encountered in these systems. The challenge is to accurately account and bridge (as seamlessly as possible) the length and time scales involved in the problem. First, the problem is introduced using biomass gasifier/pyrolyser and nuclear fuel coater with sample results as examples and provide an overview of the various models currently used at the different scales. In particular, the critical role of the granular dynamics in the overall performance of the reactors will be highlighted. The ongoing development of a multiphysics and multiscale mathematics framework for coupling various modeling methods over a range of scales will be presented. The development of a general wavelet-based multiscale methodology called compound wavelet matrix (CWM) for bridging spatial and temporal scales will be reported. Finally, the steps needed to generalize the current methodology for arbitrary heterogeneous chemically reacting flows or other applications involving multiscale/multiphysics coupling will be elucidated. The challenges and opportunities of employing these models for rapid deployment of clean energy solutions based on multiphase flow reactors to the market place will be discussed.

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.

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.

We experimentally investigate the statistical features of the stationary states reached by two idealized granular liquids able to exchange volume. The system consists in two binary mixtures of the same number of soft disks, hence covering the same area, but with different surface properties. The disks sit on a horizontal air table, which provides ultra low friction at the cell bottom, and are separated by a mobile wall. Energy is injected in the system by means of an array of randomly activated coil bumpers standing as the edges of the cell. Due to the energy injection, the system acts like a slow liquid and eventually jams at higher packing fraction. We characterize the macroscopic states by studying the motion of the piston. We find that its average position is different from one half, and a non monotonic function of the overall packing fraction, which reveals the crucial role played by the surface properties in the corresponding density of states. We then study the bulk statistics of the packing fraction and the dynamics in each subsystem. We find that the measured quantities do not equilibrate, and become dramatically different as the overall packing fraction is increased beyond the onset of supercooling. However, the local fluctuations of the packing fraction are uniquely determined by its average, and hence independent of the interaction between disks. We then focus on the mixing properties of such an assembly. We characterize mixing by computing the topological entropy of the braids formed by the stationary trajectories of the grains at each pressure. This quantity is shown to be well defined, very sensitive to onset of supercooling, reflecting the dynamical arrest of the assembly, and to equilibrate in the two subsystems. Joint work with Karen Daniels.

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.

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.

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).

Asymmetric exclusion processes, with periodic or open boundaries, have been studied extensively in the mathematics and statistical physics communities, as paradigmatic models for stochastic particle transport far from equilibrium. Though significant progress was made only recently, the original model was actually introduced decades ago to model protein synthesis1. In this talk, I will describe recent efforts to develop a comprehensive theory for protein synthesis, building on asymmetric exclusion processes with extended objects, modeling ribosomes covering multiple codons. We discuss the effects of local hopping rates and ribosome size on density profiles and particle currents. The latter translate directly into synthesis rates for the corresponding protein. Some intriguing results for real genes will be presented. 1C.T. MacDonald, J.H. Gibbs and A.C. Pipkin, Kinetics of biopolymerization on nucleic acid templates, Biopolymers,6 1 (1968); C.T. MacDonald and J.H. Gibbs, Concerning the kinetics of polypeptide synthesis on polyribosomes, Biopolymers, 7, 707, (1969).

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).

We present experiments on pattern formation and front propagation in the Belousov-Zhabotinsky (BZ) chemical reaction in flowing systems with chaotic advection. The flow is a chain of alternating vortices that oscillate and/or drift in the lateral direction. Mixing between the vortices is chaotic in this flow with either (enhanced) diffusive or superdiffusive transport. Experiments with the excitable BZ reaction are used to study the motion of reaction fronts in this system. If the vortices oscillates laterally, reaction fronts typically mode-lock to the external forcing. If the vortices drift with constant velocity, fronts typically pin to the leading vortex, remaining motionless in a reference frame that drifts with the vortices. Experiments with the oscillatory BZ reaction are used to study synchronization of a network of oscillators by chaotic mixing. We find that the system is globally-synchronized only if the long-range transport is superdiffusive, characterized by Levy flight trajectories. Time-permitting, we will also present results of experiments on chemical fronts and patterns in a two-dimensional array of vortices.

