Quasi-periodic Patterns Research Articles

Influence of Bond Pattern on the in-plane Behavior of URM Piers

ABSTRACT The overall seismic resistance of unreinforced masonry (URM) systems that exhibit box-behavior mainly relies on the lateral force capacity of structural components. Despite the fact that it is widely accepted that masonry bond pattern might considerably affect the in-plane performance of URM members, this aspect has not fully addressed experimentally or numerically. In this paper, calibrated numerical models, developed within the framework of the Distinct Element Method, are used to simulate the quasi-static lateral response of URM piers under several combinations of boundary conditions, vertical pressures and aspect ratios, as well as a large number of typically-employed periodic and quasi-periodic bond patterns. The employment of time, size and mass scaling, and dynamic relaxation procedures, combined with the introduction of equivalent interface properties to represent the effect of cyclic damage through monotonic loading schemes, provided a significant reduction of computational cost, thus enabling a comprehensive parametric study to be carried out within an acceptable timeframe. The results show that the bond pattern has an appreciable influence on the response of laterally-loaded URM panels, motivating the possibility of including this aspect in the assessment of existing URM structures. Analytical formulations were also inferred by fitting numerical data, thus enabling the findings of this work to be readily implemented in assessment using simplified models.

CHANG-ES

Aims. NGC 4631 is an interacting galaxy which exhibits one of the largest gaseous halos observed among edge-on galaxies. We aim to examine the synchrotron and polarization properties of its disk and halo emission with new radio continuum data. Methods. Radio continuum observations of NGC 4631 were performed with the Karl G. Jansky Very Large Array at C-band (5.99 GHz) in the C and D array configurations, and at L-band (1.57 GHz) in the B, C, and D array configurations. The Rotation Measure Synthesis algorithm was utilized to derive the polarization properties. Results. We detected linearly polarized emission at C-band and L-band. The magnetic field in the halo is characterized by strong vertical components above and below the central region of the galaxy. The magnetic field in the disk is only clearly seen in the eastern side of NGC 4631, where it is parallel to the plane of the major axis of the galaxy. We detected for the first time a large-scale, smooth Faraday depth pattern in a halo of an external spiral galaxy, which implies the existence of a regular (coherent) magnetic field. A quasi-periodic pattern in Faraday depth with field reversals was found in the northern halo of the galaxy. Conclusions. The field reversals in the northern halo of NGC 4631, together with the observed polarization angles, indicate giant magnetic ropes with alternating directions. To our knowledge, this is the first time such reversals are observed in an external galaxy.

Geometry dependent performance limits of stretchable reduced graphene oxide interconnects: The role of wrinkles

We study the effect of geometrical confinement of reduced graphene oxide (rGO) films on strain-induced wrinkling patterns, which strongly affects their electromechanical response. Quasi-periodic wrinkle patterns are characteristics of uniaxially strained large-area thin films, both free-standing and supported on soft substrates. The universality of their scaling behaviour is known across a wide spectrum of length scales ranging from curtains to atomically thin crystals. Distinct wrinkle patterns oriented orthogonal to those on large-area films are observed in narrow micro-stripes of electrically conducting rGO films on polydimethylsiloxane (PDMS) substrates. Furthermore, as the width is reduced from 100 μm to 5 μm, the onset of the electromechanical response progressively shifts to lower strain, and importantly a breakdown is observed beyond a critical strain of less than 2.5%. Morphology studies suggest this irreversible response to arise as a consequence of local delamination of the strained micro-stripes subsequent to crack propagation. In contrast, large-area films have subdued electromechanical response which is also characterized by reversibility despite cracking. The altered electromechanical response, when going from large-area films to narrow micro-stripes, is reconciled as a consequence of the peculiar wrinkle pattern in the strained films arising from the free edge of the micro-stripes.

Robust minimal matching rules for quasicrystals.

A unified framework is proposed for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real-world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching rules, directly from the phased diffraction data. The construction yields precise values for the spatial density of distinct atomic positions and tolerates the presence of defects in a robust way.

