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A null controllability data assimilation methodology applied to a large scale ocean circulation model*

Galina C. García, Axel Osses, Jean Pierre Puel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris335 (2002) 161–166] and [Puel, SIAM J. Control Optim.48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...

A rainfall forecasting method using machine learning models and its application to the Fukuoka city case

S. Monira Sumi, M. Faisal Zaman, Hideo Hirose (2012)

International Journal of Applied Mathematics and Computer Science

In the present article, an attempt is made to derive optimal data-driven machine learning methods for forecasting an average daily and monthly rainfall of the Fukuoka city in Japan. This comparative study is conducted concentrating on three aspects: modelling inputs, modelling methods and pre-processing techniques. A comparison between linear correlation analysis and average mutual information is made to find an optimal input technique. For the modelling of the rainfall, a novel hybrid multi-model...

A reduced model for Darcy’s problem in networks of fractures

Luca Formaggia, Alessio Fumagalli, Anna Scotti, Paolo Ruffo (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Subsurface flows are influenced by the presence of faults and large fractures which act as preferential paths or barriers for the flow. In literature models were proposed to handle fractures in a porous medium as objects of codimension 1. In this work we consider the case of a network of intersecting fractures, with the aim of deriving physically consistent and effective interface conditions to impose at the intersection between fractures. This new model accounts for the angle between fractures...

A review on the improved regularity for the primitive equations

Francisco Guillén-González, María Ángeles Rodríguez-Bellido (2005)

Banach Center Publications

In this work we will study some types of regularity properties of solutions for the geophysical model of hydrostatic Navier-Stokes equations, the so-called Primitive Equations (PE). Also, we will present some results about uniqueness and asymptotic behavior in time.

A simple mechanical model to analyse the rocking and sliding response of rigid blocks to earthquakes

Giancarlo Bilotti, Leonardo Giliberti (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In order to study the effects of earthquakes on tombstones and monumental columns in recent years the dynamical analysis of rigid blocks subjected to ground accelerations has interested many researchers. Mainly, the rocking motion has been investigated and many numerical difficulties have been pointed out in such analysis [1-2-3-4]. Some computational advantages can be obtained by modelling the bonding between two blocks or between block and foundation by means of an elastic layer of Winkler's springs...

A stationary flow of fresh and salt groundwater in a heterogeneous coastal aquifer

S. Challal, A. Lyaghfouri (2000)

Bollettino dell'Unione Matematica Italiana

Si stabilisce l'esistenza e l'unicità di una soluzione monotona per il problema di frontiera libera correlato al flusso stazionare d'acqua dolce e salata intorno ad un acquifero eterogeneo. Si provano la continuità e l'esistenza di un limite asintotico della frontiera libera.

A strongly nonlinear problem arising in glaciology

Jacques Colinge, Jacques Rappaz (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The computation of glacier movements leads to a system of nonlinear partial differential equations. The existence and uniqueness of a weak solution is established by using the calculus of variations. A discretization by the finite element method is done. The solution of the discrete problem is proved to be convergent to the exact solution. A first simple numerical algorithm is proposed and its convergence numerically studied.

A survey on wavelet methods for (geo) applications.

Willi Freeden, Thorsten Maier, Steffen Zimmermann (2003)

Revista Matemática Complutense

Wavelets originated in 1980's for the analysis of (seismic) signals and have seen an explosion of applications. However, almost all the material is based on wavelets over Euclidean spaces. This paper deals with an approach to the theory and algorithmic aspects of wavelets in a general separable Hilbert space framework. As examples Legendre wavelets on the interval [-1,+1] and scalar and vector spherical wavelets on the unit sphere 'Omega' are discussed in more detail.

Adaptive modeling for free-surface flows

Simona Perotto (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

This work represents a first step towards the simulation of the motion of water in a complex hydrodynamic configuration, such as a channel network or a river delta, by means of a suitable “combination” of different mathematical models. In this framework a wide spectrum of space and time scales is involved due to the presence of physical phenomena of different nature. Ideally, moving from a hierarchy of hydrodynamic models, one should solve throughout the whole domain the most complex model (with...

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