774 research outputs found
Forced Burgers Equation in an Unbounded Domain
The inviscid Burgers equation with random and spatially smooth forcing is
considered in the limit when the size of the system tends to infinity. For the
one-dimensional problem, it is shown both theoretically and numerically that
many of the features of the space-periodic case carry over to infinite domains
as intermediate time asymptotics. In particular, for large time we
introduce the concept of -global shocks replacing the notion of main shock
which was considered earlier in the periodic case (1997, E et al., Phys. Rev.
Lett. 78, 1904). In the case of spatially extended systems these objects are no
anymore global. They can be defined only for a given time scale and their
spatial density behaves as for large . The
probability density function of the age of shocks behaves
asymptotically as . We also suggest a simple statistical model for
the dynamics and interaction of shocks and discuss an analogy with the problem
of distribution of instability islands for a simple first-order stochastic
differential equation.Comment: 9 pages, 10 figures, revtex4, J. Stat. Phys, in pres
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
Kicked Burgers Turbulence
Burgers turbulence subject to a force ,
where the 's are ``kicking times'' and the ``impulses'' have
arbitrary space dependence, combines features of the purely decaying and the
continuously forced cases. With large-scale forcing this ``kicked'' Burgers
turbulence presents many of the regimes proposed by E, Khanin, Mazel and Sinai
(1997) for the case of random white-in-time forcing. It is also amenable to
efficient numerical simulations in the inviscid limit, using a modification of
the Fast Legendre Transform method developed for decaying Burgers turbulence by
Noullez and Vergassola (1994). For the kicked case, concepts such as
``minimizers'' and ``main shock'', which play crucial roles in recent
developments for forced Burgers turbulence, become elementary since everything
can be constructed from simple two-dimensional area-preserving Euler--Lagrange
maps.
One key result is for the case of identical deterministic kicks which are
periodic and analytic in space and are applied periodically in time: the
probability densities of large negative velocity gradients and of
(not-too-large) negative velocity increments follow the power law with -7/2
exponent proposed by E {\it et al}. (1997) in the inviscid limit, whose
existence is still controversial in the case of white-in-time forcing. (More in
the full-length abstract at the beginning of the paper.)Comment: LATEX 30 pages, 11 figures, J. Fluid Mech, in pres
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
Topological Shocks in Burgers Turbulence
The dynamics of the multi-dimensional randomly forced Burgers equation is
studied in the limit of vanishing viscosity. It is shown both theoretically and
numerically that the shocks have a universal global structure which is
determined by the topology of the configuration space. This structure is shown
to be particularly rigid for the case of periodic boundary conditions.Comment: 4 pages, 4 figures, RevTex4, published versio
Trunk - crown growth trade off in pollarded trees: influence on wood production
info:eu-repo/semantics/publishedVersio
Universality of Velocity Gradients in Forced Burgers Turbulence
It is demonstrated that Burgers turbulence subject to large-scale
white-noise-in-time random forcing has a universal power-law tail with exponent
-7/2 in the probability density function of negative velocity gradients, as
predicted by E, Khanin, Mazel and Sinai (1997, Phys. Rev. Lett. 78, 1904). A
particle and shock tracking numerical method gives about five decades of
scaling. Using a Lagrangian approach, the -7/2 law is related to the shape of
the unstable manifold associated to the global minimizer.Comment: 4 pages, 2 figures, RevTex4, published versio
Non-perturbative renormalisation of four fermion operators and B-bar B mixing with Wilson fermions
We present new results for the renormalisation and subtraction constants for
the four fermion Delta F=2 operators, computed non-perturbatively in the RI-MOM
scheme (in the Landau gauge). From our preliminary analysis of the lattice data
at beta=6.45, for the B-bar B mixing bag-parameter we obtain B_B^{RGI} =
1.46(7)(1).Comment: 3 pages (4 figures), Lattice2002(heavyquark
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