10,846 research outputs found
Linear feedback control of transient energy growth and control performance limitations in subcritical plane Poiseuille flow
Suppression of the transient energy growth in subcritical plane Poiseuille
flow via feedback control is addressed. It is assumed that the time derivative
of any of the velocity components can be imposed at the walls as control input,
and that full-state information is available. We show that it is impossible to
design a linear state-feedback controller that leads to a closed-loop flow
system without transient energy growth.
In a subsequent step, full-state feedback controllers -- directly targeting
the transient growth mechanism -- are designed, using a procedure based on a
Linear Matrix Inequalities approach. The performance of such controllers is
analyzed first in the linear case, where comparison to previously proposed
linear-quadratic optimal controllers is made; further, transition thresholds
are evaluated via Direct Numerical Simulations of the controlled
three-dimensional Poiseuille flow against different initial conditions of
physical interest, employing different velocity components as wall actuation.
The present controllers are effective in increasing the transition thresholds
in closed loop, with varying degree of performance depending on the initial
condition and the actuation component employed
Chiral behaviour of the lattice -parameter with the Wilson and Clover Actions at
We present results for the kaon -parameter from a sample of
configurations using the Wilson action and configurations using the
SW-Clover action, on a lattice at . We compare
results obtained by renormalizing the relevant operator with different
``boosted" values of the strong coupling constant . In the case of
the SW-Clover action, we also use the operator renormalized non-perturbatively.
In the Wilson case, we observe a strong dependence of on the prescription
adopted for , contrary to the results of the Clover case which are
almost unaffected by the choice of the coupling. We also find that the matrix
element of the operator renormalized non-perturbatively has a better chiral
behaviour. This gives us our best estimate of the renormalization group
invariant -parameter, .Comment: LaTeX, 17 pages, 3 postscript figures uuencode
Relaxation times of kinetically constrained spin models with glassy dynamics
We analyze the density and size dependence of the relaxation time for
kinetically constrained spin systems. These have been proposed as models for
strong or fragile glasses and for systems undergoing jamming transitions. For
the one (FA1f) or two (FA2f) spin facilitated Fredrickson-Andersen model at any
density and for the Knight model below the critical density at which
the glass transition occurs, we show that the persistence and the spin-spin
time auto-correlation functions decay exponentially. This excludes the
stretched exponential relaxation which was derived by numerical simulations.
For FA2f in , we also prove a super-Arrhenius scaling of the form
. For FA1f in = we
rigorously prove the power law scalings recently derived in \cite{JMS} while in
we obtain upper and lower bounds consistent with findings therein.
Our results are based on a novel multi-scale approach which allows to analyze
in presence of kinetic constraints and to connect time-scales and
dynamical heterogeneities. The techniques are flexible enough to allow a
variety of constraints and can also be applied to conservative stochastic
lattice gases in presence of kinetic constraints.Comment: 4 page
Cutoff for the Ising model on the lattice
Introduced in 1963, Glauber dynamics is one of the most practiced and
extensively studied methods for sampling the Ising model on lattices. It is
well known that at high temperatures, the time it takes this chain to mix in
on a system of size is . Whether in this regime there is
cutoff, i.e. a sharp transition in the -convergence to equilibrium, is a
fundamental open problem: If so, as conjectured by Peres, it would imply that
mixing occurs abruptly at for some fixed , thus providing
a rigorous stopping rule for this MCMC sampler. However, obtaining the precise
asymptotics of the mixing and proving cutoff can be extremely challenging even
for fairly simple Markov chains. Already for the one-dimensional Ising model,
showing cutoff is a longstanding open problem.
We settle the above by establishing cutoff and its location at the high
temperature regime of the Ising model on the lattice with periodic boundary
conditions. Our results hold for any dimension and at any temperature where
there is strong spatial mixing: For this carries all the way to the
critical temperature. Specifically, for fixed , the continuous-time
Glauber dynamics for the Ising model on with periodic boundary
conditions has cutoff at , where is
the spectral gap of the dynamics on the infinite-volume lattice. To our
knowledge, this is the first time where cutoff is shown for a Markov chain
where even understanding its stationary distribution is limited.
The proof hinges on a new technique for translating to mixing
which enables the application of log-Sobolev inequalities. The technique is
general and carries to other monotone and anti-monotone spin-systems.Comment: 34 pages, 3 figure
Quenched -parameter with the Wilson and Clover actions at
We present results for the Kaon parameter from a sample of
configurations using the Wilson action and configurations using the
Clover action, on a lattice at . A slight
improvement of the chiral behaviour of is observed due to the Clover
action. We have also compared the results for obtained from two different
procedures for the boosting of the coupling constant . We observe a strong
dependence of on the prescription adopted for in the Wilson case,
contrary to the results of the Clover case which are almost unaffected by the
choice of . Combining some recently obtained non perturbative estimates for
the renormalisation constants with our Clover matrix element, we observe a
significant improvement in the chiral behaviour of .Comment: 3 pages, Latex, Postscript file with figures available at
ftp://hpteo.roma1.infn.it/pub/preprints/lat94/donini ; to appear in Lattice
'94, Nucl. Phys. (Proc.Suppl.
Non-perturbative Renormalization of Quark bilinears
We compute non-perturbatively the renormalization constants of quark
bilinears on the lattice in the quenched approximation at three values of the
coupling beta=6/g_0^2=6.0,6.2,6.4 using both the Wilson and the tree-level
improved SW-Clover fermion action. We perform a Renormalization Group analysis
at the next-to-next-to-leading order and compute Renormalization Group
invariant values for the constants. The results are applied to obtain a fully
non-perturbative estimate of the vector and pseudoscalar decay constants.Comment: 21 pages, latex, five latex figures include
2000 CKM-Triangle Analysis A Critical Review with Updated Experimental Inputs and Theoretical Parameters
Within the Standard Model, a review of the current determination of the sides
and angles of the CKM unitarity triangle is presented, using experimental
constraints from the measurements of |\epsilon_K|, |V_{ub}/V_{cb}|, \Delta m_d
and from the limit on \Delta m_s, available in September 2000. Results from the
experimental search for {B}^0_s-\bar{B}^0_s oscillations are introduced in the
present analysis using the likelihood. Special attention is devoted to the
determination of the theoretical uncertainties. The purpose of the analysis is
to infer regions where the parameters of interest lie with given probabilities.
The BaBar "95 %, C.L. scanning" method is also commented.Comment: 44 pages (revised version
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