Quasiperiodic Structures Research Articles

Chapter 5 - Temporal coding in the auditory cortex

Speech is a complex acoustic signal showing a quasiperiodic structure at several timescales. Integrated neural signals recorded in the cortex also show periodicity at different timescales. In this chapter we outline the neural mechanisms that potentially allow the auditory cortex to segment and encode continuous speech. This chapter focuses on how the human auditory cortex uses the temporal structure of the acoustic signal to extract phonemes and syllables, the two major constituents of connected speech. We argue that the quasiperiodic structure of collective neural activity in auditory cortex represents the ideal mechanical infrastructure to fractionate continuous speech into linguistic constituents of variable sizes.

Compression of ECG Signal Based on Compressive Sensing and the Extraction of Significant Features

Diagnoses of heart diseases can be done effectively on long term recordings of ECG signals that preserve the signals’ morphologies. In these cases, the volume of the ECG data produced by the monitoring systems grows significantly. To make the mobile healthcare possible, the need for efficient ECG signal compression algorithms to store and/or transmit the signal efficiently has been rising exponentially. Currently, ECG signal is acquired at Nyquist rate or higher, thus introducing redundancies between adjacent heartbeats due to its quasi-periodic structure. Existing compression methods remove these redundancies by achieving compression and facilitate transmission of the patient’s imperative information. Based on the fact that these signals can be approximated by a linear combination of a few coefficients taken from different basis, an alternative new compression scheme based on Compressive Sensing (CS) has been proposed. CS provides a new approach concerned with signal compression and recovery by exploiting the fact that ECG signal can be reconstructed by acquiring a relatively small number of samples in the “sparse” domains through well-developed optimization procedures. In this paper, a single-lead ECG compression method has been proposed based on improving the signal sparisty through the extraction of the signal significant features. The proposed method starts with a preprocessing stage that detects the peaks and periods of the Q, R and S waves of each beat. Then, the QRS-complex for each signal beat is estimated. The estimated QRS-complexes are subtracted from the original ECG signal and the resulting error signal is compressed using the CS technique. Throughout this process, DWT sparsifying dictionaries have been adopted. The performance of the proposed algorithm, in terms of the reconstructed signal quality and compression ratio, is evaluated by adopting DWT spatial domain basis applied to ECG records extracted from the MIT-BIH Arrhythmia Database. The results indicate that average compression ratio of 11:1 with PRD1 = 1.2% are obtained. Moreover, the quality of the retrieved signal is guaranteed and the compression ratio achieved is an improvement over those obtained by previously reported algorithms. Simulation results suggest that CS should be considered as an acceptable methodology for ECG compression.

Hydrodynamic instability in a magnetically driven suspension of paramagnetic red blood cells.

We investigate the magnetically driven motion in suspensions of paramagnetic particles. Our object is diluted deoxygenated whole blood with paramagnetic red blood cells (RBCs). We use direct observations in a closed vertical Hele-Shaw channel, and a well-defined magnetic force field applied horizontally in the channel plane. At very low cell concentrations, we register single-particle motion mode, track individual cells and determine their hydrodynamic and magnetic characteristics. Above 0.2 volume percent concentration, we observe local swirls and a global transient quasi-periodic vortex structure, intensifying with increasing cell concentration, but surprisingly this does not influence the time and purity of the magnetic extraction of RBCs. Our observations shed light on the behavioral complexity of magnetically driven submagnetic suspensions, an important issue for the emerging microfluidic technology of direct magnetic cell separation and intriguing for the mechanics of particulate soft matter.

