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.

Estudi energètic de les llars del barri de Haër (Senegal)

En el present estudi s’han analitzat quines són les fonts energètiques utilitzades a les llars de Haër, així com les repercussions que aquestes tenen sobre el medi natural i socioeconòmic de les famílies. Per tal de poder identificar quines són aquestes fonts i els seus efectes, s’ha realitzat un inventari i una diagnosi energètica. S’ha estudiat l’ús de l’energia en dos àmbits domèstics principals: la il·luminació i el cuinat, analitzant la freqüència d’ús i quantificant el consum energètic familiar. Les fonts energètiques detectades són: llenya, carbó, gas, querosè, piles i espelmes, de les quals, la llenya, el querosè i el carbó són les majoritàriament utilitzades. El consum energètic per càpita és de 2.100 kWh/any. Per altra banda, l’obtenció d’algunes d’aquestes fonts energètiques, suposen un cost econòmic molt elevat per les economies familiars, arribant a suposar un 60% dels ingressos. A partir de les dades obtingudes a la diagnosi, s’ha aplicat un indicador per tal de quantificar la magnitud de l’impacte sobre el medi produït pel model energètic seguit dins de les llars. L’indicador estudiat ha estat la petjada energètica, amb la qual s’ha traduït aquest consum en unitats de superfície biològicament productiva, requerida per absorbir el CO2 emès. El resultat ha estat que una persona produeix anualment 2,09·10-2 tCO2, que requereix de 7,53·10-3 gha/persona de superfície forestal per ser absorbides. S’ha comparat aquest resultat amb la petjada energètica domèstica calculada pel poble d’Araós, el qual, amb un model energètic totalment diferent, té una petjada energètica de 1,53 gha/persona. Un cop detectats els problemes o impactes causats pel model energètic actual, es proposa una alternativa energètica per tal de reemplaçar algunes fonts convencionals, principalment el querosè dels quinqués. Així doncs, mitjançant l’aprofitament de l’energia solar, es plantegen dos models fotovoltaics adaptats a dues tipologies de llars diferents, amb l’objectiu de minimitzar el cost i optimitzar els recursos energètics. Finalment es planteja una solució financera per abordar el cost inicial de la instal·lació solar.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

On slicewise monotone parameterized problems and optimal proof systems for TAUT

"Vegeu el resum a l'inici del document del fitxer adjunt"

Application of the combined integral method to Stefan problems

In this paper we present a new, accurate form of the heat balance integral method, termed the Combined Integral Method (or CIM). The application of this method to Stefan problems is discussed. For simple test cases the results are compared with exact and asymptotic limits. In particular, it is shown that the CIM is more accurate than the second order, large Stefan number, perturbation solution for a wide range of Stefan numbers. In the initial examples it is shown that the CIM reduces the standard problem, consisting of a PDE defined over a domain specified by an ODE, to the solution of one or two algebraic equations. The latter examples, where the boundary temperature varies with time, reduce to a set of three first order ODEs.

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.

An axiomatic justification of mediation in bankruptcy problems.

This paper provides a natural way of reaching an agreement between two prominent proposals in a bankruptcy problem. Particularly, using the fact that such problems can be faced from two different points of views, awards and losses, we justify the average of any pair of dual bankruptcy rules through the definition a double recursive process. Finally, by considering three posible sets of equity principles that a particular society may agree on, we retrieve the average of old and well known bankruptcy rules, the Constrained Equal Awards and the Constrained Equal Losses rules, Piniles’ rule and its dual rule, and the Constrained Egalitarian rule and its dual rule. Keywords: Bankruptcy problems, Midpoint, Bounds, Duality, Recursivity. JEL classification: C71, D63, D71.

A way to play bankruptcy problems.

