C-MEMS Based Micro Enzymatic Biofuel Cells

Miniaturized, self-sufficient bioelectronics powered by unconventional micropower may lead to a new generation of implantable, wireless, minimally invasive medical devices, such as pacemakers, defibrillators, drug-delivering pumps, sensor transmitters, and neurostimulators. Studies have shown that micro-enzymatic biofuel cells (EBFCs) are among the most intuitive candidates for in vivo micropower. In the fisrt part of this thesis, the prototype design of an EBFC chip, having 3D intedigitated microelectrode arrays was proposed to obtain an optimum design of 3D microelectrode arrays for carbon microelectromechanical systems (C-MEMS) based EBFCs. A detailed modeling solving partial differential equations (PDEs) by finite element techniques has been developed on the effect of 1) dimensions of microelectrodes, 2) spatial arrangement of 3D microelectrode arrays, 3) geometry of microelectrode on the EBFC performance based on COMSOL Multiphysics. In the second part of this thesis, in order to investigate the performance of an EBFC, behavior of an EBFC chip performance inside an artery has been studied. COMSOL Multiphysics software has also been applied to analyze mass transport for different orientations of an EBFC chip inside a blood artery. Two orientations: horizontal position (HP) and vertical position (VP) have been analyzed. The third part of this thesis has been focused on experimental work towards high performance EBFC. This work has integrated graphene/enzyme onto three-dimensional (3D) micropillar arrays in order to obtain efficient enzyme immobilization, enhanced enzyme loading and facilitate direct electron transfer. The developed 3D graphene/enzyme network based EBFC generated a maximum power density of 136.3 μWcm-2 at 0.59 V, which is almost 7 times of the maximum power density of the bare 3D carbon micropillar arrays based EBFC. To further improve the EBFC performance, reduced graphene oxide (rGO)/carbon nanotubes (CNTs) has been integrated onto 3D mciropillar arrays to further increase EBFC performance in the fourth part of this thesisThe developed rGO/CNTs based EBFC generated twice the maximum power density of rGO based EBFC. Through a comparison of experimental and theoretical results, the cell performance efficiency is noted to be 67%.

Ion-acoustic envelope modes in a degenerate relativistic electron-ion plasma

A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schrödinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case - in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed.

Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico

LINS, Filipe C. A. et al. Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico. In: CONGRESSO BRASILEIRO DE PESQUISA E DESENVOLVIMENTO EM PETRÓLEO E GÁS, 5. 2009, Fortaleza, CE. Anais... Fortaleza: CBPDPetro, 2009.

Funzioni di Sobolev

In questa tesi cercherò di analizzare le funzioni di Sobolev su R}^{n}, seguendo le trattazioni Measure Theory and Fine Properties of Functions di L.C. Evans e R.F.Gariepy e l'elaborato Functional Analysis, Sobolev Spaces and Partial Differential Equations di H. Brezis. Le funzioni di Sobolev si caratterizzano per essere funzioni con le derivate prime deboli appartenenti a qualche spazio L^{p}. I vari spazi di Sobolev hanno buone proprietà di completezza e compattezza e conseguentemente sono spesso i giusti spazi per le applicazioni di analisi funzionale. Ora, come vedremo, per definizione, l'integrazione per parti è valida per le funzioni di Sobolev. È, invece, meno ovvio che altre regole di calcolo siano allo stesso modo valide. Così, ho inteso chiarire questa questione di carattere generale, con particolare attenzione alle proprietà puntuali delle funzioni di Sobolev. Abbiamo suddiviso il lavoro svolto in cinque capitoli. Il capitolo 1 contiene le definizioni di base necessarie per la trattazione svolta; nel secondo capitolo sono stati derivati vari modi di approssimazione delle funzioni di Sobolev con funzioni lisce e sono state fornite alcune regole di calcolo per tali funzioni. Il capitolo 3 darà un' interpretazione dei valori al bordo delle funzioni di Sobolev utilizzando l'operatore Traccia, mentre il capitolo 4 discute l' estensione su tutto R^{n} di tali funzioni. Proveremo infine le principali disuguaglianze di Sobolev nel Capitolo 5.

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

A Discretization of the Hadamard fractional derivative

We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the Hadamard fractional derivative.

The parallel solution of early-exercise Asian options with stochastic volatility

This paper describes an parallel semi-Lagrangian finite difference approach to the pricing of early exercise Asian Options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices. Asian options are contingent claims with payoffs that depend on the average price of an asset over some time interval. The payoff may depend on this average and a fixed strike price (Fixed Strike Asians) or it may depend on the average and the asset price (Floating Strike Asians). The option may also permit early exercise (American contract) or confine the holder to a fixed exercise date (European contract). The Fixed Strike Asian with early exercise is considered here where continuous arithmetic averaging has been used. Pricing such an option where the asset price has a stochastic volatility leads to the requirement to solve a tri-variate partial differential inequation in the three state variables of asset price, average price and volatility (or equivalently, variance). The similarity transformations [6] used with Floating Strike Asian options to reduce the dimensionality of the problem are not applicable to Fixed Strikes and so the numerical solution of a tri-variate problem is necessary. The computational challenge is to provide accurate solutions sufficiently quickly to support realtime trading activities at a reasonable cost in terms of hardware requirements.

Waves, bumps, and patterns in neural field theories

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons.

Analytical and Experimental Investigation of an Ammonia/Air Opposed Reacting Jet

The point-by-point properties of an ammonia/air opposed-reacting-jet flowfield are described by solving the governing partial differential elliptic equations. Analytical descriptions of the reacting flowfield are compared to experimentally measured profiles of temperature and composition. Calculated distributions of stream function, temperature and fuel mole fraction are also presented. © 1972, Taylor & Francis Group, LLC. All rights reserved.

Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico

LINS, Filipe C. A. et al. Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico. In: CONGRESSO BRASILEIRO DE PESQUISA E DESENVOLVIMENTO EM PETRÓLEO E GÁS, 5. 2009, Fortaleza, CE. Anais... Fortaleza: CBPDPetro, 2009.

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement. The theoretical results are illustrated by a series of numerical experiments.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite element spaces employed. In particular, we prove a priori hp-error bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensor-product polynomial basis functions. The theoretical results are illustrated by a numerical experiment.

A bistable reaction-diffusion system in a stretching flow

We examine the evolution of a bistable reaction in a one-dimensional stretching flow, as a model for chaotic advection. We derive two reduced systems of ordinary differential equations (ODEs) for the dynamics of the governing advection-reaction-diffusion partial differential equations (PDE), for pulse-like and for plateau-like solutions, based on a non-perturbative approach. This reduction allows us to study the dynamics in two cases: first, close to a saddle-node bifurcation at which a pair of nontrivial steady states are born as the dimensionless reaction rate (Damkoehler number) is increased, and, second, for large Damkoehler number, far away from the bifurcation. The main aim is to investigate the initial-value problem and to determine when an initial condition subject to chaotic stirring will decay to zero and when it will give rise to a nonzero final state. Comparisons with full PDE simulations show that the reduced pulse model accurately predicts the threshold amplitude for a pulse initial condition to give rise to a nontrivial final steady state, and that the reduced plateau model gives an accurate picture of the dynamics of the system at large Damkoehler number. Published in Physica D (2006)