We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C*-subalgebra to discuss a Shubin trace formula. 相似文献
Sr2TiSi2O8 single crystals were grown by Czochralski pulling and from a high-temperature solution. X-ray diffractometry revealed the modulated crystal structure of Sr2TiSi2O8 to belong to the 5D superspace group P4bm (−α, α, 1/2; α, α, 1/2) with α=0.3. Atomic positions, anisotropic displacement factors and positional modulation parameters for Sr2TiSi2O8 are determined and discussed. The positional modulation is further investigated by electron diffraction and high-resolution transmission electron microscopy. In the latter experiments, the 2D modulation appears to be superimposed by some 1D modulation waves. This effect is discussed in terms of growth conditions. 相似文献
Conventional optics is diffraction limited due to the cutoff of spatial frequency components, and evanescent waves allow subdiffraction optics at the cost of complex near‐field manipulation. Recently, optical superoscillatory phenomena were employed to realize superresolution lenses in the far field, but suffering from very narrow working wavelength band due to the fragility of the superoscillatory light field. Here, an ultrabroadband superoscillatory lens (UBSOL) is proposed and realized by utilizing the metasurface‐assisted law of refraction and reflection in arrayed nanorectangular apertures with variant orientations. The ultrabroadband feature mainly arises from the nearly dispersionless phase profile of transmitted light through the UBSOL for opposite circulation polarization with respect to the incident light. It is demonstrated in experiments that subdiffraction light focusing behavior holds well with nearly unchanged focal patterns for wavelengths spanning across visible and near‐infrared light. This method is believed to find promising applications in superresolution microscopes or telescopes, high‐density optical data storage, etc.
A 3‐phase Barker array is a matrix of third roots of unity for which all out‐of‐phase aperiodic autocorrelations have magnitude 0 or 1. The only known truly two‐dimensional 3‐phase Barker arrays have size 2 × 2 or 3 × 3. We use a mixture of combinatorial arguments and algebraic number theory to establish severe restrictions on the size of a 3‐phase Barker array when at least one of its dimensions is divisible by 3. In particular, there exists a double‐exponentially growing arithmetic function T such that no 3‐phase Barker array of size with exists for all . For example, , , and . When both dimensions are divisible by 3, the existence problem is settled completely: if a 3‐phase Barker array of size exists, then . 相似文献
In this paper, the effects of a bistable potential function U(x)=-ax2/2+b|x|2γ/(2γ) on stochastic resonance (SR) is discussed. We investigate the effects of index γ on the performance of the SR system with fixed parameters a and b, and with fixed potential barriers, respectively. To measure the performance of the SR system in the presence of an aperiodic input, the bit error rate is employed, as is commonly used in binary communications. The numerical simulations strongly support the theoretical results. The goal of this investigation is to explore the effects of the shape of potential functions on SR and give a guidance of nonlinear systems in the application of information processing. 相似文献
We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of ech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like tiling spaces. We also introduce a module structure on cohomology which is very convenient as well as of intuitive value. 相似文献
We consider tiling models of round quasicrystals which would have diffraction patterns which are fully rotation invariant—rings instead of Bragg peaks. They can be distinguished from glasses by self-similarity of the pattern of radii of the rings. 相似文献
Dielectric metasurfaces are two‐dimensional structures composed of nano‐scatterers that manipulate the phase and polarization of optical waves with subwavelength spatial resolution, thus enabling ultra‐thin components for free‐space optics. While high performance devices with various functionalities, including some that are difficult to achieve using conventional optical setups have been shown, most demonstrated components have fixed parameters. Here, we demonstrate highly tunable dielectric metasurface devices based on subwavelength thick silicon nano‐posts encapsulated in a thin transparent elastic polymer. As proof of concept, we demonstrate a metasurface microlens operating at 915 nm, with focal distance tuning from 600 μm to 1400 μm (over 952 diopters change in optical power) through radial strain, while maintaining a diffraction limited focus and a focusing efficiency above 50%. The demonstrated tunable metasurface concept is highly versatile for developing ultra‐slim, multi‐functional and tunable optical devices with widespread applications ranging from consumer electronics to medical devices and optical communications.