Non-universal Casimir Forces at Approach to Bose–Einstein Condensation of an Ideal Gas: Effect of Dirichlet Boundary Conditions

We analyze the Casimir forces for an ideal Bose gas enclosed between two infinite parallel walls separated by the distance D. The walls are characterized by the Dirichlet boundary conditions. We show that if the thermodynamic state with Bose–Einstein condensate present is correctly approached along the path pertinent to the Dirichlet b.c. then the leading term describing the large-distance decay of thermal Casimir force between the walls is ∼ 1 / D2 with a non-universal amplitude. The next order correction is ∼ ln D/ D3. These observations remain in contrast with the decay law for both the periodic and Neumann boundary conditions for which the leading term is ∼ 1 / D3 with a universal amplitude. We associate this discrepancy with the D-dependent positive value of the one-particle ground state energy in the case of Dirichlet boundary conditions.SCOPUS: ar.jDecretOANoAutActifinfo:eu-repo/semantics/publishe

On the importance of training methods and ensemble aggregation for runoff prediction by means of artificial neural networks

<p>Artificial neural networks (ANNs) become widely used for runoff forecasting in numerous studies. Usually classical gradient-based methods are applied in ANN training and a single ANN model is used. To improve the modelling performance, in some papers ensemble aggregation approaches are used whilst in others, novel training methods are proposed. In this study, the usefulness of both concepts is analysed. First, the applicability of a large number of population-based metaheuristics to ANN training for runoff forecasting is tested on data collected from four catchments, namely upper Annapolis (Nova Scotia, Canada), Biala Tarnowska (Poland), upper Allier (France) and Axe Creek (Victoria, Australia). Then, the importance of the search for novel training methods is compared with the importance of the use of a very simple ANN ensemble aggregation approach. It is shown that although some metaheuristics may slightly outperform the classical gradient-based Levenberg-Marquardt algorithm for a specific catchment, none performs better for the majority of the tested ones. One may also point out a few metaheuristics that do not suit ANN training at all. On the other hand, application of even the simplest ensemble aggregation approach clearly improves the results when the ensemble members are trained by any suitable algorithms.</p><p><b>EDITOR</b> D. Koutsoyiannis; <b>ASSOCIATE EDITOR</b> E. Toth</p><p></p> <p><b>EDITOR</b> D. Koutsoyiannis; <b>ASSOCIATE EDITOR</b> E. Toth</p