Random Slab Research Articles

TE Plane Wave Reflection and Transmission from a One-Dimensional Random Slab — Slanted Fluctuation —

TE Plane Wave Reflection and Transmission from a One-Dimensional Random Slab — Slanted Fluctuation —

A simple stereological method for estimating the number and the volume of the pancreatic beta cells.

Number of the beta cells as well as their volume is a fundamental variable in the pancreatic research.This study describes a simple method for stereological estimation of the volume of the pancreas, the total volume of the islets, and the total number, as well as the mean volume, of the beta cells in rat.The primary volume of the pancreas was measured using the immersion method. Also, tissue shrinkage was estimated and the final pancreas volume was corrected without the need for serial sectioning. A limited number (i.e., 10-13) of the isotropic uniform random slabs of each pancreas was embedded in the same block. One 5 µm and one 20 µm sections were obtained and stained with a modified aldehyde fuchsin. The point counting, optical disector and point-sampled intercept methods were used to estimate the volume density of the islet, the numerical density of the beta cells, and the mean cell volume, respectively.After calculating the tissue shrinkage, the mean primary volume of the pancreas (628 mm3; CV: 25%) was corrected to obtain the final volume (442 mm3; CV: 39%). The mean islet volume was reported as 3.8 mm3 (CV: 22%). Besides, the total number of the beta cells was estimated as 2.9x10(6) (CV: 20%). Moreover, the mean volume of the beta cells was obtained (1,158 µm3; CV: 9%).It takes almost one hour to estimate the volume of the islets and two hours to count the cells and estimate the intercepts per animal.

TE Plane Wave Reflection and Transmission from a Two-Dimensional Random Slab - Slanted Fluctuation -

This paper deals with reflection and transmission of a TE plane wave from a two-dimensional random slab with slanted fluctuation by means of the stochastic functional approach. Such slanted fluctuation of the random slab is written by a homogeneous random field having a power spectrum with a rotation angle. By starting with the previous paper [IEICE Trans. Electron., Vol. E92-C, no.1, pp.77-84, January 2009], any statistical quantities are immediately obtained even for slanted fluctuation cases. The first-order incoherent scattering cross section is numerically calculated and illustrated in figures. It is then newly found that shift and separation phenomena of the leading or enhanced peaks at four characteristic scattering angles take place in the transmission and reflection sides, respectively.

Steady state and time-dependent energy equilibration in two-dimensional random elastic slabs

The static and dynamic transport properties of elastic wave propagation through two-dimensional random slabs without internal reflection were studied at two different scattering parameters: one for Rayleigh scattering and the other for Rayleigh-Gans scattering. The spatial distribution and temporal evolution of shear (s-) and compressional (p-) wave energy densities inside the slabs were calculated by solving the radiative transfer equation and the generalized diffusion equation (GDE). The comparison of their results can determine the region of validity of the GDE. The process of energy equilibration between the two wave modes was demonstrated explicitly as well as the process of diffusion. The depth inside a slab that is needed to reach energy equilibration or diffusive behavior is found to be dependent on source polarization. The results also show that the bulk equilibration ratio can be found inside a sample only when the sample is sufficiently thick. Deviations of the equilibration ratio from its bulk value are found near the output surface due to the absence of in-flow energy flux. The behavior of the deviations is sensitive to the scattering parameter but independent of source polarization.

TE Plane Wave Reflection and Transmission from a Two-Dimensional Random Slab

This paper reexamines reflection and transmission of a TE plane wave from a two-dimensional random slab discussed in the previous paper [IEICE Trans. Electron., Vol.E79-C, no.10, pp.1327-1333, October 1996] by means of the stochastic functional approach with the multiply renormalizing approximation. A random wavefield representation is explicitly shown in terms of a Wiener-Hermite expansion. The first-order incoherent scattering cross section and the optical theorem are numerically calculated. Enhanced scattering as gentle peaks or dips on the angular distribution of the incoherent scattering is reconfirmed in the directions of reflection and backscattering, and is newly found in the directions of forward scattering and `symmetrical forward scattering.' The mechanism of enhanced scattering is deeply discussed.

Reflection and Transmission of a TE Plane Wave from a Two-Dimensional Random Slab-Anisotropic Fluctuation-

This paper studies reflection and transmission of a TE plane wave from a two-dimensional random slab with statistically anisotropic fluctuation by means of the stochastic functional approach. By starting with a representation of the random wavefield presented in the previous paper [IEICE Trans. Electron., vol.E92-C, no.1, pp.77-84, Jan. 2009], a solution algorithm of the multiple renormalized mass operator is newly shown even for anisotropic fluctuation. The multiple renormalized mass operator, the first-order incoherent scattering cross section and the optical theorem are numerically calculated and illustrated in figures. The relation between statistical properties and anisotropic fluctuation is discussed.

