24,053 research outputs found
Uranium(III) coordination chemistry and oxidation in a flexible small-cavity macrocycle
U(III) complexes of the conformationally flexible, small-cavity macrocycle trans-calix[2]benzene[2]pyrrolide (L)2–, [U(L)X] (X = O-2,6-tBu2C6H3, N(SiMe3)2), have been synthesized from [U(L)BH4] and structurally characterized. These complexes show binding of the U(III) center in the bis(arene) pocket of the macrocycle, which flexes to accommodate the increase in the steric bulk of X, resulting in long U–X bonds to the ancillary ligands. Oxidation to the cationic U(IV) complex [U(L)X][B(C6F5)4] (X = BH4) results in ligand rearrangement to bind the smaller, harder cation in the bis(pyrrolide) pocket, in a conformation that has not been previously observed for (L)2–, with X located between the two ligand arene rings
Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation
It is shown that the hodograph solutions of the dispersionless coupled KdV
(dcKdV) hierarchies describe critical and degenerate critical points of a
scalar function which obeys the Euler-Poisson-Darboux equation. Singular
sectors of each dcKdV hierarchy are found to be described by solutions of
higher genus dcKdV hierarchies. Concrete solutions exhibiting shock type
singularities are presented.Comment: 19 page
Thermodynamic phase transitions and shock singularities
We show that under rather general assumptions on the form of the entropy
function, the energy balance equation for a system in thermodynamic equilibrium
is equivalent to a set of nonlinear equations of hydrodynamic type. This set of
equations is integrable via the method of the characteristics and it provides
the equation of state for the gas. The shock wave catastrophe set identifies
the phase transition. A family of explicitly solvable models of
non-hydrodynamic type such as the classical plasma and the ideal Bose gas are
also discussed.Comment: revised version, 18 pages, 6 figure
High-energy gluon bremsstrahlung in a finite medium: harmonic oscillator versus single scattering approximation
A particle produced in a hard collision can lose energy through
bremsstrahlung. It has long been of interest to calculate the effect on
bremsstrahlung if the particle is produced inside a finite-size QCD medium such
as a quark-gluon plasma. For the case of very high-energy particles traveling
through the background of a weakly-coupled quark-gluon plasma, it is known how
to reduce this problem to an equivalent problem in non-relativistic
two-dimensional quantum mechanics. Analytic solutions, however, have always
resorted to further approximations. One is a harmonic oscillator approximation
to the corresponding quantum mechanics problem, which is appropriate for
sufficiently thick media. Another is to formally treat the particle as having
only a single significant scattering from the plasma (known as the N=1 term of
the opacity expansion), which is appropriate for sufficiently thin media. In a
broad range of intermediate cases, these two very different approximations give
surprisingly similar but slightly differing results if one works to leading
logarithmic order in the particle energy, and there has been confusion about
the range of validity of each approximation. In this paper, I sort out in
detail the parametric range of validity of these two approximations at leading
logarithmic order. For simplicity, I study the problem for small alpha_s and
large logarithms but alpha_s log << 1.Comment: 40 pages, 23 figures [Primary change since v1: addition of new
appendix reviewing transverse momentum distribution from multiple scattering
Photometric Variability in Earthshine Observations
The identification of an extrasolar planet as Earth-like will depend on the
detection of atmospheric signatures or surface non-uniformities. In this paper
we present spatially unresolved flux light curves of Earth for the purpose of
studying a prototype extrasolar terrestrial planet. Our monitoring of the
photometric variability of earthshine revealed changes of up to 23 % per hour
in the brightness of Earth's scattered light at around 600 nm, due to the
removal of specular reflection from the view of the Moon. This variability is
accompanied by reddening of the spectrum, and results from a change in surface
properties across the continental boundary between the Indian Ocean and
Africa's east coast. Our results based on earthshine monitoring indicate that
specular reflection should provide a useful tool in determining the presence of
liquid water on extrasolar planets via photometric observations.Comment: To appear in Astrobiology 9(3). 17 pages, 3 figures, 1 tabl
Comment on "c-axis Josephson tunneling in -wave superconductors''
This comment points out that the recent paper by Maki and Haas [Phys. Rev. B
{\bf 67}, 020510 (2003)] is completely wrong.Comment: 1 page, submittted to Phys. Rev.
Criteria for strong and weak random attractors
The theory of random attractors has different notions of attraction, amongst
them pullback attraction and weak attraction. We investigate necessary and
sufficient conditions for the existence of pullback attractors as well as of
weak attractors
Universal Irreversibility of Normal Quantum Diffusion
Time-reversibility measured by the deviation of the perturbed time-reversed
motion from the unperturbed one is examined for normal quantum diffusion
exhibited by four classes of quantum maps with contrastive physical nature.
Irrespective of the systems, there exist a universal minimal quantum threshold
above which the system completely loses the past memory, and the time-reversed
dynamics as well as the time-reversal characteristics asymptotically trace
universal curves independent of the details of the systems.Comment: 4 pages, 4 figure
Linearisable Mappings and the Low-Growth Criterion
We examine a family of discrete second-order systems which are integrable
through reduction to a linear system. These systems were previously identified
using the singularity confinement criterion. Here we analyse them using the
more stringent criterion of nonexponential growth of the degrees of the
iterates. We show that the linearisable mappings are characterised by a very
special degree growth. The ones linearisable by reduction to projective systems
exhibit zero growth, i.e. they behave like linear systems, while the remaining
ones (derivatives of Riccati, Gambier mapping) lead to linear growth. This
feature may well serve as a detector of integrability through linearisation.Comment: 9 pages, no figur
Controlling uranyl oxo group interactions to group 14 elements using polypyrrolic Schiff-base macrocyclic ligands
Heterodinuclear uranyl/group 14 complexes of the aryl- and anthracenyl-linked Schiff-base macrocyclic ligands LMe and LA were synthesised by reaction of UO2(H2L) with M{N(SiMe3)2}2 (M = Ge, Sn, Pb). For complexes of the anthracenyl-linked ligand (LA) the group 14 metal sits out of the N4-donor plane by up to 0.7 Å resulting in relatively short M⋯OUO distances which decrease down the group; however, the solid state structures and IR spectroscopic analyses suggest little interaction occurs between the oxo and group 14 metal. In contrast, the smaller aryl-linked ligand (LMe) enforces greater interaction between the metals; only the PbII complex was cleanly accessible although this complex was relatively unstable in the presence of HN(SiMe3)2 and some organic oxidants. In this case, the equatorial coordination of pyridine-N-oxide causes a 0.08 Å elongation of the endo UO bond and a clear interaction of the uranyl ion with the Pb(II) cation in the second donor compartment
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