## Ana Barros : Down the Predictability Hole - Searching for Metrics to Understand and Replace Physical Parameterizations of Nonlinear Processes in Atmospheric Models

- Nonlinear and Complex Systems ( 274 Views )Short-term forecast skill in weather forecasting over the last 15 years has
been achieved mostly through data assimilation. Predictive ability however
has hit barriers that have not been overcome by increasing computer power
and model resolution. Model tuning has come out from hiding, and it is
arguably ``trending'' in peer-review over the last 2-3 years. The open
question is what (and how) to do next. I will address this question relying
on two-decades of research on the representation of moist processes in the
atmosphere, specifically targeting the following issues:

1) Evaluating Models to Elucidate the Physics that Matter

2) Detecting and Isolating Sources, Sinks and Barriers of Predictability

3) Meeting the Utility Challenge - Projections vs Predictability

## Beatriz Seoane : The Gardner threshold: a border between two glasses

- Nonlinear and Complex Systems ( 211 Views )Glasses (aka amorphous solids) exhibit various anomalies when compared with crystals (aka ordered solids), for instance, they display enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye's theory (the so-called Boson Peak) or respond drastically to very small mechanical deformations. In this work, we identify the common, universal origin to these anomalies in a realistic, three-dimensional model of glasses. We show that in highly packed hard spheres, vibrations become highly correlated in space and time at a sharply defined threshold, which we call the "Gardner threshold". This work is deeply related with the last developments in the analytical theory of glasses, where the glass problem has been finally solved exactly in the artificial limit of infinite spatial dimensions. The analytical solution predicts the existence of a genuine phase transition (a Gardner phase transition) within the glass, separating the glass and the jamming transitions. In this work we, not only establish the relevance of the (remanent of the) Gardner transition for real glasses, but also characterize it using well-defined observables, including time-dependent quantities and spatial correlations, that should be experimentally measurable. See arxiv.org/abs/1511.04201

## Peter Morse : Generic failure in granular packings: finding the relationship between shear and random forces

- Nonlinear and Complex Systems ( 208 Views )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.

## Lenka Zdeborova : Network Dismantling

- Nonlinear and Complex Systems ( 200 Views )Many systems of interest can be represented by a network of nodes connected by edges. In many circumstances the existence of a giant component is necessary for the network to fulfill its function. Motivated by the need to understand optimal attack strategies, optimal spread of information or immunization policies, we study the network dismantling problem, i.e. the search of a minimal set of nodes whose removal leaves the network broken into components of sub-extensive size. Building on the statistical mechanics perspective we compute the size of the optimal dismantling set for random networks, propose an efficient dismantling algorithm for general networks that outperforms by a large margin existing strategies, and we provide various insights about the problem.

## Brenton D. Hoffman : Assessing the Effects of Protein Load on Protein Function in Living Cells

- Nonlinear and Complex Systems ( 194 Views )Cells exist in a complex mechanical environment that is both a source of applied forces and a means of mechanical support. An incomplete understanding of the mechanisms cells use to detect mechanical stimuli, a process termed mechanotransduction, is currently preventing advances in tissue engineering and hindering the understanding of several mechanosensitive disease states. Mechanical stimuli are sensed at focal adhesions (FAs), complex dynamic structures comprised of several hundred types of proteins that mediate physical connections between the extracellular matrix and the cytoskeleton. Detection of mechanical cues is thought to be mediated by mechanically-induced changes in protein structure, which, in elegant in vitro single molecule experiments, have been shown to induce new biochemical functions, such as changes in binding affinity as well as the formation of distinct protein-protein interactions. However, the existence and role of these mechanically-induced changes in protein function in living cells are not well understood. To enable the visualization of protein loading, we create Forster Resonance Energy Transfer (FRET)-based tension sensors that emit different colors of light in response to applied forces. The next step in the development of this technology is the use of these sensors to study the effects of mechanical loading on protein functions in living cells. To begin this process, we have refined two commonly used and powerful approaches, Fluorescence Recovery After Photobleaching (FRAP) and fluorescence co-localization to be compatible with FRET-based tension sensors. Initial efforts have focused on the mechanical linker protein vinculin due to its established role in regulating the response of FAs to mechanical loading. These novel techniques reveal that force affects both vinculin turnover as well as its ability to form distinct protein-protein interactions. Further use of these techniques should enable a wide variety of studies in mechanobiology involving different load-bearing proteins, subcellular structures, extracellular contexts, and cellular functions.

