scholarly journals Experimental spatial rogue patterns in an optical feedback system

2010 ◽  
Vol 10 (12) ◽  
pp. 2727-2732 ◽  
Author(s):  
V. Odent ◽  
M. Taki ◽  
E. Louvergneaux
Keyword(s):  
Pattern Formation ◽  
Optical Feedback ◽  
Modulational Instability ◽  
Feedback System ◽  
Probability Density Functions ◽  
Kerr Medium ◽  
Density Functions ◽  
Long Tail ◽  
One Dimensional ◽  
Highly Nonlinear

Abstract. We study pattern formation in an optical system composed of a Kerr medium subjected to optical feedback but in a regime very far from the modulational instability threshold. In this highly nonlinear regime, the dynamics is turbulent and the associated one-dimensional patterns depict rare and intense localized optical peaks. We analyse numerically and experimentally the statistics and features of these intense optical peaks and show that their probability density functions (PDF) have a long tail indicating the occurrence of rogue events.

First-passage-time densities for time-non-homogeneous diffusion processes

1997 ◽  
Vol 34 (3) ◽  
pp. 623-631 ◽  
Author(s):  
R. Gutiérrez ◽  
L. M. Ricciardi ◽  
P. Román ◽  
F. Torres
Keyword(s):  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Continuous Functions ◽  
Probability Density Functions ◽  
Density Functions ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Natural Boundaries

In this paper we study a Volterra integral equation of the second kind, including two arbitrary continuous functions, in order to determine first-passage-time probability density functions through time-dependent boundaries for time-non-homogeneous one-dimensional diffusion processes with natural boundaries. These results generalize those which were obtained for time-homogeneous diffusion processes by Giorno et al. [3], and for some particular classes of time-non-homogeneous diffusion processes by Gutiérrez et al. [4], [5].

scholarly journals An Efficient Near-Field Localization Method of Coherently Distributed Strictly Non-circular Signals

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5176
Author(s):  
Meidong Kuang ◽  
Ling Wang ◽  
Yuexian Wang ◽  
Jian Xie
Keyword(s):  
Near Field ◽  
Integral Form ◽  
Approximate Expression ◽  
Probability Density Functions ◽  
Estimation Accuracy ◽  
Density Functions ◽  
Classical Probability ◽  
One Dimensional ◽  
Spatially Distributed ◽  
Field Localization

For the near-field localization of non-circular distributed signals with spacial probability density functions (PDF), a novel algorithm is proposed in this paper. The traditional algorithms dealing with the distributed source are only for the far-field sources, and they need two-dimensional (2D) search or omit the angular spread parameter. As a result, these algorithms are no longer inapplicable for near-filed localization. Hence the near-filed sources that obey a classical probability distribution are studied and the corresponding specific expressions are given, providing merits for the near-field signal localization. Additionally, non-circularity of the incident signal is taken into account in order to improve the estimation accuracy. For the steering vector of spatially distributed signals, we first give an approximate expression in a non-integral form, and it provides the possibility of separating the parameters to be estimated from the spatially discrete parameters of the signal. Next, based on the rank-reduced (RARE) algorithm, direction of arrival (DOA) and range can be obtained through two one-dimensional (1-D) searches separately, and thus the computational complexity of the proposed algorithm is reduced significantly, and improvements to estimation accuracy and identifiability are achieved, compared with other existing algorithms. Finally, the effectiveness of the algorithm is verified by simulation.

scholarly journals Probabilistic neural network-based 2D travel-time tomography

2020 ◽  
Vol 32 (22) ◽  
pp. 17077-17095 ◽  
Author(s):  
Stephanie Earp ◽  
Andrew Curtis
Keyword(s):  
Travel Time ◽  
Prior Information ◽  
Velocity Structure ◽  
Probability Density Functions ◽  
High Dimensional ◽  
Density Functions ◽  
Time Data ◽  
Informative Prior ◽  
Travel Time Data ◽  
Highly Nonlinear