Detection of Spatio-Temporal Recurrent Patterns in Dynamical Systems

Background: The study of repetitive (quasi-periodic) spatio-temporal patterns in complex dynamical systems with a well defined spatial structure may be complicated if the recurrent behavior is confined to specific local regions, where it lasts for a limited time. This can decrease the efficacy of recurrence plots (RPs) in recognizing such patterns. It then becomes important to first detect whether repetitive spatio-temporal patterns are present, and if so, where they are located (both in space and time), to facilitate a focused RP analysis approach. This study proposes a novel framework for spatio-temporal detection of local recurrence of a quasi-periodic nature in complex dynamical systems. A motivating application for this framework is the analysis of atrial fibrillation to better understand the heart tissue involved. Methods: The spatio-temporal data observed from the system are decomposed by means of principal component analysis to identify the points in the spatial structure exhibiting quasi-periodic recurrent patterns. The frequency content of the principal components is used to determine if such patterns are present, and the corresponding eigenvectors are used to identify the points associated with those components. Geometric information about proximity of these points is used to cluster them into local regions. A sliding temporal window is used to detect the start and end of each pattern. Results: A first simulation shows how the proposed framework can handle multiple recurrent patterns simultaneously occurring in a spatial structure of a dynamical system. A second simulation shows how the method can handle more complicated patterns like 2D nonlinear spiraling waves, typical of many diffusion processes. The framework is then applied to real data to detect recurrent patterns in wave fronts propagating inside the heart during atrial fibrillation. This analysis can unveil regions of recurrence in the atria that were not visible with standard RP analysis. Conclusion: A novel framework for detecting spatio-temporal repetitive patterns in complex dynamical systems is introduced. It allows retrieve the correct recurrences associated with known 2D traveling waves, while the same information is not visible with standard RP analysis. This framework can be effectively used to investigate recurrence in real dynamical systems as cardiac arrhythmia.

Ice Scallops: A Laboratory Investigation of the Ice-Water Interface.

Ice scallops are a small-scale (5-20cm) quasi-periodic ripple pattern that occurs at the ice-water interface. Previous work has suggested that scallops form due to a self-reinforcing interaction between an evolving ice-surface geometry, an adjacent turbulent flow field, and the resulting differential melt rates that occur along the interface. In this study, we perform a series of laboratory experiments in a refrigerated flume to quantitatively investigate the mechanisms of scallop formation and evolution in high resolution. Using particle-image velocimetry, we probe an evolving ice-water boundary layer at sub-millimeter scales and 15Hz frequency. Our data reveals three distinct regimes of ice-water interface evolution: A transition from flat to scalloped ice; an equilibrium scallop geometry; and an adjusting scallop interface. We find that scalloped ice geometry produces a clear modification to the ice-water boundary layer, characterized by a time-mean recirculating eddy feature that forms in the scallop trough. Our primary finding is that scallops form due to a self reinforcing feedback between the ice-interface geometry and shear production of turbulent kinetic energy in the flow interior. The length of this shear production zone is therefore hypothesized to set the scallop wavelength.

Varieties of 12-fold rosettes and their applications in Moroccan geometric ornament

This work is devoted to the study of the 12-fold rosettes frequently encountered in Islamic art, especially in Moroccan ornamentation. Several types of 12-fold rosettes are described according to the geometric shape of their petals. They have a large number of variants and offer the possibility of building new, previously unknown rosettes, while respecting the construction methodHasbaused by master craftsmen. Artisans developed a technique for combining different types of 12-fold rosettes to construct infinite periodic tiling belonging to the 17 crystallographic groups. This technique enabled them to diversify the repeated patterns based on 12-fold rosettes. An analysis of their tiling suggests a method based on elementary geometry to build new patterns with different types of 12-fold overlapped rosettes and their variants. A procedure based on combination of the distances between two overlapped rosettes is then proposed, which enables generation of new periodic and quasiperiodic patterns.

Sampling Rate Effects on Resting State fMRI Metrics.

