Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

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Convex Analysisの二,三の進展について

Couplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge-Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.

Optimal Transport: Old and New

Preface.- Primal and Dual Problems.- One-Dimensional Issues.- L^1 and L^infinity Theory.- Minimal Flows.- Wasserstein Spaces.- Numerical Methods.- Functionals over Probabilities.- Gradient Flows.- Exercises.- References.- Index.

Optimal Transport for Applied Mathematicians : Calculus of Variations, PDEs, and Modeling

Optimal Transport: A Semi-Discrete Approach

En utilisant des arguments geometriques elementaires, on demontre des inegalites de correlation pour des mesures de probabilite a symetrie radiale. Plus precisement on montre que, parmi la famille des ensembles width-decreasing, le ratio de correlation est minimise par des bandes. Comme les ouverts convexes symetriques appartiennent a cette famille, on retrouve comme corollaire le resultat de Pitt sur la validite de la conjecture de correlation gaussiennne en dimension 2, qui est etendue dans ce papier a une large classe de mesures a symetrie radiale.

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A geometric approach to correlation inequalities in the plane

In this paper we show the stability of the ball as maximizer of the Riesz potential among sets of given volume. The stability is proved with sharp exponent $1/2$, and is valid for any dimension $N\geq 2$ and any power $1<\alpha<N$.

Sharp stability for the Riesz potential

Let $\Omega\subseteq\mathbb R^2$ be a domain and let $f\in W^{1,1}(\Omega,\mathbb R^2)$ be a homeomorphism (between $\Omega$ and $f(\Omega)$). Then there exists a sequence of smooth diffeomorphisms $f_k$ converging to $f$ in $W^{1,1}(\Omega,\mathbb R^2)$ and uniformly.

Diffeomorphic approximation of w 1;1 planar sobolev homeomorphisms

We characterize the (sequentially) weak and strong closure of planar diffeomorphisms in the Sobolev topology and we show that they always coincide. We also provide some sufficient condition for a planar map to be approximable by diffeomorphisms in terms of the connectedness of its counter-images, in the spirit of Young's characterisation of monotone functions. We finally show that the closure of diffeomorphisms in the Sobolev topology is strictly contained in the class INV introduced by Muller and Spector.

The closure of planar diffeomorphisms in Sobolev spaces

In this paper we consider the mass transport problem in the case of a relativistic cost; we can establish the continuity of the total cost, together with a general estimate about the directions in which the mass can actually move, under mild assumptions. These results generalize those recently obtained by J.Bertrand, A.Pratelli and M.Puel, also positively answering some of the open questions there.

https://hal.archives-ouvertes.fr/hal-01419526/document

Aldo Pratelli

Papers

A geometric approach to correlation inequalities in the plane

Sharp stability for the Riesz potential

Diffeomorphic approximation of w 1;1 planar sobolev homeomorphisms

The closure of planar diffeomorphisms in Sobolev spaces

On the continuity of the total cost in the mass transport problem with relativistic cost functions