Boundary value problems in spaces of distributions on smooth and polygonal domains

We study boundary value problems of the form -Δu=f$-\mathrm{\Delta }u=f$ on Ω$\Omega$ and Bu=g$\mathit{Bu}=g$ on the boundary ∂Ω$\mathrm{\partial }\Omega$, with either Dirichlet or Neumann boundary conditions, where Ω$\Omega$ is a smooth bounded domain in Rⁿ${\mathbb{R}}^n$ and the data f,g$f,g$ are distributions  . This problem has to be first properly reformulated and, for practical applications, it is of crucial importance to obtain the continuity of the solution u$u$ in terms of f and g  . For f=0$f=0$, taking advantage of the fact that u$u$ is harmonic on Ω$\Omega$, we provide four formulations of this boundary value problem (one using nontangential limits of harmonic functions, one using Green functions, one using the Dirichlet-to-Neumann map, and a variational one); we show that these four formulations are equivalent. We provide a similar analysis for f≠0$f\ne 0$ and discuss the roles of f and g, which turn to be somewhat interchangeable in the low regularity case. The weak formulation is more convenient for numerical approximation, whereas the nontangential limits definition is closer to the intuition and easier to check in concrete situations. We extend the weak formulation to polygonal domains using weighted Sobolev spaces. We also point out some new phenomena for the “concentrated loads” at the vertices in the polygonal case.     

De Sitter spacetime as a momentum measuring apparatus

We discuss the evolution of a quantum wave packet in the expanding de Sitter spacetime using the plane wave solutions of the Dirac equation. We concentrate on the case of large negative times when the packet approaches the event horizon and confirm that the evolution accords with that expected from the classical trajectories. We point out that in certain conditions the packet can split into two components that become localized at different parts of the horizon and that this effect can be seen, in an idealized sense, as a measuring process for the momentum of the particle, in direct analogy with the measurement of spin in a Stern-Gerlach experiment.     

Synthesis of gold nanoparticles by microemulsion assisted photoreduction method

A new, clean, cost-effective and rapid method for the synthesis of stable spherical gold nanoparticles (AuNPs) is developed. This novel technique combines microemulsion as one of soft-nanotechnology techniques of wet chemistry, with photo-physics of UV-radiation in a unique versatile method to design and obtain controlled nanostructures for multifunctional materials. Based on a phase diagram in ternary water/Brij 30/n-heptane system pristine, and thiol functionalized, gold nanoparticles were obtained by a microemulsion assisted photoreduction technique, allowing increased flexibility during the synthesis and selection of materials. The spherical nanoparticles obtained by this route show a homogeneous size distribution, with an average diameter of 11 nm, for pristine gold nanoparticles and of 12 nm, for functionalized species. The evolution of the system at the nanoscale has been studied using, in tandem, UV-VIS and DLS measurements. The structure, size and shape of the final nanoparticles obtained have been evaluated by adequate instrumental techniques: FTIR, XRD and TEM image analysis. Kinetic studies have also been performed in order to follow the evolution of nanospecies during irradiation procedure.     

Single and Double Layer Potentials on Domains with Conical Points I: Straight Cones

Let \({\Omega = \mathbb{R}^+ \omega}\) be an open straight cone in \({\mathbb{R}^n, n\geq3}\) , where \({\omega \subset S^{n-1}}\) is a smooth subdomain of the unit sphere. Denote by K and S the double and single layer potential operators associated to Ω and the Laplace operator Δ. Let r be the distance to the origin. We consider a natural class of dilation invariant operators on ?Ω, called Mellin convolution operators and show that \({K_a :=r^{a}Kr^{-a}}\) and \({S_b := r^{b-\frac{1}{2}}Sr^{-b-\frac{1}{2}}}\) are Mellin convolution operators for \({a \in (-1, n-1)}\) and \({b \in (\frac{1}{2}, n-\frac{3}{2})}\) . It is known that a Mellin convolution operator T is invertible if, and only if, its Mellin transform \({\hat T( \lambda)}\) is invertible for any real λ. We establish a reduction procedure that relates the Mellin transforms of K _a and S _b to the single and, respectively, double layer potential operators associated to some other elliptic operators on ω, which can be shown to be invertible using the classical theory of layer potential operators on smooth domains. This reduction procedure thus allows us to prove that \({\frac{1}{2}\pm K}\) and S are invertible between suitable weighted Sobolev spaces. A classical consequence of the invertibility of these operators is a solvability result in weighted Sobolev spaces for the Dirichlet problem on Ω.     

Optical implementation of quantum orienteering

We present results from an optical implementation of quantum orienteering, a protocol for communicating directions in space using quantum bits. We show how different types of measurements and encodings can be used to increase the communication efficiency. In particular, if Alice and Bob use two spin- particles for communication and employ joint measurements, they do better than is possible with local operations and classical communication. Furthermore, by using oppositely oriented spins, the achievable communication efficiency is further increased. Finally, we discuss the limitations of an optical approach: our results highlight the usually overlooked nonequivalence of different physical encodings of quantum bits.     

