Analysis of multiple scattering iterations for high-frequency scattering problems. II: The three-dimensional scalar case

In this paper, we continue our analysis of the treatment of multiple scattering effects within a recently proposed methodology, based on integral-equations, for the numerical solution of scattering problems at high frequencies. In more detail, here we extend the two-dimensional results in part I of this work to fully three-dimensional geometries. As in the former case, our concern here is the determination of the rate of convergence of the multiple-scattering iterations for a collection of three-dimensional convex obstacles that are inherent in the aforementioned high-frequency schemes. To this end, we follow a similar strategy to that we devised in part I: first, we recast the (iterated, Neumann) multiple-scattering series in the form of a sum of periodic orbits (of increasing period) corresponding to multiple reflections that periodically bounce off a series of scattering sub-structures; then, we proceed to derive a high-frequency recurrence that relates the normal derivatives of the fields induced on these structures as the waves reflect periodically; and, finally, we analyze this recurrence to provide an explicit rate of convergence associated with each orbit. While the procedure is analogous to its two-dimensional counterpart, the actual analysis is significantly more involved and, perhaps more interestingly, it uncovers new phenomena that cannot be distinguished in two-dimensional configurations (e.g. the further dependence of the convergence rate on the relative orientation of interacting structures). As in the two-dimensional case, and beyond their intrinsic interest, we also explain here how the results of our analysis can be used to accelerate the convergence of the multiple-scattering series and, thus, to provide significant savings in computational times.     

The dual geometry of Boolean semirings

It is well known that the variety of Boolean semirings, which is generated by the three element semiring ${\mathbb{S}}$ , is dual to the category of partially Stone spaces. We place this duality in the context of natural dualities. We begin by introducing a topological structure S? and obtain an optimal natural duality between the quasi-variety ISP( ${\mathbb{S}}$ ) and the category IS _c P+(S?). Then we construct an optimal and very small structure S? _os that yields a strong duality. The geometry of some of the partially Stone spaces that take part in these dualities is presented, and we call them “hairy cubes”, as they are n-dimensional cubes with unique incomparable covers for each element of the cube. We also obtain a polynomial representation for the elements of the hairy cube.     

Developing a market-based approach to managing the US strategic petroleum reserve

The Strategic Petroleum Reserve has not been used effectively to manage the consequences of oil shocks in the United States. The main reason is that political decision makers tend to hoard the reserves during crises and bureaucratic processes delay the sale of the reserves. Also, the enabling legislation focused on ameliorating shortages whereas disruptions result price spikes rather than shortages. We develop a Markov game of the buildup and drawdown of the reserve in which a public player aims to maximize consumer welfare at the same time private holders of inventory maximize their profit. The methodological contribution in this paper is the development of financial options to implement the public player’s optimal policy. We use the solution of this game to calculate the number and value of options necessary for the private marketplace to trigger the optimal buildup and drawdown of the reserve.     

Properties of alkali-halide salt solutions about polarizable nanoparticle solutes for different ion models

We investigate the distributions of various salts about large hydrophobic polarizable solutes in aqueous electrolyte solutions. The solutes are modeled as nanometer-sized cylindrical objects, a scale relevant to biomolecules and nanomaterials, and particularly high aspect ratio nanoparticles. Interactions, including image charge forces arising from the finite polarizability of the solute, between explicit solvent/ions and the solute are computed explicitly using a molecular dynamics simulation methodology we have recently introduced. Comparisons are made between several salt species and different models of the force fields for each ionic component of the salt. We find evidence that both small cations, Li(+), and large anions, I(-), adsorb at hydrophobic interfaces. Our results indicate that the ion structure about the solute is strongly dependent on the force field investigated, suggesting that ion selectivity is quite sensitive to the respective parameters defining the ion's size and binding energy as well as to the polarizability of the solute.     

Rapid direct analysis in real time (DART) mass spectrometric detection of juvenile hormone III and its terpene precursors

Direct analysis in real time (DART) is a plasma-based ambient ionization technique that enables rapid ionization of small molecules with high sample throughput. In this work, DART was coupled to an orthogonal (oa) time-of-flight (TOF) mass spectrometer and the system was optimized for analyzing a vital hormonal regulator in insects, juvenile hormone (JH) III and its terpene precursors, namely, farnesol, farnesoic acid, and methyl farnesoate. Optimization experiments were planned using design of experiments (DOE) full factorial models to identify the most significant DART variables contributing to JH III analysis sensitivity by DART-TOF mass spectrometry (MS). The optimized DART-TOF MS method had femtomole to sub-picomole detection limits for terpene standards, along with mass accuracies below 5 ppm. Finally, the possibility of distinguishing between two farnesol isomers by in-source-collision-induced dissociation (CID) in the first differentially pumped region of the oaTOF mass spectrometer was investigated. DART-MS enabled high-throughput, sensitive analysis with acquisition times ranging from 30 s to a minute. To the best of our knowledge, this is the first report on the application of DART-MS to the detection and identification of volatile or semi-volatile insect terpenoids, and on the use of DOE approaches to optimize DART-MS analytical procedures.     

