40 research outputs found

    Mode-by-mode fluid dynamics for relativistic heavy ion collisions

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    We propose to study the fluid dynamic propagation of fluctuations in relativistic heavy ion collisions differentially with respect to their azimuthal, radial and longitudinal wavelength. To this end, we introduce a background-fluctuation splitting and a Bessel-Fourier decomposition of the fluctuating modes. We demonstrate how the fluid dynamic evolution of realistic events can be build up from the propagation of individual modes. We describe the main elements of this mode-by-mode fluid dynamics, and we discuss its use in the fluid dynamic analysis of heavy ion collisions. As a first illustration, we quantify to what extent only fluctuations of sufficiently large radial wave length contribute to harmonic flow coefficients. We find that fluctuations of short wave length are suppressed not only due to larger dissipative effects, but also due to a geometrical averaging over the freeze-out hyper surface. In this way, our study further substantiates the picture that harmonic flow coefficients give access to a coarse-grained version of the initial conditions for heavy ion collisions, only.Comment: 6 pages, 5 figures, published versio

    Avoiding Geometry Improvement in Derivative-Free Model-Based Methods via Randomization

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    We present a technique for model-based derivative-free optimization called \emph{basis sketching}. Basis sketching consists of taking random sketches of the Vandermonde matrix employed in constructing an interpolation model. This randomization enables weakening the general requirement in model-based derivative-free methods that interpolation sets contain a full-dimensional set of affinely independent points in every iteration. Practically, this weakening provides a theoretically justified means of avoiding potentially expensive geometry improvement steps in many model-based derivative-free methods. We demonstrate this practicality by extending the nonlinear least squares solver, \texttt{POUNDers} to a variant that employs basis sketching and we observe encouraging results on higher dimensional problems
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