Search results for "Poisson distribution"
showing 10 items of 110 documents
Stochastic ship roll motion via path integral method
2010
ABSTRACTThe response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple …
Force-clamp spectroscopy of reversible bond breakage.
2008
We consider reversible breaking of adhesion bonds or folding of proteins under the influence of a constant external force. We discuss the stochastic properties of the unbinding/rebinding events and analyze their mean number and their variance in the framework of simple two-state models. In the calculations, we exploit the analogy to single molecule fluorescence and particularly between unbinding/rebinding and photon emission events. Environmental fluctuation models are used to describe deviations from Markovian behavior. The second moment of the event-number distribution is found to be very sensitive to possible exchange processes and can thus be used to identify temporal fluctuations of th…
Relativistic second-order perturbations of the Einstein-de Sitter universe
1998
We consider the evolution of relativistic perturbations in the Einstein-de Sitter cosmological model, including second-order effects. The perturbations are considered in two different settings: the widely used synchronous gauge and the Poisson (generalized longitudinal) one. Since, in general, perturbations are gauge dependent, we start by considering gauge transformations at second order. Next, we give the evolution of perturbations in the synchronous gauge, taking into account both scalar and tensor modes in the initial conditions. Using the second-order gauge transformation previously defined, we are then able to transform these perturbations to the Poisson gauge. The most important feat…
Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator
2021
Abstract In this paper we present a study on random processes consisting of delta pulses characterized by strongly super-Poisson statistics and calculate its spectral density. We suggest a method for replacing a strongly super-Poisson process with a wide-pulse Poisson process, while demonstrating that these two processes can be set in such a way to have similar spectral densities, the same mean values, and the same correlation times. We also present a billiard system that can be used to generate random pulse noise of arbitrary statistical properties. The particle dynamics is considered in terms of delta and wide pulses simultaneously. The results of numerical experiments with the billiard s…
Widespread Nanoflare Variability Detected with Hinode/X-Ray Telescope in a Solar Active Region
2011
It is generally agreed that small impulsive energy bursts called nanoflares are responsible for at least some of the Sun's hot corona, but whether they are the explanation for most of the multimillion-degree plasma has been a matter of ongoing debate. We present here evidence that nanoflares are widespread in an active region observed by the X-Ray Telescope on board the Hinode mission. The distributions of intensity fluctuations have small but important asymmetries, whether taken from individual pixels, multipixel subregions, or the entire active region. Negative fluctuations (corresponding to reduced intensity) are greater in number but weaker in amplitude, so that the median fluctuation i…
Boundary correspondence of Nevanlinna counting functions for self-maps of the unit disc
2003
Let ϕ \phi be a holomorphic self-map of the unit disc D \mathbb {D} . For every α ∈ ∂ D \alpha \in \partial \mathbb {D} , there is a measure τ α \tau _\alpha on ∂ D \partial \mathbb {D} (sometimes called Aleksandrov measure) defined by the Poisson representation Re ( α + ϕ ( z ) ) / ( α − ϕ ( z ) ) = ∫ P ( z , ζ ) d τ α ( ζ ) \operatorname {Re}(\alpha +\phi (z))/(\alpha -\phi (z)) = \int P(z,\zeta ) \,d\tau _\alpha (\zeta ) . Its singular part σ α \sigma _\alpha measures in a natural way the “affinity” of ϕ \phi for the boundary value α \alpha . The affinity for values w w inside D \mathbb {D} is provided by the Nevanlinna counting function N ( w ) N(w) of ϕ \phi . We introduce a natural …
Cohomology and Deformation of Leibniz Pairs
1995
Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebra $A$ together with a Lie algebra $L$ mapped into the derivations of $A$. A bicomplex (with both Hochschild and Chevalley-Eilenberg cohomologies) is essential.
The Poisson embedding approach to the Calderón problem
2020
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large class of Calder\'on type inverse problems for quasilinear equations in the real analytic case. The approach also leads to a new proof of the result by Lassas and Uhlmann (2001) solving the Calder\'on problem on real analytic Riemannian manifolds. The proof uses the Poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism. The method also involves various Runge approximation results for linear elliptic equations.
Results of the measurements carried out in order to verify the validity of the poisson-exponential distribution in radioactive decay events
1978
Abstract Berkson, examining a series of 250,000 disintegration time intervals, found a significant departure of the distribution from the Poisson-exponential law. Therefore he proposed to repeat the experiment using a large number of intervals and to check the interval recordings by using more than one recording instrument simultaneously. Accepting these suggestions we developed two systems of data collecting provided with different controls. In several experiments we collected data for more than one million decay intervals. The results elaborated using the Pearson ξ 2 test reflect a Poisson process of the radioactive decay events.
Multivariate statistical analysis for water demand modelling: implementation, performance analysis, and comparison with the PRP model
2015
Water demand is the driving force behind hydraulic dynamics in water distribution systems. Consequently, it is crucial to accurately estimate the actual water use to develop reliable simulation models. In this study, copula-based multivariate analysis was proposed and used for demand prediction for a given return period. The analysis was applied to water consumption data collected in the water distribution network of Palermo (Italy). The approach produced consistent demand patterns and could be a powerful tool when coupled with water distribution network models for design or analysis problems. The results were compared with those obtained using a classical water demand model, the Poisson re…