Asymmetric Cycles Research Articles

How to couple identical ring oscillators to get quasiperiodicity, extended chaos, multistability, and the loss of symmetry

We study the dynamical regimes demonstrated by a pair of identical 3-element ring oscillators (reduced version of synthetic 3-gene genetic Repressilator) coupled using the design of the ‘quorum sensing (QS)’ process natural for interbacterial communications. In this work QS is implemented as an additional network incorporating elements of the ring as both the source and the activation target of the fast diffusion QS signal. This version of indirect nonlinear coupling, in cooperation with the reasonable extension of the parameters which control properties of the isolated oscillators, exhibits the formation of a very rich array of attractors. Using a parameter-space defined by the individual oscillator amplitude and the coupling strength, we found the extended area of parameter-space where the identical oscillators demonstrate quasiperiodicity, which evolves to chaos via the period doubling of either resonant limit cycles or complex antiphase symmetric limit cycles with five winding numbers. The symmetric chaos extends over large parameter areas up to its loss of stability, followed by a system transition to an unexpected mode: an asymmetric limit cycle with a winding number of 1:2. In turn, after long evolution across the parameter-space, this cycle demonstrates a period doubling cascade which restores the symmetry of dynamics by formation of symmetric chaos, which nevertheless preserves the memory of the asymmetric limit cycles in the form of stochastic alternating “polarization” of the time series. All stable attractors coexist with some others, forming remarkable and complex multistability including the coexistence of torus and limit cycles, chaos and regular attractors, symmetric and asymmetric regimes. We traced the paths and bifurcations leading to all areas of chaos, and presented a detailed map of all transformations of the dynamics.

Baseline varus deformity is associated with increased joint loading and pain of non-operated knee two years after unilateral total knee arthroplasty

BackgroundThe goals of this study were (1) to document the gait pattern of patients with unilateral knee osteoarthritis (OA), (2) to determine the knee adduction moment (KAM) changes in the non-operated knee, and (3) to identify the predictors of change in KAM in the non-operated knee. MethodsThe study recruited 23 patients with advanced unilateral knee OA. The preoperative Kellgren–Lawrence (KL) grade of the non-operated knee was one or two; non-operated knee pain, rated using a numeric rating scale (NRS), was less than three out of 10 points. We used a commercial gait analysis system to evaluate kinetics and kinematics. Radiological and gait measurements at the two-year follow-up were compared with baseline data. ResultsThe preoperative asymmetrical gait cycle characterized by elongation of the stance phase of the non-operated knee became symmetrical after TKA. The average KAM of the non-operated knee increased (P=0.010) and it was best predicted by the baseline mechanical axis of the non-operated knee. If the baseline mechanical axis was varus four degrees or above (varus group), the average KAM increased by 0.64 (% body weight×height, P=0.015), while for varus less than four degrees (non-varus group), KAM was unchanged. The KL grade was increased in the varus group (P=0.020) but it was unchanged in the non-varus group. Average pain NRS score was also higher (P=0.044) in the varus group. ConclusionsClose follow-up is necessary for patients with a baseline varus deformity of the non-operated knee because of the higher possibility of developing pain, subsequent arthritis and increased joint loading of the non-operated knee. Level of evidenceIII, retrospective cohort study.

Depositional environments and cyclicity of the Early Ordovician carbonate ramp in the western Tarim Basin (NW China)

