Multiple-scattering in radar systems: a review

Although extensively studied within the lidar community, the multiple scattering phenomenon has always been considered a rare curiosity by radar meteorologists. Up to few years ago its appearance has only been associated with two- or three-body-scattering features (e.g. hail flares and mirror images) involving highly reflective surfaces. Recent atmospheric research aimed at better understanding of the water cycle and the role played by clouds and precipitation in affecting the Earth's climate has driven the deployment of high frequency radars in space. Examples are the TRMM 13.5 GHz, the CloudSat 94 GHz, the upcoming EarthCARE 94 GHz, and the GPM dual 13-35 GHz radars. These systems are able to detect the vertical distribution of hydrometeors and thus provide crucial feedbacks for radiation and climate studies. The shift towards higher frequencies increases the sensitivity to hydrometeors, improves the spatial resolution and reduces the size and weight of the radar systems. On the other hand, higher frequency radars are affected by stronger extinction, especially in the presence of large precipitating particles (e.g. raindrops or hail particles), which may eventually drive the signal below the minimum detection threshold. In such circumstances the interpretation of the radar equation via the single scattering approximation may be problematic. Errors will be large when the radiation emitted from the radar after interacting more than once with the medium still contributes substantially to the received power. This is the case if the transport mean-free-path becomes comparable with the instrument footprint (determined by the antenna beam-width and the platform altitude). This situation resembles to what has already been experienced in lidar observations, but with a predominance of wide- versus small-angle scattering events. At millimeter wavelengths, hydrometeors diffuse radiation rather isotropically compared to the visible or near infrared region where scattering is predominantly in the forward direction. A complete understanding of radiation transport modeling and data analysis methods under wide-angle multiple scattering conditions is mandatory for a correct interpretation of echoes observed by space-borne millimeter radars. This paper reviews the status of research in this field. Different numerical techniques currently implemented to account for higher order scattering are reviewed and their weaknesses and strengths highlighted. Examples of simulated radar backscattering profiles are provided with particular emphasis given to situations in which the multiple scattering contributions become comparable or overwhelm the single scattering signal. We show evidences of multiple scattering effects from air-borne and from CloudSat observations, i.e. unique signatures which cannot be explained by single scattering theory. Ideas how to identify and tackle the multiple scattering effects are discussed. Finally perspectives and suggestions for future work are outlined. This work represents a reference-guide for studies focused at modeling the radiation transport and at interpreting data from high frequency space-borne radar systems that probe highly opaque scattering media such as thick ice clouds or precipitating clouds.

On the quantum mechanical scattering statistics of many particles

The probability of a quantum particle being detected in a given solid angle is determined by the S-matrix. The explanation of this fact in time-dependent scattering theory is often linked to the quantum flux, since the quantum flux integrated against a (detector-) surface and over a time interval can be viewed as the probability that the particle crosses this surface within the given time interval. Regarding many particle scattering, however, this argument is no longer valid, as each particle arrives at the detector at its own random time. While various treatments of this problem can be envisaged, here we present a straightforward Bohmian analysis of many particle potential scattering from which the S-matrix probability emerges in the limit of large distances.

Aerosol scattering and absorption during the EUCAARI-LONGREX flights of the Facility for Airborne Atmospheric Measurements (FAAM) BAe-146: can measurements and models agree?

Scattering and absorption by aerosol in anthropogenically perturbed air masses over Europe has been measured using instrumentation flown on the UK’s BAe-146-301 large Atmospheric Research Aircraft (ARA) operated by the Facility for Airborne Atmospheric Measurements (FAAM) on 14 flights during the EUCAARI-LONGREX campaign in May 2008. The geographical and temporal variations of the derived shortwave optical properties of aerosol are presented. Values of single scattering albedo of dry aerosol at 550 nm varied considerably from 0.86 to near unity, with a campaign average of 0.93 ± 0.03. Dry aerosol optical depths ranged from 0.030 ± 0.009 to 0.24 ± 0.07. An optical properties closure study comparing calculations from composition data and Mie scattering code with the measured properties is presented. Agreement to within measurement uncertainties of 30% can be achieved for both scattering and absorption,but the latter is shown to be sensitive to the refractive indices chosen for organic aerosols, and to a lesser extent black carbon, as well as being highly dependent on the accuracy of the absorption measurements. Agreement with the measured absorption can be achieved either if organic carbon is assumed to be weakly absorbing, or if the organic aerosol is purely scattering and the absorption measurement is an overestimate due to the presence of large amounts of organic carbon. Refractive indices could not be inferred conclusively due to this uncertainty, despite the enhancement in methodology compared to previous studies that derived from the use of the black carbon measurements. Hygroscopic growth curves derived from the wet nephelometer indicate moderate water uptake by the aerosol with a campaign mean f (RH) value (ratio in scattering) of 1.5 (range from 1.23 to 1.63) at 80% relative humidity. This value is qualitatively consistent with the major chemical components of the aerosol measured by the aerosol mass spectrometer, which are primarily mixed organics and nitrate and some sulphate.

