1,004 research outputs found
A numerical study of two-photon ionization of helium using the Pyprop framework
Few-photon induced breakup of helium is studied using a newly developed ab
initio numerical framework for solving the six-dimensional time-dependent
Schroedinger equation. We present details of the method and calculate
(generalized) cross sections for the process of two-photon nonsequential
(direct) double ionization at photon energies ranging from 39.4 to 54.4 eV, a
process that has been very much debated in recent years and is not yet fully
understood. In particular, we have studied the convergence property of the
total cross section in the vicinity of the upper threshold (54.4 eV), versus
the pulse duration of the applied laser field. We find that the cross section
exhibits an increasing trend near the threshold, as has also been observed by
others, and show that this rise cannot solely be attributed to an unintended
inclusion of the sequential two-photon double ionization process, caused by the
bandwidth of the applied field.Comment: 7 pages, 3 figure
Functions preserving nonnegativity of matrices
The main goal of this work is to determine which entire functions preserve
nonnegativity of matrices of a fixed order -- i.e., to characterize entire
functions with the property that is entrywise nonnegative for every
entrywise nonnegative matrix of size . Towards this goal, we
present a complete characterization of functions preserving nonnegativity of
(block) upper-triangular matrices and those preserving nonnegativity of
circulant matrices. We also derive necessary conditions and sufficient
conditions for entire functions that preserve nonnegativity of symmetric
matrices. We also show that some of these latter conditions characterize the
even or odd functions that preserve nonnegativity of symmetric matrices.Comment: 20 pages; expanded and corrected to reflect referees' remarks; to
appear in SIAM J. Matrix Anal. App
A combined R-matrix eigenstate basis set and finite-differences propagation method for the time-dependent Schr\"{od}dinger equation: the one-electron case
In this work we present the theoretical framework for the solution of the
time-dependent Schr\"{o}dinger equation (TDSE) of atomic and molecular systems
under strong electromagnetic fields with the configuration space of the
electron's coordinates separated over two regions, that is regions and
. In region the solution of the TDSE is obtained by an R-matrix basis
set representation of the time-dependent wavefunction. In region a grid
representation of the wavefunction is considered and propagation in space and
time is obtained through the finite-differences method. It appears this is the
first time a combination of basis set and grid methods has been put forward for
tackling multi-region time-dependent problems. In both regions, a high-order
explicit scheme is employed for the time propagation. While, in a purely
hydrogenic system no approximation is involved due to this separation, in
multi-electron systems the validity and the usefulness of the present method
relies on the basic assumption of R-matrix theory, namely that beyond a certain
distance (encompassing region ) a single ejected electron is distinguishable
from the other electrons of the multi-electron system and evolves there (region
II) effectively as a one-electron system. The method is developed in detail for
single active electron systems and applied to the exemplar case of the hydrogen
atom in an intense laser field.Comment: 13 pages, 6 figures, submitte
Patients with IgA nephropathy exhibit high systemic PDGF-DD levels
Background. Platelet-derived growth factor (PDGF) is a central mediator of mesangioproliferative glomerulonephritis (GN). In experimental mesangioproliferative GN, PDGF-DD serum levels, unlike PDGF-BB, increased up to 1000-fold. Methods. We assessed disease activity in 72 patients with GN, established a novel PDGF-D ELISA and then determined their PDGF-DD levels. In parallel, we studied renal PDGF-DD mRNA expression by RT-PCR. Results. PDGF-DD serum levels in patients with IgA nephropathy (IgAN) were significantly higher (1.67 ± 0.45 ng/ml) and in patients with lupus nephritis significantly lower (0.66 ± 0.86 ng/ml) compared to healthy controls (1.17 ± 0.46 ng/ml), while patients with focal segmental glomerulosclerosis, membranous GN and ANCA-positive vasculitis did not differ from controls. The subgroup of IgAN patients with elevated PDGF-DD levels (27% of samples) did not differ in their clinical features from those with normal PDGF-DD levels. In IgAN patients with repetitive PDGF-DD determinations, most exhibited only minor fluctuations of serum levels over time. Intrarenal PDGF-DD mRNA expression did not differ between controls and patients, suggesting an extrarenal source of the elevated PDGF-DD in IgAN. Conclusions. Serum PDGF-DD levels were specifically elevated in patients with IgAN, in particular in those with early disease, i.e. preserved renal function. Our data support the rationale for anti-PDGF-DD therapy in mesangioproliferative G
