Solutions to and Validation of Matrix-Diffusion Models

A model transport system is considered in which a pulse of tracer molecules is advected along a flow channel with porous walls. The advected tracer thus undergoes diffusion, matrix-diffusion, inside the walls, which affects the breakthrough curve of the tracer. Analytical solutions in the form of series expansions are derived for a number of situations which include a finite depth of the porous matrix, varying aperture of the flow channel, and longitudinal diffusion and Taylor dispersion of the tracer in the flow channel. Novel expansions for the Laplace transforms of the concentration in the channel facilitated closed-form expressions for the solutions. A rigorous result is also derived for the asymptotic form of the breakthrough curve for a finite depth of the porous matrix, which is very different from that for an infinite matrix. A specific experimental system was created for validation of matrix-diffusion modeling for a matrix of finite depth. A previously reported fracture-column experiment was also modeled. In both cases model solutions gave excellent fits to the measured breakthrough curves with very consistent values for the diffusion coefficients used as the fitting parameters. The matrix-diffusion modeling performed could thereby be validated.     

Quantum Diffusion and Delocalization for Band Matrices with General Distribution

We consider Hermitian and symmetric random band matrices H in d \geqslant 1{d \geqslant 1} dimensions. The matrix elements H _xy , indexed by x,y ? L ì \mathbbZ^d{x,y \in \Lambda \subset \mathbb{Z}^d}, are independent and their variances satisfy s_xy²:=\mathbbE |H_xy|² = W^-d f((x - y)/W){\sigma_{xy}^2:=\mathbb{E} |{H_{xy}}|^2 = W^{-d} f((x - y)/W)} for some probability density f. We assume that the law of each matrix element H _xy is symmetric and exhibits subexponential decay. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales t << W^d/3{t\ll W^{d/3}} . We also show that the localization length of the eigenvectors of H is larger than a factor W^d/6{W^{d/6}} times the band width W. All results are uniform in the size |Λ| of the matrix. This extends our recent result (Erdős and Knowles in Commun. Math. Phys., 2011) to general band matrices. As another consequence of our proof we show that, for a larger class of random matrices satisfying ?_xs_xy²=1{\sum_x\sigma_{xy}^2=1} for all y, the largest eigenvalue of H is bounded with high probability by 2 + M^{-2/3 + e}{2 + M^{-2/3 + \varepsilon}} for any ${\varepsilon > 0}${\varepsilon > 0}, where M : = 1 / (max_x,ys_xy²){M := 1 / (\max_{x,y}\sigma_{xy}^2)} .     

Coexistence of Two Different Distorted Octahedral [MnF6]3− Sites in K3[MnF6]: Manifestation in Spectroscopy and Magnetism

As a consequence of the static Jahn-Teller effect of the ⁵E ground state of Mn^III in cubic structures with octahedral parent geometries, their octahedral coordination spheres become distorted. In the case of six fluorido ligands, [MnF₆]³⁻ anions with two longer and four shorter Mn−F bonds making elongated octahedra are usually observed. Herein, we report the synthesis of the compound K₃[MnF₆] through a high-temperature approach and its crystallization by a high-pressure/high-temperature route. The main structural motifs are two quasi-isolated, octahedron-like [MnF₆]³⁻ anions of quite different nature compared to that met in ideal octahedral Mn^III Jahn-Teller systems. Owing to the internal electric field of C_i symmetry dominated by the next-neighbour K⁺ ions acting on the Mn^III sites, both sites, the pseudo-rhombic (site 1) and the pseudo-tetragonally elongated (site 2) [MnF₆]³⁻ anions are present in K₃[MnF₆]. The compound was characterized by single-crystal and powder X-ray diffraction, and magnetometry as well as by FTIR, Raman, and ligand field spectroscopy. A theoretical interpretation of the electronic structure and molecular geometry of the two Mn sites in the lattice is given by using a vibronic coupling model with parameters adjusted from multireference ab-initio cluster calculations.     

Comparative Modelling of Organic Anion Transporting Polypeptides: Structural Insights and Comparison of Binding Modes

To better understand the functionality of organic anion transporting polypeptides (OATPs) and to design new ligands, reliable structural data of each OATP is needed. In this work, we used a combination of homology model with molecular dynamics simulations to generate a comprehensive structural dataset, that encompasses a diverse set of OATPs but also their relevant conformations. Our OATP models share a conserved transmembrane helix folding harbouring a druggable binding pocket in the shape of an inner pore. Our simulations suggest that the conserved salt bridges at the extracellular region between residues on TM1 and TM7 might influence the entrance of substrates. Interactions between residues on TM1 and TM4 within OATP1 family shown their importance in transport of substrates. Additionally, in transmembrane (TM) 1/2, a known conserved element, interact with two identified motifs in the TM7 and TM11. Our simulations suggest that TM1/2-TM7 interaction influence the inner pocket accessibility, while TM1/2-TM11 salt bridges control the substrate binding stability.     

