1,621 research outputs found
Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
In this article we study the fan-beam Radon transform of
symmetrical solenoidal 2D tensor fields of arbitrary rank in a unit disc
as the operator, acting from the object space to the data space
The orthogonal polynomial basis of solenoidal tensor
fields on the disc was built with the help of Zernike polynomials
and then a singular value decomposition (SVD) for the operator
was obtained. The inversion formula for the fan-beam tensor transform follows from this decomposition. Thus obtained inversion formula can be
used as a tomographic filter for splitting a known tensor field into potential
and solenoidal parts. Numerical results are presented.Comment: LaTeX, 37 pages with 5 figure
Point force manipulation and activated dynamics of polymers adsorbed on structured substrates
We study the activated motion of adsorbed polymers which are driven over a
structured substrate by a localized point force.Our theory applies to
experiments with single polymers using, for example, tips of scanning force
microscopes to drag the polymer.We consider both flexible and semiflexible
polymers,and the lateral surface structure is represented by double-well or
periodic potentials. The dynamics is governed by kink-like excitations for
which we calculate shapes, energies, and critical point forces. Thermally
activated motion proceeds by the nucleation of a kink-antikink pair at the
point where the force is applied and subsequent diffusive separation of kink
and antikink. In the stationary state of the driven polymer, the collective
kink dynamics can be described by an one-dimensional symmetric simple exclusion
process.Comment: 7 pages, 2 Figure
Magnetic Field Amplification by Small-Scale Dynamo Action: Dependence on Turbulence Models and Reynolds and Prandtl Numbers
The small-scale dynamo is a process by which turbulent kinetic energy is
converted into magnetic energy, and thus is expected to depend crucially on the
nature of turbulence. In this work, we present a model for the small-scale
dynamo that takes into account the slope of the turbulent velocity spectrum
v(l) ~ l^theta, where l and v(l) are the size of a turbulent fluctuation and
the typical velocity on that scale. The time evolution of the fluctuation
component of the magnetic field, i.e., the small-scale field, is described by
the Kazantsev equation. We solve this linear differential equation for its
eigenvalues with the quantum-mechanical WKB-approximation. The validity of this
method is estimated as a function of the magnetic Prandtl number Pm. We
calculate the minimal magnetic Reynolds number for dynamo action, Rm_crit,
using our model of the turbulent velocity correlation function. For Kolmogorov
turbulence (theta=1/3), we find that the critical magnetic Reynolds number is
approximately 110 and for Burgers turbulence (theta=1/2) approximately 2700.
Furthermore, we derive that the growth rate of the small-scale magnetic field
for a general type of turbulence is Gamma ~ Re^((1-theta)/(1+theta)) in the
limit of infinite magnetic Prandtl numbers. For decreasing magnetic Prandtl
number (down to Pm approximately larger than 10), the growth rate of the
small-scale dynamo decreases. The details of this drop depend on the
WKB-approximation, which becomes invalid for a magnetic Prandtl number of about
unity.Comment: 13 pages, 8 figures; published in Phys. Rev. E 201
The Generation of Magnetic Fields Through Driven Turbulence
We have tested the ability of driven turbulence to generate magnetic field
structure from a weak uniform field using three dimensional numerical
simulations of incompressible turbulence. We used a pseudo-spectral code with a
numerical resolution of up to collocation points. We find that the
magnetic fields are amplified through field line stretching at a rate
proportional to the difference between the velocity and the magnetic field
strength times a constant. Equipartition between the kinetic and magnetic
energy densities occurs at a scale somewhat smaller than the kinetic energy
peak. Above the equipartition scale the velocity structure is, as expected,
nearly isotropic. The magnetic field structure at these scales is uncertain,
but the field correlation function is very weak. At the equipartition scale the
magnetic fields show only a moderate degree of anisotropy, so that the typical
radius of curvature of field lines is comparable to the typical perpendicular
scale for field reversal. In other words, there are few field reversals within
eddies at the equipartition scale, and no fine-grained series of reversals at
smaller scales. At scales below the equipartition scale, both velocity and
magnetic structures are anisotropic; the eddies are stretched along the local
magnetic field lines, and the magnetic energy dominates the kinetic energy on
the same scale by a factor which increases at higher wavenumbers. We do not
show a scale-free inertial range, but the power spectra are a function of
resolution and/or the imposed viscosity and resistivity. Our results are
consistent with the emergence of a scale-free inertial range at higher Reynolds
numbers.Comment: 14 pages (8 NEW figures), ApJ, in press (July 20, 2000?
On magnetic field generation in Kolmogorov turbulence
We analyze the initial, kinematic stage of magnetic field evolution in an
isotropic and homogeneous turbulent conducting fluid with a rough velocity
field, v(l) ~ l^alpha, alpha<1. We propose that in the limit of small magnetic
Prandtl number, i.e. when ohmic resistivity is much larger than viscosity, the
smaller the roughness exponent, alpha, the larger the magnetic Reynolds number
that is needed to excite magnetic fluctuations. This implies that numerical or
experimental investigations of magnetohydrodynamic turbulence with small
Prandtl numbers need to achieve extremely high resolution in order to describe
magnetic phenomena adequately.Comment: 4 pages, revised, new material adde
Features of martensitic transformation and fine structure of intermetallic compound Ni50Mn50
Transmission and scanning electron microscopy and Xray and electron diffraction are used to investigate the martensitic transformation and martensitic phase structure of the Ni50Mn50 alloy. Its resistivity and coefficient of thermal expansion are measured over a wide temperature range. © 2013 Pleiades Publishing, Ltd
State-dependent, addressable subwavelength lattices with cold atoms
We discuss how adiabatic potentials can be used to create addressable
lattices on a subwavelength scale, which can be used as a tool for local
operations and readout within a lattice substructure, while taking advantage of
the faster timescales and higher energy and temperature scales determined by
the shorter lattice spacing. For alkaline-earth-like atoms with non-zero
nuclear spin, these potentials can be made state dependent, for which we give
specific examples with Yb atoms. We discuss in detail the limitations
in generating the lattice potentials, in particular non-adiabatic losses, and
show that the loss rates can always be made exponentially small by increasing
the laser power.Comment: replaced with the published version. 23 pages, 11 figure
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