Approximate controllability for the semilinear heat equation in RN involving gradient terms

We prove the approximate controllability of the semilinear heat equation in R^N, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient Ñu. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings, we work with the similarity variables and use weighted Sobolev spaces.

Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement

We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the noninteracting Fermi gas under the action of the spatially growing tightness of the one- or two-dimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermi-von Weizsäcker (TF-vW) density functional. It is found that the vW correction to the simple TF approximation (the gradient term) is nearly negligible in all situations. The properties of the ground state under the action of the 2D and 1D HO confinement with the tightness growing in the transverse directions are investigated too for the Bose-Einstein condensate with the self-repulsive nonlinearity. © 2013 American Physical Society.

A model for diffusive and displacive phase transitions in steels

Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.

Black-scholes type equations

In this work we are concerned with the analysis and numerical solution of Black-Scholes type equations arising in the modeling of incomplete financial markets and an inverse problem of determining the local volatility function in a generalized Black-Scholes model from observed option prices. In the first chapter a fully nonlinear Black-Scholes equation which models transaction costs arising in option pricing is discretized by a new high order compact scheme. The compact scheme is proved to be unconditionally stable and non-oscillatory and is very efficient compared to classical schemes. Moreover, it is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. In the next chapter we turn to the calibration problem of computing local volatility functions from market data in a generalized Black-Scholes setting. We follow an optimal control approach in a Lagrangian framework. We show the existence of a global solution and study first- and second-order optimality conditions. Furthermore, we propose an algorithm that is based on a globalized sequential quadratic programming method and a primal-dual active set strategy, and present numerical results. In the last chapter we consider a quasilinear parabolic equation with quadratic gradient terms, which arises in the modeling of an optimal portfolio in incomplete markets. The existence of weak solutions is shown by considering a sequence of approximate solutions. The main difficulty of the proof is to infer the strong convergence of the sequence. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution, but without additional regularity assumptions on the solution. The results are illustrated by a numerical example.

Comparative study of symmetric and asymmetric cylindrical MRI gradient Y-coils in terms of induced eddy currents

We have recently introduced the concept of whole-body asymmetric MRI systems [1]. In this theoretical study, we investigate the PNS characteristics of whole-body asymmetric gradient systems as compared to conventional symmetric systems. Recent experimental evidence [2] supports the hypothesis of transverse gradients being the largest contributor of PNS due to induced electric currents. Asymmetric head gradient coils have demonstrated benefits in the past [3]. The numerical results are based on an anatomically-accurate 2mm-human voxel-phantom NORMAN [4]. The results of this study can facilitate the optimization of whole-body asymmetric gradients in terms of patient comfort/safety (less PNS), while prospering the use of asymmetric MRI systems for in-vivo medical interventions.

Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses

We present finite element simulations of temperature gradient driven rock alteration and mineralization in fluid saturated porous rock masses. In particular, we explore the significance of production/annihilation terms in the mass balance equations and the dependence of the spatial patterns of rock alteration upon the ratio of the roll over time of large scale convection cells to the relaxation time of the chemical reactions. Special concepts such as the gradient reaction criterion or rock alteration index (RAI) are discussed in light of the present, more general theory. In order to validate the finite element simulation, we derive an analytical solution for the rock alteration index of a benchmark problem on a two-dimensional rectangular domain. Since the geometry and boundary conditions of the benchmark problem can be easily and exactly modelled, the analytical solution is also useful for validating other numerical methods, such as the finite difference method and the boundary element method, when they are used to dear with this kind of problem. Finally, the potential of the theory is illustrated by means of finite element studies related to coupled flow problems in materially homogeneous and inhomogeneous porous rock masses. (C) 1998 Elsevier Science S.A. All rights reserved.

Obesity and socioeconomic gradient

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Economics from the NOVA – School of Business and Economics

Snapshot gradient-recalled echo-planar images of rat brains at long echo time at 9.4 T.

With improved B 0 homogeneity along with satisfactory gradient performance at high magnetic fields, snapshot gradient-recalled echo-planar imaging (GRE-EPI) would perform at long echo times (TEs) on the order of T2*, which intrinsically allows obtaining strongly T2*-weighted images with embedded substantial anatomical details in ultrashort time. The aim of this study was to investigate the feasibility and quality of long TE snapshot GRE-EPI images of rat brain at 9.4 T. When compensating for B 0 inhomogeneities, especially second-order shim terms, a 200 x 200 microm2 in-plane resolution image was reproducibly obtained at long TE (>25 ms). The resulting coronal images at 30 ms had diminished geometric distortions and, thus, embedded substantial anatomical details. Concurrently with the very consistent stability, such GRE-EPI images should permit to resolve functional data not only with high specificity but also with substantial anatomical details, therefore allowing coregistration of the acquired functional data on the same image data set.

Obese, smoker, and obese smoker : is there a general lifestyle gradient?

Aim: Obesity and smoking are major CVD risk factors and may be associated with other unfavourable lifestyle behaviours. Our aim was to investigate the significance of obesity, heavy smoking, and both combined in terms of prevalence trends and their relationship with other lifestyle factors. Methods: We used data from the population-based cross-sectional Swiss Health Survey (5 waves, 1992-2012) comprising 85,575 individuals aged 18 years. Height, weight, and smoking status were self-reported. We used multinomial logistic regression to analyse differences in lifestyle for the combinations of BMI category and smoking status, focusing on obese and heavy smokers. We defined normal-weight never smokers as reference.

Heat Source Estimation with the Conjugate Gradient Method in Inverse Linear Diffusive Problems

In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms, with no prior information of the functional forms of timewise and spatial dependence of the source strength, using the conjugate gradient method with an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems: a one-dimensional cylindrical problem; a two-dimensional cylindrical problem; and a one-dimensional problem with two plates.

