Equilibrium Plane Research Articles

Extreme multistability of fractional-order hyperchaotic system based on dual memristors and its implementation

In this paper, a fractional-order hyperchaotic system based on dual memristors is proposed by introducing flux-controlled and charge-controlled memristors into a simple RLC circuit. Dynamics of the hyperchaotic system are investigated using bifurcation diagrams, Lyapunov exponents spectrum (LEs), phase diagrams, time-domain diagrams, spectral entropy (SE) and C0 complexity. The results show that it has a plane of equilibria and exhibits rich dynamical characteristics, including hyperchaos, homogeneous and heterogeneous extreme multistability. Meanwhile, the transient transition phenomena as well as the effect of parameters on the complexity and chaotic behavior of the system are also studied. Furthermore, the practical implementation of the system is realized through analog and digital circuit. The experimental results validate the correctness of the theoretical analysis and help to make better use of the hyperchaotic system in applications such as secure communications.

Bidirectional static loading tests on barrette piles. A case history from Ho Chi Minh City, Vietnam

Bidirectional static loading tests were conducted on two strain-gage instrumented barrettes installed to 72 m depth in Ho Chi Minh City, Vietnam. The barrettes were to support a 16-storey building with 5 basements. The soil profile comprised layers of medium coarse to fine sand, medium clay, firm to stiff clayey soil, and dense sandy silt. The region is experiencing an ongoing land subsidence affecting the upper about 40 m of soil and, on average in the city, the ground surface is currently settling 16 mm/year. The test records were processed by means of effective stress analysis to provide the axial pile force distribution, load transfer functions, and equivalent head-down load–movement curve. The analysis was then used to obtain the equivalent pile-head load–movement response adjusted to the planned 22 m deep basement excavation. Load transfer functions were back-calculated from the test records and indicate that the construction will show somewhat large load-transfer movement. However, because the equilibrium plane will be below the subsiding layers, below 40 m depth, downdrag is not expected to affect the building. The load response of the barrettes is compared to the results of a bidirectional (BD) loading test on a 1.8 m diameter bored pile at an adjacent project.

Large Casimir Flipping Torque in Quantum Trap.

Casimir torque between parallel plates, a macroscopic quantum electrodynamics effect, is known to be induced by dielectric anisotropy and related to the rotational degree of freedom. We here reveal a different type of Casimir torque generated on a Au plate suspended in a quantum trap without recourse to materials anisotropy. As the Au plate deflects from the equilibrium plane with a nonzero flipping angle, the regions departing from and approaching the Teflon-coated Au substrate are subjected to attractive and repulsive Casimir forces, respectively, resulting in a restoring torque about the axis of flipping. For a quantum trap with an equilibrium separation of ∼10 nm, the stiffness per unit area of the Casimir flipping torque can be an order of magnitude larger than those of previously reported dielectric anisotropy-induced rotational torques at the same separation. The large Casimir flipping torque provides the possibility of designing a mechanical oscillator completely dominated by quantum and thermal fluctuations.

A layered roll stability control strategy for commercial vehicles based on adaptive model predictive control

Due to the high centre of mass, commercial vehicles are prone to ultimate rollover under extreme steering conditions. The rollover of commercial vehicles leads to serious traffic accidents and poses a threat to road traffic. In this paper, the mechanism of vehicle rollover is revealed by static equilibrium and phase plane analysis. Meanwhile, a robust roll angle observer is designed by combining Kalman filter and sliding mode observation. Considering the influence of wheel lifting on roll dynamics, a novel layered control strategy is proposed by employing engine torque limit, differential braking and active front-wheel steering. Moreover, the layered control of roll stability is realised by adaptive model predictive control with time-varying weights and constraints. To verify the validity and reliability of the proposed algorithm, the hardware-in-loop tests under typical driving conditions have been carried out. The results show that the proposed method can effectively restrain the divergence of roll state and prevent vehicle rollover.

