(Table 1) Age model of sediment core MD03-2705

A reconstruction of northwest African summer monsoon strength during the cold marine isotopic stage (MIS) 6 indicates a link to the seasonal migration of the Intertropical Convergence Zone (ITCZ). High-resolution studies of eolian dust supply and sea surface temperature recorded in marine core MD03-2705, on the Mauritanian margin, provide a better understanding about the penultimate glacial history of northwestern African aridity/humidity and upwelling coastal activity. Today, site MD03-2705 experiences increased upwelling and dust flux during the winter months, when the ITCZ is in a southerly position. Analyses of foraminifera isotopic composition suggest that during MIS 6.5 (180-168 ka) the average position of the ITCZ migrated north, marked by an increase in the strength of the summer monsoon, which decreased eolian dust transport and the coastal upwelling activity. The northward migration is in phase with a specific orbital combination of a low precessional index with a high obliquity signal. High-resolution analysis of stable isotopes (d18O and d13C) and microscale resolution geochemical (Ti/Al and quartz grain counts) determinations reveal that the transition between monsoonal humid (MIS 6.5) and dry (MIS 6.4) conditions has occurred in less than 1.3 ka. Such rapid changes suggest a nonlinear link between the African monsoonal rainfall system and environmental changes over the continent. This study provides new insights about the influence of vegetation and oceanic temperature feedbacks on the onset of African summer monsoon and demonstrates that, during the penultimate glacial period, changes in tropical dynamics had regional and global impacts.

Quantum transport and integrability of the Anderson model for a quantum dot with multiple leads

We show that an Anderson Hamiltonian describing a quantum dot connected to multiple leads is integrable. A general expression for the nonlinear conductance is obtained by combining the Bethe ansatz exact solution with Landauer-Buttiker theory. In the Kondo regime, a closed form expression is given for the matrix conductance at zero temperature and when all the leads are close to the symmetric point. A bias-induced splitting of the Kondo resonance is possible for three or more leads. Specifically, for N leads, with each at a different chemical potential, there can be N-1 Kondo peaks in the conductance.

Functionality, Robustness and Control of Nonlinear Network Dynamics: Modeling and Understanding the C. elegans Connectome

Thesis (Ph.D.)--University of Washington, 2016-06

Ground water model calibration using pilot points and regularization

Use of nonlinear parameter estimation techniques is now commonplace in ground water model calibration. However, there is still ample room for further development of these techniques in order to enable them to extract more information from calibration datasets, to more thoroughly explore the uncertainty associated with model predictions, and to make them easier to implement in various modeling contexts. This paper describes the use of pilot points as a methodology for spatial hydraulic property characterization. When used in conjunction with nonlinear parameter estimation software that incorporates advanced regularization functionality (such as PEST), use of pilot points can add a great deal of flexibility to the calibration process at the same time as it makes this process easier to implement. Pilot points can be used either as a substitute for zones of piecewise parameter uniformity, or in conjunction with such zones. In either case, they allow the disposition of areas of high and low hydraulic property value to be inferred through the calibration process, without the need for the modeler to guess the geometry of such areas prior to estimating the parameters that pertain to them. Pilot points and regularization can also be used as an adjunct to geostatistically based stochastic parameterization methods. Using the techniques described herein, a series of hydraulic property fields can be generated, all of which recognize the stochastic characterization of an area at the same time that they satisfy the constraints imposed on hydraulic property values by the need to ensure that model outputs match field measurements. Model predictions can then be made using all of these fields as a mechanism for exploring predictive uncertainty.

Nonlinear quantum optical computing via measurement

We show how the measurement induced model of quantum computation proposed by Raussendorf and Briegel ( 2001, Phys. Rev. Letts., 86, 5188) can be adapted to a nonlinear optical interaction. This optical implementation requires a Kerr nonlinearity, a single photon source, a single photon detector and fast feed forward. Although nondeterministic optical quantum information proposals such as that suggested by KLM ( 2001, Nature, 409, 46) do not require a Kerr nonlinearity they do require complex reconfigurable optical networks. The proposal in this paper has the benefit of a single static optical layout with fixed device parameters, where the algorithm is defined by the final measurement procedure.

An experimental and finite element poroelastic creep response analysis of an intervertebral hydrogel disc model in axial compression

A hydrogel intervertebral disc (lVD) model consisting of an inner nucleus core and an outer anulus ring was manufactured from 30 and 35% by weight Poly(vinyl alcohol) hydrogel (PVA-H) concentrations and subjected to axial compression in between saturated porous endplates at 200 N for 11 h, 30 min. Repeat experiments (n = 4) on different samples (N = 2) show good reproducibility of fluid loss and axial deformation. An axisymmetric nonlinear poroelastic finite element model with variable permeability was developed using commercial finite element software to compare axial deformation and predicted fluid loss with experimental data. The FE predictions indicate differential fluid loss similar to that of biological IVDs, with the nucleus losing more water than the anulus, and there is overall good agreement between experimental and finite element predicted fluid loss. The stress distribution pattern indicates important similarities with the biological lVD that includes stress transference from the nucleus to the anulus upon sustained loading and renders it suitable as a model that can be used in future studies to better understand the role of fluid and stress in biological IVDs. (C) 2005 Springer Science + Business Media, Inc.

