New results on a classical operator

It is remarkable how the classical Volterra integral operator, which was one of the first operators which attracted mathematicians' attention, is still worth of being studied. In this essentially survey work, by collecting some of the very recent results related to the Volterra operator, we show that there are new (and not so new) concepts that are becoming known only at the present days. Discovering whether the Volterra operator satisfies or not a given operator property leads to new methods and ideas that are useful in the setting of Concrete Operator Theory as well as the one of General Operator Theory. In particular, a wide variety of techniques like summability kernels, theory of entire functions, Gaussian cylindrical measures, approximation theory, Laguerre and Legendre polynomials are needed to analyze different properties of the Volterra operator. We also include a characterization of the commutator of the Volterra operator acting on L-P[0, 1], 1

One-dimensional particle simulation of the filamentation instability: Electrostatic field driven by the magnetic pressure gradient force

Two counterpropagating cool and equally dense electron beams are modeled with particle-in-cell simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasiplanar filament boundary. It is confirmed that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away, limiting the peak density. The confining time-averaged total potential permits an overlap of current filaments with an opposite flow direction.

SERS enhancement by aggregated Au colloids: effect of particle size

Aggregated Au colloids have been widely used as SERS enhancing media for many years but to date there has been no systematic investigation of the effect of the particle size on the enhancements given by simple aggregated Au colloid solutions. Previous systematic studies on isolated particles in solution or multiple particles deposited onto surfaces reported widely different optimum particle sizes for the same excitation wavelength and also disagreed on the extent to which surface plasmon absorption spectra were a good predictor of enhancement factors. In this work the spectroscopic properties of a range of samples of monodisperse Au colloids with diameters ranging from 21 to 146 nm have been investigated in solution. The UV/visible absorption spectra of the colloids show complex changes as a function of aggregating salt (MgSO4) concentration which diminish when the colloid is fully aggregated. Under these conditions, the relative SERS enhancements provided by the variously sized colloids vary very significantly across the size range. The largest signals in the raw data are observed for 46 nm colloids but correction for the total surface area available to generate enhancement shows that particles with 74 nm diameter give the largest enhancement per unit surface area. The observed enhancements do not correlate with absorbance at the excitation wavelength but the large differences between differently sized colloids demonstrate that even in the randomly aggregated particle assemblies studied here, inhomogeneous broadening does not mask the underlying changes due to differences in particle diameter.