Interfacial behaviour and stress transfer mechanism of additively manufactured laser cladding sheet-covered steel plates

Laser cladding (LC), a metal additive manufacturing process, is employed to strengthen steel plate which has benefits over traditional steel structure retrofit approaches. In this study, the interfacial behaviour between the substrate and LC sheet of laser cladding sheet (LCS)-covered steel plates is investigated, through a series of mechanical tensile coupon tests by considering the effects of the scanning pattern and the thickness and length of the LC sheet. Double-shear pull tests, metallographic tests and microindentation hardness tests are also carried out to reveal the microstructure of the interfacial zone. It is observed from the macro and micro experimental results that the stresses in the LCS-covered plates in tension can be transferred effectively through the interface between the substrate and LC sheet, and perfect interfacial bonding behaviour with no slip could be assumed. A series of finite element (FE) analyses are further undertaken to calibrate such an assumption. Based on the fully bonded interface assumption, for convenient engineering application, a theoretical model is developed to describe the elastic stress/strain distributions of LCS-covered steel plates subject to tension, by following the equilibrium considerations and plane strain elastic theory. The theoretical model is validated by comparing its predictions with the experimental and FE analysis results. The proposed theoretical model would provide baseline solution for future elastic strain/stress analysis of the LCS-covered steel plates.

A magnetically enabled simulation of microgravity represses the auxin response during early seed germination on a microfluidic platform

For plants on Earth, the phytohormone auxin is essential for gravitropism-regulated seedling establishment and plant growth. However, little is known about auxin responses under microgravity conditions due to the lack of a tool that can provide an alteration of gravity. In this paper, a microfluidic negative magnetophoretic platform is developed to levitate Arabidopsis seeds in an equilibrium plane where the applied magnetic force compensates for gravitational acceleration. With the benefit of the microfluidic platform to simulate a microgravity environment on-chip, it is found that the auxin response is significantly repressed in levitated seeds. Simulated microgravity statistically interrupts auxin responses in embryos, even after chemical-mediated auxin alterations, illustrating that auxin is a critical factor that mediates the plant response to gravity alteration. Furthermore, pretreatment with an auxin transportation inhibitor (N-1-naphthylphthalamic acid) enables a decrease in the auxin response, which is no longer affected by simulated microgravity, demonstrating that polar auxin transportation plays a vital role in gravity-regulated auxin responses. The presented microfluidic platform provides simulated microgravity conditions in an easy-to-implement manner, helping to study and elucidate how plants correspond to diverse gravity conditions; in the future, this may be developed into a versatile tool for biological study on a variety of samples.

Real-Time Shape Estimation for Concentric Tube Continuum Robots with a Single Force/Torque Sensor.

Shape-sensing in real-time is a key requirement for the development of advanced algorithms for concentric tube continuum robots when safe interaction with the environment is important e.g., for path planning, advanced control, and human-machine interaction. We propose a real-time shape-estimation algorithm for concentric tube continuum robots based on the force-torque information measured at the tubes’ basis. It extends a shape estimation algorithm for elastic rods based on discrete Kirchhoff rod theory. For simplicity and efficiency of calculation, we combine it with a model under piece-wise constant curvature assumption, in which we model a concentric tube continuum robot as a combination of segments of planar constant curvatures lying on different equilibrium planes. We evaluate our approach for a single and two combined additively manufactured tubes and achieve an estimation frequency of 333 Hz for two combined tubes with a mean deviation along the backbone of the tubes of 1.91–5.22 mm.

A New Memristive Chaotic System with a Plane and Two Lines of Equilibria

A new 4D memristive chaotic system with an infinite number of equilibria is proposed via exhaustive computer search. Interestingly, such a new memristive system has a plane of equilibria and two other lines of equilibria. Lyapunov exponent and bifurcation analysis show that this system has chaotic solutions with coexisting attractors. The basins of attraction of the coexisting attractors show chaos, stable fixed-points, and unbounded solutions. Furthermore, the 2D parameter space of the system is explored to find the optimum values of the parameters using the ALO (Ant Lion Optimizer) optimization algorithm.