Entrapment of photosystem I within self-assembled films

We have developed a process to incorporate an integral membrane protein, Photosystem I (PSI), into an organic thin film at an electrode surface and thereby insulate the protein complex on the surface while mimicking its natural environment. The PSI complex, which is primarily more hydrophobic on the exterior than interior, is hydrophobically confined in vivo within the thylakoid membrane. To mimic the thylakoid membrane and entrap PSI on an electrode, we have designed a series of steps using a thin self-assembled monolayer (SAM) to adsorb and orient PSI followed by exposures to longer-chained methyl-terminated alkanethiols that place exchange with components of the original SAM in the interprotein domains. In this process, PSI is first adsorbed onto a HOC(6)S/Au substrate through a short exposure to a dilute solution of the protein to achieve a protein coverage of approximately 25%. The PSI/HOC(6)S/Au substrate is then placed into a solution containing one of various longer-chained alkanethiols including C(22)SH or C(18)OC(19)SH. Changes in thickness, interfacial capacitance, infrared spectra, and surface wettability were used to assess the extent of backfilling by the long-chained thiols. The coverage of the protein layer and the solvent used for backfilling affected the rate and quality of the SAM formed in the interprotein regions. After exposure of the PSI layer to solvents containing alkanethiols, there was only minor loss of protein on the surface and no real change in protein secondary structure as evidenced by reflectance absorption infrared spectroscopy.     

Organophosphorus insecticides extraction and heterogeneous oxidation on column for analysis with an acetylcholinesterase (AChE) biosensor

This paper presents an analysis method for organophosphorus insecticides based on AChE biosensors coupled with a preconcentration and oxidation on a solid phase column. Three organic solvents, acetonitrile (ACN), ethanol and methanol were tested for their influence on AChE activity, insecticide inhibition and their ability to elute the adsorbed insecticides. Our results showed that ACN in a concentration of 5% (v/v) had the less negative effect on biosensor analysis and was the most appropriate organic solvent for the column elution. The presence of the organic solvent in the incubation media of the biosensor was found to induce a reduction of the inhibition percentages. The inhibition of the biosensors was performed in phosphate buffer with 5% (v/v) ACN, while the initial and remaining response of the biosensors were measured in PBS. In these conditions, the LODs of paraoxon and dichlorvos were measured with or without a preconcentration step. The LODs of the AChE biosensor without sample preconcentration were 8 × 10⁻⁸ M for paraoxon and 1 × 10⁻⁷ M dichlorvos and the LOD obtained after the preconcentration step were 2.5 × 10⁻⁸ M for paraoxon and 2.5 × 10⁻⁸ M for dichlorvos. Moreover, the use of the column allowed the heterogeneous oxidation of organophosphorus insecticides for improved LOD.     

A new modified conducting carbon composite electrode as sensor for ascorbate and biosensor for glucose

A new carbon-based conducting composite has been developed as electrochemical sensor and biosensor for the amperometric detection of ascorbate and glucose. Electrocatalytic oxidation of ascorbate has been done successfully at unmodified cellulose acetate-graphite composite electrodes, the sensor being highly sensitive, selective and with a low detection limit at 0.0 V vs. SCE and was successfully applied for ascorbate determination in commercial fruit juice samples. An interference free glucose biosensor has also been developed, based on the immobilisation of glucose oxidase by cross-linking with glutaraldehyde on poly (neutral red) modified composite electrodes. The biosensor exhibits a higher sensitivity of 31.5 ± 1.7 µA cm^− 2 mM^− 1 than other carbon-composite-based glucose biosensors, a detection limit of 20.3 µM and a very short response time.     

Silver Nanoparticles Incorporated on Natural Clay as an Inhibitor against the New ISO SS Bacteria Isolated from Sewage Sludge,Involved in Malachite Green Dye Oxidation

A facile, ecofriendly, and cost-effective method was developed to prepare a microporous material based on natural chemically modified bentonite with silver ions (BN-Ag⁰). This material presents a good catalytic activity against Malachite Green (MG) dye and bacteriostatic activity against a newly isolated bacterium from sewage sludge named hereafter “ISO SS” and Escherichia coli (E. coli). BN-Ag⁰ was characterized by the following methods: energy-dispersive X-ray spectroscopy (EDX), scanning electron microscopy (SEM), Brunauer–Emmett–Teller (BET), Fourier-transform infrared (FTIR) spectroscopy, temperature programmed desorption (TPD) and X-ray Diffraction (XRD). The new bacterium ISO SS, was isolated using the technique of isolating a pure culture of anaerobically stabilized sludge. A mandatory characterization of ISO SS isolated strains from anaerobic stabilized sludge was performed in the process of identifying bacterial species. The cationic clay-based nanomaterial showed appreciable antibacterial activity against ISO SS, a Gram-negative bacterium. It also showed good activity against E. coli bacteria. As a catalyst in the catalytic ozonation of MG dye, BN-Ag⁰ significantly improves the oxidation time of the dye, due to its good adsorption and catalytic properties. The catalytic and antibacterial activities of the natural bentonite (BN) and of BN-Ag⁰ were examined using performant characterization techniques. The lifetime of the BN-Ag⁰ catalyst was also evaluated. Results obtained are expected to provide valuable findings for the preparation of a good microporous material with multiple functionalities.     

Preparation and properties of ultratransparent NaCl single crystals

The preparation of up to 100 mm diameter single crystalline ingots of ultratransparent NaCl by injecting the reactive atmosphere is reported. The resulting material exhibits high optical quality and bulk absorption coefficient at 10.6 μm of 0.91 × 10⁻³ cm⁻¹, close to the intrinsic value, which makes it suitable for transmissive components in high-power CO₂ lasers.