Stochastic Plane Research Articles

Particle-beam scattering from strong-field QED

We consider the scattering of probe particles on an ultra-boosted beam of charge, in the case that the fields of the beam are strong and must be treated non-perturbatively. We show that the fields of the ultra-boosted beam act as stochastic plane waves - scattering amplitudes (of elastic scattering, nonlinear Compton and nonlinear Breit-Wheeler) are obtained without approximation by averaging plane wave scattering amplitudes over all possible plane wave parameters. The relevant plane waves are ultra-short and, as such, scattering on ultra-boosted beams does not exhibit the conjectured strong-field behaviour of QED based on the locally constant field approximation.

Вихревой генератор стохастических плоскостей

Various pseudorandom number generation algorithms may be used to create a discrete stochastic plane. If a Cartesian completeness property is required of the plane, it must be uniform. The point is, employing the concept of uncontrolled random number generation may yield low-quality results, since original sequences may omit random numbers or not be sufficiently uniform. We present a novel approach for generating stochastic Cartesian planes according to the model of complete twister sequences featuring uniform random numbers without omissions or repetitions. Simulation results confirm that the random planes obtained are indeed perfectly uniform. Moreover, recombining the original complete uniform sequence parameters allows the number of planes created to be significantly increased without using any extra random access memory.

Damage localization in offshore structures using shaped inputs

Input shaping is an active control procedure by which vibrations in a structural subdomain are suppressed. Recently, a scheme based on shaped inputs has been proposed for damage localization purposes; cast on the premise that the vibration signature of a structural domain in a damaged phase will be identical to the signature of the healthy, reference counterpart if, for the same loading conditions, the subdomain containing damage is inactive in terms of vibrations. The idea is, thus, to apply controllable inputs that are shaped such that particular vibration quantities (depending on the type of damage one seeks to localize) are suppressed in one subdomain at the time, hereby resulting in damage being localized when the vibration signature induced by the shaped inputs in the damaged phase corresponds to that obtained in the reference phase. The present paper treats an application study that illustrates the damage localization scheme in simulations on a finite element model of an offshore jacket structure exposed to stochastic plane wave fields generated from a directional wave spectrum, and with fluid-structure interaction considered in terms of the Morison equation. In both structural phases, that is, the reference and the damaged one with a single mass perturbation, four inputs to be shaped are applied, and the resulting displacements are extracted from a single spatial location within the model. It is contended that the damage is localized when suppressing displacements (and their time-derivatives) near or, ideally, directly at its location.

Hybrid stress quadrilateral finite element approximation for stochastic plane elasticity equations

SummaryThis paper considers stochastic hybrid stress quadrilateral finite element analysis of plane elasticity equations with stochastic Young's modulus and stochastic loads. Firstly, we apply Karhunen–Loève expansion to stochastic Young's modulus and stochastic loads so as to turn the original problem into a system containing a finite number of deterministic parameters. Then we deal with the stochastic field and the space field by k−version/p−version finite element methods and a hybrid stress quadrilateral finite element method, respectively. We derive a priori error estimates, which are uniform with respect to the Lamè constant λ∈(0,+∞). Finally, we provide some numerical results. Copyright © 2016 John Wiley & Sons, Ltd.

A Fast and Robust Feature-Based Scan-Matching Method in 3D SLAM and the Effect of Sampling Strategies

Simultaneous localization and mapping (SLAM) plays an important role in fully autonomous systems when a GNSS (global navigation satellite system) is not available. Studies in both 2D indoor and 3D outdoor SLAM are based on the appearance of environments and utilize scan-matching methods to find rigid body transformation parameters between two consecutive scans. In this study, a fast and robust scan-matching method based on feature extraction is introduced. Since the method is based on the matching of certain geometric structures, like plane segments, the outliers and noise in the point cloud are considerably eliminated. Therefore, the proposed scan-matching algorithm is more robust than conventional methods. Besides, the registration time and the number of iterations are significantly reduced, since the number of matching points is efficiently decreased. As a scan-matching framework, an improved version of the normal distribution transform (NDT) is used. The probability density functions (PDFs) of the reference scan are generated as in the traditional NDT, and the feature extraction - based on stochastic plane detection - is applied to the only input scan. By using experimental dataset belongs to an outdoor environment like a university campus, we obtained satisfactory performance results. Moreover, the feature extraction part of the algorithm is considered as a special sampling strategy for scan-matching and compared to other sampling strategies, such as random sampling and grid-based sampling, the latter of which is first used in the NDT. Thus, this study also shows the effect of the subsampling on the performance of the NDT.

