THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS

This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=0.The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions satisfy.Furthermore,the exact bound of a special case is given using the Chebyshev system.At the end,some numerical simulations are given to illustrate the existence of limit cycles.

Existence of Two Limit Cycles in Zeeman’s Class 30 for 3D Lotka-Volterra Competitive System

Gyllenberg and Yan(Discrete Contin Dyn Syst Ser B 11(2):347–352,2009)presented a system in Zeeman’s class 30 of 3-dimensional Lotka-Volterra(3D LV)competitive systems to admit at least two limit cycles,one of which is generated by the Hopf bifurcation and the other is obtained by the Poincaré-Bendixson theorem.Yu et al.(J Math Anal Appl 436:521–555,2016,Sect.3.4)recalculated the first Liapunov coefficient of Gyllenberg and Yan’s system to be positive,rather than negative as in Gyllenberg and Yan(2009),and pointed out that the Poincaré-Bendixson theorem is not applicable for that system.Jiang et al.(J Differ Equ 284:183–218,2021,p.213)proposed an open question:“whether Zeeman’s class 30 can be rigorously proved to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem?”This paper provides four systems in Zeeman’s class 30 to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem and gives an answer to the above question.

Crossing Limit Cycles of Planar Piecewise Hamiltonian Systems with Linear Centers Separated by Two Parallel Straight Lines

In this paper, we have studied several classes of planar piecewise Hamiltonian systems with three zones separated by two parallel straight lines. Firstly, we give the maximal number of limit cycles in these classes of systems with a center in two zones and without equilibrium points in the other zone (or with a center in one zone and without equilibrium points in the other zones). In addition, we also give examples to illustrate that it can reach the maximal number.

Dynamic simulation analysis of molten salt reactor-coupled air-steam combined cycle power generation system

A nonlinear dynamic simulation model based on coordinated control of speed and flow rate for the molten salt reactor and combined cycle systems is proposed here to ensure the coordination and stability between the molten salt reactor and power system.This model considers the impact of thermal properties of fluid variation on accuracy and has been validated with Simulink.This study reveals the capability of the control system to compensate for anomalous situations and maintain shaft stability in the event of perturbations occurring in high-temperature molten salt tank outlet parameters.Meanwhile,the control system’s impact on the system’s dynamic characteristics under molten salt disturbance is also analyzed.The results reveal that after the disturbance occurs,the controlled system benefits from the action of the control,and the overshoot and disturbance amplitude are positively correlated,while the system power and frequency eventually return to the initial values.This simulation model provides a basis for utilizing molten salt reactors for power generation and maintaining grid stability.

Effect of drying-wetting cycles on pore characteristics and mechanical properties of enzyme-induced carbonate precipitation-reinforced sea sand

Enzyme-induced carbonate precipitation(EICP)is an emanating,eco-friendly and potentially sound technique that has presented promise in various geotechnical applications.However,the durability and microscopic characteristics of EICP-treated specimens against the impact of drying-wetting(D-W)cycles is under-explored yet.This study investigates the evolution of mechanical behavior and pore charac-teristics of EICP-treated sea sand subjected to D-W cycles.The uniaxial compressive strength(UCS)tests,synchrotron radiation micro-computed tomography(micro-CT),and three-dimensional(3D)recon-struction of CT images were performed to study the multiscale evolution characteristics of EICP-reinforced sea sand under the effect of D-W cycles.The potential correlations between microstructure characteristics and macro-mechanical property deterioration were investigated using gray relational analysis(GRA).Results showed that the UCS of EICP-treated specimens decreases by 63.7% after 15 D-W cycles.The proportion of mesopores gradually decreases whereas the proportion of macropores in-creases due to the exfoliated calcium carbonate with increasing number of D-W cycles.The micro-structure in EICP-reinforced sea sand was gradually disintegrated,resulting in increasing pore size and development of pore shape from ellipsoidal to columnar and branched.The gray relational degree suggested that the weight loss rate and UCS deterioration were attributed to the development of branched pores with a size of 100-1000 m m under the action of D-W cycles.Overall,the results in this study provide a useful guidancee for the long-term stability and evolution characteristics of EICP-reinforced sea sand under D-W weathering conditions.

