96,287 research outputs found
A first step toward higher order chain rules in abelian functor calculus
One of the fundamental tools of undergraduate calculus is the chain rule. The
notion of higher order directional derivatives was developed by Huang,
Marcantognini, and Young, along with a corresponding higher order chain rule.
When Johnson and McCarthy established abelian functor calculus, they proved a
chain rule for functors that is analogous to the directional derivative chain
rule when . In joint work with Bauer, Johnson, and Riehl, we defined an
analogue of the iterated directional derivative and provided an inductive proof
of the analogue to the chain rule of Huang et al.
This paper consists of the initial investigation of the chain rule found in
Bauer et al., which involves a concrete computation of the case when . We
describe how to obtain the second higher order directional derivative chain
rule for abelian functors. This proof is fundamentally different in spirit from
the proof given in Bauer et al. as it relies only on properties of cross
effects and the linearization of functors
Fully Coherent X-ray Pulses from a Regenerative Amplifier Free Electron Laser
We propose and analyze a novel regenerative amplifier free electron laser
(FEL) to produce fully coherent x-ray pulses. The method makes use of
narrow-bandwidth Bragg crystals to form an x-ray feedback loop around a
relatively short undulator. Self-amplified spontaneous emission (SASE) from the
leading electron bunch in a bunch train is spectrally filtered by the Bragg
reflectors and is brought back to the beginning of the undulator to interact
repeatedly with subsequent bunches in the bunch train. The FEL interaction with
these short bunches not only amplifies the radiation intensity but also
broadens its spectrum, allowing for effective transmission of the x-rays
outside the crystal bandwidth. The spectral brightness of these x-ray pulses is
about two to three orders of magnitude higher than that from a single-pass SASE
FEL.Comment: 11 pages, 6 figure
Effects of Line-tying on Magnetohydrodynamic Instabilities and Current Sheet Formation
An overview of some recent progress on magnetohydrodynamic stability and
current sheet formation in a line-tied system is given. Key results on the
linear stability of the ideal internal kink mode and resistive tearing mode are
summarized. For nonlinear problems, a counterexample to the recent
demonstration of current sheet formation by Low \emph{et al}. [B. C. Low and
\AA. M. Janse, Astrophys. J. \textbf{696}, 821 (2009)] is presented, and the
governing equations for quasi-static evolution of a boundary driven, line-tied
magnetic field are derived. Some open questions and possible strategies to
resolve them are discussed.Comment: To appear in Phys. Plasma
Atomic electron energies including relativistic effects and quantum electrodynamic corrections
Atomic electron energies have been calculated relativistically. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all orbitals in all atoms with 2 less than or equal to Z less than or equal to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. These results will serve for detailed comparison of calculations based on other approaches. The magnitude of quantum electrodynamic corrections is exhibited quantitatively for each state
Methods for detection and characterization of signals in noisy data with the Hilbert-Huang Transform
The Hilbert-Huang Transform is a novel, adaptive approach to time series
analysis that does not make assumptions about the data form. Its adaptive,
local character allows the decomposition of non-stationary signals with
hightime-frequency resolution but also renders it susceptible to degradation
from noise. We show that complementing the HHT with techniques such as
zero-phase filtering, kernel density estimation and Fourier analysis allows it
to be used effectively to detect and characterize signals with low signal to
noise ratio.Comment: submitted to PRD, 10 pages, 9 figures in colo
Possible eta-mesic 3He states within the finite rank approximation
We extend the method of time delay proposed by Eisenbud and Wigner, to search
for unstable states formed by eta mesons and the 3He nucleus. Using few body
equations to describe eta-3He elastic scattering, we predict resonances and
unstable bound states within different models of the eta-N interaction. The
eta-3He states predicted within this novel approach are in agreement with the
recent claim of the evidence of eta-mesic 3He made by the TAPS collaboration.Comment: 10 pages LaTex, 3 figure
Theoretical L-shell Coster-Kronig energies 11 or equal to z or equal to 103
Relativistic relaxed-orbital calculations of L-shell Coster-Kronig transition energies have been performed for all possible transitions in atoms with atomic numbers. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order approximation to the local approximation was thus included. Quantum-electrodynamic corrections were made. Each transition energy was computed as the difference between results of separate self-consistent-field calculations for the initial, singly ionized state and the final two-hole state. The following quantities are listed: total transition energy, 'electric' (Dirac-Hartree-Fock-Slater) contribution, magnetic and retardation contributions, and contributions due to vacuum polarization and self energy
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