1,982 research outputs found
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 is studied, assuming that with and satisfying , , . 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 of a certain quadratic differential according to the
equilibrium measure on in an external field. However, when either
, or are geometrically close to ,
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 bosons produced in proton-proton collisions at TeV with the ATLAS detector
This paper presents measurements of the and 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
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