Second-order statistics of complex observables in fully stochastic electromagnetic interactions: Applications to EMC

[1] The usefulness of stochastic methods to efficiently quantify uncertainties in computational models of electromagnetic interactions is illustrated. A refined study of the second-order moments of a complex-valued Thevenin model, which represents the coupling between a wire structure and a time-harmonic electromagnetic field, is presented. The configuration of a stochastically undulating thin wire illuminated by a stochastic incident plane wave is investigated in detail. Three computational methods are used to evaluate the mean values and covariance coefficients of the observable: a straightforward Cartesian-product quadrature method, a Monte-Carlo method, and a space-filling-curve method. The underlying patterns of the randomness are revealed by analyzing the covariance matrix' principal components. The study of this interaction configuration shows some general characteristics, which are expected to show up in any stochastic electromagnetic interaction problem. In particular, the results indicate that fluctuations in self-interaction coefficients (impedances) have distinct features and are quite different from the coefficients describing the interaction with externally generated fields (voltages).

Analytically determining of the absolute inaccuracy (error) of indirectly measurable variable and dimensionless scale characterising the quality of the experiment

Abstract In the following paper we present an easily applicable new method for the analytical representation of the maximum absolute inaccuracy (error) of an indirectly measurable variable f = f(x1, x2, ..., xn) as a function of the maximum absolute inaccuracies (errors) of the directly measurable variables x1, x2, ..., xn. Our new approach is more adequate for the objective reality. The gist of it is that in order to find the analytical form of the maximum absolute inaccuracy of the variable f we take for being fixed variables the statistical mean values ∂ f ∂ x 1 ― , ∂ f ∂ x 2 ― , ... , ∂ f ∂ x n ― of the modules of the moment velocities of alteration of f in respect of the variables x1, x2, ..., xn and the numerical value of the maximum absolute inaccuracy of the variable f is found using the statistical mean values of the absolute values of the absolute inaccuracies Δ x 1 ― , Δ x 2 ― , ... , Δ x n ― . Having this in mind we develop the theory of errors, which we will call with what we feel is a more precise term — theory of inaccuracies. We introduce some new terms — space of the absolute inaccuracy and stochastic plane of the absolute inaccuracy of f. We also define a sample plane of the ideal absolutely accurate experiment and using it we define a universal numerical characteristic — a dimensionless scale for evaluation of the quality (accuracy) of the experiment.

Statistics of the Polarimetric Weibull-Distributed Electromagnetic Wave

The statistical properties of partially polarized light in Gaussian stochastic plane wave fields have been reported in the literature. In this paper, we examine the statistics of the stochastic plane electromagnetic (EM) wave fields that are Weibull distributed. The polarimetric Weibull-distributed wave is characterized by three parameters: the sum of the intensities of the two electric vector components, the orientation angle that the major axis makes with the reference coordinate system, and the ratio of the minor to the major axis. The joint and marginal probability densities of these random variables are determined as a function of the covariance matrix. The main properties of this important distribution are shown. Then, the statistical properties of the normalized Stokes parameters are described in detail in Weibull-distributed stochastic fields. The joint and marginal probability density functions of the three components of the normalized Stokes parameters are presented. Numerical simulations are operated, which coincide with the theoretical derivations. Comparisons between Gaussian and Weibull stochastic fields have been made. The presented statistics of the Weibull polarimetric wave will be useful to random medium scattering and speckle filtering, which can also be extended to deal with the characterization of the scattering matrix elements in radar polarimetry.

Statistics of the instantaneous polarization in Weibull——distributed fields-the same shape parameter case

The statistical properties of partially polarized light in Gaussian stochastic plane wave fields have been studied. In this paper, the statistics of the stochastic plane electromagnetic （EM） wave fields with Weibull distributed is examined. The polarimetric Weibull_distributed wave is characterized by three parameters: the sum of the amplitudes of the two electric vector components, the angle which the major axis makes with the reference coordinate system, and the ratio of the minor to the major axis. The joint and marginal probability densities of these random variables are determined as a function of the covariance matrix. The main properties of this important distribution are shown. Then the statistical properties of the normalized Stokes parameters are described in detail in Weibull_distributed stochastic fields. The joint and marginal probability density functions （PDF） of the three components of the normalized Stokes parameters are presented. Results of some numerical calculation are obtained. The description of the Weibull polarimetric wave field may be useful to random medium scattering and speckle filtering.

