Quasiperiodic Structures Research Articles

Quasiperiodic Frank–Kasper phases derived from the square–triangle dodecagonal tiling

Frank–Kasper (F-K) phases form an important set of large-cell crystalline structures describing many intermetallic alloys. They are usually described in term of their atomic environments, with atoms having 12, 14, 15 and 16 neighbours, coded into the canonical $$Z_p$$ cells (with p the coordination number), the case $$p=12$$ corresponding to a local icosahedral environment. In addition, the long-range structure is captured by the geometry of a network (called either “major skeleton” or “disclination network”) connecting only the non-icosahedral sites (with $$p\ne 12$$ ). Another interesting description, valid for the so-called layered F-K phases, amounts to give simple rules to decorate specific periodic 2d tilings made of triangles and squares and eventually get the 3d periodic F-K phases. Quasicrystalline phases can sometime be found in the vicinity, in the phase diagram , of the F-K crystalline alloys; it is therefore of interest to understand whether and how the standard F-K construction rules can be generalized on top of an underlying quasiperiodic structure. It is in particular natural to investigate how well square–triangle quasiperiodic tilings with dodecagonal symmetry, made of square and (equilateral) triangles, can be used as building frames to generate some F-K-like quasicrystalline structures . We show here how to produce two types of such structures, which are quasiperiodic in a plane and periodic in the third direction, and containing (or not) $$Z_{16}$$ sites.

Pyroelectromagnetic Effects of a Piezocomposite in the Binary Refinement of the Method of Quasi-Periodic Polydisperse Correlation Components

A numerical analysis of two-point correlation functions of correlated quasi-periodic mono- and polydisperse unidirectional fibrous composite structures is carried out. The features of application of an earlier obtained solution of the method of polydisperse correlation components to monodisperse quasi-periodic pyroelectromagneticelastic piezostructures, with the example of numerical calculation of the effective coefficients of pyroelectric and pyromagnetic couplings of a composite whose constituents do not exhibit these effects, are considered. The solution for the required tensors of effective transverse isotropic pyroelectromagnetoelastic properties of a monodisperse quasi-periodic fibrous structure is given as a linear expansion in terms of corresponding known analytical solutions for traditional polydisperse structures by using the correlation coefficients of quasi-periodic mono- and polydisperse structures.

Quasiperiodicity and Chaos in a Generalized Nosé–Hoover Oscillator

This paper reports on an investigation of the two-dimensional parameter-space of a generalized Nosé–Hoover oscillator. It is a mathematical model of a thermostated harmonic oscillator, which consists of a set of three autonomous first-order nonlinear ordinary differential equations. By using Lyapunov exponents to numerically characterize the dynamics of the model at each point of this parameter-space, it is shown that dissipative quasiperiodic structures are present, embedded in a chaotic region. The same parameter-space is also used to confirm the multistability phenomenon in the investigated mathematical model.

Design of tunable devices using one-dimensional Fibonacci photonic crystals incorporating graphene at terahertz frequencies

For the one-dimensional generalized Fibonacci photonic crystals incorporating graphene, we present many valuable properties and design the tunable devices accordingly with the help of the transfer matrix method in the frequency range of terahertz. For the common structure, all of dielectric layers are cladded by graphene, we design the high-Q tunable filter with double peaks by changing the Fibonacci distribution and chemical potential. In order to reduce the crosstalk of signals through this filter, a heterostructure based on the current structure and the one without graphene is utilized to separate the two peaks. Also, we fabricate the tunable switch by altering the parity of periodic number. Besides, through cladding the graphene on the one of the dielectrics only, we obtain other two kinds of cells. Combining these cells arbitrarily as the supercell to develop the periodic structure, the number of forbidden bands is increased in accordance with certain rules so that this structure with supercell is suitable as the multi-stop filter. If the active medium is introduced, the imaginary part of the complex permittivity of the material would be negative, which means the energy amplification. For our quasi-periodic structures with active medium, the functions of chemical potential, damping constant and reference wavelength are investigated.

Convection roll-driven generation of supra-wavelength periodic surface structures on dielectrics upon irradiation with femtosecond pulsed lasers

The significance of the magnitude of Prandtl number of a fluid in the propagation direction of induced convection rolls is elucidated. Specifically, we report on the physical mechanism to account for the formation and orientation of previously unexplored supra-wavelength periodic surface structures in dielectrics, following melting and subsequent capillary effects induced upon irradiation with ultrashort laser pulses. Counterintuitively, it is found that such structures exhibit periodicities, which are markedly, even multiple times, higher than the laser excitation wavelength. It turns out that the extent to which the hydrothermal waves relax depends upon the laser beam energy, produced electron densities upon excitation with femtosecond pulsed lasers, magnitude of the induced initial local roll disturbances and the magnitude of the Prandtl number with direct consequences on the orientation and size of the induced structures. It is envisaged that this elucidation may be useful for the interpretation of similar, albeit large-scale periodic or quasi-periodic structures formed in other natural systems due to thermal gradients, while it can also be of great importance for potential applications in biomimetics.

