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

Sph propagation modelling of an earthflow from southern italy

Natural slopes in clayey soils are often affected by failures which may cause the onset of landslides of the flow type travelling large distances and damaging buildings and major infrastructures. Particularly, the so-called earthflows pose challenging tasks for the individuation and forecasting of the remobilized masses; as a consequence, the mathematical modelling of the propagation stage allows enhancing the understanding of earthflows in order to obtain reliable assessments of run-out distances and displaced soil volumes. This paper deals with the reactivations of Montaguto earthflow (Southern Italy) occurred from 1998 to 2009 that are simulated, through the depth-integrated “GeoFlow-SPH” model, thanks to the availability of a detailed data-set. The achieved results provide a satisfactory agreement with the in-situ information and outline how a change of the rheology of the mobilized masses can affect the whole phenomenon

Improvement of irregular dtm for sph modelling of flow-like landslides

Irregular topography of real slopes largely affects the propagation stage of flowlike landslides and accurate digital terrain models (DTMs) are absolutely necessary for realistic simulations and assessments. In this paper a simple yet effective method is proposed to improve the accuracy of existing DTMs which is applied to the topographical models used in well equipped laboratory experiments. Aimed at evaluating the effects of different DTMs in the results of the propagation modelling, a depth-integrated SPH model is used to simulate two series of laboratory tests referring to a frictional rheological model while using either the available DTM or the DTM improved through the proposed procedure. The obtained results show that the proposed method provides a more accurate topographical model for all the analyzed cases. Particularly, the new topographical model allows better reproducing the laboratory evidences in terms of run-out distances, inundated areas and geometrical characteristics of the final deposits. Furthermore, SPH analyses with progressively finer topographical inputs outline the role of DTM’s precision towards the accuracy of the numerical simulations

On the force density method for slack cable nets

AbstractThe design of cable nets and light tenso-structures requires a non conventional mechanical analysis, due either to the various sources of non linearity (large displacements, unilateral behaviour of the cables, non conservative loads) and to the fact that the initial configuration of the cable net is not known, depending on the prestress applied and, in general, on the dead load acting on it. As a consequence, the first problem that the engineer has to face is to determine the initial state of the structure under its own weight compatible with a set of fixed supports (the so called zero state). This problem is known as form finding.The paper examines the force density method for form finding, and it is presented a generalization that uses the exact expressions of the equilibrium derived from the equation of the catenary. The method allows to obtain an exact configuration that may be used as a starting point for subsequent incremental non linear analyses.In the paper it is shown that the use of the exact equilibrium conditions leads to a form finding method that is very similar to the FDM, but yields significant differences in the initial form when the weight of the cables is not negligible. A dimensionless parameter is introduced as degree of freedom of the form

Slower Speed and Stronger Coupling: Adaptive Mechanisms of Self-Organized Chaos Synchronization

We show that two initially weakly coupled chaotic systems can achieve self-organized synchronization by adaptively reducing their speed and/or enhancing the coupling strength. Explicit adaptive algorithms for speed-reduction and coupling-enhancement are provided. We apply these algorithms to the self-organized synchronization of two coupled Lorenz systems. It is found that after a long-time self-organized process, the two coupled chaotic systems can achieve synchronization with almost minimum required coupling-speed ratio.Comment: 4 pages, 5 figure

Modelling the post-failure stage of rainfall-induced landslides of the flow type

The geomechanical modeling of failure and post failure stages of rainfall induced shallow landslides represents a fundamental issue to properly assess the failure conditions and recognize the potential for long travel distances of the failed soil masses

Correlation between oesophageal acid exposure and dyspeptic symptoms in patients with nonerosive reflux disease.

Oesophageal acidification induces dyspeptic symptoms in healthy individuals. This study aimed to evaluate the correlation between oesophageal acid exposure and dyspeptic symptoms in patients with nonerosive reflux disease. METHODS: A total of 68 patients with dominant symptoms of heartburn, negative upper gastrointestinal endoscopy and concomitant dyspeptic symptoms participated in the study. The severity of dyspepsia and reflux-related symptoms was evaluated, and 24-h gastro-oesophageal pH-monitoring study was performed in all patients at baseline and after 4 weeks of therapy with esomeprazole 40 mg. RESULTS: Oesophageal basal acid exposure was pathological in 43 patients and normal in 25 patients, with a similar prevalence and severity of individual dyspeptic symptoms in the two groups. A significant correlation between reflux and dyspepsia scores was observed in the subgroup of patients with normal, but not in those with abnormal pHmetry (r=0.4, P=0.04 and r=0.2 P=0.07, respectively). After esomeprazole, a reduction in severity of dyspepsia (>or=50% with respect to baseline) was observed, independent of improvement of reflux-associated symptoms. Improvement in dyspepsia was, however, similar in patients with normal and abnormal basal acid exposure (14/25 vs. 33/43, respectively, P=NS). CONCLUSION: Dyspeptic symptoms coexist in a subset of nonerosive reflux disease patients, but prevalence and severity of the symptoms seems to be independent of oesophageal acid exposure

Synchronization Based Approach for Estimating All Model Parameters of Chaotic Systems

The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of noise, enables online estimation of the parameters and is also able to rapidly track changes in operating parameters of the experimental system. The method is demonstrated using the Lorenz, Rossler chaos and hyperchaos models. Its possible application in decoding communications using chaos is discussed.Comment: 13 pages, 4 figure