public 01:34:03

Amilcare Porporato : Random Jumps in Eco-Hydrology: Non-Gaussian Forcing in the Nonlinear Soil-Plant-Atmosphere System

  -   Nonlinear and Complex Systems ( 169 Views )

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’.

Rodriguez-Iturbe I. and A. Porporato, Ecohydrology of water controlled ecosystems: plants and soil moisture dynamics. Cambridge University Press, Cambridge, UK. 2004.
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.
Porporato A., D’Odorico P., Phase transitions driven by state-dependent Poisson noise, Phys. Rev. Lett. 92(11), 110601, 2004.
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.
Porporato A., G. Vico, and P. Fay, Interannual hydroclimatic variability and Ecosystem Superstatistics. Geophys. Res. Lett., 33, L5402, 2006.
Daly, E., and A. Porporato, Inter-time jump statistics of state-dependent Poisson processes, Phys. Rev. E, 75, 011119, 2007.

public 01:34:44

Luis Bonilla : Bifurcation theory of swarm formation

  -   Nonlinear and Complex Systems ( 191 Views )

In nature, insects, fish, birds and other animals flock. A simple two-dimensional model due to Vicsek et al treats them as self-propelled particles that move with constant speed and, at each time step, tend to align their velocities to an average of those of their neighbors except for an alignment noise (conformist rule). The distribution function of these active particles satisfies a kinetic equation. Flocking appears as a bifurcation from an uniform distribution of particles whose order parameter is the average of the directions of their velocities (polarization). This bifurcation is quite unusual: it is described by a system of partial differential equations that are hyperbolic on the short time scale and parabolic on a longer scale. Uniform solutions provide the usual diagram of a pitchfork bifurcation but disturbances about them obey the Klein-Gordon equation in the hyperbolic time scale. Then there are persistent oscillations with many incommensurate frequencies about the bifurcating solution, they produce a shift in the critical noise and resonate with a periodic forcing of the alignment rule. These predictions are confirmed by direct numerical simulations of the Vicsek model. In addition, if the active particles may choose with probability p at each time step to follow the conformist Vicsek rule or to align their velocity contrary or almost contrary to the average one, the bifurcations are of either period doubling or Hopf type and we find stable time dependent solutions. Numerical simulations demonstrate striking effects of alignment noise on the polarization order parameter: maximum polarization length is achieved at an optimal nonzero noise level. When contrarian compulsions are more likely than conformist ones, non-uniform polarized phases appear as the noise surpasses threshold.

public 01:33:51

Ken Kamrin : Toward a predictive continuum model for dense granular flows

  -   Nonlinear and Complex Systems ( 124 Views )

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

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

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

public 01:34:44

Brad Murray : TBA

  -   Nonlinear and Complex Systems ( 170 Views )

public 01:39:36

Pedro Saenz : Spin lattices of walking droplets

  -   Nonlinear and Complex Systems ( 237 Views )

Understanding the self-organization principles and collective dynamics of non-equilibrium matter remains a major challenge despite considerable progress over the last decade. In this talk, I will introduce a hydrodynamic analog system that allows us to investigate simultaneously the wave-mediated self-propulsion and interactions of effective spin degrees of freedom in inertial and rotating frames. Millimetric liquid droplets can walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own guiding wave fields. A walking droplet, or `walker, may be trapped by a submerged circular well at the bottom of the fluid bath, leading to a clockwise or counter-clockwise angular motion centered at the well. When a collection of such wells is arranged in a 1D or 2D lattice geometry, a thin fluid layer between wells enables wave-mediated interactions between neighboring walkers. Through experiments and mathematical modeling, we demonstrate the spontaneous emergence of coherent droplet rotation dynamics for different types of lattices. For sufficiently strong pair-coupling, wave interactions between neighboring droplets may induce local spin flips leading to ferromagnetic or antiferromagnetic order. Transitions between these two forms of order can be controlled by tuning the lattice parameters or by imposing a Coriolis force mimicking an external magnetic field. More generally, our results reveal a number of surprising parallels between the collective spin dynamics of wave-driven droplets and known phases of classical condensed matter systems. This suggests that our hydrodynamic analog system can be used to explore universal aspects of active matter and wave-mediated particle interactions, including spin-wave propagation and topologically protected dynamics far from equilibrium.

public 01:34:56

John Cain : Stabilization of Periodic Wavetrains in Excitable Media

  -   Nonlinear and Complex Systems ( 113 Views )

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

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

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

public 01:39:44

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

  -   Nonlinear and Complex Systems ( 152 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).

public 01:39:58

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

  -   Nonlinear and Complex Systems ( 188 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.

public 01:39:49

Clarence W. Rowley : Low-order models for control of fluids

  -   Nonlinear and Complex Systems ( 140 Views )

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

public 01:31:38

Suliana Manley : Super-resolution imaging and single-molecule tracking, from viruses to chromatin

  -   Nonlinear and Complex Systems ( 113 Views )

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