A two-step explicit P-stable method of high phase-lag order for linear periodic IVPs

In this paper, we present a nonlinear two-step explicit P-stable method of fourth algebraic order and 12th phase-lag order for solving one-dimensional second-order linear periodic initial value problems (IVPs) of ordinary differential equations. Based on a special vector arithmetic with respect to an analytic function, the method can be extended to be vector-applicable for multi-dimensional problems directly. Some numerical results are reported to illustrate the efficiency of the method.     

Effect of size of catalytically active phases in the dehydrogenation of alcohols and the challenging selective oxidation of hydrocarbons

The size of the active phase is one of the most important factors in determining the catalytic behaviour of a heterogeneous catalyst. This Feature Article focuses on the size effects in two types of reactions, i.e., the metal nanoparticle-catalysed dehydrogenation of alcohols and the metal oxide nanocluster-catalysed selective oxidation of hydrocarbons (including the selective oxidation of methane and ethane and the epoxidation of propylene). For Pd or Au nanoparticle-catalysed oxidative or non-oxidative dehydrogenation of alcohols, the size of metal nanoparticles mainly controls the catalytic activity by affecting the activation of reactants (either alcohol or O(2)). The size of oxidic molybdenum species loaded on SBA-15 determines not only the activity but also the selectivity of oxygenates in the selective oxidation of ethane; highly dispersed molybdenum species are suitable for acetaldehyde formation, while molybdenum oxide nanoparticles exhibit higher formaldehyde selectivity. Cu(II) and Fe(III) isolated on mesoporous silica are highly efficient for the selective oxidation of methane to formaldehyde, while the corresponding oxide clusters mainly catalyse the complete oxidation of methane. The lattice oxygen in iron or copper oxide clusters is responsible for the complete oxidation, while the isolated Cu(I) or Fe(II) generated during the reaction can activate molecular oxygen forming active oxygen species for the selective oxidation of methane. Highly dispersed Cu(I) and Fe(II) species also function for the epoxidation of propylene by O(2) and N(2)O, respectively. Alkali metal ions work as promoters for the epoxidation of propylene by enhancing the dispersion of copper or iron species and weakening the acidity.     

Cover picture: transition-metal-catalyzed unzipping of single-walled carbon nanotubes into narrow graphene nanoribbons at low temperature (angew. Chem. Int. Ed. 35/2011)

Narrow, smooth-edged graphene nanoribbons are needed for graphene electronics to replace the current silicon technology. In their Communication on page?8041?ff., J. Wang, F. Ding, et?al. report a smart strategy for cutting single-walled carbon nanotubes (gray) into narrow graphene nanoribbons in H(2) gas (green) with a single transition-metal atom (Cu, red) as the chemical scissors.     

The minimal cone for conic linear programming

It is known that the minimal cone for the constraint system of a conic linear programming problem is a key component in obtaining strong duality without any constraint qualification. For problems in either primal or dual form, the minimal cone can be written down explicitly in terms of the problem data. However, due to possible lack of closure, explicit expressions for the dual cone of the minimal cone cannot be obtained in general. In the particular case of semidefinite programming, an explicit expression for the dual cone of the minimal cone allows for a dual program of polynomial size that satisfies strong duality. In this paper we develop a recursive procedure to obtain the minimal cone and its dual cone. In particular, for conic problems with so-called nice cones, we obtain explicit expressions for the cones involved in the dual recursive procedure. As an example of this approach, the well-known duals that satisfy strong duality for semidefinite programming problems are obtained. The relation between this approach and a facial reduction algorithm is also discussed.     

Sudden birth of entanglement between two atoms successively passing a thermal cavity

We study the dynamics of entanglement of two initially separate atoms passing through a cavity one after another by employing the concurrence and negativity. The effects of the atomic coherence and mean photon number on the time evolution of atom-atom entanglement are examined when the field is initially in thermal field. We show that the phenomenon of sudden birth of entanglement occurs in some certain conditions and the threshold time for the creation of the entanglement can be controlled by the atomic coherence and mean photon number of the field. It is also shown that the entanglement between two atoms can be created even if the two atoms are initially in excited states.     

Optimality Conditions and Duality in Nonsmooth Semiinfinite Programming

In this article, we utilize the semiinfinite versions of Guignard's constraint qualification and Motzkin's theorem of the alternative to establish a set of Karush–Kuhn–Tucker-type necessary optimality conditions for a nonsmooth and nonconvex semiinfinite programming problem. Furthermore, we discuss some sufficient optimality conditions and duality relations for our semiinfinite programming problem.     

THE ASYMPTOTIC PRESERVING UNIFIED GAS KINETIC SCHEME FOR GRAY RADIATIVE TRANSFER EQUATIONS ON DISTORTED QUADRILATERAL MESHES

In this paper, we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes. Different from the former scheme [J. Comput. Phys. 285(2015), 265-279] on uniform meshes, in this paper, in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme (UGKS), we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations. We can prove that the scheme is asymptotic preserving, and especially for the distorted quadrilateral meshes, a nine-point scheme [SIAM J. SCI. COMPUT. 30(2008), 1341-1361] for the diffusion limit equations is obtained, which is naturally reduced to standard five-point scheme for the orthogonal meshes. The numerical examples on distorted meshes are included to validate the current approach.     

Identification between Fimbristylis miliacea (L.) Vahl and Fimbristhlis stauntonii Debeaux et Franch.by CWT-FTIR-RBFNN

Horizontal attenuation total reflection‐Fourier transform infrared spectroscopy (HATR‐FTIR) is used to measure the FTIR of Fimbristylis miliacea (L.) Vahl seed and Fimbristhlis stauntonii Debeaux et Franch. seed. In order to extrude the difference between Fimbristylis miliacea (L.) Vahl seed and Fimbristhlis stauntonii Debeaux et Franch. seed, continuous wavelet transform (CWT) is used to decompose the FTIR of Fimbristylis miliacea (L.) Vahl seed and Fimbristhlis stauntonii Debeaux et Franch. seed. Three main scales are selected as the feature extracting space in the CWT domain. According to the distribution of FTIR of Fimbristylis miliacea (L.) Vahl seed and Fimbristhlis stauntonii Debeaux et Franch. seed, three feature regions are determined at every spectra band at selected three scales in the CWT domain. Thus nine feature parameters form the feature vector. The feature vector is input to the radial basis function neural network (RBFNN) to train so as to accurately classify the Fimbristylis miliacea (L.) Vahl seed and Fimbristhlis stauntonii Debeaux et Franch. seed. 110 couples of FTIR are used to train and test the proposed method, where 60 couples are used as training samples and 50 couples are used as testing samples. Experimental results show that the accurate recognition rate between Fimbristylis miliacea (L.) Vahl seed and Fimbristhlis stauntonii Debeaux et Franch. seed is respectively 96% and 98% by using the proposed method.