Search results for "Gauss"

Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach

2011

Fractional power-law nonlinear drift arises in many applications of engineering interest, as in structures with nonlinear fluid viscous–elastic dampers. The probabilistic characterization of such structures under external Gaussian white noise excitation is still an open problem. This paper addresses the solution of such a nonlinear system providing the equation governing the evolution of the characteristic function, which involves the Riesz fractional operator. An efficient numerical procedure to handle the problem is also proposed.

Gaussian and non-Gaussian stochastic sensitivity analysis of discrete structural systems

2000

Abstract The derivatives of the response of a structural system with respect to the system parameters are termed sensitivities. They play an important role in assessing the effect of uncertainties in the mathematical model of the system and in predicting changes of the response due to changes of the design parameters. In this paper, a time domain approach for evaluating the sensitivity of discrete structural systems to deterministic, as well as to Gaussian or non-Gaussian stochastic input is presented. In particular, in the latter case, the stochastic input has been assumed to be a delta-correlated process and, by using Kronecker algebra extensively, cumulant sensitivities of order higher t…

Analytical solution for multisingular vortex Gaussian beams: The mathematical theory of scattering modes

2016

We present a novel procedure to solve the Schr\"odinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use the scattering modes, which are solutions of the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore permit to solve the problem. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role than Laguerre polynomials for Laguerre-Gaussian modes. We demonstrate here the recurrence relations need…

Fast and robust phase-shift estimation in two-dimensional structured illumination microscopy.

2019

A method of determining unknown phase-shifts between elementary images in two-dimensional Structured Illumination Microscopy (2D-SIM) is presented. The proposed method is based on the comparison of the peak intensity of spectral components. These components correspond to the inherent structured illumination spectral content and the residual compo- nent that appears from wrongly estimated phase-shifts. The estimation of the phase-shifts is carried out by finding the absolute maximum of a function defined as the normalized peak intensity difference in the Fourier domain. This task is performed by an optimization method providing a fast estimation of the phase-shift. The algorithm stability an…

Instantaneous hourly and daily radiation on tilted surfaces

1991

A simple model to evaluate the irradiance incident on tilted surfaces of various orientations is proposed in this paper. It is based on the knowledge of the monthly daily average values of global and diffuse radiation on horizontal surfaces and their distributions over a period of a day. These distributions are approximated by a modified Gaussian expression with two parameters, which take into account the morning-to-afternoon asymmetries. Integrating the irradiance over a period of an hour or a day, values of monthly hourly average and daily on variously oriented surfaces have been calculated for the locations of Barcelona, Genoa, and Montreal. The calculated values are generally in good ag…

Instantaneous distribution of global and diffuse radiation on horizontal surfaces

1991

Abstract The aim of this paper is to obtain a general expression for estimating both the instantaneous global and diffuse radiations on horizontal surfaces from the respective daily values. The proposed expression is a modified Gaussian distribution with two parameters which take into account its width and the asymmetries between morning and afternoon hours. The performance of the method has been tested by comparing the theoretical hourly results with the experimental data of six actinometric stations with different geographical location and climatic conditions. The comparison has shown that the method here proposed is accurate for both the diffuse and global radiation.

Generalized Wiener Process and Kolmogorov's Equation for Diffusion induced by Non-Gaussian Noise Source

2005

We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker-Planck equation for nonlinear system driven by white Gaussian noise, the Kolmogorov-Feller equation for discontinuous Markovian processes, and the fractional Fokker-Planck equation for anomalous diffusion. The stationary probability distributions for some simple cas…

Il Filtro Integrale Auto-Regressivo Continuo (I-ARC) per l’Analisi di Strutture Esposte al Vento

2010

In questo studio viene proposto un metodo per la rappresentazione di processi aleatori Gaussiani e stazionari, utile a modellare la turbolenza della velocità del vento, introducendo la versione integrale del modello auto-regressivo discreto già proposto in precedenza. La rappresentazione di un processo aleatorio di assegnata funzione di correlazione viene condotta integrando un’equazione integro-differenziale in cui viene coinvolto un nucleo, che rappresenta la memoria del processo, in presenza di un rumore bianco Gaussiano. La soluzione dell’equazione rappresenta un campione del processo aleatorio della turbolenza della velocità del vento. E’ stato mostrato che il modello I-ARC fornisce, n…

The variance of the $\ell _p^n$-norm of the Gaussian vector, and Dvoretzky’s theorem

2019

A Potential Field Function for Overlapping Point Set and Graph Cluster Visualization

2015

In this paper we address the problem of visualizing overlapping sets of points with a fixed positioning in a comprehensible way. A standard visualization technique is to enclose the point sets in isocontours generated by bounding a potential field function. The most commonly used functions are various approximations of the Gaussian distribution. Such an approach produces smooth and appealing shapes, however it may produce an incorrect point nesting in generated regions, e.g. some point is contained inside a foreign set region. We introduce a different potential field function that keeps the desired properties of Gaussian distribution, and in addition guarantees that every point belongs to a…