Quantum pseudocritical point in the unbounded quasiperiodic transverse field Ising chain

We study the quantum pseudocritical points in the unbounded quasiperiodic transverse field Ising chain of finite-size systematically. Firstly, we study the derivatives of averaged magnetic moment and the averaged concurrence with transverse fields. Both of them show two visible peaks, with are nearly not raised when the length of chain is increased. Moreover, the places where the peaks occur in the transverse field are obviously different from that of the quantum phase transition point in the thermodynamic limit. These results are very different from those of the bounded quasiperiodic transverse field Ising chain and the disordered transverse field Ising chain. Then, we analyze the origin of the two visible peaks. For that we study the derivative of magnetic moment for each spin with transverse field. For all spins, the single magnetic moment only show one peak. However, the places where the peaks occur are not random. The peaks always occur in two regions. Thus, the derivatives of averaged magnetic moment reveal two peaks. Furthermore, we study the probability distribution of the pseudocritical points through finding out the peaks of the single magnetic moment in 1000 samples. The distribution is not Guassian. This result is obviously different from that of the disordered case. Besides, the pseudocritical points nearly do not occur at the quantum phase transition point. Finally, we analyze the origin of the pseudocritical points. For that we study the relationship between the spin places and the corresponding places of pseudocritical points. It is found that the pseudocritical points are caused by the two groups that exist in the nearest neighboring interactions of the unbounded quasiperiodic structure. When a spin is in one group, this group will decide the probable place of the pseudocritical point. Through this study, we find that although the quantum phase transition behaviors of the unbounded quasiperiodic transverse field Ising chain and the disordered transverse field Ising chain belong to the same universal class in the thermodynamic limit, the thermodynamic behaviors of the two Ising chains are very different as in finite sizes. The differences are caused by the special structure in the unbounded quasiperiodic system.

Role of magnetic fluctuations in mode selection of magnetically driven instabilities

The influences of magnetic fluctuations on quasiperiodic structure formation and fundamental wavelength selection of the instability have been studied using two 25-μm-diameter tungsten wires on a 100 ns rise time, 220 kA pulsed power facility. Two different load configurations were adopted to make end surfaces of electrodes approximately satisfy reflecting and absorbing boundary conditions, respectively. The experimental results that the fundamental wavelength in the case of absorbing boundary condition is about one half of that in the case of reflecting boundary condition have demonstrated that magnetic fluctuations appear to play a key role in mode selection of magnetically driven instabilities. The dominant wavelength should be proportional to magnetic field and inversely proportional to square root of mass density, provided that the magnetosonic wave propagating perpendicular to magnetic fields provides a leading candidate for magnetic fluctuations. Therefore, magnetic fluctuation is one of the three key perturbations, along with surface contaminants and surface roughness, that seeds magnetically driven instabilities.

Continuous generation and two‐dimensional structure of equatorial plasma bubbles observed by high‐density GPS receivers in Southeast Asia

AbstractHigh‐density GPS receivers located in Southeast Asia (SEA) were utilized to study the two‐dimensional structure of ionospheric plasma irregularities in the equatorial region. The longitudinal and latitudinal variations of tens of kilometer‐scale irregularities associated with equatorial plasma bubbles (EPBs) were investigated using two‐dimensional maps of the rate of total electron content change index (ROTI) from 127 GPS receivers with an average spacing of about 50–100 km. The longitudinal variations of the two‐dimensional maps of GPS ROTI measurement on 5 April 2011 revealed that 16 striations of EPBs were generated continuously around the passage of the solar terminator. The separation distance between the subsequent onset locations varied from 100 to 550 km with 10 min intervals. The lifetimes of the EPBs observed by GPS ROTI measurement were between 50 min and over 7 h. The EPBs propagated 440–3000 km toward the east with velocities of 83–162 m s−1. The longitudinal variations of EPBs by GPS ROTI keogram coincided with the depletions of 630 nm emission observed using the airglow imager. Six EPBs were observed by GPS ROTI along the meridian of Equatorial Atmosphere Radar (EAR), while only three EPBs were detected by the EAR. The high‐density GPS receivers in SEA have an advantage of providing time continuous descriptions of latitudinal/longitudinal variations of EPBs with both high spatial resolution and broad geographical coverage. The spatial periodicity of the EPBs could be associated with a wavelength of the quasiperiodic structures on the bottomside of the F region which initiate the Rayleigh‐Taylor instability.

