Optical Möbius strips in isotropic random non-paraxial light

In modeling electromagnetic phenomena randomness of the propagation medium and of the dielectric object should be taken up. The usually applied Monte-Carlo based methods reveal true characteristics of the random electromagnetic field at the expense of large computation time and computer memory. Use of expansion based methods and their resulting algorithm is an efficient alternative. In this paper the focus is on characteristics of electromagnetic fields that satisfy integral equations where the integral kernel has a random component, typically, electromagnetic fields that describe scattering due to dielectric objects with an inhomogeneous random contrast field. The assumption is that the contrast is affinely related to a random variable. The integral equation is of second kind Fredholm type so that its solutions are determined by the resolvent, a random operator field. The key idea is to expand that operator field with respect to orthogonal polynomials defined by the probability measure on the underlying sample space and to derive the properties of the solution from that expansion. Two types of illustration are presented: an inhomogeneous dielectric slab and a 2D dielectric grating with 1D periodicity.

It is theorized that the quantum vacuum is a random electromagnetic field that permeates the universe. It will be shown that acceleration between a quark and a random electromagnetic energy field is an analog of the reaction between a charge moving at constant velocity with respect to an organized electromagnetic field. The difference is that with a quark any natural perpendicular deflection during that motion, as predicted by Lorentz, is contained by the strong force, which results in a change in the angular momentum of the spin of a quark. The first derivative of the equations of motion of charges in an organized electromagnetic field may be used when applied to a random electromagnetic field to invoke the same fields modeled by Maxwell’s equations. Mass is intimately bound up with a quark’s spin angular momentum and the energy for that increase comes directly from the local field. The underlying randomness of the local field normally remains intact through these energy exchanges but it is speculated that in a quantum entanglement, an absolute level of order is imposed on the field along a path between two particles. This causes the non local effects seen in quantum entanglement. The mechanism that may cause this effect is discussed and a simple experiment is proposed that can test the hypothesis. Also discussed are new theoretical constructs for electromagnetic radiation, mass, the skin effect, self‐inductance, superposition, and gravity. The emphasis will be on an intuitive and logical approach more than a mathematical approach.

Part 1 Approximate modelling of homogeneous Gaussian fields on the basis of spectral decomposition: spectral models of random processes and fields basic principles of constructing spectral models - generalized scheme, about numerical analysis of the error, examples of spectral models of stationary processes, examples of spectral models for isotropic fields on a plane, spectral models for isotropic fields in three-dimensional space technique of successive refinement of spectral models on the same probability space description of the algorithm - auxillary statements and examples, conditional spectral models statement of the problem - method of solving the problem, on realization of numerical algorithm specialized models for isotropic fields on a k-dimensional space and on a sphere models of isotropic fields on a k-dimensional space - spectral models of isotropic fields on a sphere certain applications of scalar spectral models simulation of clouds - spectral model of the sea surface undulation further remarks nonhomogeneous spectral models - approximate modelling of Gaussian vectors of stationary type by discrete Fourier transform. Part 2 Spectral models for vector-valued fields: spectral representations spectral representations for complex-valued vector random fields, spectral representations or real-valued vector random fields isotropy simulation of random harmonics complex-valued harmonics - real-valued harmonics, about simulation of complex-valued Gaussian vectors spectral models of homogeneous Gaussian vector-valued fields examples of simulation gradient of isotropic scalar field, solenoidal and potential isotropic random fields, vector-valued isotropic fields on plane and in space. Part 3 Convergence of spectral models of random fields in Monte Carlo methods: conditions of weak convergence in spaces C and Cp weak convergence in the space of continuous functions, weak convergence of probability measures in space of continuously differentiable functions convergence of spectral models of Gaussian homogeneous fields spectral models - weak convergence of spectral models in spaces of continuously differentiable functions. (Part ocntents).

In this paper we consider the ℏ→0 asymptotics for the solutions to stochastic Schrödinger equations for quantum mechanical particles in random electromagnetic fields in Rn. We obtain semi-classical expansions for their solutions up to any order in L2(Rn) a.s. by using a stochastic Hamilton Jacobi equation and a stochastic continuity equation. We conclude that as ℏ→0 the stochastic quantum mechanics with random electromagnetic fields tends to stochastic classical mechanics.

