Optimal estimation of pulse signals with random amplitudes and times of occurrence

We have obtained an algorithm for optimal evaluation of pulse signals of a given shape with random amplitudes and times of occurrence observed against a background of Gaussian white noise. Equations for real-time estimates that are optimal in the rms sense and the a posteriori variances of signal amplitudes and times of occurrence are found. Computer simulation results illustrating the operation of synthesized algorithms are given.N. I. Lobachevskii State University, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 12, pp. 1257–1266, December, 1995.     

Charge exchange of muons in gases: Experimental implications from rate theory

The effects of the charge exchange process on muon spin dynamics have been investigated using a density operator formalism with special interest placed upon the diamagnetic muon and paramagnetic muonium signals observed after thermalization. In the charge exchange region the dynamics of the spin density operator is assumed to be determined by the muonium hyperfine interaction and by electron capture and loss processes for muons. Analytical expressions are obtained for the amplitudes and phases of the diamagnetic muon and paramagnetic muonium signals as a function of the duration of the charge exchange region,t _c, which is inversely proportional to the number density of the moderating gas. The theoretical signals exhibit three features which have, as yet, to be experimentally observed, namely: (i) that the amplitudes associated with the muonium Larmor frequency and with the hyperfine frequency are not, in general, equal, (ii) that all the amplitudes are, in general, damped oscillatory functions oft _c (temperature/pressure) and (iii) that phase jumps occur when an amplitude decreases to zero and then increases with falling pressure. Fits to the experimental argon data are discussed in light of the above points.     

Japan megathrust earthquake on March 11, 2011: GPS-TEC evidence for ionospheric disturbances

Two-dimensional distributions of the vertical total electron content in the ionosphere above the Japan under-sea mega-earthquake on March 11, 2011 are reconstructed using high-temporal-resolution (2-min) data from the Japan GPS network. A diverging ionospheric perturbation with multicomponent spectral composition is identified emerging after the main shock. The disturbances in the ionospheric electron concentration caused by acoustic gravity waves generated by the earthquake-related processes. The initial phase of this disturbance can be used as a marker in the tsunami early warning systems. The surface energy of the earthquake estimated from the amplitude of the ionospheric disturbance is close to the estimate based on the seismic data. Other disturbances (ionospheric responses to the Rayleigh and tsunami waves, a solitary ionospheric pulse) are also analyzed. Physical interpretation of the identified ionospheric disturbances is presented.     

光纤和半导体光放大器的非线性过程噪声特性的一致性研究

提出一种在光信号上叠加正态分布研究随机扰动的方法,分别研究了光纤中的拍信号演化和SOA中的光脉冲演化。光纤与SOA分别是无源器件和有源器件,在这两种不同元件中,光信号的传输是两种完全不同的过程。得到了随机扰动对这两种不同过程中光信号传输的影响,计算了输出相对标准差。结果表明,该方法在研究非线性过程及其相关的全光信号处理中,可用于讨论器件或系统的噪声特性,从而研究输出光脉冲的噪声特性。     

Spectral editing in solid-state NMR using scalar multiple quantum filters.

In this paper we describe the use of heteronuclear scalar couplings in solid-state NMR in order to generate multiple-quantum filtering (MQF) pulse sequences. These sequences can be used to edit CP/MAS spectra according to carbon multiplicity. Analytic expressions for the intensity of the MQF signals are obtained using the standard product operator formalism. Experiments that demonstrate the technique are shown in powder samples of camphor and a tripeptide.     

