Scattering in thick multifractal clouds, Part II: Multiple scattering

In Part I of this paper, we developed asymptotic approximations for single photon scattering in thick, highly heterogeneous, “Log-Lévy” multifractal clouds. In Part II, theoretical multiple scattering predictions are numerically tested using Monte Carlo techniques, which show that, due to long range correlations, the photon paths are “subdiffusive” with the corresponding fractal dimensions tending to increase slowly with mean optical thickness. We develop reasonably accurate statistical relations between N scatter statistics in thick clouds and single scatter statistics in thin clouds. This is explored further using discrete angle radiative transfer (DART) approach in which the radiances decouple into non-interacting families with only four (for 2-D clouds) radiance directions each. Sparse matrix techniques allow for rapid and extremely accurate solutions for the transfer; the accuracy is only limited by the spatial discretization.By “renormalizing” the cloud density, we relate the mean transmission statistics to those of an equivalent homogeneous cloud. This simple idea is remarkably effective because two complicating effects act in contrary directions: the “holes” which lead to increased single scatter transmission and the tendency for multiply scattered photons to become “trapped” in optically dense regions, thus decreasing the overall transmission.     

Characterization of inhomogeneous colloidal layers using adapted coherence probe microscopy

Colloidal layers play an important role in environmental studies, for example in the movement of radionuclides in nuclear waste management. New characterization techniques are required for studying such complex, porous layers. The purpose of this work is to adapt coherence probe microscopy (CPM), which is typically used for measuring the surface roughness of single surfaces, to the analysis of thick inhomogeneous colloidal layers. Two types of layers, either composed of 80 nm or 400 nm alumina colloidal particles deposited on glass slides by decantation have been studied. One of the problems in performing routine roughness measurements of colloidal layers using CPM is the appearance of apparent pits below the level of the substrate surface. We demonstrate that this is due to partial detection of the buried colloid/substrate interface. Further, we have developed the “Z-scan” technique, which consists of building up an XYZ image stack by scanning the full depth of the sample. Any point in an XY image can then be investigated to study the local buried internal structure, layer thickness, and effective refractive index. Comparison of results with AFM and SEM confirm the structure found with CPM and the new “Z-scan” technique, which opens up new and useful applications.     

Comparison of single and multiple scattering approaches for the simulation of limb-emission observations in the mid-IR

The validity of single scattering radiative transfer calculations for simulation of limb-emission measurements of clouds in the mid-infrared spectral region was investigated by comparison with a multiple scattering model. For in limb direction optically thin clouds, like polar stratospheric clouds, errors of the single scattering scheme range below 3%. For optically thick clouds deviations are below 3% in case of low single scattering albedo (ω₀=0.24) increasing up to 10-30% for ω₀=0.84. Clouds which are optically thick in limb, but thin in nadir direction, can cause limb radiances which are by a factor of 1.7 higher than the blackbody radiance at cloud altitude.     

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.     

Light scattering by “soft” particles of arbitrary shape and size: II—Arbitrary orientation of particles in the space

In this part of the article a new version analysis of light scattering by “soft” particles is presented that makes it possible to reduce and simplify the process of numerical calculations. The calculation results of the integral scattering cross-sections and indicatrices for spheroid, parallelepiped and cylinder for their arbitrary orientation in space are given as an illustration. The results are accompanied by transparent physical interpretations, based on the examination of the contour graphs of the three-dimensional spectra of particles.     

Forecasting volatility in Shanghai and Shenzhen markets based on multifractal analysis

This paper analyzes the multifractality in Shanghai and Shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis. We find that the main source of multifractality is long-range correlations of large and small fluctuations. Then, we introduce a multifractal volatility measure (MV) and find that by taking MV as daily conditional volatility, the simulated series displayed similar “stylized facts” to the original daily return series. By capturing the dynamics of MV using the ARFIMA model, we find that the out-of-sample forecasting performance of the ARFIMA-MV model is better than some GARCH-class models and the ARFIMA-RV model under some criteria of loss function.     

Dynamics of molybdenum nano structure formation on the TiO2(1 1 0) surface: A kinetic Monte Carlo approach

The rutile TiO₂(1 1 0) surface is a highly anisotropic surface exhibiting “channels” delimited by oxygen rows. In previous experimental and theoretical DFT works we could identify the molybdenum adsorption sites. They are located inside the channels. Moreover, experimental studies have shown that during subsequent annealing after deposition, special molybdenum nano structures can be formed, especially two monolayer high pyramidal chains of atoms.In order to better understand the dynamics of nano structure formation, we present a kinetic Monte Carlo study on diffusion and adsorption of molybdenum atoms on a TiO₂(1 1 0) surface. A quasi one-dimensional lattice gas model has been used which describes the possible adsorption sites of a Mo atom in a single channel of the surface. The atomic positions of a 1.5 monolayer thick Mo film formed of pyramidal chains define the lattice sites of the model. Thereby the formation of three-dimensional clusters could be studied. Here we have studied the cluster formation as a function of parameters that can be controlled in a growth experiment by physical vapor deposition: deposition and annealing temperature, flux and total amount of deposited Mo. Good qualitative agreement with recent experiments is obtained.     

