A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer

The objective of this paper is to construct and analyze a fitted operator finite difference method (FOFDM) for the family of time‐dependent singularly perturbed parabolic convection–diffusion problems. The solution to the problems we consider exhibits an interior layer due to the presence of a turning point. We first establish sharp bounds on the solution and its derivatives. Then, we discretize the time variable using the classical Euler method. This results in a system of singularly perturbed interior layer two‐point boundary value problems. We propose a FOFDM to solve the system above. Through a rigorous error analysis, we show that the scheme is uniformly convergent of order one with respect to both time and space variables. Moreover, we apply Richardson extrapolation to enhance the accuracy and the order of convergence of the proposed scheme. Numerical investigations are carried out to demonstrate the efficacy and robustness of the scheme.     

Mechanism of Al(III)-catalyzed transamidation of unactivated secondary carboxamides

The carbon-nitrogen bond of secondary carboxamides is generally thermodynamically and kinetically unreactive; however, we recently discovered that the trisamidoaluminum(III) dimer Al2(NMe2)6 catalyzes facile transamidation between simple secondary carboxamides and primary amines under moderate conditions. The present report describes kinetic and spectroscopic studies that illuminate the mechanism of this unusual transformation. The catalytic reaction exhibits a bimolecular rate law with a first-order dependence on the Al(III) and amine concentrations. No rate dependence on the carboxamide concentration is observed. Spectroscopic studies (1H and 13C NMR, FTIR) support a catalyst resting state that consists of a mixture of tris-(kappa2-amidate)aluminum(III) complexes. These results, together with the presence of a significant kinetic isotope effect when deuterated amine substrate (RND2) is used, implicate a mechanism in which the amine undergoes preequilibrium coordination to aluminum and proton transfer to a kappa2-amidate ligand to yield an Al(kappa2-amidate)2(kappa1-carboxamide)(NHR) complex, followed by rate-limiting intramolecular delivery of the amido ligand (NHR) to the neutral Al(III)-activated kappa1-carboxamide. Noteworthy in this mechanism is the bifunctional character of Al(III), which is capable of activating both the amine nucleophile and the carboxamide electrophile in the reaction.     

Biomimetic Total Synthesis of Hyperjapones A–E and Hyperjaponols A and C

Hyperjapones A–E and hyperjaponols A–C are complex natural products of mixed aromatic polyketide and terpene biosynthetic origin that have recently been isolated from Hypericum japonicum. We have synthesized hyperjapones A–E using a biomimetic, oxidative hetero‐Diels–Alder reaction to couple together dearomatized acylphloroglucinol and cyclic terpene natural products. Hyperjapone A is proposed to be the biosynthetic precursor of hyperjaponol C through a sequence of: 1) epoxidation; 2) acid‐catalyzed epoxide ring‐opening; and 3) a concerted, asynchronous alkene cyclization and 1,2‐alkyl shift of a tertiary carbocation. Chemical mimicry of this proposed biosynthetic sequence allowed a concise total synthesis of hyperjaponol C to be completed in which six carbon–carbon bonds, six stereocenters, and three rings were constructed in just four steps.     

The Role of Methoxy Group in the Nazarov Cyclization of 1,5-bis-(2-Methoxyphenyl)-1,4-Pentadien-3-one in the Gas Phase and Condensed Phase

ESI-protonated 1,5-bis-(2-methoxyphenyl)-1,4-pentadien-3-one (1) undergoes a gas-phase Nazarov cyclization and dissociates via expulsions of ketene and anisole. The dissociations of the [M + D]⁺ ions are accompanied by limited HD scrambling that supports the proposed cyclization. Solution cyclization of 1 was effected to yield the cyclic ketone, 2,3-bis-(2-methoxyphenyl)-cyclopent-2-ene-1-one, (2) on a time scale that is significantly shorter than the time for cyclization of dibenzalacetone. The dissociation characteristics of the ESI-generated [M + H]⁺ ion of the synthetic cyclic ketone closely resemble those of 1, suggesting that gas-phase and solution cyclization products are the same. Additional mechanistic studies by density functional theory (DFT) methods of the gas-phase reaction reveals that the initial cyclization is followed by two sequential 1,2-aryl migrations that account for the observed structure of the cyclic product in the gas phase and solution. Furthermore, the DFT calculations show that the methoxy group serves as a catalyst for the proton migrations necessary for both cyclization and fragmentation after aryl migration. An isomer formed by moving the 2-methoxy to the 4-position requires relatively higher collision energy for the elimination of anisole, as is consistent with DFT calculations. Replacement of the 2-methoxy group with an OH shows that the cyclization followed by aryl migration and elimination of phenol occurs from the [M + H]⁺ ion at low energy similar to that for 1.

