Combination–combination synchronization among four identical or different chaotic systems

Based on one drive system and one response system synchronization model, a new type of combination–combination synchronization is proposed for four identical or different chaotic systems. According to the Lyapunov stability theorem and adaptive control, numerical simulations for four identical or different chaotic systems with different initial conditions are discussed to show the effectiveness of the proposed method. Synchronization about combination of two drive systems and combination of two response systems is the main contribution of this paper, which can be extended to three or more chaotic systems. A universal combination of drive systems and response systems model and a universal adaptive controller may be designed to our intelligent application by our synchronization design.     

Meshfree modelling of fracture—a comparative study of different methods

Different fracture methods in meshfree methods are studied and compared. Our studies focuses on the elementfree Galerkin (EFG) method though similar results were obtained with SPH and MPM. Three major fracture approaches are tested: Natural fracture, smeared crack method and discrete crack method. In the latter method, the crack is represented as continuous line and as set of discrete crack segment. Natural fracture is a key feature of meshfree methods. In some numerical examples, we will show that natural fracture criterion cannot handle even simple fracture adequately. Moreover, we will show in our numerical examples that smeared crack models can capture global behavior appropriately for simple examples but not for complex examples involving branching cracks. The most accurate methods are discrete fracture methods.     

Generalized projective lag synchronization between?different hyperchaotic systems with uncertain parameters

Generalized projective lag synchronization (GPLS) is characterized by the output of the drive system proportionally lagging behind the output of the response system. In this paper, GPLS between different hyperchaotic systems with uncertain parameters, i.e., GPLS between Lorenz and Lü hyperchaotic systems, and between Lorenz?CStenflo and Lorenz hyperchaotic systems, is studied by applying an adaptive control method. Based on Lyapunov stability theory, the adaptive controllers and corresponding parameter update rules are constructed to make the states of two diverse hyperchaotic systems asymptotically synchronize up to the desired scaling matrix and to estimate the uncertain parameters. Some numerical simulations are provided to show the effectiveness of our results.     

Detonation initiation of JP-8–oxygen mixtures at different initial temperatures

Liquid fuel with sufficient vapor proportion at micron scale is essentially required to increase specific energy density and reduce volume requirements for application of pulse detonation engine. For JP-8, the fully vaporized temperature ranges from 380 to 410 K. In this study, the fuel vapor with oxygen is not enough to induce the reaction and leads to failure of detonation initiation at the initial temperature of 373 K. Condensed fuel was also observed on the bottom of detonation tube. At 393 K, the detonation wave was successfully generated even though a portion of fuel was in a liquid state. The deflagration-to-detonation run-up distance and the pressure trace at fully vaporized conditions, in which the initial temperatures were at 413, 433, and 453 K, were similar to those of gaseous mixtures, such as propane–oxygen mixture.     

An appraisal of liquid–liquid slug flow in different pipe orientations

Gas–liquid slug flow occurs over a wide range of phase flow rates and in a variety of practical applications during gas–liquid two-phase flows. The range of slug flow increases further in narrow pipes (<0.0254 m), undulated pipelines, riser tube, etc. On the other hand, the past literature shows that slug flow is rarely observed for liquid–liquid cases. In the present study, an interest was felt to investigate whether liquid–liquid slug flow occurs in situations known for excessive slugging in gas–liquid cases. For this, experiments have been performed in narrow (0.012 m ID) vertical and horizontal pipes and an undulated pipeline of 0.0254 m internal diameter where the V-shaped undulation comprises of an uphill and a downhill section between two horizontal pipes. The studies have been performed for both peak and valley orientation of the undulation. Kerosene and water have been selected as the test fluids and the optical probe technique has been used to supplement visual observations especially at higher flow rates. The studies have revealed the existence of the slug flow pattern over a wide range of phase flow rates in all the three geometries. Interestingly, it has been noted that the introduction of an undulation induces flow patterns which bear a closer resemblance to gas–liquid flows as compared to liquid–liquid flows through a horizontal pipe of 0.0254 m diameter.     