Radiative transfer with internal reflection via the converged discrete ordinates method

In response to the challenge of establishing highly accurate solutions to the plane layer radiative transfer equation with the simplest of methods, the converged discrete ordinates method is presented. With this algorithm of only finite difference, quadrature and acceleration, we show how to obtain highly accurate intensities for radiative transfer in a finite layer with internal surface reflection. The method features angular smoothing and angular interpolation through “faux” quadrature. In addition, a manufactured solution demonstrates the high accuracy of the method for forward peaked scattering. We consider scattering in a heterogeneous medium as a final demonstration.     

Notes on nonlocal projective measurements in relativistic systems

In quantum mechanical bipartite systems, naive extensions of von Neumann’s projective measurement to nonlocal variables can produce superluminal signals and thus violate causality. We analyze the projective quantum nondemolition state-verification in a two-spin system and see how the projection introduces nonlocality without entanglement. For the ideal measurements of “R-nonlocal” variables, we argue that causality violation can be resolved by introducing further restrictions on the post-measurement states, which makes the measurement “Q-nonlocal”. After we generalize these ideas to quantum mechanical harmonic oscillators, we look into the projective measurements of the particle number of a single mode or a wave-packet of a relativistic quantum field in Minkowski space. It turns out that the causality-violating terms in the expectation values of the local operators, generated either by the ideal measurement of the “R-nonlocal” variable or the quantum nondemolition verification of a Fock state, are all suppressed by the IR and UV cutoffs of the theory. Thus relativistic quantum field theories with such projective measurements are effectively causal.     

Multifractal analysis on international crude oil markets based on the multifractal detrended fluctuation analysis

The multifractal nature of WTI and Brent crude oil markets is studied employing the multifractal detrended fluctuation analysis. We find that two crude oil markets become more and more efficient for long-term and two Gulf Wars cannot change time scale behavior of crude oil return series. Considering long-term influence caused by Gulf Wars, we find such “turning windows” in generalized Hurst exponents obtained from three periods divided by two Gulf Wars so that WTI and Brent crude oil returns possess different properties above and below the windows respectively. Comparing with the results obtained from three periods we conclude that, before the First Gulf War, international crude oil markets possessed the highest multifractality degree, small-scope fluctuations presented the strongest persistence and large-scope fluctuations presented the strongest anti-persistence. We find that, for two Gulf Wars, the first one made a greater impact on international oil markets; for two markets, Brent was more influenced by Gulf Wars. In addition, we also verified that the multifractal structures of two markets’ indices are not only mainly attributed to the broad fat-tail distributions and persistence, but also affected by some other factors.     

Relationship between neural and hemodynamic signals during spontaneous activity studied with temporal kernel CCA

Functional magnetic resonance imaging (fMRI) based on the so-called blood oxygen level-dependent (BOLD) contrast is a powerful tool for studying brain function not only locally but also on the large scale. Most studies assume a simple relationship between neural and BOLD activity, in spite of the fact that it is important to elucidate how the “when” and “what” components of neural activity are correlated to the “where” of fMRI data. Here we conducted simultaneous recordings of neural and BOLD signal fluctuations in primary visual (V1) cortex of anesthetized monkeys. We explored the neurovascular relationship during periods of spontaneous activity by using temporal kernel canonical correlation analysis (tkCCA). tkCCA is a multivariate method that can take into account any features in the signals that univariate analysis cannot. The method detects filters in voxel space (for fMRI data) and in frequency–time space (for neural data) that maximize the neurovascular correlation without any assumption of a hemodynamic response function (HRF). Our results showed a positive neurovascular coupling with a lag of 4–5 s and a larger contribution from local field potentials (LFPs) in the γ range than from low-frequency LFPs or spiking activity. The method also detected a higher correlation around the recording site in the concurrent spatial map, even though the pattern covered most of the occipital part of V1. These results are consistent with those of previous studies and represent the first multivariate analysis of intracranial electrophysiology and high-resolution fMRI.     

Electromagnetic scattering by a morphologically complex object: Fundamental concepts and common misconceptions

Following Keller (Proc Symp Appl Math 1962;13:227-46), we classify all theoretical treatments of electromagnetic scattering by a morphologically complex object into first-principle (or “honest” in Keller's terminology) and phenomenological (or “dishonest”) categories. This helps us identify, analyze, and dispel several profound misconceptions widespread in the discipline of electromagnetic scattering by solitary particles and discrete random media. Our goal is not to call for a complete renunciation of phenomenological approaches but rather to encourage a critical and careful evaluation of their actual origin, virtues, and limitations. In other words, we do not intend to deter creative thinking in terms of phenomenological short-cuts, but we do want to raise awareness when we stray (often for practical reasons) from the fundamentals. The main results and conclusions are illustrated by numerically-exact data based on direct numerical solutions of the macroscopic Maxwell equations.     

