The decoupling of damped linear systems in free or forced vibration

The purpose of this paper is to extend classical modal analysis to decouple any viscously damped linear system in non-oscillatory free vibration or in forced vibration. Based upon an exposition of how exponential decay in a system can be regarded as imaginary oscillations, the concept of damped modes of imaginary vibration is introduced. By phase synchronization of these real and physically excitable modes, a time-varying transformation is constructed to decouple non-oscillatory free vibration. When time drifts caused by viscous damping and by external excitation are both accounted for, a time-varying decoupling transformation for forced vibration is derived. The decoupling procedure devised herein reduces to classical modal analysis for systems that are undamped or classically damped. This paper constitutes the second and final part of a solution to the “classical decoupling problem.” Together with an earlier paper, a general methodology that requires only the solution of a quadratic eigenvalue problem is developed to decouple any damped linear system.     

A Singular System with Precise Dosing and Spatiotemporal Control of CRISPR‐Cas9

Several genome engineering applications of CRISPR‐Cas9, an RNA‐guided DNA endonuclease, require precision control of Cas9 activity over dosage, timing, and targeted site in an organism. While some control of Cas9 activity over dose and time have been achieved using small molecules, and spatial control using light, no singular system with control over all the three attributes exists. Furthermore, the reported small‐molecule systems lack wide dynamic range, have background activity in the absence of the small‐molecule controller, and are not biologically inert, while the optogenetic systems require prolonged exposure to high‐intensity light. We previously reported a small‐molecule‐controlled Cas9 system with some dosage and temporal control. By photocaging this Cas9 activator to render it biologically inert and photoactivatable, and employing next‐generation protein engineering approaches, we have built a system with a wide dynamic range, low background, and fast photoactivation using a low‐intensity light while rendering the small‐molecule activator biologically inert. We anticipate these precision controls will propel the development of practical applications of Cas9.     

A Spinor Approach to Walker Geometry

A four-dimensional Walker geometry is a four-dimensional manifold M with a neutral metric g and a parallel distribution of totally null two-planes. This distribution has a natural characterization as a projective spinor field subject to a certain constraint. Spinors therefore provide a natural tool for studying Walker geometry, which we exploit to draw together several themes in recent explicit studies of Walker geometry and in other work of Dunajski [11] and Pleba?ski [30] in which Walker geometry is implicit. In addition to studying local Walker geometry, we address a global question raised by the use of spinors.     

Quantum phase transition between a Luttinger liquid and a gas of cold molecules

We consider cold polar molecules confined in a helical optical lattice similar to those used in holographic microfabrication. An external electric field polarizes molecules along the axis of the helix. The large-distance intermolecular dipolar interaction is attractive but the short-scale interaction is repulsive due to geometric constraints and thus prevents collapse. The interaction strength depends on the electric field. We show that a zero-temperature second-order liquid-gas transition occurs at a critical field. It can be observed under experimentally accessible conditions.     

Exploring the oxidation chemistry of diisopropyl ether: Jet-stirred reactor experiments and kinetic modeling

Diisopropyl ether (DIPE) is considered as a promising gasoline additive due to the favorable blending Reid vapor pressure and the low water solubility. To get a good understanding of the DIPE oxidation chemistry, oxidation experiments of a stoichiometric mixture of DIPE/O₂/Ar/Kr were performed in a jet-stirred reactor (JSR) at atmospheric pressure over the temperature range of 525–900 K in this work. About 30 intermediates and products were identified and quantified using a photoionization molecular-beam mass spectrometer (PI-MBMS). Furthermore, a detailed kinetic model was proposed for DIPE oxidation, which showed satisfactory performances in predicting the species concentration profiles in this work as well as those in literature. For DIPE oxidation, the fuel consumption was observed only above 750 K, even though DIPE has two tertiary hydrogen atoms that are easy to be abstracted so that low-temperature oxidation reactivity is expected. The low oxidation reactivity at low temperature is because the formed OOQOOH radical mostly dissociates back to QOOH+O₂, instead of undergoing intramolecular isomerization which leads to the low-temperature chain-branching. At higher temperature, DIPE is mainly consumed by hydrogen abstraction reactions from the carbon atoms adjacent to the oxygen atom, producing dominantly the IC₃H₇OC(CH₃)₂ fuel radical, which then decomposes rapidly via CO bond β-scission instead of combining with O₂. In contrast, the minor fuel radical IC₃H₇OCH(CH₃)CH₂ tends to go through the O₂ addition reaction and the subsequent chain branching reactions, as confirmed by the detection of cyclic ether intermediates. Propylene and acetone are the most abundant intermediates in DIPE oxidation, both of which predominantly come from the initial fuel decomposition steps. Other intermediates are mainly formed via the consumption of these two species.     

Fast Exfoliation and Functionalisation of Two‐Dimensional Crystalline Carbon Nitride by Framework Charging

Two‐dimensional (2D) layered graphitic carbon nitride (gCN) nanosheets offer intriguing electronic and chemical properties. However, the exfoliation and functionalisation of gCN for specific applications remain challenging. We report a scalable one‐pot reductive method to produce solutions of single‐ and few‐layer 2D gCN nanosheets with excellent stability in a high mass yield (35 %) from polytriazine imide. High‐resolution imaging confirmed the intact crystalline structure and identified an AB stacking for gCN layers. The charge allows deliberate organic functionalisation of dissolved gCN, providing a general route to adjust their properties.     

Stickelberger elements for -extensions of function fields

We study Stickelberger elements associated to -extensions over global function fields of characteristic p>0 and show that they are in some sense generically irreducible in the Iwasawa algebras.     

Flexible CDOCKER: Development and application of a pseudo‐explicit structure‐based docking method within CHARMM

Protein‐ligand docking is a commonly used method for lead identification and refinement. While traditional structure‐based docking methods represent the receptor as a rigid body, recent developments have been moving toward the inclusion of protein flexibility. Proteins exist in an interconverting ensemble of conformational states, but effectively and efficiently searching the conformational space available to both the receptor and ligand remains a well‐appreciated computational challenge. To this end, we have developed the Flexible CDOCKER method as an extension of the family of complete docking solutions available within CHARMM. This method integrates atomically detailed side chain flexibility with grid‐based docking methods, maintaining efficiency while allowing the protein and ligand configurations to explore their conformational space simultaneously. This is in contrast to existing approaches that use induced‐fit like sampling, such as Glide or Autodock, where the protein or the ligand space is sampled independently in an iterative fashion. Presented here are developments to the CHARMM docking methodology to incorporate receptor flexibility and improvements to the sampling protocol as demonstrated with re‐docking trials on a subset of the CCDC/Astex set. These developments within CDOCKER achieve docking accuracy competitive with or exceeding the performance of other widely utilized docking programs. © 2015 Wiley Periodicals, Inc.     

Almost Kähler-Einstein Structures on 8-Dimensional Walker Manifolds

We study almost K?hler-Einstein structures on 8-dimensional Walker manifolds, i.e., pseudo-Riemannian 8-manifolds admitting a field of parallel null 4-planes, whence the metric is of neutral signature. We construct on explicit almost K?hler-Einstein Walker metrics which are not K?hler. An appropriate restriction induces examples of such metrics on the 8-torus, thereby producing a counterexample to Goldberg’s conjecture in the case of neutral signature. S. Haze passed away on 15 March 2006.