Publicaties
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Two-point Padé approximation to Herglotz-Riesz transforms KU Leuven
Padé approximation is the rational generalization of Hermite interpolating polynomial. On its own merits, it has earned a relevant place in the theory of constructive approximation. In this article, we will develop an exhaustive analysis of two-point Padé approximations to Herglotz-Riesz transforms. We study the convergence problem when the poles are partially preassigned. In this analysis, the Stieltjes polynomials on the unit circle naturally ...
Zeros of quasi-paraorthogonal polynomials and positive quadrature KU Leuven
In this paper we illustrate that paraorthogonality on the unit circle is the counterpart to orthogonality on when we are interested in the spectral properties. We characterize quasi-paraorthogonal polynomials on the unit circle as the analogues of the quasi-orthogonal polynomials on . We analyse the possibilities of preselecting some of its zeros, in order to build positive quadrature formulas with prefixed nodes and maximal domain of ...
Coordination-dependent kinetics in the catalysis of gold nanoclusters KU Leuven
A coordination-based kinetic model was used to explore the turnover frequency (TOF) in the oxidation of carbon monoxide on gold polyhedral nanoclusters. The Debye energy model was used to determine the Gibbs energy of bare nanoclusters. An empirical energy model derived from density functional theory (DFT) and thermodynamics was used to determine the size dependence of the Gibbs adsorption energy. A thermodynamic approach was used to model the ...
Magical mathematical formulas for nanoboxes KU Leuven
Hollow nanostructures are at the forefront of many scientific endeavors. These consist of nanoboxes, nanocages, nanoframes, and nanotubes. We examine the mathematics of atomic coordination in nanoboxes. Such structures consist of a hollow box with n shells and t outer layers. The magical formulas we derive depend on both n and t. We find that nanoboxes with t = 2 or 3, or walls with only a few layers generally have bulk coordinated atoms. The ...
Catalytic thermodynamic model for nanocluster adsorbates KU Leuven
We present an approach to study nanocatalysis using density functional theory (DFT), statistical mechanics, andthermodynamics. The analysis starts by using a coordination style approach, which is key to producing a me-soscale model free of arbitrary parameters for sizes of∼3nm < 100 nm. We apply DFT in a coordinationtype calculation of the nanocrystal binding energy and the adatom adsorption energy to give us a Hamiltonian ofthe ...
Polyhedral effects on the mass activity of platinum nanoclusters KU Leuven
We use a coordination-based kinetics model to look at the kinetics of the turnover frequency (TOF) for the oxygen reduction reaction (ORR) for platinum nanoclusters. Clusters of octahedral, cuboctahedral, cubic, and icosahedral shape and size demonstrate the validity of the coordination-based approach. The Gibbs adsorption energy is computed using an empirical energy model based on density functional theory (DFT), statistical mechanics, and ...
Magic Mathematical Relationships for Nanoclusters - Errata and Addendum KU Leuven
We correct magic formulas for body centered cubic (bcc) structures. The logical rational for this is further corroborated by calculations of the radial distribution function (RDF) for several crystal structures. We add results for truncated cubes which may be found in nature.
Magic Mathematical Relationships for Nanoclusters KU Leuven
Size and surface properties such as catalysis, optical quantum dot photoluminescense, and surface plasmon resonances depend on the coordination and chemistry of metal and semiconducting nanoclusters. Such coordination-dependent properties are quantified herein via "magic formulas" for the number of shells, n, in the cluster. We investigate face-centered cubic, body-centered cubic, simple cubic clusters, hexagonal close-packed clusters, and the ...