The variation of transition location in response to the variation of the amplitudes of initial disturbances

The transition location of a boundary layer depends on the amplitude and characteristic of initial disturbances. The larger the amplitude and the amplification rate of the initial disturbances are,the more upstream the transition location is. However,the environment surrounding the flying vehicle is variable,so the amplitude and characteristic of the disturbances triggered in the boundary layer through receptivity are also variable. In this paper,how the transition location varies in response to the variation of the initial disturbance amplitudes is studied by using direct numerical simulation. The results show that if the initial disturbance amplitudes become smaller,the transition location moves downstream correspondingly,but there is a time delay compared to the time of arrival of the disturbances with reduced amplitudes. Moreover,the speed of moving downstream is appreciably lower than the propagation speed of the disturbances. On the other hand,if the amplitudes of the initial disturbances recover their original value,the transition would immediately take place whenever the disturbances reach the former transition location,but the laminar flow between the new and old transition locations would not become turbulent immediately. Theoretical explanations are provided based on the transition mechanism found by our group.     

STUDY OF ALGORITHMS FOR ESTIMATING SIGNALS WITH A PULSED-DISTURBANCE FLOW

Using the methods of the Markov theory of optimal nonlinear filtering, we derive equations of the algorithm for estimating random signals described by linear difference equations in discrete time in the case of a pulsed-disturbance flow. Optimal estimates of signals are represented as the sum of auxiliary estimates allowing for the influence of pulsed disturbances spaced apart by a multiple number of pulses. The results of mathematical simulation are given and the algorithm structure is discussed.     

Pervasive randomness in physics: an introduction to its modelling and spectral characterisation

An introduction to the modelling and spectral characterisation of random phenomena is detailed at a level consistent with a first exposure to the subject at an undergraduate level. A signal framework for defining a random process is provided and this underpins an introduction to common random processes including the Poisson point process, the random walk, the random telegraph signal, shot noise, information signalling random processes, jittered pulse trains, birth–death random processes and Markov chains. An introduction to the spectral characterisation of signals and random processes, via either an energy spectral density or a power spectral density, is detailed. The important case of defining a white noise random process concludes the paper.     

Solving the Bethe-Salpeter equation for two fermions in Minkowski space

The method of solving the Bethe-Salpeter equation in Minkowski space, developed previously for spinless particles (V.A. Karmanov, J. Carbonell, Eur. Phys. J. A 27, 1 (2006)), is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the amplitude and on projecting the equation on the light-front plane. The singularities in the projected two-fermion kernel are regularized without modifying the original BS amplitudes. The numerical solutions for the J = 0 bound state with the scalar, pseudoscalar and massless vector exchange kernels are found. The stability of the scalar and positronium states without vertex form factor is discussed. Binding energies are in close agreement with the Euclidean results. Corresponding amplitudes in Minkowski space are obtained.     

Reconstruction from computer-generated holograms displayed by a line printer

Experimental results are shown of optically reconstructed images from computer-generated holograms made with only binary-quantized levels in the real parts of the Fourier-transform complex disturbance of a signal and displayed by a line printer. Relatively good images having no distortion due to the high-pass filtering effect are reconstructed from computer generated holograms multiplied by the random phase factor. Reconstruction is also possible from the present holograms for signals having various degrees of light intensity.     

The symmetry,inferable from Bogoliubov transformation,between processes induced by a mirror in two-dimensional and a charge in four-dimensional space-time

We consider the symmetry between creation of pairs of massless bosons or fermions by an accelerated mirror in (1+1)-dimensional space and emission of single photons or scalar quanta by an electric or scalar charge in (3+1)-dimensional space. The relation of Bogoliubov coefficients describing the processes generated by a mirror to Fourier components of the current or charge density implies that the spin of any disturbances bilinear in the scalar or spinor field coincides with the spin of quanta emitted by the electric or scalar charge. The mass and invariant momentum transfer of these disturbances are essential for the relation of Bogoliubov coefficients to invariant singular solutions and the Green functions of wave equations for both (1+1)-and (3+1)-dimensional spaces, and especially for the integral relations between these solutions. One of these relations leads to the coincidence of the self-action changes and vacuum-vacuum amplitudes for an accelerated mirror in two-dimensional space-time and a charge in four-dimensional space-time. Both invariants of the Lorentz group, spin and mass, play an essential role in the established symmetry. The symmetry embraces not only the processes of real quanta radiation, but also the processes of the mirror and charge interactions with fields carrying spacelike momenta. These fields accompany their sources and determine the Bogoliubov matrix coefficients α _ω′ω ^{B, F} . It is shown that the Lorentz-invariant traces ±trα^B,F describe the vector and scalar interactions of the accelerated mirror with a uniformly moving detector. This interpretation rests essentially on the relation between propagators of the waves with spacelike momenta in two-and four-dimensional spaces. The traces ±trα^{B, F} coincide with the products of the mass shift Δm_{1, 0} of the accelerated electric or scalar charge and the proper time of the shift formation. The symmetry fixes the value of the bare fine structure constant α₀=1/4π.     