The commitment among agents has always been a difficult task, especially when they have to decide how to distribute the available amount of a scarce resource among all. On the one hand, there are a multiplicity of possible ways for assigning the available amount; and, on the other hand, each agent is going to propose that distribution which provides her the highest possible award. In this paper, with the purpose of making this agreement easier, firstly we use two different sets of basic properties, called Commonly Accepted Equity Principles, to delimit what agents can propose as reasonable allocations. Secondly, we extend the results obtained by Chun (1989) and Herrero (2003), obtaining new characterizations of old and well known bankruptcy rules. Finally, using the fact that bankruptcy problems can be analyzed from awards and losses, we define a mechanism which provides a new justification of the convex combinations of bankruptcy rules. Keywords: Bankruptcy problems, Unanimous Concessions procedure, Diminishing Claims mechanism, Piniles’ rule, Constrained Egalitarian rule. JEL classification: C71, D63, D71.

A Proportional Approach to Bankruptcy Problems with a guaranteed minimum

In a distribution problem, and specfii cally in bankruptcy issues, the Proportional (P) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. The Constrained Equal Awards rule (CEA) is introduced in bankruptcy literature to ensure that no agent receives more than her claim, a problem that can arise when using the egalitarian division. We propose an alternative modi cation, by using a convex combination of P and EA. The recursive application of this new rule finishes at the CEA rule. Our solution concept ensures a minimum amount to each agent, and distributes the remaining estate in a proportional way. Keywords: Bankruptcy problems, Proportional rule, Equal Awards, Convex combination of rules, Lorenz dominance. JEL classi fication: C71, D63, D71.

Solidarity and uniform rules in bankruptcy problems

The idea of ensuring a guarantee (a minimum amount of the resources) to each agent has recently acquired great relevance, in both social and politi- cal terms. Furthermore, the notion of Solidarity has been treated frequently in redistribution problems to establish that any increment of the resources should be equally distributed taking into account some relevant characteris- tics. In this paper, we combine these two general concepts, guarantee and solidarity, to characterize the uniform rules in bankruptcy problems (Con- strained Equal Awards and Constrained Equal Losses rules). Keywords: Constrained Equal Awards, Constrained Equal Losses, Lower bounds, Bankruptcy problems, Solidarity. JEL classification: C71, D63, D71.

A New Approach for Bounding Awards in Bankruptcy Problems

The solution for the ‘Contested Garment Problem’, proposed in the Babylonic Talmud, suggests that each agent should receive at least some part of the resources whenever the demand overcomes the available amount. In this context, we propose a new method to define lower bounds on awards, an idea that has underlied the theoretical analysis of bankruptcy problems from its beginning (O’Neill, 1982) to present day (Dominguez and Thomson, 2006). Specifically, starting from the fact that a society establishes its own set of ‘Commonly Accepted Equity Principles’, our proposal ensures to each agent the smallest amount she gets according to all the admissible rules. As in general this new bound will not exhaust the estate, we analyze its recursive application for different sets of equity principles. Keywords: Bankruptcy problems, Bankruptcy rules, Lower bounds, Recursive process

Family-based affirmative action? Subversion and resilience strategies of gay father families

The present doctoral dissertation is aimed at analyzing how and with what consequences gay father families and their children’s schools negotiate possible differences in the construction of family and gender at home and in the families’ social milieus. This objective fits in with the broader goal of researching how family-school interactons are influenced by the social context such as hegemonic masculinity (Connell, 2002). The thesis is based on qualitative fieldwork carried out with 18 nonheterosexual parent families in Spain, comprising 30 interviews with 44 people. The principal participant group were 14 de novo (adoptive and surrogacy) gay father families with resident preadolescent children. The findings revealed that all the de novo families assumed open communication strategies at school with inclusive consequences: apart from incidental questions and reactions of surprise, the children did not suffer homophobic bullying. The analisis showed that the necessary condition for inclusion was not the open communication but rather illocutionary orientation (Habermas, 1984; Soler & Flecha, 2010), understood as the parents’ sensitivity to the attitudes of their children and schools. The schools received the families in an inclusive manner, which, however, was only receptive and not proactive, therefore some of the families (reconstituted ones), coerced by the social context, got excluded. Gender relations at home were predominantly androgynous, and outside home predominantly traditional, yet the children negotiated this difference with inclusive consequences. They participated in hegemonic collective practices, thus confirming the thesis on the similarity between homo- and heterosexual-parent families (Golombok, 2006). Consistently, also the families’ identity politics was “assimilationist” and non-queer. Admittedly, the analisis showed that such a politics was increased by social expectations. Still, the findings suggest that educational and other family policies should draw on broad agendas of gender and family diversity rather than on the politics of difference and the unique status of LGB families.