Local Electron Correlations in a Two-Dimensional Hubbard Model on the Penrose Lattice

We study electron correlations in the half-filled Hubbard model on two-dimensional Penrose lattice. Applying the real-space dynamical mean-field theory to large clusters, we discuss how low-temperature properties are affected by the quasiperiodic structure. By calculating the double occupancy and renormalization factor at each site, we clarify the existence of the Mott transition. The spatially-dependent renormalization characteristic of geometrical structure is also addressed.

Localization of light in the atomic medium induced by the Hermite-cosine-Gauss field.

This paper provides a way of realizing light wave localization via electromagnetically induced transparency, which is quite different from the traditional, off-resonant mechanism-based Aubry-Andre model. The localization of light in a one-dimensional atomic medium is reported in this paper. The medium suggested in this paper is a resonant cold atomic ensemble with N-configuration, which can be modulated to be a quasi-periodic structure in the center area. As the paraxial signal field propagates in the medium, localization can be realized. The localization point and the propagation properties of the signal field are studied in this paper.

Lateral shift in one-dimensional quasiperiodic chiral photonic crystal

We investigate the lateral shift of a one-dimensional quasiperiodic photonic crystal consisting of chiral and conventional dielectric materials. The effect of structural irregularity on lateral shift is evaluated by stationary-phase approach. Our results show that the lateral shift can be modulated by varying the structural irregularity in quasiperiodic structure. Besides, the position of peak in lateral shift spectrum stays sensitive to the chiral factor of chiral materials. In comparison with that of periodic structure, quasiperiodic structure provides an extra degree of freedom to manipulate the lateral shift.

Application of the multiband -models to quantum transport in quasi-periodic crystals

We consider the quantum transport of a particle in a crystal where the global three-dimensional translation symmetry is removed. Our analysis concerns solid state structures where the microscopic potential of the ions is no longer periodic. This includes materials with variable chemical composition, intergrowth compounds and abrupt junctions. The application of the kp multiband envelope function models to the description of the quantum mechanical motion in such a quasi-periodic structure is investigated. By using a spectral decomposition technique, we show that when the interatomic distance is asymptotically small, the particle probability density can be obtained by the envelope kp model with variable coefficients.

Structure of a proton wire in the harmonic model with allowance for the interproton interaction for the first and second neighbors

Differential equations based on the one-component harmonic model of a water chain are proposed for description of the proton wire structure with allowance for the interproton interaction of near and far neighbors. The solution to the Sturm-Liouville problem is considered for a fourth-order differential equation that takes into account interproton interactions with the first and second adjacent links of a one-dimensional chain. The function of proton displacements in such a wire is shown to describe a quasi-periodical structure, depending on the ratio of constants D1 and D2 for the interproton interaction of the first and second neighbors. According to calculations using the parameters characteristic of the water chain, the curve of the proton displacement is a plot of function y = cosk1x + sink2x and is similar to the curve of the hydrogen bond length distribution obtained earlier in the quantum-chemical calculations of the proton channel model.

Study of possible chaotic, quasi-periodic and periodic structures in quantum dusty plasma

Existence of chaotic, quasi-periodic, and periodic structures of dust-ion acoustic waves is studied in quantum dusty plasmas through dynamical system approach. A system of coupled differential equations is derived from the fluid model and subsequently, variational matrix is obtained. The characteristic equation is obtained at the equilibrium point, and the behavior of nonlinear waves is studied numerically using Runge-Kutta method. The behavior of the dynamical system changes significantly when any of plasma parameters, such as the dust concentration parameter, temperature ratio, or the quantum diffraction parameter, is varied. The change of the characteristic of solution of the system is extensively studied. It is found that the system changes its behavior from chaotic pattern to limit cycle behavior.

Biologically inspired flexible quasi-single-mode random laser: an integration of Pieris canidia butterfly wing and semiconductors.

