Light scattering by large Saharan dust particles: Comparison of modeling and experimental data for two samples

Light scattering by large mineral-dust particles with small-scale surface roughness is investigated by comparing model simulations with laboratory-measured scattering matrices of two distinct dust samples collected from the Sahara desert. The samples have been chosen on the basis of their large effective radii, and the simulations are based on their measured size distributions. Size parameters larger than about 30 are modeled using a modified ray-optics model RODS (Ray optics with diffuse and specular interactions), while smaller particles are simulated with a T-matrix model. RODS allows us to mimic the surface roughness of large dust particles by covering the particle surface by a thin layer of external scatterers with specific single-scattering properties. The Gaussian-random-sphere geometry is used for the shapes of large dust particles. Small particles are modeled as an axial-ratio distribution of spheroids with smooth surfaces. One of the samples consists wholly of large particles and its scattering matrix can be reproduced very well by the RODS model, except for the phase function. The incorporation of wavelength-scale roughness is, however, necessary for good fits. The other sample, consisting of both small and large particles, proves more challenging to match with simulations. The analysis indicates, however, that the difficulties arise at least partially from the small-particle contribution, while RODS results are consistent with the measurements. Further, the results imply that the agreement with measurements would improve if roughness could also be accounted for in the small-particle simulations. Overall, the RODS method seems promising for modeling the optical properties of mineral-dust particles much larger than the wavelength.     

Testing for a $$delta $$ -neighborhood of a generalized Pareto copula

Annals of the Institute of Statistical Mathematics - A multivariate distribution function F is in the max-domain of attraction of an extreme value distribution if and only if this is true for the...     

Reversible Live-Cell Labeling with Retro-engineered HaloTags Enables Long-Term High- and Super-Resolution Imaging

Self-labeling enzymes (SLE) such as the HaloTag have emerged as powerful tools in high and super-resolution fluorescence microscopy. Newly developed fluorogenic SLE substrates enable imaging in the presence of excess dye. To exploit this feature for reversible labeling, we engineered two variants of HaloTag7 with restored dehalogenase activity. Kinetic studies in vitro showed different turnover kinetics for reHaloTagS (≈0.006 s⁻¹) and reHaloTagF (≈0.055 s⁻¹). Imaging by confocal and stimulated emission depletion microscopy yielded 3-5-time enhanced photostability of reHaloTag labeling. Prominently, single molecule imaging with reHaloTags enabled controlled and stable labeling density over extended time periods. By combination with structured illumination, simultaneous visualization of single molecule diffusion and organellar dynamics was achieved. These applications highlight the potential of reHaloTag labeling for pushing the limits of advanced fluorescence microscopy techniques.     

Studies toward frondosin A and its analogues. Formal total synthesis of (+/-)-frondosin A

Two reaction sequences commencing with different starting materials were successfully employed for the synthesis of frondosin A analogues, including (+/-)-frondosin A dimethyl ether. Construction of the bicyclo[5.4.0]undecane core in each case was achieved through an expedient microwave-assisted tandem 5-exo cyclization--Claisen rearrangement process.     

Shear induced phase transition in PbO under high pressure

We have studied the structural behavior of lead monoxide (PbO) as a function of pressure via angular dispersive X-ray diffraction employing two different pressure transmitting media that were quasi-hydrostatic (N₂) and non-hydrostatic (MgO), respectively. Besides litharge (-PbO) and massicot (β-PbO), which are both stable at ambient pressure, there is an orthorhombic γ-PbO phase which appears upon application of pressure to -PbO. We have found that the orthorhombic γ-PbO phase is favored by shear stress under non-hydrostatic conditions. -PbO shows strong anisotropy in compressibility. The a-axis is rather incompressible with a linear stiffness coefficient of K_a0=540(30) GPa whereas the c-axis stiffness is K_c0=25(1) GPa. The bulk modulus of -PbO is K₀=23.1(3) GPa and its derivative .     

Comparing adult mathematical literacy with PISA students: results of a pilot study

In Germany, very little empirical data about the mathematical competence of adults is available. The aim of this study is to test the level of mathematical competence in an adult sample. For this purpose, a mathematics test was constructed using the PISA mathematics framework as a guideline. The test consisted of fourteen public items from the mathematics test in PISA 2000. The study was implemented by carrying out house visits (Germany). The sample was comprised of 64 adults (90% women, age: 41 years). The test results were scaled in the metric of PISA 2000. Compared with the average German student competencies in PISA 2000, the average competency in the adult sample was on the same level as the fifteen-year-old comprehensive secondary school student (at a German Gymnasium). Further analysis shows that the mathematics competency level in the adult sample is positively connected to the individual vocational education degree.     

Positive definiteness in the numerical solution of Riccati differential equations

Summary. In this work we address the issue of integrating symmetric Riccati and Lyapunov matrix differential equations. In many cases -- typical in applications -- the solutions are positive definite matrices. Our goal is to study when and how this property is maintained for a numerically computed solution. There are two classes of solution methods: direct and indirect algorithms. The first class consists of the schemes resulting from direct discretization of the equations. The second class consists of algorithms which recover the solution by exploiting some special formulae that these solutions are known to satisfy. We show first that using a direct algorithm -- a one-step scheme or a strictly stable multistep scheme (explicit or implicit) -- limits the order of the numerical method to one if we want to guarantee that the computed solution stays positive definite. Then we show two ways to obtain positive definite higher order approximations by using indirect algorithms. The first is to apply a symplectic integrator to an associated Hamiltonian system. The other uses stepwise linearization. Received April 21, 1993     

Anomalous absorption of bulk shear sagittal acoustic waves in a layered structure with viscous fluid

It is demonstrated theoretically that the absorptivity of bulk shear sagittal waves by an ultra-thin layer of viscous fluid between two different elastic media has a strong maximum (in some cases as good as 100%) at an optimal layer thickness. This thickness is usually much smaller than the penetration depths and lengths of transverse and longitudinal waves in the fluid. The angular dependencies of the absorptivity are demonstrated to have significant and unusual structure near critical angles of incidence. The effect of non-Newtonian properties and non-uniformities of the fluid layer on the absorptivity is also investigated. In particular, it is shown that the absorption in a thin layer of viscous fluid is much more sensitive to non-zero relaxation time(s) in the fluid layer than the absorption at an isolated solid-fluid interface.     

High‐molar‐mass polypropene with tunable elastic properties by hafnocene/borate catalysts

Elastic polypropene has gained growing industrial and academic interest as a thermoplastic elastomer. In this study, “rac”‐ and “meso”‐dimethylsilyl(3‐benzylindenyl)(2‐methylindenyl)hafnium dichloride complexes (Hfr and Hfm, respectively), activated with [NHMe₂Ph][B(C₆F₅)₄]/triisobutyl aluminum, were used in propene polymerization. Using these catalyst systems, we obtained polymers with high molar masses, up to 550 kg/mol, and moderate isotacticities between 34 and 52%. By varying the polymerization conditions, we could modify the polymer microstructure and molar mass. ¹³C NMR was used to calculate the polymer pentad sequence distributions. The crystalline parts of the polymers were analyzed with the differential scanning calorimetry successive self‐nucleation and annealing (SSA) technique. The SSA thermograms revealed that Hfr produced polypropene with a more uniform lamellar structure than Hfm. The mechanical properties were tested with dynamic mechanical analysis creep‐recovery tests. In the series, the polymers with the lowest isotacticities and therefore lowest crystallinities showed the best elastic properties. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4743–4751, 2006