Mesoscopic correlation in electromagnetic wave polarization

Four relationships between the intensity and field correlation functions are used in the analysis of measured intensity correlation functions in dynamic light scattering with data obtained for four different polymer gel samples. The evaluation of diffusion coefficients has been performed using inverse Laplace transformation (ILT) and the cumulants method, respectively. Diffusion coefficients derived from the nonergodic medium method are almost the same as those from the heterodyne method when ILT is used. ILT gives similar results by all four procedures even when large baselines exist, whereas the cumulants method leads to incorrect diffusion coefficients from the correlation function derived using the nonergodic medium method

In the present paper, we considered Galilean conformal algebras (GCAs), which arises as a contraction relativistic conformal algebras (xi→ϵxi, t→t, ϵ→0). We can use the Galilean conformal (GC) symmetry to constrain two-point and three-point functions. Correlation functions in space–time without boundary condition were found [A. Bagchi and I. Mandal, Phys. Lett. B675, 393 (2009).]. In real situations, there are boundary conditions in space–time, so we have calculated correlation functions for GC invariant fields in semi-infinite space with boundary condition in r = 0. We have calculated two-point and three-point functions with boundary condition in fixed time.

Intensity correlation in a disordered medium with large scatterers

For perfect surface roughness description is not enough to know characteristics of surface profile. It is necessary to use topography methods, so called microtopography. Thereby, surface roughness in microtopographycal understanding must be described with three coordinates, whose in Cartesian coordinates system compose point under consideration height h, abscissa and ordinate, determines point position in the plane. Most efficient methods in irregular surface roughness research are random function theory methods. Therefore, microtopography, analogically to profile, may consider as random function, but two dimensional function, i.e. two variable x and y random field h(x,y). From analogy with random process, random field can be normal – ordinates are distributed by normal (Gaussian) distribution. Moreover, random field can be homogeneous and heterogeneous. Random field is deemed homogeneous if its mean value is discretionary and correlation function depends only from distance between surface points. Important characteristic of random field is correlation function, whose depends of two variables t1 and t2 – orthogonal Cartesian coordinates of vector t. Random field is homogeneous and isotropic when its characteristics are equivalent in any direction. There are three types of surface anisotropy: • General event of surface anisotropy. Characteristics of this event roughness parameters are depend of surface split direction. • Surface roughness with direct anisotropy. Those surfaces are with typical traces of tool and they proper two mutually perpendicular surface roughness directions. • Extended anisotropy area – special event of anisotropy roughness. Of analytical opinion, gainfully anisotropy roughness see as extended occasional isotropy area. This let easy cross from anisotropy surface to isotropy and contrariwise, thereby embrace amount class of surface roughness. Let’s formulate microtopography model of rough surface [1]. Surface roughness is described with homogeneous normal random field h(x,y) that has uninterrupted correlation function and uninterrupted deriviates. We may consider that E{h(x,y)}=0. The mean random field value is plane called mean plane. For describing random field we must know mathematical expectation and field correlation function, what in fact reduces on determining dispersion and rationed correlation function r(t1, t2). Homogeneous random field dispersion D{h} doesn’t depends of direction and can be founded in any surface split. Given model of rough surface let inspect surfaces produced by abrasive instruments and friction surfaces after wear-in period.

In this paper, we attempt to find a unified framework in which the statistics of wave propagation in random media can be understood as strengths of scattering and absorption increase. First, we discuss the weak scattering, diffusive limit without absorption. In this limit, the suppression of transmission by weak localization, the distribution of total transmission and the intensity correlation functions with displacement and polarization rotation are all described in terms of the dimensionless conductance so that these effects are explicitly linked. When absorption is introduced, the dimensionless conductance can no longer serve as a fundamental scaling parameter, but the variance of the total transmission is still able to chart the changing statistical character of propagation and localization with sample size. By examining transport at a fixed time following pulsed excitation, the affect of absorption can be removed while the growing impact of localization can be clearly discerned. The functional form of probability distributions of intensity and total transmission and of the spatial and polarization intensity correlation functions in the time domain are the same as in the frequency domain. The connection of mesoscopic fluctuations to localization can be seen in the spectral correlation function of the field, which is the Fourier transform of average pulsed transmission. The spectral field correlation function can be expressed as a product of the correlation function of the field normalized to the average amplitude in a given configuration and of the square root of the total transmission.

