Related papers: Lattice Structures for Attractors III
It is known that every relatively pseudocomplemented lattice is residuated and, moreover, it is distributive. Unfortunately, non-distributive lattices with a unary operation satisfying properties similar to relative pseudocomplementation…
A combinatorial framework for dynamical systems provides an avenue for connecting classical dynamics with data-oriented, algorithmic methods. Combinatorial vector fields introduced by Forman and their recent generalization to multivector…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Convergence is a fundamental topic in analysis that is most commonly modelled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable…
We consider the dynamics of lattices which have constrained constitutive units flexible in only their mutual orientations. A continuum description is derived through which it is shown that the models have zero shear velocity, free-particle…
The divergence of the thermal conductivity in the thermodynamic limit is thoroughly investigated. The divergence law is consistently determined with two different numerical approaches based on equilibrium and non-equilibrium simulations. A…
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
We consider posets of lattice paths (endowed with a natural order) and begin the study of such structures. We give an algebraic condition to recognize which ones of these posets are lattices. Next we study the class of Dyck lattices (i.e.,…
Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results…
We describe several new ways of specifying the behaviour of Lemaitre-Tolman (LT) models, in each case presenting the method for obtaining the LT arbitrary functions from the given data, and the conditions for existence of such solutions. In…
For a modular lattice $L$ of finite length, we prove that the distributivity of $L$ is a sufficient condition while its 2-distributivity is a necessary condition that those sublattices of $L$ that are closed under taking relative…
Shaken optical lattices permit to coherently modify the tunneling of particles in a controllable manner. We introduce a general relation between the geometry of shaken lattices and their admissible effective dynamics. Using three different…
We introduce a variant of transition systems, where activation of transitions depends on conditions of the environment and upgrades during runtime potentially create additional transitions. Using a cornerstone result in lattice theory, we…
If a partition of a lattice in R^d is selfsimilar, it is called lattice substitution system (LSS). Such sets represent nonperiodic, but highly ordered structures. An important property of such structures is, whether they are model sets or…
We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied…
We present a theory of automata with boundary for designing, modelling and analysing distributed systems. Notions of behaviour, design and simulation appropriate to the theory are defined. The problem of model checking for deadlock…
The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…
We provide a generic scheme to separate the particles of a mixture by their physical properties like mass, friction or size. The scheme employs a periodically shaken two dimensional dissipative lattice and hinges on a simultaneous transport…
Skew lattices are non-commutative generalizations of lattices. The coset structure decomposition is an original approach to the study of these algebras describing the relation between its rectangular classes. In this paper we will look at…