Finite Time Extinction for Nonlinear Schrödinger Equation in 1D and 2D

We consider a nonlinear Schrödinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in 1D, and that the same phenomenon is present in the case of small mass initial data in 2D.     

Behaviour of ‘free-standing’ hollow Au nanocages at finite temperatures: a BOMD study

Finite-temperature behaviour of a hollow golden cage (HGC) plays a crucialrole in its potential applications as a catalyst, drug delivery agent, contrasting agent and so on. This physico-chemical property of HGCs is not well understood so far. In that context, Born–Oppenheimer molecular dynamics (BOMD) simulations are performed on a well-known ‘free-standing’ HGC. The cluster considered in this study is the ground state Au₁₈ cluster (a cage with a diameter of about >5.5 Å). The results thus obtained are compared with the BOMD simulation results reported earlier on Au₃₂ icosahedron cage, a conformation with a diameter of nearly. The sphericity of both the clusters is studied using a shape deformation parameter as a function of time and temperature. These results are supplemented by radial distribution function at various temperatures. The observations and analysis of results indicate that, both the clusters retain an HGC conformation from 300 to 400 K, admitting structural fluxionality by the Au₁₈ cluster. Remarkably, the Au₁₈ cluster is able to maintain its hollowness and sphericity up to a high temperature of 1000 K. Underlying structural and electronic properties influencing the individualistic behaviour of cages are highlighted. Composition of the frontier molecular orbitals and the charge distribution play a crucial role in the finite-temperature behaviour of the Au cages. The conclusions are supplemented by supporting calculations on another degenerate ground state Au₁₈ hollow cage and a well-known pyramidal Au₁₈ cage at 300 and 400 K.     

Theoretical study of electronic structure of rhodium mononitride and interpretation of experimental spectra

Potential energy curves of 22 electronic states of RhN have been calculated by the complete active space second‐order perturbation theory method. The X¹Σ₀⁺ is assigned as the ground state, and the first excited state a³Π₀+ is 978 cm^?1 higher. The ¹Δ(I) and B¹Σ⁺ states are located at 9521 and 13,046 cm^?1 above the ground state, respectively. The B¹Σ⁺ state should be the excited state located 12,300 cm^?1 above the ground state in the experimental study. Moreover, two excited states, C¹Π and b³Σ⁺, are found 14,963 and 15,082 cm^?1 above the X¹Σ⁺ state, respectively. The transition C¹Π₁–X¹Σ₀⁺ may contribute to the experimentally observed bands headed at 15,071 cm^?1. There are two excited states, D¹Δ and E¹Σ⁺, situate at 20,715 and 23,145 cm^?1 above the X¹Σ⁺ state. The visible bands near 20,000 cm^?1 could be generated by the electronic transitions D¹Δ₂–a³Π₁ and E¹Σ⁺₀–X¹Σ⁺₀ because of the spin–orbit coupling effect. © 2013 Wiley Periodicals, Inc.     

129Xe NMR chemical shift in Xe@C60 calculated at experimental conditions: Essential role of the relativity,dynamics, and explicit solvent

The isotropic ¹²⁹Xe nuclear magnetic resonance (NMR) chemical shift (CS) in Xe@C₆₀ dissolved in liquid benzene was calculated by piecewise approximation to faithfully simulate the experimental conditions and to evaluate the role of different physical factors influencing the ¹²⁹Xe NMR CS. The ¹²⁹Xe shielding constant was obtained by averaging the ¹²⁹Xe nuclear magnetic shieldings calculated for snapshots obtained from the molecular dynamics trajectory of the Xe@C₆₀ system embedded in a periodic box of benzene molecules. Relativistic corrections were added at the Breit–Pauli perturbation theory (BPPT) level, included the solvent, and were dynamically averaged. It is demonstrated that the contribution of internal dynamics of the Xe@C₆₀ system represents about 8% of the total nonrelativistic NMR CS, whereas the effects of dynamical solvent add another 8%. The dynamically averaged relativistic effects contribute by 9% to the total calculated ¹²⁹Xe NMR CS. The final theoretical value of 172.7 ppm corresponds well to the experimental ¹²⁹Xe CS of 179.2 ppm and lies within the estimated errors of the model. The presented computational protocol serves as a prototype for calculations of ¹²⁹Xe NMR parameters in different Xe atom guest–host systems. © 2013 Wiley Periodicals, Inc.     

Synthesis,Structure, and Reactivity of Lewis Base Stabilized Plumbacyclopentadienylidenes

Plumbacyclopentadienylidenes, in which the lead atoms have divalent states and are coordinated by THF, pyridine and N‐heterocyclic carbene, were synthesized and characterized. The THF‐ and pyridine‐stabilized compounds can be regarded as rare examples of hypervalent 10‐X‐4 species. The equilibrium between the THF adduct and the free plumbacyclopentadienylidene was evidenced by spectroscopic analysis and theoretical calculations. The THF adduct in benzene converted into a plumbylene dimer, where one of the lead centers is coordinated by THF and the other lead atom is coordinated by a divalent lead atom, the dimer gradually decomposing into spiroplumbole. The THF adduct unexpectedly reacted with trifluoroborane and trichlorogallane to afford fluoroborole and chlorogallole, which are the first examples of non‐annulated fluoroborole and gallole, respectively.     

Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions

In this article, we are concerned with the interactions of delta shock waves with contact discontinuities for the relativistic Euler equations for Chaplygin gas by using split delta functions method. The solutions are obtained constructively and globally when the initial data consists of three piecewise constant states. The global structure and large time‐asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, the strengths of delta shock waves are computed completely. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with special initial data by letting perturbed parameter ε tends to zero. Copyright © 2014 John Wiley & Sons, Ltd.     

Existence of global weak solutions for Navier‐Stokes‐Poisson equations with quantum effect and convergence to incompressible Navier‐Stokes equations

In this paper, we consider a three dimensional quantum Navier‐Stokes‐Poisson equations. Existence of global weak solutions is obtained, and convergence toward the classical solution of the incompressible Navier‐Stokes equation is rigorously proven for well prepared initial data. Furthermore, the associated convergence rates are also obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

UiO-66 and hcp UiO-66 Catalysts Synthesized from Ionic Liquids as Linker Precursors

Using ionic liquids (ILs) as linker precursors, the well-known metal-organic framework (MOF) UiO-66 (Universitetet i Oslo) and the recently reported MOF hcp UiO-66 (hexagonal closed packed) have been successfully synthesized and characterized. The advantage of the applied novel synthesis approach is an economically and environmentally benign work-up procedure, due to the better solubility of the IL. Additionally, the reactivity of the terephthalate anions is increased compared to terephthalic acid, resulting in faster MOF formation with an increased amount of defects in the MOF structure. In order to explore to the influence of defects on the catalytic performance, the cyclisation of citronellal to isopulegol was employed as test reaction. The activity of hcp UiO-66 and fcc UiO-66 (face centered cubic) is improved compared to other MOF or zeolite based catalysts, while the selectivity is similar.