447 research outputs found
Spatiotemporal Response of Crystals in X-ray Bragg Diffraction
The spatiotemporal response of crystals in x-ray Bragg diffraction resulting
from excitation by an ultra-short, laterally confined x-ray pulse is studied
theoretically. The theory presents an extension of the analysis in symmetric
reflection geometry [1] to the generic case, which includes Bragg diffraction
both in reflection (Bragg) and transmission (Laue) asymmetric scattering
geometries. The spatiotemporal response is presented as a product of a
crystal-intrinsic plane wave spatiotemporal response function and an envelope
function defined by the crystal-independent transverse profile of the incident
beam and the scattering geometry. The diffracted wavefields exhibit amplitude
modulation perpendicular to the propagation direction due to both angular
dispersion and the dispersion due to Bragg's law. The characteristic measure of
the spatiotemporal response is expressed in terms of a few parameters: the
extinction length, crystal thickness, Bragg angle, asymmetry angle, and the
speed of light. Applications to self-seeding of hard x-ray free electron lasers
are discussed, with particular emphasis on the relative advantages of using
either the Bragg or Laue scattering geometries. Intensity front inclination in
asymmetric diffraction can be used to make snapshots of ultra-fast processes
with femtosecond resolution
Time dependence of Bragg forward scattering and self-seeding of hard x-ray free-electron lasers
Free-electron lasers (FELs) can now generate temporally short, high power
x-ray pulses of unprecedented brightness, even though their longitudinal
coherence is relatively poor. The longitudinal coherence can be potentially
improved by employing narrow bandwidth x-ray crystal optics, in which case one
must also understand how the crystal affects the field profile in time and
space. We frame the dynamical theory of x-ray diffraction as a set of coupled
waves in order to derive analytic expressions for the spatiotemporal response
of Bragg scattering from temporally short incident pulses. We compute the
profiles of both the reflected and forward scattered x-ray pulses, showing that
the time delay of the wave is linked to its transverse spatial shift
through the simple relationship , where
is the grazing angle of incidence to the diffracting planes. Finally,
we apply our findings to obtain an analytic description of Bragg forward
scattering relevant to monochromatically seed hard x-ray FELs.Comment: 11 pages, 6 figure
Takagi-Taupin Description of X-ray Dynamical Diffraction from Diffractive Optics with Large Numerical Aperture
We present a formalism of x-ray dynamical diffraction from volume diffractive
optics with large numerical aperture and high aspect ratio, in an analogy to
the Takagi-Taupin equations for strained single crystals. We derive a set of
basic equations for dynamical diffraction from volume diffractive optics, which
enable us to study the focusing property of these optics with various grating
profiles. We study volume diffractive optics that satisfy the Bragg condition
to various degrees, namely flat, tilted and wedged geometries, and derive the
curved geometries required for ultimate focusing. We show that the curved
geometries satisfy the Bragg condition everywhere and phase requirement for
point focusing, and effectively focus hard x-rays to a scale close to the
wavelength.Comment: 18 pages, 12 figure
General model selection estimation of a periodic regression with a Gaussian noise
This paper considers the problem of estimating a periodic function in a
continuous time regression model with an additive stationary gaussian noise
having unknown correlation function. A general model selection procedure on the
basis of arbitrary projective estimates, which does not need the knowledge of
the noise correlation function, is proposed. A non-asymptotic upper bound for
quadratic risk (oracle inequality) has been derived under mild conditions on
the noise. For the Ornstein-Uhlenbeck noise the risk upper bound is shown to be
uniform in the nuisance parameter. In the case of gaussian white noise the
constructed procedure has some advantages as compared with the procedure based
on the least squares estimates (LSE). The asymptotic minimaxity of the
estimates has been proved. The proposed model selection scheme is extended also
to the estimation problem based on the discrete data applicably to the
situation when high frequency sampling can not be provided
Predictability in the large: an extension of the concept of Lyapunov exponent
We investigate the predictability problem in dynamical systems with many
degrees of freedom and a wide spectrum of temporal scales. In particular, we
study the case of turbulence at high Reynolds numbers by introducing a
finite-size Lyapunov exponent which measures the growth rate of finite-size
perturbations. For sufficiently small perturbations this quantity coincides
with the usual Lyapunov exponent. When the perturbation is still small compared
to large-scale fluctuations, but large compared to fluctuations at the smallest
dynamically active scales, the finite-size Lyapunov exponent is inversely
proportional to the square of the perturbation size. Our results are supported
by numerical experiments on shell models. We find that intermittency
corrections do not change the scaling law of predictability. We also discuss