The influence of random drift of resonance-scattering harmonics on the frequency spectrum of surface acoustic reverberation in the ocean

We propose a modified model for the frequency spectrum of surface reverberation with allowance for random drift of Bragg resonance harmonics due to long wind-generated waves. The dependence of this effect on the parameters of large-scale surface waves is analyzed. Analytical expressions for the reverberation frequency spectrum are obtained for both narrow-band and wideband sounding signals. It is shown that for matched filtering of wideband signals, the considered effect leads to an increase in the effective pulse reverberation volume. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 1, pp. 20–30, January 2007.     

Signal detection in computer-synthesized noise.

Human observers detected sinusoidal and pulse-train signals in noise derived from two computer-synthesized sources and from a Gaussian noise source. The synthesized noise stimuli were generated from sequences of pulses whose amplitudes were drawn from two divergent types of probability distributions: a centrally peaked distribution and a bimodal distribution. No differences in the detectability of signals in these noise stimuli were evident at pulse rates of 1000, 2000, 4000, or 10 000 Hz. subjects could not discriminate between the two types of computer-generated maskers at any pulse rate. The data support a spectrum-analyzer model of detection in which multiband filtering of the input smooths the masker energy in each spectral region to approximate the Gaussian case.     

Mathematical test criteria for filtering complex systems: Plentiful observations

An important emerging scientific issue is the real time filtering through observations of noisy turbulent signals for complex systems as well as the statistical accuracy of spatio-temporal discretizations for such systems. These issues are addressed here in detail for the setting with plentiful observations for a scalar field through explicit mathematical test criteria utilizing a recent theory [A.J. Majda, M.J. Grote, Explicit off-line criteria for stable accurate time filtering of strongly unstable spatially extended systems, Proceedings of the National Academy of Sciences 104 (4) (2007) 1124–1129]. For plentiful observations, the number of observations equals the number of mesh points. These test criteria involve much simpler decoupled complex scalar filtering test problems with explicit formulas and elementary numerical experiments which are developed here as guidelines for filter performance. The theory includes information criteria to avoid filter divergence with large model errors, asymptotic Kalman gain, filter stability, and accurate filtering with small ensemble size as well as rigorous results delineating the role of various turbulent spectra for filtering under mesh refinement. These guidelines are also applied to discrete approximations for filtering the stochastically forced dissipative advection equation with very turbulent and noisy signals with either an equipartition of energy or ?5/3 turbulent spectrum with infrequent observations as severe test problems. The theory and companion simulations demonstrate accurate statistical filtering in this context with implicit schemes with large time step with very small ensemble sizes and even with unstable explicit schemes under appropriate circumstances provided the filtering strategies are guided by the off-line theoretical criteria. The surprising failure of other strongly stable filtering strategies is also explained through these off-line criteria.     