Limit Cycle for the RC Circuit with Square-Wave-Type Voltage

The goal of this paper is to prove, by means of calculations the existence of the ω-limit cycle of a simple circuit where a resistor, a capacitor and a square-wave-type voltage source are in series.

Lateral earth pressure of granular backfills on retaining walls with expanded polystyrene geofoam inclusions under limited surcharge loading

Existing studies have focused on the behavior of the retaining wall equipped with expanded polystyrene(EPS)geofoam inclusions under semi-infinite surcharge loading rather than limited surcharge loading.In this paper,the failure mode and the earth pressure acting on the rigid retaining wall with EPS geofoam inclusions and granular backfills(henceforth referred to as EPS-wall),under limited surcharge loading are investigated through two-and three-dimensional model tests.The testing results show that different from the sliding of almost all the backfill in the EPS-wall under semi-infinite surcharge loading,only an approximately triangular backfill slides in the wall under limited surcharge loading.The distribution of the lateral earth pressure on the EPS-wall under limited surcharge loading is non-linear,and the distribution changes from the increase of the wall depth to the decrease with the increase of the limited surcharge loading.An approach based on the force equilibrium of a differential element is developed to predict the lateral earth pressure behind the EPS-wall subjected to limited surcharge loading,and its performance was fully validated by the three-dimensional model tests.

Multi-objective optimization and evaluation of supercritical CO_(2) Brayton cycle for nuclear power generation

The supercritical CO_(2) Brayton cycle is considered a promising energy conversion system for Generation IV reactors for its simple layout,compact structure,and high cycle efficiency.Mathematical models of four Brayton cycle layouts are developed in this study for different reactors to reduce the cost and increase the thermohydraulic performance of nuclear power generation to promote the commercialization of nuclear energy.Parametric analysis,multi-objective optimizations,and four decision-making methods are applied to obtain each Brayton scheme’s optimal thermohydraulic and economic indexes.Results show that for the same design thermal power scale of reactors,the higher the core’s exit temperature,the better the Brayton cycle’s thermo-economic performance.Among the four-cycle layouts,the recompression cycle(RC)has the best overall performance,followed by the simple recuperation cycle(SR)and the intercooling cycle(IC),and the worst is the reheating cycle(RH).However,RH has the lowest total cost of investment(C_(tot))of$1619.85 million,and IC has the lowest levelized cost of energy(LCOE)of 0.012$/(kWh).The nuclear Brayton cycle system’s overall performance has been improved due to optimization.The performance of the molten salt reactor combined with the intercooling cycle(MSR-IC)scheme has the greatest improvement,with the net output power(W_(net)),thermal efficiencyη_(t),and exergy efficiency(η_(e))improved by 8.58%,8.58%,and 11.21%,respectively.The performance of the lead-cooled fast reactor combined with the simple recuperation cycle scheme was optimized to increase C_(tot) by 27.78%.In comparison,the internal rate of return(IRR)increased by only 7.8%,which is not friendly to investors with limited funds.For the nuclear Brayton cycle,the molten salt reactor combined with the recompression cycle scheme should receive priority,and the gas-cooled fast reactor combined with the reheating cycle scheme should be considered carefully.