A probabilistic switch model of information flow in social networks: Application for virtual circuits to organizational design

Network building and exchange of information by people within networks is crucial to the innovation process. Contrary to older models, in social networks the flow of information is noncontinuous and nonlinear. There are critical barriers to information flow that operate in a problematic manner. New models and new analytic tools are needed for these systems. This paper introduces the concept of virtual circuits and draws on recent concepts of network modelling and design to introduce a probabilistic switch theory that can be described using matrices. It can be used to model multistep information flow between people within organisational networks, to provide formal definitions of efficient and balanced networks and to describe distortion of information as it passes along human communication channels. The concept of multi-dimensional information space arises naturally from the use of matrices. The theory and the use of serial diagonal matrices have applications to organisational design and to the modelling of other systems. It is hypothesised that opinion leaders or creative individuals are more likely to emerge at information-rich nodes in networks. A mathematical definition of such nodes is developed and it does not invariably correspond with centrality as defined by early work on networks.

General foundation for the nonlinear ponderomotive four-force in laser-plasma interactions

The interaction of electromagnetic radiation with plasmas is studied in relativistic four-vector formalism. A gauge and Lorentz invariant ponderomotive four-force is derived from the time dependent nonlinear three-force of Hora (1985). This four-force, due to its Lorentz invariance, contains new magnetic field terms. A new gauge and Lorentz invariant model of the response of plasma to electromagnetic radiation is then devised. An expression for the dispersion relation is obtained from this model. It is then proved that the magnetic permeability of plasma is unity for a general reference frame. This is an important result since it has been previously assumed in many plasma models.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

Construction of an Intraplate Fault System Model of South Australia, and Simulation Tool for the iSERVO Institute Seed Project

To foster ongoing international cooperation beyond ACES (APEC Cooperation for Earthquake Simulation) on the simulation of solid earth phenomena, agreement was reached to work towards establishment of a frontier international research institute for simulating the solid earth: iSERVO = International Solid Earth Research Virtual Observatory institute (http://www.iservo.edu.au). This paper outlines a key Australian contribution towards the iSERVO institute seed project, this is the construction of: (1) a typical intraplate fault system model using practical fault system data of South Australia (i.e., SA interacting fault model), which includes data management and editing, geometrical modeling and mesh generation; and (2) a finite-element based software tool, which is built on our long-term and ongoing effort to develop the R-minimum strategy based finite-element computational algorithm and software tool for modelling three-dimensional nonlinear frictional contact behavior between multiple deformable bodies with the arbitrarily-shaped contact element strategy. A numerical simulation of the SA fault system is carried out using this software tool to demonstrate its capability and our efforts towards seeding the iSERVO Institute.

The lattice solid model to simulate the physics of rocks and earthquakes: Incorporation of friction

The particle-based lattice solid model developed to study the physics of rocks and the nonlinear dynamics of earthquakes is refined by incorporating intrinsic friction between particles. The model provides a means for studying the causes of seismic wave attenuation, as well as frictional heat generation, fault zone evolution, and localisation phenomena. A modified velocity-Verlat scheme that allows friction to be precisely modelled is developed. This is a difficult computational problem given that a discontinuity must be accurately simulated by the numerical approach (i.e., the transition from static to dynamical frictional behaviour). This is achieved using a half time step integration scheme. At each half time step, a nonlinear system is solved to compute the static frictional forces and states of touching particle-pairs. Improved efficiency is achieved by adaptively adjusting the time step increment, depending on the particle velocities in the system. The total energy is calculated and verified to remain constant to a high precision during simulations. Numerical experiments show that the model can be applied to the study of earthquake dynamics, the stick-slip instability, heat generation, and fault zone evolution. Such experiments may lead to a conclusive resolution of the heat flow paradox and improved understanding of earthquake precursory phenomena and dynamics. (C) 1999 Academic Press.

Probability distribution modelling to improve stability in nonlinear MIMO control

We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.

A general linear model for MEG beamformer imaging

A new general linear model (GLM) beamformer method is described for processing magnetoencephalography (MEG) data. A standard nonlinear beamformer is used to determine the time course of neuronal activation for each point in a predefined source space. A Hilbert transform gives the envelope of oscillatory activity at each location in any chosen frequency band (not necessary in the case of sustained (DC) fields), enabling the general linear model to be applied and a volumetric T statistic image to be determined. The new method is illustrated by a two-source simulation (sustained field and 20 Hz) and is shown to provide accurate localization. The method is also shown to locate accurately the increasing and decreasing gamma activities to the temporal and frontal lobes, respectively, in the case of a scintillating scotoma. The new method brings the advantages of the general linear model to the analysis of MEG data and should prove useful for the localization of changing patterns of activity across all frequency ranges including DC (sustained fields). © 2004 Elsevier Inc. All rights reserved.

Motion, flash, and flicker:A unified spatiotemporal model of perceived edge sharpening

Blurred edges appear sharper in motion than when they are stationary. We proposed a model of this motion sharpening that invokes a local, nonlinear contrast transducer function (Hammett et al, 1998 Vision Research 38 2099-2108). Response saturation in the transducer compresses or 'clips' the input spatial waveform, rendering the edges as sharper. To explain the increasing distortion of drifting edges at higher speeds, the degree of nonlinearity must increase with speed or temporal frequency. A dynamic contrast gain control before the transducer can account for both the speed dependence and approximate contrast invariance of motion sharpening (Hammett et al, 2003 Vision Research, in press). We show here that this model also predicts perceived sharpening of briefly flashed and flickering edges, and we show that the model can account fairly well for experimental data from all three modes of presentation (motion, flash, and flicker). At moderate durations and lower temporal frequencies the gain control attenuates the input signal, thus protecting it from later compression by the transducer. The gain control is somewhat sluggish, and so it suffers both a slow onset, and loss of power at high temporal frequencies. Consequently, brief presentations and high temporal frequencies of drift and flicker are less protected from distortion, and show greater perceptual sharpening.