Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

Compilation of reported noble gas effluent monitor capabilities at operating nuclear power plants /

"NUREG-0592."

Parallel 3D Simulation of a Fault Gouge using the Lattice Solid Model

Despite the insight gained from 2-D particle models, and given that the dynamics of crustal faults occur in 3-D space, the question remains, how do the 3-D fault gouge dynamics differ from those in 2-D? Traditionally, 2-D modeling has been preferred over 3-D simulations because of the computational cost of solving 3-D problems. However, modern high performance computing architectures, combined with a parallel implementation of the Lattice Solid Model (LSM), provide the opportunity to explore 3-D fault micro-mechanics and to advance understanding of effective constitutive relations of fault gouge layers. In this paper, macroscopic friction values from 2-D and 3-D LSM simulations, performed on an SGI Altix 3700 super-cluster, are compared. Two rectangular elastic blocks of bonded particles, with a rough fault plane and separated by a region of randomly sized non-bonded gouge particles, are sheared in opposite directions by normally-loaded driving plates. The results demonstrate that the gouge particles in the 3-D models undergo significant out-of-plane motion during shear. The 3-D models also exhibit a higher mean macroscopic friction than the 2-D models for varying values of interparticle friction. 2-D LSM gouge models have previously been shown to exhibit accelerating energy release in simulated earthquake cycles, supporting the Critical Point hypothesis. The 3-D models are shown to also display accelerating energy release, and good fits of power law time-to-failure functions to the cumulative energy release are obtained.

Modelling the dynamics of genetic algorithms using statistical mechanics

A formalism for modelling the dynamics of Genetic Algorithms (GAs) using methods from statistical mechanics, originally due to Prugel-Bennett and Shapiro, is reviewed, generalized and improved upon. This formalism can be used to predict the averaged trajectory of macroscopic statistics describing the GA's population. These macroscopics are chosen to average well between runs, so that fluctuations from mean behaviour can often be neglected. Where necessary, non-trivial terms are determined by assuming maximum entropy with constraints on known macroscopics. Problems of realistic size are described in compact form and finite population effects are included, often proving to be of fundamental importance. The macroscopics used here are cumulants of an appropriate quantity within the population and the mean correlation (Hamming distance) within the population. Including the correlation as an explicit macroscopic provides a significant improvement over the original formulation. The formalism is applied to a number of simple optimization problems in order to determine its predictive power and to gain insight into GA dynamics. Problems which are most amenable to analysis come from the class where alleles within the genotype contribute additively to the phenotype. This class can be treated with some generality, including problems with inhomogeneous contributions from each site, non-linear or noisy fitness measures, simple diploid representations and temporally varying fitness. The results can also be applied to a simple learning problem, generalization in a binary perceptron, and a limit is identified for which the optimal training batch size can be determined for this problem. The theory is compared to averaged results from a real GA in each case, showing excellent agreement if the maximum entropy principle holds. Some situations where this approximation brakes down are identified. In order to fully test the formalism, an attempt is made on the strong sc np-hard problem of storing random patterns in a binary perceptron. Here, the relationship between the genotype and phenotype (training error) is strongly non-linear. Mutation is modelled under the assumption that perceptron configurations are typical of perceptrons with a given training error. Unfortunately, this assumption does not provide a good approximation in general. It is conjectured that perceptron configurations would have to be constrained by other statistics in order to accurately model mutation for this problem. Issues arising from this study are discussed in conclusion and some possible areas of further research are outlined.

Random walks in local dynamics of network losses

We suggest a model for data losses in a single node (memory buffer) of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that for a finite-capacity buffer at the critical point the loss rate exhibits strong fluctuations and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process.

