An error estimate of Gaussian Recursive Filter in 3Dvar problem

Computational kernel of the three-dimensional variational data assimilation (3D-Var) problem is a linear system, generally solved by means of an iterative method. The most costly part of each iterative step is a matrix-vector product with a very large covariance matrix having Gaussian correlation structure. This operation may be interpreted as a Gaussian convolution, that is a very expensive numerical kernel. Recursive Filters (RFs) are a well known way to approximate the Gaussian convolution and are intensively applied in the meteorology, in the oceanography and in forecast models. In this paper, we deal with an oceanographic 3D-Var data assimilation scheme, named OceanVar, where the linear system is solved by using the Conjugate Gradient (GC) method by replacing, at each step, the Gaussian convolution with RFs. Here we give theoretical issues on the discrete convolution approximation with a first order (1st-RF) and a third order (3rd-RF) recursive filters. Numerical experiments confirm given error bounds and show the benefits, in terms of accuracy and performance, of the 3-rd RF.Comment: 9 page

One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in RN^N

In this paper, we prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R N , as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. We also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities

Estimative for the size of the compactification radius of a one extra dimension Universe

In this work, we use the Casimir effect to probe the existence of one extra dimension. We begin by evaluating the Casimir pressure between two plates in a $M^4\times S^1$ manifold, and then use an appropriate statistical analysis in order to compare the theoretical expression with a recent experimental data and set bounds for the compactification radius

Time-dependent Robin boundary conditions in the dynamical Casimir effect

Motivated by experiments in which moving boundaries are simulated by time-dependent properties of static systems, we discuss the model of a massless scalar field submitted to a time-dependent Robin boundary condition (BC) at a static mirror in 1+1 dimensions. Using a perturbative approach, we compute the spectral distribution of the created particles and the total particle creation rate, considering a thermal state as the initial field state.Comment: 10 pages, 3 figures. To appear in proceedings of Conference on Quantum Field Theory under the Influence of External Condition

Drying kinetics and physico-chemical quality of mango slices

Mango (Mangifera indica L.) is an important tropical fruit consumed worldwide and grown in Italy only in Sicily, where the areas of the Tyrrhenian coast have proved to be suitable to produce valuable fruits. Mango fruit has a pleasant aroma and taste, which are important qualities for consumer’s sensorial acceptance. However, they are highly perishable, prone to progressive undesired changes if stored untreated, resulting in around 25% postharvest losses, which is further increased during storage and transportation. An alternative for reducing the above-mentioned undesired changes is the dehydration of the cut fruit, which reduce the fruit water activity, thereby avoiding the deteriorative process and extending the shelf-life. This study investigates the effect of dehydration at different temperatures (50, 60 and 70°C) on drying kinetics and volatile compounds of two cultivars (Keitt and Osteen) of mango fruits cultivated in Sicily. Significant losses of volatile constituents of fresh mango occurred at higher temperature, especially for the Osteen cultivar. A diffusion model including the effect of shrinkage is also proposed, which may be used to describe drying behaviour of fruits and to define the optimal drying conditions.. Experimental data of the moisture ratio during drying were well predicted by the model