Smallholder pig production systems along a periurban-rural gradient in the Western provinces of the Democratic Republic of the Congo

In the Democratic Republic of the Congo (DRC), pigs are raised almost exclusively by smallholders either in periurban areas of major cities such as Kinshasa or in rural villages. Unfortunately, little information is available regarding pig production in the Western part of the DRC, wherefore a survey was carried out to characterize and compare 319 pig production systems in their management and feeding strategies, along a periurban - rural gradient inWestern provinces of the DRC. Pig breeding was the main source of income (43%) and half of respondents were active in mixed pig and crop production, mainly vegetable garden. Depending on the location, smallholders owned on average 18 pigs, including four sows. Piglet mortality rate varied from 9.5 to 21.8% while average weaned age ranged between 2.2 and 2.8 months. The major causes of mortality reported by the farmers were African swine fever 98 %, swine erysipelas (60 %), erysipelas trypanosomiasis (31 %), swine worm infection (17 %), and diarrhoea (12 %). The majority of the pigs were reared in pens without free roaming and fed essentially with locally available by-products and forage plants whose nature varied according with the location of the farm. The pig production systems depended on the local environment; particularly in terms of workforces, herd structure and characteristics, production parameters, pig building materials, selling price and in feed resources. It can be concluded that an improvement of Congolese pig production systems should consider (1) a reduction of inbreeding, (2) an improvement in biosafety to reduce the incidence of African swine fever and the spread of other diseases, and (3) an improvement in feeding practices.

Gradient-based reinforcement learning techniques for underwater robotics behavior learning

Darrerament, l'interès pel desenvolupament d'aplicacions amb robots submarins autònoms (AUV) ha crescut de forma considerable. Els AUVs són atractius gràcies al seu tamany i el fet que no necessiten un operador humà per pilotar-los. Tot i això, és impossible comparar, en termes d'eficiència i flexibilitat, l'habilitat d'un pilot humà amb les escasses capacitats operatives que ofereixen els AUVs actuals. L'utilització de AUVs per cobrir grans àrees implica resoldre problemes complexos, especialment si es desitja que el nostre robot reaccioni en temps real a canvis sobtats en les condicions de treball. Per aquestes raons, el desenvolupament de sistemes de control autònom amb l'objectiu de millorar aquestes capacitats ha esdevingut una prioritat. Aquesta tesi tracta sobre el problema de la presa de decisions utilizant AUVs. El treball presentat es centra en l'estudi, disseny i aplicació de comportaments per a AUVs utilitzant tècniques d'aprenentatge per reforç (RL). La contribució principal d'aquesta tesi consisteix en l'aplicació de diverses tècniques de RL per tal de millorar l'autonomia dels robots submarins, amb l'objectiu final de demostrar la viabilitat d'aquests algoritmes per aprendre tasques submarines autònomes en temps real. En RL, el robot intenta maximitzar un reforç escalar obtingut com a conseqüència de la seva interacció amb l'entorn. L'objectiu és trobar una política òptima que relaciona tots els estats possibles amb les accions a executar per a cada estat que maximitzen la suma de reforços totals. Així, aquesta tesi investiga principalment dues tipologies d'algoritmes basats en RL: mètodes basats en funcions de valor (VF) i mètodes basats en el gradient (PG). Els resultats experimentals finals mostren el robot submarí Ictineu en una tasca autònoma real de seguiment de cables submarins. Per portar-la a terme, s'ha dissenyat un algoritme anomenat mètode d'Actor i Crític (AC), fruit de la fusió de mètodes VF amb tècniques de PG.

Analytical attitude propagation with non-singular variables and gravity gradient torque for spin stabilized satellite

An analytical approach for the spin stabilized satellite attitude propagation is presented using the non-singular canonical variables to describe the rotational motion. Two sets of variables were introduced for Fukushima in 1994 by a canonical transformation and they are useful when the angle between z-satellite axis of a coordinate system fixed in artificial satellite and the rotational angular momentum vector is zero or when the angle between Z-equatorial axis and rotation angular momentum vector is zero. Analytical solutions for rotational motion equations and torque-free motion are discussed in terms of the elliptic functions and by the application of some simplification to get an approximated solution. These solutions are compared with a numerical solution and the results show a good agreement for many rotation periods. When the mean Hamiltonian associated with the gravity gradient torque is included, an analytical solution is obtained by the application of the successive approximations' method for the satellite in an elliptical orbit. These solutions show that the magnitude of the rotation angular moment is not affected by the gravity gradient torque but this torque causes linear and periodic variations in the angular variables, long and short periodic variations in Z-equatorial component of the rotation angular moment and short periodic variations in x-satellite component of the rotation angular moment. The goal of this analysis is to emphasize the geometrical and physical meaning of the non-singular variables and to validate the approximated analytical solution for the rotational motion without elliptic functions for a non-symmetrical satellite. The analysis can be applied for spin stabilized satellite and in this case the general solution and the approximated solution are coincidence. Then the results can be used in analysis of the space mission of the Brazilian Satellites. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Influence of the resonance in a gravity-gradient stabilized satellite

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A note on the local power of the LR, Wald, score and gradient tests

This paper examines the local power of the likelihood ratio, Wald, score and gradient tests under the presence of a scalar parameter, phi say, that is orthogonal to the remaining parameters. We show that some of the coefficients that define the local powers remain unchanged regardless of whether phi is known or needs to be estimated, where as the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if phi were known, and the second, an additional term yielded by the fact that phi is unknown. The contribution of each set of parameters on the local powers of the tests can then be examined. Various implications of our main result are stated and discussed. Several examples are presented for illustrative purposes