TM Plane Wave Reflection and Transmission from a One-Dimensional Random Slab

This paper deals with a TM plane wave reflection and transmission from a one-dimensional random slab with stratified fluctuation by means of the stochastic functional approach. Based on a previous manner [IEICE Trans. Electron. E88-C, 4, pp. 713-720, 2005], an explicit form of the random wavefield is obtained in terms of a Wiener-Hermite expansion with approximate expansion coefficients (Wiener kernels) under small fluctuation. The optical theorem and coherent reflection coefficient are illustrated in figures for several physical parameters. It is then found that the optical theorem by use of the first two or three order Wiener kernels holds with good accuracy and a shift of Brewster's angle appears in the coherent reflection.

Productivity Aspects of Urban Freeway Rehabilitation with Accelerated Construction

Over the last 5years the California Department of Transportation (Caltrans) has completed three experimental long-life urban freeway rehabilitation projects by utilizing a fast-track (accelerated) construction approach of around-the-clock operations under extended closure. This paper presents the fast-track rehabilitation approaches and the as-built production rates of major rehabilitation operations monitored at the three experimental projects. The monitoring results show that the contractor’s production rates varied considerably depending upon the construction logistics, material delivery and hauling methods, lane-closure tactics, and/or pavement designs being implemented. A higher production rate and a noticeable “learning-curve effect” were observed when full-width rehabilitation was compared with partial-width rehabilitation, when continuous lane reconstruction was compared with random slab replacements, and when full roadbed closures were compared with partial lane closures. Findings in this study suggest that Caltrans should evaluate project-specific conditions and constraints, which might restrict use of a preferred rehabilitation scheme, by taking production rate variances into account when establishing schedule baselines of construction staging plans and incentive/disincentive contracts for urban freeway rehabilitation projects.

Wave transport in two-dimensional random media: The ballistic to diffusive transition and the extrapolation length

By using a first-principles approach based on the Bethe-Salpeter equation, we study the behavior of wave propagation through a two-dimensional random slab as a function of thickness, L , in the region where L is much smaller than the localization length. A general two-dimensional vertex function for the ladder diagrams is derived from the Ward identity. We calculate both the static and the time-resolved transmitted intensities as functions of L/l , where l is the mean free path. When L is comparable to l , we study the ballistic to diffusive transition. A sharp crossover is observed when L(c) approximately = 6l, which is significantly larger than the crossover thickness of L(c) approximately = 3l found in three dimensions. When L>>l , we obtain the extrapolation length in two dimensions, i.e., z2De approximately = 0.82l, which is noticeably larger than the previously used value of z2De = pi/4 obtained by an analytical approach.

TE Plane Wave Reflection and Transmission from a One-Dimensional Random Slab

This paper deals with a TE plane wave reflection and transmission from a one-dimensional random slab by means of the stochastic functional approach. The relative permittivity of the random slab is written by a Gaussian random field in the vertical direction with finite thickness, and is uniform in the horizontal direction with infinite extent. An explicit form of the random wavefield is obtained in terms of a Wiener-Hermite expansion with approximate expansion coefficients (Wiener kernels) under a small fluctuation case. By using the first three terms of the random wavefield representation, the optical theorem is illustrated in figures for several physical parameters. It is then found that the optical theorem holds with good accuracy.

Multiple scattering of light from a random slab: a density-fluctuation approach

The problem of multiple scattering of light from a slab composed of randomly distributed point scatterers is reformulated by using a density-fluctuation approach. Under the assumption of independent scatterers, the intensity of scattered light averaged over all possible configurations of the scatterers is calculated and compared to the results obtained by other authors. The main advantage of our approach is the clarity with which it reveals the physical basis of the multiple scattering process.

Radiation transport in random slabs with binomial statistics

The transport of radiation through a random array of purely absorbing slabs is considered assuming that the cross section of the slabs fluctuates according to binomial statistics. An exact solution is constructed for the transmission factor through N slabs and the mean value and variance calculated. It is also shown how the complete probability distribution may be recovered. The results are extended to the case of two different types of slab material and thickness and also to the case where the slab thickness is random subject to a constant total thickness of the system. Simple results are obtained and these are compared with the solution of an analogous problem using the dichotomic Markov process method favored by Pomraning and his co-workers. No particular conclusions are drawn regarding the relative merits of these two statistics and the matter is left open for futher discussion.

A Limit Theorem for Linear Boundary Value Problems in Random Media

The asymptotic behavior of the solutions of linear equations with random coefficients, random external forces and with affine boundary conditions is studied, motivated by a transmission-reflection problem for a one-dimensional wave equation in a random slab. The fluctuations of the coefficients are on a small scale in such a way that our problem is a diffusion-approximation problem except that we impose boundary conditions which force the solution to be anticipating. In the limit we obtain linear stochastic differential equations with affine boundary conditions, studied by Ocone and Pardoux. Our main tools are diffusion approximation results (Papanicolaou, Stroock and Varadhan or Ethier and Kurtz) and the properties of the limiting equations involving generalized Stratonovich integrals (Ocone and Pardoux). As an application, the transmission-reflection problem is discussed. We prove that the solution has a density with respect to the Lebesgue measure and satisfies the Markov field property.

