1,250 research outputs found
Palladacycles: Effective Catalysts for a Multicomponent Reaction with Allylpalladium(II)-Intermediates
Palladium(II) complexes with an auxiliary bidentate ligand featuring one C-Pd bond and a Pd-N-donor bond (palladacycles) have been shown to afford improved yields of homoallylic amines from a three-component coupling of boronic acids, allenes and imines in comparison to the yields of homoallylic amines achieved with the originally reported catalyst (Pd(OAc)2/P(t-Bu)3), thus extending the scope of the reaction. 31P NMR monitoring studies indicate that distinct intermediates featuring Pd-P bonds originate in the reactions catalyzed by either Pd(OAc)2/P(t-Bu)3 or the pallada(II)cycle/P(t-Bu)3 systems, suggesting that the role of the pallada(II)cycles is more complex than just precatalysts. The importance of an additional phosphine ligand in the reactions catalyzed the pallada(II)cycles was established, and its role in the catalytic cycle has been proposed. Insights into the nature of the reactive intermediates that limit the performance of the originally reported catalytic systems has been gained
Mechanical properties of Pt monatomic chains
The mechanical properties of platinum monatomic chains were investigated by
simultaneous measurement of an effective stiffness and the conductance using
our newly developed mechanically controllable break junction (MCBJ) technique
with a tuning fork as a force sensor. When stretching a monatomic contact
(two-atom chain), the stiffness and conductance increases at the early stage of
stretching and then decreases just before breaking, which is attributed to a
transition of the chain configuration and bond weakening. A statistical
analysis was made to investigate the mechanical properties of monatomic chains.
The average stiffness shows minima at the peak positions of the
length-histogram. From this result we conclude that the peaks in the
length-histogram are a measure of the number of atoms in the chains, and that
the chains break from a strained state. Additionally, we find that the smaller
the initial stiffness of the chain is, the longer the chain becomes. This shows
that softer chains can be stretched longer.Comment: 6 pages, 5 figure
Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral
In these lectures three different methods of computing the asymptotic
expansion of a Hermitian matrix integral is presented. The first one is a
combinatorial method using Feynman diagrams. This leads us to the generating
function of the reciprocal of the order of the automorphism group of a tiling
of a Riemann surface. The second method is based on the classical analysis of
orthogonal polynomials. A rigorous asymptotic method is established, and a
special case of the matrix integral is computed in terms of the Riemann
-function. The third method is derived from a formula for the
-function solution to the KP equations. This method leads us to a new
class of solutions of the KP equations that are
\emph{transcendental}, in the sense that they cannot be obtained by the
celebrated Krichever construction and its generalizations based on algebraic
geometry of vector bundles on Riemann surfaces. In each case a mathematically
rigorous way of dealing with asymptotic series in an infinite number of
variables is established
Final Report for: "Bis-pi-allylpalladium Complexes in Catalysis of Multicomponent Reactions"
The research project involved the development of new and functionally improved Pd(II) catalyst for a three-component reaction of boronic acids, allenes and imines to afford homoallylic amines that are useful in synthesis of biologically active heterocycles. Furthermore, insights into the reaction mechanism and the structure and reactivity of the catalytically active intermediates involved in this process were sought. As a result of this work, a new type of Pd-catalysts possessing an auxiliary ligand attached to the Pd center via a C-Pd and N-Pd bonds were identified, and found to be more active than the traditional catalysts derived from Pd(OAc)2. The new catalysts provided an access to a broader range of homoallylic amine products. Although the final unequivocal evidence regarding the structure of the Pd(II) complex involved in the nucleophilic transfer of the allyl fragment from the palladium center to the imine could not be obtained, mechanistic insights into the events that are detrimental to the activity of the originally reported Pd(OAc)2-based catalytic systems were uncovered
Three Dimensional Structure and Energy Balance of a Coronal Mass Ejection
The Ultraviolet Coronagraph Spectrometer (UVCS) observed Doppler shifted
material of a partial Halo Coronal Mass Ejection (CME) on December 13 2001. The
observed ratio of [O V]/O V] is a reliable density diagnostic important for
assessing the state of the plasma. Earlier UVCS observations of CMEs found
evidence that the ejected plasma is heated long after the eruption. We have
investigated the heating rates, which represent a significant fraction of the
CME energy budget. The parameterized heating and radiative and adiabatic
cooling have been used to evaluate the temperature evolution of the CME
material with a time dependent ionization state model. The functional form of a
flux rope model for interplanetary magnetic clouds was also used to
parameterize the heating. We find that continuous heating is required to match
the UVCS observations. To match the O VI-bright knots, a higher heating rate is
required such that the heating energy is greater than the kinetic energy. The
temperatures for the knots bright in Ly and C III emission indicate
that smaller heating rates are required for those regions. In the context of
