Hugo L. D. de S. Cavalcante : Digital Chaotic Circuits: part II - Characterization and Application
- Nonlinear and Complex Systems ( 153 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.
Daniella E. Raveh : Nonlinear Dynamics of Aeroelastic Airfoil Systems in Buffeting Flows
- Nonlinear and Complex Systems ( 142 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.
Frederic Lechenault : Experimental investigation of equilibration properties in model granular subsystems
- Nonlinear and Complex Systems ( 166 Views )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.
Dezhe Z. Jin : Associative chain as the foundation for action sequence and timing: a case study with birdsong
- Nonlinear and Complex Systems ( 135 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.
Karin Dahmen : Unifying theory for tuned-critical quake statistics: from compressed nanopillars to earthquakes
- Nonlinear and Complex Systems ( 97 Views )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.
Emanuela Del Gado : Gelation and densification of cement hydrates: a soft matter in construction
- Nonlinear and Complex Systems ( 171 Views )5-8 % of the global human CO2 production comes from the production of
cement, concrete main binder. The material strength emerges through the
development, once in contact with water, of calcium-silicate-hydrate (C-S-H)
gels that literally glue together the final compound. Current industrial
research aims at exploring alternative and more environmentally friendly
chemical compositions while enhancing rheology and mechanics, to overcome
the many technological challenges and guarantee concrete standards.
Identifying the fundamental mechanisms that control the gel properties at
the early stages of hydration and setting is crucial, although challenging,
because of far-from-equilibrium conditions, closely intertwined to the
evolution of the chemical environment, that are a hallmark of cement
hydration.
I will discuss a recently developed statistical physics approach, which
allows us to investigate the gel formation under the out-of-equilibrium
conditions typical of cement hydration and the role of the nano-scale
structure in C-S-H mechanics upon hardening. Our approach, combining Monte
Carlo and Molecular Dynamics simulations, unveils for the first time how
some distinctive features of the kinetics of cement hydration can be related
to the nano-scale effective interactions and to the changes in the
morphology of the gels. The novel emerging picture is that the changes of
the physico-chemical environment, which dictate the evolution of the
effective interactions, specifically favor the gel formation and its
continuous densification. Our findings provide new handles to design
properties of this complex material and an extensive comparison of numerical
findings for the hardened paste with experiments ranging from SANS, SEM,
adsorption/desorption of N2 and water to nano-indentation provide new,
fundamental insights into the microscopic origin of the properties measured.
K. Ioannidou, R.J.-M. Pellenq and E. Del Gado Controlling local packing and
growth in calcium-silicate-hydrate gels
E. Del Gado, K. Ioannidou, E. Masoero, A. Baronnet, R. J.-M. Pellenq, F. J.
Ulm and S. Yip, A soft matter in construction - Statistical physics approachfor formation and mechanics of C--S--H gels in cement,
K. Ioannidou, K.J. Krakowiak, M. Bauchy, C.G. Hoover, E. Masoero, S. Yip,
F.-J. Ulm, P. Levitz, R.J.-M. Pellenq and E. Del Gado, The mesoscale textureof cement hydrates
K. Ioannidou, M. Kanduc, L. Li, D. Frenkel, J. Dobnikar and E. Del Gado,
The crucial effect of early-stage gelation on the mechanical properties of
cement hydrates , under review
Eric DeGiuli : Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions
- Nonlinear and Complex Systems ( 155 Views )The rheology of dense flows of hard particles is singular near the jamming threshold where flow ceases, both for aerial granular flows dominated by inertia, and for over-damped suspensions. At the same time, the length scale characterizing velocity correlations appears to diverge at jamming. We introduce a theoretical framework that proposes a potentially complete scaling description of stationary flows of frictionless particles. We compare our predictions with the empirical literature, as well as with new numerical data. Overall we find a very good agreement between theory and observations. Finally, we use simulations of frictional inertial flow to outline the regime of the phase diagram where the theory holds, and show where friction adds new physics.
Volkan Sevim : Modeling Gene Regulatory Networks and Evolution of Genetic Robustness
- Nonlinear and Complex Systems ( 139 Views )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.
Andrew D Bragg : Lagrangian irreversibility and inversions in 3 and 2 dimensional turbulence
- Nonlinear and Complex Systems ( 167 Views )Studying how small inertial particles suspended in turbulent flows
move relative to each other provides fundamental insights into their
transport, mixing and collisions. These insights are crucial for
tackling diverse problems ranging from droplet growth in warm clouds,
to planetesimal formation through collisional aggregation in turbulent
protoplanetary nebula. A deeper understanding of the relative motion
of the particles can be obtained by investigating both their
forward-in-time (FIT) and backward-in-time (BIT) dispersion. When FIT
and BIT dispersion are different it signifies irreversibility, and
since FIT and BIT dispersion are related to different problems,
understanding the irreversibility is of fundamental and practical
importance.
