Quasiperiodic Structures Research Articles

Inducing Strong Non-Linearities in a Phonon Trapping Quartz Bulk Acoustic Wave Resonator Coupled to a Superconducting Quantum Interference Device

A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10 18 Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID) amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structure of the spectrum in both incident power and frequency. The result gives an insight into the open loop behaviour of a future Cryogenic Quartz Oscillator in the strong signal regime.

Strong coupling superconductivity in a quasiperiodic host-guest structure.

We examine the low-temperature states supported by the quasiperiodic host-guest structure of elemental bismuth at high pressure, Bi-III. Our electronic transport and magnetization experiments establish Bi-III as a rare example of type II superconductivity in an element, with a record upper critical field of ~ 2.5 T, unusually strong electron-phonon coupling, and an anomalously large, linear temperature dependence of the electrical resistivity in the normal state. These properties may be attributed to the peculiar phonon spectrum of incommensurate host-guest structures, which exhibit additional quasi-acoustic sliding modes, suggesting a pathway toward strong coupling superconductivity with the potential for enhanced transition temperatures and high critical fields.

Oscillations and Waves in Radio Source of Drifting Pulsation Structures

Drifting pulsation structures (DPSs) are considered to be radio signatures of the plasmoids formed during magnetic reconnection in the impulsive phase of solar flares. In the present paper we analyze oscillations and waves in seven examples of drifting pulsation structures, observed by the 800-2000 MHz Ondrejov radiospectrograph. For their analysis we use a new type of oscillation maps which give us a much more information about processes in DPSs than that in previous analyzes. Based on these oscillation maps, made from radio spectra by the wavelet technique, we recognized quasi-periodic oscillations with periods ranging from about 1 to 108 s in all studied DPSs. This strongly supports the idea that DPSs are generated during a fragmented magnetic reconnection. Phases of most the oscillations in DPSs, especially for the period around 1 s, are synchronized ("infinite" frequency drift) in the whole frequency range of DPSs. For longer periods in some DPSs we found that the phases of the oscillations drift with the frequency drift in the interval from -17 to +287 MHz\s. We propose that these drifting phases can be caused (a) by the fast or slow magnetosonic waves generated during the magnetic reconnection and propagating through the plasmoid, (b) by a quasi-periodic structure in the plasma inflowing to the reconnection forming a plasmoid, and (c) by a quasi-periodically varying reconnection rate in the X-point of the reconnection close to the plasmoid.

Simultaneous localization of photons and phonons in defect-free dodecagonal phoxonic quasicrystals

In dodecagonal phoxonic quasicrytals (PhXQCs) with a very high rotational symmetry, we demonstrate numerically large phoxonic band gaps (PhXBGs, the coexistence of photonic and phononic band gaps). By computing the existence and dependence of PhXBGs on the choice of radius of holes, we find that PhXQCs can possess simultaneous photonic and phononic band gaps over a rather wide range of geometric parameters. Furthermore, localized modes of THz photons and tens of MHz phonons may exist inside and outside band gaps in defect-free PhXQCs. The electromagnetic and elastic field can be confined simultaneously around the quasicrytals center and decay in a length scale of several basic cells. As a kind of quasiperiodic structures, 12-fold PhXQCs provide a good candidate for simultaneously tailoring electromagnetic and elastic waves. Moreover, these structures exhibit some interesting characteristics due to the very high symmetry.

Filtering properties of Thue–Morse nano-photonic crystals containing high-temperature superconductor

In this paper, we introduced new design of quasi-periodic layered structures by choosing order two of ternary Thue–Morse structure. We considered Superconductor-dielectric photonic crystal with mirror symmetric as (ABSSAB)N(BASSBA)N composed of two kinds of nano-scale dielectric layers (A and B) and high-temperature superconductor layers where N is the number of period. This structure is assumed to be the free space. By using the transfer matrix method and the two fluid model, we theoretically study the transmission spectrum of ternary Thue–Morse superconducting photonic crystals with mirror symmetry and introduce this structure as a narrow optical filter. We showed that transmission peak so-called defect mode appears itself inside the transmission spectrum of suggested structure as same as defective layered structure. Also, we analyzed the influence of various related parameters such as the operating temperature of superconductor layer on position of defect mode. The redshift of defect mode with increasing the operating temperature was observed.