During the Early Ordovician, the Tarim Basin (NW China) was mainly occupied by an extensive shallow-water carbonate platform, on which a carbonate ramp system was developed in the Bachu-Keping area of the western part of the basin. Three well-exposed typical outcrop sections of the Lower Ordovician Penglaiba Formation were investigated in order to identify the depositional facies and to clarify origins of meter-scale cycles and depositional sequences, thereby the platform evolution. Thirteen lithofacies are identified and further grouped into three depositional facies (associations): peritidal, restricted and open-marine subtidal facies. These lithofacies are vertically stacked into meter-scale, shallowing-upward peritidal and subtidal cycles. The peritidal cycles are mainly distributed in the lower and uppermost parts of the Penglaiba Formation deposited in the inner-middle ramp, and commonly start with shallow subtidal to intertidal facies followed by inter- to supratidal facies. In contrast, the subtidal cycles occur throughout the formation mostly in the middle-outer ramp and are dominated by shallow to relatively deep (i.e., intermediate) subtidal facies. The dominance of asymmetrical and incomplete cycles suggests a dominant control of Earth’s orbital forcing on the cyclic deposition on the platform. On the basis of vertical facies and cycle stacking patterns, and accommodation changes illustrated by the Fischer plots from all studied sections, five third-order depositional sequences are recognized in the Penglaiba Formation. Individual sequences comprise a lower transgressive part and an upper regressive one. In shallow-water depositional environments, the transgressive packages are dominated by thicker-than-average subtidal cycles, indicating an increase in accommodation space, whereas regressive parts are mainly represented by thinner-than-average peritidal and subtidal cycles, denoting a decrease in accommodation space. In contrast, in intermediate to deep subtidal environments, transgressive and regressive packages display an opposite trend in accommodation space changes. Sequence boundaries (except the basal and top boundaries of the Penglaiba Formation) are usually represented by laterally traceable, transitional boundary zones without apparent subaerial exposure features. Good correlation of the long-term changes in accommodation space (or sea-level) inferred from vertical stacking patterns of facies and cycles suggests an overriding eustatic control on the formation of meter-scale cycles and third-order depositional sequences as well as platform evolution superimposed with local and/or regional tectonic influence during the Early Ordovician. This study would help understand the controls on the tempo-spatial facies distribution, stratal cyclicity and carbonate platform evolution in the western Tarim Basin during the Early Ordovician, facilitating prediction for favorable subsurface carbonate reservoirs and future hydrocarbon exploration and production in the Penglaiba Formation.

Swimming mechanics and propulsive efficiency in the chambered nautilus.

The chambered nautilus (Nautilus pompilius) encounters severe environmental hypoxia during diurnal vertical movements in the ocean. The metabolic cost of locomotion (Cmet) and swimming performance depend on how efficiently momentum is imparted to the water and how long on-board oxygen stores last. While propulsive efficiency is generally thought to be relatively low in jet propelled animals, the low Cmet in Nautilus indicates that this is not the case. We measured the wake structure in Nautilus during jet propulsion swimming, to determine their propulsive efficiency. Animals swam with either an anterior-first or posterior-first orientation. With increasing swimming speed, whole cycle propulsive efficiency increased during posterior-first swimming but decreased during anterior-first swimming, reaching a maximum of 0.76. The highest propulsive efficiencies were achieved by using an asymmetrical contractile cycle in which the fluid ejection phase was relatively longer than the refilling phase, reducing the volume flow rate of the ejected fluid. Our results demonstrate that a relatively high whole cycle propulsive efficiency underlies the low Cmet in Nautilus, representing a strategy to reduce the metabolic demands in an animal that spends a significant part of its daily life in a hypoxic environment.

The Scarring Effect of Asymmetric Business Cycles

Business cycle fluctuations in the U.S. employment-to-population ratio are asymmetric: deviations below trend (troughs) are larger than deviations above trend (peaks). This asymmetry has a scarring effect, which reduces the average level of the employment-to-population ratio around which the economy fluctuates. To quantify such a scar, we formulate an equilibrium business cycle model featuring frictional unemployment and a labor force participation choice that produces the observed labor market asymmetry in the face of symmetric business cycle shocks. We quantify that the employment-to-population ratio would be 0.3 percentage points higher in the absence of cyclical fluctuations. Further, by dampening business cycles, counter-cyclical stabilization policy reduces the job loss by 70%.