Lagrangian and Eulerian models for simulating turbulent dispersion and coalescence of droplets within a spray

Lagrangian and Eulerian modelling approaches are compared for simulating turbulent dispersion and coalescence of droplets within a spray. Both models predict similar droplet dispersion rates and shifts in droplet size distribution due to coalescence within the spray, over a wide range of droplet and gas flows, and for sprays with different droplet-size distributions at the nozzle exit. The computer time required for simulating coalescence within a steady axisymmetric spray is of a similar order of magnitude regardless of which formulation, Eulerian or Lagrangian, is adopted. However, the Lagrangian formulation is more practical in terms of the range of applicability and ease of implementation.     

Low temperature synthesis of ITO nanoparticles using polyol process

A low temperature synthesis technique to prepare indium tin oxide (ITO) nanoparticles by the polyol process is proposed. On examining the phase formation of ITO nanoparticles in polyols and alcohols such as ethylene glycol, trimethylene glycol, and 1-heptanol, it was found that ITO nanoparticles could be synthesized directly without any post--annealing treatments at 175 °C in 1-heptanol. The morphology of the particles is influenced by the type of polyol. The composition of Sn in the ITO system could be easily controlled by simply varying the In/Sn precursor ratio in 1-heptanol. The low temperature synthesis method has enabled the formation of highly crystalline ITO nanoparticles with diameters less than 25 nm even at annealing temperatures as high as 700 °C.     

Collisional activation of protein complexes: Picking up the pieces

Mass spectrometry is fast becoming a vital approach not only for the identification and quantification of proteins, but also for the study of the noncovalent assemblies they form. Approaches for ionizing, transmitting, and detecting protein complexes intact in the mass spectrometer are now well established. The challenge has therefore shifted to developing and applying mass spectrometry approaches to elucidate the structure of such species. A crucial aspect to this goal is inducing their disassembly in the gas phase to mine information as to their composition and organization. Here the consequences of collisionally activating protein complexes are illustrated through ion mobility mass spectrometry measurements and discussed in the context of the current literature. Although a consensus view of the mechanism of dissociation is starting to emerge, it is also clear that a number of aspects remain unresolved. These outstanding questions and frontier challenges must be addressed if gas-phase dissociative approaches are to reach their full potential in the study of protein assemblies.     

Monitoring the heterogeneity in single cell responses to drugs using electrochemical impedance and electrochemical noise

Impedance spectroscopy is a widely used technique for monitoring cell–surface interactions and morphological changes, typically based on averaged signals from thousands of cells. However, acquiring impedance data at the single cell level, can potentially reveal cell-to-cell heterogeneity for example in response to chemotherapeutic agents such as doxorubicin. Here, we present a generic platform where light is used to define and localize the electroactive area, thus enabling the impedance measurements for selected single cells. We firstly tested the platform to assess phenotypic changes in breast cancer cells, at the single cell level, using the change in the cell impedance. We next show that changes in electrochemical noise reflects instantaneous responses of the cells to drugs, prior to any phenotypical changes. We used doxorubicin and monensin as model drugs and found that both drug influx and efflux events affect the impedance noise signals. Finally, we show how the electrochemical noise signal can be combined with fluorescence microscopy, to show that the noise provides information on cell susceptibility and resistance to drugs at the single cell level. Together the combination of electrochemical impedance and electrochemical noise with fluorescence microscopy provides a unique approach to understanding the heterogeneity in the response of single cells to stimuli where there is not phenotypic change.

A light addressable single-cell impedance technique for cell adhesion monitoring and measurement of a cell''s drug response based on electrochemical noise is introduced.     

Optical nonlinearity of organic dyes as studied by Z-scan and transient grating techniques

The excited state absorption cross-section of 5,5′-dichloro-11-diphenyl-amino-3,3′-diethyl-10, 12-ethylinethiatricarbocyanine perchlorate (IR140) have been measured by using a single beam transmission technique. Z-scan experiments have been used to find out a few nonlinear parameters. The excited state relaxation times have also been measured by using laser induced transient grating (LITG) technique.     

Synthesis of highly substituted 2,6-anti-configured tetrahydropyrans. First steps towards an efficient access to amphidinol 3 ring system

Highly functionalised and polysubstituted tetrahydropyrans, akin to the middle core of the amphidinols, can be efficiently synthesised, with full stereocontrol and in good yields, using as key steps an anti-allylation reaction coupled with an intramolecular Sakurai cyclisation. Three approaches were devised in order to reach a broad range of substitution patterns.