Both the 'reverse engineering' of biological networks (for example, by integrating sequence data and expression data) and the analysis of their underlying design (by revealing the evolutionary mechanisms responsible for the resulting topologies) can be re-cast as problems in machine learning: learning an accurate prediction function from high-dimensional data. In the case of inferring biological networks, predicting up- or down- regulation of genes allows us to learn ab intio the transcription factor binding sites (or `motifs') and to generate a predictive model of transcriptional regulation. In the case of inferring evolutionary designs, quantitative, unambiguous model validation can be performed, clarifying which of several possible theoretical models of how biological networks evolve might best (or worst) describe real-world networks. In either case, by taking a machine learning approach, we statistically validate the models both on held-out data and via randomizations of the original dataset to assess statistical significance. By allowing the data to reveal which features are the most important (based on predictive power rather than overabundance relative to an assumed null model) we learn models which are both statically validated and biologically interpretable.

Many processes in nature occur in the form of rare but important events. Well known examples of such events include conformation changes of biomolecules, chemical reactions, and nucleation events during phase transformation. Rare events do not happen very often on the internal clock of the system (which makes their simulation very challenging), but this clock can be very fast and this leaves plenty of room for the appearance of rare events in our daily life. I will review classical theories for the description of rare events, recent theoretical developments such as Transition Path Theory, concept such as reaction coordinate or free energy of a reaction and I will discuss how to compute the pathway and rate of rare events efficiently using the String Method. As illustrations, I will discuss the hydrophobic collapse of a polymeric chain, phase transitions in the Ising model, and a genetic toggle switch.

The detailed characterization of the overall free energy landscape associated with the folding process of a protein is the ultimate goal in protein folding studies. Modern experimental techniques provide accurate thermodynamic and kinetic measurements on restricted regions of a protein landscape. Although simplified protein models can access larger regions of the landscape, they are oftentimes built on assumptions and approximations that affect the accuracy of the results. We present new methodologies that allows to combine the complementary strengths of theory and experiment for a more complete characterization of a protein folding landscape at multiple resolutions. Recent results and possible applications will be discussed.

Robustness to mutations and noise has been shown to be evolvable through stabilizing selection for optimal phenotypes in model gene regulatory networks. The ability to evolve robust mutants is known to depend on the network architecture. How do the dynamical properties and state space structures of these networks with high and low robustness differ? Does selection operate on the global dynamical behavior of the networks? What kind of state space structures are favored by the selection? Using an extensive statistical analysis of state spaces of these model networks and damage-propagation analysis, I show that the change in their dynamical properties due to stabilizing selection for optimal phenotypes is minor. In agreement with recent studies, robustness to noise evolves along with robustness to mutations. Most notably, the networks that are most robust to both mutations and noise are highly chaotic. Certain properties of chaotic systems, such as being able to produce large attractor basins, seem to be useful to maintain a stable gene expression pattern.

The terrestrial water balance is forced by highly intermittent and unpredictable pulses of rainfall. This in turn impacts several related hydrological and ecological processes, such as plant photosynthesis, soil biogeochemistry and has feedbacks on the local climate. We treat the rainfall forcing at the daily time scale as a of marked (Poisson) point processes, which is then used the main driver of the stochastic soil water balance equation. We analyze the main nonlinearities in the soil water losses and discuss the probabilistic dynamics of soil water content as a function of soil-plant and vegetation characteristics. Crossing and mean-first-passage-time properties of the stochastic soil moisture process define the statistics of plant water stress, which in turn control plant dynamics, as shown in application to tree-grass coexistence in the Kalahari transect.
In the second part of this overview, we briefly illustrate: i) the propagation of soil moisture fluctuations through the nonlinear soil carbon and nitrogen cycles, ii) the possible emergence of persistence and preferential states in rainfall occurrence due to soil moisture feedback, and iii) the impact of inter-annual rainfall variability in connection to recent theory of ‘superstatistics’.

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Laio F., Porporato A., Ridolfi L., and Rodriguez-Iturbe I. (2001) Plants in water controlled ecosystems: Active role in hydrological processes and response to water stress. II. Probabilistic soil moisture dynamics. Advances in Water Research, 24, 707-723.
Porporato A., Laio F., Ridolfi L., and Rodriguez-Iturbe I. (2001) Plants in water controlled ecosystems: Active role in hydrological processes and response to water stress. III. Vegetation water stress. Advances in Water Research, 24, 725-744.
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D’Odorico P., Porporato A., Preferential states in soil moisture and climate dynamics, Proc. Nat. Acad. Sci. USA, 101(24), 8848-8851, 2004. Manzoni S., Porporato A., D’Odorico P. and I. Rodriguez-Iturbe. Soil nutrient cycles as a nonlinear dynamical system. Nonlin. Proc. in Geophys. 11, 589-598, 2004.
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