On the recognition problem of quasi-homogeneous locally nilpotent derivations in dimension three

We give a criterion to decide if a given w-homogeneous derivation on A?k[X₁,X₂,X₃] is locally nilpotent. We deduce an algorithm which decides if a k-subalgebra of A, which is finitely generated by w-homogeneous elements, is the kernel of some locally nilpotent derivation.     

Large effect of polydispersity on defect concentrations in colloidal crystals

We compute the equilibrium concentration of stacking faults and point defects in polydisperse hard-sphere crystals. We find that, while the concentration of stacking faults remains similar to that of monodisperse hard-sphere crystals, the concentration of vacancies decreases by about a factor of 2. Most strikingly, the concentration of interstitials in the maximally polydisperse crystal may be some six orders of magnitude larger than in a monodisperse crystal. We show that this dramatic increase in interstitial concentration is due to the increased probability of finding small particles and that the small-particle tail of the particle size distribution is crucial for the interstitial concentration in a colloidal crystal.     

Modeling the phase diagram of carbon

We determined the phase diagram involving diamond, graphite, and liquid carbon using a recently developed semiempirical potential. Using accurate free-energy calculations, we computed the solid-solid and solid-liquid phase boundaries for pressures and temperatures up to 400 GPa and 12 000 K, respectively. The graphite-diamond transition line that we computed is in good agreement with experimental data, confirming the accuracy of the employed empirical potential. On the basis of the computed slope of the graphite melting line, we rule out the hotly debated liquid-liquid phase transition of carbon. Our simulations allow us to give accurate estimates of the location of the diamond melting curve and of the graphite-diamond-liquid triple point.     

The Construction of cubature rules for multivariate highly oscillatory integrals

We present an efficient approach to evaluate multivariate highly oscillatory integrals on piecewise analytic integration domains. Cubature rules are developed that only require the evaluation of the integrand and its derivatives in a limited set of points. A general method is presented to identify these points and to compute the weights of the corresponding rule.

The accuracy of the constructed rules increases with increasing frequency of the integrand. For a fixed frequency, the accuracy can be improved by incorporating more derivatives of the integrand. The results are illustrated numerically for Fourier integrals on a circle and on the unit ball, and for more general oscillators on a rectangular domain.

     

The design of Helmholtz resonator based acoustic lenses by using the symmetric Multi-Level Wave Based Method and genetic algorithms

Sonic crystals can be used as acoustic lenses in certain frequencies and the design of such systems by creating vacancies and using genetic algorithms has been proven to be an effective method. So far, rigid cylinders have been used to create such acoustic lens designs. On the other hand, it has been proven that Helmholtz resonators can be used to construct acoustic lenses with higher refraction index as compared to rigid cylinders, especially in low frequencies by utilizing their local resonances. In this paper, these two concepts are combined to design acoustic lenses that are based on Helmholtz resonators. The Multi-Level Wave Based Method is used as the prediction method. The benefits of the method in the context of design procedure are demonstrated. In addition, symmetric boundary conditions are derived for more efficient calculations. The acoustic lens designs that use Helmholtz resonators are compared with the acoustic lens designs that use rigid cylinders. It is shown that using Helmholtz resonator based sonic crystals leads to better acoustic lens designs, especially at the low frequencies where the local resonances are pronounced.     

Asymptotic expansions and fast computation of oscillatory Hilbert transforms

In this paper, we study the asymptotics and fast computation of the one-sided oscillatory Hilbert transforms of the form $$\begin{aligned} H^{+}(f(t)e^{i\omega t})(x)=-\!\!\!\!\!\!\int \nolimits _{\!\!\!0}^{\infty }e^{i\omega t}\frac{f(t)}{t-x}\,dt,\quad \omega >0,\quad x\ge 0, \end{aligned}$$ where the bar indicates the Cauchy principal value and $f$ is a real-valued function with analytic continuation in the first quadrant, except possibly a branch point of algebraic type at the origin. When $x=0$ , the integral is interpreted as a Hadamard finite-part integral, provided it is divergent. Asymptotic expansions in inverse powers of $\omega $ are derived for each fixed $x\ge 0$ , which clarify the large $\omega $ behavior of this transform. We then present efficient and affordable approaches for numerical evaluation of such oscillatory transforms. Depending on the position of $x$ , we classify our discussion into three regimes, namely, $x=\mathcal O (1)$ or $x\gg 1$ , $0<x\ll 1$ and $x=0$ . Numerical experiments show that the convergence of the proposed methods greatly improve when the frequency $\omega $ increases. Some extensions to oscillatory Hilbert transforms with Bessel oscillators are briefly discussed as well.     

Local Probe Oxidation of Self‐Assembled Monolayers: Templates for the Assembly of Functional Nanostructures

Surfaces with purposes : The electroinitiated patterning of self‐assembled monolayers enables the fabrication of a variety of complex nanostructures (see picture). The possibilities offered by the introduction of chemical selectivity through the local generation of chemically active groups and subsequent derivatization are reviewed, with a focus on progress in this area of research over the last four years.

     

Direct Bioelectrocatalysis by NADP‐Reducing Hydrogenase from Pyrococcus furiosus

The direct bioelectrocatalysis by an NAD(P)‐reducing hydrogenase is reported for the first time. In contrast to previous attempts to involve similar enzymes in bioelectrocatalysis [1–4], which were in fact unsuccessful, in our report an effective electrocatalysis by Pyrococcus furiosus hydrogenase is convincingly shown by (i) achievement of the hydrogen equilibrium potential and (ii) a high current of hydrogen oxidation (0.3 mA cm^?2 at 100 mV overpotential and at 75 °C). The latter is just a few times lower compared to enzyme electrodes based on NAD(P)‐independent hydrogenases.     

TiO2修饰La0.6Sr0.4Co0.2Fe0.8O3-δ用于中温固体氧化物燃料电池的阴极

纳米TiO2修饰的La0.6Sr0.4Co0.2Fe0.8O3-δ(LSCF)阴极被直接应用于YSZ电解质电池上. TiO2可阻止LSCF和YSZ间的化学反应,抑制SrZrO3的形成. LSCF-0.25 wt% TiO2阴极电池在0.7 V和600°C下的电流密度是LSCF阴极电池的1.6倍.电化学阻抗谱结果表明, TiO2修饰显著加快了氧离子注入电解质的过程,这可能与TiO2抑制了阴极/电解质界面处高电阻SrZrO3层的形成有关.本文为在ZrO2基电解质上使用高性能的(La,Sr)(Co,Fe)O3阴极材料提供了一种简单有效的方法.