Spin-glass behaviour on random lattices

The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction w of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that w = 1/2, corresponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase (w < 1/2) from a region with spin-glass, ferromagnetic, mixed and paramagnetic phases (w > 1/2).

Modeling random corrosion processes via polynomial chaos expansion

Polynomial Chaos Expansion (PCE) is widely recognized as a flexible tool to represent different types of random variables/processes. However, applications to real, experimental data are still limited. In this article, PCE is used to represent the random time-evolution of metal corrosion growth in marine environments. The PCE coefficients are determined in order to represent data of 45 corrosion coupons tested by Jeffrey and Melchers (2001) at Taylors Beach, Australia. Accuracy of the representation and possibilities for model extrapolation are considered in the study. Results show that reasonably accurate smooth representations of the corrosion process can be obtained. The representation is not better because a smooth model is used to represent non-smooth corrosion data. Random corrosion leads to time-variant reliability problems, due to resistance degradation over time. Time variant reliability problems are not trivial to solve, especially under random process loading. Two example problems are solved herein, showing how the developed PCE representations can be employed in reliability analysis of structures subject to marine corrosion. Monte Carlo Simulation is used to solve the resulting time-variant reliability problems. However, an accurate and more computationally efficient solution is also presented.

Model for the Dynamics of the Cytoskeleton.

Particle tracking of microbeads attached to the cytoskeleton (CSK) reveals an intermittent dynamic. The mean squared displacement (MSD) is subdiffusive for small Δt and superdiffusive for large Δt, which are associated with periods of traps and periods of jumps respectively. The analysis of the displacements has shown a non-Gaussian behavior, what is indicative of an active motion, classifying the cells as a far from equilibrium material. Using Langevin dynamics, we reconstruct the dynamic of the CSK. The model is based on the bundles of actin filaments that link themself with the bead RGD coating, trapping it in an harmonic potential. We consider a one- dimensional motion of a particle, neglecting inertial effects (over-damped Langevin dynamics). The resultant force is decomposed in friction force, elastic force and random force, which is used as white noise representing the effect due to molecular agitation. These description until now shows a static situation where the bead performed a random walk in an elastic potential. In order to modeling the active remodeling of the CSK, we vary the equilibrium position of the potential. Inserting a motion in the well center, we change the equilibrium position linearly with time with constant velocity. The result found exhibits a MSD versus time ’tau’ with three regimes. The first regime is when ‘tau’ < ‘tau IND 0’, where ‘tau IND 0’ is the relaxation time, representing the thermal motion. At this regime the particle can diffuse freely. The second regime is a plateau, ‘tau IND 0’ < ‘tau’ < ‘tau IND 1’, representing the particle caged in the potential. Here, ‘tau IND 1’ is a characteristic time that limit the confinement period. And the third regime, ‘tau’ > ‘tau IND 1’, is when the particles are in the superdiffusive behavior. This is where most of the experiments are performed, under 20 frames per second (FPS), thus there is no experimental evidence that support the first regime. We are currently performing experiments with high frequency, up to 100 FPS, attempting to visualize this diffusive behavior. Beside the first regime, our simple model can reproduce MSD curves similar to what has been found experimentally, which can be helpful to understanding CSK structure and properties.

A Multilevel Model with Time Series Components for the Analysis of Tribal Art Prices

In the present work we perform an econometric analysis of the Tribal art market. To this aim, we use a unique and original database that includes information on Tribal art market auctions worldwide from 1998 to 2011. In Literature, art prices are modelled through the hedonic regression model, a classic fixed-effect model. The main drawback of the hedonic approach is the large number of parameters, since, in general, art data include many categorical variables. In this work, we propose a multilevel model for the analysis of Tribal art prices that takes into account the influence of time on artwork prices. In fact, it is natural to assume that time exerts an influence over the price dynamics in various ways. Nevertheless, since the set of objects change at every auction date, we do not have repeated measurements of the same items over time. Hence, the dataset does not constitute a proper panel; rather, it has a two-level structure in that items, level-1 units, are grouped in time points, level-2 units. The main theoretical contribution is the extension of classical multilevel models to cope with the case described above. In particular, we introduce a model with time dependent random effects at the second level. We propose a novel specification of the model, derive the maximum likelihood estimators and implement them through the E-M algorithm. We test the finite sample properties of the estimators and the validity of the own-written R-code by means of a simulation study. Finally, we show that the new model improves considerably the fit of the Tribal art data with respect to both the hedonic regression model and the classic multilevel model.