Algorithm for Optimal Estimation of Appearance Times of Pulsed Signals in Discrete Time

Using the methods of optimal nonlinear Markov filtering, we obtain an algorithm for optimal mean-square estimation of appearance times of random pulsed variations in signal parameters against the background of white Gaussian noise in discrete time. Linear difference equations are used to describe signals, noise, and the observed processes. Equations of the algorithm permitting real-time calculations of the a posteriori variances and optimal estimations of pulse-appearance times are obtained in the approximation of Gaussian conditional probability densities. We present simulation results for algorithm operation in the particular problem of estimating the appearance times of two pulsed signals having the known shapes and observed against noise background.     

Scalar mesons in a chiral quark model with glueball

Ground-state scalar isoscalar mesons and a scalar glueball are described in a U(3)×U(3) chiral quark model of the Nambu-Jona-Lasinio (NJL) type with 't Hooft interaction. The latter interaction produces singlet-octet mixing in the scalar and pseudoscalar sectors. The glueball is introduced into the effective meson Lagrangian as a dilaton on the base of scale invariance. The mixing of the glueball with scalar isoscalar quarkonia and amplitudes of their decays into two pseudoscalar mesons are shown to be proportional to current quark masses, vanishing in the chiral limit. Mass spectra of the scalar mesons and the glueball and their main modes of strong decay are described. Received: 14 July 2000 / Accepted: 31 July 2000     

Scalar length scales and spatial averaging effects in turbulent piloted methane/air jet flames

The effects of spatial averaging in measurements of scalar variance and scalar dissipation in three piloted methane/air jet flames (Sandia flames C, D, and E) are investigated. Line imaging of Raman scattering, Rayleigh scattering, and laser-induced CO fluorescence is applied to obtain simultaneous single-shot measurements of temperature, the mass fractions of all major species, and mixture fraction, ξ, along 7-mm segments. Spatial filters are applied to ensembles of instantaneous profiles to quantify effects of spatial averaging on the Favre mean and variance of mixture fraction and scalar dissipation at several locations in the three flames. The radial contribution to scalar dissipation, χ_r = 2D_ξ (∂ξ/∂r)², is calculated from the filtered instantaneous profiles. The variance of mixture fraction tends to decrease linearly with increasing filter width, while the mean and variance of scalar dissipation are observed to follow an exponential dependence. In each case, the observed functional dependence is used to extrapolate to zero filter width, yielding estimates of the “fully resolved” profiles of measured quantities. Length scales for resolution of scalar variance and scalar dissipation are also extracted from the spatial filtering analysis and compared with length scales obtained from spatial autocorrelations. These results provide new insights on the small scale structure of turbulent jet flames and on the spatial resolution requirements for measurements of scalar variance and scalar dissipation.     

Radiative transfer theory with time delay for the effect of pulse entrapping in a resonant random medium: General transfer equation and point-like scatterer model

Abstract

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe–Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii) the energy accumulation inside scatterers, (iii) the time delay in three terms, namely in terms with the Rayleigh phase tensor, the extinction coefficient and a coefficient of the energy accumulation inside scatterers, respectively (i.e. not only in a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's theorem for non-stationary radiation, unlike the Sobolev equation. The derived radiative transfer equation is applied to study the Compton–Milne effect of a pulse entrapping by its diffuse reflection from the semi-infinite random medium when the pulse, while propagating in the medium, spends most of its time inside scatterers. This specific albedo problem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance principle. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H-function which satisfies a governing nonlinear integral equation. Simple analytic asymptotics are obtained for the scattering function of the front and the back parts of the diffusely reflected Dirac delta function incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the energy accumulation inside scatterers. These asymptotics show quantitatively how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.     

PartiallyU(1) compactified scalar massless field on the compact Riemann surface and the bosonic string amplitudes

The theory of the partiallyU(1) compactified scalar massless field on the compact Riemann surface with Nambu-Goto action is defined. The partition function is determined completely by a choice of the finite-dimensional approximations. The correlation functions are the only correctly defined objects of the theory. The averages of the correlation function asymptotic values provide the amplitudes. For the compact Riemann surfaces of any genus the usual bosonic string amplitudes are the special cases of the above amplitudes.