Related papers: On a minimum set of equations for parameterisation…
The description of complex physical phenomena often involves sophisticated models that rely on a large number of parameters, with many dimensions and scales. One practical way to simplify that kind of models is to discard some of the…
This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…
Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents…
This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from…
One-dimensional (vertical) models of planetary atmospheres typically balance the net solar and internal energy fluxes against the net thermal radiative and convective heat fluxes to determine an equilibrium thermal structure. Thus,simple…
With the success of machine learning (ML) applied to climate reaching further every day, emulators have begun to show promise not only for weather but for multi-year time scales in the atmosphere. Similar work for the ocean remains nascent,…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
A set of idealized experiments are performed to analyze the competing effects of declining atmospheric CO2 concentrations, the opening of an ocean gateway, and varying orbital parameters. These forcing mechanisms, which influence the global…
General circulation models (GCMs) typically have a grid size of 25--200 km. Parametrizations are used to represent diabatic processes such as radiative transfer and cloud microphysics and account for sub-grid-scale motions and variability.…
Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…
In this work, we study a phase transition model in atmospheric dynamics, inspired by the works [6,14,15], which analyze the primitive equations governing the evolution of velocity, temperature, and specific humidity. The main difficulty…
The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
For real matrices of full column-rank, we analyze the conditioning of several types of normal equations that are preconditioned by a randomized preconditioner computed in lower precision. These include symmetrically preconditioned normal…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
Planetary Climate Models (PCMs) are developed to explore planetary climates other than the Earth. Therefore, the methods implemented need to be suitable for a large diversity of conditions. Every planet with a significant atmosphere has…
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…
The correct description of the surface water dynamics in the model of shallow water requires accounting for friction. To simulate a channel flow in the Chezy model the constant Manning roughness coefficient is frequently used. The Manning…
This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for…