Neutron-C-19 scattering near an Efimov state

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Quantum scattering in one dimension

A self-contained discussion of non-relativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three dimensions. The present discussion illustrates in a simple way the concepts of partial-wave decomposition, phase shift, optical theorem and effective-range expansion.

A sampling method for detecting buried objects using electromagnetic scattering

We consider a simple (but fully three-dimensional) mathematical model for the electromagnetic exploration of buried, perfect electrically conducting objects within the soil underground. Moving an electric device parallel to the ground at constant height in order to generate a magnetic field, we measure the induced magnetic field within the device, and factor the underlying mathematics into a product of three operations which correspond to the primary excitation, some kind of reflection on the surface of the buried object(s) and the corresponding secondary excitation, respectively. Using this factorization we are able to give a justification of the so-called sampling method from inverse scattering theory for this particular set-up.

Investigation of the nuclear matter density distributions of the exotic 12 Be, 14 Be and 8 B nuclei by elastic proton scattering in inverse kinematics

The proton-nucleus elastic scattering at intermediate energies is a well-established method for the investigation of the nuclear matter distribution in stable nuclei and was recently applied also for the investigation of radioactive nuclei using the method of inverse kinematics. In the current experiment, the differential cross sections for proton elastic scattering on the isotopes $^{7,9,10,11,12,14}$Be and $^8$B were measured. The experiment was performed using the fragment separator at GSI, Darmstadt to produce the radioactive beams. The main part of the experimental setup was the time projection ionization chamber IKAR which was simultaneously used as hydrogen target and a detector for the recoil protons. Auxiliary detectors for projectile tracking and isotope identification were also installed. As results from the experiment, the absolute differential cross sections d$sigma$/d$t$ as a function of the four momentum transfer $t$ were obtained. In this work the differential cross sections for elastic p-$^{12}$Be, p-$^{14}$Be and p-$^{8}$B scattering at low $t$ ($t leq$~0.05~(GeV/c)$^2$) are presented. The measured cross sections were analyzed within the Glauber multiple-scattering theory using different density parameterizations, and the nuclear matter density distributions and radii of the investigated isotopes were determined. The analysis of the differential cross section for the isotope $^{14}$Be shows that a good description of the experimental data is obtained when density distributions consisting of separate core and halo components are used. The determined {it rms} matter radius is $3.11 pm 0.04 pm 0.13$~fm. In the case of the $^{12}$Be nucleus the results showed an extended matter distribution as well. For this nucleus a matter radius of $2.82 pm 0.03 pm 0.12$~fm was determined. An interesting result is that the free $^{12}$Be nucleus behaves differently from the core of $^{14}$Be and is much more extended than it. The data were also compared with theoretical densities calculated within the FMD and the few-body models. In the case of $^{14}$Be, the calculated cross sections describe the experimental data well while, in the case of $^{12}$Be there are discrepancies in the region of high momentum transfer. Preliminary experimental results for the isotope $^8$B are also presented. An extended matter distribution was obtained (though much more compact as compared to the neutron halos). A proton halo structure was observed for the first time with the proton elastic scattering method. The deduced matter radius is $2.60pm 0.02pm 0.26$~fm. The data were compared with microscopic calculations in the frame of the FMD model and reasonable agreement was observed. The results obtained in the present analysis are in most cases consistent with the previous experimental studies of the same isotopes with different experimental methods (total interaction and reaction cross section measurements, momentum distribution measurements). For future investigation of the structure of exotic nuclei a universal detector system EXL is being developed. It will be installed at the NESR at the future FAIR facility where higher intensity beams of radioactive ions are expected. The usage of storage ring techniques provides high luminosity and low background experimental conditions. Results from the feasibility studies of the EXL detector setup, performed at the present ESR storage ring, are presented.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Stationary scattering from a nonlinear network

Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a large number of sharp resonances that dominate scattering. The latter resonances are then shown to be extremely sensitive to the nonlinearity and display multistability and hysteresis. This work provides a framework for the study of light propagation in complex optical networks.

Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Nonequilibrium charge transport in an interacting open system: Two-particle resonance and current asymmetry

We use the Lippman-Schwinger scattering theory to study nonequilibrium electron transport through an interacting open quantum dot. The two-particle current is evaluated exactly while we use perturbation theory to calculate the current when the leads are Fermi liquids at different chemical potentials. We find an interesting two-particle resonance induced by the interaction and obtain criteria to observe it when a small bias is applied across the dot. Finally, for a system without spatial inversion symmetry, we find that the two-particle current is quite different depending on whether the electrons are incident from the left or the right lead.

Charge transport in a Tomonaga-Luttinger liquid: Effects of pumping and bias

We study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, pointlike impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the dc and ac components of the current have power-law dependences on the bias and pumping frequencies with an exponent 2K-1 for spinless electrons, where K is the interaction parameter. For K < 1/2, the current grows large for special values of the bias. For noninteracting electrons with K=1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons.

Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances

We study the effect that resistive regions have on the conductance of a quantum wire with interacting electrons which is connected to Fermi liquid leads. Using the bosonization formalism and a Rayleigh dissipation function to model the power dissipation, we use both scattering theory and Green's function techniques to derive the DC conductance. The resistive regions are generally found to lead to incoherent transport. For a single wire, we find that the resistance adds in series to the contact resistance of h/e(2) for spinless electrons, and the total resistance is independent of the Luttinger parameter K-W of the wire. We numerically solve the bosonic equations to illustrate what happens when a charge density pulse is incident on the wire; the results depend on the parameters of the resistive and interacting regions in interesting ways. For a junction of Tomonaga-Luttinger liquid wires, we use a dissipationless current splitting matrix to model the junction. For a junction of three wires connected to Fermi liquid leads, there are two families of such matrices; we find that the conductance matrix generally depends on K-W for one family but is independent of K-W for the other family, regardless of the resistances present in the system. Copyright (c) EPLA, 2011

Theoretical analysis of x-ray-absorption near-edge fine structure at the O and metal K edges of LaFeO3 and LaCoO3

We present experimental x-ray-absorption spectra at the oxygen and 3d transition-metal K edges of LaFeO3 and LaCoO3. We interpret the experimental results in terms of detailed theoretical calculations based on multiple-scattering theory. Along with providing an understanding of the origin of various experimental features, we investigate the effects of structural distortions and the core-hole potential in determining the experimental spectral shape. The results indicate that the core-hole potential as well as many-body effects within the valence electrons do not have any strong effect on the spectra suggesting that the spectral features can be directly interpreted in terms of the electronic structure of such compounds.

A method for measurement of planar liquid volume fraction in dense sprays

A methodology for measurement of planar liquid volume fraction in dense sprays using a combination of Planar Laser-Induced Fluorescence (PLIF) and Particle/Droplet Imaging Analysis (PDIA) is presented in this work. The PLIF images are corrected for loss of signal intensity due to laser sheet scattering, absorption and auto-absorption. The key aspect of this work pertains to simultaneously solving the equations involving the corrected PLIF signal and liquid volume fraction. From this, a quantitative estimate of the planar liquid volume fraction is obtained. The corrected PLIF signal and the corrected planar Mie scattering can be also used together to obtain the Sauter Mean Diameter (SMD) distribution by using data from the PDIA technique at a particular location for calibration. This methodology is applied to non-evaporating sprays of diesel and a more viscous pure plant oil at an injection pressure of 1000 bar and a gas pressure of 30 bar in a high pressure chamber. These two fuels are selected since their viscosity values are very different with a consequently very different spray structure. The spatial distribution of liquid volume fraction and SMD is obtained for two fuels. The proposed method is validated by comparing liquid volume fraction obtained by the current method with data from PDIA technique. (C) 2012 Elsevier Inc. All rights reserved.