Uniform shrinking and expansion under isotropic Brownian flows

We study some finite time transport properties of isotropic Brownian flows. Under a certain nondegeneracy condition on the potential spectral measure, we prove that uniform shrinking or expansion of balls under the flow over some bounded time interval can happen with positive probability. We also provide a control theorem for isotropic Brownian flows with drift. Finally, we apply the above results to show that under the nondegeneracy condition the length of a rectifiable curve evolving in an isotropic Brownian flow with strictly negative top Lyapunov exponent converges to zero as $t\to \infty$ with positive probability

Caustics in turbulent aerosols

Networks of caustics can occur in the distribution of particles suspended in a randomly moving gas. These can facilitate coagulation of particles by bringing them into close proximity, even in cases where the trajectories do not coalesce. We show that the long-time morphology of these caustic patterns is determined by the Lyapunov exponents lambda_1, lambda_2 of the suspended particles, as well as the rate J at which particles encounter caustics. We develop a theory determining the quantities J, lambda_1, lambda_2 from the statistical properties of the gas flow, in the limit of short correlation times.Comment: 4 pages, 3 figure

Flow Synthesis of Ethyl Isocyanoacetate Enabling the Telescoped Synthesis of 1,2,4-Triazoles and Pyrrolo-[1,2-c]pyrimidines

The efficient flow synthesis of important heterocyclic building blocks based on the 1,2,4-triazole and pyrrolo[1,2-c]pyrimidine scaffold has been achieved. Crucially, a telescoped continuous flow process was developed based on the reaction of N-formylglycine with triphosgene to deliver a stream of ethyl isocyanoacetate in situ, which subsequently yielded the desired heterocyclic entities in a telescoped reaction. Additionally, the functionalisation of the pyrrolo[1,2-c]pyrimidine core via subsequent SEAr reactions was studied revealing insight into a ‘halogen dance’ phenomenon associated with these medicinally relevant architectures

Ab initio molecular dynamics calculations of ion hydration free energies

We apply ab initio molecular dynamics (AIMD) methods in conjunction with the thermodynamic integration or "lambda-path" technique to compute the intrinsic hydration free energies of Li+, Cl-, and Ag+ ions. Using the Perdew-Burke-Ernzerhof functional, adapting methods developed for classical force field applications, and with consistent assumptions about surface potential (phi) contributions, we obtain absolute AIMD hydration free energies (Delta G(hyd)) within a few kcal/mol, or better than 4%, of Tissandier 's [J. Phys. Chem. A 102, 7787 (1998)] experimental values augmented with the SPC/E water model phi predictions. The sums of Li+/Cl- and Ag+/Cl- AIMD Delta G(hyd), which are not affected by surface potentials, are within 2.6% and 1.2 % of experimental values, respectively. We also report the free energy changes associated with the transition metal ion redox reaction Ag++Ni+-> Ag+Ni2+ in water. The predictions for this reaction suggest that existing estimates of Delta G(hyd) for unstable radiolysis intermediates such as Ni+ may need to be extensively revised.Comment: 18 pages, 8 figures. This version is essentially the one published in J. Chem. Phy

The Automated Root Exudate System (ARES): a method to apply solutes at regular intervals to soils in the field.

Root exudation is a key component of nutrient and carbon dynamics in terrestrial ecosystems. Exudation rates vary widely by plant species and environmental conditions, but our understanding of how root exudates affect soil functioning is incomplete, in part because there are few viable methods to manipulate root exudates in situ. To address this, we devised the Automated Root Exudate System (ARES), which simulates increased root exudation by applying small amounts of labile solutes at regular intervals in the field. The ARES is a gravity-fed drip irrigation system comprising a reservoir bottle connected via a timer to a micro-hose irrigation grid covering c. 1 m2; 24 drip-tips are inserted into the soil to 4-cm depth to apply solutions into the rooting zone. We installed two ARES subplots within existing litter removal and control plots in a temperate deciduous woodland. We applied either an artificial root exudate solution (RE) or a procedural control solution (CP) to each subplot for 1 min day-1 during two growing seasons. To investigate the influence of root exudation on soil carbon dynamics, we measured soil respiration monthly and soil microbial biomass at the end of each growing season. The ARES applied the solutions at a rate of c. 2 L m-2 week-1 without significantly increasing soil water content. The application of RE solution had a clear effect on soil carbon dynamics, but the response varied by litter treatment. Across two growing seasons, soil respiration was 25% higher in RE compared to CP subplots in the litter removal treatment, but not in the control plots. By contrast, we observed a significant increase in microbial biomass carbon (33%) and nitrogen (26%) in RE subplots in the control litter treatment. The ARES is an effective, low-cost method to apply experimental solutions directly into the rooting zone in the field. The installation of the systems entails minimal disturbance to the soil and little maintenance is required. Although we used ARES to apply root exudate solution, the method can be used to apply many other treatments involving solute inputs at regular intervals in a wide range of ecosystems

A Robust and Scalable Continuous Flow Process for Glycerol Carbonate

We report a robust continuous flow procedure for the synthesis of glycerol carbonate (2‐GLC) from green reagents glycerol and dimethyl carbonate (DMC), mediated by an inexpensive polymer‐supported base catalyst using methanol as co‐solvent. High conversion and selectivity were obtained, while residence times were typically shorter than 10 minutes

Self-adaptive context aware audio localization for robots using parallel cerebellar models

An audio sensor system is presented that uses multiple cerebellar models to determine the acoustic environment in which a robot is operating, allowing the robot to select appropriate models to calibrate its audio-motor map for the detected environment. The use of the adaptive filter model of the cerebellum in a variety of robotics applications has demonstrated the utility of the so-called cerebellar chip. This paper combines the notion of cerebellar calibration of a distorted audio-motor map with the use of multiple parallel models to predict the context (acoustic environment) within which the robot is operating. The system was able to correctly predict seven different acoustic contexts in almost 70% of cases tested