Related papers: An Exceptional Combinatorial Sequence and Standard…
Owing to the presence of exceptional points (EPs), non-Hermitian (NH) systems can display intriguing topological phenomena without Hermitian analogs. However, experimental characterizations of exceptional topological invariants have been…
In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. Remarkably, they permit interesting…
In this paper we consider a model of particles jumping on a row of cells, called in physics the one dimensional totally asymmetric exclusion process (TASEP). More precisely we deal with the TASEP with open or periodic boundary conditions…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
A closed plane meander of order $n$ is a closed self-avoiding curve intersecting an infinite line $2n$ times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm,…
We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
Systems of identical particles possessing non-local interactions are capable of exhibiting extra-classical properties beyond the characteristic quantum length scales. This letter derives the dynamics of such systems in the non-relativistic…
In this paper, we give a procedure for derivation of higher dimensional periodic recurrence equations(PREs) by nested structure of complex numbers.
Exceptional modules are tree modules. A tree module usually has many tree bases and the corresponding coefficient quivers may look quite differently. The aim of this note is to introduce a class of exceptional modules which have a…
Since the introduction of higher order nonclassical effects, higher order squeezing has been reported in a number of different physical systems but higher order antibunching is predicted only in three particular cases. In the present work,…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
We define a proper differential sequence of ordinary differential equations and introduce a method to derive an alternative sequence of integrals for such a sequence. We describe some general properties which are illustrated by several…
By generalizing the algebra of operators of the Asymmetric Simple Exclusion Process (ASEP), a multi-species ASEP in which particles can overtake each other,is defined on both open and closed one dimensional chains. On the ring the steady…
Exceptional points (EPs) of non-Hermitian (NH) systems have recently attracted increasing attention due to their rich phenomenology and intriguing applications. Compared to the predominantly studied second-order EPs, higher-order EPs have…
Resonant chains are groups of planets for which each pair is in resonance, with an orbital period ratio locked at a rational value (2/1, 3/2, etc.). Such chains naturally form as a result of convergent migration of the planets in the…
We extend the algorithms of Robinson, Smyth, and McKee--Smyth to enumerate all real-rooted integer polynomials of a fixed degree, where the first few (at least three) leading coefficients are specified. Additionally, we introduce new linear…
We generalize the definition and properties of root systems to complex reflection groups - roots become rank one projective modules over the ring of integers of a number field k. In the irreducible case, we provide a classification of root…
Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible…
Systems exhibiting degeneracies known as exceptional points have remarkable properties with powerful applications, particularly in sensor design. These degeneracies are formed when eigenstates coincide, and the remarkable effects are…