Analytical centrifugation (AC) has recently shown great potential for the accurate determination of particle size distributions. The well‐established LUMiSizer(R) is customized by a new design allowing for higher rotor speeds, improved thermal insulation, and measurement cell assembly. The latter enables sedimentation analysis of nanoparticles (NPs) in sector‐shaped centerpieces. The measurement window of AC experiments is assessed by the Peclet (Pe) number. It is shown that at low Pe numbers (0.7 < Pe < 30), sedimentation, and diffusion can be accurately and simultaneously analyzed from the sedimentation boundaries within one experiment. Moreover, sedimentation properties can be reliably determined up to Pe numbers of 4000. The thermal characteristic throughout the sedimentation analysis is validated by measuring polystyrene particles at elevated temperatures. Moreover, the performance of the setup is demonstrated by determining the sedimentation properties of SiO2 NPs at intermediate Pe numbers in excellent agreement with results from analytical ultracentrifugation experiments. Finally, for the first time, an accurate analysis of the core–shell properties of Au NPs via AC is presented. By combining the analysis of sedimentation and diffusional properties at low Pe numbers, the shell thickness of the stabilizer cetyltrimethylammonium bromide alongside the core diameter distribution of the Au NPs is determined.
Abstract. We present a new description of the spectrum of the (spin-) Dirac operator D on lens spaces. Viewing a spin lens space L as a locally symmetric space Γ\ Spin(2m)/ Spin(2m−1) and exploiting the representation theory of the Spin groups, we obtain explicit formulas for the multiplicities of the eigenvalues of D in terms of finitely many integer operations. As a consequence, we present conditions for lens spaces to be Dirac isospectral. Tackling classic questions of spectral geometry, we prove with the tools developed that neither spin structures nor isometry classes of lens spaces are spectrally determined by giving infinite families of Dirac isospectral lens spaces. These results are complemented by examples found with the help of a computer.
Let Q be a differential operator of order ď 1 on a complex metric vector bundle E Ñ M with metric connection ∇ over a possibly noncompact Riemannian manifold M . Under very mild regularity assumptions on Q that guarantee that ∇ : ∇{2 `Q generates a holomorphic semigroup e ´zH ∇ Q in Γ L 2 pM , E q (where z runs through a complex sector which contains r0, 8q), we prove an explicit Feynman-Kac type formula for e ´tH ∇ Q , t ą 0, generalizing the standard self-adjoint theory where Q is a self-adjoint zeroth order operator. For compact M 's we combine this formula with Berezin integration to derive a Feynman-Kac type formula for an operator trace of the formwhere V, r V are of zeroth order and P is of order ď 1. These formulae are then used to obtain a probabilistic representations of the lower order terms of the equivariant Chern character (a differential graded extension of the JLO-cocycle) of a compact even-dimensional Riemannian spin manifold, which in combination with cyclic homology play a crucial role in the context of the Duistermaat-Heckmann localization formula on the loop space of such a manifold.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.