Third order residual distribution schemes for the Navier–Stokes equations

We construct a third order multidimensional upwind residual distribution scheme for the system of the Navier–Stokes equations. The underlying approximation is obtained using standard P² Lagrange finite elements. To discretise the inviscid component of the equations, each element is divided in sub-elements over which we compute a high order residual defined as the integral of the inviscid fluxes on the boundary of the sub-element. The residuals are distributed to the nodes of each sub-element in a multi-dimensional upwind way. To obtain a discretisation of the viscous terms consistent with this multi-dimensional upwind approach, we make use of a Petrov–Galerkin analogy. The analogy allows to find a family of test functions which can be used to obtain a weak approximation of the viscous terms. The performance of this high-order method is tested on flows with high and low Reynolds number.     

Insights into unusual stability of 5‐membered‐ring endocyclic benzyl carbocations in aqueous solution

The acyclic o‐oxygen benzyl carbocation 1 , the 6‐membered‐ring endocyclic o‐oxygen benzyl carbocation 2 , and the 5‐membered‐ring endocyclic o‐oxygen benzyl carbocation 3 were used as model compounds to get insights into the general phenomenon for the unusual stability of the 5‐membered‐ring endocyclic benzyl carbocations in aqueous solution. The hydride‐ion affinities of 1 , 2 , and 3 in gas phase, acetonitrile, and DMSO were calculated and compared by the density functional theory method, and 3 isodesmic reactions were designed to confirm their thermodynamic stability. What we found is that the 5‐membered‐ring endocyclic o‐oxygen stabilizes the benzyl carbocation 3 less than the acyclic o‐oxygen stabilizes the benzyl carbocation 1 in gas phase because of ring strain and through‐bond induction. However, the high solvation energies of the 5‐membered‐ring endocyclic o‐oxygen benzyl carbocation 3 not only offset the destabilizing effects of ring strain and through‐bond induction but also make it even more stable than the acyclic o‐oxygen benzyl carbocation 1 in polar solvents like acetonitrile, DMSO, and water.     

Stability of equilibrium solutions of a double power reaction-diffusion equation with a Dirac interaction

In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction-diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed.     

Segregation of Pt at clean surfaces of (Pt, Ni)3Al

Experimental evidence for surface segregation of Pt at (1 1 1) surfaces of ternary (Pt, Ni)₃Al alloys is presented, based upon Auger electron spectroscopy, low energy ion scattering, and angle-resolved X-ray photoelectron spectroscopy. Density functional calculations in the dilute limit confirm that Pt segregation is energetically favored.     

Hydration,entropy, and energy relationships for periodate oxidations

Periodate oxidations of ethanediol and pinacol each occur in two phases; these are (1) formation and (2) decomposition of the intermediate complex. In phase (1), an increase in acidity gives . The rate of oxidation of ethanediol decreases with increasing acidity, whereas the rate of oxidation of pinacol maximizes with H₅IO₆. For both glycols, the activation energy increases and ΔS_act decreases with increasing acidity. In phase (2), the energy of activation is essentially constant with pH, whereas the rate decreases, and the entropy of activation decreases modestly as pH decreases. The latter correlates with the nonhomogeniuty of product formation. Rates for 3‐chloro‐1,2‐propanediol are also listed. Pentaerythritol forms an inactive complex with or H₅IO₆ indicating the importance of chelation in the formation of the intermediate complex. Copyright © 2007 John Wiley & Sons, Ltd.     

通过不同烷基链取代调控喹吖啶酮分子在Ag(110)表面上的自组织结构

采用低能电子衍射、扫描隧道显微镜、第一性原理密度泛函理论计算以及分子力学计算,分别对不同烷基链取代的喹吖啶酮(QA)分子在Ag(110)基底上的吸附和生长进行了研究.QA和Ag基底的相互作用主要来自分子中O原子和Ag基底的共价键,它决定了分子的取向和最优吸附位置;而烷基链决定了分子吸附层的取向,QA分子间的排列可以通过烷基链的长度来调节.由此借助调节烷基链的长度,能够可控地制备具有不同物理性质的单层分子薄膜.     

Adaptive extremal optimization by detrended fluctuation analysis

Global optimization is one of the key challenges in computational physics as several problems, e.g. protein structure prediction, the low-energy landscape of atomic clusters, detection of community structures in networks, or model-parameter fitting can be formulated as global optimization problems. Extremal optimization (EO) has become in recent years one particular, successful approach to the global optimization problem. As with almost all other global optimization approaches, EO is driven by an internal dynamics that depends crucially on one or more parameters. Recently, the existence of an optimal scheme for this internal parameter of EO was proven, so as to maximize the performance of the algorithm. However, this proof was not constructive, that is, one cannot use it to deduce the optimal parameter itself a priori. In this study we analyze the dynamics of EO for a test problem (spin glasses). Based on the results we propose an online measure of the performance of EO and a way to use this insight to reformulate the EO algorithm in order to construct optimal values of the internal parameter online without any input by the user. This approach will ultimately allow us to make EO parameter free and thus its application in general global optimization problems much more efficient.     

Exciton states and interband optical transitions in wurtzite InGaN/GaN quantum dot nanowire heterostructures

Within the framework of the effective-mass approximation, the exciton states and interband optical transitions in In_xGa_1−xN/GaN strained quantum dot (QD) nanowire heterostructures are investigated using a variational method, in which the important built-in electric field (BEF) effects, dielectric-constant mismatch and three-dimensional confinement of the electron and hole in In_xGa_1−xN QDs are considered. We find that the strong BEF gives rise to an obvious reduction of the effective band gap of QDs and leads to a remarkable electron-hole spatial separation. The BEF, QD height and radius, and dielectric mismatch effects have a significant influence on exciton binding energy, electron interband optical transitions, and the exciton oscillator strength.     

Convexity properties,moment inequalities and asymptotic exponential approximations for delay distributions in G1/G/1 systems

Pollaczek distributions pervade the class of delay distibutions in G1/G/1 systems with concave service time distributions. When the service time distribution has finite support and the delay distribution is absolutely continuous on (0, ∞), one can find a distribution with a pure exponential tail that satisfies the corresponding Wiener-Hopf integral equation except for values of the argument that belong to the support in question or to a translate thereof. Again for an exponentially decaying delay distribution, one can formulate sufficient moment inequalities which ensure the existence of asymptotic upper and lower bounds derived from M/D/1 and M/M/1 delay distributions which agree with the former in terms of the first two moments.