Multichannel Broadcast in Duty-Cycling WBANs via Channel Hopping

We formulate and study a broadcast problem arising in multichannel duty-cycling wireless body area networks (WBANs) which the sink needs to broadcast control information to all sensor nodes on or implanted in the human body. Despite its fundamental importance for the network configuration and secure key management, the multichannel broadcast problem is largely unaddressed in duty-cycling WBANs. In this paper, we devise novel 2-D scheduling specifying the rule of channel hopping and wake-up time slot selection, which achieves the order-minimal worst-case broadcast delay while guaranteeing the full broadcast diversity regardless of clock drifts and asymmetric duty cycles and channel perceptions. Specifically, we first employ the Chinese remainder theorem to design an effective multichannel broadcast (MCB) algorithm and further propose improved MCB that enhances the granularity of MCB in matching actual duty cycles and number of channels, reducing the theoretically worst-case broadcast delay of MCB by up to 75%. We demonstrate the performance of the proposed algorithms through theoretical analysis and extensive simulations.

Simulation of climate, ice sheets and CO<sub>2</sub> evolution during the last four glacial cycles with an Earth system model of intermediate complexity

Abstract. In spite of significant progress in paleoclimate reconstructions and modelling of different aspects of the past glacial cycles, the mechanisms which transform regional and seasonal variations in solar insolation into long-term and global-scale glacial–interglacial cycles are still not fully understood – in particular, in relation to CO2 variability. Here using the Earth system model of intermediate complexity CLIMBER-2 we performed simulations of the co-evolution of climate, ice sheets, and carbon cycle over the last 400 000 years using the orbital forcing as the only external forcing. The model simulates temporal dynamics of CO2, global ice volume, and other climate system characteristics in good agreement with paleoclimate reconstructions. These results provide strong support for the idea that long and strongly asymmetric glacial cycles of the late Quaternary represent a direct but strongly nonlinear response of the Northern Hemisphere ice sheets to orbital forcing. This response is strongly amplified and globalised by the carbon cycle feedbacks. Using simulations performed with the model in different configurations, we also analyse the role of individual processes and sensitivity to the choice of model parameters. While many features of simulated glacial cycles are rather robust, some details of CO2 evolution, especially during glacial terminations, are sensitive to the choice of model parameters. Specifically, we found two major regimes of CO2 changes during terminations: in the first one, when the recovery of the Atlantic meridional overturning circulation (AMOC) occurs only at the end of the termination, a pronounced overshoot in CO2 concentration occurs at the beginning of the interglacial and CO2 remains almost constant during the interglacial or even declines towards the end, resembling Eemian CO2 dynamics. However, if the recovery of the AMOC occurs in the middle of the glacial termination, CO2 concentration continues to rise during the interglacial, similar to the Holocene. We also discuss the potential contribution of the brine rejection mechanism for the CO2 and carbon isotopes in the atmosphere and the ocean during the past glacial termination.

STRATIGRAPHIC CORRELATION OF THE LATE SILURIAN-DEVONIAN OF THE AMAZON BASIN (BRAZIL) BASED ON GENETIC STRATIGRAPHIC SEQUENCE APPROACH

The current study consists in the stratigraphic analysis of Late Silurian-Devonian interval in the Amazon Basin (Brazil) using the concepts of the Modern Stratigraphy, more specifically the genetic stratigraphic sequence, proposed by Galloway. that uses the marine flooding surface as a boundary of sequence. This methodology is since the sediments of studied interval are related to marine transgressions which were part of the basin paleogeographic context. Thus, the maximum flood surfaces, which are presented in four sections (AA ', B-B', CC 'and D-D') throughout the basin, represent chronostratigraphic events, which stand out in gamma ray profiles and are used as correlation data in thirteen exploration wells. Analysis of these sections allowed the identification of four fourth-order sequences (AB, BC, CD and DE) bounded by maximum flooding surfaces on the top and the base. Each sequence consists of asymmetric regressive-transgressive cycles, represented by highstand systems tract and transgressive systems tract. The analysis of these sections integrated with the stratigraphic maps (isopach and isolith) allowed the identification of the depocenter and two main source areas of sandy sediments (west and south). Besides, it was possible to infer that the marine transgression during the Paleozoic induced the deposition of pelitic sediments and followed a trend from northeast to southwest.

Asymmetric business cycles and sovereign default

What accounts for asymmetric (negatively skewed) business cycles in emerging economies? We show the asymmetry is tied to default risk and that a sovereign default model delivers negative skew.