Temporal dynamics in an immunological synapse:role of thermal fluctuations in signaling

The article analyzes the contribution of stochastic thermal fluctuations in the attachment times of the immature T-cell receptor TCR: peptide-major-histocompatibility-complex pMHC immunological synapse bond. The key question addressed here is the following: how does a synapse bond remain stabilized in the presence of high-frequency thermal noise that potentially equates to a strong detaching force? Focusing on the average time persistence of an immature synapse, we show that the high-frequency nodes accompanying large fluctuations are counterbalanced by low-frequency nodes that evolve over longer time periods, eventually leading to signaling of the immunological synapse bond primarily decided by nodes of the latter type. Our analysis shows that such a counterintuitive behavior could be easily explained from the fact that the survival probability distribution is governed by two distinct phases, corresponding to two separate time exponents, for the two different time regimes. The relatively shorter timescales correspond to the cohesion:adhesion induced immature bond formation whereas the larger time reciprocates the association:dissociation regime leading to TCR:pMHC signaling. From an estimate of the bond survival probability, we show that, at shorter timescales, this probability PΔ(τ) scales with time τ as a universal function of a rescaled noise amplitude DΔ2, such that PΔ(τ)∼τ-(ΔD+12),Δ being the distance from the mean intermembrane (T cell:Antigen Presenting Cell) separation distance. The crossover from this shorter to a longer time regime leads to a universality in the dynamics, at which point the survival probability shows a different power-law scaling compared to the one at shorter timescales. In biological terms, such a crossover indicates that the TCR:pMHC bond has a survival probability with a slower decay rate than the longer LFA-1:ICAM-1 bond justifying its stability.

IRAS 00183-7111: ALMA and X-ray view of an ultra luminous infrared galaxy

The aim of this Thesis work is to study the multi-frequency properties of the Ultra Luminous Infrared Galaxy (ULIRG) IRAS 00183-7111 (I00183) at z = 0.327, connecting ALMA sub-mm/mm observations with those at high energies in order to place constraints on the properties of its central power source and verify whether the gas traced by the CO may be responsible for the obscuration observed in X-rays. I00183 was selected from the so-called Spoon diagnostic diagram (Spoon et al. 2007) for mid-infrared spectra of infrared galaxies based on the equivalent width of the 6.2 μm Polycyclic Aromatic Hydrocarbon (PAH) emission feature versus the 9.7 μm silicate strength. Such features are a powerful tool to investigate the contribution of star formation and AGN activity in this class of objects. I00183 was selected from the top-left region of the plot where the most obscured sources, characterized by a strong Si absorption feature, are located. To link the sub-mm/mm to the X-ray properties of I00183, ALMA archival Cycle 0 data in Band 3 (87 GHz) and Band 6 (270 GHz) have been calibrated and analyzed, using CASA software. ALMA Cycle 0 was the Early Science program for which data reprocessing is strongly suggested. The main work of this Thesis consisted in reprocessing raw data to provide an improvement with respect to the available archival products and results, which were obtained using standard procedures. The high-energy data consists of Chandra, XMM-Newton and NuSTAR observations which provide a broad coverage of the spectrum in the energy range 0.5 − 30 keV. Chandra and XMM archival data were used, with an exposure time of 22 and 22.2 ks, respectively; their reduction was carried out using CIAO and SAS software. The 100 ks NuSTAR are still private and the spectra were obtained by courtesy of the PI (K. Iwasawa). A detailed spectral analysis was done using XSPEC software; the spectral shape was reproduced starting from simple phenomenological models, and then more physical models were introduced to account for the complex mechanisms that involve this source. In Chapter 1, an overview of the scientific background is discussed, with a focus on the target, I00183, and the Spoon diagnostic diagram, from which it was originally selected. In Chapter 2, the basic principles of interferometry are briefly introduced, with a description of the calibration theory applied to interferometric observations. In Chapter 3, ALMA and its capabilities, both current and future, are shown, explaining also the complex structure of the ALMA archive. In Chapter 4, the calibration of ALMA data is presented and discussed, showing also the obtained imaging products. In Chapter 5, the analysis and discussion of the main results obtained from ALMA data is presented. In Chapter 6, the X-ray observations, data reduction and spectral analysis are reported, with a brief introduction to the basic principle of X-ray astronomy and the instruments from which the observations were carried out. Finally, the overall work is summarized, with particular emphasis on the main obtained results and the possible future perspectives.

