Stereoselective electrocatalytic transformation of arylidene- or alkylidenemalononitriles and malonate into alkyl (1R,5R,6R)* 6-substituted 5-cyano-4,4-dialkoxy-2-oxo-3-azabicyclo[3.1.0]hexane-1-carboxylates

Electrolysis of arylidene- or alkylidenemalononitriles and malonate in alcohol in an undivided cell in the presence of sodium halide as mediator results in the stereoselective formation of alkyl (1R,5R,6R)* 6-substituted 5-cyano-4,4-dialkoxy-2-oxo-3-azabicyclo[3.1.0]hexan-1-carboxylates in 50-70% yields.     

Back-and-forth shooting method for solving two-point boundary-value problems

The paper proposes a special iterative method for a nonlinear TPBVP of the form (t)=f(t, x(t),p(t)), (t)=g(t, x(t),p(t)), subject toh(x(0),p(0))=0,e(x(T),p(T))=0. Certain stability properties of the above differential equations are taken into consideration in the method, so that the integration directions associated with these equations respectively are opposite to each other, in contrast with the conventional shooting methods. Via an embedding and a Riccati-type transformation, the TPBVP is reduced to consecutive initial-value problems of ordinary differential equations. A preliminary numerical test is given by a simple example originating in an optimal control problem.     

一个1+1维Boussinesq系统的Darboux变换及其应用

主要考虑1+1维Boussinesq系统的一个Darboux变换,反复利用该Darboux变换,可以从该系统的一个已知解出发,通过代数运算和求导运算得到系统的新解.     

Advances in Electrochemical Decarboxylative Transformation Reactions

Owing to their non-toxic, stable, inexpensive properties, carboxylic acids are considered as environmentally benign alternatives as coupling partners in various organic transformations. Electrochemical mediated decarboxylation of carboxylic acid has emerged as a new and efficient methodology for the construction of carbon-carbon or carbon-heteroatom bonds. Compared with transition-metal catalysis and photoredox catalysis, electro-organic decarboxylative transformations are considered as a green and sustainable protocol due to the absence of chemical oxidants and strong bases. Further, it exhibits good tolerance with various functional groups. In this Minireview, we summarize the recent advances and discoveries on the electrochemical decarboxylative transformations on C−C and C−heteroatoms bond formations.     

High-order rogue waves for the Hirota equation

The Hirota equation is better than the nonlinear Schrödinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux transformation. Several types of this kind of solutions are classified by their structures.     

MgCu metallic glass

We generate an amorphous MgCu model using the rapid solidification of the melt through a first-principles molecular dynamics approach within a generalised gradient approximation and reveal, for the first time, its structural features and mechanical properties in details. The liquid and glassy MgCu are found to acquire slightly distinct local structures. Yet in both forms of MgCu, most Cu atoms have a tendency to form the ideal and defective icosahedrons while Mg atoms are arranged in complex configurations. The mean coordination number of Cu and Mg at 300 K is 11.31 and 13.73, respectively. The short-range order of MgCu glass is projected to be different than the known crystalline MgCu and Mg₂Cu phases. The mechanical properties of MgCu glass and the CsCl-type MgCu crystal are computed and compared. On the basis of the enthalpy analyses, a possible pressure-induced crystallisation of the MgCu glass into a CsCl-type structure is proposed to occur at around 11 GPa.     

Phase field approach with anisotropic interface energy and interface stresses: Large strain formulation

A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the “usual” manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the deformed configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the Herring (thermodynamic) torque is imparting an unphysical angular momentum to the system. In addition, this non-symmetric stress implies a violation of the principle of material objectivity. These problems in the formulation can be resolved by insisting that the gradient energy is an isotropic function of the gradient of the order parameters in the deformed configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the undeformed configuration. We find that for a propagating nonequilibrium interface, the structural part of the interfacial Cauchy stress is symmetric and reduces to a biaxial tension with the magnitude equal to the temperature- and orientation-dependent interface energy. Ginzburg–Landau equations for the evolution of the order parameters and temperature evolution equation, as well as the boundary conditions for the order parameters are derived. Small strain simplifications are presented. Remarkably, this anisotropy yields a first order correction in the Ginzburg–Landau equation for small strains, which has been neglected in prior works. The next strain-related term is third order. For concreteness, specific orientation dependencies of the gradient energy coefficients are examined, using published molecular dynamics studies of cubic crystals. In order to consider a fully specified system, a typical sixth order polynomial phase field model is considered. Analytical solutions for the propagating interface and critical nucleus are found, accounting for the influence of the anisotropic gradient energy and elucidating the distribution of components of interface stresses. The orientation-dependence of the nonequilibrium interface energy is first suitably defined and explicitly determined analytically, and the associated width is also found. The developed formalism is applicable to melting/solidification and crystal-amorphous transformation and can be generalized for martensitic and diffusive phase transformations, twinning, fracture, and grain growth, for which interface energy depends on interface orientation of crystals from either side.     

Face-centred cubic to body-centred cubic phase transformation under [1 0 0] tensile loading

Molecular dynamics simulation was used to verify a speculation of the existence of a certain face-centred cubic (FCC) to body-centred cubic (BCC) phase transformation pathway. Four FCC metals, Ni, Cu, Au and Ag, were stretched along the [1?0?0] direction at various strain rates and temperatures. Under high strain rate and low temperature, and beyond the elastic limit, the bifurcation of the FCC phase occurred with sudden contraction along one lateral direction and expansion along the other lateral direction. When the lattice constant along the expansion direction converged with that of the stretched direction, the FCC phase transformed into an unstressed BCC phase. By reducing the strain rate or increasing the temperature, dislocation or ‘momentum-induced melting’ mechanisms began to control the plastic deformation of the FCC metals, respectively.     

Efficient Synthesis of Cyclic Block Copolymers by Rotaxane Protocol by Linear/Cyclic Topology Transformation

High‐yielding synthesis of cyclic block copolymer (CBC) using the rotaxane protocol by linear‐cyclic polymer topology transformation was first demonstrated. Initial complexation of OH‐terminated sec‐ammonium salt and a crown ether was followed by the successive living ring‐opening polymerizations of two lactones to a linear block copolymer having a rotaxane structure by the final capping of the propagation end. CBC was obtained in a high yield by an exploitation of the mechanical linkage through the translational movement of the rotaxane component to transform polymer structure from linear to cyclic. Furthermore, the change of the polymer topology was translated into a macroscopic change in crystallinity of the block copolymer.