Biocatalytic Strategies towards [4+2] Cycloadditions

Long sought after [4+2] cyclases have sprouted up in numerous biosynthetic pathways in recent years, raising hopes for biocatalytic solutions to cycloaddition catalysis, an important problem in chemical synthesis. In a few cases, detailed pictures of the inner workings of these catalysts have emerged, but intense efforts to gain deeper understanding are underway by means of crystallography and computational modelling. This Minireview aims to shed light on the catalytic strategies that this highly diverse family of enzymes employs to accelerate and direct the course of [4+2] cycloadditions with reference to small-molecule catalysts and designer enzymes. These catalytic strategies include oxidative or reductive triggers and lid-like movements of enzyme domains. A precise understanding of natural cycloaddition catalysts will be instrumental for customizing them for various synthetic applications.     

True spin and pseudo spin entanglement around Dirac Points in graphene with Rashba spin–orbit interaction

We analytically obtained the Schmidt decomposition of the entangled state between the pseudo spin and the true spin in graphene with Rashba spin–orbit coupling. The entangled state has the standard form of the Bell state, where the SU(2) spin symmetry is broken. These states can be explicitly expressed as the superposition of two nonorthogonal, but mirror symmetrical spin states entangled with the pseudo spin states. Because of the closely locking between the pseudo spin and the true spin, it is found that the orbit curve in the spin-polarization parameter space for the fixed equi-energy contour around Dirac points has the same shape as the $\delta \overrightarrow{k}$-contour. Due to the spin–orbit coupling that cause the topological transition in the local geometry of the dispersion relation, the new equi-energy contours around the new emergent Dirac Points can be obtained by squeezing the one around the original Dirac point. The spin texture in the momentum space around the Dirac points is analyzed under the Rashba spin–orbit interaction and it is found that the orientation of the spin polarization at each crystal momentum $\overrightarrow{k}$ is independent of the Rashba coupling strength.     

An explicit compact universal space for real flows

The Kakutani–Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.     

Host (Nanocavity of Aluminium-Incorporated Mesoporous KIT-6)–guest (12-tungesto(molybdato) Phosphoric Acid) Nanocomposite Material: Efficient and Reusable Catalysts for the Hosomi–Sakurai Three-Component Coupling Reaction

Abstract

The immobilization of heteropoly acids (HPAs) into the Al-functionalized KIT-6 mesoporous molecular sieve has been carried out to see the effect of Al-KIT-6 as a host matrix on the HPA activities. These modified mesoporous molecular sieves are effective catalysts for the Hosomi–Sakurai three-component coupling reaction via condensation of aldehydes, silyl ethers, and allylsilanes.

Supplemental materials are available for this paper. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Extraction Properties of Oligodentate Carbamoylmethylphosphine Oxides and β-Aminophosphine Oxides Toward Lanthanides and Rhenium(VII)

Abstract

The extraction properties of a series of carbamoylmethylphosphine oxides and β-aminophosphine oxides with lanthanide metal ions is presented. Tris[bis(2-diphenyl- phosphorylethyl)-aminoethyl]amine is shown to be highly effective for extraction of Re(VII).     

Alternative routes to equivalent classical models of a quantum system

<正>Coarse-graining of some sort is a fundamental and unavoidable step in any attempt to derive the classical mechanical behavior from the quantum formalism.We utilize the two-mode Bose-Hubbard model to illustrate how different coarse-grained systems can be naturally associated with a fixed quantum system if it is compatible with different dynamical algebras.Alternative coarse-grained systems generate different evolutions of the same physical quantities,and the difference becomes negligible only in the appropriate macro-limit.     

Dislocation-density-based constitutive modelling of tensile flow and work-hardening behaviour of P92 steel

The flow and work-hardening behaviour of tempered martensitic P92 steel have been investigated using phenomenological constitutive model in the temperature range 300–873 K for the strain rates ranging from 3.16 × 10^?5 to 1.26 × 10^?3 s^?1. The analysis indicated that the hybrid model reduced to Estrin–Mecking (E–M) one-internal-variable model at intermediate and high temperatures. Further, the analysis also indicated that dislocation dense martensite lath/cell boundaries and precipitates together act as effective barriers to dislocation glide in P92 steel. The flow behaviour of the steel was adequately described by the E–M approach for the range of temperatures and strain rates examined. Three distinct temperature regimes have been obtained for the variations in work-hardening parameters with respect to temperature and strain rate. Signatures of dynamic strain ageing in terms of the anomalous variations in work-hardening parameters at intermediate temperatures and the dominance of dynamic recovery at high temperatures have been observed. The evaluation of activation energy suggested that deformation is controlled by the dominance of cross-slip of dislocations at room and intermediate temperatures, and climb of dislocations at high temperatures.     

The Spin-Coating Process: Analysis of the Free Boundary Value Problem

In this paper, an accurate model of the spin-coating process is presented and investigated from the analytical point of view. More precisely, the spin-coating process is being described as a one-phase free boundary value problem for Newtonian fluids subject to surface tension and rotational effects. It is proved that for T > 0 there exists a unique, strong solution to this problem in (0, T) belonging to a certain regularity class provided the data and the speed of rotation are small enough in suitable norms. The strategy of the proof is based on a transformation of the free boundary value problem to a quasilinear evolution equation on a fixed domain. The keypoint for solving the latter equation is the so-called maximal regularity approach. In order to pursue in this direction one needs to determine the precise regularity classes for the associated inhomogeneous linearized equations. This is being achieved by applying the Newton polygon method to the boundary symbol.     

Long-time simulation of a highly oscillatory Vlasov equation with an exponential integrator

We change a previous time-stepping algorithm for solving a multi-scale Vlasov–Poisson system within a Particle-In-Cell method, in order to perform accurate long-time simulations. As an exponential integrator, the new scheme allows us to use large time steps compared to the size of the oscillations in the solution.