Quasi-periodic structures of natural biomaterial membranes have great potentials to serve as resonance cavities to generate ecological friendly optoelectronic devices with low cost. To achieve the first attempt for the illustration of the underlying principle, the Pieris canidia butterfly wing was embedded with ZnO nanoparticles. Quite interestingly, it is found that the bio-inspired quasi-single-mode random laser can be achieved by the assistance of the skeleton of the membrane, in which ZnO nanoparticles act as emitting gain media. Such unique characteristics can be interpreted well by the Fabry-Perot resonance existing in the window-like quasi-periodic structure of butterfly wing. Due to the inherently promising flexibility of butterfly wing membrane, the laser action can still be maintained during the bending process. Our demonstrated approach not only indicates that the natural biological structures can provide effective scattering feedbacks but also pave a new avenue towards designing bio-controlled photonic devices.

The localization of light in a 2D quasi-periodic coherently prepared atomic medium

We study the localization of light in two-dimensional (2D) atomic systems. The system proposed in this paper is a resonant cold atomic ensemble with N configuration, which is coherently prepared by four pairs of control fields. Under the condition of the electromagnetically induced transparency, the propagation of the signal field is modelled as a system that is uniform along the propagating direction (z) but shows quasi-periodic structure on the transverse plane (x–y plane). Through numerical simulations, we find that the 2D quasi-periodic coherently prepared atomic medium can make the signal field anisotropic localized transversely during the propagation, and the localization direction can be manipulated by the phase of the control field.

Quasi-periodic Fibonacci and periodic one-dimensional hypersonic phononic crystals of porous silicon: Experiment and simulation

A one-dimensional Fibonacci phononic crystal and a distributed Bragg reflector were constructed from porous silicon. The structures had the same number of layers and similar acoustic impedance mismatch, and were electrochemically etched in highly boron doped silicon wafers. The thickness of the individual layers in the stacks was approximately 2 μm. Both types of hypersonic band gap structure were studied by direct measurement of the transmittance of longitudinal acoustic waves in the 0.1–2.6 GHz range. Acoustic band gaps deeper than 50 dB were detected in both structures. The experimental results were compared with model calculations employing the transfer matrix method. The acoustic properties of periodic and quasi-periodic structures in which half-wave retarding bi-layers do not consist of two quarter-wave retarding layers are discussed. The strong correlation between width and depth of gaps in the transmission spectra is demonstrated. The dominant mechanisms of acoustic losses in porous multilayer structures are discussed. The elastic constants remain proportional over our range of porosity, and hence, the Grüneisen parameter is constant. This simplifies the expression for the porosity dependence of the Akhiezer damping.

Directional scaling symmetry of high-symmetry two-dimensional lattices.

Two-dimensional lattices provide the arena for many physics problems of essential importance, a scale symmetry, which rarely exists as noticed by Galileo, in such lattices can help reveal the underlying physics. Here we report the discovery and proof of directional scaling symmetry for high symmetry 2D lattices, i.e., the square lattice, the equilateral triangular lattice and thus the honeycomb lattice, with aid of the function y = arcsin(sin(2πxn)), where the parameter x is either the platinum number or the silver number , which are related to the 12-fold and 8-fold quasiperiodic structures, respectively. The directions and scale factors for the symmetric scaling transformation are determined. The revealed scale symmetry may have a bearing on various physical problems modeled on 2D lattices, and the function adopted here can be used to generate quasiperiodic lattices with enumeration of lattice points. Our result is expected to initiate the search of directional scaling symmetry in more complicated geometries.

Study on flow behind backward-facing step in a narrow channel

Both statistics and dynamics of the flow-field behind a backward-facing step in a narrow channel is studied experimentally using time-resolved PIV technique. The channel width is 4 step heights, Reynolds number based on the step height was about 35 thousands. Secondary flow effect is detected clearly in the region behind the step resulting in strong 3D flow structure just behind the step. The low-frequency quasi-periodical structures appearing in the region behind the step and in the region of the flow reattachment close to the channel bottom are studied using the Oscillation Pattern Decomposition (OPD) technique. Strouhal numbers of those phenomena are very low, order of 0.01. Typical time-mean structures as well as dynamical structures are to be presented.

