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

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

Annalen der Physik

Let Ω be a domain in R n whose boundary is C 1 if n≥3 or C 1,β if n=2. We consider a magnetic Schrodinger operator L W , q in Ω and show how to recover the boundary values of the tangential component of the vector potential W from the Dirichlet to Neumann map for L W , q . We also consider a steady state heat equation with convection term Δ+2W·∇ and recover the boundary values of the convection term W from the Dirichlet to Neumann map. Our method is constructive and gives a stability result at the boundary.

/pdf/identifiability-at-the-boundary-for-first-order-terms-2tpxg3fnz8.pdf

Identifiability at the boundary for first-order terms

We survey mathematical developments in the inverse method of electrical impedance tomography which consists in determining the electrical properties of a medium by making voltage and current measurements at the boundary of the medium. In the mathematical literature, this is also known as Calderon's problem from Calderon's pioneer contribution (Calderon 1980 Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980) p 65 (Soc. Brasil. Mat.)). We concentrate this review around the topic of complex geometrical optics solutions that have led to many advances in the field. In the last section, we review some counterexamples to Calderon's problems that have attracted a lot of interest because of connections with cloaking and invisibility.

http://www.dim.uchile.cl/~axosses/calderoniprevised.pdf

Electrical impedance tomography and Calderón's problem

Boundary Value Problems for Elliptic Pseudodifferential Equations

In this article we consider the Schrodinger operator inR

 n
 ,n≧3, with electric and magnetic potentials which decay exponentially as |x|→∞. We show that the scattering amplitude at fixed positive energy determines the electric potential and the magnetic field.

/pdf/inverse-scattering-problem-for-the-schrodinger-equation-with-9ceyhk1qsn.pdf

Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy

We derive three results on the inverse problem of determining the Lame parameters λ(x) and μ(x) for an isotropic elastic body from its Dirichlet-to-Neumann map.

http://iopscience.iop.org/article/10.1088/0266-5611/18/3/324/pdf

On the inverse boundary value problem for linear isotropic elasticity

This book is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces with many examples and applications to equations with constant coefficients. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory. The book also covers microlocal analysis, including the theory of pseudodifferential and Fourier integral operators, and the propagation of singularities for operators of real principal type. Among the more advanced topics are the global theory of Fourier integral operators and the geometric optics construction in the large, the Atiyah-Singer index theorem in Rn , and the oblique derivative problem.

Lectures on Linear Partial Differential Equations

We present a modification of the BC method in inverse hyperbolic problems. The main novelty is the study of the restrictions of the solutions to the characteristic surfaces instead of the fixed time hyperplanes. The main result is that the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the self-adjoint hyperbolic operator up to a diffeomorphism and a gauge transformation. In this paper, we prove the crucial local step. The global step of the proof will be presented in a forthcoming paper.

https://iopscience.iop.org/article/10.1088/0266-5611/22/3/005/pdf

Gregory Eskin

Papers

Boundary Value Problems for Elliptic Pseudodifferential Equations

Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy

On the inverse boundary value problem for linear isotropic elasticity

Lectures on Linear Partial Differential Equations

A new approach to hyperbolic inverse problems