## Stephen Teitel : Shear Banding, Discontinuous Shear Thickening, and Rheological Transitions in Athermally Sheared Frictionless Disks

- Nonlinear and Complex Systems ( 190 Views )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.

## Changhui Tan : Self-organized dynamics: aggregation and flocking

- Nonlinear and Complex Systems ( 181 Views )Self-organized behaviors are commonly observed in nature and human societies, such as bird flocks, fish swarms and human crowds. In this talk, I will present some celebrated mathematical models, with simple small-scale interactions which lead to the emergence of global behaviors: aggregation and flocking. I will discuss the models in different scales: from microscopic agent-based dynamics, through kinetic mean-field descriptions, to macroscopic fluid systems. In particular, the macroscopic models can be viewed as compressible Euler equations with nonlocal interactions. I will show some recent results on the global wellposedness theory of the systems, large time behaviors, and interesting connections to some classical equations in fluid mechanics.

## Xuanhe Zhao : Engineering and Physics of Electroactive Polymers: From Micropatterning to Taylor Cone

- Nonlinear and Complex Systems ( 175 Views )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.

## Philippe H. Trinh : The role of exponentially small effects in the physical sciences

- Nonlinear and Complex Systems ( 173 Views )Recently, the development of specialized techniques in mathematics known as
exponential asymptotics has led to the successful resolution of
long-standing problems in topics as varied as crystal growth, dislocations,
pattern formation, turbulence, thin film flow, and hydrodynamics. These
developments have emerged from the realization that in many such problems,
exponentially small effects can significantly change the solutions of the
underlying mathematical models.

In this talk, we will introduce the audience to the history, ideas, and
basic techniques of exponential asymptotics, with particular emphasis on
how to recognize when such approaches are necessary. We will discuss the
19th century struggles of the great Cambridge physicist G.G. Stokes to
better understand what is now known as the Stokes Phenomenon. We will then
show how this understanding would provide the key insight into resolving
two famous problems: the problem of modelling dendritic crystal growth, and
the Saffman-Taylor viscous fingering problem.

Our discussion will conclude with a glimpse of the present and future
applications of exponential asymptotics, notably within the context of
hydrodynamics and ship waves, and for the mathematical modelling of rupture
and singularity formation in fluid flows.

## Zohar Nussinov : The detection of hidden structures in glasses and complex systems by multi-scale clustering

- Nonlinear and Complex Systems ( 170 Views )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.

## Peter J. Mucha : Stochastic Dynamics in Near-Wall Velocimetry

- Nonlinear and Complex Systems ( 162 Views )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.

## Hugo L. D. de S. Cavalcante : Digital Chaotic Circuits: part II - Characterization and Application

- Nonlinear and Complex Systems ( 162 Views )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.

## Cecilia Clementi : Multi-resolution protein modeling by combining theory and experiment

- Nonlinear and Complex Systems ( 161 Views )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.

## Michael W. Deem : Antigenic Distance, Glassy Dynamics, and Localization in the Immune System

- Nonlinear and Complex Systems ( 161 Views )The immune system normally protects the human host against death by infection. I will introduce a hierarchical spin glass model of the evolutionary dynamics that occurs in the antibody-mediated and T cell-mediated immune responses. The theory will be used to provide a mechanism for original antigenic sin, wherein an initial exposure to antigen degrades the response of the immune system upon subsequent exposure to related, but different, antigens. A new order parameter to characterize antigenic distance will be introduced from the theory. This order parameter predicts effectiveness of the influenza vaccine more reliably than do results from animal model studies currently used by world health authorities. This order parameter would seem to be a valuable new tool for making vaccine-related public health policy decisions. Next, I will note that while the immune system normally protects the human host against death by infection, the method used by the immune system to search sequence space is rather slow --- interestingly there exist biological mechanisms that can find antibodies with higher affinity and also find them more quickly. Thus, one would think that these more powerful evolutionary mechanisms would give an immune system that responds faster and more effectively against disease. So, why didn't we evolve that kind of adaptive response? I will show that the slow glassy dynamics of the immune system serves a functional role of inhibiting the autoimmune diseases that these more powerful searching mechanisms would induce. I will suggest that the controversy related to the correlation between chronic infection and autoimmune disease might be addressed by searching for the broad distribution of onset times for autoimmune disease predicted from the theory.

