Characterization of Generalized Gradient Young Measures Generated by Sequences in W1,1 and BV

Generalized Young measures as introduced by DiPerna and Majda (Commun Math Phys 108:667–689, 1987) provide a quantitative tool for studying the one-point statistics of oscillation and concentration in sequences of functions. In this work, after developing a functional-analytic framework for such measures, including a compactness theorem and results on the generation of such Young measures by L¹-bounded sequences (or even by sequences of bounded Radon measures), we turn to investigation of those Young measures that are generated by bounded sequences of W^1,1-gradients or BV-derivatives. We provide several techniques to manipulate such measures (including shifting, averaging and approximation by piecewise-homogeneous Young measures) and then establish the main new result of this work, the duality characterization of the set of (BV- or W^1,1-)gradient Young measures in terms of Jensen-type inequalities for quasiconvex functions with linear growth at infinity. This result is the natural generalization of the Kinderlehrer–Pedregal Theorem (Arch Ration Mech Anal 115:329–365, 1991; J Geom Anal 4:59–90, 1994) for classical Young measures to the W^1,1- and BV-case and contains its version for weakly converging sequences in W^1,1 as a special case. Finally, we give an application to a new lower semicontinuity theorem in BV.     

Fractional decay of quantum dots in real photonic crystals

We show that fractional decay may be observable in experiments using quantum dots and photonic crystals with parameters that are currently achievable. We focus on the case of inverse opal photonic crystals and locate the position in the crystal where the effect is most pronounced. Furthermore, we quantify the influence of absorptive loss and show that it is a limiting but not prohibitive effect.     

Investigating porcine pancreatic phospholipase A2 action on vesicles and supported planar bilayers using a quartz crystal microbalance with dissipation

We present an investigation of the activity of porcine pancreatic phospholipase A2 towards phospholipids. The phospholipids are presented in three different ways, namely as tethered vesicles, intact surface-bound vesicles, and supported planar bilayers (SPBs). The process is followed using a quartz crystal microbalance which measures both the frequency shift and the energy dissipation factor. This technique is very sensitive not only to the mass of the material deposited on the crystal, but also to its viscoelasticity. The breakdown of the phospholipid vesicles and bilayers consequently gives rise to very large signal changes. Enzyme binding is separated from vesicle hydrolysis using nonhydrolyzable ether lipids. Intact and tethered vesicles give rise to the same profile, indicating that direct immobilization of the vesicles does not affect hydrolysis significantly. The data fit well to a Voight-based model describing the change in film structure with time. Initial enzyme binding to intact vesicles is accompanied by a significant increase in layer thickness as well as a decrease in viscosity and shear modulus. This effect, which is less pronounced in SPBs, is probably mainly due to the accumulation of hydrolysis products in the vesicle prior to rupture of the vesicles and release of bound water, since it disappears when lysolipid is included in the vesicles prior to hydrolysis.     

High resolution inductively coupled plasma mass spectrometry (HR-ICPMS) determination and multivariate evaluation of 10 trace elements in mussels from 7 sites in Limfjorden, Denmark

The contents of V, Cr, Co, Ni, Cu, Ga, Rb, Cd, Ba, and Pb in the soft tissue of blue mussel (Mytilus edulis) were determined by a high resolution inductively coupled plasma mass spectrometry (HR-ICPMS) method. Sample digestions were performed in closed microwave vessels using nitric acid and hydrogen peroxide. Using HR-ICPMS it is possible to resolve the analytical peaks from otherwise interfering polyatomic ions with a mass resolution setting of 4,000 (Cr, Ni, Cu). The proposed method was validated using a mussel tissue reference material (NIST SRM 2974). The proposed method was applied to real samples of blue mussel from seven sites in the inlet "Limfjorden", Denmark, and the levels of trace elements found were compared with the levels found in an earlier study. For the mussel samples large inter-regional differences in trace element concentrations in the tissues were recorded. The mussels from the different sites could be separated using principal component analysis (PCA). Comparison with the levels of trace elements in mussels found in 1982 showed that the trace elemental contamination has increased during the last 15 years. From the data obtained, mussel tissue appears to be good bio-indicator for identification of coastal areas exposed to metallic contaminants.     