A cubic quasicrystal in a rapidly-solidified Mg-Al alloy

It is commonly accepted that the definition of quasicrystal should include a rotational symmetry forbidden in periodic crystals. On the other hand, the quasicrystal with a conventional point group is theoretically possible [1,2]. In a rapidly-solidified Mg-Al alloy, intriguing electron diffraction patterns (EDPs) were reported, which show a cubic symmetry with aperiodic arrays of Bragg reflections [2]. In the present work, we investigate the detailed structure of the rapidly-solidified Mg-Al phase based on direct structure observations using STEM. In a rapidly-solidified Mg-61 at.% Al alloy, 2-fold, 3-fold, and 4-fold EDPs are obtained (Fig. a), which shows that the structure has the cubic point group. However, the relevant diffraction spots are arranged aperiodically. Especially in the 2-fold EDP, a high density of the spots is observed, and the corresponding HADDF-STEM image shows several remarkable features (Fig. b). Two length scales, L and S, can be definitely observed, and they are arranged quasiperiodically along the 3-fold axis. Their arrangement can be well described by the hyperspace crystallography; a physical space tilted by the angle θ , where tanθ ∼ 1.4, successfully generates the observed quasiperiodic pattern. Simulated EDPs from a simple model without detailed atomic decoration reproduces fairly well the experimental patterns. Further analysis of the images reveals that the present quasiperiodic structure has similar local structure to the stable β-Mg2Al3phase; two lengths correspond to L and S may be reasonably defined. The quasicrystal with a cubic symmetry is unambiguously determined for the first time, based on a direct structural observation. The present results strongly suggest that the noncrystallographic rotational symmetry is not an essential factor to form the quasiperiodic structure, raising a very fundamental, universal question on the physical origin of a long-range order of condensed matters.

Construction of quasiperiodic patterns in the Moroccan ornamental art

The similarity between the structure of Islamic decorative patterns and quasicrystal, aroused the interest of several crystallographers. They analyzed these patterns, by different approaches, various kinds of ornamental quasiperiodic patterns encountered in the Morocco and Alhambra (Andalusia) as well as in the eastern of Islamic world. In this work, we are interesting in the quasiperiodic patterns found in several Moroccan historical buildings constructed in the 14th century. We first describe the Zellige panels (fine mosaics) decorating the Madrasas (schools) Attarine and Bou Inania in Fez in term of Penrose tiling, to confirm that both panels have quasiperiodic structure (Makovicky et al, 1998). The panel Madrasas Attarine appears as a finite part of this quasiperiodic pattern (Figure 1-c). As already mentioned by several authors, we can notice the similarity of the decagonal pattern with the diffraction pattern of the quasicrystal Al Mn (Schechtman et al, 1984) (Figure 1-a and c). The multigrid method developed by De Bruijn (1981) and reformulated by Gratias (2002) to obtain a quasiperiodic paving, is used to construct known quasiperiodic patterns from periodic patterns extracted from the Madrasas Bou Inania and Ben Youssef (Marrakech). At last, we propose a method of construction of heptagonal, enneagonal, tetradecagonal and octadecagonal quasiperiodic patterns, not encountered in the Moroccan ornamental art. They are built from tiling (skeleton) generated by the multigrid method and decorated by motifs obtained by the craftsmen method.

Theoretical study of light localization in photonic bandgaps of organic octagonal quasiperiodic photonic crystal slabs

Based on the polystyrene material of low refractive index, light localization in photonic bandgaps of two kinds of 2D octagonal quasiperiodic photonic crystal slabs are investigated in theory, including the air-rod polystyrene slab and polystyrene-rod slab. The properties of bandgaps and localized modes in both two defect-free patterns are analyzed in detail. When a single-point defect is introduced into two quasiperiodic structures, the position of emerging defect modes and the red-shifting of resonant modes in wavelength are observed quite differently when the defect microcavity is increased in size. This difference is caused by the competition of two physical mechanisms, which are the effect of defect energy levels caused by defects introduced into photonic crystals and the resonance of modes in the defect cavity. These results will provide theoretical support for experimental fabrication of organic light-emitting quasiperiodic photonic crystal devices.