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The impacts of a tropical cyclone after landfall depend not only on storm intensity but also on the size and structure of the wind field. Hence, a simple predictive model for the wind field after landfall has significant potential value.…
Foundation models have enormous potential in advancing Earth and climate sciences, however, current approaches may not be optimal as they focus on a few basic features of a desirable Earth and climate foundation model. Crafting the ideal…
General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General…
Models of random phylogenetic networks have been used since the inception of the field, but the introduction and rigorous study of mathematically tractable models is a much more recent topic that has gained momentum in the last 5 years.…
Modern weather and climate models share a common heritage, and often even components, however they are used in different ways to answer fundamentally different questions. As such, attempts to emulate them using machine learning should…
The recent 1/2-equation model of turbulence is a simplification of the standard Kolmogorov-Prandtl 1-equation URANS model. Surprisingly, initial numerical tests indicated that the 1/2-equation model produces comparable velocity statistics…
The generation of ocean surface waves by wind is a classic fluid mechanics problem whose theoretical study dates back to 1957, when the two seminal papers by Phillips and Miles were published in the incipient Journal of Fluid Mechanics.…
Vapor condensation with removing of latent heat by emission of characteristic frequencies allows fast droplets formation in big volumes, which becomes possible with spatial redistribution and spreading of condensation nuclei and ions formed…
This paper reviews our current understanding of terrestrial planets formation. The focus is on computer simulations of the dynamical aspects of the accretion process. Throughout the chapter, we combine the results of these theoretical…
We give a simple, semianalytic theory of the development of the hadronic and neutrino/muon components of a cascade induced by a primary which produces hadrons at the initial interaction. The main purpose of the theory is to allow the user…
The history and present state of large-scale magnetohydrodynamic (MHD) modeling of the solar corona and the solar wind with steady or quasi-steady coronal physics is reviewed. We put the evolution of ideas leading to the recognition of the…
This chapter is dedicated to the slow dynamics of the climate system, at time scales of one~thousand to one million years. We focus specifically on the phenomenon of ice ages that has characterised the slow evolution of climate over the…
Relation of ultrametric analysis, wavelet theory and cascade models of turbulence is discussed. We construct the explicit solutions for the nonlinear ultrametric integral equation with quadratic nonlinearity. These solutions are built by…
Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of…
We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, and linear equivalence on tropical complexes, analogous both…
In this article, we review the different models and methods to understand and estimate correlated evolution within the same genome, individual or species. We describe correlated evolution among traits, among genetic components and finally…
This paper is the second of two papers devoted to the study of the evolution of the cosmological horizons (particle and event horizons). Specifically, in this paper we consider the extremely general case of an accelerated universe with…
This work is an attempt to give a brief overview of the implementation of the statistical ther- modynamics to hadronic matter. The possibility to use the hydrodynamic approach for developing the physical model of the formation of exotic…
We summarise some of the recent progress in understanding the formation and evolution of globular clusters (GCs) in the context of galaxy formation and evolution. It is discussed that an end-to-end model for GC formation and evolution…
We examine the hydrodynamics of a granular gas using numerical simulation. We demonstrate the appearance of shearing and clustering instabilities predicted by linear stability analysis, and show that their appearance is directly related to…