Maths Research Associates 2021 Reading

Lead Research Organisation: University of Reading
Department Name: Mathematics and Statistics

Abstract

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Publications

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Carigi G (2022) Exponential ergodicity for a stochastic two-layer quasi-geostrophic model in Stochastics and Dynamics

 
Description This awarded has funded three short-term Postdoctoral Research positions focused on:

(i) the study of the long-time behaviour of systems describing the atmosphere and the ocean by means of so-called ergodic theory of dynamical systems;

(ii) establishing the existence of a special type of mathematical minimiser in the area of Calculus of Variations, which solves a system of partial differential equations with auxiliary parameters; and

(iii) a simple model of the mid-latitude atmosphere and found a connection between some particular macroscopic features and local properties of the attractor of the system.

Work from (i) has already been published and further publications from each of these pieces of work are pending.
Exploitation Route The work here will inform research in similar areas being undertaken by mathematicians and physicists relevant to each problem area. This includes pure mathematics, applied mathematics and atmospheric and climate science. In respect of each problem area these are as follows.

(i) The work carried out provides two sets of general conditions for equations like the Navier-Stokes equations with additive random perturbations to establish exponential ergodicity and linear response. The toolboxes are designed to be flexible enough to be able to establish such properties for other models, for example for geophysical fluid models like the primitive equations or other fluid models like the compressible Navier-Stokes equation.

(ii) Research into the topic of Calculus of Variations has several long-term beneficiaries in the academic, industrial, and commercial world. For example, in the academic sector, there will be sustained substantial impact to the physical, natural and earth sciences. With further developments these methods will lead to improved results reducing the need to purchase, for example, more powerful computers to speed up model simulations.

(iii) This work will be important in the study of higher dimensional and more realistic atmospheric models, characterised by heterogeneity in the tangent space.
Sectors Education,Environment