5,105 research outputs found
Complex-space singularities of 2D Euler flow in Lagrangian coordinates
We show that, for two-dimensional space-periodic incompressible flow, the
solution can be evaluated numerically in Lagrangian coordinates with the same
accuracy achieved in standard Eulerian spectral methods. This allows the
determination of complex-space Lagrangian singularities. Lagrangian
singularities are found to be closer to the real domain than Eulerian
singularities and seem to correspond to fluid particles which escape to
(complex) infinity by the current time. Various mathematical conjectures
regarding Eulerian/Lagrangian singularities are presented.Comment: 5 pages, 2 figures, submitted to Physica
Singularities of Euler flow? Not out of the blue!
Does three-dimensional incompressible Euler flow with smooth initial
conditions develop a singularity with infinite vorticity after a finite time?
This blowup problem is still open. After briefly reviewing what is known and
pointing out some of the difficulties, we propose to tackle this issue for the
class of flows having analytic initial data for which hypothetical real
singularities are preceded by singularities at complex locations. We present
some results concerning the nature of complex space singularities in two
dimensions and propose a new strategy for the numerical investigation of
blowup.(A version of the paper with higher-quality figures is available at
http://www.obs-nice.fr/etc7/complex.pdf)Comment: RevTeX4, 10 pages, 9 figures. J.Stat.Phys. in press (updated version
Theory of two-dimensional macroscopic quantum tunneling in a Josephson junction coupled with an LC circuit
We investigate classical thermal activation (TA) and macroscopic quantum
tunneling (MQT) for a Josephson junction coupled with an LC circuit
theoretically. The TA and MQT escape rate are calculated analytically by taking
into account the two-dimensional nature of the classical and quantum phase
dynamics. We find that the MQT escape rate is largely suppressed by the
coupling to the LC circuit. On the other hand, this coupling gives rise to
slight reduction of the TA escape rate. These results are relevant for the
interpretation of a recent experiment on the MQT and TA phenomena in grain
boundary YBCO Josephson junctions.Comment: 4 pages, 1 figure, Proceedings of LT2
Optimal cloning of mixed Gaussian states
We construct the optimal 1 to 2 cloning transformation for the family of
displaced thermal equilibrium states of a harmonic oscillator, with a fixed and
known temperature. The transformation is Gaussian and it is optimal with
respect to the figure of merit based on the joint output state and norm
distance. The proof of the result is based on the equivalence between the
optimal cloning problem and that of optimal amplification of Gaussian states
which is then reduced to an optimization problem for diagonal states of a
quantum oscillator. A key concept in finding the optimum is that of stochastic
ordering which plays a similar role in the purely classical problem of Gaussian
cloning. The result is then extended to the case of n to m cloning of mixed
Gaussian states.Comment: 8 pages, 1 figure; proof of general form of covariant amplifiers
adde
Multifractality of the Feigenbaum attractor and fractional derivatives
It is shown that fractional derivatives of the (integrated) invariant measure
of the Feigenbaum map at the onset of chaos have power-law tails in their
cumulative distributions, whose exponents can be related to the spectrum of
singularities . This is a new way of characterizing multifractality
in dynamical systems, so far applied only to multifractal random functions
(Frisch and Matsumoto (J. Stat. Phys. 108:1181, 2002)). The relation between
the thermodynamic approach (Vul, Sinai and Khanin (Russian Math. Surveys 39:1,
1984)) and that based on singularities of the invariant measures is also
examined. The theory for fractional derivatives is developed from a heuristic
point view and tested by very accurate simulations.Comment: 20 pages, 5 figures, J.Stat.Phys. in pres
The analytic structure of 2D Euler flow at short times
Using a very high precision spectral calculation applied to the
incompressible and inviscid flow with initial condition , we find that the width of its analyticity
strip follows a law at short times over eight decades. The
asymptotic equation governing the structure of spatial complex-space
singularities at short times (Frisch, Matsumoto and Bec 2003, J.Stat.Phys. 113,
761--781) is solved by a high-precision expansion method. Strong numerical
evidence is obtained that singularities have infinite vorticity and lie on a
complex manifold which is constructed explicitly as an envelope of analyticity
disks.Comment: 19 pages, 14 figures, published versio
Quantum Statistics of Interacting Dimer Spin Systems
The compound TlCuCl3 represents a model system of dimerized quantum spins
with strong interdimer interactions. We investigate the triplet dispersion as a
function of temperature by inelastic neutron scattering experiments on single
crystals. By comparison with a number of theoretical approaches we demonstrate
that the description of Troyer, Tsunetsugu, and Wuertz [Phys. Rev. B 50, 13515
(1994)] provides an appropriate quantum statistical model for dimer spin
systems at finite temperatures, where many-body correlations become
particularly important.Comment: 4 pages, 4 figures, to appear in Physical Review Letter
A Theoretical Light-Curve Model for the 1999 Outburst of U Scorpii
A theoretical light curve for the 1999 outburst of U Scorpii is presented in
order to obtain various physical parameters of the recurrent nova. Our U Sco
model consists of a very massive white dwarf (WD) with an accretion disk and a
lobe-filling, slightly evolved, main-sequence star (MS). The model includes a
reflection effect by the companion and the accretion disk together with a
shadowing effect on the companion by the accretion disk. The early visual light
curve (t ~ 1-15 days after maximum) is well reproduced by a thermonuclear
runaway model on a very massive WD close to the Chandrasekhar limit (M_{WD}=
1.37 \pm 0.01 M_\odot), in which optically thick winds blowing from the WD play
a key role in determining the nova duration. The duration of the strong wind
phase (t~0-17 days) is very consistent with the BeppoSAX supersoft X-ray
detection at t~19-20 days because supersoft X-rays are self-absorbed by the
massive wind. The envelope mass at the peak is estimated to be ~3x10^{-6}
M_\odot, which is indicating an average mass accretion rate ~2.5x10^{-7}
M_\odot yr^{-1} during the quiescent phase between 1987 and 1999. These
quantities are exactly the same as those predicted in a new progenitor model of
Type Ia supernovae.Comment: 7 pages, 3 figures, to appear in ApJL, vol. 52
Nature of complex singularities for the 2D Euler equation
A detailed study of complex-space singularities of the two-dimensional
incompressible Euler equation is performed in the short-time asymptotic
r\'egime when such singularities are very far from the real domain; this allows
an exact recursive determination of arbitrarily many spatial Fourier
coefficients. Using high-precision arithmetic we find that the Fourier
coefficients of the stream function are given over more than two decades of
wavenumbers by \hat F(\k) = C(\theta) k^{-\alpha} \ue ^ {-k \delta(\theta)},
where \k = k(\cos \theta, \sin \theta). The prefactor exponent ,
typically between 5/2 and 8/3, is determined with an accuracy better than 0.01.
It depends on the initial condition but not on . The vorticity diverges
as , where and is the distance to the
(complex) singular manifold. This new type of non-universal singularity is
permitted by the strong reduction of nonlinearity (depletion) which is
associated to incompressibility. Spectral calculations show that the scaling
reported above persists well beyond the time of validity of the short-time
asymptotics. A simple model in which the vorticity is treated as a passive
scalar is shown analytically to have universal singularities with exponent
.Comment: 22 pages, 24 figures, published version; a version of the paper with
higher-quality figures is available at http://www.obs-nice.fr/etc7/euler.pd
- …