Finite Element Methods for a Model for Full Waveform Acoustic Logging

A model is defined to simulate the propagation of waves in aradially symmetric, isotropic, composite system consisting ofa fluid-filled well bore ^f through a fluid-saturated poroussolid ^p. Biot's equations of motion are chosen to describe thepropagation of waves in ^p, while the standard equation of motionfor compressible inviscid fluids is used for ^f, with appropriateboundary conditions at the contact surface between ^f and ^p.Also, absorbing boundary conditions for the artificial boundariesof ^p are derived for the model, their effect being to make themtransparent for waves arriving normally First, results on the existence and uniqueness of the solutionof the differential problem are given and then a discrete-time,explicit finite element procedure is defined and analysed, withfinite element spaces suited for radially symmetric problemsbeing used for the spatial discretisation.     

Structural characterization of a degradation product of tin ethyl etiopurpurin (SnET2): Comparison of the long‐range heteronuclear correlations detected using conventional GHMBC and IMPEACH‐MBC in conjunction with submicro NMR probe technology

During the terminal heat sterilization of the lipid emulsion final dose formulation of the photodynamic therapeutic (PDT) agent tin ethyl etiopurpurin (SnET2), a new degradant was observed at very low levels. The degradant, which was prone to photo‐instability, was isolated by preparative chromatography and subsequently characterized by mass spectrometry and NMR methods. Reproducible parent ion clusters were only observable via negative ion APCI methods. Because of the limited isolate sample, NMR characterization was done using 1.7 mm SMIDG (SubMicro Inverse‐Detection Gradient) NMR probe technology in conjunction with the accordion‐optimized IMPEACH‐MBC long‐range heteronuclear shift correlation experiment. The “static” 8 Hz optimization of the GHMBC experiment failed to allow the observation of a number of long‐range correlations that were of critical importance to the determination of the structure of the impurity. In contrast, all of the correlations required to assemble the structure were obtained from an IMPEACH‐MBC experiment optimized for long‐range heteronuclear couplings in the range from 2–10 Hz.     

Oxygen as a paramagnetic probe of membrane protein structure by cysteine mutagenesis and (19)F NMR spectroscopy

Oxygen solubility increases toward the hydrophobic interior of membranes. Using NMR, this O(2) solubility gradient gives rise to an exquisite range of position-dependent paramagnetic effects at partial pressures of 100 atm (PO(2)), which may be used to probe membrane protein structure and positioning. In this study, fluorinated probes were introduced at selected positions of the transmembrane 1 domain of the intact homotrimer of the integral membrane protein, diacylglycerol kinase. Using (19)F NMR, O(2)-induced chemical shift perturbations revealed secondary structure, membrane immersion depth, and regions of the helix in contact with the protein or with the micelle.     

Geometric phase of three-level systems in interferometry

We present the first scheme for producing and measuring an Abelian geometric phase shift in a three-level system where states are invariant under a non-Abelian group. In contrast to existing experiments and proposals for experiments, based on U(1)-invariant states, our scheme geodesically evolves U(2)-invariant states in a four-dimensional SU(3)/U(2) space and is physically realized via a three-channel optical interferometer.     

Modelling,simulation, animation,and real-time control (MoSART) for a class of electromechanical systems: a system-theoretic approach

This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of ‘cart-pendulum’ electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts through computer-aided analysis, design, graphical visualization, and 3D animation. Referred to as Cart-Pendulum Control3D-Lab1Control3D-Lab-short for control 3D animation laboratory. The author to whom correspondence should be addressed., the environment is based on Microsoft Windows/Visual C++/Direct-3D and MATLAB/Simulink2MATLAB and Simulant are trademarks of The Masterworks, Inc.. Pull-down menus provide access to systems/models/control laws, exogenous signals, parameters, animation models and visual indicators, a suite of (easy-to-modify) Simulant diagrams containing models and control laws, MATLAB m-files for detailed analysis and design, and detailed documentation for each of the above. Three blocks enable animation, joystick inputs, and real-time animation within Simulant. Examples are presented to illustrate the utility of the environment as a valuable tool for analysing/visualizing the above class of electromechanical systems and for enhancing mathematics instruction.     

Sensitive Spectroscopic Detection of Large and Denatured Protein Aggregates in Solution by Use of the Fluorescent Dye Nile Red

The fluorescent dye Nile red was used as a probe for the sensitive detection of large, denatured aggregates of the model protein β-galactosidase (E. coli) in solution. Aggregates were formed by irreversible heat denaturation of β-galactosidase below and above the protein’s unfolding temperature of 57.4°C, and the presence of aggregates in heated solutions was confirmed by static light scattering. Interaction of Nile red with β-galactosidase aggregates led to a shift of the emission maximum (λ _max) from 660 to 611 nm, and to an increase of fluorescence intensity. Time-resolved fluorescence and fluorescence correlation spectroscopy (FCS) measurements showed that Nile red detected large aggregates with hydrodynamic radii around 130 nm. By steady-state fluorescence measurements, it was possible to detect 1 nM of denatured and aggregated β-galactosidase in solution. The comparison with size exclusion chromatography (SEC) showed that native β-galactosidase and small aggregates thereof had no substantial effect on the fluorescence of Nile red. Large aggregates were not detected by SEC, because they were excluded from the column. The results with β-galactosidase demonstrate the potential of Nile red for developing complementary analytical methods that overcome the size limitations of SEC, and can detect the formation of large protein aggregates at early stages.     

Molecular amplification of two different receptors using diastereomeric templates

Two different macrocyclic members of a pseudo-peptide hydrazone dynamic combinatorial library were amplified using the diastereomeric templates quinine and quinidine.     

The {ell}1-norm of the Fourier transform on compact vector spaces

Suppose that G is a compact Abelian group. If A G, then howsmall can ||_A||_A(G) be? In general, there is no non-triviallower bound. In a recent preprint, Green and Konyagin show thatif has sparse small subgroup structure and A has density with (1 – ) >> 1, then||_A||_A(G) does admit a non-trivial lower bound. In this paperwe address the complementary case of groups with duals havingrich small subgroup structure, specifically the case when Gis a compact vector space over ₂. The results themselves arerather technical to state, but the following consequence capturestheir essence: if is a set of density as close to 1/3 as possible, then we show that . We include a number of examples andconjectures which suggest that what we have shown is very farfrom a complete picture.     

The Saffman-Taylor problem for an extremely shear-thinning fluid

We consider a steady flow driven by pushing a finger of gasinto a highly shear-thinning power-law fluid, with exponentn, in a Hele-Shaw channel. We formulate the problem in termsof the streamfunction , which satisfies the p-Laplacian equation (with ), and investigate travelling wave solutions in the large-n (extreme shear-thinning) limit.We take a Legendre transform of the free-boundary problem for, which reduces it to a linear problem on a fixed domain. The solution to this problem is foundby using matched asymptotic expansions and the resulting shapeof the finger deduced (being, to leading order, a semi-infinitestrip). The nonlinear problem for the streamfunction is alsotreated using matched asymptotic expansion in the physical plane.The finger-width selection problem is briefly discussed in termsof our results.