Low image sampling rates used in resting state functional magnetic resonance imaging (rs-fMRI) may cause aliasing of the cardiorespiratory pulsations over the very low frequency (VLF) BOLD signal fluctuations which reflects to functional connectivity (FC). In this study, we examine the effect of sampling rate on currently used rs-fMRI FC metrics. Ultra-fast fMRI magnetic resonance encephalography (MREG) data, sampled with TR 0.1 s, was downsampled to different subsampled repetition times (sTR, range 0.3–3 s) for comparisons. Echo planar k-space sampling (TR 2.15 s) and interleaved slice collection schemes were also compared against the 3D single shot trajectory at 2.2 s sTR. The quantified connectivity metrics included stationary spatial, time, and frequency domains, as well as dynamic analyses. Time domain methods included analyses of seed-based functional connectivity, regional homogeneity (ReHo), coefficient of variation, and spatial domain group level probabilistic independent component analysis (ICA). In frequency domain analyses, we examined fractional and amplitude of low frequency fluctuations. Aliasing effects were spatially and spectrally analyzed by comparing VLF (0.01–0.1 Hz), respiratory (0.12–0.35 Hz) and cardiac power (0.9–1.3 Hz) FFT maps at different sTRs. Quasi-periodic pattern (QPP) of VLF events were analyzed for effects on dynamic FC methods. The results in conventional time and spatial domain analyses remained virtually unchanged by the different sampling rates. In frequency domain, the aliasing occurred mainly in higher sTR (1–2 s) where cardiac power aliases over respiratory power. The VLF power maps suffered minimally from increasing sTRs. Interleaved data reconstruction induced lower ReHo compared to 3D sampling (p < 0.001). Gradient recalled echo-planar imaging (EPI BOLD) data produced both better and worse metrics. In QPP analyses, the repeatability of the VLF pulse detection becomes linearly reduced with increasing sTR. In conclusion, the conventional resting state metrics (e.g., FC, ICA) were not markedly affected by different TRs (0.1–3 s). However, cardiorespiratory signals showed strongest aliasing in central brain regions in sTR 1–2 s. Pulsatile QPP and other dynamic analyses benefit linearly from short TR scanning.

Pattern at the boundaries of order

Chaos, in the sense used by mathematicians and physicists, contains a beautiful co-mingling of order and disorder. Here, we consider the interplay between periodic order, and disorder, in both space and time. This boundary is considered in both mathematical terms, and in terms of our experiences of order and pattern in our everyday routines. Periodic spatial patterns can exist in two dimensions, and finite sections can be made on paper (drawings, designs). These two-dimensional patterns are described by the seventeen ‘wallpaper groups’, a mathematical classification also used to describe the structure of crystals found in nature. In this article, supported by discussion of disrupted, non-regular and quasiperiodic patterns, we present a series of Lucy’s drawings, showing how one periodic order can deform into another. The drawings attempt to represent experienced patterns (habits and routines) as decorative pattern.

An efficient SPDE approach for El Niño

We consider the numerical approximation of stochastic partial differential equations (SPDEs) based models for a quasi-periodic climate pattern in the tropical Pacific Ocean known as El Niño phenomenon. We show that for these models the mean and the covariance are given by a deterministic partial differential equation and by an operator differential equation, respectively. In this context, we provide a numerical framework to approximate these parameters directly. We compare this method to stochastic differential equations and SPDEs based models from the literature solved by Taylor methods and stochastic Galerkin methods, respectively. Numerical results for different scenarios taking as a reference measured data of the years 2014 and 2015 (last Niño event) validate the efficiency of our approach.

Quasi-periodic patterns contribute to functional connectivity in the brain

Functional connectivity is widely used to study the coordination of activity between brain regions over time. Functional connectivity in the default mode and task positive networks is particularly important for normal brain function. However, the processes that give rise to functional connectivity in the brain are not fully understood. It has been postulated that low-frequency neural activity plays a key role in establishing the functional architecture of the brain. Quasi-periodic patterns (QPPs) are a reliably observable form of low-frequency neural activity that involve the default mode and task positive networks. Here, QPPs from resting-state and working memory task-performing individuals were acquired. The spatiotemporal pattern, strength, and frequency of the QPPs between the two groups were compared and the contribution of QPPs to functional connectivity in the brain was measured. In task-performing individuals, the spatiotemporal pattern of the QPP changes, particularly in task-relevant regions, and the QPP tends to occur with greater strength and frequency. Differences in the QPPs between the two groups could partially account for the variance in functional connectivity between resting-state and task-performing individuals. The QPPs contribute strongly to connectivity in the default mode and task positive networks and to the strength of anti-correlation seen between the two networks. Many of the connections affected by QPPs are also disrupted during several neurological disorders. These findings contribute to understanding the dynamic neural processes that give rise to functional connectivity in the brain and how they may be disrupted during disease.

