Related papers: Fractal Generalized Zone Plates
These are the lecture notes for a course at the Summer School on "Applied Analysis" at the Technical University Chemnitz in September 2011. We start with the definition of a fractal algebra and show that the fractal property is enormously…
A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the literature in ad hoc ways, as well as new examples, can be…
The increasing use of freeform optical surfaces raises the demand for optical design tools developed for generalized systems. In the design process surface-by-surface aberration contributions are of special interest. The expansion of the…
The local structure of a fractal set is described by its dimension $D$, which is the exponent of a power-law relating the mass ${\cal N}$ in a ball to its radius $\epsilon$: ${\cal N}\sim \epsilon^D$. It is desirable to characterise the…
The spectral zeta function of the Laplacian on self-similar fractal sets has been previously studied and shown to meromorphically extend to the complex plane. In this work we establish under certain conditions a relationship between the…
Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules.…
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…
We derive new general expressions for the fluctuating electromagnetic field outside a homogeneous material surface. The analysis is based on general results from the thermodynamics of irreversible processes, and requires no consideration of…
We study the optical properties of crystals with spatial dispersion and show that the usual Fresnel approach becomes invalid near frequencies where the group velocity of the wave packets inside the crystal vanishes. Near these special…
In this paper, we establish local fractional Fourier Cosine and Sine Transforms on fractal space, considered some properties of local fractional Cosine and Sine Transforms, show applications of local fractional Fourier Cosine and Sine…
We present results of first-principles calculations of the frequency-dependent polarizabilities of all alkali atoms for light in the wavelength range 300-1600 nm, with particular attention to wavelengths of common infrared lasers. We…
We consider generation of diffusive radiation by a charged particle passing through a random stack of plates in the infrared region. Diffusive radiation originates due to multiple scattering of pseudophotons on the plates. To enhance the…
Fractal interpolation technique is an alternative to the classical interpolation methods especially when a chaotic signal is involved. The logic behind the formulation of an iterated function system for the construction of fractal…
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation…
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…
Reciprocal spin-orbit coupling (SOC) via geometric phase with flat optics provides a promising platform for shaping and controlling paraxial structured light. Current devices, from the pioneering q-plates to the recent J-plates, provide…
The present study focuses on the optical properties of functionalized surfaces and how the surface geometry impacts them. Physical measurements of reflected light are required to understand the visual aspect of such surfaces. Bidirectional…
The well-known plastic number substitution gives rise to a ternary inflation tiling of the real line whose inflation factor is the smallest Pisot-Vijayaraghavan number. The corresponding dynamical system has pure point spectrum, and the…
We present an introduction to fractal interpolation beginning with a global set-up and then extending to a local, a non-stationary, and finally the novel quaternionic setting. Emphasis is placed on the overall perspective with references…
Recent data on diffractive photoproduction of dijets are analyzed within the framework of fracture functions and paying special attention to the consequences of the use of different rapidity gap definitions in order to identify diffractive…