Involvement of the ABA-and H_(2)O_(2)-Mediated Ascorbate-Glutathione Cycle in the Drought Stress Responses of Wheat Roots

Abscisic acid(ABA),hydrogen peroxide(H_(2)O_(2)) and ascorbate(AsA)–glutathione(GSH)cycle are widely known for their participation in various stresses.However,the relationship between ABA and H_(2)O_(2) levels and the AsA–GSH cycle under drought stress in wheat has not been studied.In this study,a hydroponic experiment was conducted in wheat seedlings subjected to 15%polyethylene glycol(PEG)6000–induced dehydration.Drought stress caused the rapid accumulation of endogenous ABA and H_(2)O_(2) and significantly decreased the number of root tips compared with the control.The application of ABA significantly increased the number of root tips,whereas the application of H_(2)O_(2) markedly reduced the number of root tips,compared with that under 15%PEG-6000.In addition,drought stress markedly increased the DHA,GSH and GSSG levels,but decreased the AsA levels,AsA/DHA and GSH/GSSG ratios compared with those in the control.The activities of the four enzymes in the AsA–GSH cycle were also markedly increased under drought stress,including glutathione reductase(GR),ascorbate peroxidase(APX),monodehydroascorbate reductase(MDHAR)and dehydroascorbate reductase(DHAR),compared with those in the control.However,the application of an ABA inhibitor significantly inhibited GR,DHAR and APX activities,whereas the application of an H_(2)O_(2) inhibitor significantly inhibited DHAR and MDHAR activities.Furthermore,the application of ABA inhibitor significantly promoted the increases of H_(2)O_(2) and the application of H_(2)O_(2) inhibitor significantly blocked the increases of ABA,compared with those under 15% PEG-6000.Taken together,the results indicated that ABA and H_(2)O_(2) probably interact under drought stress in wheat;and both of them can mediate drought stress by modulating the enzymes in AsA–GSH cycle,where ABA acts as the main regulator of GR,DHAR,and APX activities,and H_(2)O_(2) acts as the main regulator of DHAR and MDHAR activities.

有向图上基于层次树索引的最大cycle truss社区搜索

社区搜索旨在从信息网络中找出包含用户查询顶点的高内聚连通子图,cycle truss是一种基于cycle三角形的社区搜索模型,而现有的基于索引的cycle truss社区搜索方法存在索引空间大、搜索效率低、社区内聚性低的缺点。为了解决这一问题,提出一种基于层次树索引的最大cycle truss社区搜索方法。首先,提出了k-cycle truss分解算法,并引入了两个重要的概念:cycle三角连通与k-层次等价。基于k-层次等价设计了层次树索引TreeCIndex与表结构索引SuperTable,在此基础上,并基于这两个新的索引,提出了两个高效的cycle truss社区搜索算法。在4个真实数据集上与已有的基于TrussIndex与EquiTruss的社区搜索算法进行了比较,实验结果表明,TreeCIndex与SuperTable比TrussIndex与EquiTruss节省至少41.5%的空间,索引构建的时间节省8.2%至98.3%,且搜索最大cycle truss社区的效率分别高出了一个和两个数量级。

Performance Limits and Advancements in Single 2D Transition Metal Dichalcogenide Transistor

Two-dimensional(2D)transition metal dichalcogenides(TMDs)allow for atomic-scale manipulation,challenging the conventional limitations of semiconductor materials.This capability may overcome the short-channel effect,sparking significant advancements in electronic devices that utilize 2D TMDs.Exploring the dimension and performance limits of transistors based on 2D TMDs has gained substantial importance.This review provides a comprehensive investigation into these limits of the single 2D-TMD transistor.It delves into the impacts of miniaturization,including the reduction of channel length,gate length,source/drain contact length,and dielectric thickness on transistor operation and performance.In addition,this review provides a detailed analysis of performance parameters such as source/drain contact resistance,subthreshold swing,hysteresis loop,carrier mobility,on/off ratio,and the development of p-type and single logic transistors.This review details the two logical expressions of the single 2D-TMD logic transistor,including current and voltage.It also emphasizes the role of 2D TMD-based transistors as memory devices,focusing on enhancing memory operation speed,endurance,data retention,and extinction ratio,as well as reducing energy consumption in memory devices functioning as artificial synapses.This review demonstrates the two calculating methods for dynamic energy consumption of 2D synaptic devices.This review not only summarizes the current state of the art in this field but also highlights potential future research directions and applications.It underscores the anticipated challenges,opportunities,and potential solutions in navigating the dimension and performance boundaries of 2D transistors.

