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Advances in extragalactic astronomy have prompted the development of increasingly realistic models which aim to describe the formation and evolution of galaxies. We review the philosophy behind one such technique, called semi-analytic…
A hydrodynamic formulation of the evolution of large-scale structure in the Universe is presented. It relies on the spatially coarse-grained description of the dynamical evolution of a many-body gravitating system. Because of the assumed…
For the mathematical modeling of highly non-equilibrium and nonlinear processes in a tornado in this paper a new approach based on nonlinear equations of momentum transfer with function of sources and sinks is suggested. In constructing the…
Since the 1990s, RANS practitioners have observed spontaneous unsteadiness in RANS simulations. Some have suggested deliberately using this as a method of resolving large turbulent structures. However, to date, no one has produced a…
The understanding and prediction of large wildland fire events around the world is a growing interdisciplinary research area advanced rapidly by development and use of computational models. Recent models bidirectionally couple computational…
Our understanding of the processes that are relevant to the formation and maintenance of habitable planetary systems is advancing at a rapid pace, both from observation and theory. The present review focuses on recent research that bears on…
The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to…
In previous work we have analysed the Atlantic basin hurricane number time-series to identify decadal time-scale change points. We now repeat the analysis but for US landfalling hurricanes. The results are very different.
In this review, I provide an overview of theoretical aspects related to the evolution of galaxies as a function of environment. I discuss the main physical processes at play, their characteristic time-scales and environmental dependency,…
We perform an objective change-point analysis on 106 years of historical hurricane number data. The algorithm we use looks at all possible combinations of change-points and compares them in terms of the variances of the differences between…
The radius of maximum wind ($R_{max}$) in a hurricane governs the footprint of hazards, particularly damaging wind and rainfall. However, $R_{max}$ is noisy to observe directly and is poorly resolved in reanalyses and climate models. In…
In previous work, we have shown how to combine long and short historical baselines to make predictions of future hurricane numbers. We now ask: how should such combinations change if we are interested in predicting the future number of…
The evolution equations for the generalized microscopic phase densities are introduced. The evolution equations of average values of microscopic phase densities are derived and a solution of the initial-value problem of the obtained…
While extensive guidance exists for ensuring the reproducibility of one's own study, there is little discussion regarding the reproduction and replication of external studies within one's own research. To initiate this discussion, drawing…
Hurricanes are cyclones circulating about a defined center whose closed wind speeds exceed 75 mph originating over tropical and subtropical waters. At landfall, hurricanes can result in severe disasters. The accuracy of predicting their…
Models of planet formation are built on underlying physical processes. In order to make sense of the origin of the planets we must first understand the origin of their building blocks. This review comes in two parts. The first part presents…
The generation of synthetic tropical cyclone(TC) tracks for risk assessment is a critical application of preparedness for the impacts of climate change and disaster relief, particularly in North America. Insurance companies use these…
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
In this article, we address both recent advances and open questions in some mathematical and computational issues in geophysical fluid dynamics (GFD) and climate dynamics. The main focus is on 1) the primitive equations (PEs) models and…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…