Thermodynamic Properties of Crystalline Cellulose Allomorphs Studied with Dispersion-Corrected Density Functional Methods

The phonon properties and thermodynamics of four crystalline cellulose allomorphs, Iα, Iβ, II, and III1, have been investigated using dispersion-corrected density functional theory (DFT). In line with experimental findings, the free energy differences between the studied cellulose allomorphs are small, less than 1 kJ/mol per atom. The calculated specific heat at constant volume (Cv) has been compared with the available experimental data in the temperature range 10–300 K. Quasiharmonic approximation has been employed to study thermodynamics and specific heat at constant pressure (Cp). For the studied temperature range of 10–400 K, the specific heat of all cellulose allomorphs shows very similar behavior. The calculated and experimental specific heat agree well at low temperatures below 100 K, but the deviation between theory and experiment increases with temperature. This may be due to increasing phonon anharmonicity as the temperature increases.     

Feasibility of a liquid-phase microextraction sample clean-up and liquid chromatographic/mass spectrometric screening method for selected anabolic steroid glucuronides in biological samples

Anabolic androgenic steroids (AAS) are metabolized extensively in the human body, resulting mainly in the formation of glucuronide conjugates. Current detection methods for AAS are based on gas chromatographic/mass spectrometric (GC/MS) analysis of the hydrolyzed steroid aglycones. These analyses require laborious sample preparation steps and are therefore time consuming. Our interest was to develop a rapid and straightforward method for intact steroid glucuronides in biological samples, using liquid-phase microextraction (LPME) sample clean-up and concentration method combined with liquid chromatographic/tandem mass spectrometric (LC/MS/MS) analysis. The applicability of LPME was optimized for 13 steroid glucuronides, and compared with conventional liquid-liquid extraction (LLE) and solid-phase extraction (SPE) procedures. An LC/MS/MS method was developed for the quantitative detection of AAS glucuronides, using a deuterium-labeled steroid glucuronide as the internal standard. LPME, owing to its high specificity, was shown to be better suited than conventional LLE and SPE for the clean-up of urinary AAS glucuronides. The LPME/LC/MS/MS method was fast and reliable, offering acceptable reproducibility and linearity with detection limits in the range 2-20 ng ml(-1) for most of the selected AAS glucuronides. The method was successfully applied to in vitro metabolic studies, and also tested with an authentic forensic urine sample. For a urine matrix the method still has some unsolved problems with specificity, which should be overcome before the method can be reliably used for doping analysis, but still offering additional and complementary data for current GC/MS analyses.     

A frequency doubler for 200 GHz with a planar Schottky varactor

A frequency doubler for 200 GHz utilising a planar surface channel Schottky varactor was designed, constructed and tested. The doubler employes novel split-waveguide mount design with two sliding backshorts at both input and output waveguides. The theoretical maximum efficiency of the doubler is 44.0 % with input power level of 32 mW and the maximum output power is 16.5 mW with input power level of 50 mW. The measured maximum efficiency of the doubler was 7.1 % and the maximum output power was 2.6 mW     

Ab initio study on the adsorption of hydrated Na+ and Ag+ cations on a Ag(111) surface

The interactions of Na(+) and Ag(+) cations with an Ag(111) surface in the presence and absence of water molecules were investigated with cluster models and ab initio methods. The Ag surface was described with two-layered Ag(10) and Ag(18) cluster models, and MP2/RECP/6-31+G(d) was used as the computational method. The effect of the basis set superposition error (BSSE) was taken into account with counterpoise (CP) correction. The interactions between Na(+) and Ag(111) surface were found to be primarily electrostatic, and the interaction energies and equilibrium distances at the different adsorption sites were closely similar. The largest CP-corrected MP2 adsorption energy for Na(+) was -190.2 kJ/mol. Owing to the electrostatic nature of the Na(+)-Ag(111) interaction, Na(+) prefers to be completely surrounded by water molecules rather than directly adsorbed to the surface. Ag(+)-Ag(111) interactions were much stronger than Na(+)-Ag(111) interactions because they were dominated by orbital contributions. The largest CP-corrected MP2 adsorption energy for Ag(+) was -358.9 kJ/mol. Ag(+) prefers to adsorb on sites where it can bind to several surface atoms, and in the presence of water molecules, it remains adsorbed to the surface while the water molecules form hydrogen bonds with one another. The CP correction had an effect on the interaction energies but did not change the relative trends.     

Approach to Equilibrium for the Phonon Boltzmann Equation

We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends diffusively to equilibrium. The solution is the sum of a local equilibrium state, associated to conserved quantities that diffuse to zero, and fast variables that are slaved to the slow ones. This slaving implies the Fourier law, which relates the induced currents to the gradients of the conserved quantities. Partially supported by the Belgian IAP program P6/02. Partially supported by the Academy of Finland.     

Glass‐embedded silver nanoparticle patterns by masked ion‐exchange process for surface‐enhanced Raman scattering

Glass‐embedded silver nanoparticle patterns were fabricated by masked silver–sodium ion‐exchange process followed by etching to reveal the particles for surface‐enhanced Raman scattering (SERS). The intensity of the enhanced Raman signal is comparable to that of the fluorescence, and the detection limit of 1 nM for Rhodamine 6G has been achieved. Raman images at different etching depths and corresponding morphological images are compared to find optimal SERS signal. Our results demonstrate that silver nanoparticle patterns embedded in glass can be used as SERS‐active substrates. Nanoparticles can be formed in a glass of high optical quality and have potential to be integrated with optical waveguides for a sensor chip. Copyright © 2010 John Wiley & Sons, Ltd.