3,252 research outputs found
An anisotropic adaptive method for the numerical approximation of orthogonal maps
No full textOrthogonal maps are two-dimensional mappings that are solutions of the so-called origami problem obtained when folding a paper. These mappings are piecewise linear, and the discontinuities of their gradient form a singular set composed of straight lines representing the folding edges. The proposed algorithm relies on the minimization of a variational principle discussed in Caboussat et al. (2019). A splitting algorithm for the corresponding flow problem derived from the first-order optimality conditions alternates between local nonlinear problems and linear elliptic variational problems at each time step. Anisotropic adaptive techniques allow to obtain refined triangulations near the folding edges while keeping the number of vertices as low as possible. Numerical experiments validate the accuracy and efficiency of the adaptive method in various situations. Appropriate convergence properties are exhibited, and solutions with sharp edges are recovered
La filosofía del derecho de Alexandre Kojève
No full textThis article is a presentation of Alexandre Kojève’s philosophy of law, exposed in his Esquisse d’une phénoménologie du droit (1981). Little attention has been paid to this work. So there is a gap that has to be filled with a critical reflection of its strengths. Among them, undoubtedly, we count the fact that Kojève is introducing a conception of international justice that casts a singular light on current debates about cosmopolitanism and globalization. According to this author, citizenship is the key element of the process of global expansion of the juridical sphere. In sum, Kojève’s philosophy is useful to reflect upon the contrast between the juridical and the political, which is the basis for all philosophy of law, in order to achieve world peace and international justice.Este artículo es una presentación de la filosofía del derecho de Alexandre Kojève contenida en su Esquisse d’une phénoménologie du droit (1981). La poca atención que dicha obra ha recibido es un vacío que debiera llenarse con una reflexión crítica de sus puntos fuertes. Entre ellos destaca una concepción de la justicia internacional que proyecta una luz muy singular sobre los actuales debates en torno a la globalización y el cosmopolitismo. A ojos de este autor, la ciudadanía es el elemento clave para aquilatar la expansión global de lo jurídico. En suma, Kojève aparece como un valioso referente en la labor de pensar la contraposición entre lo jurídico y lo político que está en la base de toda filosofía del derecho, con la aspiración al logro de la justicia internacional y la paz mundial en el horizonte
Reconfiguração do consensualismo contratual: as ações tituladas nominativas e os limites à transmissão
No full textPartimos da evolução histórica do consensualismo contratual salientando os
principais carateres que, nos diversos momentos históricos, se foram evidenciando.
Numa segunda etapa exploramos os fundamentos dogmáticos do modelo de
transmissão contratual assumido pelo legislador e a sua viabilidade no sistema
jurídico global, em particular, no direito dos valores mobiliários. Constatamos a
crescente necessidade na prática mercantil e inevitabilidade no sistema jurídico
global da admissibilidade da existência de contratos de compra e venda de natureza
meramente obrigacional. Num terceiro momento desenvolvemos os principais
aspetos do regime jurídico aplicável às ações tituladas nominativas fora do mercado
regulado, em particular, os principais limites à transmissão, enquanto instrumentos/barreiras ao consensualismo contratual.We start from the historical evolution of contractual consensualism emphasizing the
main aspects that, in different historical moments, were showing up. In a second
stage we explore the dogmatic foundations of the transmission model contractual
assumed by the legislator and its viability in the global legal system, in particular, in
securities law. We note the growing need in commercial practice and inevitability in
the global legal system the admissibility of the existence of contracts of sale purely
obligatory. In the third stage we develop the main aspects of the legal regime
applicable to nominative titled actions outside the regulated market, in particular,
the main limits to the transmission, as instruments / barriers to contractual
consensualism
Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations
No full textThis thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps, the prescribed Jacobian equation and inequality, the elliptic and parabolic Monge-Ampère equations.