Study of a wind-wave numerical model and its integration with ocean and oil-spill numerical models

The ability to represent the transport and fate of an oil slick at the sea surface is a formidable task. By using an accurate numerical representation of oil evolution and movement in seawater, the possibility to asses and reduce the oil-spill pollution risk can be greatly improved. The blowing of the wind on the sea surface generates ocean waves, which give rise to transport of pollutants by wave-induced velocities that are known as Stokes’ Drift velocities. The Stokes’ Drift transport associated to a random gravity wave field is a function of the wave Energy Spectra that statistically fully describe it and that can be provided by a wave numerical model. Therefore, in order to perform an accurate numerical simulation of the oil motion in seawater, a coupling of the oil-spill model with a wave forecasting model is needed. In this Thesis work, the coupling of the MEDSLIK-II oil-spill numerical model with the SWAN wind-wave numerical model has been performed and tested. In order to improve the knowledge of the wind-wave model and its numerical performances, a preliminary sensitivity study to different SWAN model configuration has been carried out. The SWAN model results have been compared with the ISPRA directional buoys located at Venezia, Ancona and Monopoli and the best model settings have been detected. Then, high resolution currents provided by a relocatable model (SURF) have been used to force both the wave and the oil-spill models and its coupling with the SWAN model has been tested. The trajectories of four drifters have been simulated by using JONSWAP parametric spectra or SWAN directional-frequency energy output spectra and results have been compared with the real paths traveled by the drifters.

Random lattice models

This thesis deals with three different physical models, where each model involves a random component which is linked to a cubic lattice. First, a model is studied, which is used in numerical calculations of Quantum Chromodynamics.In these calculations random gauge-fields are distributed on the bonds of the lattice. The formulation of the model is fitted into the mathematical framework of ergodic operator families. We prove, that for small coupling constants, the ergodicity of the underlying probability measure is indeed ensured and that the integrated density of states of the Wilson-Dirac operator exists. The physical situations treated in the next two chapters are more similar to one another. In both cases the principle idea is to study a fermion system in a cubic crystal with impurities, that are modeled by a random potential located at the lattice sites. In the second model we apply the Hartree-Fock approximation to such a system. For the case of reduced Hartree-Fock theory at positive temperatures and a fixed chemical potential we consider the limit of an infinite system. In that case we show the existence and uniqueness of minimizers of the Hartree-Fock functional. In the third model we formulate the fermion system algebraically via C*-algebras. The question imposed here is to calculate the heat production of the system under the influence of an outer electromagnetic field. We show that the heat production corresponds exactly to what is empirically predicted by Joule's law in the regime of linear response.

Fluctuation properties in random walks on networks and simple integrate and fire models

In questa tesi si è studiato l’insorgere di eventi critici in un semplice modello neurale del tipo Integrate and Fire, basato su processi dinamici stocastici markoviani definiti su una rete. Il segnale neurale elettrico è stato modellato da un flusso di particelle. Si è concentrata l’attenzione sulla fase transiente del sistema, cercando di identificare fenomeni simili alla sincronizzazione neurale, la quale può essere considerata un evento critico. Sono state studiate reti particolarmente semplici, trovando che il modello proposto ha la capacità di produrre effetti "a cascata" nell’attività neurale, dovuti a Self Organized Criticality (auto organizzazione del sistema in stati instabili); questi effetti non vengono invece osservati in Random Walks sulle stesse reti. Si è visto che un piccolo stimolo random è capace di generare nell’attività della rete delle fluttuazioni notevoli, in particolar modo se il sistema si trova in una fase al limite dell’equilibrio. I picchi di attività così rilevati sono stati interpretati come valanghe di segnale neurale, fenomeno riconducibile alla sincronizzazione.

Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights

We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375-395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u (*)/u (*R) , where u (*) is the friction velocity and u (*R) is the friction velocity from the uniform building height case, is expressed well as an algebraic function of lambda and sigma (h) /h (m) , where lambda is the frontal area index, sigma (h) is the standard deviation of the building height, and h (m) is the mean building height. The simulations also resulted in a simple algebraic relation for z (0)/z (0R) as a function of lambda and sigma (h) /h (m) , where z (0) is the aerodynamic roughness length and z (0R) is z (0) found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.

A Model to Predict Percolation Threshold and Effective Conductivity of Infiltrated Electrodes for Solid Oxide Fuel Cells

We present a mechanistic modeling methodology to predict both the percolation threshold and effective conductivity of infiltrated Solid Oxide Fuel Cell (SOFC) electrodes. The model has been developed to mirror each step of the experimental fabrication process. The primary model output is the infiltrated electrode effective conductivity which provides results over a range of infiltrate loadings that are independent of the chosen electronically conducting material. The percolation threshold is utilized as a valuable output data point directly related to the effective conductivity to compare a wide range of input value choices. The predictive capability of the model is demonstrated by favorable comparison to two separate published experimental studies, one using strontium molybdate and one using La0.8Sr0.2FeO3-δ as infiltrate materials. Effective conductivities and percolation thresholds are shown for varied infiltrate particle size, pore size, and porosity with the infiltrate particle size having the largest impact on the results.