Block combination–based asynchronous wake-up schedule in wireless sensor networks

In wireless sensor networks, when sensor nodes are operated with different ratios of active slots, this is called asymmetric duty cycles. Furthermore, cycles with the same ratio of active slots per cycle for all nodes are called symmetric duty cycles. In wireless sensor networks, most applications require both symmetric and asymmetric duty cycles. The balanced incomplete block design–based wake-up schedule is known to be the optimal solution for symmetric duty cycles. However, because this schedule cannot support asymmetric duty cycles, the balanced incomplete block design–based wake-up schedule is not suitable for wireless sensor networks. Herein, we propose a new scheme called the block combination–based asynchronous wake-up schedule to resolve this issue for asymmetric duty cycles. Block combination–based asynchronous wake-up schedule combines different blocks using a block combination operation. The combined schedule guarantees common active slots between sensor nodes in asymmetric duty cycles. To demonstrate the superior performance of block combination–based asynchronous wake-up schedule, we implement a TOSSIM-based simulation and compare the experimental results with recent neighbor discovery protocols such as balanced incomplete block design, prime-based block design, Disco, U-Connect, SearchLight, Hedis, and Todis. We then prove that block combination–based asynchronous wake-up schedule outperforms the others.

Local Ratcheting Response in Dissimilar Metal Weld Joint: Characterization Through Digital Image Correlation Technique

Ratcheting fatigue behavior of different alloys and their weld joints has been a topic of interest in the past few decades. However, little information is available about the ratcheting response in different zones, when a composite weld section is subjected to asymmetric loading cycle. This work aims at understanding the local ratcheting response in various zones of a dissimilar metal weld (DMW) joint. Digital image correlation technique has been used to measure local ratcheting strain components of a DMW joint. Accumulation of ratcheting strain in various zones of a DMW joint was found to be different, harder region accumulating negligible and softer region accumulating larger local ratcheting strain. Fatigue crack initiation or neck formation occurred in soft region owing to high ratcheting strain accumulation.

Ratcheting response of nylon fiber reinforced natural rubber/styrene butadiene rubber composites under uniaxial stress cycles: Experimental studies

AbstractThe present study intends to study the ratcheting response of nylon fiber reinforced natural rubber (NR)‐styrene butadiene rubber (SBR) composite samples under asymmetric stress cycles. Uniaxial tests conducted on composite samples have shown how influential the weight fraction of short nylon fibers on the stress‐strain curves/loops under monotonic and cyclic loads is. NR/SBR composite samples with various fiber contents of 0, 10, 20, 30, and 40 per hundred rubber (phr) were tested under asymmetric stress cycles. In these tests, stress‐strain hysteresis loops were progressively shifted over stress cycles resulting in progressive plastic strain accumulation. Over stress cycles, ratcheting strain progressed within the first few cycles with a relatively high rate, and as the number of cycles increased, this rate decayed resulting in a plateau in strain accumulation (shakedown). The ratcheting strain rate and magnitude resulting in shakedown were highly affected by the nylon fiber content. The experimental observations showed that this plateau (shakedown) occurred after a number of cycles in NR/SBR composite samples where the widths of hysteresis loops stayed unchanged. Samples with no fiber and that with 10 phr fiber content possessed high ratcheting rates leading samples to failure after a few stress cycles. Fracture surfaces in these samples were further analyzed through SEM investigation.

Non-saturated cyclic softening and uniaxial ratcheting of a high-strength steel: Experiments and viscoplastic constitutive modeling

The aim of the present investigation is to construct a constitutive model suitable for describing the cyclic behavior of 10Ni5CrMoV high-strength steel, which displays both cyclic softening and asymptotic ratcheting. Uniaixal tests of monotonic loading, symmetrical and asymmetrical strain cycling and stress controlled cyclic loading are conducted. Results reveal that the material exhibits non-saturated cyclic softening with combined nonlinear and linear softening rates, both isotropic and kinematic hardening are responsible for cyclic softening. A long period of steady-state ratcheting has been experimentally detected. Cyclic softening is found to have a considerable effect on the uniaxial ratcheting of the material. Significantly larger monotonic yield stress than that at cyclic loading is also observed. The dependence of cyclic softening on strain amplitude is revealed by a low-high sequence strain controlled cyclic test. Based on the experimental findings, a new constitutive model extended from Abdel-Karim–Ohno model has been constructed for 10Ni5CrMoV steel. The identification procedure of the material parameters is scrutinized critically by quantifying the contributions of the isotropic hardening and kinematic hardening on cyclic softening. Verification of the proposed model is achieved by simulating uniaxial strain and stress controlled cyclic loading tests. Fairly good modeling results are obtained. The superiority of the proposed model over other kinds of Ohno–Wang type models is also illustrated.

