Related papers: Aerodynamic Models for Hurricanes IV. On the hurri…
We connect an appropriate feedback loop to a model of 2D vertical eddy of airflow which unfolds a wide range of vorticity behavior. Computational fluid dynamics of the twisted roll display a class of long lifespan 3D vortices. On the one…
This paper discusses the mathematical representation of an empirically observed phenomenon, referred to as Incremental Similarity. We discuss this feature from the viewpoint of stochastic processes and present a variety of non-trivial…
The problem of intermittency in developed hydrodynamic turbulence is considered. Explicit formulae taking into account effects of finite size of the inertial range are presented for the whole set of intermittency exponents. The formulae fit…
The method and results of the first theory description of 4He Compton scattering at nuclear energies is presented, with a focus on figures. An upcoming publication [1] contains details and a comprehensive list of references.
The aggravating effects of climate change and the growing population in hurricane-prone areas escalate the challenges in large-scale hurricane evacuations. While hurricane preparedness and response strategies vastly rely on the accuracy and…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
Building on recent research for prediction of hurricane trajectories using recurrent neural networks (RNNs), we have developed improved methods and generalized the approach to predict Bayesian intervals in addition to simple point…
A non-statistical theory of continuous, but irreversible, evolution can be constructed in terms of the Cartan calculus. The fundamental postulate, for an evolutionary theory which admits irreversible processes, is that the topology of the…
In mean-field theory, the non-local state of fluid molecules can be taken into account using a statistical method. The molecular model combined with a density expansion in Taylor series of the fourth order yields an internal energy value…
The universal instability mechanism in an ascending moist air flow is theoretically proposed and analyzed. Its origin comes to the conflict between two processes: the increasing of pressure forcing applied to the boundary layer and the…
In this paper, we consider an equation on random variables which can be reduced to the equation which describes the evolution of systems of fermions. We give some results of well-posedness for this equation on the spheres and torus of…
A previous paper (M.F.Atiyah and N.S.Manton, Complex geometry of nuclei and atoms, arXiv:1609.02816) modelled atoms and their isotopes by complex algebraic surfaces, with the projective plane modelling Hydrogen. In this paper, models of the…
Recent theoretical developments of relativistic hydrodynamics applied to ultrarelativistic heavy-ion collisions are briefly reviewed. In particular, the concept of a formal gradient expansion is discussed, which is a tool to compare…
A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of…
We briefly review some of the scientific challenges and epistemological issues related to climate science. We discuss the formulation and testing of theories and numerical models, which, given the presence of unavoidable uncertainties in…
We develop two models for the temporal evolution of extreme events of multivariate $k$th order Markov processes. The foundation of our methodology lies in the conditional extremes model of Heffernan & Tawn (2004), and it naturally extends…
This paper demonstrates how principle component analysis can be used to determine the distinct factors that house the terms that explain the variance among the co-dependent variables and how non-response analysis can be applied to model the…
We present a personal view of the state of the art in turbulence research. We summarize first the main achievements in the recent past, and then point ahead to the main challenges that remain for experimental and theoretical efforts.
Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical…
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…