21,472 research outputs found

### Euler's fluid equations: Optimal Control vs Optimization

An optimization method used in image-processing (metamorphosis) is found to
imply Euler's equations for incompressible flow of an inviscid fluid, without
requiring that the Lagrangian particle labels exactly follow the flow lines of
the Eulerian velocity vector field. Thus, an optimal control problem and an
optimization problem for incompressible ideal fluid flow both yield the \emph
{same} Euler fluid equations, although their Lagrangian parcel dynamics are
\emph{different}. This is a result of the \emph{gauge freedom} in the
definition of the fluid pressure for an incompressible flow, in combination
with the symmetry of fluid dynamics under relabeling of their Lagrangian
coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.Comment: 12 page

### A subset solution to the sign problem in random matrix simulations

We present a solution to the sign problem in dynamical random matrix
simulations of a two-matrix model at nonzero chemical potential. The sign
problem, caused by the complex fermion determinants, is solved by gathering the
matrices into subsets, whose sums of determinants are real and positive even
though their cardinality only grows linearly with the matrix size. A detailed
proof of this positivity theorem is given for an arbitrary number of fermion
flavors. We performed importance sampling Monte Carlo simulations to compute
the chiral condensate and the quark number density for varying chemical
potential and volume. The statistical errors on the results only show a mild
dependence on the matrix size and chemical potential, which confirms the
absence of sign problem in the subset method. This strongly contrasts with the
exponential growth of the statistical error in standard reweighting methods,
which was also analyzed quantitatively using the subset method. Finally, we
show how the method elegantly resolves the Silver Blaze puzzle in the
microscopic limit of the matrix model, where it is equivalent to QCD.Comment: 18 pages, 11 figures, as published in Phys. Rev. D; added references;
in Sec. VB: added discussion of model satisfying the Silver Blaze for all N
(proof in Appendix E

### An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow

In this paper we consider the Hamiltonian formulation of the equations of
incompressible ideal fluid flow from the point of view of optimal control
theory. The equations are compared to the finite symmetric rigid body equations
analyzed earlier by the authors. We discuss various aspects of the Hamiltonian
structure of the Euler equations and show in particular that the optimal
control approach leads to a standard formulation of the Euler equations -- the
so-called impulse equations in their Lagrangian form. We discuss various other
aspects of the Euler equations from a pedagogical point of view. We show that
the Hamiltonian in the maximum principle is given by the pairing of the
Eulerian impulse density with the velocity. We provide a comparative discussion
of the flow equations in their Eulerian and Lagrangian form and describe how
these forms occur naturally in the context of optimal control. We demonstrate
that the extremal equations corresponding to the optimal control problem for
the flow have a natural canonical symplectic structure.Comment: 6 pages, no figures. To appear in Proceedings of the 39th IEEEE
Conference on Decision and Contro

### Charm spectroscopy in DELPHI

The production of charmed particles has been studied using 3.5 milllion hadronic Z decays collected by the DELPHI collaboration at LEP between 1992 and 1995. Large samples of D meson decays have been exclusively reconstructed, allowing to look for D$^*pi$ and D$^*pipi$ final states. The production fractions of the narrow D$_1^0(2420)$ and D$_2^{*0}(2460)$ orbital states are measured in c and b quark jets separately. Evidence for a radial state D$^{*'}(2637)$ is presented in the D$^{*+}pi^+pi^-$ decay mode. %DB Interesting perspectives to look for the wide orbital states in semileptonic B %DB decays are discussed

### Beauty and charm physics at LEP

Recent results in charm and beauty physics at LEP are reported. They allow refined tests of strong and electroweak interactions. The importance of measuring as accurately as possible the apex of the unitarity is emphasized

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