A wavelet threshold denoising procedure for multimodel predictions: An application to economic time series

Noise‐affected economic time series, realizations of stochastic processes exhibiting complex and possibly nonlinear dynamics, are dealt with. This is often the case of time series found in economics, which notoriously suffer from problems such as low signal‐to‐noise ratios, asymmetric cycles and multiregimes patterns. In such a framework, even sophisticated statistical models might generate suboptimal predictions, whose quality can further deteriorate unless time consuming updating or deeper model revision procedures are carried out on a regular basis. However, when the models' outcomes are expected to be disseminated in timeliness manner (as in the case of Central Banks or national statistical offices), their modification might not be a viable solution, due to time constraints. On the other hand, if the application of simpler linear models usually entails relatively easier tuning‐up procedures, this would come at the expenses of the quality of the predictions yielded. A mixed, self‐tuning forecasting method is therefore proposed. This is an automatic, 2‐stage procedure, able to generate predictions by exploiting the denoising capabilities provided by the wavelet theory in conjunction with a compounded forecasting generator. Its out‐of‐sample performances are evaluated through an empirical study carried out on macroeconomic time series.

Output Voltage Control of the SP topology IPT system based on Primary side Controller operating at ZVS

This paper presents a technique to control the output voltage of a series-parallel (SP) topology inductive power transfer (IPT) system using only a controller, located on the primary side. This reduces the cost, size, complexity and loss of the system compared to conventional IPT dual-side controllers. An asymmetrical duty cycle control (ADC) of full-bridge inverters was used to control the DC output voltage to its designed value. Additionally, a zero voltage switching (ZVS) operation can be obtained at all power levels by varying the switching frequency of the inverter. Theoretical analysis was performed through a mutual inductance coupling model and verified by computer simulation. Experimental results of the circular magnetic structure IPT system with an adjustable air-gap confirm the validity of the proposed controller. The system efficiency was improved throughout the operation and the improvement became obvious as the output power was decreased.

Numerical analysis of flame instabilities in narrow channels: Laminar premixed methane/air combustion

Premixed flames propagating within small channels show complex combustion phenomena that differ from flame propagation at conventional scales. Available experimental and numerical studies have documented stationary, non-stationary, or asymmetric modes that depend on properties of the incoming reactant flow as well as channel geometry and wall temperatures. This work seeks to illuminate mechanisms leading to symmetry breaking and limit cycle behavior that are fundamental to these combustion modes. Specifically, four cases of lean premixed methane/air combustion—two equivalence ratios (0.53 and 0.7) and two channel widths (2 mm and 5 mm)—are investigated in a 2D configuration with constant channel length and bulk inlet velocity, where numerical simulations are performed using detailed chemistry. External wall heating is simulated by imposing a linear temperature gradient as a boundary condition on both walls. In the 2 mm channel, both equivalence ratios produce flames that stabilize with symmetric flame fronts after propagating upstream. In the 5 mm channel, flame fronts start symmetrically, although symmetry is broken almost immediately after ignition. Further, 5 mm channels produce non-stationary combustion modes with dramatically different limit cycles: in the leaner case ( φ = 0.53), the asymmetric flame front flops periodically, whereas in the richer case ( φ = 0.7), flames with repetitive extinctions and ignitions (FREI) are observed. To further understand the flame dynamics, reaction fronts and flame fronts are captured and differentiated. Results show that the loss of flame front symmetry originates in a region close to the flame cusp, where flow and chemical characteristics exhibit large gradients and curvatures. Limit cycle behavior is illuminated by investigating flame edges that are formed along the wall, and accompany local or global ignition and extinction processes. In the flopping mode ( φ = 0.53), local ignition and extinction in regions adjacent to the wall result in oblique fronts that advance and recede along the wall and redirect the flow ahead of the flame. In the FREI mode, asymmetric flames propagate much farther upstream, where they experience global extinction due to heat losses, and re-ignite far downstream with opposite flame front orientation. In both cases, an interaction of flow and chemical effects drives the asymmetric limit cycles. The lack of instabilities and asymmetries for the 2mm cases is attributed to insufficient wall separation, which is of the same order of magnitude as the flame thickness.

