相关论文: What is Aperiodic Order?

A growth mechanism for a perfect one-dimensional (1D) quasiperiodic structure is presented with a local covering rule. We use rectangular tiles with two different types of string decorations. The string position in a tile is allowed to move…

The concept of quasiresonance was introduced in connection with inelastic collisions between one atom and a vibro-rotationally excited diatomic molecule. In its original form, the collisions induce {\sl quasiresonant} transfer of energy…

In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…

For a three dimensional system we answer two questions, how simple a particle system might be to show the quasicrystal order and, what system features are the most important for quasicrystal formation? One-component system of particles with…

According to classical nucleation theory, a crystal grows from a small nucleus that already bears the symmetry of its end phase - but experiments with colloids now reveal that, from an amorphous precursor, crystallites with different…

Some partial orderings which compare probability distributions with the expo- nential distribution, are found to be very useful to understand the phenomenon of ageing. Here, we introduce some new generalized partial orderings which de-…

We prove that the order of an ordered group is an interval order if and only if it is a semiorder. Next, we prove that every semiorder is isomorphic to a collection $\mathcal J$ of intervals of some totally ordered abelian group, these…

Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one…

A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…

It is pointed out that quantum states, in general, contain a new kind of orders that cannot be characterized by symmetry. A concept of quantum order is introduced to describe such orders. As two concrete examples, we discussed quantum…

We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…

Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as…

The microscopic description of spin-Peierls substances is discussed. Particular attention is paid to the ordered (dimerised and incommensurably modulated) phases. Important points are the adiabatic and the antiadiabatic approach, generic…

Existence theory in economics is usually in real domains such as the findings of chaotic trajectories in models of economic growth, tatonnement, or overlapping generations models. Computational examples, however, sometimes converge rapidly…

The article is devoted to linear quasigroups and some of their generalizations. In the first part main definitions and notions of the theory of quasigroups are given. In the second part some elementary properties of linear quasigroups and…

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…

Artificial quasicrystals are nowadays routinely manufactured, yet only two naturally occurring examples are known. We present a class of systems with the potential to be realized both artificially and in nature, in which the lowest energy…

We track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo an incomplete periodic doubling cascade that ends with a crisis bifurcation. We introduce a symbolic dynamics for the orbits and show…

Recent studies on fully dielectric multilayered metamaterials have shown that the negligibly small nonlocal effects (spatial dispersion) typically observed in the limit of deeply subwavelength layers may be significantly enhanced by…

We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…