The Model of Electric Connection of a Low-Conductivity Liquid in High-Frequency Electric Field

This paper describes the study of electroconvection of low-conductivity fluid in a capacitor with boundary conditions of adhesion on a solid surface in the case of rapid charge relaxation. The linear stability of fluid equilibrium in a constant electric field is investigated. The model describing the averaged fluid flow in a high-frequency electric field is obtained. The nonlinear regimes of electroconvection are described. A regime map is constructed. It is obtained that, depending on the frequency of the external field, the transition to chaotic state occurs through quasiperiodic or intermittent structures.

Effects of Externally Mounted Store on the Nonlinear Response of Slender Wings

The nonlinear characteristics of slender wings have been studied for many years, and the influences of the geometric structural nonlinearity on the postflutter responses of the wing have been received significant attention. In this paper, the effects of the external store on the nonlinear responses of the slender wing will be discussed. Based on the Hodges–Dowell beam model, the dynamical equations of the wing which include the geometric structural nonlinearity and store effects are constructed. The unsteady aerodynamic loading of the wing will be calculated by employing Wagner function and strip theory. The slender body theory is adopted to get the aerodynamic forces of the store. The Galerkin method is used to obtain the state equations of the system and the appropriate mode combination is obtained for the cases studied in this paper. Numerical simulations are given to show that the store spanwise position and the distance between the store mass center and the elastic center of the wing are two important factors which will affect the nonlinear characteristics of the wing. These two parameters will induce the occurrence of quasi-periodic motion and branch structure in bifurcation diagrams to the system. The peak of postflutter response is also related to these parameters and the lower response peak can be obtained when the store mass center is in front of the elastic center. The models and results are helpful to the design procedure of the slender wing with store in the preliminary stage.

Spin wave propagation spectra in Octonacci one-dimensional magnonic quasicrystals

In this paper, we study spin wave propagation in quasiperiodic magnonic superlattices that follow the so-called Octonacci quasiperiodic sequence, where the N-th stage can be obtained through the recurrence rule SN=SN-1SN-2SN-1, for N⩾3, and starting with S1=A and S2=B. The multilayered magnonic nanostructure is composed of two simple cubic ferromagnetic materials, labeled A and B, which interact through bilinear and biquadratic exchange couplings at their interfaces. The ferromagnetic materials are described by the Heisenberg model, and a transfer matrix treatment is employed, with the calculations performed for the exchange-dominated regime, taking the random phase approximation (RPA) into account. The obtained numerical results show the effects of both (i) the Octonacci quasiperiodic sequence and (ii) the biquadratic exchange coupling on the band structure and transmission spectra of spin waves. Comparisons are also performed with the spectra found in other periodic and quasiperiodic structures.

Global control of colored moiré pattern in layered optical structures

Accurate description of visual effect of colored moiré pattern caused by layered optical structures consisting of gratings and Fresnel lens is proposed in this work. The colored moiré arising from the periodic and quasi-periodic structures is numerically simulated and experimentally verified. It is found that the visibility of moiré pattern generated by refractive optical elements is related to not only the spatial structures of gratings but also the viewing angles. To effectively control the moiré visibility, two constituting gratings are slightly separated. Such scheme is proved to be effective to globally eliminate moiré pattern for displays containing refractive optical films with quasi-periodic structures.

Thin structure of the transit time distributions of open billiards.

