arXiv subjects

Georg Muntingh

Publications and source records attributed to Georg Muntingh.

24 records · Page 2Linked to original sources

arXiv2013

Exact regularity of pseudo-splines

In this paper we review and refine a technique of Rioul to determine the Hölder regularity of a large class of symmetric subdivision schemes from the spectral radius of a single matrix. These schemes include those of Dubuc and Deslauriers, their dual versions, and more generally all the pseudo-spline and dual pseudo-spline schemes. We also derive various comparisons between their regularities using the Fourier transform. In particular we show that the regularity of the Dubuc-Deslauriers family increases with the size of the mask.

math.NA↗

arXiv2013

Solar induced growth of silver nanocrystals

The effect of solar irradiation on plasmonic silver nanocrystals has been investigated using Transmission Electron Microscopy and size distribution analysis, in the context of solar cell applications for light harvesting. Starting from an initial collection of spherical nanocrystals on a carbon film whose sizes are log-normally distributed, solar irradiation causes the nanocrystals to grow, with one particle reaching a diameter of 638 nm after four hours of irradiation. In addition some of the larger particles lose their spherical shape. The average nanocrystal diameter was found to grow as predicted by the Ostwald ripening model, taking into account the range of area fractions of the samples. The size distribution stays approximately log-normal and does not reach one of the steady-state size distributions predicted by the Ostwald ripening model. This might be explained by the system being in a transient state.

cond-mat.mtrl-sci↗

arXiv2012

Divided Differences of Multivariate Implicit Functions

Under general conditions, the equation $g(x^1, ..., x^q, y) = 0$ implicitly defines $y$ locally as a function of $x^1, ..., x^q$. In this article, we express divided differences of $y$ in terms of divided differences of $g$, generalizing a recent formula for the case where $y$ is univariate. The formula involves a sum over a combinatorial structure whose elements can be viewed either as polygonal partitions or as plane trees. Through this connection we prove as a corollary a formula for derivatives of $y$ in terms of derivatives of $g$.

math.NA↗

arXiv2012

Divided Differences of Implicit Functions

Under general conditions, the equation $g(x,y) = 0$ implicitly defines $y$ locally as a function of $x$. In this article, we express divided differences of $y$ in terms of bivariate divided differences of $g$, generalizing a recent result on divided differences of inverse functions.

math.NA↗

arXiv2012

Order one equations with the Painlevé property

Differential equations with the Painlevé property have been studied extensively due to their appearance in many branches of mathematics and their applicability in physics. Although a modern, differential algebraic treatment of the order one equations appeared before, the connection with the classical theory did not. Using techniques from algebraic geometry we provide the link between the classical and the modern treatment, and with the help of differential Galois theory a new classification is derived, both for characteristic 0 and p.

math.AG↗

arXiv2012

Size distributions of chemically synthesized Ag nanocrystals

Silver nanocrystals made by a chemical reduction of silver salts (AgNO$_3$) by sodium borohydride (NaBH$_4$) were studied using Transmission Electron Microscopy (TEM) and light scattering simulations. For various AgNO$_3$/NaBH$_4$ molar ratios, the size distributions of the nanocrystals were found to be approximately log-normal. In addition, a linear relation was found between the mean nanocrystal size and the molar ratio. In order to relate the size distribution of Ag nanocrystals of the various molar ratios to the scattering properties of Ag nanocrystals in solar cell devices, light scattering simulations of Ag nanocrystals in Si, SiO$_2$, SiN, and Al$_2$O$_3$ matrices were carried out using Mie Plot. These light scattering spectra for the individual nanocrystal sizes were combined into light scattering spectra for the fitted size distributions. The evolution of these scattering spectra with respect to an increasing mean nanocrystal size was then studied. From these findings, it is possible to find the molar ratio for which the corresponding nanocrystal size distribution has maximum scattering at a particular wavelength in the desired matrix.

cond-mat.mtrl-sci↗