Intensity correlation in a disordered medium with large scatterers

We consider the long-range intensity correlation in a speckle pattern. We find an analytical solution for the intensity correlation function for the case of a plane wave propagation through a random slab with large scatters (their size a is much larger than the wavelength λ). Both single and multiple wave scattering are assumed to have a sharply anisotropic (small-angle) character. The qualitative differences between the intensity correlations in a disordered medium with purely elastic scattering and those in an absorbing medium are analyzed in detail.

Coherent enhancement of light-pulse backscattering by random slab

An exact analytic solution is found for the problem of enhancement of backscattering of a short pulse signal from a slab of finite thickness with isotropic scattering centers.

A thermal microwave emission model for row-structured vegetation

Abstract It has been known that the emission from row crops strongly depends on the direction of vegetation row structures relative to the polarization of radiometric receiving antenna. The purpose of the paper is to develop an emission model to interpret the existing emission data of row crop canopy and to aid in understanding the emission process for a row structured vegetation layer or other anisotropically-emitting medium. The vegetation layer of row crops is modelled as a random slab embedded with small thermally emitting spheroids with major axis aligned parallel to the row crop direction. The effects of geometric row structure of vegetation layer can be accounted for by assuming that each thermally-emitting object such as a leaf is aligned to a certain preferred direction. The vegetation canopy is a tenuous medium at microwave frequency so that it is possible to use the radiative transfer theory in emission model. The total emission from the canopy is given in a simple algebraic form based on the z...

Probability density of the reflection coefficient of a semi-infinite array of random slabs

It is shown that the probability density of the reflection coefficient of a semi-infinite array of random slabs undergoes qualitative changes as the parameters of the slabs are varied. Specifically, it is found that the density function changes from a smooth curve with a single peak to a highly noisy curve and then further to a discrete distribution whose support has a Cantor set structure.

Coherent wave backscattering by random medium. Exact solution of the albedo problem

We study the effect of coherent wave backscattering by a system of point-like scatterers. An exact solution of the albedo problem is found both for a semi-finite medium and for a random slab. It is shown that in the cases considered the diffusion approximation breaks down rapidly when oblique incidence and finite slab thickness are taken into account. It is determined that the intensity of the coherent peak tails falls off as 1 θ , where θ is the angle between backscattering and observation directions.

On obtaining the forward phase functions of Saturn ring features from radio occultation observations

It is noted that the near-forward scattering functions of particles in Saturn ring features are related to 3.6 cm radio occultation power spectra by a Fredholm integral equation of the first kind. The equation reduces to an algebraic system of equation whose solution by usual inversion techniques (that is, least mean squares) is ruled out by the near singularity of the forward transformation matrix. A combination of constrained linear inversion and a filtering algorithm based on eigenvector decomposition of the matrix reduces the instabilities; this yields derived phase functions valid over the range of zero to about 12 mrad. It is noted that these functions represent the collective forward diffraction lobe of particles greater than about 1 m in radius. Since multiple scattering of the signal is a significant effect, the measured phase functions must be adjusted to obtain the singly scattered component. This single-scattering correction is examined for two physical models, namely the monolayer and the classical discrete random slab; in addition, the fraction of opacity in submeter particles for each model for particular ring features is estimated.

Analytic solution for the two‐frequency mutual coherence function for spherical wave propagation

The quadratic approximation for the phase structure function is used to obtain the two‐frequency mutual coherence function Γ(Δρ, Δω) for spherical wave propagation through a finite slab with transmitter and receiver located in free space on opposite sides of the slab. General analytic solutions are derived for two cases. In the first case the random slab is represented by a one‐dimensional power spectrum of electron density fluctuations corresponding to propagation through elongated irregularities as would occur for an equatorial satellite link to a ground station. In the second case the random slab consists of isotropic ionization irregularities. Both cases taken together represent the extremes of the range of results to be expected for propagation through ionospheric fluctuations, solar wind irregularities, or ionization irregularities caused by barium cloud instabilities. For both cases the complex general analytic results are simplified by use of the thin phase screen approximation to obtain useful analytic expressions for Γ as well as the resulting impulse response function. It is shown that the impulse response to a transmitted power delta function reduces to an exponential form in the limit of strong diffraction and to a Gaussian form in the geometrical optics limit. The Gaussian form corresponds to pulse wander while the exponential form corresponds to diffractive spreading produced by multipath effects. The relationship between the generalized power spectrum and the impulse response function is given, and results are presented for the mean time delay and time delay jitter. The accuracy of the thin phase screen calculation of these quantities is investigated in detail.