This paper concerns the kinetic limit of the Dirac equation with a random electromagnetic field. We give a detailed mathematical analysis of the radiative transport limit for the phase space energy density of solutions to the Dirac equation. Our derivation is based on a martingale method and a perturbed test function expansion. This requires the electromagnetic field to be a Markovian space-time random field. The main mathematical tool in the derivation of the kinetic limit is the matrix-valued Wigner transform of the vector-valued Dirac solution. The major novelty compared with the scalar (Schrödinger) case is the proof of the weak convergence of cross modes to zero. The propagating modes are shown to converge in an appropriate probabilistic sense to their deterministic limit.

Summary This is the first of a series of papers, the general subject of which is how to interpret a set of simultaneous measurements of the three electric and three magnetic components of a random electromagnetic wave field in a magnetoplasma. The point at which the measurements are made is assumed to be stationary with respect to the plasma. In this first paper, the following problems are treated: how to define, within the framework of classical electrodynamics, a distribution function that characterizes the statistics of a linear random electromagnetic wave field in a lossless magnetoplasma; the direct problem of predicting the statistical properties of measurements of the six components of a field of this type, when the distribution function is known.

Random electromagnetic fields have a number of distinctive statistical properties that may depend on their origin. We show here that when two mutually coherent fields are overlapped, the individual characteristics are not completely lost. In particular, we demonstrate that if assumptions can be made regarding the coherence properties of one of the fields, both the relative average strength and the field correlation length of the second one can be retrieved using higher-order polarization properties of the combined field.

On the degree of polarization of random electromagnetic fields

The Fokker-Planck equation which describes the motion of charged particles in a random electromagnetic field is derived from the Liouville equation by a new method. The size of the perturbing magnetic field, for the Fokker-Planck equation to be valid, is calculated in a regime appropriate for cosmic-ray diffusion.

This paper examines the electromagnetic and flow field modification caused by the placement of electrically conducting media in the vicinity of the coil and molten metal and the corresponding influences of coil operating frequency. The electromagnetic field characteristics were numerically calculated using the mutual inductance technique. An improved dual-zone model was employed to describe flow behavior in the mushy region, and accounts for flow damping via interactions between the crystallites and the turbulent eddies. Calculations were performed for unidirectional solidification of an Al-4.5 wt% Cu alloy in a bottom-chill mold undergoing EM stirring. It was found that the presence of shields greatly modified the Lorentz force distribution within the melt. This led to noteworthy changes in the flow directionality, as well as changes in the spatial variation of temperature as solidification progressed. It was also found that these effects were most pronounced at low frequencies. The significance of these findings with respect to solidification process design will be discussed.

One of critical issues of bone tissue engineering is the establishment of technique to effectively promote the calcification of regenerative bone in culture. We have found that a random pulse tram electromagnetic fields (EMF) can promote more the calcification of osteoblasts than a periodic pulse train EMF in vitro. However, the mechanism behind this result is unknown. Cellular proliferation and alkaline phosphatase (ALP) activity are two of factors related to osteoblastic calcification. The purpose of this study is to investigate the effect of random pulse train EMF on the proliferation and ALP activity of osteoblasts in vitro MC3T3-E1 osteoblastic cells were seeded on a φ 35-mm culture dish at the density of 100 cells/mm^2. The cells on the central area within a radius of 9 mm were exposed to EMF for three minutes per day. The effect of random pulse train (RdPT) EMF was compared with those of periodic pulse tram (PrPT) EMF, continuous constant (CC) EMF, and no EMF stimulation control. The detection of ALP activity was conducted by using the lead citrate method on the culture dish. The cells proliferation did not show any difference among all the groups. On the other hand, in ALP activity, RdPT group showed the highest values among all the groups. These results suggest that the osteogenic effect of random pulse train EMF depends on the differentiation stage of osteoblasts, giving us useful information about the mechanism.

International audience

A method is developed for the analysis of measurements of n components of a random electromagnetic wave field (n ⩽6). This field observed at a fixed point in a magnetoplasma is described statistically by the distribution of wave energy with respect to the variables frequency and wave-normal direction. The frequency is supposed to be fixed. The distribution function considered as the most reasonable one maximizes the entropy and satisfies the values of the n × n elements of the spectral matrix of the n components. This solution obeys the nonnegativity constraint on the wave distribution function. Its properties are discussed in terms of stability and predictive power. Applications are proposed to simulated data and to satellite data.

Experimental study on fouling inhibition characteristics of a variable frequency electromagnetic field on the CaCO3 fouling of a heat transfer surface

Point sources and rays in the phase-space representation of random electromagnetic fields