Non-additive model for specific heat of electrons

By using non-additive Tsallis entropy we demonstrate numerically that one-dimensional quasicrystals, whose energy spectra are multifractal Cantor sets, are characterized by an entropic parameter, and calculate the electronic specific heat, where we consider a non-additive entropy Sq. In our method we consider an energy spectra calculated using the one-dimensional tight binding Schrödinger equation, and their bands (or levels) are scaled onto the [0,1] interval. The Tsallis' formalism is applied to the energy spectra of Fibonacci and double-period one-dimensional quasiperiodic lattices. We analytically obtain an expression for the specific heat that we consider to be more appropriate to calculate this quantity in those quasiperiodic structures.

Enhancement of Light Localization in Hybrid Thue-Morse/Periodic Photonic Crystals

The electric field intensity in one-dimensional (1D) quasiperiodic and hybrid photonics band-gap structures is studied in the present paper. The photonic structures are ordered according to Fibonacci, Thue-Morse, Cantor, Rudin-Shapiro, Period-Doubling, Paper-Folding, and Baum-Sweet sequences. The study shows that the electric field intensity is higher for the Thue-Morse multilayer systems. After that the Thue-Morse structure will be combined with a periodic structure to form a hybrid photonic structure. It is shown that this hybrid system is the best for a strong localization of light. The proposed structures have been modeled using the Transfer Matrix Method.

Omnidirectional broadband THz filter based on a one-dimensional Thue–Morse quasiperiodic structure containing graphene nanolayers

The transmission properties of a one-dimensional graphene-based Thue–Morse quasiperiodic structure in which graphene nanolayers are embedded between dissimilar adjacent dielectric layers have been investigated. From the numerical results performed by transfer matrix method, it is found that the structure possesses an omnidirectional photonic bandgap called a graphene-induced photonic bandgap (GIPBG) due to the existence of the graphene nanolayers, in addition to the structural Bragg gaps. To design an omnidirectional broadband THz filter, the effects of many parameters such as the scale length and relative permittivity of the layers on the properties of GIPBG are discussed. Our findings show that the frequency range of the omnidirectional GIPBG increases as the scaling decreases. In contrast to Bragg gaps, the width of such an omnidirectional bandgap is notably enhanced by reducing the contrast of the layers’ permittivity and reaches a maximum value when the constituent layers have the same relative permittivity. Our investigations also reveal that in the case of a uniform material, the lowest permittivity of the dielectric material would result in the widest omnidirectional GIPBG. Moreover, the possibility of external control of the omnidirectional bandwidth using a gate voltage is shown. Finally, the application of the structure as a polarizing beam splitter has been shown.

Enhanced light extraction efficiency of OLEDs with quasiperiodic diffraction grating layer.

We presented enhanced light extraction efficiency of organic light emitting diodes (OLEDs) cells with a nano-sized diffraction grating layer. Various diffraction gratings of different morphologies including linear, cubic, hexagonal and quasiperiodic patterns were fabricated by multiplexing light interference exposure on an azobenzene thin film. The effect of diffraction grating layer on device performances including luminous properties and quantum efficiency was investigated. In contrast to periodic grating patterns, the quasiperiodic structures leading broadband light extraction resulted in improved external quantum efficiency and power efficiency by 73% and 63%, respectively, compared to conventional OLED with flat surface of glass substrate.

Effect of temperature on terahertz photonic and omnidirectional band gaps in one-dimensional quasi-periodic photonic crystals composed of semiconductor InSb.

Engineering of thermally tunable terahertz photonic and omnidirectional bandgaps has been demonstrated theoretically in one-dimensional quasi-periodic photonic crystals (PCs) containing semiconductor and dielectric materials. The considered quasi-periodic structures are taken in the form of Fibonacci, Thue-Morse, and double periodic sequences. We have shown that the photonic and omnidirectional bandgaps in the quasi-periodic structures with semiconductor constituents are strongly depend on the temperature, thickness of the constituted semiconductor and dielectric material layers, and generations of the quasi-periodic sequences. It has been found that the number of photonic bandgaps increases with layer thickness and generation of the quasi-periodic sequences. Omnidirectional bandgaps in the structures have also been obtained. Results show that the bandwidths of photonic and omnidirectional bandgaps are tunable by changing the temperature and lattice parameters of the structures. The generation of quasi-periodic sequences can also change the properties of photonic and omnidirectional bandgaps remarkably. The frequency range of the photonic and omnidirectional bandgaps can be tuned by the change of temperature and layer thickness of the considered quasi-periodic structures. This work will be useful to design tunable terahertz PC devices.

