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.

Italy's urban waste metabolism

The problem of waste management is causing growing concern due to increasing generation rates, the emissions into soil, water and air, the social conflicts derived from the election of disposal sites and the loss of resources and energy among others. In this work, an innovative methodology is used to enable a better understanding of the waste generation and management system in Italy. Two new waste indicators are built to complement the conventional indicators used by official statistics. Then a multi-scale analysis of the Density of Waste Disposed (DWD) is carried out to highlight the territorial diversity of waste performances and test its contribution to detect plausible risky areas. Starting from Italian regions, the scale down goes on to the provincial level and, only for the region of Campania, the municipal one. First, the analysis shows that the DWD is able to complement the information provided by the conventional waste indicators. Second, the analysis shows the limitations of using a unique institutional solution to waste management problems. In this sense the multi-scale analysis provides with a more realistic picture of Italian waste system than using a single scale.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

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.

Recepció de literatura infantil i juvenil anglosaxona a la Catalunya noucentista: Treasure Island

Translation during the noucentisme was a very important resource for standardising the modern Catalan language and for filling in the historical gaps of Catalan Literature. The literati of the noucentisme looked to Europe to find works that had similar ideals to their own and that could be presented in Catalonia to educate and instruct its new generations. The translation of children and young adults’ literature, therefore, formed a major part of the project. Together with the best writers and illustrators of the period and the support of the publishing industry, the golden era in the history of children and young adults’ literature emerged. In this project our aim is to study the reception of British children and young adults’ literature during the noucentisme. This will be done by using Treasure Island and two of its translations, the first of which is from 1926 by Joan Arús and the second from 2008 by Joan Sellent. Cultural references and the illustrations will be analysed, and we shall ascertain whether the two translators and illustrators used domesticating or foreignising strategies and whether they followed the tendencies of translation of children and young adults’ literature.