Extracellular Electrophysiology in the Prostate Cancer Cell Model PC-3.

Although prostate cancer is one of the most common cancers in the male population, its basic biological function at a cellular level remains to be fully understood. This lack of in depth understanding of its physiology significantly hinders the development of new, targeted and more effective treatment strategies. Whilst electrophysiological studies can provide in depth analysis, the possibility of recording electrical activity in large populations of non-neuronal cells remains a significant challenge, even harder to address in the picoAmpere-range, which is typical of cellular level electrical activities. In this paper, we present the measurement and characterization of electrical activity of populations of prostate cancer cells PC-3, demonstrating for the first time a meaningful electrical pattern. The low noise system used comprises a multi-electrode array (MEA) with circular gold electrodes on silicon oxide substrates. The extracellular capacitive currents present two standard patterns: an asynchronous sporadic pattern and a synchronous quasi-periodic biphasic spike pattern. An amplitude of ±150 pA, a width between 50–300 ms and an inter-spike interval around 0.5 Hz characterize the quasi-periodic spikes. Our experiments using treatment of cells with Gd3⁺, known as an inhibitor for the Ca2⁺ exchanges, suggest that the quasi-periodic signals originate from Ca2⁺ channels. After adding the Gd3⁺ to a population of living PC-3 cells, their electrical activity considerably decreased; once the culture was washed, thus eliminating the Gd3⁺ containing medium and addition of fresh cellular growth medium, the PC-3 cells recovered their normal electrical activity. Cellular viability plots have been carried out, demonstrating that the PC-3 cells remain viable after the use of Gd3⁺, on the timescale of this experiment. Hence, this experimental work suggests that Ca2⁺ is significantly affecting the electrophysiological communication pattern among PC-3 cell populations. Our measuring platform opens up new avenues for real time and highly sensitive investigations of prostate cancer signalling pathways.

Quasi-periodic patterns of brain activity in individuals with attention-deficit/hyperactivity disorder.

Individuals with attention-deficit/hyperactivity disorder have disrupted functional connectivity in the default mode and task positive networks. Traditional fMRI analysis techniques that focus on ‘static’ changes in functional connectivity have been successful in identifying differences between healthy controls and individuals with ADHD. However, such analyses are unable to explain the mechanisms behind the functional connectivity differences observed. Here, we study dynamic changes in functional connectivity in individuals with ADHD through investigation of quasi-periodic patterns (QPPs). QPPs are reliably recurring low-frequency spatiotemporal patterns in the brain linked to infra-slow electrical activity. They have been shown to contribute to functional connectivity observed through static analysis techniques. We find that QPPs contribute to functional connectivity specifically in regions that are disrupted in individuals with ADHD. Individuals with ADHD also show differences in the spatiotemporal pattern observed within the QPPs. This difference results in a weaker contribution of QPPs to functional connectivity in the default mode and task positive networks. We conclude that quasi-periodic patterns provide insight into the mechanisms behind functional connectivity differences seen in individuals with ADHD. This allows for a better understanding of the etiology of the disorder and development of effective treatments.

Three-dimensional Magnetic Reconnection Triggering an X-class Confined Flare in Active Region 12192

Abstract We present an extensive analysis of the X2.0-class confined flare on 2014 October 27 in the great active region, AR 12192, observed by the Interface Region Imaging Spectrograph and the Solar Dynamics Observatory. The slipping motion of the substructures within the negative-polarity flare ribbon (R1) and continual reconnection-induced flows during the confined flare are first presented. The substructures within ribbon R1 were observed to slip in opposite directions at apparent speeds of 10–70 km s−1. The slipping motion exhibited the quasi-periodic pattern with a period of 80–110 s, which can be observed since the flare start and throughout the impulsive phase of the flare. Simultaneously quasi-periodic flows moved along a reverse S-shaped filament, with an average period of about 90 s. The period of reconnection-induced flows is similar to that of the slippage of ribbon substructures, implying the occurrence of quasi-periodic slipping magnetic reconnection. The spectral observations showed that the Si iv line was blueshifted by 50–240 km s−1 at the location of the flows. During the process of the flare, the filament did not show the rise phase and was not associated with any failed eruption. The flare mainly consisted of two sets of magnetic systems, with both of their east ends anchoring in ribbon R1. We suggest that the slipping magnetic reconnection between two magnetic systems triggers the confined flare.

