Related papers: Statistical Regularity of Apollonian Gaskets
We analyze in the context of geometrothermodynamics a Legendre invariant metric structure in the equilibrium space of an ideal gas. We introduce the concept of thermodynamic geodesic as a succession of points, each corresponding to a state…
We present a general construction of Salem numbers via rational functions whose zeros and poles mostly lie on the unit circle and satisfy an interlacing condition. This extends and unifies earlier work. We then consider the "obvious" limit…
We call a packing of hyperspheres in $n$ dimensions an Apollonian sphere packing if the spheres intersect tangentially or not at all; they fill the $n$-dimensional space; and every sphere in the packing is a member of a cluster of $n+2$…
We study the dynamics of an array of nearest-neighbor coupled spatially distributed systems each generating a periodic sequence of short pulses. We demonstrate that unlike a solitary system generating a train of equidistant pulses, an array…
Disks of low-mass bodies on high-eccentricity orbits in near-Keplerian potentials can be dynamically unstable to buckling out of the plane. In this letter, we present $N$-body simulations of the long-term behavior of such a system, finding…
The ellipsoid fitting conjecture of Saunderson, Chandrasekaran, Parrilo and Willsky considers the maximum number $n$ random Gaussian points in $\mathbb{R}^d$, such that with high probability, there exists an origin-symmetric ellipsoid…
We describe a thought experiment using an isolated system of known parameters and assuming the correctness of Clausius and Boltzmann descriptions of entropy. The experiment produced an astronomical increase in the number of possible ways…
We study equivalence relation of the set of triangles generated by similarity and operation on a triangle to get a new one by joining division points of three edges with the same ratio. Using the moduli space of similarity classes of…
We present a microscopic theory of fluctuation-mediated pairing mechanism in a two-dimensional extended Hubbard model. In contrast to conventional wisdom, odd-frequency spin-triplet pairing can be stabilized near the spin-density-wave…
We estimate the entropy associated to a background of squeezed cosmic gravitons, and we argue that the process of cosmological pair production from the vacuum may explain the large amount of entropy of our present universe.
Water vortices are known to develop polygon structures inside their cores. The apexes of the polygonal manifestations are the result of satellite vortices attached to the parent vortex. Exploiting the analogy between the shallow water…
We demonstrate that the fission of higher-order N-solitons with a subsequent ejection of fundamental quasi-solitons creates solitonic cavities, formed by a pair of solitons with dispersive light trapped between them. As a result of multiple…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
The intrinsic non-linearities of the spin dynamics in condensed matter systems give rise to a rich phenomenology that can be strongly affected by topology. Here we study formation of magnonic solitons in the topologically nontrivial bandgap…
I develop simple thermodynamic relations for a collection of noninteracting classical particles confined in a harmonic trap. The volume of such a trap is not a good thermodynamic variable, so conventional expressions of the first law of…
We construct families of ordinary and gap solitons (GSs), including solitary vortices, in the two-dimensional (2D) system based on the nonlinear-Schr\"Aodinger/Gross-Pitaevskii equation with the 2D or quasi-1D (Q1D) periodic linear…
$k$-level correlation is a local statistic of sequences modulo 1, describing the local spacings of $k$-tuples of elements. For $k = 2$ this is also known as pair correlation. We show that there exists a well spaced increasing sequence of…
We study the formation of the spiral structure of barred spiral galaxies, using an $N$-body model. The evolution of this $N$-body model in the adiabatic approximation maintains a strong spiral pattern for more than 10 bar rotations. We find…
We consider the general process of pair-creation of charged rotating black holes. We find that instantons which describe this process are necessarily complex due to regularity requirements. However their associated probabilities are real,…
We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the…