I will present new theoretical arguments and asymptotic predictions,
along with results from Direct Numerical Simulations (DNS) of the
governing equations, to show that inertial particle dispersion can be
very strongly irreversible in turbulence, with BIT being much faster
than FIT dispersion in 3-dimensional turbulence. The results also show
that inertial particles can disperse much faster than fluid
(interialess) particles. I will also present arguments, confirmed by
DNS results, that in 2-dimensional turbulence the nature of the
irreversibility and the direction of the particle energy fluxes can
invert when the particle inertia exceeds a certain threshold. These
results significantly advance our understanding of dispersion
problems, and lead to new capabilities for predicting the effect of
inertia on the rate at which particles spread out and mix together in
turbulence, and the rate at which they collide.
Peter Morse : Generic failure in granular packings: finding the relationship between shear and random forces
- Nonlinear and Complex Systems ( 196 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.
Michael W. Deem : Antigenic Distance, Glassy Dynamics, and Localization in the Immune System
- Nonlinear and Complex Systems ( 145 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.
Thomas Ward : Electrohydrodynamically driven chaotic advection in a translating drop
- Nonlinear and Complex Systems ( 99 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.
Peter J. Mucha : Stochastic Dynamics in Near-Wall Velocimetry
- Nonlinear and Complex Systems ( 145 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.
Joshua Socolar : Hierarchical freezing in a lattice model
- Nonlinear and Complex Systems ( 94 Views )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.
Beatte Schmittmann : From asymmetric exclusion processes to protein synthesis
- Nonlinear and Complex Systems ( 159 Views )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).
Sidney Nagel : Exploiting disorder for global response: independence of bond-level contributions
- Nonlinear and Complex Systems ( 197 Views )We are customarily taught to understand ordinary solids by considering perturbations about a perfect crystal. This approach becomes increasingly untenable as the amount of disorder in the solid increases; for a glass with no well-defined long-range order, a crystal is a terrible starting point for understanding the glasss rigidity or its excitations. Is there an alternative the opposite of a crystal where order, rather than disorder is the perturbation? Jamming is an alternate way of creating rigid solids that are qualitatively different from crystals. In a crystal with only one atom per unit cell, all atoms play the same role in producing the solid's global response to external perturbations. Jammed disordered materials are not similarly constrained and a new principle emerges: independence of bond-level response. Using networks where individual bonds can be successively removed, one can drive the overall system to different regimes of behavior. Consequently one can exploit disorder to achieve unique, varied, textured and tunable global response.
Thomas Halsey : Dense granular flow
- Nonlinear and Complex Systems ( 136 Views )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.
Daniel Gauthier : Nonlinear stability analysis of a time-delay opto-electronic oscillator
- Nonlinear and Complex Systems ( 157 Views )I will describe some recent work on the dynamics of an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. A nonlinear stability analysis is required to understand the device dynamics. Through such an analysis, an approximate mapping is derived that does an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks. The results of this study recently appeared in print and can be found here: PRL The work is the part of Kristine Callan's PhD dissertation research and was in collaboration with Zheng Gao, Lucas Illing, and Eckehard Schoell.
Beatriz Seoane : The Gardner threshold: a border between two glasses
- Nonlinear and Complex Systems ( 195 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
Marija Vucelja : A glass transition in population genetics: Emergence of clones in populations
- Nonlinear and Complex Systems ( 205 Views )The fields of evolution and population genetics are undergoing a renaissance, due to the abundance of sequencing data. On the other hand, the existing theories are often unable to explain the experimental findings. It is not clear what sets the time scales of evolution, whether for antibiotic resistance, an emergence of new animal species, or the diversification of life. The emerging picture of genetic evolution is that of a strongly interacting stochastic system with large numbers of components far from equilibrium. In this talk, I plan to focus on the clone competition and discuss the diversity of a random population that undergoes selection and recombination (sexual reproduction). Recombination reshuffles genetic material while selection amplifies the fittest genotypes. If recombination is more rapid than selection, a population consists of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime, selection can amplify individual genotypes into large clones, and the population reaches the so-called "clonal condensation". I hope to convince you that our work provides a qualitative explanation of clonal condensation. I will point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. I will conclude with a summary of our present understanding of the clonal condensation phenomena and describe future directions and connections to statistical physics.
Holger Stark : Active motion: Understanding the nonequilibrium
- Nonlinear and Complex Systems ( 160 Views )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.
[1] A. Zoettl and H. Stark, Phys. Rev. Lett. 108, 218104 (2012).