Related papers: Duality in percolation via outermost boundaries II…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
We analyze site percolation on directed and undirected graphs with site-dependent open-site probabilities. We construct upper bounds on cluster susceptibilities, vertex connectivity functions, and the expected number of simple open cycles…
Close binary stars are binary stars where the component stars are close enough such that they can exchange mass and/or energy. They are subdivided into semi-detached, overcontact or ellipsoidal binary stars. A challenging problem in the…
In this paper, we study connected components of strata of the space of quadratic differentials lying over $\T_g$. We use certain general properties of sections of line bundles to put a upper bound on the number of connected components, and…
Extending the well-known star-comb lemma for infinite graphs, we characterise the graphs that do not contain an infinite comb or an infinite star, respectively, attached to a given set of vertices. We offer several characterisations: in…
We extend to infinite graphs the matroidal characterization of finite graph duality, that two graphs are dual iff they have complementary spanning trees in some common edge set. The naive infinite analogue of this fails. The key in an…
Supermassive black holes reside in cores of galaxies, where they are often surrounded by a nuclear cluster and a clumpy torus of gas and dust. Mutual interactions can set some stars on a plunging trajectory towards the black hole. We model…
Jets from young stellar objects provide insight into the workings of the beating heart at the centre of star forming cores. In some cases, multiple pulsed outflows are detected such as the atomic and molecular jets from a proposed binary…
Consider random sequential adsorption on a chequerboard lattice with arrivals at rate $1$ on light squares and at rate $\lambda$ on dark squares. Ultimately, each square is either occupied, or blocked by an occupied neighbour. Colour the…
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
In this paper we prove a duality between $k$-noncrossing partitions over $[n]=\{1,...,n\}$ and $k$-noncrossing braids over $[n-1]$. This duality is derived directly via (generalized) vacillating tableaux which are in correspondence to…
The partition functions of refined topological strings(A-models) are computed, which give rise to the circle-compactified five-dimensional supersymmetric linear quiver gauge theories in generic (not necessarily self-dual) Omega backgrounds.…
We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thick subcategories of the bounded derived category of a locally…
Recent years have seen a renewed interest in using `edge modes' to extend the pre-symplectic structure of gauge theory on manifolds with boundaries. Here we further the investigation undertaken in \cite{FP2018} by using the formalism of…
In some recent theories including Quantum SuperString theory we encounter duality - it arises due to a non commutative geometry which in effect adds an extra term to the Heiserberg Uncertainity Principle. The result is that the micro world…
The notions of $k$-separability and $k$-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this…
Motivated by suggestions that binaries with almost equal-mass components ("twins") play an important role in the formation of double neutron stars and may be rather abundant among binaries, we study the stability of synchronized close and…
We present a panoptic view of the stellar structure in the Galactic disk's outer reaches commonly known as the Monoceros Ring, based on data from Pan-STARRS1. These observations clearly show the large extent of the stellar overdensities on…
We prove absence of infinite clusters and contours in a class of critical constrained percolation models on the square lattice. The percolation configuration is assumed to satisfy certain hard local constraints, but only weak symmetry and…
Overcontact binary stars are systems of two stars where the component stars are in contact with each other. This implies that they share a common envelope of gas. In this work we seek signatures of nonlinearity and chaos in these stars by…