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

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Level set methods: an overview and some recent results

Convex bodies: the brunn–minkowski theory

The novel concept of total generalized variation of a function $u$ is introduced, and some of its essential properties are proved. Differently from the bounded variation seminorm, the new concept involves higher-order derivatives of $u$. Numerical examples illustrate the high quality of this functional as a regularization term for mathematical imaging problems. In particular this functional selectively regularizes on different regularity levels and, as a side effect, does not lead to a staircasing effect.

http://gpu4vision.icg.tugraz.at/papers/2009/pock_tgv.pdf

Total Generalized Variation

These are the lecture notes of a course taught in Linz in Sept., 2009, at the school "summer school on sparsity", organized by Massimo Fornasier and Ronny Romlau. They address various theoretical and practical topics related to Total Variation-based image reconstruction. They focu first on some theoretical results on functions which minimize the total variation, and in a second part, describe a few standard and less standard algorithms to minimize the total variation in a finite-differences setting, with a series of applications from simple denoising to stereo, or deconvolution issues, and even more exotic uses like the minimization of minimal partition problems.

/pdf/an-introduction-to-total-variation-for-image-analysis-12cghgypka.pdf

An introduction to Total Variation for Image Analysis

The Total Variation Flow in RN

The main purpose of this paper is to prove that the jump discontinuity set of the solution of the total variation based denoising problem is contained in the jump set of the datum to be denoised. We also prove some extensions of this result for the total variation minimization flow, for anisotropic norms, and for some more general convex functionals, which include the minimal surface equation case and its anisotropic extensions.

/pdf/the-discontinuity-set-of-solutions-of-the-tv-denoising-jvw2onnztr.pdf

The Discontinuity Set of Solutions of the TV Denoising Problem and Some Extensions

We consider the motion by curvature of a network of smooth curves
with multiple junctions in the plane, that is, the geometric gradient flow associated
to the length functional.
Such a flow represents the evolution of a two–dimensional multiphase system
where the energy is simply the sum of the lengths of the interfaces, in particular it
is a possible model for the growth of grain boundaries.
Moreover, the motion of these networks of curves is the simplest example of
curvature flow for sets which are “essentially” non regular.
As a first step, in this paper we study in detail the case of three curves in the plane
meeting at a single triple junction and with the other ends fixed. We show some
results about the existence, uniqueness and, in particular, the global regularity of
the flow, following the line of analysis carried on in the last years for the evolution
by mean curvature of smooth curves and hypersurfaces.

/pdf/motion-by-curvature-of-planar-networks-25q1q4zbiu.pdf

Motion by curvature of planar networks

We prove a local existence and uniqueness result of crystalline mean curvature flow starting from a compact convex admissible set in Open image in new window. This theorem can handle the facet breaking/bending phenomena, and can be generalized to any anisotropic mean curvature flow. The method provides also a generalized geometric evolution starting from any compact convex set, existing up to the extinction time, satisfying a comparison principle, and defining a continuous semigroup in time. We prove that, when the initial set is convex, our evolution coincides with the flat φ-curvature flow in the sense of Almgren-Taylor-Wang. As a by-product, it turns out that the flat φ-curvature flow starting from a compact convex set is unique.

/pdf/crystalline-mean-curvature-flow-of-convex-sets-zbpyqk0pdt.pdf

Matteo Novaga

Papers

An introduction to Total Variation for Image Analysis

The Total Variation Flow in RN

The Discontinuity Set of Solutions of the TV Denoising Problem and Some Extensions

Motion by curvature of planar networks

Crystalline Mean Curvature Flow of Convex Sets