Kinetic theory of radiation in non-equilibrium relativistic plasmas

The two-point, two-time correlation functions of classical and quantum mechanical fields in thermal equilibrium in an arbitrary domain are considered. For classical fields that satisfy linear equations of motion, the correlation functions are expressed in terms of certain Green's functions of the domain. It is also shown, by evaluating the characteristic functional of the field, that a classical field is Gaussian distributed, so that all higher-order correlations can be expressed in terms of the second-order correlations. Then the second-order correlations are evaluated in various cases, and the classical and quantum mechanical results are compared. They are found to agree except within layers, about a thermal wavelength wide, near the boundaries of the domain and near the characteristic surface or light cone emanating from either of the two points. Thus the quantum mechanical correlation function can be approximated by the classical one with quantum-mechanical boundary-layer corrections.

Kraichnan's model of passive scalar advection in which the driving (Gaussian) velocity field has fast temporal decorrelation is studied as a case model for understanding the anomalous scaling behavior in the anisotropic sectors of turbulent fields. We show here that the solutions of the Kraichnan equation for the n-order correlation functions foliate into sectors that are classified by the irreducible representations of the SO(d) symmetry group. We find a discrete spectrum of universal anomalous exponents, with a different exponent characterizing the scaling behavior in every sector. Generically the correlation functions and structure functions appear as sums over all these contributions, with nonuniversal amplitudes that are determined by the anisotropic boundary conditions. The isotropic sector is always characterized by the smallest exponent, and therefore for sufficiently small scales local isotropy is always restored. The calculation of the anomalous exponents is done in two complementary ways. In the first they are obtained from the analysis of the correlation functions of gradient fields. The theory of these functions involves the control of logarithmic divergences that translate into anomalous scaling with the ratio of the inner and the outer scales appearing in the final result. In the second method we compute the exponents from the zero modes of the Kraichnan equation for the correlation functions of the scalar field itself. In this case the renormalization scale is the outer scale. The two approaches lead to the same scaling exponents for the same statistical objects, illuminating the relative role of the outer and inner scales as renormalization scales. In addition we derive exact fusion rules, which govern the small scale asymptotics of the correlation functions in all the sectors of the symmetry group and in all dimensions.

Fractal speckles

On the basis of the theory of microwave scattering from the ocean surface the correlation function of the synthetic aperture radar (SAR) signal intensity was obtained as a sum of two items. The first item is the proper image correlation function, i.e. the correlation function free of speckle noise SAR signal intensity, which has been investigated in many works (mostly by Alpers et al.). The second item describes the speckle structure in the image. It has been shown that at sufficiently large values of the well‐known velocity bunching parameter the speckle energy is significant within the spectral interval, where the spectrum of large ocean waves is concentrated. In this case the speckle noise can not be suppressed efficiently by means of image filtering. Meanwhile, the mentioned second item is nothing other than half of the correlation function of the complex intensity, which is the square of the SAR signal complex amplitude (unlike the usual real intensity, i.e. the square of the modulus). Therefore, the unspeckled image correlation function can be presented as the difference between the real intensity correlation function and half of the complex intensity function. This leads to a new spectral estimate, free of speckle noise, for the SAR image. The corresponding expression for the new estimate is presented.

