Stochastic radiative transfer in Markovian mixtures: Past, present, and future

The Markovian approach, originally suggested in the early 1900s, has widespread practical use in many of our present-day studies and allows one to build bridges between diverse research areas such as statistical physics, astronomy, and computational science. This overview takes a broad sweep of several important examples with the emphasis on the stochastic radiative transfer in a cloudy atmosphere. In particular, the overview (i) highlights important contributions made by Pomraning and Titov to the neutron and radiation transport theory in a stochastic medium with homogeneous statistics and (ii) illustrates that ideas and tools introduced by these two distinguished scientists are gaining increasing impact and recognition in the atmospheric science.     

Edge resonance in an elastic semi-infinite cylinder

We study the three-dimensional elasticity operator in a semi-infinite circular cylinder subject to free boundary conditions, in the case of zero Poisson ratio. We prove, adapting the method from [15], i.e., by first finding an invariant subspace for the elasticity operator such that the essential spectrum has a strictly positive lower bound and then finding a test function in this space for which the variational quotient takes a value below the bottom of the essential spectrum, that there is an eigenvalue embedded in the continuous spectrum. Physically, an eigenvalue corresponds to a "trapped mode", that is, a harmonic oscillation localized near the edge. This effect, known in mechanics as the "edge resonance" has been extensively studied numerically and experimentally. Our paper extends the mathematical justification of such phenomena provided by [15] to a three-dimensional setting     

On the Initiation Mechanism of Syndiospecific Styrene Polymerization Catalyzed by Single‐Component ansa‐Lanthanidocenes

Single‐site catalysts : Syndiospecific styrene polymerization promoted by single‐site ansa‐lanthanidocene catalysts proceeds selectively in a secondary (2,1) fashion, both at the initiation and propagation steps. The steric hindrance between the phenyl ring of the incoming styrene monomer and the ancillary ligands (Cp′, Flu′), induced by the change of either the bridge or the “active” R ligand in the catalyst precursor, is proposed to control the reactivity of the complexes (see scheme).

     

STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION

Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measurevalued functions. This main result implies existence of solutions to degenerate parabolic convection-diffusion equations with discontinuous flux. Moreover, it provides a framework in which one can prove convergence of various types of approximate solutions, such as those generated by the vanishing viscosity method and numerical schemes.     

Kolmogorov-Arnold-Moser transition and laser action on scar modes in semiconductor diode lasers with deformed resonators

Measurements of the optical spectra of semiconductor injection lasers with deformed cylinder resonators show strong indications of the classical Kolmogorov-Arnold-Moser transition from integrability to chaos for devices with small deformation. At larger deformation, evidence for laser action on scar modes is obtained. The diode lasers operate with TE polarization, resulting in laser action on (partially) chaotic whispering-gallery modes for all deformations.     

Leibenzon's backward shift and composition operators

We apply Leibenzon's backward shift to show that the composition operator on the unit ball of always maps the weighted Hardy space into the Hardy class .

     

Kinetics and mechanism of the formation and reduction of oxide layers on platinum part I. Oxidation and reduction of platinum electrodes

Oxidation and reduction of platinum electrodes have been investigated in the potential range up to 3.0 V in acid, alkaline and phosphate buffer solutions with pH from 0 to 14. It is shown that oxygen adsorption and absorption on platinum are usually superimposed, but they may be artificially separated using a strong dependence of the second process upon platinum pretreatment and potential sweep rate. The dependence of oxygen surface coverage on potential has several characteristic regions, each corresponding to the formation of a definite surface oxycompound.     

Highly syndiospecific polymerization of styrene catalyzed by allyl lanthanide complexes

Allylic complexes of lanthanides bearing a fluorenyl-based ligand are active single-component catalysts for the polymerization of styrene, giving highly syndiotactic polymers (rrrr > 99%) with low to high molecular weight (Mn = 8000-135 000) and narrow polydispersities (Mw/Mn = 1.25-2.1).