New methods for calculating \alpha BB-type underestimators

Most branch-and-bound algorithms in global optimization depend on convex underestimators to calculate lower bounds of a minimization objective function. The $\alpha $ BB methodology produces such underestimators for sufficiently smooth functions by analyzing interval Hessian approximations. Several methods to rigorously determine the $\alpha $ BB parameters have been proposed, varying in tightness and computational complexity. We present new polynomial-time methods and compare their properties to existing approaches. The new methods are based on classical eigenvalue bounds from linear algebra and a more recent result on interval matrices. We show how parameters can be optimized with respect to the average underestimation error, in addition to the maximum error commonly used in $\alpha $ BB methods. Numerical comparisons are made, based on test functions and a set of randomly generated interval Hessians. The paper shows the relative strengths of the methods, and proves exact results where one method dominates another.     

Non-branching geodesics and optimal maps in strong CD(K,\infty )-spaces

We prove that in metric measure spaces where the entropy functional is \(K\) -convex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures with finite second moments lives on a non-branching set of geodesics. As a corollary we obtain that in these spaces there exists only one optimal transport plan between any two absolutely continuous measures with finite second moments and this plan is given by a map. The results are applicable in metric measure spaces having Riemannian Ricci curvature bounded below, and in particular they hold also for Gromov-Hausdorff limits of Riemannian manifolds with Ricci curvature bounded from below by some constant.     

Models for thermal dissociation of silane on a polysilicon surface

Simple models for the thermally activated dissociation reaction of silane and silicon growth on a polycrystalline silicon surface are presented. The models are fitted to recent experimental molecular beam scattering data for the low-pressure reactive sticking coefficient. Thermally activated few-step models fit the data reasonably well, and thus, we are able to explain the temperature and pressure dependencies of the observed deposition rate.     

Templated in-situ synthesis of gold nanoclusters conjugated to drug target bacterial enoyl-ACP reductase,and their application to the detection of mercury ions using a test stripe

Fluorescent gold nanoclusters (AuNCs) were synthesized using a drug target bacterial enoyl-ACP reductase (FabI) as a template. The physical and chemical properties of the AuNCs were studied by UV-vis absorption, fluorescence, X-ray photoelectron spectroscopy and TEM. The AuNCs-FabI conjugate was prepared by in situ reduction of tetrachloroaurate in the presence of FabI. The conjugated particles were loaded onto nylon membranes by taking advantage of the electrostatic interaction between the negatively charged AuNCs@FabI and the nylon film which is positively charged at pH 7.4. This results in the formation of a test stripe with sensor spots that can be used to detect Hg(II) ion in the 1 nM to 10 μM concentration range. The test stripes are simple, convenient, selective, sensitive, and can be quickly read out with bare eyes after illumination with a UV lamp.

Fluctuating lattice-Boltzmann model for complex fluids

We develop and test numerically a lattice-Boltzmann (LB) model for nonideal fluids that incorporates thermal fluctuations. The fluid model is a momentum-conserving thermostat, for which we demonstrate how the temperature can be made equal at all length scales present in the system by having noise both locally in the stress tensor and by shaking the whole system in accord with the local temperature. The validity of the model is extended to a broad range of sound velocities. Our model features a consistent coupling scheme between the fluid and solid molecular dynamics objects, allowing us to use the LB fluid as a heat bath for solutes evolving in time without external Langevin noise added to the solute. This property expands the applicability of LB models to dense, strongly correlated systems with thermal fluctuations and potentially nonideal equations of state. Tests on the fluid itself and on static and dynamic properties of a coarse-grained polymer chain under strong hydrodynamic interactions are used to benchmark the model. The model produces results for single-chain diffusion that are in quantitative agreement with theory.     

Hydrophobicity within the three-dimensional Mercedes-Benz model: potential of mean force

We use the three-dimensional Mercedes-Benz model for water and Monte Carlo simulations to study the structure and thermodynamics of the hydrophobic interaction. Radial distribution functions are used to classify different cases of the interaction, namely, contact configurations, solvent separated configurations, and desolvation configurations. The temperature dependence of these cases is shown to be in qualitative agreement with atomistic models of water. In particular, while the energy for the formation of contact configurations is favored by entropy, its strengthening with increasing temperature is accounted for by enthalpy. This is consistent with our simulated heat capacity. An important feature of the model is that it can be used to account for well-converged thermodynamics quantities, e.g., the heat capacity of transfer. Microscopic mechanisms for the temperature dependence of the hydrophobic interaction are discussed at the molecular level based on the conceptual simplicity of the model.     

HXeOBr in a xenon matrix

We report on a new noble-gas molecule HXeOBr prepared in a low-temperature xenon matrix from the HBr and N(2)O precursors by UV photolysis and thermal annealing. This molecule is assigned with the help of deuteration experiments and ab initio calculations including anharmonic methods. The H-Xe stretching frequency of HXeOBr is observed at 1634 cm(-1), which is larger by 56 cm(-1) than the frequency of HXeOH identified previously. The experiments show a higher thermal stability of HXeOBr molecules in a xenon matrix compared to HXeOH.     

Nucleation, Growth, and Scaling in Slow Combustion

We study the nucleation and growth of flame fronts in slow combustion. This is modeled by a set of reaction-diffusion equations for the temperature field, coupled to a background of reactants and augmented by a term describing random temperature fluctuations for ignition. We establish connections between this model and the classical theories of nucleation and growth of droplets from a metastable phase. Our results are in good agreement with theoretical predictions.     

Preparation of dimethoxyborane and analysis by Fourier transform infrared spectroscopy

Dimethoxyborane was prepared by the reaction of trimethoxyboroxine, sodium borohydride and trimethyl borate in diethylene glycol dimethyl ether solvent at 70°C under atmospheric pressure followed by distillation to increase the purity and analyzed in liquid phase by FT-IR. The concentration of dimethoxyborane was identified by hydrolysis with water, which yields boric acid, methanol and hydrogen, whereas the generated hydrogen was analyzed by the mass detector of a volumetric flow apparatus. The FT-IR absorbance peak area showed a linear dependence on dimethoxyborane concentration in the wavenumber range 873 to 950 cm⁻¹ for samples with dimethoxyborane concentrations 0 to 6.2 wt% in trimethyl borate. Data fitting using the least square method gave an R ² value of 97%.