A multi vector energy analysis for interconnected power and gas systems

This paper presents the first multi vector energy analysis for the interconnected energy systems of Great Britain (GB) and Ireland. Both systems share a common high penetration of wind power, but significantly different security of supply outlooks. Ireland is heavily dependent on gas imports from GB, giving significance to the interconnected aspect of the methodology in addition to the gas and power interactions analysed. A fully realistic unit commitment and economic dispatch model coupled to an energy flow model of the gas supply network is developed. Extreme weather events driving increased domestic gas demand and low wind power output were utilised to increase gas supply network stress. Decreased wind profiles had a larger impact on system security than high domestic gas demand. However, the GB energy system was resilient during high demand periods but gas network stress limited the ramping capability of localised generating units. Additionally, gas system entry node congestion in the Irish system was shown to deliver a 40% increase in short run costs for generators. Gas storage was shown to reduce the impact of high demand driven congestion delivering a reduction in total generation costs of 14% in the period studied and reducing electricity imports from GB, significantly contributing to security of supply.

A Generalized Fuzzy Linguistic Model for Predicting Component Concentrations in an Optical Gas Sensing System

Motivated by environmental protection concerns, monitoring the flue gas of thermal power plant is now often mandatory due to the need to ensure that emission levels stay within safe limits. Optical based gas sensing systems are increasingly employed for this purpose, with regression techniques used to relate gas optical absorption spectra to the concentrations of specific gas components of interest (NOx, SO2 etc.). Accurately predicting gas concentrations from absorption spectra remains a challenging problem due to the presence of nonlinearities in the relationships and the high-dimensional and correlated nature of the spectral data. This article proposes a generalized fuzzy linguistic model (GFLM) to address this challenge. The GFLM is made up of a series of “If-Then” fuzzy rules. The absorption spectra are input variables in the rule antecedent. The rule consequent is a general nonlinear polynomial function of the absorption spectra. Model parameters are estimated using least squares and gradient descent optimization algorithms. The performance of GFLM is compared with other traditional prediction models, such as partial least squares, support vector machines, multilayer perceptron neural networks and radial basis function networks, for two real flue gas spectral datasets: one from a coal-fired power plant and one from a gas-fired power plant. The experimental results show that the generalized fuzzy linguistic model has good predictive ability, and is competitive with alternative approaches, while having the added advantage of providing an interpretable model.

A generalized fuzzy linguistic model for predicting component concentrations in an optical gas sensing system

Motivated by environmental protection concerns, monitoring the flue gas of thermal power plant is now often mandatory due to the need to ensure that emission levels stay within safe limits. Optical based gas sensing systems are increasingly employed for this purpose, with regression techniques used to relate gas optical absorption spectra to the concentrations of specific gas components of interest (NO_x, SO₂ etc.). Accurately predicting gas concentrations from absorption spectra remains a challenging problem due to the presence of nonlinearities in the relationships and the high-dimensional and correlated nature of the spectral data. This article proposes a generalized fuzzy linguistic model (GFLM) to address this challenge. The GFLM is made up of a series of “If-Then” fuzzy rules. The absorption spectra are input variables in the rule antecedent. The rule consequent is a general nonlinear polynomial function of the absorption spectra. Model parameters are estimated using least squares and gradient descent optimization algorithms. The performance of GFLM is compared with other traditional prediction models, such as partial least squares, support vector machines, multilayer perceptron neural networks and radial basis function networks, for two real flue gas spectral datasets: one from a coal-fired power plant and one from a gas-fired power plant. The experimental results show that the generalized fuzzy linguistic model has good predictive ability, and is competitive with alternative approaches, while having the added advantage of providing an interpretable model.

Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators.

We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.

Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.