It is known that typical open billiards distribution of transit times is an exponentially decaying function, possibly with a power-law tail. In the paper we show that on small scales some of such distributions change their appearance. These distributions contain a quasiperiodic thin structure, which carries a significant amount of information about the system. Origin and properties of this structure are discussed.

A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures

A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures

Topography-induced symmetry transition of droplets on quasi-periodically patterned surfaces.

Quasi-periodic structures of quasicrystals yield novel effects in diverse systems. However, there is little investigation on employing quasi-periodic structures in morphology control. Here, we show the use of quasi-periodic surface structures in controlling the transition of liquid droplets. Although surface structures seem random-like, we find that on these surfaces, droplets spread to well-defined 5-fold symmetric shapes and the symmetry of droplet shapes spontaneously restores during spreading, hitherto unreported in the morphology control of droplets. To obtain physical insights into these symmetry transitions, we conduct energy analysis and perform systematic experiments by varying the properties of both liquid droplets and patterned surfaces. The results show the dominant factors in determining droplet shapes to be surface topography and the self-similarity of the surface structure. Quantified results of the droplet spreading process show distinct dynamics from the spreading experiments on periodically micropatterned surfaces. Our findings significantly advance the control capability of the droplet morphology. Such a quasi-periodic patterning strategy can offer a new method to achieve complex patterns, and may be used to model patterns in the study of rough surfaces.

Optimization of vibration energy localization in quasi-periodic structures

A mechanical periodic structure in presence of component perturbations can be a seat of a localization of vibration energy. In fact, it is well known that mistuned components have larger response levels than those of perfect components. This results in a localized energy, which can be tapped via harvesting devices. In this study, the dynamic behavior of a quasi-periodic system consisting in weakly connected linear oscillators is investigated. The main objective is to optimize the mistuning parameter, the coupling stiffness and the damping coefficient in order to functionalize the imperfection, which leads to the maximization of the localized vibration energy.

Induced waveform transitions of dissipative solitons.

The effect of an externally applied force upon the dynamics of dissipative solitons is analyzed in the framework of the one-dimensional cubic-quintic complex Ginzburg-Landau equation supplemented by a potential term with an explicit coordinate dependence. The potential accounts for the external force manipulations and consists of three symmetrically arranged potential wells whose depth varies along the longitudinal coordinate. It is found out that under an influence of such potential a transition between different soliton waveforms coexisting under the same physical conditions can be achieved. A low-dimensional phase-space analysis is applied in order to demonstrate that by only changing the potential profile, transitions between different soliton waveforms can be performed in a controllable way. In particular, it is shown that by means of a selected potential, stationary dissipative soliton can be transformed into another stationary soliton as well as into periodic, quasi-periodic, and chaotic spatiotemporal dissipative structures.

Extraordinary Effects in Quasi-Periodic Gold Nanocavities: Enhanced Transmission and Polarization Control of Cavity Modes.

Plasmonic quasi-periodic structures are well-known to exhibit several surprising phenomena with respect to their periodic counterparts, due to their long-range order and higher rotational symmetry. Thanks to their specific geometrical arrangement, plasmonic quasi-crystals offer unique possibilities in tailoring the coupling and propagation of surface plasmons through their lattice, a scenario in which a plethora of fascinating phenomena can take place. In this paper we investigate the extraordinary transmission phenomenon occurring in specifically patterned Thue-Morse nanocavities, demonstrating noticeable enhanced transmission, directly revealed by near-field optical experiments, performed by means of a scanning near-field optical microscope (SNOM). SNOM further provides an intuitive picture of confined plasmon modes inside the nanocavities and confirms that localization of plasmon modes is based on size and depth of nanocavities, while cross talk between close cavities via propagating plasmons holds the polarization response of patterned quasi-crystals. Our performed numerical simulations are in good agreement with the experimental results. Thus, the control on cavity size and incident polarization can be used to alter the intensity and spatial properties of confined cavity modes in such structures, which can be exploited in order to design a plasmonic device with customized optical properties and desired functionalities, to be used for several applications in quantum plasmonics.