A Stroke-Limitation AMD Control System with Variable Gain and Limited Area for High-Rise Buildings

Collisions between a moving mass and an anti-collision device increase structural responses and threaten structural safety.An active mass damper(AMD)with stroke limitations is often used to avoid collisions.However,a strokelimited AMD control system with a fixed limited area shortens the available AMD stroke and leads to significant control power.To solve this problem,the design approach with variable gain and limited area(VGLA)is proposed in this study.First,the boundary of variable-limited areas is calculated based on the real-time status of the moving mass.The variable gain(VG)expression at the variable limited area is deduced by considering the saturation of AMD stroke.Then,numerical simulations of a stroke-limited AMD control system with VGLA are conducted on a high-rise building structure.These numerical simulations show that the proposed approach has superior strokelimitation performance compared with a stroke-limited AMD control system with a fixed limited area.Finally,the proposed approach is validated through experiments on a four-story steel frame.

Supplementary Information to“Balancing the quantum speed limit and instantaneous energy cost in adiabatic quantum evolution”

I.SUPPLEMENTARY NOTE 1:THEORETICAL MATERIALS.The quantum speed limit(QSL)is essential for quantum computing and quantum communication,referring to the minimum time required for a quantum system to evolve from one state to another.Two well-known forms of the QSL are the Mandelstam-Tamm(MT)relation TqsL≥πh/2△E[S1]and the Margolus-Levitin(ML)relation TqsL≥πh/2(E)[S2]where Tqst is denoted as the QSL time,h is the reduced Planck's constant,△E is the energy uncertainty(standard deviation)of the system,and(E)is the average energy of the system above its ground state.Both of relations provide a lower bound on the evolution time.

Cosmology-Independent Photon Mass Limits from Localized Fast Radio Bursts by Using Artificial Neural Networks

A hypothetical photon mass m_(γ) can produce a frequency-dependent vacuum dispersion of light, which leads to an additional time delay between photons with different frequencies when they propagate through a fixed distance. The dispersion measure and redshift measurements of fast radio bursts(FRBs) have been widely used to constrain the rest mass of the photon. However, all current studies analyzed the effect of the frequency-dependent dispersion for massive photons in the standard ΛCDM cosmological context. In order to alleviate the circularity problem induced by the presumption of a specific cosmological model based on the fundamental postulate of the masslessness of photons, here we employ a new model-independent smoothing technique, artificial neural network(ANN), to reconstruct the Hubble parameter H(z) function from 34 cosmic-chronometer measurements.By combining observations of 32 well-localized FRBs and the H(z) function reconstructed by ANN, we obtain an upper limit of m_(γ) ≤ 3.5 × 10^(-51)kg, or equivalently m_(γ) ≤ 2.0 × 10^(-15)eV/c^(2)(m_(γ) ≤ 6.5 × 10^(-51)kg, or equivalently m_(γ) ≤ 3.6 × 10^(-15)eV/c_(2)) at the 1σ(2σ) confidence level. This is the first cosmology-independent photon mass limit derived from extragalactic sources.

