Related papers: Periodic Functions, Lattices and Their Projections
Crystal structures are characterised by repeating atomic patterns within unit cells across three-dimensional space, posing unique challenges for graph-based representation learning. Current methods often overlook essential periodic boundary…
When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge. We review some recent developments on both the theoretical underpinnings and experimental…
Periodic Geometry studies isometry invariants of periodic point sets that are also continuous under perturbations. The motivations come from periodic crystals whose structures are determined in a rigid form but any minimal cells can…
We prove the effectivity of the dynatomic cycles for morphisms of projective varieties. We then analyze the degrees of the dynatomic cycles and multiplicities of formal periodic points and apply these results to the existence of periodic…
We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called…
The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time.…
Lattice QCD allows computations of moments of structure functions from first principles. An overview of the present status of the calculations is given. Recent results and future perspectives are discussed.
Geometrical constraints imposed on higher dimensional harmonic lattices generally lead to nonlinear dynamical lattice models. Helical lattices obtained by such a procedure are shown to be described by sine- plus linear-lattice equations.…
A two-dimensional system of soft particles interacting via a two-length-scale potential is studied. Density functional theory and Brownian dynamics simulations reveal a fluid phase and two crystalline phases with different lattice spacing.…
Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…
The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…
A method for calculating pair correlation functions in a crystal is developed. The method is based on separating the one- and two- particle correlation functions into the symmetry conserving and the symmetry broken parts. The conserving…
We provide an algorithm for computing an effective basis of homology of elliptic surfaces over the complex projective line on which integration of periods can be carried out. This allows the heuristic recovery of several algebraic…
The relationship between the Hamiltonian and Lagrangean functions in analytical mechanics is a type of duality. The two functions, while distinct, are both descriptive functions encoding the behavior of the same dynamical system. One…
We analyze temporal and spatial meson correlators in quenched lattice QCD at T>0. Below T_c we observe little change in the meson properties as compared with T=0. Above T_c we observe new features: chiral symmetry restoration and signals of…
We show that real tight frames that generate lattices must be rational, and use this observation to describe a construction of lattices from vertex transitive graphs. In the case of irreducible group frames, we show that the corresponding…
A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle…
Properties of 2-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutation of their two variables are described. It is shown that the functions are orthogonal when integrated over a finite…
The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to…
A common approach for analyzing hypergraphs is to consider the projected adjacency or Laplacian matrices for each order of interactions (e.g., dyadic, triadic, etc.). However, this method can lose information about the hypergraph structure…