Three-Phase Three-Level Soft Switching Dc-Dc Converter for Industrial Applications

In high power DC applications, the single-phase DC-DC converter will face large voltage and current stress in each control switch and thereby the power handling capacity is less. To overcome this problem, three-phase DC-DC converter is used and it is suitable for high power applications with reduced number of switches as compared with the conventional topologies. The asymmetrical duty cycle control is considered to operate the switches under soft switching and hence the switching losses are reduced. The transformer leakage inductances are used along with junction capacitances in order to form resonance and hence ZVS commutation is possible in a wider load range. The modified phase shift control method is used for the proposed converter.The operational modes and design equations of the proposed converter have been observed. The simulation is carried out with a load of 1000W for validating the proposed work.

Ratcheting strain and its effect on low cycle fatigue behavior of Al 7075-T6 alloy

The aim of this investigation was to examine the role of accumulation of ratcheting strain on low cycle fatigue behavior of aluminum 7075-T6 alloy. For this purpose, first ratcheting behavior of the alloy was studied using asymmetric stress-controlled low cycle fatigue tests up to 2000 cycles. Post-ratcheting stain-controlled low cycle fatigue tests were done on ratcheted specimens up to failure. Further, stain-controlled low cycle fatigue tests without any previous ratcheting were also conducted up to failure in order to compare the behavior with and without previous ratcheting. A few ratcheted specimens were studied using transmission electron microscope to assess the dislocation features generated due to ratcheting. The results indicated that increase of either stress amplitude or mean stress increased the ratcheting strain accumulated in the material. Ladder-like dislocation structure prevailed in the specimens deformed at lower stress levels while dislocation tangles were predominantly present in specimens deformed at higher stresses. Analysis of post-ratcheting low cycle fatigue behavior showed that fatigue life of the alloy decreased with the increase of previously imposed ratcheting strain. Comparison of low cycle fatigue behavior of the investigated alloy with and without ratcheting indicated that ratcheting strain was detrimental to fatigue life of aluminum 7075-T6 alloy.

Asymmetric Business Cycle Effects and Tourism Demand Cycles

This study examines the relationship between business and tourism demand cycles in Aruba and Barbados during 1970–2015. The study uses a 2SLS method and is grounded in the output gap approach. The results indicate that business cycles explain nearly 49% of tourism demand flows to Aruba and nearly 91% to Barbados. Thus, the study sheds light on the nature of the relationship between business and tourism demand cycles, which could help managers and policy makers refine their strategies to further tourism development. Procyclical and asymmetric movements characterized the long-term co-movements between the business cycles and tourism demand variables. However, individual variables were stationary, hence transitory in nature, and therefore mainly driven by demand motivations. The asymmetric fluctuations were defined by positive and negative gaps, with the former displaying stronger duration effects compared to the latter. The relationship between the two variables seems country specific in nature.

Threshold Estimation via Group Orthogonal Greedy Algorithm

A threshold autoregressive (TAR) model is an important class of nonlinear time series models that possess many desirable features such as asymmetric limit cycles and amplitude-dependent frequencies. Statistical inference for the TAR model encounters a major difficulty in the estimation of thresholds, however. This article develops an efficient procedure to estimate the thresholds. The procedure first transforms multiple-threshold detection to a regression variable selection problem, and then employs a group orthogonal greedy algorithm to obtain the threshold estimates. Desirable theoretical results are derived to lend support to the proposed methodology. Simulation experiments are conducted to illustrate the empirical performances of the method. Applications to U.S. GNP data are investigated.