8,057 research outputs found
Automatic sets of rational numbers
The notion of a k-automatic set of integers is well-studied. We develop a new
notion - the k-automatic set of rational numbers - and prove basic properties
of these sets, including closure properties and decidability.Comment: Previous version appeared in Proc. LATA 2012 conferenc
The role of long waves in the stability of the plane wake
This work is directed towards investigating the fate of three-dimensional
long perturbation waves in a plane incompressible wake. The analysis is posed
as an initial-value problem in space. More specifically, input is made at an
initial location in the downstream direction and then tracing the resulting
behavior further downstream subject to the restriction of finite kinetic
energy. This presentation follows the outline given by Criminale and Drazin
[Stud. in Applied Math. \textbf{83}, 123 (1990)] that describes the system in
terms of perturbation vorticity and velocity. The analysis is based on large
scale waves and expansions using multi scales and multi times for the partial
differential equations. The multiscaling is based on an approach where the
small parameter is linked to the perturbation property independently from the
flow control parameter. Solutions of the perturbative equations are determined
numerically after the introduction of a regular perturbation scheme
analytically deduced up to the second order. Numerically, the complete linear
system is also integrated. Since the results relevant to the complete problem
are in very good agreement with the results of the first order analysis, the
numerical solution at the second order was deemed not necessary. The use for an
arbitrary initial-value problem will be shown to contain a wealth of
information for the different transient behaviors associated to the symmetry,
angle of obliquity and spatial decay of the long waves. The amplification
factor of transversal perturbations never presents the trend - a growth
followed by a long damping - usually seen in waves with wavenumber of order one
or less. Asymptotical instability is always observed.Comment: accepted Physical Review E, March 201
New challenges for agricultural research: climate change, food security, rural development, agricultural knowledge systems. 2nd SCAR Foresight exercise
A weakly nonlinear analysis of the magnetorotational instability in a model channel flow
We show by means of a perturbative weakly nonlinear analysis that the
axisymmetric magnetorotational instability (MRI) of a viscous, resistive,
incompressible rotating shear flow in a thin channel gives rise to a real
Ginzburg-Landau equation for the disturbance amplitude. For small magnetic
Prandtl number (), the saturation amplitude is and the resulting momentum transport scales as , where is the {\em hydrodynamic} Reynolds number. Simplifying
assumptions, such as linear shear base flow, mathematically expedient boundary
conditions and continuous spectrum of the vertical linear modes, are used to
facilitate this analysis. The asymptotic results are shown to comply with
numerical calculations using a spectral code. They suggest that the transport
due to the nonlinearly developed MRI may be very small in experimental setups
with .Comment: Accepted to Physical Review Letters - Nov. 30, 2006. In final for
Coarse-Grained Simulations of Membranes under Tension
We investigate the properties of membranes under tension by Monte-Carlo
simulations of a generic coarse-grained model for lipid bilayers. We give a
comprising overview of the behavior of several membrane characteristics, such
as the area per lipid, the monolayer overlap, the nematic order, and pressure
profiles. Both the low-temperature regime, where the membranes are in a gel
phase, and the high-temperature regime, where they are in the fluid phase, are
considered. In the gel state, the membrane is hardly influenced by tension. In
the fluid state, high tensions lead to structural changes in the membrane,
which result in different compressibility regimes. The ripple state, which is
found at tension zero in the transition regime between the fluid and the gel
phase, disappears under tension and gives way to an interdigitated phase. We
also study the membrane fluctuations in the fluid phase. In the low tension
regime the data can be fitted nicely to a suitably extended elastic theory. At
higher tensions the elastic fit consistently underestimates the strength of
long-wavelength fluctuations. Finally, we investigate the influence of tension
on the effective interaction between simple transmembrane inclusions and show
that tension can be used to tune the hydrophobic mismatch interaction between
membrane proteins.Comment: 14 pages, 14 figures, accepted for publication in The Journal of
Chemical Physic
Three-body breakup within the fully discretized Faddeev equations
A novel approach is developed to find the three-body breakup amplitudes and
cross sections within the modified Faddeev equation framework. The method is
based on the lattice-like discretization of the three-body continuum with a
three-body stationary wave-packet basis in momentum space. The approach makes
it possible to simplify drastically all the three- and few-body breakup
calculations due to discrete wave-packet representations for the few-body
continuum and simultaneous lattice representation for all the scattering
operators entering the integral equation kernels. As a result, the few-body
breakup can be treated as a particular case of multi-channel scattering in
which part of the channels represents the true few-body continuum states. As an
illustration for the novel approach, an accurate calculations for the
three-body breakup process with non-local and local
interactions are calculated. The results obtained reproduce nicely the
benchmark calculation results using the traditional Faddeev scheme which
requires much more tedious and time-consuming calculations.Comment: 17 pages, 13 figure
Microcavities coupled to multilevel atoms
A three-level atom in the -configuration coupled to a microcavity is
studied. The two transitions of the atom are assumed couple to different
counterpropagating mode pairs in the cavity. We analyze the dynamics both, in
the strong-coupling and the bad cavity limit. We find that compared to a
two-level setup, the third atomic state and the additional control field modes
crucially modify the system dynamics and enable more advanced control schemes.
All results are explained using appropriate dressed state and eigenmode
representations. As potential applications, we discuss optical switching and
turnstile operations and detection of particles close to the resonator surface.Comment: 14 pages, 9 figure
Decomposition of time-resolved tomographic PIV
International audienceAn experimental study has been conducted on a transitional water jet at a Reynolds number of Re = 5000. Flow fields have been obtained by means of time-resolved tomographic particle image velocimetry (TR-TOMO PIV) capturing all relevant spatial and temporal scales. The measured three-dimensional flow fields have then been postprocessed by the dynamic mode decomposition (DMD) which identifies coherent structures that contribute significantly to the dynamics of the jet. Where the jet exhibits a primary axisymmetric instability followed by a pairing of the vortex rings, dominant dynamic modes have been extracted together with their amplitude distribution. These modes represent a basis for the low-dimensional description of the dominant flow features
Influence of strain on magnetization and magnetoelectric effect in La0.7A0.3MnO3 / PMN-PT(001) (A = Sr; Ca)
We investigate the influence of a well-defined reversible biaxial strain
<=0.12 % on the magnetization (M) of epitaxial ferromagnetic manganite films. M
has been recorded depending on temperature, strain and magnetic field in 20 -
50 nm thick films. This is accomplished by reversibly compressing the isotropic
in-plane lattice parameter of the rhombohedral piezoelectric 0.72PMN-0.28PT
(001) substrates by application of an electric field E <= 12 kV cm-1. The
magnitude of the total variable in-plane strain has been derived.
Strain-induced shifts of the ferromagnetic Curie temperature (Tc) of up to 19 K
were found in La0.7Sr0.3MnO3 (LSMO) and La0.7Ca0.3MnO3 films and are
quantitatively analysed for LSMO within a cubic model. The observed large
magnetoelectric coupling coefficient alpha=mu0 dM/dE <= 6 10-8 s m-1 at ambient
temperature results from the strain-induced M change in the
magnetic-film-ferroelectric-substrate system. It corresponds to an enhancement
of mu0 DeltaM <= 19 mT upon biaxial compression of 0.1 %. The extraordinary
large alpha originates from the combination of three crucial properties: (i)
the strong strain dependence of M in the ferromagnetic manganites, (ii) large
piezo-strain of the PMN-PT substrates and (iii) effective elastic coupling at
the film-substrate interface.Comment: 15 pages, 6 figures, 1 tabl
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