Physical state of 2-methylbutane-1,2,3,4-tetraol in pure and internally mixed aerosols

2-Methylbutane-1,2,3,4-tetraol (hereafter named tetraol) is an important oxidation product of isoprene and can be considered as a marker compound for isoprene-derived secondary organic aerosols (SOAs). Little is known about this compound's physical phase state, although some field observations indicate that isoprene-derived secondary organic aerosols in the tropics tend to be in a liquid rather than a solid state. To gain more knowledge about the possible phase states of tetraol and of tetraol-containing SOA particles, we synthesized tetraol as racemates as well as enantiomerically enriched materials. Subsequently the obtained highly viscous dry liquids were investigated calorimetrically by differential scanning calorimetry revealing subambient glass transition temperatures Tg. We also show that only the diastereomeric isomers differ in their Tg values, albeit only by a few kelvin. We derive the phase diagram of water–tetraol mixtures over the whole tropospheric temperature and humidity range from determining glass transition temperatures and ice melting temperatures of aqueous tetraol mixtures. We also investigated how water diffuses into a sample of dry tetraol. We show that upon water uptake two homogeneous liquid domains form that are separated by a sharp, locally constrained concentration gradient. Finally, we measured the glass transition temperatures of mixtures of tetraol and an important oxidation product of α-pinene-derived SOA: 3-methylbutane-1,2,3-tricarboxylic acid (3-MBTCA). Overall, our results imply a liquid-like state of isoprene-derived SOA particles in the lower troposphere at moderate to high relative humidity (RH), but presumably a semisolid or even glassy state at upper tropospheric conditions, particularly at low relative humidity, thus providing experimental support for recent modeling calculations.</p

The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials

We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansatz defines a new class of generalised Hermite polynomials which are explicit functions of the coupling parameter and tend to ordinary Hermite polynomials in the limit of vanishing coupling constant. The polynomials become orthogonal as parts of the eigenvectors of a Hermitian matrix and, consequently, the exponential part of the solution can not be excluded. We have conjectured the general structure of the solution, both with respect to the quantum number and the order of the expansion. An explicit proof is given for the three leading orders of the asymptotical solution and we sketch a proof for the asymptotical convergence of eigenvectors with respect to norm. From a more practical point of view, we can estimate the required effort for improving the known solution and the accuracy of the eigenvectors. The applied method can be generalised in order to accommodate several variables.Comment: 18 pages, ReVTeX, the final version with rather general expression

Strong asymptotics for Jacobi polynomials with varying nonstandard parameters

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$\lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B,$$ with $A$ and $B$ satisfying $A > -1$, $B>-1$, $A+B < -1$. The asymptotic analysis is based on the non-Hermitian orthogonality of these polynomials, and uses the Deift/Zhou steepest descent analysis for matrix Riemann-Hilbert problems. As a corollary, asymptotic zero behavior is derived. We show that in a generic case the zeros distribute on the set of critical trajectories $\Gamma$ of a certain quadratic differential according to the equilibrium measure on $\Gamma$ in an external field. However, when either $\alpha_n$, $\beta_n$ or $\alpha_n+\beta_n$ are geometrically close to $\Z$, part of the zeros accumulate along a different trajectory of the same quadratic differential.Comment: 31 pages, 12 figures. Some references added. To appear in Journal D'Analyse Mathematiqu

Canonical moments and random spectral measures

We study some connections between the random moment problem and the random matrix theory. A uniform draw in a space of moments can be lifted into the spectral probability measure of the pair (A,e) where A is a random matrix from a classical ensemble and e is a fixed unit vector. This random measure is a weighted sampling among the eigenvalues of A. We also study the large deviations properties of this random measure when the dimension of the matrix grows. The rate function for these large deviations involves the reversed Kullback information.Comment: 32 pages. Revised version accepted for publication in Journal of Theoretical Probabilit

Measurement of the cross-section and charge asymmetry of WW bosons produced in proton-proton collisions at s=8\sqrt{s}=8 TeV with the ATLAS detector

This paper presents measurements of the $W^+ \rightarrow \mu^+\nu$ and $W^- \rightarrow \mu^-\nu$ cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables, submitted to EPJC. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13