Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities

We analyze the rate of convergence towards self-similarity for the subcritical Keller-Segel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a proof of the logarithmic Hardy-Littlewood-Sobolev inequality in the one dimensional and radially symmetric two dimensional case based on optimal transport arguments. In addition we prove that the onedimensional equation is a contraction with respect to Fourier distance in the subcritical case.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Síntesi i control de qualitat de biodièsel

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. Aquest treball té com a base donar les pautes necessàries per a l'obtenció de biodièsel i determinar-ne la seva acceptabilitat. Per tal de que això sigui possible, s'han sintetitzat biodièsels provinents d'oli de girasol refinat, d'oli d'oliva refinat, i d'aquests mateixos fregits al emprar-los al cuinar. Un cop sintetitzats se'ls hi ha realitzat una sèrie d'anàlisis fisicoquímics per tal de determinar-ne la seva acceptabilitat mitjançant una comparativa amb els resultats obtinguts amb un dièsel comercial, així com amb els límits que marca la unió europea en l'esborrany final de la norma prEN 14214.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

Processament de música basat en el seu contingut

Projecte de recerca elaborat a partir d’una estada a la National University of Singapore Singapur, entre juliol i octubre del 2007. Donada l'explosió de la música a l'internet i la ràpida expansió de les col•leccions de música digital, un repte clau en l'àrea de la informació musical és el desenvolupament de sistemes de processament musical eficients i confiables. L'objectiu de la investigació proposada ha estat treballar en diferents aspectes de l'extracció, modelatge i processat del contingut musical. En particular, s’ha treballat en l'extracció, l'anàlisi i la manipulació de descriptors d'àudio de baix nivell, el modelatge de processos musicals, l'estudi i desenvolupament de tècniques d'aprenentatge automàtic per a processar àudio, i la identificació i extracció d'atributs musicals d'alt nivell. S’han revisat i millorat alguns components d'anàlisis d'àudio i revisat components per a l'extracció de descriptors inter-nota i intra-nota en enregistraments monofónics d'àudio. S’ha aplicat treball previ en Tempo a la formalització de diferents tasques musicals. Finalment, s’ha investigat el processat d'alt nivell de música basandonos en el seu contingut. Com exemple d'això, s’ha investigat com músics professionals expressen i comuniquen la seva interpretació del contingut musical i emocional de peces musicals, i hem usat aquesta informació per a identificar automàticament intèrprets. S’han estudiat les desviacions en paràmetres com to, temps, amplitud i timbre a nivell inter-nota i intra-nota.

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densitiesby generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

A system to evaluate the accuracy of a visual mosaicking methodology

When underwater vehicles navigate close to the ocean floor, computer vision techniques can be applied to obtain motion estimates. A complete system to create visual mosaics of the seabed is described in this paper. Unfortunately, the accuracy of the constructed mosaic is difficult to evaluate. The use of a laboratory setup to obtain an accurate error measurement is proposed. The system consists on a robot arm carrying a downward looking camera. A pattern formed by a white background and a matrix of black dots uniformly distributed along the surveyed scene is used to find the exact image registration parameters. When the robot executes a trajectory (simulating the motion of a submersible), an image sequence is acquired by the camera. The estimated motion computed from the encoders of the robot is refined by detecting, to subpixel accuracy, the black dots of the image sequence, and computing the 2D projective transform which relates two consecutive images. The pattern is then substituted by a poster of the sea floor and the trajectory is executed again, acquiring the image sequence used to test the accuracy of the mosaicking system

High-SNR power offset in multiantenna communication

The analysis of the multiantenna capacity in the high-SNR regime has hitherto focused on the high-SNR slope (or maximum multiplexing gain), which quantifies the multiplicative increase as function of the number of antennas. This traditional characterization is unable to assess the impact of prominent channel features since, for a majority of channels, the slope equals the minimum of the number of transmit and receive antennas. Furthermore, a characterization based solely on the slope captures only the scaling but it has no notion of the power required for a certain capacity. This paper advocates a more refined characterization whereby, as function of SNRjdB, the high-SNR capacity is expanded as an affine function where the impact of channel features such as antenna correlation, unfaded components, etc, resides in the zero-order term or power offset. The power offset, for which we find insightful closed-form expressions, is shown to play a chief role for SNR levels of practical interest.

Job satisfaction and life satisfaction: Analysis of a reciprocal model with social demographic moderators

The general objective of the study was to empirically test a reciprocal model of job satisfaction and life satisfaction while controlling for some social demographic variables. 827 employees working in 34 car dealerships in Northern Quebec (56% responses rate) were surveyed. The multiple item questionnaires were analysed using correlation analysis, chi square and ANOVAs. Results show interesting patterns emerging for the relationships between job and life satisfaction of which 49.2% of all individuals have spillover, 43.5% compensation, and 7.3% segmentation type of relationships. Results, nonetheless, are far richer and the model becomes much more refined when social demographic indicators are taken into account. Globally, social demographic variables demonstrate some effects on each satisfaction individually but also on the interrelation (nature of the relations) between life and work satisfaction.

On Rothschild-Stiglitz as competitive pooling

Dubey and Geanakoplos [2002] have developed a theory of competitive pooling, which incorporates adverse selection and signaling into general equilibrium. By recasting the Rothschild-Stiglitz model of insurance in this framework, they find that a separating equilibrium always exists and is unique.We prove that their uniqueness result is not a consequence of the framework, but rather of their definition of refined equilibria. When other types of perturbations are used, the model allows for many pooling allocations to be supported as such: in particular, this is the case for pooling allocations that Pareto dominate the separating equilibrium.

Adaptive dynamics and the implementation problem with complete information

This paper studies the equilibrating process of several implementationmechanisms using naive adaptive dynamics. We show that the dynamics convergeand are stable, for the canonical mechanism of implementation in Nash equilibrium.In this way we cast some doubt on the criticism of ``complexity'' commonlyused against this mechanism. For mechanisms that use more refined equilibrium concepts,the dynamics converge but are not stable. Some papers in the literatureon implementation with refined equilibrium concepts have claimed that themechanisms they propose are ``simple'' and implement ``everything'' (incontrast with the canonical mechanism). The fact that some of these ``simple''mechanisms have unstable equilibria suggests that these statements shouldbe interpreted with some caution.

Max-convex decompositions for cooperative TU games

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with non-negative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition

Seasonal dependence in the solar neutrino flux

Mikheyev-Smirnov-Wolfenstein (MSW) solutions of the solar neutrino problem predict a seasonal dependence of the zenith angle distribution of the event rates, due to the nonzero latitude at the Super-Kamiokande site. We calculate this seasonal dependence and compare it with the expectations in the no-oscillation case as well as just-so scenario, in the light of the latest Super-Kamiokande 708-day data. The seasonal dependence can be sizable in the large mixing angle MSW solution and would be correlated with the day-night effect. This may be used to discriminate between MSW and just-so scenarios and should be taken into account in refined fits of the data.