Abstract Travel-time tomography for the velocity structure of a medium is a highly nonlinear and nonunique inverse problem. Monte Carlo methods are becoming increasingly common choices to provide probabilistic solutions to tomographic problems but those methods are computationally expensive. Neural networks can often be used to solve highly nonlinear problems at a much lower computational cost when multiple inversions are needed from similar data types. We present the first method to perform fully nonlinear, rapid and probabilistic Bayesian inversion of travel-time data for 2D velocity maps using a mixture density network. We compare multiple methods to estimate probability density functions that represent the tomographic solution, using different sets of prior information and different training methodologies. We demonstrate the importance of prior information in such high-dimensional inverse problems due to the curse of dimensionality: unrealistically informative prior probability distributions may result in better estimates of the mean velocity structure; however, the uncertainties represented in the posterior probability density functions then contain less information than is obtained when using a less informative prior. This is illustrated by the emergence of uncertainty loops in posterior standard deviation maps when inverting travel-time data using a less informative prior, which are not observed when using networks trained on prior information that includes (unrealistic) a priori smoothness constraints in the velocity models. We show that after an expensive program of network training, repeated high-dimensional, probabilistic tomography is possible on timescales of the order of a second on a standard desktop computer.

scholarly journals Small-Scale and Mesoscale Variability of Scalars in Cloudy Boundary Layers: One-Dimensional Probability Density Functions

2001 ◽  
Vol 58 (14) ◽  
pp. 1978-1994 ◽  
Author(s):  
Vincent E. Larson ◽  
Robert Wood ◽  
Paul R. Field ◽  
Jean-Christophe Golaz ◽  
Thomas H. Vonder Haar ◽  
...  
Keyword(s):  
Probability Density ◽  
Boundary Layers ◽  
Probability Density Functions ◽  
Small Scale ◽  
Density Functions ◽  
Mesoscale Variability ◽  
One Dimensional

scholarly journals PROBABILITY DENSITY FUNCTIONS OF BREAKING WAVES

1978 ◽  
Vol 1 (16) ◽  
pp. 28
Author(s):  
Edward B. Thornton ◽  
George Schaeffer
Keyword(s):  
Probability Density ◽  
Surf Zone ◽  
Wave Spectrum ◽  
Joint Probability ◽  
Nonlinear Process ◽  
Breaking Waves ◽  
Probability Density Functions ◽  
Density Functions ◽  
Highly Nonlinear ◽  
Highly Correlated

Waves in the surf zone are a highly nonlinear process which is evident by the appearance of secondary waves. The secondary waves appear as strong peaks in the period PDFs corresponding to the first harmonic of the peak of the wave spectrum. The strong first harmonic period peak is also reflected in the highly correlated height and velocity PDFs. Due to the high probability of the secondary waves, the mean wave period for breakers is a poor descriptor of the average period of the offshore incident waves. The joint probability density functions for periods and heights of the breaking waves show high correlation (0.60-0.80) which says that greater wave periods are associated with larger breaker heights. The joint PDFs of period and particle velocity, and velocity and height, suggest that the maximum onshore particle velocities are correlated with both the wave periods and wave heights.

First-passage-time densities for time-non-homogeneous diffusion processes

1997 ◽  
Vol 34 (03) ◽  
pp. 623-631 ◽  
Author(s):  
R. Gutiérrez ◽  
L. M. Ricciardi ◽  
P. Román ◽  
F. Torres
Keyword(s):  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Continuous Functions ◽  
Probability Density Functions ◽  
Density Functions ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Natural Boundaries

In this paper we study a Volterra integral equation of the second kind, including two arbitrary continuous functions, in order to determine first-passage-time probability density functions through time-dependent boundaries for time-non-homogeneous one-dimensional diffusion processes with natural boundaries. These results generalize those which were obtained for time-homogeneous diffusion processes by Giorno et al. [3], and for some particular classes of time-non-homogeneous diffusion processes by Gutiérrez et al. [4], [5].

Modulational-induced optical pattern formation in a passive optical-feedback system

1990 ◽  
Vol 7 (6) ◽  
pp. 1039 ◽  
Author(s):  
R. Indik ◽  
J. V. Moloney ◽  
H. Adachihara ◽  
C. Lizarraga ◽  
R. Northcutt ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Optical Feedback ◽  
Feedback System ◽  
Optical Pattern
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