the relation between finite-size Lyapunov exponent and information entropy.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed
with uufile
Theory and Applications of X-ray Standing Waves in Real Crystals
Theoretical aspects of x-ray standing wave method for investigation of the
real structure of crystals are considered in this review paper. Starting from
the general approach of the secondary radiation yield from deformed crystals
this theory is applied to different concreat cases. Various models of deformed
crystals like: bicrystal model, multilayer model, crystals with extended
deformation field are considered in detailes. Peculiarities of x-ray standing
wave behavior in different scattering geometries (Bragg, Laue) are analysed in
detailes. New possibilities to solve the phase problem with x-ray standing wave
method are discussed in the review. General theoretical approaches are
illustrated with a big number of experimental results.Comment: 101 pages, 43 figures, 3 table
Application of ECH to the Study of Transport in ITER Baseline Scenario-like Discharges in DIII-D
Recent DIII-D experiments in the ITER Baseline Scenario (IBS) have shown strong increases in fluctuations and correlated reduction of confinement associated with entering the electron-heating-dominated regime with strong electron cyclotron heating (ECH). The addition of 3.2 MW of 110 GHz EC power deposited at ρ~0.42 to IBS discharges with ~3 MW of neutral beam injection causes large increases in low-k and medium-k turbulent density fluctuations observed with Doppler backscatter (DBS), beam emission spectroscopy (BES) and phase-contrast imaging (PCI) diagnostics, correlated with decreases in the energy, particle, and momentum confinement times. Power balance calculations show the electron heat diffusivity χ[subscript e] increases significantly in the mid-radius region 0.4<ρ<0.8, which is roughly the same region where the DBS and BES diagnostics show the increases in turbulent density fluctuations. Confinement of angular momentum is also reduced during ECH. Studies with the TGYRO transport solver show that the model of turbulent transport embodied in the TGLF code quantitatively reproduces the measured transport in both the neutral beam (NB)-only and in the NB plus EC cases. A simple model of the decrease in toroidal rotation with EC power is set forth, which exhibits a bifurcation in the rotational state of the discharge.United States. Dept. of Energy (DE-FC02-04ER54698)United States. Dept. of Energy (DE-FC02-08ER54966)United States. Dept. of Energy (DE-AC03-09CH11466)United States. Dept. of Energy (DE-FG02-04ER54235)United States. Dept. of Energy (DE-FG0289ER53296)United States. Dept. of Energy (DE-FG02-08ER54999)United States. Dept. of Energy (DE-FG02-08ER54984)United States. Dept. of Energy (DE-FG02-04ER54461
Consequences of converting graded to action potentials upon neural information coding and energy efficiency
Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ~50% in generator potentials, to ~3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation
Spontaneous spin bifurcations and ferromagnetic phase transitions in a spinor exciton-polariton condensate
We observe a spontaneous parity breaking bifurcation to a ferromagnetic state in a spatially trapped exciton-polariton condensate. At a critical bifurcation density under nonresonant excitation, the whole condensate spontaneously magnetizes and randomly adopts one of two elliptically polarized (up to 95% circularly polarized) states with opposite handedness of polarization. The magnetized condensate remains stable for many seconds at 5 K, but at higher temperatures, it can flip from one magnetic orientation to another. We optically address these states and demonstrate the inversion of the magnetic state by resonantly injecting 100- fold weaker pulses of opposite spin. Theoretically, these phenomena can be well described as spontaneous symmetry breaking of the spin degree of freedom induced by different loss rates of the linear polarizations.Publisher PDFPeer reviewe
Properties of field functionals and characterization of local functionals
Functionals (i.e. functions of functions) are widely used in quantum field
theory and solid-state physics. In this paper, functionals are given a rigorous
mathematical framework and their main properties are described. The choice of
the proper space of test functions (smooth functions) and of the relevant
concept of differential (Bastiani differential) are discussed.
The relation between the multiple derivatives of a functional and the
corresponding distributions is described in detail. It is proved that, in a
neighborhood of every test function, the support of a smooth functional is
uniformly compactly supported and the order of the corresponding distribution
is uniformly bounded. Relying on a recent work by Yoann Dabrowski, several
spaces of functionals are furnished with a complete and nuclear topology. In
view of physical applications, it is shown that most formal manipulations can
be given a rigorous meaning.
A new concept of local functionals is proposed and two characterizations of
them are given: the first one uses the additivity (or Hammerstein) property,
the second one is a variant of Peetre's theorem. Finally, the first step of a
cohomological approach to quantum field theory is carried out by proving a
global Poincar\'e lemma and defining multi-vector fields and graded functionals
within our framework.Comment: 32 pages, no figur
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