Molecular depth profiling of organic and biological materials

Atomic depth profiling using secondary ion mass spectrometry, SIMS, is common in the field micro-electronics; however, the generation of molecular information as a function of sample depth is difficult due to the accumulation of damage both on and beneath the sample surface. The introduction of polyatomic ion beams such as SF₅ and C₆₀ have raised the possibility of overcoming this problem as they deposit the majority of their energy in the upper surface of the sample resulting in increased sputter yields but with a complimentary reduction in sub-surface damage accumulation. In this paper we report the depth profile analysis of the bio-polymer polycaprolactone, PCL, using the polyatomic ions and and the monoatomic Au⁺. Results are compared to recent analysis of a similar sample using . depth profiling of cellulose is also demonstrated, an experiment that has been reported as unsuccessful when attempted with implications for biological analysis are discussed.     

One-Pot Synthesis of Chiral N-Arylamines by Combining Biocatalytic Aminations with Buchwald–Hartwig N-Arylation

The combination of biocatalysis and chemo-catalysis increasingly offers chemists access to more diverse chemical architectures. Here, we describe the combination of a toolbox of chiral-amine-producing biocatalysts with a Buchwald–Hartwig cross-coupling reaction, affording a variety of α-chiral aniline derivatives. The use of a surfactant allowed reactions to be performed sequentially in the same flask, preventing the palladium catalyst from being inhibited by the high concentrations of ammonia, salts, or buffers present in the aqueous media in most cases. The methodology was further extended by combining with a dual-enzyme biocatalytic hydrogen-borrowing cascade in one pot to allow for the conversion of a racemic alcohol to a chiral aniline.     

Synthesis of Polymers Containing Potassium Acyltrifluoroborates (KATs) and Post-polymerization Ligation and Conjugation

We report the synthesis of monomers for atom-transfer radical polymerization (ATRP) and a reversible addition-fragmentation chain transfer (RAFT) agent bearing trifluoroborate iminiums (TIMs), which are quantitatively converted into potassium acyltrifluoroborates (KATs) after polymerization. The resulting KAT-containing polymers are suitable for rapid amide-forming ligations for both post-polymerization modification and polymer conjugation. The polymer conjugation occurs rapidly, even under dilute (micromolar) aqueous conditions at ambient temperatures, thereby enabling the synthesis of a variety of linear and star-shaped block copolymers. In addition, we applied post-polymerization modification to the covalent linking of a photocaged cyclic antibiotic (gramicidin S) to the side chains of the KAT-containing copolymer. Cellular assays revealed that the polymer–antibiotic conjugate is biocompatible and provides efficient light-controlled release of the antibiotic on demand.     

Nowcasting Avalanches as Earthquakes and the Predictability of Strong Avalanches in the Olami-Feder-Christensen Model

Nowcasting earthquakes, suggested recently as a method to estimate the state of a fault and hence the seismic risk, is based on the concept of natural time. Here, we generalize nowcasting to a prediction method the merits of which are evaluated by means of the receiver operating characteristics. This new prediction method is applied to a simple (toy) model for the waiting (natural) time of the stronger earthquakes, real seismicity, and the Olami-Feder-Christensen earthquake model with interesting results revealing acceptable to excellent or even outstanding performance.     

Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.     

Tate cohomology and periodic localization of polynomial functors

In this paper, we show that Goodwillie calculus, as applied to functors from stable homotopy to itself, interacts in striking ways with chromatic aspects of the stable category. Localized at a fixed prime p, let T(n) be the telescope of a v_n self map of a finite S–module of type n. The Periodicity Theorem of Hopkins and Smith implies that the Bousfield localization functor associated to T(n)_* is independent of choices. Goodwillies general theory says that to any homotopy functor F from S–modules to S–modules, there is an associated tower under F, {P_dF}, such that FP_dF is the universal arrow to a d–excisive functor. Our first main theorem says that P_dFP_d-1F always admits a homotopy section after localization with respect to T(n)_* (and so also after localization with respect to Morava K–theory K(n)_*). Thus, after periodic localization, polynomial functors split as the product of their homogeneous factors. This theorem follows from our second main theorem which is equivalent to the following: for any finite group G, the Tate spectrum is weakly contractible. This strengthens and extends previous theorems of Greenlees–Sadofsky, Hovey–Sadofsky, and Mahowald–Shick. The Periodicity Theorem is used in an essential way in our proof. The connection between the two theorems is via a reformulation of a result of McCarthy on dual calculus. Mathematics Subject Classification (2000) 55P65, 55N22, 55P60, 55P91     

Curve following in illiquid markets

In this article the problem of curve following in an illiquid market is addressed. The optimal control is characterised in terms of the solution to a coupled FBSDE involving jumps via the technique of the stochastic maximum principle. Analysing this FBSDE, we further show that there are buy and sell regions. In the case of quadratic penalty functions the FBSDE admits an explicit solution which is determined via the four step scheme. The dependence of the optimal control on the target curve is studied in detail.     

On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems

It was recently proven in Case et al. (2010) [2] that, under mild restrictions, grad-div stabilized Taylor-Hood solutions of Navier-Stokes problems converge to the Scott-Vogelius solution of that same problem. However, even though the analytical rate was only shown to be (where γ is the stabilization parameter), the computational results suggest the rate may be improvable to γ−1. We prove herein the analytical rate is indeed γ−1, and extend the result to other incompressible flow problems including Leray-α and MHD. Numerical results are given that verify the theory.     

Localization algebras and deformations of Koszul algebras

We show that the center of a flat graded deformation of a standard Koszul algebra A behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed point set. In particular, the center of A acts by characters on the deformed standard modules, providing a “localization map”. We construct a universal graded deformation of A and show that the spectrum of its center is supported on a certain arrangement of hyperplanes which is orthogonal to the arrangement coming from the algebra Koszul dual to A. This is an algebraic version of a duality discovered by Goresky and MacPherson between the equivariant cohomology rings of partial flag varieties and Springer fibers; we recover and generalize their result by showing that the center of the universal deformation for the ring governing a block of parabolic category O{\mathcal{O}} for \mathfrakgl_n{\mathfrak{gl}_n} is isomorphic to the equivariant cohomology of a Spaltenstein variety. We also identify the center of the deformed version of the “category O{\mathcal{O}}” of a hyperplane arrangement (defined by the authors in a previous paper) with the equivariant cohomology of a hypertoric variety.     

Characterization of silicon nanowires grown on silicon, stainless steel and indium tin oxide substrates

Silicon nanowires (SiNWs) have been grown on crystalline silicon (Si), indium tin oxide (ITO) and stainless steel (SS) substrates using a gold catalyst coating with a thickness of 200 nm via pulsed plasma-enhanced chemical vapor deposition (PPECVD). Their morphological, mineralogical and surface characteristics have been investigated using scanning electron microscopy (SEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and Raman analysis. SiNWs growth is accompanied by oxidation, thus yielding partially (SiO _x ) and fully oxidized (SiO₂) Si sheaths. The mean diameters of these SiNWs range from 140 to 185 nm. Si with (111) and (220) planes exists in SiNWs grown on all three substrates while Si with a (311) plane is detected only for Si and ITO substrates. Computational simulation using density functional theory (DFT) has also been conducted to supplement the experimental Raman analyses for crystalline Si and SiO₂. XPS results reveal that ca. 30 % of the SiNWs have been oxidized for all substrates. The results presented in this paper can be used to aid selection of appropriate substrates for SiNW growth, depending on specific applications.