Mapping Multi-Disease Risk during El Niño: An Ecosyndemic Approach.

El Niño is a quasi-periodic pattern of climate variability and extremes often associated with hazards and disease. While El Niño links to individual diseases have been examined, less is known about the cluster of multi-disease risk referred to as an ecosyndemic, which emerges during extreme events. The objective of this study was to explore a mapping approach to represent the spatial distribution of ecosyndemics in Piura, Peru at the district-level during the first few months of 1998. Using geographic information systems and multivariate analysis, descriptive and analytical methodologies were employed to map disease overlap of 7 climate-sensitive diseases and construct an ecosyndemic index, which was then mapped and applied to another El Niño period as proof of concept. The main findings showed that many districts across Piura faced multi-disease risk over several weeks in the austral summer of 1998. The distribution of ecosyndemics were spatially clustered in western Piura among 11 districts. Furthermore, the ecosydemic index in 1998 when compared to 1983 showed a strong positive correlation, demonstrating the potential utility of the index. The study supports PAHO efforts to develop multi-disease based and interprogrammatic approaches to control and prevention, particularly for climate and poverty-related infections in Latin America and the Caribbean.

Effect of electromagnetic radiation on the dynamics of spatiotemporal patterns in memristor-based neuronal network

Modulational instability, as a mechanism of wave trains and soliton formation in biological system, is explored in the frame work of the new FitzHugh–Nagumo model. This model considered chain networks with memristive synaptic connection between adjacent neurons. This connection replaces the synaptic coupling and neurons bridged for signal exchange. From the physical law of electromagnetic induction, we interpret the traditional current term as magnetic flux variable. Magnetic flux is used to describe time-varying electromagnetic field setup in cells as a result of internal bioelectricity of the nervous system as well as when cells are exposed to external electromagnetic field. We reduced the whole network dynamical equations through multi-scale expansion to obtain a single differential–difference nonlinear equation of Schrodinger type. Linear stability is then performed with emphasis on memristive synaptic coupling. The conditions under which uniform plane waves propagating in the network become stable or unstable under small perturbation are calculated and plotted. Numerical experiments confirm our analytical predictions as the network supports localized mode excitations, spike-like, identified as quasi-periodic patterns, with some features of synchronization. It is confirmed that under strong electromagnetic radiation, the propagating waves encountered turbulent electrical activities, with patterns breakdown into a homogeneous state. This disordered state, collapse and instability of traveling pulse are monitored and analyzed using the sampled time series for membrane potential. It decreases to quiescent state under strong electromagnetic field. This could provide some guidance to understanding some neurodegenerative manifestations linked with high radiation exposure.

Stationary, non-stationary and invasive patterns for a prey-predator system with additive Allee effect in prey growth

This study deals with the pattern formation scenarios of a reaction-diffusion system of prey-predator interactions with Allee effect in prey growth, Holling type-II functional response and density dependent death rate for predator. The necessary conditions, such as the presence of Hopf and Turing bifurcations, to get pattern formation are rendered and exhaustive numerical simulations are performed to validate the analytical results. Numerical simulations affirm the existence of stationary patterns such as hot spot, cold spot, labyrinthine and mixture of spot and stripe patterns along with the non-stationary patterns such as spatiotemporal chaotic and quasi-periodic patterns in presence of both weak and strong Allee effects in prey growth. Numerical simulations also reveal the coexistence of both species (either stationary or chaotic in nature depending on the values for diffusion coefficients) in contrast to the extinction scenario for the corresponding temporal model. Further, we investigate the invasion of exotic species for the considered model for strong Allee effect. In this case, we find out the patchy invasion scenario apart from the invasion through propagation of continuous population fronts which is a common invasion scenario for deterministic prey-predator models. In the patchy invasion regime, we observe a striking patchy spatial distribution of species in the wake of an expanding population front as well as complete patchy invasion.

