Related papers: Some Mathematical and Numerical Issues in Geophysi…
Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the…
When studying fluid mechanics in terms of instability, bifurcation and invariant solutions one quickly finds out how little can be done by pen and paper. For flows on sufficiently simple domains and under sufficiently simple boundary…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
The advantages and disadvantages of two approaches to astrophysical hydrodynamics, Smoothed Particle Hydrodynamics and Adaptive Mesh Refinement, are briefly discussed together with some current problems of computational hydrodynamics.
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
Over the last few decades, climate scientists have devoted much effort to the development of large numerical models of the atmosphere and the ocean. While there is no question that such models provide important and useful information on…
These are notes prepared for presentation at the workshop "Challenges in Granular Matter" at the Abdus Salam Institute for Theoretical Physics, Trieste, August 2001. Revisions and figures will be added at a later date. Many features of real…
The dynamics of fluids is a long standing challenge that remained as an unsolved problem for centuries. Understanding its main features, chaos and turbulence, is likely to provide an understanding of the principles and non-linear dynamics…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
The primitive equations for geophysical flows are studied under the influence of {\em stochastic wind driven boundary conditions} modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary…
Turbulent flow physics regulates the aerodynamic properties of lifting surfaces, the thermodynamic efficiency of vapor power systems, and exchanges of natural and anthropogenic quantities between the atmosphere and ocean, to name just a few…
Earth System Models (ESMs) are the state of the art for projecting the effects of climate change. However, longstanding uncertainties in their ability to simulate regional and local precipitation extremes and related processes inhibit…
This paper addresses the theoretical foundations of pedestrian models for crowd dynamics. While the topic gains momentum, current models differ widely in their mathematical structure, even if we only consider continuous agent-based models.…
The Glansdorff and Prigogine General Evolution Criterion (GEC) is an inequality that holds for macroscopic physical systems obeying local equilibrium and that are constrained under timeindependent boundary conditions. The latter, however,…
Traditional general circulation models, or GCMs -- i.e. 3D dynamical models with unresolved terms represented in equations with tunable parameters -- have been a mainstay of climate research for several decades, and some of the pioneering…
The Gas-Kinetic Scheme (GKS), widely used in computational fluid dynamics for simulating hypersonic and other complicated flow phenomena, is extended in this work to electromagnetic problems by solving Maxwell's equations. In contrast to…
Motivated by the results of recent laboratory experiments (Yoshida et al. Nature, 424, 303-306 (2003)) as well as many earlier field observations that evolutionary changes can take place in ecosystems over relatively short ecological time…
Computational Fluid Dynamics (CFD) plays a pivotal role in fluid mechanics, enabling precise simulations of fluid behavior through partial differential equations (PDEs). However, traditional CFD methods are resource-intensive, particularly…
Some recent developments in exact results in relativistic hydrodynamics is reviewed. We discuss phenomenological applications in high-energy collisions and theoretical features of the solutions. We compare the method of numerical modelling…