Spectral analysis of finite convolution operators with matrix kernels

Let N be a finite dimensional complex Hilbert space. A finite convolution operator on the vector function space L _N ² (0,1) is an operator T of the form (Tf) (x) = ₀ ^x k (x–t)f(t)dt, where k(t) is a norm integrableB(N)-valued function on [0,1]. A symbol for T is any function A(z) of the form A(z) = ₀ ¹ k(t)e^itzdt + e^izG(z), where G(z) is aB(N)-valued function which is bounded and analytic in a half plane y > . It is shown that under suitable restrictions two finite convolution operators are similar if their symbols are asymptotically close as z in a half plane y > .This paper was written at the University of Virginia and is based on the author's doctoral dissertation [6], which was supervised by James Rovnyak.     

Fused biconical tapered fiber-optic devices: Application to data buses

The technology of fiber-optic couplers based on fused biconical tapered structures is reviewed, and the linear and star data-bus configurations that can be constructed using these couplers are discussed. A useful network topology for interconnecting star couplers using the hybrid transmission-reflection star coupler is also proposed. This network configuration has the advantage of requiring significantly less optical fiber than networks employing a single transmission or reflection star.     

On the stability and uniqueness of the flow of a fluid through a porous medium

In this short note, we study the stability of flows of a fluid through porous media that satisfies a generalization of Brinkman’s equation to include inertial effects. Such flows could have relevance to enhanced oil recovery and also to the flow of dense liquids through porous media. In any event, one cannot ignore the fact that flows through porous media are inherently unsteady, and thus, at least a part of the inertial term needs to be retained in many situations. We study the stability of the rest state and find it to be asymptotically stable. Next, we study the stability of a base flow and find that the flow is asymptotically stable, provided the base flow is sufficiently slow. Finally, we establish results concerning the uniqueness of the flow under appropriate conditions, and present some corresponding numerical results.     

The adduction behavior of water reactant ions with mobility shift reagents in ion mobility spectrometry is determined by the number of locations for adduction,interaction energies,proton affinities,and steric hindrance of these species

The introduction of mobility shift reagents (SRs) into the buffer gas of mobility spectrometers yields SR-ion clusters that decrease ion mobilities and allow the separation of overlapping ions. With a large amount of papers on the introduction of SRs in ion mobility spectrometry (IMS) few investigations explain the behavior of the adducts of reactant ions with SRs and it is not clear what type of peaks to expect which obscures the interpretation of spectra. Electrospray-ionization IMS was coupled to quadrupole mass spectrometry, and 2-butanol (B), ethyl lactate (L), and methanol were introduced as SRs into the buffer gas. The hybrid functional X3LYP/6–311++(d,p) with Gaussian 09 was used for theoretical calculations of SR-ion interaction energies. Adducts of the reactant ions with B and L presented different behaviors; even at low flow rates, L consumed all sodium, reactant ions, and water by adduction, because a) in the experimental conditions, SRs were more concentrated in the buffer gas than reactant ions, b) L’s high proton affinity and c) L’s three electron-donor oxygens, increases adduction. Therefore, chemical equilibria in the buffer gas were only between L and L_nH⁺, L_mH₃O⁺, or L_xNa⁺ adducts and, consequently, these sets of adducts had different mobilities. The lower mobility of L_mH₃O⁺ compared to L_nH⁺ was explained on the base of the lower steric hindrance in LH₃O⁺ for attachment of L molecules. The behavior of reactant ions with B was different: B_nH₃O⁺ and B_nH⁺ overlapped because the relatively low proton affinity and the single and weaker interaction site in B allowed protons and water to be exchanged between species. Finally, L₄H⁺, L₄H₃O⁺, B₄H⁺ and B₅H⁺ ions, not reported before, were seen for large SR concentrations. This study explains two different behaviors of the adducts of SRs with reactant ions using interaction energies, proton affinities, steric hindrance, and the number of locations for adduction.     

"Three-dimensional hybridization" with polyvalent DNA-gold nanoparticle conjugates

We have determined the minimum number of base pairings necessary to stabilize DNA-Au NP aggregates as a function of salt concentration for particles between 15 and 150 nm in diameter. Significantly, we find that sequences containing a single base pair interaction are capable of effecting hybridization between 150 nm DNA-Au NPs. While traditional DNA hybridization involves two strands interacting in one dimension (1D, Z), we propose that hybridization in the context of an aggregate of polyvalent DNA-Au NP conjugates occurs in three dimensions (many oligonucleotides oriented perpendicular to the X, Y plane engage in base pairing), making nanoparticle assembly possible with three or fewer base pairings per DNA strand. These studies enabled us to compare the stability of duplex DNA free in solution and bound to the nanoparticle surface. We estimate that 4-8, 6-19, or 8-33 additional DNA bases must be added to free duplex DNA to achieve melting temperatures equivalent to hybridized systems formed from 15, 60, or 150 nm DNA-Au NPs, respectively. In addition, we estimate that the equilibrium binding constant (K(eq)) for 15 nm DNA-Au NPs (3 base pairs) is approximately 3 orders of magnitude higher than the K(eq) for the corresponding nanoparticle free system.     

Cooperative and Orthogonal Switching in the Solid State Enabled by Metal-Organic Framework Confinement Leading to a Thermo-Photochromic Platform

Cooperative behavior and orthogonal responses of two classes of coordinatively integrated photochromic molecules towards distinct external stimuli were demonstrated on the first example of a photo-thermo-responsive hierarchical platform. Synergetic and orthogonal responses to temperature and excitation wavelength are achieved by confining the stimuli-responsive moieties within a metal–organic framework (MOF), leading to the preparation of a novel photo-thermo-responsive spiropyran-diarylethene based material. Synergistic behavior of two photoswitches enables the study of stimuli-responsive resonance energy transfer as well as control of the photoinduced charge transfer processes, milestones required to advance optoelectronics development. Spectroscopic studies in combination with theoretical modeling revealed a nonlinear effect on the material electronic structure arising from the coordinative integration of photoresponsive molecules with distinct photoisomerization mechanisms. Thus, the reported work covers multivariable facets of not only fundamental aspects of photoswitch cooperativity, but also provides a pathway to modulate photophysics and electronics of multidimensional functional materials exhibiting thermo-photochromism.     

Calculating stacking interactions in nucleic acid base-pair steps using spin-component scaling and local second order Møller-Plesset perturbation theory

Stacking interaction energies for ten B-DNA base-pair steps are computed with density fitted local second-order M?ller-Plesset perturbation theory (DF-LMP2), and with the spin-component scaled (SCS) and spin-component scaled for nucleobases (SCSN) variants of DF-LMP2. Comparison with existing CBS(T) reference data indicates larger than expected energy differences for both SCS variants. After an analysis of the errors involved, an alternative method of producing reference data is proposed where DF-LMP2/aug-cc-pVTZ and DF-LMP2/aug-cc-pVQZ energies for the whole complex are extrapolated to produce interaction energies that do not require many-body correction and show reduced error in estimation of the basis set limit. A literature correction term from coupled cluster theory with perturbative triples is then added to the DF-LMP2 estimated basis set limit. These new reference data are consistently around 1 kcal mol(-1) less than previous literature data. DF-SCSN-LMP2/aug-cc-pVTZ is found to reproduce the new reference interaction energies with a root mean square error (RMSE) of 0.71 kcal mol(-1), while SCS consistently underestimates the binding energy.