Efficient integration of stiff kinetics with phase change detection for reactive reservoir processes

We propose the use of implicit one-step Explicit Singly Diagonal Implicit Runge–Kutta (ESDIRK) methods for integration of the stiff kinetics in reactive, compositional and thermal processes that are solved using operator-splitting type approaches. To facilitate the algorithmic development we construct a virtual kinetic cell model. The model serves both as a tool for the development and testing of tailored solvers as well as a testbed for studying the interactions between chemical kinetics and phase behavior. As case study, two chemical kinetics models with 6 and 14 components, respectively, are implemented for in situ combustion, a thermal oil recovery process. Through benchmark studies using the 14 component reaction model the new ESDIRK solvers are shown to improve computational speed when compared to the widely used multi-step BDF methods DASSL and LSODE. Phase changes are known to cause convergence problems for the integration method. We propose an algorithm for detection and location of phase changes based on discrete event system theory. Experiments show that the algorithm improves the robustness of the integration process near phase boundaries by lowering the number convergence and error test failures by more than 50% compared to direct integration without the new algorithm.     

Auditory brainstem responses to chirps delivered by an insert earphone with equalized frequency response

Recently it has been demonstrated that auditory brainstem responses, ABRs, to chirps are larger with the ER-2 than with the ER-3A insert earphone due to differences between the corresponding amplitude-frequency responses. Therefore a modified chirp, which equalizes the amplitude-frequency response of the ER-3A, is constructed and subsequently compared to the unmodified chirp. ABRs are recorded from 20 normal-hearing subjects in response to the two chirps delivered by the ER-3A earphone at a wide range of levels. The results confirm that the modified chirp generates significantly larger ABRs than the unmodified chirp at levels below 60?dB nHL.     

Assembled monolayers of Mo3S4(4+) clusters on well-defined surfaces

A class of inorganic monolayers formed by assembling the molybdenum-sulfur cluster, Mo3S4(4+), onto a well-defined Au(111) surface is presented. The monolayers have been comprehensively characterized by electrochemistry, X-ray photoelectron spectroscopy (XPS), and in situ scanning tunneling microscopy (in situ STM). The voltammetric data show strong reductive and oxidative desorption signals from Au-S interactions, supported by the presence of both S and Mo signals in XPS. In situ STM shows many small pits in the dense adlayers uniformly spread over the surface, which is a typical feature of self-assembled monolayers (SAMs) of alkanethiols. The density of the pits is ca. 23 (+/-5)% and is significantly higher than for straight-chain alkanethiol SAMs with a single -SH group. The pit shapes are irregular, suggesting multiple Au-S interactions from Mo3S4(4+). High resolution images disclose bright round spots of ca. 8 A diameter representing individual molecules in the SAM. This is the first example of in situ monolayer formation by a metal-chalcogenide cluster directly anchored onto the gold surface through core ligands and offers a simple way to prepare a new class of functionalized inorganic monolayers.     

Lab-on-a-chip with integrated optical transducers

Taking the next step from individual functional components to higher integrated devices, we present a feasibility study of a lab-on-a-chip system with five different components monolithically integrated on one substrate. These five components represent three main domains of microchip technology: optics, fluidics and electronics. In particular, this device includes an on-chip optically pumped liquid dye laser, waveguides and fluidic channels with passive diffusive mixers, all defined in one layer of SU-8 polymer, as well as embedded photodiodes in the silicon substrate. The dye laser emits light at 576 nm, which is directly coupled into five waveguides that bring the light to five different locations along a fluidic channel for absorbance measurements. The transmitted portion of the light is collected at the other side of this cuvette, again by waveguides, and finally detected by the photodiodes. Electrical read-out is accomplished by integrated metal connectors. To our knowledge, this is the first time that integration of all these components has been demonstrated.     

Diophantine approximation and badly approximable sets

Let (X,d) be a metric space and (Ω,d) a compact subspace of X which supports a non-atomic finite measure m. We consider ‘natural’ classes of badly approximable subsets of Ω. Loosely speaking, these consist of points in Ω which ‘stay clear’ of some given set of points in X. The classical set Bad of ‘badly approximable’ numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Ω have full Hausdorff dimension. Applications of our general framework include those from number theory (classical, complex, p-adic and formal power series) and dynamical systems (iterated function schemes, rational maps and Kleinian groups).