The instability of vicinal electrode surfaces against step bunching I: Experiment

Using electrochemical STM we have studied the stability of arrays of parallel, single atom height steps on vicinal Ag(1 1 1) electrodes in electrolyte. We find that the steps for Ag(1 1 1) electrodes are unstable and form first double-steps and later multiple steps, separated by wide, flat terraces. In this paper denoted as “I: Experiment” we deal with the experimental aspects whereas theoretical aspects are discussed in the following paper “II: Theory”.     

ToF-SIMS cluster ion imaging of hippocampal CA1 pyramidal rat neurons

Recent studies have demonstrated the power of time-of-flight secondary ion mass spectrometry (ToF-SIMS) cluster ion imaging to characterize biological structures, such as that of the rat central nervous system. A large number of the studies to date have been carried out on the “structural scale” imaging several mm² using mounted thin sections. In this work, we present our ToF-SIMS cluster ion imaging results on hippocampal rat brain neurons, at the cellular and sub-cellular levels. As a part of an ongoing investigation to examine gut linked metabolic factors in autism spectrum disorders using a novel rat model, we have observed a possible variation in hippocampal Cornu ammonis 1 (CA1) pyramidal neuron geometry in thin, paraformaldehyde fixed brain sections. However, the fixation process alters the tissue matrix such that much biochemical information appears to be lost. In an effort to preserve as much as possible this original information, we have established a protocol using unfixed thin brain sections, along with low dose, 500 eV Cs⁺ pre-sputtering that allows imaging down to the sub-cellular scale with minimal sample preparation.     

Infrared properties of quartz fibres

The IR properties of micron-size amorphous SiO₂ fibres have been investigated between 400 cm^–1 and 1400 cm^–. For the single scattering size and shape effects have been measured and compared with theory. The observed diffuse reflection of quartz wool can be explained qualitatively by the Kubelka-Munk theory for multiple scattering.reported at the 5th International Conference on Infrared and Millimeter Waves, October 6–10, 1980     

Physical limits of inference

We show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. We call devices with that structure “inference devices”. We present a set of existence and impossibility results concerning inference devices. These results hold independent of the precise physical laws governing our universe. In a limited sense, the impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted, given sufficient knowledge of the present. Alternatively, these impossibility results can be viewed as a non-quantum-mechanical “uncertainty principle”.The mathematics of inference devices has close connections to the mathematics of Turing Machines (TMs). In particular, the impossibility results for inference devices are similar to the Halting theorem for TMs. Furthermore, one can define an analog of Universal TMs (UTMs) for inference devices. We call those analogs “strong inference devices”. We use strong inference devices to define the “inference complexity” of an inference task, which is the analog of the Kolmogorov complexity of computing a string. A task-independent bound is derived on how much the inference complexity of an inference task can differ for two different inference devices. This is analogous to the “encoding” bound governing how much the Kolmogorov complexity of a string can differ between two UTMs used to compute that string. However no universe can contain more than one strong inference device. So whereas the Kolmogorov complexity of a string is arbitrary up to specification of the UTM, there is no such arbitrariness in the inference complexity of an inference task.We informally discuss the philosophical implications of these results, e.g., for whether the universe “is” a computer. We also derive some graph-theoretic properties governing any set of multiple inference devices. We also present an extension of the framework to address physical devices used for control. We end with an extension of the framework to address probabilistic inference.     

The evaluation of binaural playback systems for virtual sound fields

By means of virtual acoustics technologies the impulse response in a location of a real enclosure can be used to create a virtual room. Also in this virtual space, typically implemented in a dead room, an impulse response can be measured. From both “real” and respective “virtual” impulse response a group of room-acoustical parameters can be calculated. The match of the two groups of indicators mostly depends on the layout of the playback system and on the implemented processing. In this paper a procedure of virtual measurement in a dead room is developed and some typical layouts of playback systems employing two loudspeakers are compared. Based on the consistency of the room-acoustical indicators derived from “real” and “virtual” impulse responses can be investigated. It is shown how the performance depends on the angular separation of loudspeakers and the efficiency of the cross-talk is also tested and discussed. Finally, a set-up which is suitable for psychoacoustics tests is indicated.     

Imaging through scattering medium by recording 3D “spatial-frequential” interferograms

Speed acquisition for image formation process through scattering medium is a challenge in optical coherence tomography (OCT) approach. Besides time domain (TD), spectral Fourier domain (FD) is now widely studied. By using a swept laser source, we demonstrate that a particular time domain OCT method (optical SISAM correlator) can be simultaneously implemented in a single set-up with the corresponding Fourier domain OCT approach (spectral interferometry). Then, FD-OCT and TD-OCT signals are obtained by processing a 3D “spatial-frequential” interferences pattern. We show that these two numerical approaches can be complementary when imaging in scattering medium is achieved.