the flux rope model, about 75% of the magnetic energy must go into heat in
order to match the O VI observations. We derive tighter constraints on the
heating than earlier analyses, and we show that thermal conduction with the
Spitzer conductivity is not sufficient to account for the heating at large
heights.Comment: 40 pages, 16 figures, accepted for publication in ApJ For associated
mpeg file, please see https://www.cora.nwra.com/~jylee/mpg/f5.mp
Functional representation of the Ablowitz-Ladik hierarchy
The Ablowitz-Ladik hierarchy (ALH) is considered in the framework of the
inverse scattering approach. After establishing the structure of solutions of
the auxiliary linear problems, the ALH, which has been originally introduced as
an infinite system of difference-differential equations is presented as a
finite system of difference-functional equations. The representation obtained,
when rewritten in terms of Hirota's bilinear formalism, is used to demonstrate
relations between the ALH and some other integrable systems, the
Kadomtsev-Petviashvili hierarchy in particular.Comment: 15 pages, LaTe
The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies
We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal
structures in space plasmas, based on in-situ spacecraft measurements. The
underlying theory is the GS equation that describes two-dimensional
magnetohydrostatic equilibrium as widely applied in fusion plasmas. The
geometry is such that the arbitrary cross section of the torus has rotational
symmetry about the rotation axis , with a major radius . The magnetic
field configuration is thus determined by a scalar flux function and a
functional that is a single-variable function of . The algorithm is
implemented through a two-step approach: i) a trial-and-error process by
minimizing the residue of the functional to determine an optimal
axis orientation, and ii) for the chosen , a minimization process
resulting in the range of . Benchmark studies of known analytic solutions
to the toroidal GS equation with noise additions are presented to illustrate
the two-step procedures and to demonstrate the performance of the numerical GS
solver, separately. For the cases presented, the errors in and are
9 and 22\%, respectively, and the relative percent error in the
numerical GS solutions is less than 10\%. We also make public the computer
codes for these implementations and benchmark studies.Comment: submitted to Sol. Phys. late Dec 2016; under review; code will be
made public once review is ove
Numerical Investigation of a Coronal Mass Ejection from an Anemone Active Region: Reconnection and Deflection of the 2005 August 22 Eruption
We present a numerical investigation of the coronal evolution of a coronal
mass ejection (CME) on 2005 August 22 using a 3-D thermodynamics
magnetohydrodynamic model, the SWMF. The source region of the eruption was
anemone active region (AR) 10798, which emerged inside a coronal hole. We
validate our modeled corona by producing synthetic extreme ultraviolet (EUV)
images, which we compare to EIT images. We initiate the CME with an
out-of-equilibrium flux rope with an orientation and chirality chosen in
agreement with observations of a H-alpha filament. During the eruption, one
footpoint of the flux rope reconnects with streamer magnetic field lines and
with open field lines from the adjacent coronal hole. It yields an eruption
which has a mix of closed and open twisted field lines due to interchange
reconnection and only one footpoint line-tied to the source region. Even with
the large-scale reconnection, we find no evidence of strong rotation of the CME
as it propagates. We study the CME deflection and find that the effect of the
Lorentz force is a deflection of the CME by about 3 deg/Rsun towards the East
during the first 30 minutes of the propagation. We also produce coronagraphic
and EUV images of the CME, which we compare with real images, identifying a
dimming region associated with the reconnection process. We discuss the
implication of our results for the arrival at Earth of CMEs originating from
the limb and for models to explain the presence of open field lines in magnetic
clouds.Comment: 14 pages, 8 Figures, accepted to Astrophysical Journa
From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators
In this letter,we present our conjecture on the connection between the
Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula
connects these two tau-functions by means of the group element. An
important feature of this group element is its simplicity: this is a group
element of the Virasoro subalgebra of . If proved, this conjecture
would allow to derive the Virasoro constraints for the Hurwitz tau-function,
which remain unknown in spite of existence of several matrix model
representations, as well as to give an integrable operator description of the
Kontsevich--Witten tau-function.Comment: 13 page
Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy
Pairs of matrices whose commutator differ from the identity by a
matrix of rank are used to construct bispectral differential operators with
matrix coefficients satisfying the Lax equations of the Matrix KP
hierarchy. Moreover, the bispectral involution on these operators has dynamical
significance for the spin Calogero particles system whose phase space such
pairs represent. In the case , this reproduces well-known results of
Wilson and others from the 1990's relating (spinless) Calogero-Moser systems to
the bispectrality of (scalar) differential operators. This new class of pairs
of bispectral matrix differential operators is different than
those previously studied in that acts from the left, but from the
right on a common eigenmatrix.Comment: 16 page
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