Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces

We consider a transmission problem consisting of two semilinear parabolic equations involving fractional diffusion operators of different orders in a general non-smooth setting with emphasis on Lipschitz interfaces and transmission conditions along the interface. We give a unified framework for the existence and uniqueness of strong and mild solutions, and their global regularity properties.     

Theoretical investigation of the apparently irregular behavior of pt-pt nuclear spin-spin coupling constants

One-bond Pt-Pt nuclear spin-spin coupling constants J(Pt-Pt) for closely related dinuclear Pt complexes can differ by an order of magnitude without any obvious correlation with Pt-Pt distances. As representative examples, the spin-spin couplings of the dinuclear Pt(I) complexes [Pt(2)(CO)(6)](2+) (1) and [Pt(2)(CO)(2)Cl(4)](2-) (2) have been computationally studied with a recently developed relativistic density functional method. The experimental values are (1)J((195)Pt-(195)Pt) = 5250 Hz for 2 but 551 Hz for 1. Many other examples are known in the literature. The experimental trends are well reproduced by the computations and can be explained based on the nature of the ligands that are coordinated to the Pt-Pt fragment. The difference for J(Pt-Pt) of an order of magnitude is caused by a sensitive interplay between the influence of different ligands on the Pt-Pt bond, and relativistic effects on metal-metal and metal-ligand bonds as well as on "atomic orbital contributions" to the nuclear spin-spin coupling constants. The results can be intuitively rationalized with the help of a simple qualitative molecular orbital diagram.     

Factors that influence the tribo-charging of insulating ducts in suction-type dilute-phase pneumatic transport systems

The aim of this study is to refine the understanding of the tribo-electrostatic phenomena that can affect the efficiency of suction-type dilute-phase transport systems. The study was conducted with mm-size ABS-PC particles, a granular material originating from genuine information technology wastes. The tribo-charging process was modelled using the response surface method of experimental design. The controlled variables were the granular material feed rate and the aspirating air speed rate. The monitored variable was the charge imparted to a well-defined section of the duct and which is equal to the charge transferred to the particles passing through that section of the pneumatic transport system. An induction type sensor connected to an electrometer has been employed for the measurements. The data were processed by a virtual instrument developed in LabView. A commercial software package was employed for estimating the effects of the various factors and predicting the optimum operating conditions, which were then confirmed by a final experiment.     

Dispersive white-light spectral interferometry including the effect of thin-film for distance measurement

A spectral-domain white-light interferometric technique is used for measuring distances in a Michelson interferometer with a mirror represented by a thin-film structure (TFS) on a substrate. A fibre-optic spectrometer is employed for recording spectral interferograms that include wide wavelength range effects of dispersion in a cube beam splitter and multiple reflection within the TFS. Knowing the effective thickness of the beam splitter, its dispersion and parameters of the TFS and substrate, the positions of the second interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones. We apply the technique to the beam splitter made of BK7 optical glass and to a uniform SiO₂ thin film on a silicon wafer. We compare the results of the processing that include and do not include the effect of the TFS.     

A Capelli type theorem for multiplicative convolutions of polynomials

We prove a Capelli type theorem on the canonical decomposition for multiplicative convolutions of polynomials. We derive then some irreducibility criteria for convolutions of polynomials in several variables over a given field. The irreducibility conditions are expressed only in terms of the degrees of the polynomials in convolution, the degrees of their coefficients, and the degrees of some suitable divisors of the resulting leading coefficient. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parameter estimation for stochastic equations with additive fractional Brownian sheet

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the the two-parameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity theory.      

On a Regularized Family of Models for Homogeneous Incompressible Two-Phase Flows

We consider a general family of regularized models for incompressible two-phase flows based on the Allen–Cahn formulation in \(n\) -dimensional compact Riemannian manifolds for \(n=2,3\) . The system we consider consists of a regularized family of Navier–Stokes equations (including the Navier–Stokes- \(\alpha \) -like model, the Leray- \(\alpha \) model, the modified Leray- \(\alpha \) model, the simplified Bardina model, the Navier–Stokes–Voight model, and the Navier–Stokes model) for the fluid velocity \(u\) suitably coupled with a convective Allen–Cahn equation for the order (phase) parameter \(\phi \) . We give a unified analysis of the entire three-parameter family of two-phase models using only abstract mapping properties of the principal dissipation and smoothing operators and then use assumptions about the specific form of the parameterizations, leading to specific models, only when necessary to obtain the sharpest results. We establish existence, stability, and regularity results and some results for singular perturbations, which as special cases include the inviscid limit of viscous models and the \(\alpha \rightarrow 0\) limit in \(\alpha \) models. Then we show the existence of a global attractor and exponential attractor for our general model and establish precise conditions under which each trajectory \(\left( u,\phi \right) \) converges to a single equilibrium by means of a Lojasiewicz–Simon inequality. We also derive new results on the existence of global and exponential attractors for the regularized family of Navier–Stokes equations and magnetohydrodynamics models that improve and complement the results of Holst et al. (J Nonlinear Sci 20(5):523–567, 2010). Finally, our analysis is applied to certain regularized Ericksen–Leslie models for the hydrodynamics of liquid crystals in \(n\) -dimensional compact Riemannian manifolds.     

Existence and Besov regularity of the density for a class of SDEs with Volterra noise

By using a simple method based on the fractional integration by parts, we prove the existence and the Besov regularity of the density for solutions to stochastic differential equations driven by an additive Gaussian Volterra process. We assume weak regularity conditions on the drift. Several examples of Gaussian Volterra noises are discussed.