# Publications

## DERRICKS THEOREM IN CURVED SPACE

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL **12** (1979) L17-L19

## COVARIANT CONSERVATION EQUATIONS AND THEIR RELATION TO THE ENERGY-MOMENTUM CONCEPT IN GENERAL RELATIVITY

PHYSICAL REVIEW D **18** (1978) 4399-4407

## COVARIANT CONSERVATION EQUATIONS AND THEIR RELATION TO THE ENERGY-MOMENTUM CONCEPT IN GENERAL RELATIVITY

PHYSICAL REVIEW C (1978) 4399-4407

## CONSERVATION EQUATIONS AND GRAVITATIONAL SYMPLECTIC FORM

JOURNAL OF MATHEMATICAL PHYSICS **19** (1978) 2324-2331

## Recovering Valuations on Demushkin Fields

ArXiv (0)

Let $K$ be a field with $G_K(2) \simeq G_{\mathbb{Q}_2}(2)$, where $G_F(2)$ denotes the maximal pro-2 quotient of the absolute Galois group of a field $F$. We prove that then $K$ admits a (non-trivial) valuation $v$ which is 2-henselian and has residue field $\mathbb{F}_2$. Furthermore, $v(2)$ is a minimal positive element in the value group $\Gamma_v$ and $[\Gamma_v:2\Gamma_v]=2$. This forms the first positive result on a more general conjecture about the structure of pro-$p$ Galois groups which we formulate precisely (cf. Conjecture 1). As an application, we prove a strong version of the birational section conjecture for smooth, complete curves $X$ over $\mathbb{Q}_2$, as well as an analogue for varieties.

## Canonical Valuations and the Birational Section Conjecture

ArXiv (0)

We develop a notion of a `canonical $\mathcal{C}$-henselian valuation' for a class $\mathcal{C}$ of field extensions, generalizing the construction of the canonical henselian valuation of a field. We use this to show that the $p$-adic valuation on a finite extension $F$ of $\mathbb{Q}_p$ can be recovered entirely (or up to some indeterminacy of the residue field) from various small quotients of $G_F$, the absolute Galois group of $F$. In particular, it can be recovered fully from the maximal solvable quotient. We use this to prove several versions of the birational section conjecture for varieties over $p$-adic fields.

## On the shallow atmosphere approximation in finite element dynamical cores

ArXiv (0)

We provide an approach to implementing the shallow atmosphere approximation in three dimensional finite element discretisations for dynamical cores. The approach makes use of the fact that the shallow atmosphere approximation metric can be obtained by writing equations on a three-dimensional manifold embedded in $\mathbb{R}^4$ with a restriction of the Euclidean metric. We show that finite element discretisations constructed this way are equivalent to the use of a modified three dimensional mesh for the construction of metric terms. We demonstrate our approach via a convergence test for a prototypical elliptic problem.

## Compatible finite element methods for numerical weather prediction

ArXiv (0)

This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often referred to as compatible finite elements, mimetic finite elements, discrete differential forms or finite element exterior calculus. We provide an elementary introduction in the case of the one-dimensional wave equation, before summarising recent results in applications to the rotating shallow water equations on the sphere, before taking an outlook towards applications in three-dimensional compressible dynamical cores.

## The impact of stochastic physics on climate sensitivity in EC-Earth

ArXiv (0)

Stochastic schemes, designed to represent unresolved sub-grid scale variability, are frequently used in short and medium-range weather forecasts, where they are found to improve several aspects of the model. In recent years, the impact of stochastic physics has also been found to be beneficial for the model's long term climate. In this paper, we demonstrate for the first time that the inclusion of a stochastic physics scheme can notably affect a model's projection of global warming, as well as its historical climatological global temperature. Specifically, we find that when including the 'stochastically perturbed parametrisation tendencies' scheme (SPPT) in the fully coupled climate model EC-Earth v3.1, the predicted level of global warming between 1850 and 2100 is reduced by 10% under an RCP8.5 forcing scenario. We link this reduction in climate sensitivity to a change in the cloud feedbacks with SPPT. In particular, the scheme appears to reduce the positive low cloud cover feedback, and increase the negative cloud optical feedback. A key role is played by a robust, rapid increase in cloud liquid water with SPPT, which we speculate is due to the scheme's non-linear interaction with condensation.

## Progress Towards a Probabilistic Earth System Model: Examining The Impact of Stochasticity in the Atmosphere and Land component of EC-Earth v3.2

Geoscientific Model Development European Geosciences Union (0)