For orthogonal map we develop an \emph{operator-splitting/finite element} approach for the numerical solution of the Dirichlet problem. This approach is built on the variational principle, the introduction of an associated flow problem, and a time-stepping splitting algorithm. Moreover, we propose an extension of this method with an \emph{anisotropic mesh adaptation algorithm}. This extension allows us to track singularities of the solution's gradient more accurately. Various numerical experiments demonstrate the accuracy and the robustness of the proposed method for both constant and adaptive mesh.
For the prescribed Jacobian equation and the three-dimensional Monge-Ampère equation, we consider a \emph{least-squares/relaxation finite element method} for the numerical solution of the Dirichlet problems. We then introduce a relaxation algorithm that splits the least-square problem, which stems from a reformulation of the original equations, into local nonlinear and variational problems. We develop dedicated solvers for the algebraic problems based on Newton method and we solve the differential problems using mixed low-order finite element method. Overall the least squares approach exhibits appropriate convergence orders in and error norms for various numerical tests.
We also design a \emph{second-order time integration method} for the approximation of a parabolic two-dimensional Monge-Ampère equation. The space discretization of this method is based on low-order finite elements, and the time discretization is achieved by the implicit Crank-Nicolson type scheme.
We verify the efficiency of the proposed method on time-dependent and stationary problems. The results of numerical experiments show that the method achieves nearly optimal orders for the and error norms when smooth solutions are approximated.
Finally, we present an adaptive mesh refinement algorithm for the elliptic Monge-Ampere equation based on the residual error estimate. The robustness of the proposed algorithm is verified using various test cases and two different solvers which are inspired by the two previous proposed numerical methods.GR-P
Numerical simulation of sediment dynamics with free surface flows
No full textWe present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum balance equation for the mixture (fluid and sediments).
The model proposed here couples the Navier-Stokes equations, with a
volume-of-fluid (VOF) approach for the tracking of the free surfaces between the liquid
and the air, plus a nonlinear advection equation for the sediments (for the transport, deposition, and resuspension of sediments).
The numerical algorithm relies on a splitting approach to decouple diffusion and advection phenomena such that we are left with a Stokes operator, an advection operator, and deposition/resuspension operators.
For the space discretization, a two-grid method couples a finite element discretization for the resolution of the Stokes problem, and a finer structured grid of small cells for the discretization of the advection operator and the sediment deposition/resuspension operator.
SLIC, redistribution, and decompression algorithms are used for post-processing to limit numerical diffusion and correct the numerical compression of the volume fraction of liquid.
The numerical model is validated through numerical experiments.
We validate and benchmark the model with deposition effects only for some specific experiments, in particular erosion experiments. Then, we validate and benchmark the model in which we introduce resuspension effects. After that, we discuss the limitations of the underlying physical models.
Finally, we consider a one-dimensional diffusion-convection equation and study an error indicator for the design of adaptive algorithms. First, we consider a finite element backward scheme, and then, a splitting scheme that separates the diffusion and the convection parts of the equation.GR-PIMATHICS
“Era por Alexandre tod’esto demostrado”: ¿pruebas verídicas y pruebas engañosas en el Libro de Alexandre?
