Stochastic theory of the Stokes parameters in randomly twisted fiber

A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker–Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

Download Full-text

Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Mathematics ◽

10.3390/math9121329 ◽

2021 ◽

Vol 9 (12) ◽

pp. 1329

Author(s):

Lev Ryashko ◽

Dmitri V. Alexandrov ◽

Irina Bashkirtseva

Keyword(s):

Multiplicative Noise ◽

Nonlinear Dynamical Systems ◽

Stochastic Theory ◽

Slow Variable ◽

Theoretical Description ◽

Mathematical Study ◽

Stochastic Generation ◽

Nonlinear Dynamical ◽

Additive And Multiplicative Noise ◽

And Shifts

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

Download Full-text

E and B families of the Stokes parameters in the polarized synchrotron and thermal dust foregrounds

Journal of Cosmology and Astroparticle Physics ◽

10.1088/1475-7516/2018/05/059 ◽

2018 ◽

Vol 2018 (05) ◽

pp. 059-059 ◽

Cited By ~ 7

Author(s):

Hao Liu ◽

James Creswell ◽

Pavel Naselsky

Keyword(s):

Stokes Parameters

Download Full-text

New diagonal micropolarizer arrays designed by an improved model in fourier domain

Scientific Reports ◽

10.1038/s41598-021-85103-x ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Jia Hao ◽

Yan Wang ◽

Kui Zhou ◽

Xiaochang Yu ◽

Yiting Yu

Keyword(s):

Stokes Parameters ◽

Fourier Domain ◽

Extended Model ◽

Reconstruction Accuracy ◽

Polarization Imaging ◽

New Class ◽

Reconstruction Quality ◽

Improved Design ◽

Improved Model

AbstractThe design of micropolarizer array (MPA) patterns in Fourier domain provides an efficient approach to reconstruct and investigate the polarization information. Inspired by Alenin’s works, in this paper, we propose an improved design model to cover both 2 × N MPAs and other original MPAs, by which an entirely new class of MPA patterns is suggested. The performance of the new patterns is evaluated through Fourier domain analysis and numerical simulations compared with the existing MPAs. Particularly, we analyze the reconstruction accuracy of the first three Stokes parameters and degree of linear polarization (DoLP) in detail. The experimental results confirm that the 2 × 2 × 2 MPA provides the highest reconstruction quality of s0, s1, s2 and DoLP in terms of quantitative measures and visual quality, while the 3 × 3 diagonal MPA achieves the state-of-the-art best results in case of single-snapshot systems. The guidance of this extended model and new diagonal MPAs show its massive potential for the division of focal plane (DoFP) polarization imaging applications.

Download Full-text

A Framework for Modelling Economic Regional Location Processes Under Uncertainty

Journal of Quantitative Economics ◽

10.1007/s40953-021-00248-w ◽

2021 ◽

Author(s):

Roy Cerqueti ◽

Eleonora Cutrini

Keyword(s):

Theoretical Model ◽

Theoretical Analysis ◽

Site Selection ◽

Decision Problem ◽

Stochastic Theory ◽

Spatial Location ◽

Probabilistic Framework ◽

Location Patterns ◽

Regional Location ◽

Quantitative Tool

AbstractThis paper deals with the theoretical analysis of the spatial concentration and localization of firms and employees over a set of regions. In particular, it provides a simple site-selection theoretical model to describe the probabilistic framework of the location patterns. The adopted quantitative tool is the stochastic theory of urns. The model moves from the empirical evidence of the deviation of the spatial location of companies from the uniform distribution and of employees from the distribution of firms. Factors leading to such deviations are taken into consideration. Specifically, we formalize a decision problem grounded on the economic attributes of the regions and also on the distribution of the existing firms and employees in the territory. To our purpose, the site-selection model is presented as a stepwise process.

Download Full-text