A Review on Technologies for the Use of CO2 as a Working Fluid in Refrigeration and Power Cycles

The use of carbon dioxide as a working fluid has been the subject of extensive studies in recent years, particularly in the field of refrigeration where it is at the heart of research to replace CFC and HCFC. Its thermodynamic properties make it a fluid of choice in the efficient use of energy at low and medium temperatures in engine cycles. However, the performance of transcritical CO2 cycles weakens under high temperature and pressure conditions, especially in refrigeration systems;On the other hand, this disadvantage becomes rather interesting in engine cycles where CO2 can be used as an alternative to the organic working fluid in small and medium-sized electrical systems for low quality or waste heat sources. In order to improve the performance of systems operating with CO2 in the field of refrigeration and electricity production, research has made it possible to develop several concepts, of which this article deals with a review of the state of the art, followed by analyzes in-depth and critical of the various developments to the most recent modifications in these fields. Detailed discussions on the performance and technical characteristics of the different evolutions are also highlighted as well as the factors affecting the overall performance of the systems studied. Finally, perspectives on the future development of the use of CO2 in these different cycles are presented.

Long-Cycle Lithium Batteries with LiNi_(0.8)Co_(0.1)Mn_(0.1)O_(2) Cathodes above 4.5 V Enabled by Uniform Coating of Nanosized Garnet Electrolytes

The pursuit of high-energy cathode materials has been focused on raising the charging cutoff voltage of nickel (Ni)-rich layered oxide cathode such as LiNi_(0.8)Co_(0.1)Mn_(0.1)O2 (NCM811). However, the NCM811 suffers from rapid capacity fading upon cycling at cutoff voltage higher than 4.5 V, owing to their structural degradation and labile surface reactivity. Surface-coating with solid electrolytes has been recognized as an effective method to mitigate the performance failure of NCM811 at high voltage. Herein, the nano-sized Li_(6.4)La_(3)Ta_(0.6)Zr_(1.4)O_(12) (LLZTO) is uniformly coated on the surface of single-crystal NCM811 particles, accompanied with the long-range Ta^(5+) diffusion into the transition metal layer of NCM811 lattice. It is revealed that the LLZTO coating can not only inhibit the surface reactions of NCM811 with liquid electrolytes but also play an important role in suppressing the bulk microcracking within the NCM811 particles. The incorporation of Ta^(5+) ion expands the lattice spacing and thereby improves the homogeneity of the Li^(+) diffusion in the single-crystal NCM811, which alleviates the mechanical strain and intragranular cracks caused by nonuniform phases-transformation at high charging voltage. The synergy of surface protection and structural stabilization realized by LLZTO coating enables the NCM811-based lithium batteries to achieve a remarkable electrochemical performance. Typically, LLZTO coated NCM811 delivers a high reversible specific capacity of 202.1 mAh⋅g^(−1) with an excellent capacity retention as high as 70% over 1000 cycles upon charging to 4.5 V at 1 C.

Bicycle-related traumatic injuries: a retrospective study during COVID-19 pandemic

BACKGROUND:This study aimed to review bicycle-related injuries during the COVID-19 pandemic to assist with reinforcement or implementation of new policies for injury prevention.METHODS:This is a retrospective descriptive analysis of injuries sustained during cycling for patients 18 years old and above who presented to Singapore General Hospital from January to June 2021.Medical records were reviewed and consolidated.Descriptive analyses were used to summarize patient characteristics,and differences in characteristics subgrouped by triage acuity and discharge status were analyzed.RESULTS:The study included 272 patients with a mean age of 43 years and a male predominance(71.7%).Most presented without referrals(88.2%)and were not conveyed by ambulances(70.6%).Based on acuity category,there were 24(8.8%)Priority 1(P1)patients with 7 trauma activations,174(64.0%)and 74(27.2%)P2 and P3 patients respectively.The most common injuries were fractures(34.2%),followed by superficial abrasion/contusion(29.4%)and laceration/wound(19.1%).Thirteen(4.8%)patients experienced head injury and 85 patients(31.3%)were documented to be wearing a helmet.The majority occurred on the roads as traffic accidents(32.7%).Forty-two patients(15.4%)were admitted with a mean length of stay of 4.1 d and 17(6.3%)undergone surgical procedures.Out of 214(78.7%)discharged patients,no re-attendances or mortality were observed.In the subgroup analysis,higher acuity patients were generally older,with higher proportions of head injuries leading to admission.CONCLUSION:Our study highlights significant morbidities in bicycle-related injuries.There is also a high proportion of fractures in the young healthy male population.Injury prevention is paramount and we propose emphasizing helmet use and road user safety.

