On the oscillation of the Brownian motion process

Paley, Wiener and Zygmund proved that, with probability 1, Brownian paths never satisfy a Lipschitz condition of order greater than 1/2. This result is improved by showing that they never satisfy even a Lipschitz condition of order 1/2 with a sufficiently small Lipschitz constant. This research was sponsored by National Science Grant NSF-GP-316 at Columbia University.     

Sonochemical preparation of GaSb nanoparticles

A room temperature sonochemical method for the preparation of GaSb nanoparticles using less hazardous Ga and antimony chloride (SbCl(3)) as the precursors has been described. The formation of GaSb has been confirmed by means of XRD, EDAX, and XPS characterization. TEM and SAED results show that the as-prepared solid consists of nanosized GaSb crystals with sizes in the range 20-30 nm. The photoacoustic spectrum result reveals that the GaSb nanoparticles have a direct band gap of about 1.21 eV. On the basis of the control experiments and the extreme conditions produced by ultrasound, an ultrasound-assisted in-situ reduction/combination mechanism has been proposed to explain the reaction.     

Aprotic metal-oxygen batteries: recent findings and insights

During the last two decades, we have observed a dramatic increase in the electrification of many technologies. What has enabled this transition to take place was the commercialization of Li-ion batteries in the early nineties. Mobile technologies such as cellular phones, laptops, and medical devices make these batteries crucial for our contemporary lifestyle. Like any other electrochemical cell, the Li-ion batteries are restricted to the thermodynamic limitations of the materials. It might be that the energy density of the most advance Li-ion battery is still too low for demanding technologies such as a full electric vehicle. To really convince future customers to switch from the internal combustion engine, new batteries and chemistry need to be developed. Non-aqueous metal-oxygen batteries—such as lithium–oxygen, sodium–oxygen, magnesium–oxygen, and potassium–oxygen—offer high capacity and high operation voltages. Also, by using suitable polar aprotic solvents, the oxygen reduction process that occurs during discharge can be reversed by applying an external potential during the charge process. Thus, in theory, these batteries could be electrically recharged a number of times. However, there are many scientific and technical challenges that need to be addressed. The current review highlights recent scientific insights related to these promising batteries. Nevertheless, the reader will note that many conclusions are applicable in other kinds of batteries as well.     

The dynamic nature of amyloid beta (1-40) aggregation

In this paper, we characterize the dynamic nature of the full amyloid beta (1-40) (Aβ (1-40)) aggregates. We labeled the peptide with either 5-carboxytetramethylrhodamine (TAMRA) or with fluorescein-isothiocyanate (FITC). The labeled peptides were mixed after separate fibrillization, and the dynamic changes in the structure of the fibrils were imaged using confocal microscopy. Fluorescence resonance energy transfer (FRET) measurements showed that the Aβ (1-40) peptides detach from and reattach to the fibrils in a biologically relevant timescale (days). With time, the two peptides mix at the molecular level. This process is concentration dependent and occurs primarily in the external parts of the aggregates with a half time between 4 and 7 days. This study shows that the combination of confocal microscopy and FRET analysis is a facile method for studying dynamic processes in supra-molecular aggregates.     

Umbrella sampling for nonequilibrium processes

The authors introduce an algorithm for determining the steady-state probability distribution of an ergodic system arbitrarily far from equilibrium. By enforcing equal sampling of different regions of phase space, as in umbrella sampling simulations of systems at equilibrium, low probability regions are explored to a much greater extent than in physically weighted simulations. The algorithm can be used to accumulate joint statistics for an arbitrary number of order parameters for a system governed by any stochastic dynamics. They demonstrate the efficiency of the algorithm by applying it to a model of a genetic toggle switch which evolves irreversibly according to a continuous time Monte Carlo procedure.     

