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The Lorenz equations [1] are a severe Galerkin-truncation of the Oberbeck-Boussinesq (OB) equations describing Rayleigh-B\'enard convection (RBC). Here we examine the mathematical connections between the chaotic lobe-switching behavior of a…
We consider the Lorentz gas in a distribution of scatterers which microscopically converges to a periodic distribution, and prove that the Lorentz gas in the low density limit satisfies a linear Boltzmann equation. This is in contrast with…
The degree sequence of the algebraic numbers in an algebraic linear recurrence sequence is shown to be virtually periodic. This is proved using the Skolem-Mahler-Lech theorem. It has applications to the degree sequence and the minimal…
Inside the discipline of graph theory exists an extension known as the hypergraph. This generalization of graphs includes vertices along with hyperedges consisting of collections of two or more vertices. One well-studied application of this…
We calculate the diffusion coefficients of persistent random walks on cubic and hypercubic lattices, where the direction of a walker at a given step depends on the memory of one or two previous steps. These results are then applied to study…
A numerical double burst model of the chemical evolution of gas-rich dwarf galaxies has been developed. The model is fitted to a sample of N/O, O/H, Y and gas fraction observations, where N/O and O/H are the relative abundances by number of…
Let $\Aa_t$ be the directed quiver of type $\Aa$ with $t$ vertices. For each dimension vector $d$ there is a dense orbit in the corresponding representation space. The principal aim of this note is to use just rank conditions to define the…
Ghirlanda et al. (2004) derived the collimation-corrected energy E_gamma for a sample of 15 bursts under the assumption of a homogeneous circumburst density profile. They found a correlation (the so-called Ghirlanda correlation) between…
The topological dynamics of the horocyclic flow $h_{\mathbb{R}}$ on the unit tangent bundle of a geometrically finite hyperbolic surface is well known. In particular, on such a surface, the flow $h_{\mathbb{R}}$ is minimal, or the minimal…
Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems.…
General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed…
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…
We explore a family of nested recurrence relations with arbitrary levels of nesting, which have an interpretation in terms of fixed points of morphisms over a countably infinite alphabet. Recurrences in this family are related to a number…
We study periodic wind-tree models, billiards in the plane endowed with $\mathbb{Z}^2$-periodically located identical connected symmetric right-angled obstacles. We show asymptotic formulas for the number of (isotopy classes of) closed…
A rotating, two-component Bose-Einstein condensate is shown to exhibit vortices of multiple quantization, which are possible due to the interatomic interactions between the two species. Also, persistent currents are absent in this system.…
We prove an Erd\H{o}s--Szekeres type result for finite words over $\mathbb{N}$ with repeated values. Specifically, we define a \emph{repeat} in a word to be an occurrence of a value which is not its first occurrence. We define an occurrence…
The aim of the present paper is to investigate new types of recurrence in Finsler geometry, namely, hyper-generalized recurrence and generalized conharmonic recurrence. The properties of such recurrences and their relations to other Finsler…
Circumstellar dust particles can be captured in a mean motion resonance with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the mean motion…
We prove a general Ramsey theorem for trees with a successor operation. This theorem is a common generalization of the Carlson-Simpson Theorem and the Milliken Tree Theorem for regularly branching trees. Our theorem has a number of…
A nonrelativistic Bose gas is represented as a grand-canonical ensemble of fluctuating closed spacetime strings of arbitrary shape and length. The loops are characterized by their string tension and the number of times they wind around the…