Prediction of transient wellbore cement circulating temperature distribution using CFD simulation

Accurate prediction of the cement slurry temperature while being circulated downhole is critical for a successful cement job. Failure to predict the cement slurry temperature correctly may result in premature or delayed cement setting. Due to the practical limitations of using temperature sensors for direct measurement and the complexity of the bottomhole circulating conditions, it is difficult to gather accurate information about how the temperature of cement slurry changes as it is being circulated through the well. To overcome these challenges and help with designing a cement system more accurately, a computational fluid dynamics (CFD) model is developed. The model simulates the balanced-plug cementing operation, which considers the continuous displacement of the drilling fluid by the cement slurry and the cement slurry by water. The CFD model predicts the transient changes in the temperatures of the cement slurry and near wellbore formation during this displacement process involving three different fluids. A new dynamic mesh method was developed to effectively handle the interface mixing of different fluids, and thus model the three-fluid displacement process in the annulus more realistically. The CFD model can also deal with complex well conditions such as deviated wellbores, variable geothermal gradients and formation rock properties. Most importantly, in the absence of the measurements allowing direct monitoring of the downhole conditions, the new CFD model allows for continuous monitoring of downhole transient fluid and formation temperature at any position along the wellbore. The results of CFD transient simulations indicate that the bottomhole circulation temperature (BHCT) values predicted by using API method are significantly overestimated. The highest cement slurry temperature in the annulus was observed at some distance above the bottom of the well. Results also confirmed the existence of an equilibrium plane (extending horizontally) into the formation across which a temperature reversal was observed. The formations above and below the equilibrium plane have opposite heat transfer patterns. The depth of the equilibrium plane rises steadily while its temperature gradually decreases as the circulation continues. The change of the cement/drilling fluid interface temperature is traced dynamically. CFD simulation is proven to be a realistic and reliable approach for prediction of the cement circulating temperature and can be easily used in combination with real time operational data. Practical guidelines and solutions derived from the simulation results can be useful for improved cement job design in field applications.

Flexión compuesta esviada en secciones de hormigón armado. Aproximación numérica

Las exigencias normativas relativas a la comprobación de los estados límites de servicio en estructuras de hormigón armado requieren del conocimiento de la tensión de tracción de la armadura en las secciones características. En situaciones de compresión o flexión compuesta esviada, la obtención de las coordenadas del plano de equilibrio con las que determinar deformación y tensión de cada punto de la sección transversal bajo solicitaciones no necesariamente de agotamiento, requiere de algún procedimiento numérico. Este trabajo presenta un método de búsqueda de la solución basado en la determinación de familias de diagramas momento-curvatura para la sección analizada y el axil de diseño exterior, y presenta la evaluación del mismo de manera experimental. El modelo es universal en cuanto a la geometría de la sección transversal, las solicitaciones exteriores, y los modelos constitutivos empleados para hormigón y acero.

Initial boosting phenomenon of a fractional-order hyperchaotic system based on dual memristors

In this paper, a fractional-order hyperchaotic system based on dual memristors is represented to analyze the nonlinear dynamic behaviors via replacing two coupled resistors with dual memristors. It is worthy to note that the fractional-order hyperchaotic system has two zero eigenvalues and three nonzero eigenvalues, therefore the equilibrium plane can be separated into diverse areas which indicates the hyperchaotic system is stable or chaotic. The simulation results illustrate that the initial states have a significant impact on the dynamic behaviors, which can be mirrored by the phase portraits, the bifurcation diagrams, the power spectrum and the time-domain waveform. In particular, the memristor initial boosting phenomenon is investigated in the proposed hyperchaotic system, which implies the memristor initial states determine the attractor offset boosting behaviors under various initial controllers. Clearly, it differs from the variable offset boosting behavior totally due to its multi-dimension and nonlinearity. Finally, numerical results under different initial controllers are exhibited to demonstrate the memristor initial boosting phenomenon. Moreover, a hardware circuit based on PSPICE software is fabricated and its experimental simulations is given to verify the dynamic behaviors effectively.

Synchronization of a Non-Equilibrium Four-Dimensional Chaotic System Using a Disturbance-Observer-Based Adaptive Terminal Sliding Mode Control Method.

