Local modal analysis of unsteady discrete systems with nodal equations of unequal form

Finite element discretisations of higher order, applied to unsteady equations, generate nodal equations of unequal form. The stability analysis of a time-discretisation scheme for this system, by the local modal approach, therefore cannot be used. In this paper it is shown how, at the expense of a limited increase in numerical work, local modal analysis can be applied to these systems.     

Biocatalytic enantioselective synthesis of N-substituted aspartic acids by aspartate ammonia lyase

The gene encoding aspartate ammonia lyase (aspB) from Bacillus sp. YM55-1 has been cloned and overexpressed, and the recombinant enzyme containing a C-terminal His(6) tag has been purified to homogeneity and subjected to kinetic characterization. Kinetic studies have shown that the His(6) tag does not affect AspB activity. The enzyme processes L-aspartic acid, but not D-aspartic acid, with a K(m) of approximately 15 mM and a k(cat) of approximately 40 s(-1). By using this recombinant enzyme in the reverse reaction, a set of four N-substituted aspartic acids were prepared by the Michael addition of hydroxylamine, hydrazine, methoxylamine, and methylamine to fumarate. Both hydroxylamine and hydrazine were found to be excellent substrates for AspB. The k(cat) values are comparable to those observed for the AspB-catalyzed addition of ammonia to fumarate ( approximately 90 s(-1)), whereas the K(m) values are only slightly higher. The products of the enzyme-catalyzed addition of hydrazine, methoxylamine, and methylamine to fumarate were isolated and characterized by NMR spectroscopy and HPLC analysis, which revealed that AspB catalyzes all the additions with excellent enantioselectivity (>97 % ee). Its broad nucleophile specificity and high catalytic activity make AspB an attractive enzyme for the enantioselective synthesis of N-substituted aspartic acids, which are interesting building blocks for peptide and pharmaceutical synthesis as well as for peptidomimetics.     

Pressure broadening of the J=5←4 transition of carbon monoxide from 17 to 200 K: A new collisional cooling experiment

A new spectroscopic experiment has been constructed at the Jet Propulsion Laboratory. This experiment employs the collisional cooling technique to study gases at temperatures below their condensation points. Specifically, the experiment has been designed to mimic the temperatures of the interstellar medium for the study of water under these conditions. The ultimate purpose is to measure state-to-state excitation rates under equilibrium conditions to provide insights into the interpretation of interstellar water spectra obtained from space-borne platforms such as the Herschel Space Observatory. This paper presents an overview of the new experiment including a discussion of its design and a detailed explanation of the system. In addition, we report a pressure broadening study of the J=5←4 transition of CO at 576 GHz used as a system validation. The new results are compared with measurements from the literature as a validation of the new experiment. In addition, the non-classical behavior of the pressure broadening of CO at low temperature observed in the measurements will be discussed.     

Electron transfer within self-assembling cyclic tetramers using chlorophyll-based donor-acceptor building blocks

The synthesis and photoinduced charge transfer properties of a series of Chl-based donor-acceptor triad building blocks that self-assemble into cyclic tetramers are reported. Chlorophyll a was converted into zinc methyl 3-ethylpyrochlorophyllide a (Chl) and then further modified at its 20-position to covalently attach a pyromellitimide (PI) acceptor bearing a pyridine ligand and one or two naphthalene-1,8:4,5-bis(dicarboximide) (NDI) secondary electron acceptors to give Chl-PI-NDI and Chl-PI-NDI(2). The pyridine ligand within each ambident triad enables intermolecular Chl metal-ligand coordination in dry toluene, which results in the formation of cyclic tetramers in solution, as determined using small- and wide-angle X-ray scattering at a synchrotron source. Femtosecond and nanosecond transient absorption spectroscopy of the monomers in toluene-1% pyridine and the cyclic tetramers in toluene shows that the selective photoexcitation of Chl results in intramolecular electron transfer from (1*)Chl to PI to form Chl(+?)-PI(-?)-NDI and Chl(+?)-PI(-?)-NDI(2). This initial charge separation is followed by a rapid charge shift from PI(-?) to NDI and subsequent charge recombination of Chl(+?)-PI-NDI(-?) and Chl(+?)-PI-(NDI)NDI(-?) on a 5-30 ns time scale. Charge recombination in the Chl-PI-NDI(2) cyclic tetramer (τ(CR) = 30 ± 1 ns in toluene) is slower by a factor of 3 relative to the monomeric building blocks (τ(CR) = 10 ± 1 ns in toluene-1% pyridine). This indicates that the self-assembly of these building blocks into the cyclic tetramers alters their structures in a way that lengthens their charge separation lifetimes, which is an advantageous strategy for artificial photosynthetic systems.     