Post-adopció i resiliència: l'ajust psicosocial i vivència de l'adopció en infants adoptats internacionalment

Antecedents. Cada cop són més els nens i nenes adoptats internacionalment que creixen en la nostra societat, i el seu ajust psicosocial s’ha convertit en un assumpte d’especial interès i rellevància. Objectius. Estudiar l'ajust psicosocial i la vivència de l'adopció en els infants adoptats internacionalment. Els objectius específics són: 1) estudiar els nivells d’adaptació personal i social en nens i nenes adoptats/des internacionalment, en comparació amb els estàndards de la població normativa; 2) estudiar la vivència de l’adopció en nens i nenes adoptats internacionalment i la percepció que mares i pares en tenen al respecte; 3) analitzar el paper de las variables estrés i estratègies d’afrontament en l’ajust psicosocial dels infants adoptats. Material i Mètode. La mostra està formada per 103 infants adoptats a l’estranger, d’entre 8 i 12 anys, i els seus respectius pares i mares. Els participants completaren les següents proves: BASC (Behavior Assessment System for Children (BASC; Reynolds & Kamphaus, 1992), Qüestionari de punts forts i febles (SDQ; Goodman, 1997, 1999), Escala de la vivència adoptiva (Reinoso, 2008), Kidcope (Spirito, Stara y Williams, 1988). En realitzen anàlisis estadístics de tipus descriptiu, comparatiu, correlacional i exploratori. Resultats. La majoria dels menors adoptats internacionalment presenta bons nivells de funcionament, si bé un 25% d’ells presenta dificultats adaptatives bàsiques. En general s’observa un elevat nivell de convergència en la visió de l’experiència adoptiva entre nens/es i mares i pares. Els infants puntuen més alt en identitat cultural i més baix en discriminació percebuda que els seus pares/mares. Principalment esmenten problemes interpersonals de relació i de salut, malalties i accidents i utilitzen predominantment estratègies d’afrontament aproximatives. Els estressors vinculats amb l’experiència adoptiva són escassament mencionats. Conclusions. L’especificitat de la condició adoptiva requereix d’intervencions ajustades a la realitat d’aquests les necessitats d’aquests nens i les seves families.

Residència Diocesana d'Estudiants : un recurs intermig de suport a la família

Projecte que pretén planificar els serveis que pot oferir la Residència Diocesana d'Estudiants, amb dues condicions: que sigui tècnicament correcta i entri dintre d'uns principis humanístics mínims i que a això se li doni un sentit d'utilitat social i ajudi, expressament, les parts menys afavorides de la societat (no només econòmicament). Entre els serveis proposats consten els següents: un internat de 300 places per a infants i adolescents; la posada en marxa, obertura i utilització d'un antic internat per a fer-ne una mena de centre de recursos alternatius a l'escola (colònies, campaments, estades educatives, etc.), així com també d'una casa de colònies que està creant-se i de dues zones d'acampada (una a la serra, l'altra a la platja); la creació de l'Escola de l'Esplai diocesana (és dels pocs bisbats de Catalunya que no en té, i aquest bisbat abasta també el nord de Castelló); la generació d'un servei per a elaborar els diversos tipus de mediacions que, a hores d'ara, demana la societat, i dels quals s'espera un fort creixement (matrimonis, menors, etc.), i la cerca d'altres serveis que es puguin oferir a menors i a famílies que tinguin dificultats econòmiques (centre d'acolliments familiars, etc.).