Is The Starry Night Turbulent?

The Starry Night
Vincent van Gogh (1889)


James Beattie, Neco Kriel
Vincent van Gogh’s painting, The Starry Night, is an iconic piece of art and cultural history. The painting portrays a night sky full of stars, with eddies (spirals) both large and small. Kolmogorov1941’s description of subsonic, incompressible turbulence gives a model for turbulence that involves eddies interacting on many length scales, and so the question has been asked: is The Starry Night turbulent? To answer this question, we calculate the azimuthally averaged power spectrum of a square region (1165×1165 pixels) of night sky in The Starry Night. We find a power spectrum, P(k), where k is the wavevector, that shares the same features as supersonic turbulence. It has a power-law P(k)∝k2.1±0.3 in the scaling range, 34≤k≤80. We identify a driving scale, kD=3, dissipation scale, kν=220 and a bottleneck. This leads us to believe that van Gogh’s depiction of the starry night closely resembles the turbulence found in real molecular clouds, the birthplace of stars in the Universe.

Read more at https://arxiv.org/pdf/1902.03381.pdf

A crowd that flows like water

Dynamic response and hydrodynamics of polarized crowds
Nicolas Bain, Denis Bartolo
Modeling crowd motion is central to situations as diverse as risk prevention in mass events and visual effects rendering in the motion picture industry. The difficulty of performing quantitative measurements in model experiments has limited our ability to model pedestrian flows. We use tens of thousands of road-race participants in starting corrals to elucidate the flowing behavior of polarized crowds by probing its response to boundary motion. We establish that speed information propagates over system-spanning scales through polarized crowds, whereas orientational fluctuations are locally suppressed. Building on these observations, we lay out a hydrodynamic theory of polarized crowds and demonstrate its predictive power. We expect this description of human groups as active continua to provide quantitative guidelines for crowd management.

Read more at http://science.sciencemag.org/content/363/6422/46

Noether’s Theorem and Symmetry

A.K. Halder, Andronikos Paliathanasis, P.G.L. Leach
In Noether’s original presentation of her celebrated theorm of 1918 allowance was made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the depenent variable(s), the so-called generalised, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to point transformations only. In recent decades this dimunition of the power of Noether’s Theorem has been partly countered, in particular in the review of Sarlet and Cantrijn. In this special issue we emphasise the generality of Noether’s Theorem in its original form and explore the applicability of even more general coefficient functions by alowing for nonlocal terms. We also look for the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables
Read more at https://arxiv.org/pdf/1812.03682.pdf

A Poet of Computation Who Uncovers Distant Truths

The theoretical computer scientist Constantinos Daskalakis has won the Rolf Nevanlinna Prize for explicating core questions in game theory and machine learning.
Guitar__CDScroll down to the bottom of Constantinos Daskalakis’ web page — past links to his theoretical computer science papers and his doctoral students at the Massachusetts Institute of Technology — and you will come upon a spare, 21-line poem by Constantine Cavafy, “The Satrapy.”

Written in 1910, it addresses an unnamed individual who is “made for fine and great works” but who, having met with small-mindedness and indifference, gives up on his dreams and goes to the court of the Persian king Artaxerxes. The king lavishes satrapies (provincial governorships) upon him, but his soul, Cavafy writes, “weeps for other things … the hard-won and inestimable Well Done; the Agora, the Theater, and the Laurels” — all the things Artaxerxes cannot give him. “Where will you find these in a satrapy,” Cavafy asks, “and what life can you live without these.”

For Daskalakis, the poem serves as a sort of talisman, to guard him against base motives. “It’s a moral compass, if you want,” he said. “I want to have this constant reminder that there are some noble ideas that you’re serving, and don’t forget that when you make decisions.” …
Read more at https://www.quantamagazine.org/computer-scientist-constantinos-daskalakis-wins-nevanlinna-prize-20180801/

Read also: The Work of Constantinos Daskalakis

Longest Straight Line Paths on Water or Land on the Earth

longest

Longest Sailable Straight Line Path on Earth


Rohan Chabukswar, Kushal Mukherjee
There has been some interest recently in determining the longest distance one can sail for on the earth without hitting land, as well as in the converse problem of determining the longest distance one could drive for on the earth without encountering a major body of water. In its basic form, this is an optimisation problem, rendered chaotic by the presence of islands and lakes, and indeed the fractal nature of the coasts. In this paper we present a methodology for calculating the two paths using the branch-and-bound algorithm.
longest2

Longest Drivable Straight Line Path on Earth

Read more at https://arxiv.org/pdf/1804.07389.pdf

Aside

Emergence of Benford’s Law in Classical Music

Azar Khosravani, Constantin Rasinariu

The histograms represents the digit distribution of time
intervals for each piano key played for the 32 piano sonatas by
Beethoven vs. the theoretical (Benford) distribution

We analyzed a large selection of classical musical pieces composed by Bach, Beethoven, Mozart, Schubert and Tchaikovsky, and found a surprising connection with mathematics. For each composer, we extracted the time intervals each note was played in each piece and found that the corresponding data sets are Benford distributed. Remarkably, the logarithmic distribution is not only present for the leading digits, but for all digits.
Read more at https://arxiv.org/pdf/1805.06506.pdf