Kernel Approximation on Manifolds II: The -norm of the -projector
This article addresses two topics of significant mathematical and practical
interest in the theory of kernel approximation: the existence of local and
stable bases and the L_p--boundedness of the least squares operator. The latter
is an analogue of the classical problem in univariate spline theory, known
there as the "de Boor conjecture". A corollary of this work is that for
appropriate kernels the least squares projector provides universal near-best
approximations for functions f\in L_p, 1\le p\le \infty.Comment: 25 pages; minor revision; new proof of Lemma 3.9; accepted for
publication in SIAM J. on Math. Ana
Integrated control of potato late blight: predicting the combined efficacy of host resistance and fungicides
Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation
We apply multivariate Lagrange interpolation to synthesize polynomial
quantitative loop invariants for probabilistic programs. We reduce the
computation of an quantitative loop invariant to solving constraints over
program variables and unknown coefficients. Lagrange interpolation allows us to
find constraints with less unknown coefficients. Counterexample-guided
refinement furthermore generates linear constraints that pinpoint the desired
quantitative invariants. We evaluate our technique by several case studies with
polynomial quantitative loop invariants in the experiments
Global Antifungal Profile Optimization of Chlorophenyl Derivatives against Botrytis cinerea and Colletotrichum gloeosporioides
Twenty-two aromatic derivatives bearing a chlorine atom and a different chain in the para or meta
position were prepared and evaluated for their in vitro antifungal activity against the phytopathogenic
fungi Botrytis cinerea and Colletotrichum gloeosporioides. The results showed that maximum inhibition
of the growth of these fungi was exhibited for enantiomers S and R of 1-(40-chlorophenyl)-
2-phenylethanol (3 and 4). Furthermore, their antifungal activity showed a clear structure-activity
relationship (SAR) trend confirming the importance of the benzyl hydroxyl group in the inhibitory
mechanism of the compounds studied. Additionally, a multiobjective optimization study of the
global antifungal profile of chlorophenyl derivatives was conducted in order to establish a rational
strategy for the filtering of new fungicide candidates from combinatorial libraries. The MOOPDESIRE
methodology was used for this purpose providing reliable ranking models that can be
used later
One-way multigrid method in electronic structure calculations
We propose a simple and efficient one-way multigrid method for
self-consistent electronic structure calculations based on iterative
diagonalization. Total energy calculations are performed on several different
levels of grids starting from the coarsest grid, with wave functions
transferred to each finer level. The only changes compared to a single grid
calculation are interpolation and orthonormalization steps outside the original
total energy calculation and required only for transferring between grids. This
feature results in a minimal amount of code change, and enables us to employ a
sophisticated interpolation method and noninteger ratio of grid spacings.
Calculations employing a preconditioned conjugate gradient method are presented
for two examples, a quantum dot and a charged molecular system. Use of three
grid levels with grid spacings 2h, 1.5h, and h decreases the computer time by
about a factor of 5 compared to single level calculations.Comment: 10 pages, 2 figures, to appear in Phys. Rev. B, Rapid Communication
Many-body theory of positron-atom interactions
A many-body theory approach is developed for the problem of positron-atom
scattering and annihilation. Strong electron-positron correlations are included
non-perturbatively through the calculation of the electron-positron vertex
function. It corresponds to the sum of an infinite series of ladder diagrams,
and describes the physical effect of virtual positronium formation. The vertex
function is used to calculate the positron-atom correlation potential and
nonlocal corrections to the electron-positron annihilation vertex. Numerically,
we make use of B-spline basis sets, which ensures rapid convergence of the sums
over intermediate states. We have also devised an extrapolation procedure that
allows one to achieve convergence with respect to the number of
intermediate-state orbital angular momenta included in the calculations. As a
test, the present formalism is applied to positron scattering and annihilation
on hydrogen, where it is exact. Our results agree with those of accurate
variational calculations. We also examine in detail the properties of the large
correlation corrections to the annihilation vertex.Comment: 25 pages, 16 figure
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