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

Annals of physics

This paper introduces five notions, including π-algebras, π-ideals, Hopf π-algebras, π-modules and Hopf π-modules, verifies the fundamental isomorphism theorem of π-algebras and studies some algebraic properties of Hopf π-algebras as well.

Hopf π- Algebras

Journal of Physics A - Mathematical and General, Special Issue. SI Aug 11 2006 ?? Preface

We extend the definition of the "flipped" loop-quantum-gravity vertex to the case of a finite Immirzi parameter. We cover the Euclidean as well as the Lorentzian case. We show that the resulting dynamics is defined on a Hilbert space isomorphic to the one of loop quantum gravity, and that the area operator has the same discrete spectrum as in loop quantum gravity. This includes the correct dependence on the Immirzi parameter, and, remarkably, holds in the Lorentzian case as well. The ad hoc flip of the symplectic structure that was initially required to derive the flipped vertex is not anymore needed for finite Immirzi parameter. These results establish a bridge between canonical loop quantum gravity and the spinfoam formalism in four dimensions.

LQG vertex with finite Immirzi parameter

http://www.nucleares.unam.mx/~chryss/papers/branes.pdf

The geometry of branes and extended superspaces

We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes in on the Poincare-plus-Heisenberg algebra in about a minute. Further ahead, along the same path, lies a three-dimensional deformation space, with an instability double cone through its origin. We give physical as well as geometrical arguments supporting our view that moment, rather than position operators, should enter as generators in the Lie algebra. With this identification, the deformation parameters give rise to invariant length and mass scales. Moreover, standard quantum relativistic kinematics of massive, spinless particles corresponds to non-commuting moment operators, a purely quantum effect that bears no relation to spacetime non-commutativity, in sharp contrast to earlier interpretations.

/pdf/generalized-quantum-relativistic-kinematics-a-stability-4vjbuxwfyk.pdf

Generalized quantum relativistic kinematics: a stability point of view

We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties; not only can the Euler-Lagrange equation be integrated to provide a quadrature for the curvature but, in addition, the embedding itself can be expressed as a local function of the curvature. The configuration space is shown to be essentially one dimensional, with surprisingly rich structure. Distinct branches of integer-indexed equilibria exhibit self-intersections and bifurcations-a gallery of plots is provided to highlight these findings. Perturbations connecting equilibria are shown to satisfy a first-order ODE which is readily solved. We also obtain analytical expressions for the energy as a function of the area in some limiting regimes.

Area-constrained planar elastica.

We examine the equilibrium conditions of a curve in space when a local energy penalty is associated with its extrinsic geometrical state characterized by its curvature and torsion. To do this we tailor the theory of deformations to the Frenet–Serret frame of the curve. The Euler–Lagrange equations describing equilibrium are obtained; Noether’s theorem is exploited to identify the constants of integration of these equations as the Casimirs of the Euclidean group in three dimensions. While this system appears not to be integrable in general, it is in various limits of interest. Let the energy density be given as some function of the curvature and torsion, f( κ, τ ) .I ff is a linear function of either of its arguments but otherwise arbitrary, we claim that the first integral associated with rotational invariance permits the torsion τ to be expressed as the solution of an algebraic equatio ni n terms ofthe bending curvature, κ. The first integral associated with translational invariance can then be cast as a quadrature for κ or for τ .

https://iopscience.iop.org/article/10.1088/0305-4470/35/31/304/pdf

Hamiltonians for curves

We show that the algebra of the recently proposed Triply Special Relativity can be brought to a linear (i.e., Lie) form by a correct identification of its generators. The resulting Lie algebra is the stable form proposed by Vilela Mendes a decade ago, itself a reapparition, up to some important sign, of Yang's algebra, dating from 1947. As a corollary we assure that, within the Lie algebra framework, there is no Quadruply Special Relativity.

/pdf/linear-form-of-3-scale-special-relativity-algebra-and-the-jmelzwpajc.pdf

Chryssomalis Chryssomalakos

Papers

The geometry of branes and extended superspaces

Generalized quantum relativistic kinematics: a stability point of view

Area-constrained planar elastica.

Hamiltonians for curves

Linear form of 3-scale special relativity algebra and the relevance of stability