My Art by the Numbers

The author explains his affinity for numbers as it relates to his work as an artist spanning his long career. This affinity helped him invent one of the first systems for making four-color digital prints. Having been only recently introduced to the book Number and Time, by Marie-Louise von Franz, the author finds that he is in full agreement with her depth psychology theories on number. Recounting a synchronicity that he experienced while writing this paper helped the author to understand Jung’s concept of the unus mundus, as explained by von Franz in Number and Time. He speculates that number archetypes must have evolved in human consciousness over very long periods of time and writes about the number zero as a “recent” example. The author also describes his experience of a spontaneous mathematical vision that led him to create an algorithm, which in turn led him to realize that crystals having fivefold symmetry could exist in nature, which was considered impossible at the time. The author discusses his new inventions of quasi-periodic and random tile patterns, which were inspired by 15th-century Islamic tile patterns, as they related to the aperiodic patterns invented by Roger Penrose in the 20th century. He speculates about the ability of artificially intelligent computer software to be able to generate random quasi-periodic patterns. Lastly, the author recounts a synchronistic experience that occurred during the month of his 72nd birthday, in which his work with numbers is seemingly reciprocated by nature.

Generating Islamic Quasi-Periodic Patterns

The discovery of quasi-crystals has led to a great debate about their unusual structure. The big surprise is that these structures were found in Islamic art several centuries ago. This latest discovery drew the attention of scientists to propose several approaches for the comprehension of these structures by analyzing several quasi-periodic patterns spread around the Islamic world. In this article, we propose a systematic method for generating new quasi-periodic patterns inspired by existing Islamic historical patterns. The method builds Islamic quasi-periodic patterns based on a quasi-periodic tiling and a few intuitive parameters. Given a quasi-periodic tiling, the method divides its tiles (rhombs) into symmetric right triangles and constructs their template motifs. The construction of these template motifs is achieved by a systematic and well-organized process. The content of the tiles is obtained by applying mirror reflections to the constructed template motifs. Finally, the pattern is drawn by putting the content of the constructed tiles in the tiling. To show the effectiveness of this generative method, examples of new quasi-periodic patterns will be presented.

Spectral Ripples in Round-Window Cochlear Microphonics: Evidence for Multiple Generation Mechanisms.

The cochlear microphonic (CM) results from the vector sum of outer hair cell transduction currents excited by a stimulus. The classical theory of CM generation-that the response measured at the round window is dominated by cellular sources located within the tail region of the basilar membrane (BM) excitation pattern-predicts that CM amplitude and phase vary little with stimulus frequency. Contrary to expectations, CM amplitude and phase-gradient delay measured in response to low-level tones in chinchillas demonstrate a striking, quasiperiodic pattern of spectral ripples, even at frequencies > 5kHz, where interference with neurophonic potentials is unlikely. The spectral ripples were reduced in the presence of a moderate-level saturating tone at a nearby frequency. When converted to the time domain, only the delayed CM energy was diminished in the presence of the saturator. We hypothesize that the ripples represent an interference pattern produced by CM components with different phase gradients: an early-latency component originating within the tail region of the BM excitation and two delayed components that depend on active cochlear processing near the peak region of the traveling wave. Using time windowing, we show that the early, middle, and late components have delays corresponding to estimated middle-ear transmission, cochlear forward delays, and cochlear round-trip delays, respectively. By extending the classical model of CM generation to include mechanical and electrical irregularities, we propose that middle components are generated through a mechanism of "coherent summation" analogous to the production of reflection-source otoacoustic emissions (OAEs), while the late components arise through a process of internal cochlear reflection related to the generation of stimulus-frequency OAEs. Although early-latency components from the passive tail region typically dominate the round-window CM, at low stimulus levels, substantial contributions from components shaped by active cochlear processing provide a new avenue for improving CM measurements as assays of cochlear health.