Uniqueness and stability for the Vlasov-Poisson system with spatial density in Orlicz spaces

In this paper, we establish uniqueness of the solution of the Vlasov-Poisson system with spatial density belonging to a certain class of Orlicz spaces. This extends the uniqueness result of Loeper (which holds for uniformly bounded density) and the uniqueness result of the second author. Uniqueness is a direct consequence of our main result, which provides a quantitative stability estimate for the Wasserstein distance between two weak solutions with spatial density in such Orlicz spaces, in the spirit of Dobrushin's proof of stability for mean-field PDEs. Our proofs are built on the second-order structure of the underlying characteristic system associated to the equation

Approximations of strongly continuous families of unbounded self-adjoint operators

The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations. However, it is shown that under an additional compactness assumption the spectrum does vary continuously, and a family of symmetric finite-dimensional approximations is constructed. An important feature of these approximations is that they are valid for the entire family uniformly. An application of this result to the study of plasma instabilities is illustrated.Comment: 22 pages, final version to appear in Commun. Math. Phy

XL-MS: Protein cross-linking coupled with mass spectrometry.

With the continuing trend to study larger and more complex systems, the application of protein cross-linking coupled with mass spectrometry (XL-MS) provides a varied toolkit perfectly suited to achieve these goals. By freezing the transient interactions through the formation of covalent bonds, XL-MS provides a vital insight into both the structure and organization of proteins in a wide variety of conditions. This review covers some of the established methods that underpin the field alongside the more recent developments that hold promise to further realize its potential in new directions.This work was support by the Medical Research Council – United Kingdom.This is the final version. It was first published by Elsevier at http://dx.doi.org/10.1016/j.ymeth.2015.06.01