Related papers: Some Mathematical and Numerical Issues in Geophysi…
Specific aspects of time series analysis are discussed. They are related to the analysis of atmospheric data that are pertinent to clouds. A brief introduction on some of the most interesting topics of current research on climate/weather…
The main objective of this addendum to the mentioned article by Park is to provide some remarks on bifurcation theories for nonlinear partial differential equations (PDE) and their applications to fluid dynamics problems. We only wish to…
We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include…
The response of precipitation extremes to climate change is considered using results from theory, modeling, and observations, with a focus on the physical factors that control the response. Observations and simulations with climate models…
In this work, we introduce an effective model for both ideal and viscous fluid dynamics within the framework of kinetic field theory (KFT). The main application we have in mind is cosmic structure formation where gaseous components need to…
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's `Global Drifter Program', this paper develops data-driven…
Many physical systems are described by partial differential equations (PDEs). Determinism then requires the Cauchy problem to be well-posed. Even when the Cauchy problem is well-posed for generic Cauchy data, there may exist characteristic…
A new hydrodynamics code aimed at astrophysical applications has been developed. The new code and algorithms are presented along with a comprehensive suite of test problems in one, two, and three dimensions. The new code is shown to be…
In this thesis we introduce the concept of a guided dynamical system, and exploit this idea to solve various problems in functional equations and PDE's. Our main results are 1) a necessary and sufficient condition for unique-solvability of…
This thesis concerns the split of Einstein's field equations (EFE's) with respect to nowhere null hypersurfaces. Areas covered include A) the foundations of relativity, deriving geometrodynamics from relational first principles and showing…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
Computational fluid dynamics (CFD) drives progress in numerous scientific and engineering fields, yet high-fidelity simulations remain computationally prohibitive. While machine learning approaches offer computing acceleration, they…
These expository notes address certain stationary and ergodic properties of the equations of fluid dynamics subject to a spatially degenerate (i.e. frequency localized), white in time gaussian forcing. In order to provide an accessible…
This review is a short introduction to numerical hydrodynamics in a cosmological context, intended for the non specialist. The main processes relevant to galaxy formation are first presented. The fluid equations are then introduced, and…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…
Projecting climate change is a generalization problem: we extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller…
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic…
An intriguing link between a wide range of problems occurring in physics and financial engineering is presented. These problems include the evolution of small perturbations of linear flows in hydrodynamics, the movements of particles in…
Biological systems are influenced by fluid mechanics at nearly all spatiotemporal scales. This broad relevance of fluid mechanics to biology has been increasingly appreciated by engineers and biologists alike, leading to continued expansion…