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

R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.

Exactly Solved Models in Statistical Mechanics

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Introduction to the Modern Theory of Dynamical Systems

Combinatorial Group Theory: COMBINATORIAL GROUP THEORY

Introduction to Mathematical Statistics. By R.V. Hogg and A. T. Craig. Pp. ix, 245. 47s. 1959. (The Macmillan Company, New York)

Time-reversal symmetry in dynamical systems: a survey

Integrable mappings and soliton equations II

Integrable mappings and soliton equations

Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems

One link between the theory of quasicrystals and the theory of nonlinear dynamics is provided by the study of so-called trace maps. A subclass of them are mappings on a one-parameter family of 2D surfaces that foliate ℝ3 (and also ℂ3). They are derived from transfer matrix approaches to properties of 1D quasicrystals. In this article, we consider various dynamical properties of trace maps. We first discuss the Fibonacci trace map and give new results concerning boundedness of orbits on certain subfamilies of its invariant 2D surfaces. We highlight a particular surface where the motion is integrable and semiconjugate to an Anosov system (i.e., the mapping acts as a pseudo-Anosov map). We identify properties of symmetry and reversibility (time-reversal symmetry) in the Fibonacci trace map dynamics and discuss the consequences for the structure of periodic orbits. We show that a conservative period-boubling sequence can be identified when moving through the one-parameter family of 2D surfaces. By using generator trace maps, in terms of which all trace maps obtained from invertible two-letter substitution rules can be expressed, we show that many features of the Fibonacci trace map hold in general. The role of the Fricke character\(\hat I(x,y,z) = x^2 + y^2 + z^2 - 2xyz - 1\), its symmetry group, and reversibility for the Nielsen trace maps are described algebraically. Finally, we outline possible higher-dimensional generalizations.

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John A. G. Roberts

Papers

Time-reversal symmetry in dynamical systems: a survey

Integrable mappings and soliton equations II

Integrable mappings and soliton equations

Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems

Trace maps as 3D reversible dynamical systems with an invariant