Statistical characteristics of the normalized Stokes parameters

The statistical properties of the normalized Stokes parameters in a Gaussian stochastic plane wave field are described in detail. Via the expression of the three normalized Stokes parameters, the mean, variance, and high-order moments are calculated, which simplify C. Brosseau’s results. The new dispersion, normalized contrast function, skewness, and kurtosis are defined to describe the non-Gaussian distribution characteristics, which can be applied to Gaussian wave fields relating to depolarization of light by a spatially random medium.

Probabilistic modelling of stochastic interactions between electromagnetic fields and systems

Rigorous deterministic models of physical phenomena are important for understanding the fundamental characteristics of interactions, but if we neglect the uncertainties in the various components of these models, the correspondence between predictions based on such models and real-life situations can be very weak. This article addresses the important question of how to account, rigorously, for uncertainties in classical macroscopic electromagnetic interactions between fields and systems of linear material (considering uncertainties in the field incident on the system as well as in the geometrical realisation of the system itself). In the first part, we develop the general ideas which lead to the expression of the variances of the observables of the problem in terms of field- and system covariance operators. In the second part, we study the covariance operator which characterises a stochastic system. In the third part, we investigate stochastic electromagnetic fields and present the definition of a canonical stochastic field of which the spatial covariance operator has the real part of the Green tensor function as kernel function. In the final part, we present an illustration by studying the interaction of a stochastic plane wave with a stochastic twisted pair of wires. To cite this article: B.L. Michielsen, C. R. Physique 7 (2006).

Covariance operators, Green functions, and canonical stochastic electromagnetic fields

In this paper, we show that for a large class of lossless reciprocal configurations, a “canonical” stochastic electromagnetic field can be defined such that its spatial covariance is proportional to the real part of the Green tensor function of the configuration. This result generalizes some relations between stochastic plane waves and free space Green functions which are well known in theoretical physics. A special application of the ideas presented here is elaborated for the configuration of a semi‐infinite, short‐circuited waveguide. It is shown that the canonical stochastic electromagnetic field in that case is a pseudoisotropic plane wave corresponding to a very special stochastic linear combination of propagating modes only. This has important consequences for the electromagnetic theory of so‐called mode‐stirred chambers.

Milne problem in stochastic plane medium with linear anisotropic scattering

The Milne problem of radiative transfer in planar stochastic medium, with linear anisotropic scattering is considered. The medium is assumed to be consisting of two randomly mixed immiscible fluids, with the mixing statistics described as two state homogeneous Markov process. Pomraning–Eddington approach is used to obtain an explicit form for the radiation energy density in deterministic case. A formalism, developed to treat radiative transfer in binary statistical mixtures, is used to obtain the ensemble averaged energy density in stochastic case for the problem under consideration. It is shown that the statistical nature of the medium leads to two contradictory different definitions for the linear extrapolated distance. In the case of isotropic scattering, numerical results are given with comparisons. Results are also given in the case of linear anisotropic scattering at different values of anisotropic coefficient.

Statistics of the normalized Stokes parameters for a Gaussian stochastic plane wave field

<p>The statistics of the normalized Stokes parameters for a stochastic plane wave field that is Gaussian distributed is examined. The resulting probability density functions and lower-order moments generalized those obtained by previous investigators. Results of some numerical calculations are discussed.</p><p>As an application of this analysis, we consider multiple scattering of light by a spatially random medium, composed of uncorrelated spherical pointlike particles, where the description of partially polarized light in terms of normalized Stokes parameters may be useful.</p>

Variability Response Functions of Stochastic Plane Stress/Strain Problems

The concept of variability response function based on the weighted‐integral method is extended to two‐dimensional plane stress/plane strain stochastic problems in order to calculate their response variability (in terms of second moments of response quantities) and reliability (in terms of the safety index) with great accuracy even when using relatively coarse finite‐element meshes. The concept of variability response function is used to establish spectral‐distribution‐free upper bounds of the response variability. In addition, the variability response function based on the local‐averaging method is introduced to reduce the computational effort associated with the weighted‐integral method. The two methods are compared to estimate the relative accuracy of the more approximate local‐averaging method. The response variability is calculated using a first‐order Taylor expansion approximation of the response quantities. The safety index is calculated using the advanced first‐order second‐moment approach. One of ...