22,890 research outputs found
Dependence of chaotic diffusion on the size and position of holes
A particle driven by deterministic chaos and moving in a spatially extended
environment can exhibit normal diffusion, with its mean square displacement
growing proportional to the time. Here we consider the dependence of the
diffusion coefficient on the size and the position of areas of phase space
linking spatial regions (`holes') in a class of simple one-dimensional,
periodically lifted maps. The parameter dependent diffusion coefficient can be
obtained analytically via a Taylor-Green-Kubo formula in terms of a functional
recursion relation. We find that the diffusion coefficient varies
non-monotonically with the size of a hole and its position, which implies that
a diffusion coefficient can increase by making the hole smaller. We derive
analytic formulas for small holes in terms of periodic orbits covered by the
holes. The asymptotic regimes that we observe show deviations from the standard
stochastic random walk approximation. The escape rate of the corresponding open
system is also calculated. The resulting parameter dependencies are compared
with the ones for the diffusion coefficient and explained in terms of periodic
orbits.Comment: 12 pages, 5 figure
Time Discrete Geodesic Paths in the Space of Images
In this paper the space of images is considered as a Riemannian manifold
using the metamorphosis approach, where the underlying Riemannian metric
simultaneously measures the cost of image transport and intensity variation. A
robust and effective variational time discretization of geodesics paths is
proposed. This requires to minimize a discrete path energy consisting of a sum
of consecutive image matching functionals over a set of image intensity maps
and pairwise matching deformations. For square-integrable input images the
existence of discrete, connecting geodesic paths defined as minimizers of this
variational problem is shown. Furthermore, -convergence of the
underlying discrete path energy to the continuous path energy is proved. This
includes a diffeomorphism property for the induced transport and the existence
of a square-integrable weak material derivative in space and time. A spatial
discretization via finite elements combined with an alternating descent scheme
in the set of image intensity maps and the set of matching deformations is
presented to approximate discrete geodesic paths numerically. Computational
results underline the efficiency of the proposed approach and demonstrate
important qualitative properties.Comment: 27 pages, 7 figure
Foerster resonance energy transfer rate and local density of optical states are uncorrelated in any dielectric nanophotonic medium
Motivated by the ongoing debate about nanophotonic control of Foerster
resonance energy transfer (FRET), notably by the local density of optical
states (LDOS), we study an analytic model system wherein a pair of ideal dipole
emitters - donor and acceptor - exhibit energy transfer in the vicinity of an
ideal mirror. The FRET rate is controlled by the mirror up to distances
comparable to the donor-acceptor distance, that is, the few-nanometer range.
For vanishing distance, we find a complete inhibition or a four-fold
enhancement, depending on dipole orientation. For mirror distances on the
wavelength scale, where the well-known `Drexhage' modification of the
spontaneous-emission rate occurs, the FRET rate is constant. Hence there is no
correlation between the Foerster (or total) energy transfer rate and the LDOS.
At any distance to the mirror, the total energy transfer between a
closely-spaced donor and acceptor is dominated by Foerster transfer, i.e., by
the static dipole-dipole interaction that yields the characteristic
inverse-sixth-power donor-acceptor distance dependence in homogeneous media.
Generalizing to arbitrary inhomogeneous media with weak dispersion and weak
absorption in the frequency overlap range of donor and acceptor, we derive two
main theoretical results. Firstly, the spatially dependent Foerster energy
transfer rate does not depend on frequency, hence not on the LDOS. Secondly the
FRET rate is expressed as a frequency integral of the imaginary part of the
Green function. This leads to an approximate FRET rate in terms of the LDOS
integrated over a huge bandwidth from zero frequency to about 10 times the
donor emission frequency, corresponding to the vacuum-ultraviolet. Even then,
the broadband LDOS hardly contributes to the energy transfer rates. We discuss
practical consequences including quantum information processing.Comment: 17 pages, 9 figure
Numerical solution of three-dimensional rectangular submerged jets with the evidence of the undisturbed region of flow
The evolution of turbulent rectangular submerged free jets has been
investigated numerically with a two-dimensional (2D) approach by the
present authors and, by using the large eddy simulations (LES) at several
Reynolds numbers. The average numerical results confirmed the presence of
the undisturbed region of flow (URF) located between the slot exit and the
beginning of the potential core region (PCR) previously observed
experimentally at the University of Rome “Tor Vergata” by Gori and
coworkers. The 2D study of the present authors carried out under the
conditions previously investigated in the literature, showed that the URF has
a self-similar behavior, and proposed a new law for the evolution of the
momentum. The present paper extends the LES to three-dimensional (3D)
rectangular submerged free jets, in the range from Re =5,000 to
Re =40,000, showing that the self-similar behavior of URF is also present
in the 3D numerical simulations, as well as in the PCR and in the fully
developed region (FDR)
Hybrid-State Free Precession in Nuclear Magnetic Resonance
The dynamics of large spin-1/2 ensembles in the presence of a varying
magnetic field are commonly described by the Bloch equation. Most magnetic
field variations result in unintuitive spin dynamics, which are sensitive to
small deviations in the driving field. Although simplistic field variations can
produce robust dynamics, the captured information content is impoverished.
Here, we identify adiabaticity conditions that span a rich experiment design
space with tractable dynamics. These adiabaticity conditions trap the spin
dynamics in a one-dimensional subspace. Namely, the dynamics is captured by the
absolute value of the magnetization, which is in a transient state, while its
direction adiabatically follows the steady state. We define the hybrid state as
the co-existence of these two states and identify the polar angle as the
effective driving force of the spin dynamics. As an example, we optimize this
drive for robust and efficient quantification of spin relaxation times and
utilize it for magnetic resonance imaging of the human brain
Diagnosing space telescope misalignment and jitter using stellar images
Accurate knowledge of the telescope's point spread function (PSF) is
essential for the weak gravitational lensing measurements that hold great
promise for cosmological constraints. For space telescopes, the PSF may vary
with time due to thermal drifts in the telescope structure, and/or due to
jitter in the spacecraft pointing (ground-based telescopes have additional
sources of variation). We describe and simulate a procedure for using the
images of the stars in each exposure to determine the misalignment and jitter
parameters, and reconstruct the PSF at any point in that exposure's field of
view. The simulation uses the design of the SNAP (http://snap.lbl.gov)
telescope. Stellar-image data in a typical exposure determines secondary-mirror
positions as precisely as . The PSF ellipticities and size, which
are the quantities of interest for weak lensing are determined to and accuracies respectively in each exposure,
sufficient to meet weak-lensing requirements. We show that, for the case of a
space telescope, the PSF estimation errors scale inversely with the square root
of the total number of photons collected from all the usable stars in the
exposure.Comment: 20 pages, 6 figs, submitted to PAS
A general numerical model for wave rotor analysis
Wave rotors represent one of the promising technologies for achieving very high core temperatures and pressures in future gas turbine engines. Their operation depends upon unsteady gas dynamics and as such, their analysis is quite difficult. This report describes a numerical model which has been developed to perform such an analysis. Following a brief introduction, a summary of the wave rotor concept is given. The governing equations are then presented, along with a summary of the assumptions used to obtain them. Next, the numerical integration technique is described. This is an explicit finite volume technique based on the method of Roe. The discussion then focuses on the implementation of appropriate boundary conditions. Following this, some results are presented which first compare the numerical approximation to the governing differential equations and then compare the overall model to an actual wave rotor experiment. Finally, some concluding remarks are presented concerning the limitations of the simplifying assumptions and areas where the model may be improved
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