Cine Substitution in 2-Oxabicyclo[4.2.0]octanones and Subsequent Unusual Rearrangements(1)

Reaction of 2-chlorooxabicyclo[4.2.0]octanone 5 with several nucleophiles was examined and found to differ significantly from those of carbon analog 1. MeO(-) and PhS(-) led either to products of cine substitution 9 or of ring opening to cyclobutenones 8. With most enolates cine substitution occured via C-alkylation of the intermediate oxidoallyl cation in spite of formation of a new C-C bond between two quaternary carbons; with nitroalkanes O-alkylation was preferred. With azide as a nucleophile, further transformations occurred, among them an oxy-promoted electrocyclic cyclobutane opening, with incorporation of a phenyl triazole unit and final formation of the unusual product 19a. Evidence for a mechanism explaining formation of 19a was obtained by isolation of intermediates. Thermolysis or photolysis of 8e or9b led via electrocyclic ring opening to a vinyl ketene which was trapped by MeOH, alkenes, dienes, or oxygen to produce polyfunctional unsaturated esters 29 and 30 or 8-membered ring lactone 31, fused cyclobutanones 33 and 34, pyranone 38, or gamma-lactone 39, respectively.     

Alloying a single and a double perovskite: a Cu+/2+ mixed-valence layered halide perovskite with strong optical absorption

Introducing heterovalent cations at the octahedral sites of halide perovskites can substantially change their optoelectronic properties. Yet, in most cases, only small amounts of such metals can be incorporated as impurities into the three-dimensional lattice. Here, we exploit the greater structural flexibility of the two-dimensional (2D) perovskite framework to place three distinct stoichiometric cations in the octahedral sites. The new layered perovskites A^I₄[Cu^II(Cu^IIn^III)_0.5Cl₈] (1, A = organic cation) may be derived from a Cu^I–In^III double perovskite by replacing half of the octahedral metal sites with Cu²⁺. Electron paramagnetic resonance and X-ray absorption spectroscopy confirm the presence of Cu²⁺ in 1. Crystallographic studies demonstrate that 1 represents an averaging of the Cu^I–In^III double perovskite and Cu^II single perovskite structures. However, whereas the highly insulating Cu^I–In^III and Cu^II perovskites are colorless and yellow, respectively, 1 is black, with substantially higher electronic conductivity than that of either endmember. We trace these emergent properties in 1 to intervalence charge transfer between the mixed-valence Cu centers. We further propose a tiling model to describe how the Cu⁺, Cu²⁺, and In³⁺ coordination spheres can pack most favorably into a 2D perovskite lattice, which explains the unusual 1 : 2 : 1 ratio of these cations found in 1. Magnetic susceptibility data of 1 further corroborate this packing model. The emergence of enhanced visible light absorption and electronic conductivity in 1 demonstrates the importance of devising strategies for increasing the compositional complexity of halide perovskites.

A novel 2D halide perovskite with stoichiometric quantities of Cu⁺, Cu²⁺, and In³⁺ in the inorganic slabs shows emergent properties not seen in Cu^II or Cu^I–In^III perovskites, including enhanced visible-light absorption and electronic conductivity.     

Harmonic response of cellular membrane pumps to low frequency electric fields

We report on harmonic generation by budding yeast cells in response to a sinusoidal electric field, which is seen to be minimal when the field amplitude is less than a threshold value. Surprisingly, sodium metavanadate, an inhibitor of P-type ATPases reportedly responsible for nonlinear response in yeast, reduces the threshold field amplitude, increasing harmonic generation at low amplitudes while reducing it at large amplitudes, whereas the addition of glucose dramatically increases the production of even harmonics. Finally, a simple model is proposed to interpret the observed behavior.     

Novel and Convenient Synthesis of Benzofurans from Dihydrocoumarins

7‐Hydroxy‐3,4‐dihydrocoumarin‐4‐carboxylic acid ( 7 ), conveniently prepared from m‐resorcinol and maleic anhydride, was surprisingly transformed by acid anhydride and pyridine into the corresponding ketone, 4‐alkanoyl analog 11 . The latter reacted in turn with acidic alcohol yielding benzofuran‐3‐yl‐acetic ester 16.