public 01:34:44

Gaby Katul : TBA

  -   Nonlinear and Complex Systems ( 202 Views )

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 01:39:46

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

  -   Nonlinear and Complex Systems ( 160 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.

public 01:17:07

Brian Mann : Nonlinear Energy Harvesting

  -   Nonlinear and Complex Systems ( 154 Views )

public 01:34:54

Sreekanth Pannala : Multiscale/Multiphysics simulation strategy for gas-solids flow reactors

  -   Nonlinear and Complex Systems ( 153 Views )

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.

public 01:39:44

Bob Behringer : TBA

  -   Nonlinear and Complex Systems ( 151 Views )

public 01:34:47

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.

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 01:34:57

Nicholas Ouellette : Multiscale Dynamics and Coherent Structures in Turbulent Flow

  -   Nonlinear and Complex Systems ( 129 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.

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 01:39:57

Lawrence Virgin : Identifying chaos using spectral content

  -   Nonlinear and Complex Systems ( 116 Views )

The characterization of chaos as a random-like response from a deterministic dynamical system with an extreme sensitivity to initial conditions is well-established, and has provided a stimulus to research in nonlinear dynamical systems in general. In a formal sense, the computation of the Lyapunov Exponent (LE) spectrum establishes a quantitative measure, with at least one positive LE (and generally bounded motion) indicating a local exponential divergence of adjacent trajectories. Other measures are associated with certain geometric features of a chaotic attractor, e.g., the fractal dimension, and broadband frequency content. However, although the extraction of LE's can be accomplished with (necessarily noisy) experimental data, this is still a relatively data-intensive, sensitive (and frustrating) endeavor.
We present here an alternative, pragmatic approach to identifying chaos as a function of system parameters, based on frequency content and extending the concept of the spectrogram. This talk will describe this approach applied to systems of increasing complexity, ranging from direct numerical simulations of familiar archetypal systems like Lorenz and the pendulum to experimental data generated from mechanical systems. The accuracy and utility of the approach, including the effect of noise, is tested relative to the standard (LE) approach.