Archimedean Voronoi spiral tilings

We study the transition of the number of spirals (called parastichy in the theory of phyllotaxis) within a Voronoi tiling for Archimedean spiral lattices. The transition of local parastichy numbers within a tiling is regarded as a transition at the base site point in a continuous family of tilings. This gives a natural description of the quasiperiodic structure of the grain boundaries. It is proved that the number of tiles in the grain boundaries are denominators of rational approximations of the argument (called the divergence angle) of the generator. The local parastichy numbers are non-decreasing functions of the plastochron parameter. The bifurcation diagram of local parastichy numbers has a Farey tree structure.We also prove Richards’ formula of spiral phyllotaxis in the case of Archimedean Voronoi spiral tilings, and show that, if the divergence angle is a quadratic irrational number, then the shapes of tiles in the grain boundaries are close to rectangles. If the divergence angle is linearly equivalent to the golden section, then the shape of tiles in the grain boundaries is close to square.

Antiferromagnetic order in the Hubbard model on the Penrose lattice

We study an antiferromagnetic order in the ground state of the half-filled Hubbard model on the Penrose lattice and investigate the effects of quasiperiodic lattice structure. In the limit of infinitesimal Coulomb repulsion $U \rightarrow +0$, the staggered magnetizations persist to be finite, and their values are determined by confined states, which are strictly localized with thermodynamics degeneracy. The magnetizations exhibit an exotic spatial pattern, and have the same sign in each of cluster regions, the size of which ranges from 31 sites to infinity. With increasing $U$, they continuously evolve to those of the corresponding spin model in the $U=\infty$ limit. In both limits of $U$, local magnetizations exhibit a fairly intricate spatial pattern that reflects the quasiperiodic structure, but the pattern differs between the two limits. We have analyzed this pattern change by a mode analysis by the singular value decomposition method for the fractal-like magnetization pattern projected into the perpendicular space.

Investigation of Transmission Properties in One-Dimensional Quasi-periodic Superconducting Photonic Crystal

This paper explores the transmission characteristics of superconducting quasi-periodic photonic crystal structure arranged in Thue-Morse and double-period sequences. We mainly focused on the cutoff frequency of transmittance spectra. The study shows that the cutoff frequency can be appreciably tuned by generation number of sequence, thicknesses of constituent layers and operating temperature. Shifting behaviour of cutoff frequency is in contrast with periodic structure on varying superconductor thickness and temperature whereas it shows opposite trend on changing the dielectric layer thickness. It is also observed that different quasi-periodic structures show distinct values of cutoff frequency and different transmission properties. This features allow to tune the cutoff frequency or band gap in the whole infrared frequency region.

Narrow stop band microwave filters by using hybrid generalized quasi-periodic photonic crystals

Using the transfer matrix method approach (TMM), the microwave transmission spectra in hybrid quasi-periodic multilayer photonic structures are studied. These structures are formed by concatenating several quasi-periodic sequences such as the generalized Cantor (GC (a, b, c)), generalized Fibonacci (GF (m, n)) and generalized Thue–Morse (GTM (m, n)). The results are presented for a normal incident wave with transverse electric (TE) polarization. The optimization of the sequences’ parameters (a, b, c, m and n) permits us to obtain polychromatic filters that cover the frequency range of Global Systems for Mobile Communication (GSM). The manipulation of these parameters fixes the number of photonic band gaps (PBGs) and the position of the transmission peaks.

Transition dipole coupling modeling of optical activity enhancements in macromolecular protein systems.

The transition dipole coupling model allows to vary systematically many parameters, such as chromophore geometries and transition dipoles. We used it to explore conditions favorable to chirality enhancement observed in many experiments on protein amyloidal precipitates. Stacking of β-sheet planes has been identified as a particularly powerful mechanism of the enhancement.