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

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Publisher Summary This chapter focuses on finite volume methods. The finite volume method is a discretization method that is well suited for the numerical simulation of various types (for instance, elliptic, parabolic, or hyperbolic) of conservation laws; it has been extensively used in several engineering fields, such as fluid mechanics, heat and mass transfer, or petroleum engineering. Some of the important features of the finite volume method are similar to those of the finite element method: it may be used on arbitrary geometries, using structured or unstructured meshes, and it leads to robust schemes. The finite volume method is locally conservative because it is based on a “balance" approach: a local balance is written on each discretization cell that is often called “control volume;” by the divergence formula, an integral formulation of the fluxes over the boundary of the control volume is then obtained. The fluxes on the boundary are discretized with respect to the discrete unknowns.

http://materias.fi.uba.ar/7538/material/Otros/EymardEtAl%20-%20Finite%20Volume%20Methods.pdf

Finite Volume Methods

Nature provides much inspiration for the design of materials capable of motion upon exposure to external stimuli, and many examples of such active systems have been created in the laboratory. However, to achieve continuous motion driven by an unchanging, constant stimulus has proven extremely challenging. Here we describe a liquid crystalline polymer film doped with a visible light responsive fluorinated azobenzene capable of continuous chaotic oscillatory motion when exposed to ambient sunlight in air. The presence of simultaneous illumination by blue and green light is necessary for the oscillating behaviour to occur, suggesting that the dynamics of continuous forward and backward switching are causing the observed effect. Our work constitutes an important step towards the realization of autonomous, persistently self-propelling machines and self-cleaning surfaces powered by sunlight.

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A chaotic self-oscillating sunlight-driven polymer actuator

A long structural system with an unstable (subcritical)post-buckling response that subsequently restabilizes typically deformsin a cellular manner, with localized buckles first forming and thenlocking up in sequence. As buckling continues over a growing number ofcells, the response can be described by a set of lengthening homoclinicconnections from the fundamental equilibrium state to itself. In thelimit, this leads to a heteroclinic connection from the fundamentalunbuckled state to a post-buckled state that is periodic. Under suchprogressive displacement the load tends to oscillate between twodistinct values. The paper is both a review and a pointer tofuture research. The response is described via a typical system, asimple but ubiquitous model of a strut on a foundation which includesinitially-destabilizing and finally-restabilizing nonlinear terms. Anumber of different structural forms, including the axially-compressedcylindrical shell, a typical sandwich structure, a model of geologicalfolding and a simple link model are shown to display such behaviour. Amathematical variational argument is outlined for determining the globalminimum postbuckling state under controlled end displacement (rigidloading). Finally, the paper stresses the practical significance of aMaxwell-load instability criterion for such systems. This criterion,defined under dead loading to be where the pre-buckled and post-buckledstate have the same energy, is shown to have significance in the presentsetting under rigid loading also. Specifically, the Maxwell load isargued to be the limit of minimum energy localized solutions asend-shortening tends to infinity.

/pdf/cellular-buckling-in-long-structures-53jot1yv4d.pdf

Cellular Buckling in Long Structures

We consider analytical and numerical aspects of the phase diagram for microphase separation of diblock copolymers. Our approach is variational and is based upon a density functional theory which entails minimization of a nonlocal Cahn–Hilliard functional. Based upon two parameters which characterize the phase diagram, we give a preliminary analysis of the phase plane. That is, we divide the plane into regions wherein a combination of analysis and numerics is used to describe minimizers. In particular we identify a regime wherein the uniform (disordered state) is the unique global minimizer; a regime wherein the constant state is linearly unstable and where numerical simulations are currently the only tool for characterizing the phase geometry; and a regime of small volume fraction wherein we conjecture that small well-separated approximately spherical objects are the unique global minimizer. For this last regime, we present an asymptotic analysis from the point of view of the energetics which will be comp...

/pdf/on-the-phase-diagram-for-microphase-separation-of-diblock-1r5ahmm9ag.pdf

On the phase diagram for microphase separation of diblock copolymers: An approach via a nonlocal Cahn-Hilliard functional

We present the first of two articles on the small volume fraction limit of a nonlocal Cahn–Hilliard functional introduced to model microphase separation of diblock copolymers. Here we focus attention on the sharp-interface version of the functional and consider a limit in which the volume fraction tends to zero but the number of minority phases (called particles) remains $O(1)$. Using the language of $\Gamma$-convergence, we focus on two levels of this convergence and derive first- and second-order effective energies, whose energy landscapes are simpler and more transparent. These limiting energies are only finite on weighted sums of delta functions, corresponding to the concentration of mass into “point particles.” At the highest level, the effective energy is entirely local and contains information about the structure of each particle but no information about their spatial distribution. At the next level we encounter a Coulomb-like interaction between the particles, which is responsible for the pattern ...

/pdf/small-volume-fraction-limit-of-the-diblock-copolymer-problem-n0a6u1701m.pdf

Small volume fraction limit of the diblock copolymer problem : II. Diffuse-interface functional

Motivated by the occurrence in rate functions of time-dependent large-deviation principles, we study a class of non-negative functions ℒ that induce a flow, given by $\mathcal{L} (\rho _{t},\dot \rho _{t})=0$
 . We derive necessary and sufficient conditions for the unique existence of a generalized gradient structure for the induced flow, as well as explicit formulas for the corresponding driving entropy and dissipation functional. In particular, we show how these conditions can be given a probabilistic interpretation when ℒ is associated to the large deviations of a microscopic particle system. Finally, we illustrate the theory for independent Brownian particles with drift, which leads to the entropy-Wasserstein gradient structure, and for independent Markovian particles on a finite state space, which leads to a previously unknown gradient structure.

/pdf/on-the-relation-between-gradient-flows-and-the-large-1sprty859n.pdf

Mark A. Peletier

Papers

A chaotic self-oscillating sunlight-driven polymer actuator

Cellular Buckling in Long Structures

On the phase diagram for microphase separation of diblock copolymers: An approach via a nonlocal Cahn-Hilliard functional

Small volume fraction limit of the diblock copolymer problem : II. Diffuse-interface functional

On the Relation between Gradient Flows and the Large-Deviation Principle, with Applications to Markov Chains and Diffusion