Related papers: Stochastic Assessment of Acceleration Probability …
Estimating the probability of collision between spacecraft is crucial for risk management and collision-avoidance strategies. Current methods often rely on Gaussian assumptions and simplifications, which can be inaccurate in highly…
We investigate the behavior of the magnetic pressure, $b^2$, in fully turbulent MHD flows in ``1+2/3'' dimensions by means of its effect on the probability density function (PDF) of the density field. We start by reviewing our previous…
The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting…
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…
We conduct numerical experiments to determine the density probability distribution function (PDF) produced in supersonic, isothermal, self-gravitating turbulence of the sort that is ubiquitous in star-forming molecular clouds. Our…
The behavior of the probability density function (PDF) transport equation at the limits of the probability space is studied from the point of view of fluid mechanics. Different boundary conditions are considered depending on the nature of…
(Abridged) We discuss the probability distribution function (PDF) of column density resulting from density fields with lognormal PDFs, applicable to isothermal gas (e.g., probably molecular clouds). We suggest that a ``decorrelation…
We investigate the single-point velocity probability density function (PDF) in three-dimensional fully developed homogeneous isotropic turbulence within the framework of PDF equations focussing on deviations from Gaussianity. A joint…
The probability density function (PDF) for critical wavefunction amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of…
Accurate reconstruction of probability density functions (PDFs) from data is essential in engineering applications. Classical global moment-based polynomial approximations often suffer from oscillations, instability in the tails, and…
Rod shaped objects suspended in a flowing liquid might be orientated by the velocity, nature of the liquid, the flow and the geometry of the channel containing the flow. Orientation settings might enhance or inhibit certain chemical…
We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state,…
In this paper we demonstrate that multi-modal Probability Distribution Functions (PDFs) may be efficiently sampled using an algorithm originally developed for numerical integrations by Monte-Carlo methods. This algorithm can be used to…
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…
Turbulence is essential for understanding the structure and dynamics of molecular clouds and star-forming regions. There is a need for adequate tools to describe and characterize the properties of turbulent flows. One-point probability…
In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A mathematically exact…
Lagrangian stochastic methods are widely used to model turbulent flows. Scarce consideration has, however, been devoted to the treatment of the near-wall region and to the formulation of a proper wall-boundary condition. With respect to…
The Boeder differential equation is solved in this work over a wide range of $\alpha$, yielding the probability density functions (PDF), that describe the average orientations of rod-like macromolecules in a flowing liquid. The quantity…
Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, optimal first-passage…
The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a…