No full textEl Libro de Alexandre es un texto de s. XIII, que se escribió en la España medieval. En este escrito, el autor pretende demostrar que, en el Alexandre, algunas de las situaciones que se ponen a prueba son aceptadas, pero eso no significa que el macedonio gane la prueba. El articulo esta dividido en tres apartados. En el primero, el autor da cuenta de la historia textual de la obra y también dedica ciertas líneas al Estado de la cuestión del texto; mientras que, en la segunda parte, nos guía a conceptos etimológicos de los términos prueba, evidencia y demás. En el tercer apartado se centra en algunas pruebas expuestas en el Libro de Alexandre.The Libro de Alexandre is a literary work, written during the medieval Spain. In this paper, the author tries to demonstrate that, carefully reading the L.A, some of the situations that are set as proves are accepted, but it does not mean that Alexander can be a victor. This paper is divided in three sections: firstly, the author tells the textual history of the L.A and, then, tries to update the State of art: on the other hand, in the second part, the author offers meanings about terms as: prueba and evidencia. Finally, the author focuses on certain passages contained in the Libro de Alexandre that can be taken as failed proves
Mixing the Immiscible: Improvisation within Fixed-Media Composition
No full textThis paper will explore ways in which mastered improvisation practice, with the studio as an instrument, is a proposed avenue to bridge the historical dichotomy between what Ted Gioia describe as ‘the aesthetics of perfection’ and ‘the aesthetics of imperfection’. It is proposed as a way to re-embody fixed music, as experimented by the author through the composition of his last fixed-media work. This will be put in the context of a wider trend observed amongst the current emerging generation of composers interested in the aesthesics of the work, by opposition to the previous generations that placed the value of the work in its poietics. The vital and primal importance of practice outcome as practice-based research’s main document will also be advocated for, as these trends are happening in the laboratory of live music
Numerical simulation of immiscible incompressible viscous, viscoelastic and elastic multiphase flows
No full textA unified numerical framework is presented for the modelling of multiphasic viscoelastic
and elastic flows. The rheologies considered range from incompressible Newtonian or
Oldroyd-B viscoelastic fluids to Neo-Hookean elastic solids. The model is formulated
in Eulerian coordinates. The unknowns are the volume fraction of each phase (liquid,
viscoelastic or solid), the velocity, pressure and the stress in each phase.
A time splitting strategy is applied in order to decouple the advection operators and the
diffusion operators. The numerical approximation in space consists of a two-grid method.
The advection equations are solved with a method of characteristics on a structured grid
of small cells and the diffusion step uses an unstructured coarser finite element mesh.
An implicit time scheme is suggested for the time discretisation of the diffusion step.
Estimates for the time and space discretisation of a simplified model are presented, which
proves unconditional stability.
Several numerical experiments are presented, first for the simulation of one phase flows
with free surfaces. The implicit time scheme is shown to be more efficient than the
explicit one. Then, the model for the deformation of an elastic material is validated for
several test cases. Finally, Signorini boundary conditions are implemented and presented
for the simulation of the bouncing of an elastic ball.
The multiphase model is validated through different test cases. Collisions between
Neo-Hookean elastic solids are explored. Simulations of multiple viscoelastic flows are
presented, for instance an immersed viscoelastic droplet and a Newtonian fluid in a
constricted cavity. The fall of an immersed Neo-Hookean elastic solid into a Newtonian
or a viscoelastic fluid is also presented.
Finally, the one phase model is extended to compressible flows. The method of characteristics
is updated in order to solve the advection equations, when the velocity is not
divergence-free. A numerical scheme is proposed and a numerical experiment is presented.GR-P
Numerical analysis of optimization-constrained differential equations : applications to atmospheric chemistry
No full textThe modeling of a system composed by a gas phase and organic aerosol particles, and its numerical resolution are studied. The gas-aerosol system is modeled by ordinary differential equations coupled with a mixed-constrained optimization problem. This coupling induces discontinuities when inequality constraints are activated or deactivated. Two approaches for the solution of the optimization-constrained differential equations are presented. The first approach is a time splitting scheme together with a fixed-point method that alternates between the differential and optimization parts. The ordinary differential equations are approximated by the Crank-Nicolson scheme and a primal-dual interior-point method combined with a warm-start strategy is used to solve the minimization problem. The second approach considers the set of equations as a system of differential algebraic equations after replacing the minimization problem by its first order optimality conditions. An implicit 5th-order Runge-Kutta method (RADAU5) is then used. Both approaches are completed by numerical techniques for the detection and computation of the events (activation and deactivation of inequality constraints) when the system evolves in time. The computation of the events is based on continuation techniques and geometric arguments. Moreover the first approach completes the computation with extrapolation polynomials and sensitivity analysis, whereas the second approach uses dense output formulas. Numerical results for gas-aerosol system made of several chemical species are proposed for both approaches. These examples show the efficiency and accuracy of each method. They also indicate that the second approach is more efficient than the first one. Furthermore theoretical examples show that the method for the computation of the activation is of second order for the first approach and exact for the second one.AS
- …
