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We study the behavior of orbits in two different galactic dynamical models, describing the motion in the central parts of a triaxial elliptical galaxy with a dense nucleus. Numerical experiments show that both models display regular motion…
We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
We investigate the representation of lattices as sublattices of the lattice of all convex subsets (intervals) of a linearly ordered set $(X,\le)$. We introduce the purely lattice-theoretic notion of a \textit{loc-lattice} and prove that…
We investigate regular and chaotic two-dimensional (2D) and three-dimensional (3D) orbits of stars in models of a galactic potential consisting in a disk, a halo and a bar, to find the origin of boxy components, which are part of the bar or…
We want to introduce a construction of spherical designs from finite graphs with the theory of crystal lattice. We start from a finite graph, and we consider standard realization of the crystal lattices as the maximal Abelian covering of…
This work develops a methodical approach to counting of walks on cartesian products, biproducts, symmetric and exterior powers and bipowers, Schur operations, coverings and semicoverings of weighted graphs. For weight and root lattices of…
Coronal loops reveal crucial information about the nature of both coronal magnetic fields and coronal heating. The shape of the corresponding flux tube cross section and how it varies with position are especially important properties. They…
At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density…
This paper presents a parametric stiffness analysis of the Orthoglide. A compliant modeling and a symbolic expression of the stiffness matrix are conducted. This allows a simple systematic analysis of the influence of the geometric design…
We study lattice points in d-dimensional spheres, and count their number in thin spherical segments. We found an upper bound depending only on the radius of the sphere and opening angle of the segment. To obtain this bound we slice the…
Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces $(M=G/H,g)$ whose geodesics are orbits of one-parameter subgroups of $G$. The corresponding metric $g$ is called a geodesic orbit metric. We study the…
We study a quantum ladder of interacting fermions with coupled s and p orbitals. Such a model describes dipolar molecules or atoms loaded into a double-well optical lattice, dipole moments being aligned by an external field. The two orbital…
How do galaxies move relative to one another? While we can examine the motion of dark matter subhalos around their hosts in simulations of structure formation, determining the orbits of satellites around their parent galaxies from…
A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition.…
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
The lazy random walk, where the walker has some probability of staying put, is a useful tool in classical algorithms. We propose a quantum analogue, the lackadaisical quantum walk, where each vertex is given $l$ self-loops, and we…
We use the IllustrisTNG cosmological hydrodynamical simulation to study the rotation curves of galaxies in the local universe. To do that, we first select the galaxies with 9.4 $<$ $\log{(M_\mathrm{star}/M_\odot)}$ $<$ 11.5 to make a sample…
Given a lattice \Gamma in a locally compact group G and a closed subgroup H of G, one has a natural action of \Gamma on the homogeneous space V=H\G. For an increasing family of finite subsets {\Gamma_T: T>0}, a dense orbit v\Gamma, v\in V,…
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…