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Related papers: Apollonian packings as physical fractals

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We show for the first time that collectively jammed disordered packings of three-dimensional monodisperse frictionless hard spheres can be produced and tuned using a novel numerical protocol with packing density $\phi$ as low as 0.6. This…

Statistical Mechanics · Physics 2011-01-10 Yang Jiao , Frank H. Stillinger , Sal Torquato

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which…

Dynamical Systems · Mathematics 2012-02-23 Hee Oh , Nimish Shah

Motivated by chromosomes enclosed in nucleus and the recently discovered active topological glass, we study a spherically confined melt of long nonconcatenated active polymer rings. Without activity, the rings exhibit the same average…

Soft Condensed Matter · Physics 2021-07-27 Iurii Chubak , Stanard Mebwe Pachong , Kurt Kremer , Christos N. Likos , Jan Smrek

This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous,…

Astrophysics · Physics 2015-06-24 Marcelo B. Ribeiro

We explore adhesive loose packings of dry small spherical particles of micrometer size using 3D discrete-element simulations with adhesive contact mechanics. A dimensionless adhesion parameter ($Ad$) successfully combines the effects of…

Soft Condensed Matter · Physics 2015-09-10 Wenwei Liu , Shuiqing Li , Adrian Baule , Hernán A. Makse

In a recent paper (cond-mat/0506445) we derived an expression for the replicated free energy of a liquid of hard spheres based on the HNC free energy functional. An approximate equation of state for the glass and an estimate of the random…

Statistical Mechanics · Physics 2009-11-11 G. Parisi , F. Zamponi

In previous papers by A. Kameyama and by J. Kigami distances on fractals have been discussed having two different but similar properties. One property is that the maps defining the fractal are Lipschitz of prescribed constants less than 1,…

Metric Geometry · Mathematics 2017-10-18 Roberto Peirone

In the last experiment with the PK-3 Plus laboratory onboard the International Space Station, interactions of millimeter-size metallic spheres with a complex plasma were studied~[M. Schwabe {\it et al.}, New J. Phys. {\bf 19}, 103019…

Plasma Physics · Physics 2019-06-05 S. Khrapak , P. Huber , H. Thomas , V. Naumkin. V. Molotkov , A. Lipaev

The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic structures. Due to the great variety of statistical methods to describe the large-scale structure of the…

Astrophysics · Physics 2008-11-26 Stefano Borgani

Axionlike particles (ALPs) are a common prediction of theories beyond the Standard Model of particle physics that could explain the entirety of the cold dark matter. These particles could be detected through their mixing with photons in…

High Energy Astrophysical Phenomena · Physics 2019-08-14 Manuel Meyer

Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and…

We introduce the notion of (abelian) similarity scheme, as a constructive model for topological self-similar fractals, in the same way in which the notion of iterated function system furnishes a constructive notion of self-similar fractals…

Functional Analysis · Mathematics 2024-07-11 Fabio E. G. Cipriani , Daniele Guido , Tommaso Isola , Jean-Luc Sauvageot

Symbolic and graphical tools, such as Mathematica, enable precise visualization and analysis of void spaces in sphere packings. In the cubic close packing (CCP, or face-centred cubic packing; FCC) arrangement these voids can be partitioned…

Computational Geometry · Computer Science 2025-08-19 Philip W. Kuchel

Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they…

Soft Condensed Matter · Physics 2018-05-09 Rose Cersonsky , Greg van Anders , Paul M. Dodd , Sharon C. Glotzer

We present results for the cosmic non-linear density-fluctuation power spectrum based on the analytical formalism developed in [1] which allows us to study cosmic structure formation based on Newtonian particle dynamics in phase-space. This…

Cosmology and Nongalactic Astrophysics · Physics 2025-01-22 Tristan Daus , Elena Kozlikin

We introduce and study two new concepts which are essential for the quantitative analysis of the statistical quality of the available galaxy samples. These are the dilution effect and the small scale fluctuations. We show that the various…

Astrophysics · Physics 2019-08-17 F. Sylos Labini , A. Gabrielli , M. Montuori , L. Pietronero

Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions…

Computational Complexity · Computer Science 2021-03-02 Neil Lutz

The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…

Number Theory · Mathematics 2015-04-21 Arash Rastegar

We introduce a duality for Affine Iterated Function Systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine…

Classical Analysis and ODEs · Mathematics 2007-10-25 Dorin Ervin Dutkay , Palle E. T. Jorgensen

Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in…

Soft Condensed Matter · Physics 2015-01-05 Carl P. Goodrich , Simon Dagois-Bohy , Brian P. Tighe , Martin van Hecke , Andrea J. Liu , Sidney R. Nagel