Related papers: Density of Binary Disc Packings: Playing with Stoi…
We investigate the coupling between rock-size solids and gas during the formation of gas giant planets by disk fragmentation in the outer regions of massive disks. In this study, we use three-dimensional radiative hydrodynamics simulations…
Compact packings are specific packings of spheres which can be seen as tilings and are good candidates to maximize the density. We show that the compact packings of the Euclidean space with two sizes of spheres are exactly those obtained by…
The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal co-crystal structures. However, binary mixtures often form amorphous or metastable phases instead…
We numerically examine binary-sized granular mixtures confined between two parallel walls subjected to vertical vibration using the discrete element method. For a size ratio of $3$ between large and small particles, we study the structure…
We have identified four circumstellar disks with a deficit of dust emission from their inner 15-50 AU. All four stars have F-G spectral type, and were uncovered as part of the Spitzer Space Telescope ``Cores to Disks'' Legacy Program…
By a compact packing of the plane by discs, $P$, we mean a collection of closed discs in the plane with pairwise disjoint interior so that, for every disc $C\in P$, there exists a sequence of discs $D_{0},\ldots,D_{m-1}\in P$ so that each…
Geometrically thick disks may form after tidal disruption events, and rapid accretion may lead to short flares followed by long-term, lower-level emission. Using a novel accretion disk code which relies primarily on global conservation laws…
We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…
Debris disc analysis and modelling provide crucial information about the structure and the processes at play in extrasolar planetary systems. In binary systems, this issue is more complex because the disc should in addition respond to the…
A considerable fraction of the massive quiescent galaxies at \emph{z} $\approx$ 2, which are known to be much more compact than galaxies of comparable mass today, appear to have a disk. How well can we measure the bulge and disk properties…
We study the dynamics and clustering of dust particles with inertia in shock-dominated compressible turbulence using the two-dimensional, stochastically forced Burgers equation. At small Stokes numbers, shock trapping leads to extreme…
The densest local packings of N identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a stochastic search of…
Dense polyhedron packings are useful models of a variety of condensed matter and biological systems and have intrigued scientists mathematicians for centuries. Recently, organizing principles for the types of structures associated with the…
We report on simulations in general relativity of magnetized disks onto black hole binaries. We vary the binary mass ratio from 1:1 to 1:10 and evolve the systems when they orbit near the binary-disk decoupling radius. We compare (surface)…
Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter---the total length of all pieces of their boundaries visible from above. We prove that if the centers…
We prove that given a fixed radius $r$, the set of isometry-invariant probability measures supported on ``periodic'' radius $r$-circle packings of the hyperbolic plane is dense in the space of all isometry-invariant probability measures on…
We explore the dynamics of stellar discs in the close vicinity of a supermassive black hole (SMBH) by means of direct $N$-body simulations. We show that an isolated nuclear stellar disc exhibits anisotropic mass segregation meaning that…
Circumstellar discs are expected to be the nursery of planets. Grain growth within such discs is the first step in the planet formation process in the core-accretion gas-capture scenario. We aim at providing selected criteria on…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
The level of dust vertical settling and radial dust concentration in disks is of critical importance for understanding the efficiency of planet formation. We present the first uniform analysis of the vertical extent of millimeter dust for a…