About optical localization in photonic quasicrystals

We employ the two stage cut and project scheme to generate a dodecagonal two-dimensional quasiperiodic structure. The finite-differences-time-domain method is applied to simulate the propagation of electromagnetic modes in the system. We compute the transmission coefficients as well as the inverse participation ratio for a quasicrystal consisting of dielectric cylindrical rods. We find that for a small crystal the band gap forms due to destructive interference between extended states. The quasiperiodic geometry exhibits modes with enhanced transmission coefficients. The inverse participation ratio analysis indicates that these modes are localized and that the localization length is estimated to be 0.3207 in the inverse units of a lattice characteristic length scale.

Dynamical playground of a higher-order cubic Ginzburg-Landau equation: From orbital connections and limit cycles to invariant tori and the onset of chaos.

The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order dispersion and stimulated Raman scattering effects gives rise to rich dynamics: this extends from Poincaré-Bendixson-type scenarios, in the sense that bounded solutions may converge either to distinct equilibria via orbital connections or to space-time periodic solutions, to the emergence of almost periodic and chaotic behavior. One of our main results is that third-order dispersion has a dominant role in the development of such complex dynamics, since it can be chiefly responsible (even in the absence of other higher-order effects) for the existence of periodic, quasiperiodic, and chaotic spatiotemporal structures. Suitable low-dimensional phase-space diagnostics are devised and used to illustrate the different possibilities and identify their respective parametric intervals over multiple parameters of the model.

The stability of the fractal properties of quasiperiodic multilayered structures

The stability of fractal characteristics has been analyzed in the optical spectra of quasi-periodic multilayered systems with the deterministic changes therein. The transformation of the summation principle of their construction, the transition to the approximant model, and the preparation of metamaterial-based layers have been shown to exert a strong influence on the scaling of the parameters in multilayered systems.

Weakly nonlinear convective regimes in a horizontal fluid layer with poorly conducting boundaries and temperature-dependent viscosity

In this work, the influence of temperature dependence of viscosity on the weakly nonlinear regimes in a horizontal fluid layer with poorly conducting boundaries is studied. A multi-scale method is used to derive the amplitude equations, which are investigated analytically and numerically. The stability of roll patterns, square cells, hexagonal cells and quasi-periodic dodecagonal structures is investigated analytically. As a numerical method we use one of modifications of the spectral method. It has been found that only hexagonal and square patterns maintain stability, the hexagonal pattern being always stable for sufficiently large values of the Prandtl number. The calculations have shown that there is the region of co-existence of hexagonal and square patterns for a small range of the parameter, which is responsible for temperature dependence of viscosity. The hexagonal cells are always excited subcritically, whereas the square cells can be excited both in a subcritical and supercritical manner. Our investigations at small values of the Prandtl number have also revealed the instability, which is associated with nonzero vertical vorticity.

Implications of L1 observations for slow solar wind formation by solar reconnection

AbstractWhile the source of the fast solar wind is known to be coronal holes, the source of the slow solar wind has remained a mystery. Long time scale trends in the composition and charge states show strong correlations between solar wind velocity and plasma parameters, yet these correlations have proved ineffective in determining the slow wind source. We take advantage of new high time resolution (12 min) measurements of solar wind composition and charge state abundances at L1 and previously identified 90 min quasiperiodic structures to probe the fundamental timescales of slow wind variability. The combination of new high temporal resolution composition measurements and the clearly identified boundaries of the periodic structures allows us to utilize these distinct solar wind parcels as tracers of slow wind origin and acceleration. We find that each 90 min (2000 Mm) parcel of slow wind has near‐constant speed yet exhibits repeatable, systematic charge state and composition variations that span the entire range of statistically determined slow solar wind values. The classic composition‐velocity correlations do not hold on short, approximately hourlong, time scales. Furthermore, the data demonstrate that these structures were created by magnetic reconnection. Our results impose severe new constraints on slow solar wind origin and provide new, compelling evidence that the slow wind results from the sporadic release of closed field plasma via magnetic reconnection at the boundary between open and closed flux in the Sun's atmosphere.

