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...

Las dunas (del desierto o en los ríos) son montículos de arena formados por la acción erosiva del viento (o del agua) sobre el substrato móvil subyacente. Los drumlins son pequeñas colinas que se forman de manera parecida por la acción erosiva de los casquetes polares en los sedimentos móviles de la base, particularmente durante las eras glaciales. Estas formaciones son causadas por una inestabilidad en el sistema acoplado que relaciona la evolución del lecho con las fuerzas de cizalla ejercidas...

This paper addresses fault-tolerant control for position mooring of a shuttle or floating production storage and offloading vessels. A complete framework for fault diagnosis is presented. A loss of a sub-sea mooring line buoyancy element and line breakage are given particular attention, since such failures might cause high-risk abortion of an oil-loading operation. With significant drift forces from waves, non-Gaussian elements dominate forces and the residuals designed for fault diagnosis. Hypothesis...

In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of $L$ lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness $h$, the $L$ surface concentrations $c_i^s$ in lithology $i$ of the sediments at the top...

In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of L lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness h, the L surface concentrations $c_i^s$ in lithology i of the sediments at the...

This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type $0\in {\partial }_{t}u-div\left\{H({\partial }_{t}u+E)\nabla u\right\}$, where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation...

In the paper the Signorini problem without friction in the linear thermoelasticity for the steady-state case is investigated. The problem discussed is the model geodynamical problem, physical analysis of which is based on the plate tectonic hypothesis and the theory of thermoelasticity. The existence and unicity of the solution of the Signorini problem without friction for the steady-state case in the linear thermoelasticity as well as its finite element approximation is proved. It is known that...

This paper deals with the method for evaluating exposures of nickel alloy structures containing both extracted and sectioned particles. The presented stereological model makes it possible to estimate two unknown spatial parameters, the mean value of the particle size distribution and the depth of etching with the use of the information obtained from the combined structure of the exposures.

The seasonality hypothesis states that climates characterized by large annual cycles select for large body sizes. In order to study the effects of seasonality on the evolution of body size, we use a model that is based on physiological rules and first principles. At the ecological time scale, our model results show that both larger productivity and seasonality may lead to larger body sizes. Our model is the first dynamic and process-based model to support the seasonality hypothesis and hence...

In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy’s law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument....

In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy's law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument....