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

BIOE 402. Medical Technology Assessment. 2 or 3 hours. Bioentrepreneur course. Assessment of medical technology in the context of commercialization. Objectives, competition, market share, funding, pricing, manufacturing, growth, and intellectual property; many issues unique to biomedical products. Course Information: 2 undergraduate hours. 3 graduate hours. Prerequisite(s): Junior standing or above and consent of the instructor.

“Bioinformatics” 특집을 내면서

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

Geometric approach to Hamiltonian dynamics and statistical mechanics

The Hamiltonian dynamics of the classical planar Heisenberg model is numerically investigated in two and three dimensions. In three dimensions peculiar behaviors are found in the temperature dependence of the largest Lyapunov exponent and of other observables related to the geometrization of the dynamics. On the basis of a heuristic argument it is conjectured that the phase transition might correspond to a change in the topology of the manifolds whose geodesics are the motions of the system.

Geometry of dynamics, lyapunov exponents, and phase transitions

This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of newtonian dynamics in the language of Riemannian geometry. A new point of view about the origin of chaos in these systems is obtained independently of homoclinic intersections. Chaos is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of Jacobi equation for geodesic spread. Under general conditions ane effective stability equation is derived; an analytic formula for the growth-rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent agreement is found the theoretical prediction and the values of the Lyapunov exponent obtained by numerical simulations for both models.

https://arxiv.org/pdf/chao-dyn/9609010.pdf

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

The Fermi-Pasta-Ulam \ensuremath{\alpha} model of harmonic oscillators with cubic anharmonic interactions is studied from a statistical mechanical point of view. Systems of N=32 to 128 oscillators appear to be large enough to suggest statistical mechanical behavior. A key element has been a comparison of the maximum Lyapunov coefficient ${\ensuremath{\lambda}}_{\mathrm{max}}$ of the FPU \ensuremath{\alpha} model and that of the Toda lattice. For generic initial conditions, ${\ensuremath{\lambda}}_{\mathrm{max}}$(t) is indistinguishable for the two models up to times that increase with decreasing energy (at fixed N). Then suddenly a bifurcation appears, which can be discussed in relation to the breakup of regular, solitonlike structures. After this bifurcation, the ${\ensuremath{\lambda}}_{\mathrm{max}}$ of the FPU model appears to approach a constant, while the ${\ensuremath{\lambda}}_{\mathrm{max}}$ of the Toda lattice appears to approach zero, consistent with its integrability. This suggests that for generic initial conditions the FPU \ensuremath{\alpha} model is chaotic and will therefore approach equilibrium and equipartition of energy. There is, however, a threshold energy density ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{c}}$(N)\ensuremath{\sim}1/${\mathrm{N}}^{2}$, below which trapping occurs; here the dynamics appears to be regular, solitonlike, and the approach to equilibrium\char22{}if any\char22{}takes longer than observable on any available computer. Above this threshold the system appears to behave in accordance with statistical mechanics, exhibiting an approach to equilibrium in physically reasonable times. The initial conditions chosen by Fermi, Pasta, and Ulam were not generic and below threshold and would have required possibly an infinite time to reach equilibrium. The picture obtained on the basis of ${\ensuremath{\lambda}}_{\mathrm{max}}$ suggests that neither the KAM nor the Nekhoroshev theorems in their present form are directly relevant for a discussion of the phenomenology of the FPU \ensuremath{\alpha} model presented here.

The fermi-pasta-ulam problem revisited : stochasticity thresholds in nonlinear hamiltonian systems

The relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant (the Euler characteristic) of certain submanifolds in the configuration space of two physical models. The models are the mean-field XY model and the one-dimensional XY model with nearest-neighbor interactions. The former model undergoes a second-order phase transition at a finite critical temperature while the latter has no phase transitions. The computation of this topologic invariant is performed within the framework of Morse theory. In both models topology changes in configuration space are present as the potential energy is varied; however, in the mean-field model there is a particularly “strong” topology change, corresponding to a big jump in the Euler characteristic, connected with the phase transition, which is absent in the one-dimensional model with no phase transition. The comparison between the two models has two major consequences: (i) it lends new and strong support to a recently proposed topological approach to the study of phase transitions; (ii) it allows us to conjecture which particular topology changes could entail a phase transition in general. We also discuss a simplified illustrative model of the topology changes connected to phase transitions using of two-dimensional surfaces, and a possible direct connection between topological invariants and thermodynamic quantities.

Lapo Casetti

Papers

Geometric approach to Hamiltonian dynamics and statistical mechanics

Geometry of dynamics, lyapunov exponents, and phase transitions

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

The fermi-pasta-ulam problem revisited : stochasticity thresholds in nonlinear hamiltonian systems

Phase Transitions and Topology Changes in Configuration Space