Half-space albedo problem for the Anlı-Güngör scattering function

One speed, time-independent and homogeneous medium neutron transport equation is solved for second order scattering using the Anlı-Güngör scattering function which is a recently investigated scattering function. The scattering function depends on Legendre polynomials and the t parameter which is defined on the interval [−1, 1]. A half-space albedo problem is examined with the FN method and the recently developed SVD method. Albedo values are calculated with two methods and tabulated. Thus, the albedo values for the Anlı-Güngör scattering are compared with these methods. The behaviour of the scattering function is similar to İnönü’s scattering function according to calculated results.

Discrete Sturm-Liouville equations with point interaction

Scattering solutions and several properties of scattering function of a discrete Sturm-Liouville boundary value problem with point interaction (PBVP) are derived. Moreover, resolvent operator, continuous and discrete spectrum of this PBVP are investigated. An asymptotic equation is utilized to get the properties of eigenvalues. An example illustrating the main results is given.

Realisation of the ITS-90 and thermodynamic temperature measurements above 960 °C using a monochromator-based radiance comparator

At LNE-Cnam, the International Temperature Scale of 1990 (ITS-90) and thermodynamic temperature measurements above the silver point, are carried out with a radiance comparator. This instrument is, more generally, devoted to any radiance comparison in temperature range from the ambient to 3000 °C. The instrument developed in the early 1990s at LNE-Cnam has the advantage of being completely adjustable. Compared to compact radiation thermometers based on lenses and a narrow-band interference filter, the radiance comparator is only made of gold coated mirrors and a Czerny-Turner monochromator to select the spectral bandwidth. The instrument offers the possibility to tune the geometric extent and the slit scattering function. In return, the radiance comparator is a complex instrument that requires a complete and a regular characterisation at the highest level of accuracy. In the first part, this paper describes the instrument and its operating principle. In a second part, a complete study of the wavelength calibration, the slit scattering function, size of source effect, out-of-band transmittance, linearity and other main sources of uncertainty are presented and discussed. Their associated uncertainties are estimated separately and are grouped together to give an example of propagation of uncertainties when performing the ITS-90.

Angle domain generalized Radon transform for elastic multi-parameter inverse scattering inversion

Linearized algorithms based on the Born approximation are well-known and popular techniques for quantitative seismic imaging and inversion. However, linearization methods usually suffer from some significant problems, such as computational cost for the required number of iterations, requirement for background models, and uncertain and unstable multi-parameter extraction, which make the methods difficult to implement in practical applications. To avoid these problems, we propose an angle-domain generalized Radon transform (AD-GRT) inversion in 2D elastic isotropic media. This AD-GRT is an approximate transform between the seismic data and an angle-domain model, which acts as a scattering function, and the seismic data can be reconstructed accurately, even when the background models are incorrect. The density and Lam短oduli perturbation parameters can be extracted stably from the inverted angle-domain scattering function. Deconvolution of the source wavelet is taken into account to remove the effect of the wavelet and improve the resolution and accuracy of the inversion results. The derived AD-GRT inversion is non-iterative and is as efficient as the traditional elastic GRT method. The additional dimension of the angle domain has little effect on the computational cost of the AD-GRT, as opposed to other extended-domain inversion/migration methods. Our method also can be used to solve non-linear Born inversion problems using iteration, which can significantly improve their convergence rate. Three numerical examples illustrate that the angle-domain scattering function inversion, data reconstruction, and multi-parameter extraction using the presented AD-GRT inversion are effective.

PHIPS-HALO: the airborne Particle Habit Imaging and Polar Scattering probe – Part 3: Single-particle phase discrimination and particle size distribution based on the angular-scattering function

A major challenge for in situ observations in mixed-phase clouds remains the phase discrimination and sizing of cloud hydrometeors. In this work, we present a new method for determining the phase of individual cloud hydrometeors based on their angular-light-scattering behavior employed by the PHIPS (Particle Habit Imaging and Polar Scattering) airborne cloud probe. The phase discrimination algorithm is based on the difference of distinct features in the angular-scattering function of spherical and aspherical particles. The algorithm is calibrated and evaluated using a large data set gathered during two in situ aircraft campaigns in the Arctic and Southern Ocean. Comparison of the algorithm with manually classified particles showed that we can confidently discriminate between spherical and aspherical particles with a 98 % accuracy. Furthermore, we present a method for deriving particle size distributions based on single-particle angular-scattering data for particles in a size range from 100 µm ≤ D ≤ 700 µm and 20 µm ≤ D ≤ 700 µm for droplets and ice particles, respectively. The functionality of these methods is demonstrated in three representative case studies.