Related papers: Accurate analytical approximation formulae for lar…
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…
Rainfall from ice-free cumulus clouds requires collisions of large numbers of microscopic droplets to create every raindrop. The onset of rain showers can be surprisingly rapid, much faster than the mean time required for a single…
Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate droplet size but fails to approximate droplet shape. This is due to a highly non-linear flow description near the…
One of the goals of climate science is to characterize the statistics of extreme and potentially dangerous events in the present and future climate. Extreme events like heat waves, droughts, or floods due to persisting rains are…
A description of the dynamics of a collisionless, self-gravitating fluid is developed and applied to follow the development of Large Scale Structures in the Universe. Such description takes on one of the assumptions of the Adhesion…
An algorithm to estimate motion from satellite imagery is presented. Dense displacement fields are computed from time-separated images of of significant convective activity using a Bayesian formulation of the motion estimation problem.…
Laboratory experiments and theoretical modelling are conducted to determine the raindrop size distribution (DSD) resulting from distinct fragmentation processes under various upward airstreams. Since weather radar echoes are proportional to…
One of the main contributions of this paper is to illustrate how large deviation theory can be used to determine the equilibrium distribution of a basic droplet model that underlies a number of important models in material science and…
The paper presents improved mathematical models and methods for statistical regularities in the behavior of some important characteristics of precipitation: duration of a wet period, maximum daily and total precipitation volumes within a…
This paper develops the large deviations theory for the point process associated with the Euclidean volume of $k$-nearest neighbor balls centered around the points of a homogeneous Poisson or a binomial point processes in the unit cube. Two…
It was previously shown that the superdroplet algorithm for modeling the collision-coalescence process can faithfully represent mean droplet growth in turbulent clouds. But an open question is how accurately the superdroplet algorithm…
We revisit the one-dimensional model of the symmetric simple exclusion process slowly coupled with two unequal reservoirs at the boundaries. In its non-equilibrium stationary state, the large deviations functions of density and current have…
For over a century, raindrop size distributions have been a subject of extensive scientific study, typically described by models including the Marshall-Palmer exponential equation, gamma, Weibull, lognormal, and other mathematical…
Large deviation theory offers a powerful and general statistical framework to study the asymptotic dynamical properties of rare events. The application of the formalism to concrete experimental situations is, however, often restricted by…
Anisotropic flow measurements in heavy-ion collisions provide important information on the properties of hot and dense matter. These measurements are based on analysis of azimuthal correlations and might be biased by contributions from…
Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster quick and a deep understanding of the data as an…
We present a first principle approach to obtain analytical predictions for spherically-averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation…
We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical…
A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…
We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on…