## Katia Koelle : Exploration, innovation, and selective sweeps in the ecology

- Nonlinear and Complex Systems ( 153 Views )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).

## Dezhe Z. Jin : Associative chain as the foundation for action sequence and timing: a case study with birdsong

- Nonlinear and Complex Systems ( 152 Views )Sequence and timing are two fundamental aspects of many critical motor actions that humans and animals must learn and perform. Human speech is a familiar example. How precisely timed action sequences are controlled by networks of neurons, and how such neural networks form through experience, are poorly understood.

Songbirds are excellent animal models for investigating these problems. Male songbirds learn to sing songs with exquisite temporal complexity and precision, similar to human speech. Unlike human brains, songbird brains are experimentally accessible. Indeed, the wealth of experimental data on songbirds makes them ideal systems for computational modeling.

In this talk, I will present a computational study of production and learning of timed action sequence, using birdsong as a concrete example. First, I will advance the idea that associative chains of neurons, also called "synfire chains" in some context, are fundamental building blocks of sequence generating networks. I will show experimental evidence of their existence in the songbird brain, including the recent discovery of a critical property of song controlling neurons, which was predicted by a computational analysis of the robustness of the associative chain dynamics against imperfects in the connectivity and other sources of noise. Second, I will demonstrate computationally that associative chains can form simply through a self-organized process, which depends on ubiquitously observed properties of neurons, including spike-time dependent plasticity of synapses, axonal remodeling, and spontaneous activity. This result suggests that associative chains are stable "attractors" of neural connectivity. The process is robust against death and renewal of neurons, which naturally occur in songbird brain. Finally, I will illustrate that associative chains are also useful for sequence recognition tasks, such as song recognition in songbirds, thus can serve as the neural substrate of sensory-motor integration.

Henry Greenside (hsg@phy.duke.edu) will be the host for his visit.

## Daniella E. Raveh : Nonlinear Dynamics of Aeroelastic Airfoil Systems in Buffeting Flows

- Nonlinear and Complex Systems ( 151 Views )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.

## Eric Weeks : Colloidal liquids, crystals, and glasses

- Nonlinear and Complex Systems ( 149 Views )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.

## Nicholas Ouellette : Multiscale Dynamics and Coherent Structures in Turbulent Flow

- Nonlinear and Complex Systems ( 130 Views )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.

## Thomas Witelski : Mean field models and transient effects for coarsening dynamics in fluid films

- Nonlinear and Complex Systems ( 117 Views )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).

## Yair Mau : Reversing desertification: a pattern formation approach

- Nonlinear and Complex Systems ( 117 Views )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.

## David M. Walker : Contact Network Analysis of Granular Media

- Nonlinear and Complex Systems ( 112 Views )The particles in a deforming assembly of a granular material continually rearrange themselves when subject to loading. This rearrangement can be usefully represented by an evolving (complex) contact network reflecting the changing connectivity. The tools of complex networks summarize the properties of these contact networks and changes in the physical material manifest in changes to these properties. We consider two different DEM systems, a biaxial compression test and a second system which allows for particle breakage, and discuss how different properties of the contact networks help to reveal different aspects of the materials'response to loading. (Joint work with Antoinette Tordesillas)

## Thomas Ward : Electrohydrodynamically driven chaotic advection in a translating drop

- Nonlinear and Complex Systems ( 106 Views )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.

## David Barton : Numerical continuation for investigating nonlinear systems: from model to experiment

- Nonlinear and Complex Systems ( 106 Views )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.