An optimised molecular model for ammonia

Based on molecular dynamics (MD) computer simulations we investigate the dynamic behaviour of a model complex fluid suspension consisting of large (A) particles (the ‘solute’) immersed in a bath of smaller ‘solvent’ (B) particles. The goal is to identify the effect of systematic simplifications (coarse-graining) of the solvent on typical microscopic time correlation functions characterizing the single-particle and collective dynamics of the solute. As a reference system we employ a binary Lennard–Jones mixture of spherical particles with significant differences in particle sizes (σ_A>σ_B) and masses (m _A>m _B). We then replace the original B particles step by step by a reduced number of larger and heavier particles such that the mass and volume fraction of B particles is kept constant. At each step of coarse-graining, the intermolecular interactions between A particles are chosen such that the static A–A structure of the reference system is preserved. Our MD results indicate that coarse-graining has a profound influence on both the single-particle dynamics as reflected by the self-diffusion constant and the collective dynamics represented by the distinct part of the van Hove time correlation function. The latter holds only at intermediate packing fractions, whereas the collective dynamics turns out to be essentially insensitive to coarse-graining at high packing fractions.     

Convexity of Reduced Energy and Mass Angular Momentum Inequalities

In this paper, we extend the work in Chru?ciel and Costa (Class. Quant. Grav. 26:235013, 2009), Chru?ciel et al. (Ann. Phy. 323:2591–2613, 2008), Costa (J. Math. Theor. 43:285202, 2010), Dain (J. Diff. Geom. 79:33–67, 2008). We weaken the asymptotic conditions on the second fundamental form, and we also give an L ⁶?norm bound for the difference between general data and Extreme Kerr data or Extreme Kerr–Newman data by proving convexity of the renormalized Dirichlet energy when the target has non-positive curvature. In particular, we give the first proof of the strict mass/angular momentum/charge inequality for axisymmetric Einstein/Maxwell data which is not identical with the extreme Kerr–Newman solution.     

Global optimization based on local searches

In this paper we deal with the use of local searches within global optimization algorithms. We discuss different issues, such as the generation of new starting points, the strategies to decide whether to start a local search from a given point, and those to decide whether to keep the point or discard it from further consideration. We present how these topics have been faced in the existing literature and express our opinion on the relative merits of different choices.     

The accelerated development of an optimized synthesis of 1,2,4-oxadiazoles: application of microwave irradiation and statistical design of experiments

Herein, we report the development of an optimized microwave-assisted synthesis of 1,2,4-oxadiazoles. The chemistry development process was significantly accelerated by employing a statistical software package (MODDE 6.0™) to guide in the optimization of the reaction conditions. The resulting optimized reaction conditions were then utilized in the synthesis of a focused library of 1,2,4-oxadiazoles.     

Direct observation of the evolving metal–support interaction of individual cobalt nanoparticles at the titania and silica interface

Understanding the metal–support interaction (MSI) is crucial to comprehend how the catalyst support affects performance and whether this interaction can be exploited in order to design new catalysts with enhanced properties. Spatially resolved soft X-ray absorption spectroscopy (XAS) in combination with Atomic Force Microscopy (AFM) and Scanning Helium Ion-Milling Microscopy (SHIM) has been applied to visualise and characterise the behaviour of individual cobalt nanoparticles (CoNPs) supported on two-dimensional substrates (SiO_xSi(100) (x < 2) and rutile TiO₂(110)) after undergoing reduction–oxidation–reduction (ROR). The behaviour of the Co species is observed to be strongly dependent on the type of support. For SiO_xSi a weaker MSI between Co and the support allows a complete reduction of CoNPs although they migrate and agglomerate. In contrast, a stronger MSI of CoNPs on TiO₂ leads to only a partial reduction under H₂ at 773 K (as observed from Co L₃-edge XAS data) due to enhanced TiO₂ binding of surface-exposed cobalt. SHIM data revealed that the interaction of the CoNPs is so strong on TiO₂, that they are seen to spread at and below the surface and even to migrate up to ∼40 nm away. These results allow us to better understand deactivation phenomena and additionally demonstrate a new understanding concerning the nature of the MSI for Co/TiO₂ and suggest that there is scope for careful control of the post-synthetic thermal treatment for the tuning of this interaction and ultimately the catalytic performance.

Understanding the metal–support interaction (MSI) is crucial to comprehend how the catalyst support affects performance and whether this interaction can be exploited in order to design new catalysts with enhanced properties.     

Proof of the positive mass theorem. II

The positive mass theorem states that for a nontrivial isolated physical system, the total energy, which includes contributions from both matter and gravitation is positive. This assertion was demonstrated in our previous paper in the important case when the space-time admits a maximal slice. Here this assumption is removed and the general theorem is demonstrated. Abstracts of the results of this paper appeared in [11] and [13].     

Computation and analysis of the dynamic structure factor S(k, ω) for small wave vectors

Molecular dynamics (MD) calculations have been performed for the Lennard-Jones (12-6) potential function using 2048 particles. Using conventional parameters the results may be compared with those for liquid argon.

The dynamic structure factor S(k, ω) has been determined both by Fourier inversion of the intermediate scattering function F(k, t) and from the longitudinal current-current correlation function C _∥(k, t). Particular attention was paid to the recurrence time of the system. The results for S(k, ω) by the two methods agree within 5 per cent for the whole region of small k-vectors considered. Double Fourier inversion of the van Hove function G(r, t) led to insufficiently accurate results for these small k-values. In view of the present data, the MD-results of Levesque et al. [1] for S(k, ω) have only a qualitative character. These latter data appear to contain truncation errors due to incomplete Fourier transformations.

Using a hydrodynamic assumption for F(k, t) we were able to extract the transport coefficients, the velocity of sound and the ratio of the specific heats in the limit of large wave lengths or small k. The velocity of sound was obtained by exploiting the MD generated anomalous dispersion curve of sound waves. Anomalous dispersion was found to set in for kσ ～ 0·25. A sound speed of 880 ms^-1 has been determined which is in excellent agreement with experimental values for liquid argon. The total error for the MD value amounts to about 5 per cent. In contrast, the ratio of the specific heats γ and the transport coefficients D _T and Γ (thermal diffusivity and sound attenuation) were determinable only with an accuracy of 15 per cent due to the need for larger extrapolations. Nevertheless, we found D _T, Γ and γ in agreement with experimental values within 5-10 per cent.     

Higher moments of convolutions

We study higher moments of convolutions of the characteristic function of a set, which generalize a classical notion of the additive energy. Such quantities appear in many problems of additive combinatorics as well as in number theory. In our investigation we use different approaches including basic combinatorics, Fourier analysis and eigenvalues method to establish basic properties of higher energies. We provide also a sequence of applications of higher energies additive combinatorics.     

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