In this paper, dynamical behavior and synchronization of a non-equilibrium four-dimensional chaotic system are studied. The system only includes one constant term and has hidden attractors. Some dynamical features of the governing system, such as invariance and symmetry, the existence of attractors and dissipativity, chaotic flow with a plane of equilibria, and offset boosting of the chaotic attractor, are stated and discussed and a new disturbance-observer-based adaptive terminal sliding mode control (ATSMC) method with input saturation is proposed for the control and synchronization of the chaotic system. To deal with unexpected noises, an extended Kalman filter (EKF) is implemented along with the designed controller. Through the concept of Lyapunov stability, the proposed control technique guarantees the finite time convergence of the uncertain system in the presence of disturbances and control input limits. Furthermore, to decrease the chattering phenomena, a genetic algorithm is used to optimize the controller parameters. Finally, numerical simulations are presented to demonstrate the performance of the designed control scheme in the presence of noise, disturbances, and control input saturation.

Infinitely many coexisting attractors of a dual memristive Shinriki oscillator and its FPGA digital implementation

In this paper, a novel chaotic oscillator is proposed, which is derived from the classical Shinriki oscillator by substituting the series-parallel diode loop with a flux-controlled memristor and connecting an active charge-controlled memristor in series with an inductor. The mathematical model of the circuit is established, and the stability distribution maps of three non-zero eigenvalues in the equilibrium plane are obtained. The basic dynamical behaviors depending on the variation of the circuit parameters and memristor initial conditions are investigated by standard nonlinear analysis tools, such as bifurcation diagrams, Lyapunov exponents and phase portraits. Particularly, some striking phenomena, including the routes to double-scroll chaotic attractors, coexisting periodic-chaotic bubbles and asymmetric coexisting behaviors are observed. Furthermore, extreme multistability of the new oscillator is revealed by attraction basins under the initial condition of different dynamic elements. Finally, the Shinriki oscillator with two memristors is realized through Field-Programmable Gate Array (i.e., FPGA) to verify the effectiveness of the numerical simulations.

Memristor-based novel complex-valued chaotic system and its projective synchronisation using nonlinear active control technique

In this paper, a flux controlled memristor-based novel complex-valued chaotic system and its projective synchronisation is investigated. The proposed complex-valued chaotic system has line and plane of equilibria, i.e. an infinite number of equilibria. Different qualitative and quantitative tools such as time series, phase plane, Poincare section, Lyapunov exponents, Lyapunov spectrum, and Lyapunov dimension are used to evidence the chaotic behaviour of the proposed complex-valued system. Further, the projective synchronisation between the proposed complex-valued chaotic systems is achieved using nonlinear active control. Active control laws are designed, by using sum of the relevant variables of the proposed complex-valued chaotic systems, to ensure the convergence of error dynamics. The required global asymptotic stability condition is derived using Lyapunov stability theory. Simulation is done in MATLAB environment to verify the theoretical approach. Simulation results reveal that the objectives of the paper are achieved successfully.

Chaos in the inert Oort cloud

Context. Distant trans-Neptunian objects are subject to planetary perturbations and galactic tides. The former decrease with the distance, while the latter increase. In the intermediate regime where they have the same order of magnitude (the “inert Oort cloud”), both are weak, resulting in very long evolution timescales. To date, three observed objects can be considered to belong to this category. Aims. We aim to provide a clear understanding of where this transition occurs, and to characterise the long-term dynamics of small bodies in the intermediate regime: relevant resonances, chaotic zones (if any), and timescales at play. Methods. The different regimes are explored analytically and numerically. We also monitored the behaviour of swarms of particles during 4.5 Gyrs in order to identify which of the dynamical features are discernible in a realistic amount of time. Results. There exists a tilted equilibrium plane (Laplace plane) about which orbits precess. The dynamics is integrable in the low and high semi-major axis regimes, but mostly chaotic in between. From about 800 to 1100 astronomical units (au), the chaos covers almost all the eccentricity range. The diffusion timescales are large, but not to the point of being indiscernible in a 4.5 Gyrs duration: the perihelion distance can actually vary from tens to hundreds of au. Orbital variations are damped near the ecliptic (where previous studies focussed), but favoured in specific ranges of inclination corresponding to well-defined resonances. Moreover, starting from uniform distributions, the orbital angles cluster after 4.5 Gyrs for semi-major axes larger than 500 au, because of a very slow differential precession. Conclusions. Even if it is characterised by very long timescales, the inert Oort cloud mostly features chaotic regions; it is therefore much less inert than it appears. Orbits can be considered inert over 4.5 Gyrs only in small portions of the space of orbital elements, which include (90377) Sedna and 2012VP113. Effects of the galactic tides are discernible down to semi-major axes of about 500 au. We advocate including the galactic tides in simulations of distant trans-Neptunian objects, especially when studying the formation of detached bodies or the clustering of orbital elements.

Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system

Abstract By substituting two resistive couplings with two memristive couplings, a two-memristor-based hyperchaotic system is proposed. This hyperchaotic system has a plane equilibrium with two zero eigenvalues and three nonzero ones, and the equilibrium plane is divided into three regions with different stabilities, including unstable saddle, stable node, and stable node-focus. Through using the local attraction basin, bifurcation diagrams and Lyapunov exponent spectra, dynamical behaviors are analyzed in the unstable saddle region, from which the bi-stability phenomenon is observed in such a hyperchaotic system. More particularly, the memristor initial boosting behaviors are found, which indicates that the attractor offset boosting is controlled by the memristor initial values. The memristor initial boosting is multi-dimension, nonlinearity and non-monotonic, completely different from the variable offset boosting. Subsequently, PSIM circuit simulations are performed to verify the numerical results.

Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability

This paper presents a novel fifth-order two-memristor-based Chua’s hyperchaotic circuit, which is synthesized from an active band pass filter-based Chua’s circuit through replacing a nonlinear resistor and a linear resistor with two different memristors. This physical circuit has a plane equilibrium and therefore emerges complex phenomenon of extreme multistability. Based on the mathematical model, stability distributions of three nonzero eigenvalues in the equilibrium plane are exhibited, from which it is observed that four different stability regions with unstable saddle-focus, and stable and unstable node-focus are distributed, thereby leading to coexisting phenomenon of infinitely many attractors. Furthermore, extreme multistability depending on two-memristor initial conditions is investigated by bifurcation diagrams and Lyapunov exponent spectra and coexisting infinitely many attractors’ behavior is revealed by phase portraits and attraction basins. At last, a hardware circuit is fabricated and some experimental observations are captured to verify that extreme multistability indeed exists in the two-memristor-based Chua’s hyperchaotic circuit.

A Simple Chaotic Flow with a Plane of Equilibria

Using a systematic computer search, a simple four-dimensional chaotic flow was found that has the unusual feature of having a plane of equilibria. Such a system belongs to a newly introduced category of chaotic systems with hidden attractors that are important and potentially problematic in engineering applications.

Influence of Dilation Angle on Drained Shallow Circular Anchor Uplift Capacity

AbstractAn experimental study of uplift capacity of 22 circular helical anchors installed in sand with peak friction angles between 40 and 50° was performed. Laboratory triaxial tests indicated that the dilation angle varied between 10 and 25° for these peak friction angles. To account for soil behavior exhibiting nonassociated flow (NAF), in which the dilation angle is much less than the friction angle, a limit equilibrium plane strain analytical solution for plate anchor uplift was updated and extended to axisymmetric conditions. Anchor test results were compared with upper bound (UB) plasticity solutions (based on associated flow) and the newly developed NAF limit equilibrium model. The UB solution overpredicted uplift capacity by more than a factor of 2, whereas the limit equilibrium model had a ratio of calculated to measured capacity of 1.15 and a coefficient of variation of 0.14. Although additional study is warranted, the consistency among the numerical, analytical, and experimental results gives ...

Unbalance Identification of Speed-Variant Rotary Machinery without Phase Angle Measurement

As rotary mechanical structure becomes more complicated, difficulty arises in receiving prime correction mass and optimum balancing plane efficiently. An innovative modal balancing process for estimating the residual unbalance from different equilibrium plane of complex flexible rotor system is presented. The method is based on a numerical approach with modal ratio among measurement points (MRMP) coefficient and triple phase method (TPM). The veracity of calculation result is verified by an academic rotor model. The latter study in this paper is subsequently put forward through a power turbine rotor modeled by finite element method. Simulation results show that proper equilibrium plane performs commendably in recognizing residual unbalance and reducing the vibration effect through the critical region. Moreover, the inherent unbalance recognized by experimental data from a turbine rotor with slender shaft is found to be in certain difference under different counterweight combination. Choosing suitable balancing planes will improve the accuracy of unbalance identification.