Surface electric potential of linear periodic charge density

Distribution of the surface electric potential allows visualizing surface plasmons and gives information about parameters of the plasmons. Some plasmonic structures have a periodic structure, for example hybrid self-assembled photonic-plasmonic crystals. Earlier we presented a new method of calculation of the potential for quasiperiodic and periodic structures. In this paper we compare the method with other methods that have different algorithms and formulas.

Features of parkinsonian and essential tremor of the human hand

Using spectral, wavelet, multifractal, and recurrence analyses we examined the features of involuntary shaking (tremor) arising during the performance of a given motor task. The task was to maintain the efforts of fingers under isometric conditions by a healthy subject, a patient with primary bilateral parkinsonism, and a patient with a syndrome of the essential tremor. The physiological tremor was characterized by the minimal amplitude, the broad power spectrum, the minimal energy of the wavelet spectrum, the maximal degree of multifractality, the minimal degree of determinism, and the maximal entropy of recurrence time density. In the case of the essential tremor we observed the significant enhancement of the wavelet spectrum energy and the decrease of the oscillation complexity. It was evident as the appearance of clear peaks in the power spectra, the fall in the multifractality degree, the emergence of a quasiperiodic structure in the recurrence diagrams, the grow of determinism and the decrease of the entropy of recurrence time density. All these trends were enhanced for the parkinsonian tremor. The suggested characteristics enable us to estimate the degree of deviation of the motor function from the healthy one.

Second-order asymptotic algorithm for heat conduction problems of periodic composite materials in curvilinear coordinates

A new second-order two-scale (SOTS) asymptotic analysis method is presented for the heat conduction problems concerning composite materials with periodic configuration under the coordinate transformation. The heat conduction problems are solved on the transformed regular domain with quasi-periodic structure in the general curvilinear coordinate system. By the asymptotic expansion, the cell problems, effective material coefficients and homogenized heat conduction problems are obtained successively. The main characteristic of the approximate model is that each cell problem defined on the microscopic cell domain is associated with the macroscopic coordinate. The error estimation of the asymptotic analysis method is established on some regularity hypothesis. Some common coordinate transformations are discussed and the reduced SOTS solutions are presented. Especially by considering the general one-dimensional problem, the explicit expressions of the SOTS solutions are derived and stronger error estimation is presented. Finally, the corresponding finite element algorithms are presented and numerical results are analyzed. The numerical errors presented agree well with the theoretical prediction, which demonstrate the effectiveness of the second-order asymptotic analysis method. By the coordinate transformation, the asymptotic analysis method can be extended to more general domain with periodic microscopic structures.

Simultaneous large band gaps and localization of electromagnetic and elastic waves in defect-free quasicrystals.

We report numerically large and complete photonic and phononic band gaps that simultaneously exist in eight-fold phoxonic quasicrystals (PhXQCs). PhXQCs can possess simultaneous photonic and phononic band gaps over a wide range of geometric parameters. Abundant localized modes can be achieved in defect-free PhXQCs for all photonic and phononic polarizations. These defect-free localized modes exhibit multiform spatial distributions and can confine simultaneously electromagnetic and elastic waves in a large area, thereby providing rich selectivity and enlarging the interaction space of optical and elastic waves. The simulated results based on finite element method show that quasiperiodic structures formed of both solid rods in air and holes in solid materials can simultaneously confine and tailor electromagnetic and elastic waves; these structures showed advantages over the periodic counterparts.

TM Wave Resonant Peaks in Defect-Free Multilayer Structures Containing Nano-Scale Y123 Superconductors

In the ultraviolet region and by using transfer matrix method, the transmission spectra of electromagnetic waves through one-dimensional quasiperiodic photonic structures consisting of high-temperature yttrium barium copper oxide (Y123) superconductor and strontium titanate (STO) dielectric layers are studied theoretically. It is shown that for TE polarization at oblique incidence two band gaps are created, while for TM polarization three band gaps are produced. The edges of both polarizations shift to higher wavelengths by increasing incident angles. Also, for angles of incidence greater than 78∘, the second gap for TM-polarized light is eliminated. It is also found that in the supposed structure the number of PBGs can be modulated by the thickness of dielectric layer, while it is nearly insensitive to the thickness of superconductor layer. Interestingly, for the incidence angles other than normal incidence the structure can exhibit some narrow resonant peaks near wavelengths where the electric permittivity of the superconductor layer changes sign. These resonant peaks are only for TM polarization and not present for TE polarization. This structure can act as a very compact polarization sensitive splitters and defect-free multichannel narrowband tunable filters.