20,833 research outputs found
Mixing in turbulent jets: scalar measures and isosurface geometry
Experiments have been conducted to investigate mixing and the geometry of scalar isosurfaces in turbulent jets. Specifically, we have obtained high-resolution, high-signal-to-noise-ratio images of the jet-fluid concentration in the far field of round, liquid-phase, turbulent jets, in the Reynolds number range 4.5 × 10^3 ≤ Re ≤ 18 × 10^3, using laser-induced-fluorescence imaging techniques. Analysis of these data indicates that this Reynolds-number range spans a mixing transition in the far field of turbulent jets. This is manifested in the probability-density function of the scalar field, as well as in measures of the scalar isosurfaces. Classical as well as fractal measures of these isosurfaces have been computed, from small to large spatial scales, and are found to be functions of both scalar threshold and Reynolds number. The coverage of level sets of jet-fluid concentration in the two-dimensional images is found to possess a scale-dependent-fractal dimension that increases continuously with increasing scale, from near unity, at the smallest scales, to 2, at the largest scales. The geometry of the scalar isosurfaces is, therefore, more complex than power-law fractal, exhibiting an increasing complexity with increasing scale. This behaviour necessitates a scale-dependent generalization of power-law-fractal geometry. A connection between scale-dependent-fractal geometry and the distribution of scales is established and used to compute the distribution of spatial scales in the flow
Quantifying the uncertainty of contour maps
Contour maps are widely used to display estimates of spatial fields. Instead
of showing the estimated field, a contour map only shows a fixed number of
contour lines for different levels. However, despite the ubiquitous use of
these maps, the uncertainty associated with them has been given a surprisingly
small amount of attention. We derive measures of the statistical uncertainty,
or quality, of contour maps, and use these to decide an appropriate number of
contour lines, that relates to the uncertainty in the estimated spatial field.
For practical use in geostatistics and medical imaging, computational methods
are constructed, that can be applied to Gaussian Markov random fields, and in
particular be used in combination with integrated nested Laplace approximations
for latent Gaussian models. The methods are demonstrated on simulated data and
an application to temperature estimation is presented
Conformal Curves on Surface
We have studied the iso-height lines on the surface as a
physical candidate for conformally invariant curves. We have shown that these
lines are conformally invariant with the same statistics of domain walls in the
critical Ising model. They belong to the family of conformal invariant curves
called Schramm-Loewner evolution (or ), with diffusivity of
. This can be regarded as the first experimental observation of
SLE curves. We have also argued that Ballistic Deposition (BD) can serve as a
growth model giving rise to contours with similar statistics at large scales.Comment: 4 pages, 6 figures. accepted in PR
Wulff construction in statistical mechanics and in combinatorics
We present the geometric solutions to some variational problems of
statistical mechanics and combinatorics. Together with the Wulff construction,
which predicts the shape of the crystals, we discuss the construction which
exhibits the shape of a typical Young diagram and of a typical skyscraper.Comment: A revie
- …