1‐(2‐Aminophenyl)‐3‐(4‐pyridyl)prop‐2‐en‐1‐one: a three‐dimensional framework structure built from N—H...N,C—H...O and C—H...π(arene) hydrogen bonds

The intramolecular dimensions of the title compound, C₁₄H₁₂N₂O, provide evidence for a polarized electronic structure. The molecule, which is almost completely planar, contains an intramolecular N—H...O hydrogen bond, and the molecules are linked by a combination of N—H...N, C—H...O and C—H...π(arene) hydrogen bonds to form a three‐dimensional framework structure.     

Reversible intercalation of ammonia molecules into a layered double hydroxide structure without exchanging nitrate counter-ions

A zinc/aluminum LDH was precipitated with recycled ammonia from a chemical vapor deposition reaction. The LDH presented a crystalline phase with basal distance of 8.9 Å, typical for nitrate-containing LDHs, and another phase with a basal distance of 13.9 Å. Thermal treatment at 150 °C eliminated the phase with the bigger basal distance leaving only the anhydrous nitrate-intercalated LDH structure with 8.9 Å. Intense N-H stretching modes in the FTIR spectra suggested that the expansion was due to intercalation of ammonia in the form of [NH₄(NH₃)_n]⁺ species. When additional samples were precipitated with pure ammonia, the conventional LDH nitrate structure was obtained (8.9 Å basal distance) at pH=7, as well as a pure crystalline phase with 13.9 Å basal distance at pH=10 due to ammonia intercalation that can be removed by heating at 150 °C or by stirring in acetone, confirming a unusual sensu stricto intercalation process into a LDH without exchanging nitrate ions.     

On the complexation of proteins and polyelectrolytes

Both natural and synthetic polyelectrolytes form strong complexes with a variety of proteins. One peculiar phenomenon is that association can take place even when the protein and the polyelectrolyte carry the same charge. This has been interpreted as if the ion-dipole interaction can overcome the repulsive ion-ion interaction. On the basis of Monte Carlo simulations and perturbation theory, we propose a different explanation for the association, namely, charge regulation. We have investigated three different protein-polymer complexes and found that the induced ionization of amino acid residues due to the polyelectrolyte leads to a surprisingly strong attractive interaction between the protein and the polymer. The extra attraction from this charge-induced charge interaction can be several kT and is for the three cases studied here, lysozyme, alpha-lactalbumin, and beta-lactoglobulin, of the same magnitude or stronger than the ion-dipole interaction. The magnitude of the induced charge is governed by a response function, the protein charge capacitance Z2-Z2. This fluctuation term can easily be calculated in a simulation or measured in a titration experiment.     

Peptide folding dynamics: a time-resolved study from the nanosecond to the microsecond time regime

Time-resolved spectroscopies, spanning from the nanosecond to the microsecond time regime, coupled with molecular mechanics calculations, allowed us to assess the most populated conformations in solution of a series of analogues of trichogin GA IV, a natural undecapeptide showing significant antimicrobial activity. This peptide is characterized by a high content of the conformationally constrained alpha-aminoisobutyric acid and by a glycine-glycine motif in the central part of the sequence. Nanosecond time-resolved fluorescence experiments were performed to determine the conformational properties of the peptide analogues in solution, while transient absorption measurements allowed us to study the peptide dynamics on the microsecond time scale. Because the peptides examined were functionalized by a fluorescent probe at the N-terminus and a nitroxide quencher placed along the backbone at three different positions, the distance-dependent fluorophore-quencher interaction was exploited to obtain a deeper insight into their three-dimensional structural and dynamical properties. Further information on the conformational and dynamical features was obtained by photophysical experiments as a function of the viscosity and polarity of the medium. Taken together, the results revealed a transition from an elongated, helical conformation to a family of compact, folded structures mimicking a helix-turn-helix motif, which may represent a model of the early steps of the protein hydrophobic collapse.