Related papers: Mathematical diffraction of aperiodic structures
Limit periodic point sets are aperiodic structures with pure point diffraction supported on a countably, but not finitely generated Fourier module that is based on a lattice and certain integer multiples of it. Examples are cut and project…
By generalising Rudin's construction of an aperiodic sequence, we derive new substitution-based structures which have purely absolutely continuous diffraction and mixed dynamical spectrum, with absolutely continuous and pure point parts. We…
Redundancies are pointed out in the widely used extension of the crystallographic concept of Bravais class to quasiperiodic materials. Such pitfalls can be avoided by abandoning the obsolete paradigm that bases ordinary crystallography on…
The recent interest in the imaging possibilities of photonic crystals (superlensing, superprism, optical mirages etc...) call for a detailed analysis of beam propagation inside a finite periodic structure. In this paper, an answer to the…
By following the trajectories of quantum particles inside a periodic lattice and preserving their classical probabilities for reflection, transmission and absorption at each lattice plane, classical scattering outcomes are obtained.…
The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to…
An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…
When propagating through periodically structured media, i. e. photonic crystals, optical waves will be modulated with the periodicity. As a result, the dispersion of waves will no longer behave as in a free space, and so called frequency…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
Development generating diffraction-related valuable expressions and formulas capable of initiating new era for diffraction and for scientific domains that use it provided. The main expression, among these, gives diffracted intensity as…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
A kinetics built upon $q$-calculus, the calculus of discrete dilatations, is shown to describe diffusion on a hierarchical lattice. The only observable on this ultrametric space is the "quasi-position" whose eigenvalues are the levels of…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
An algebraic approach to neutron scattering on a one dimensional potentials is generalized to diffraction on three dimensional single crystals.
Ultrafast electron diffraction/microscopy technique enables us to investigate the nonequilibrium dynamics of crystal structures in the femtosecond-nanosecond time domain. However, the electron diffraction intensities are in general…
Dynamical chiral symmetry breaking is a nonperturbative phenomenon that may be studied using QCD's gap equation. Model-independent results can be obtained with a nonperturbative and symmetry preserving truncation. The gap equation yields…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
X-ray Bragg coherent diffraction imaging has been demonstrated as a powerful three-dimensional (3D) microscopy approach for the investigation of sub-micrometer-scale crystalline particles. It is based on the measurement of a series of…
Uchaikin suggested a mathematical model of an anomalous diffusion in a space was suggested. This model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and…