We present a catalogue of galaxies from COSMOS scans of 16 second epoch Palomar Observatory Sky Survey (POSS-II) plates. The surveys covers an area of 386 square degrees, and covers 150,000 galaxies in the magnitude range 16.5 ≤ r ≤ 19.0. The plates are divided into a north galactic (7 plates, α ≈ 15[superscript h]0[superscript m],δ ≈ +30°(1950.0), b ≈ 65°) and south galactic (9 plates, α ≈ 0[superscript h]20[superscript m], δ ≈ +5°(1950.0), b ≈ -55°) field. The magnitude scale of each plate was brought to a common photometric system (Gunn r) using extensive CCD photometry. The total error in the zero point of the magnitude scale at the faint end is 0.06[superscript m]. The procedure for separating stars and galaxies is based on image parameters provided by the COSMOS machine and is completely objective. Visual tests indicate that the catalogue is 94% complete. We have measured the angular correlation function of galaxies w(θ). The north field is in good agreement with the results of the APM survey. The south field exhibits more power on large scales than the north field. We have performed several tests to determine the effect of possible systematic errors between the two fields and do not find any effect sufficiently large to account for the south field's excess power. The measured correlation function for both fields are incompatible with the predictions of the currently most popular model, cold dark matter (CDM). The number counts of galaxies in the two fields are substantially different. Several tests have been performed to make sure that the effect is not the result of a systematic error in zero point of the magnitude system or due to extinction or obscuration. The natural scale for structures which might be responsible for this difference is 50h[superscript -1] Mpc. We do not know if this difference is a rare event; more fields need to be surveyed to address this important question. We have developed an objective algorithm for detecting clusters of galaxies from our galaxy catalogue. The algorithm is based on fixed overdensities at varying angular scales, and is well-suited to detecting clusters over a large range of redshifts. We present a catalogue of clusters based on this algorithm, using an overdensity threshold obtained from comparing the cluster's densities to each field's overall back-ground density. The results are very sensitive to the choice of background density. The multiplicity function of the objective clusters agree well when referenced to each field's background density, but disagree sharply when referenced to the overall mean density of the survey. The objective catalogue is compared with that of Abell's. Poor agreement is found between the two catalogues. It is not possible to choose a set of parameters in our catalogue which reproduces Abell's catalogue well. The measurement of the galaxy-cluster correlation function w[subscript g-cl](θ) is in good qualitative agreement with predictions of CDM, but more detailed comparisons with theory must wait for the acquisition of redshifts for a large fraction of the clusters. At present, no theory is able to explain the amount of power on large scale observed in this survey.

We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to study the long time, large distance asymptotics of correlation functions of local fields in the gas phase. We derive differential equations which drive the correlation functions. Using a related Riemann–Hilbert problem we obtain formulae for the asymptotics of the correlation functions, which are valid at all finite temperatures. At low temperatures these formulae lead to explicit asymptotic expressions for the correlation functions, which describe power law behavior and exponential decay as functions of temperature, magnetic field and chemical potential.

We show how cosmological correlation functions of massless fields can be rewritten in terms of Minkowski correlation functions, by extracting symmetry-breaking operators from the cosmological correlators. This technique simplifies some cosmological calculations. Also, known properties of Minkowski correlation functions can be translated to non-trivial properties of cosmological correlations. To illustrate this idea, inflation to Minkowski and matter bounce to Minkowski relations are presented for the interactions of general single field inflation. And a Minkowski recursion relation is translated to a novel relation for inflation.

Scanning concentration correlation spectroscopy using the confocal laser microscope

Part I. Mode Locking and Ultrashort Laser Pulses by a Refractive Index Nonlinearity A new method for locking the longitudinal modes of a laser resonator and generating ultrashort pulses of light has been found. The cavity modes are coupled together when a medium possessing a refractive index nonlinearity is placed inside the cavity. A theoretical study is presented which analyzes the mode structure of a laser resonator containing a cell filled with an anisotropic molecular liquid. It is found that under certain conditions the energy exchange between the modes gives rise to a mode locked spectrum and to the attendant generation of ultrashort pulses of light (~10-11 sec for a ruby laser, ~10-12 sec for a Nd3+ glass laser). An experimental investigation is reported. The presence of ultrashort pulses in the output of a Q-switched ruby laser is observed when a liquid cell containing nitrobenzene or α-chloronaphthalene is placed inside the cavity. Part II. A Theoretical Study of Optical Wave Propagation Through a Random Medium and its Application to Optical Communication In this report we are interested in a theoretical study of wave propagation in a randomly turbulent medium and the application of the results to the evaluation of optical communication systems through the atmospheric turbulence. We first derive a power series expansion solution for the wave function u(→x) of a wave propagating through a medium with a random index of refraction. The average wave function u(→x) and the correlation function u(→x1) u*(→x2) are calculated in terms of the correlation function of the index of refraction, the only assumption being that the wavelength of the wave is much smaller than the smallest size of the turbulence. The intensity correlation function I(→x1) I(→x2) is investigated and recent experimental results concerning the behavior of the intensity fluctuations are discussed. Next, the performances of two schemes of optical communication through the random atmospheric turbulence are compared: (a) heterodyne detection, (b) video communication. It is found that for long propagation paths and strong turbulences, scheme (b) is preferable to scheme (a). This is due to the cancellation of the phase fluctuations between "reference" and "signal" parts of the beam in the video communication scheme.