Improving riverbed sediment classification using backscatter and depth residual features of multi-beam echo-sounder systems

Riverbed and seafloor sediment classification using acoustic remote sensing techniques is of high interest due to their high coverage capabilities at limited cost. This contribution presents the results of riverbed sediment classification using multi-beam echo-sounder data based on an empirical method. Two data sets are considered, both taken at the Waal River, namely Sint Andries and Nijmegen. This work is a follow-up to the work carried out by Amiri-Simkooei et al. [J. Acoust. Soc. Am. 126(4), 1724-1738 (2009)]. The empirical method bases the classification on features of the backscatter strength and depth residuals. A principal component analysis is used to identify the most appropriate and informative features. Clustering is then applied to the principal components resulting from this set of features to assign a sediment class to each measurement. The results show that the backscatter strength features discriminate between different classes based on the sediment properties, whereas the depth residual features discriminate classes based on riverbed forms such as the "fixed layer" (stone having riprap structure) and riverbed ripples. Combination of these two sets of features is highly recommended because they provide complementary information on both the composition and the structure of the riverbed.     

Spectrophotometric system for measuring the characteristics of light scattered by biological tissues and humoral media

The structure, assembly, and physical capabilities of a spectrophotometric system intended for studying biotissues and humoral fluids are described. It can be used to investigate all the characteristics of scattered light at wavelengths of 400–1000 nm that are of interest for various problems in biomedical optics. Examples of these problems include noninvasive diagnostics of the structural and biophysical parameters of human skin tissue, analysis of the hemoglobin composition, sizes and degree of aggregation of erythrocytes, and evaluating the depth of penetration of light into biotissue. Pilot experiments on measuring the characteristics of scattered light are conducted in order to select an optimum operating mode for the system, estimate its errors, and develop ways of minimizing these errors.     

A conservative discrete compatibility-constraint low-Mach pressure-correction algorithm for time-accurate simulations of variable density flows

In this paper, we develop the discrete compatibility-constraint pressure-correction algorithm for transient simulations of variable density flows at low-Mach numbers. The constraint for the velocity field is constructed from a combination of the discrete equations of continuity and scalar (e.g. energy) transport, imposing that the newly predicted state must be compatible, in agreement with the equation of state. This way, mass and scalar conservation are guaranteed and the equation of state is exactly fulfilled at every time step. For comparison reasons, two other types of well-known pressure-correction algorithms are also used. The first class, denoted as continuity-constraint pressure-correction, is based on a constraint for the velocity field that is derived solely from the continuity equation. The second class, denoted as analytical compatibility-constraint pressure-correction, constructs the constraint from an analytical combination of the material derivative of the equation of state and the continuity and scalar equations. The algorithms are tested for three example fluid configurations: a single-fluid ideal gas, a two-fluid inert mixture and a two-fluid reacting mixture. The latter is special in the sense that the equation of state is non-linear and not everywhere differentiable. The continuity-constraint pressure-correction algorithm yields unstable solutions if density ratios are high. The analytical compatibility-constraint pressure-correction algorithm yields stable results, but the predicted states do not correspond to the equation of state. The discrete compatibility-constraint pressure-correction algorithm performs well on all test cases: the simulation results are stable and exactly match the equation of state.     

Evidence of holes in the Arnold tongues of flow past two oscillating cylinders

The wake of two oscillating cylinders in a tandem arrangement is a nonlinear system that displays Arnold tongues. We show by numerical simulations that their geometry depends on the phase difference theta between the two oscillating cylinders. At theta = 0 there may be holes inside these intraresonance regions unlike the solid Arnold tongues encountered in single-cylinder oscillations. This implies that, surprisingly, self-excitation of the system may be suppressed inside these holes, at conditions close to its natural frequency.     

Quasi–Monte Carlo rules for numerical integration over the unit sphere {\mathbb{S}^2}

We study numerical integration on the unit sphere ${\mathbb{S}^2 \subseteq\mathbb{R}^3}$ using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly. The quadrature points are constructed by lifting a (0, m, 2)-net given in the unit square [0, 1]² to the sphere ${\mathbb{S}^2}$ by means of an area preserving map. A similar approach has previously been suggested by Cui and Freeden [SIAM J Sci Comput 18(2):595–609, 1997]. We prove three results. The first one is that the construction is (almost) optimal with respect to discrepancies based on spherical rectangles. Further we prove that the point set is asymptotically uniformly distributed on ${\mathbb{S}^2}$ . And finally, we prove an upper bound on the spherical cap L ₂-discrepancy of order N ^?1/2(log N)^1/2 (where N denotes the number of points). This improves upon the bound on the spherical cap L ₂-discrepancy of the construction by Lubotzky, Phillips and Sarnak [Commun Pure Appl Math 39(S, suppl):S149–S186, 1986] by a factor of ${\sqrt{\log N}}$ . Numerical results suggest that the (0, m, 2)-nets lifted to the sphere ${\mathbb{S}^2}$ have spherical cap L ₂-discrepancy converging with the optimal order of N ^?3/4.