A Model to Predict Percolation Threshold and Effective Conductivity of Infiltrated Electrodes for Solid Oxide Fuel Cells

We present a mechanistic modeling methodology to predict both the percolation threshold and effective conductivity of infiltrated Solid Oxide Fuel Cell (SOFC) electrodes. The model has been developed to mirror each step of the experimental fabrication process. The primary model output is the infiltrated electrode effective conductivity which provides results over a range of infiltrate loadings that are independent of the chosen electronically conducting material. The percolation threshold is utilized as a valuable output data point directly related to the effective conductivity to compare a wide range of input value choices. The predictive capability of the model is demonstrated by favorable comparison to two separate published experimental studies, one using strontium molybdate and one using La0.8Sr0.2FeO3-delta as infiltrate materials. Effective conductivities and percolation thresholds are shown for varied infiltrate particle size, pore size, and porosity with the infiltrate particle size having the largest impact on the results. (C) 2013 The Electrochemical Society. All rights reserved.

Estimation of axon counts in a rat model of glaucoma: comparison of fixed-pattern sampling with targeted sampling

Full axon counting of optic nerve cross-sections represents the most accurate method to quantify axonal damage, but such analysis is very labour intensive. Recently, a new method has been developed, termed targeted sampling, which combines the salient features of a grading scheme with axon counting. Preliminary findings revealed the method compared favourably with random sampling. The aim of the current study was to advance our understanding of the effect of sampling patterns on axon counts by comparing estimated axon counts from targeted sampling with those obtained from fixed-pattern sampling in a large collection of optic nerves with different severities of axonal injury.

Cardiac sodium channel NaV1.5 distribution in myocytes via interacting proteins: the multiple pool model

The cardiac sodium current (INa) is responsible for the rapid depolarization of cardiac cells, thus allowing for their contraction. It is also involved in regulating the duration of the cardiac action potential (AP) and propagation of the impulse throughout the myocardium. Cardiac INa is generated by the voltage-gated Na(+) channel, NaV1.5, a 2016-residue protein which forms the pore of the channel. Over the past years, hundreds of mutations in SCN5A, the human gene coding for NaV1.5, have been linked to many cardiac electrical disorders, including the congenital and acquired long QT syndrome, Brugada syndrome, conduction slowing, sick sinus syndrome, atrial fibrillation, and dilated cardiomyopathy. Similar to many membrane proteins, NaV1.5 has been found to be regulated by several interacting proteins. In some cases, these different proteins, which reside in distinct membrane compartments (i.e. lateral membrane vs. intercalated disks), have been shown to interact with the same regulatory domain of NaV1.5, thus suggesting that several pools of NaV1.5 channels may co-exist in cardiac cells. The aim of this review article is to summarize the recent works that demonstrate its interaction with regulatory proteins and illustrate the model that the sodium channel NaV1.5 resides in distinct and different pools in cardiac cells. This article is part of a Special Issue entitled: Cardiomyocyte Biology: Cardiac Pathways of Differentiation, Metabolism and Contraction.

Development And Use Of A Model To Predict Properties Of Infiltrated Solid Oxide Fuel Cell Anodes

Solid oxide fuel cells (SOFCs) provide a potentially clean way of using energy sources. One important aspect of a functioning fuel cell is the anode and its characteristics (e.g. conductivity). Using infiltration of conductor particles has been shown to be a method for production at lower cost with comparable functionality. While these methods have been demonstrated experimentally, there is a vast range of variables to consider. Because of the long time for manufacture, a model is desired to aid in the development of the desired anode formulation. This thesis aims to (1) use an idealized system to determine the appropriate size and aspect ratio to determine the percolation threshold and effective conductivity as well as to (2) simulate the infiltrated fabrication method to determine the effective conductivity and percolation threshold as a function of ceramic and pore former particle size, particle fraction and the cell¿s final porosity. The idealized system found that the aspect ratio of the cell does not affect the cells functionality and that an aspect ratio of 1 is the most efficient computationally to use. Additionally, at cell sizes greater than 50x50, the conductivity asymptotes to a constant value. Through the infiltrated model simulations, it was found that by increasing the size of the ceramic (YSZ) and pore former particles, the percolation threshold can be decreased and the effective conductivity at low loadings can be increased. Furthermore, by decreasing the porosity of the cell, the percolation threshold and effective conductivity at low loadings can also be increased

An Urn Model for Cascading Failures on a Lattice

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

Estimating the number of motor units using random sums with independently thinned terms

The problem of estimating the numbers of motor units N in a muscle is embedded in a general stochastic model using the notion of thinning from point process theory. In the paper a new moment type estimator for the numbers of motor units in a muscle is denned, which is derived using random sums with independently thinned terms. Asymptotic normality of the estimator is shown and its practical value is demonstrated with bootstrap and approximative confidence intervals for a data set from a 31-year-old healthy right-handed, female volunteer. Moreover simulation results are presented and Monte-Carlo based quantiles, means, and variances are calculated for N in{300,600,1000}.