Speed limit effect during lane change in a two-lane lattice model under V2X environment

Speed limit measures are ubiquitous due to the complexity of the road environment,which can be supplied with the help of vehicle to everything(V2X)communication technology.Therefore,the influence of speed limit on traffic system will be investigated to construct a two-lane lattice model accounting for the speed limit effect during the lane change process under V2X environment.Accordingly,the stability condition and the mKdV equation are closely associated with the speed limit effect through theory analysis.Moreover,the evolution of density and hysteresis loop is simulated to demonstrate the positive role of the speed limit effect on traffic stability in the cases of strong reaction intensity and high limited speed.

Proteomic response of Phaeocystis globosa to nitrogen limitation

Phaeocystis globosa is an important unicellular eukaryotic alga that can also form colonies.P.globosa can cause massive harmful algal blooms and plays an important role in the global carbon or sulfur cycling.Thus far,the ecophysiology of P.globosa has been investigated by numerous studies.However,the proteomic response of P.globosa to nitrogen depletion remains largely unknown.We compared four protein preparation methods of P.globosa for two-dimensional electrophoresis(2-DE)(Urea/Triton X-100 with trichloroacetic acid(TCA)/acetone precipitation;TCA/acetone precipitation;Radio Immuno Precipitation Assay(RIPA)with TCA/acetone precipitation;and Tris buffer).Results show that the combination of RIPA with TCA/acetone precipitation had a clear gel background and showed the best protein spot separation effect,based on which the proteomic response to nitrogen depletion was studied using 2-DE.In addition,we identified six differentially expressed proteins whose relative abundance increased or decreased more than 1.5-fold(P<0.05).Most proteins could not be identified,which might be attributed to the lack of genomic sequences of P.globosa.Under nitrogen limitation,replication protein-like,RNA ligase,and sn-glycerol-3-phosphate dehydrogenase were reduced,which may decrease the DNA replication level and ATP production in P.globosa cells.The increase of endonucleaseⅢand transcriptional regulator enzyme may affect the metabolic and antioxidant function of P.globosa cells and induce cell apoptosis.These findings provide a basis for further proteomic study of P.globosa and the optimization of protein preparation methods of marine microalgae.

The Impact of Network Topologies and Radio Duty Cycle Mechanisms on the RPL Routing Protocol Power Consumption

The Internet of Things(IoT)has witnessed a significant surge in adoption,particularly through the utilization of Wireless Sensor Networks(WSNs),which comprise small internet-connected devices.These deployments span various environments and offer a multitude of benefits.However,the widespread use of battery-powered devices introduces challenges due to their limited hardware resources and communication capabilities.In response to this,the Internet Engineering Task Force(IETF)has developed the IPv6 Routing Protocol for Low-power and Lossy Networks(RPL)to address the unique requirements of such networks.Recognizing the critical role of RPL in maintaining high performance,this paper proposes a novel approach to optimizing power consumption.Specifically,it introduces a developed sensor motes topology integrated with a Radio Duty Cycling(RDC)mechanism aimed at minimizing power usage.Through rigorous analysis,the paper evaluates the power efficiency of this approach through several simulations conducted across different network topologies,including random,linear,tree,and elliptical topologies.Additionally,three distinct RDC mechanisms—CXMAC,ContikiMAC,and NullRDC—are investigated to assess their impact on power consumption.The findings of the study,based on a comprehensive and deep analysis of the simulated results,highlight the efficiency of ContikiMAC in power conservation.This research contributes valuable insights into enhancing the energy efficiency of RPL-based IoT networks,ultimately facilitating their widespread deployment and usability in diverse environments.