Chaos synchronization of two different chaotic complex Chen and Lü systems

This paper investigates the phenomenon of chaos synchronization of two different chaotic complex systems of the Chen and Lü type via the methods of active control and global synchronization. In this regard, it generalizes earlier work on the synchronization of two identical oscillators in cases where the drive and response systems are different, the parameter space is larger, and the dimensionality increases due to the complexification of the dependent variables. The idea of chaos synchronization is to use the output of the drive system to control the response system so that the output of the response system converges to the output of the drive system as time increases. Lyapunov functions are derived to prove that the differences in the dynamics of the two systems converge to zero exponentially fast, explicit expressions are given for the control functions and numerical simulations are presented to illustrate the success of our chaos synchronization techniques. We also point out that the global synchronization method is better suited for synchronizing identical chaotic oscillators, as it has serious limitations when applied to the case where the drive and response systems are different.     

Dynamics of a mass–spring–pendulum system with vastly different frequencies

We investigate the dynamics of a simple pendulum coupled to a horizontal mass?Cspring system. The spring is assumed to have a very large stiffness value such that the natural frequency of the mass?Cspring oscillator, when uncoupled from the pendulum, is an order of magnitude larger than that of the oscillations of the pendulum. The leading order dynamics of the autonomous coupled system is studied using the method of Direct Partition of Motion (DPM), in conjunction with a rescaling of fast time in a manner that is inspired by the WKB method. We particularly study the motions in which the amplitude of the motion of the harmonic oscillator is an order of magnitude smaller than that of the pendulum. In this regime, a pitchfork bifurcation of periodic orbits is found to occur for energy values larger that a critical value. The bifurcation gives rise to nonlocal periodic and quasi-periodic orbits in which the pendulum oscillates about an angle between zero and ??/2 from the down right position. The bifurcating periodic orbits are nonlinear normal modes of the coupled system and correspond to fixed points of a Poincare map. An approximate expression for the value of the new fixed points of the map is obtained. These formal analytic results are confirmed by comparison with numerical integration.     

Dynamics of three coupled limit cycle oscillators with?vastly?different frequencies

A system of three coupled limit cycle oscillators with vastly different frequencies is studied. The three oscillators, when uncoupled, have the frequencies ?? ₁=O(1), ?? ₂=O(1/??) and ?? ₃=O(1/?? ²), respectively, where ???1. The method of direct partition of motion (DPM) is extended to study the leading order dynamics of the considered autonomous system. It is shown that the limit cycles of oscillators 1 and 2, to leading order, take the form of a Jacobi elliptic function whose amplitude and frequency are modulated as the strength of coupling is varied. The dynamics of the fastest oscillator, to leading order, is unaffected by the coupling to the slower oscillator. It is also found that when the coupling strength between two of the oscillators is larger than a critical bifurcation value, the limit cycle of the slower oscillator disappears. The obtained analytical results are formal and are checked by comparison to solutions from numerical integration of the system.     

Evolution of plastic zones in dynamically loaded plates using different elastic–viscoplastic laws

In the framework of viscoplastic theory many different laws were developed, accounting for material behaviors like creep, relaxation or evolution of overstresses. Though each model is able to predict in uni-axial material tests the values of stresses depending on plastic strains and plastic strain rates the question is if solutions of simulations are still realistic if the viscoplastic law is applied on structural deformations. In the present study strain rate sensitive metal plates are subjected to shock waves. The purpose is to compare simulation results obtained with different elastic–viscoplastic laws to experiments in order to determine the most appropriate material model. By subjecting circular metal plates experimentally to shock wave loadings realistic deformation histories are measured. The measurements are compared to simulation results obtained with different viscoplastic laws. The aim is to find out the accuracy of each model concerning the predictions of displacements, shape formings, spread of plastic zones and evolutions of inner bending moments.     

Interactions among different types of nonlinear waves described by the Kadomtsev–Petviashvili equation

In nonlinear science, the interactions among solitons are well studied because the multiple soliton solutions can be obtained by various effective methods. However, it is very difficult to study interactions among different types of nonlinear waves such as the solitons (or solitary waves), the cnoidal periodic waves and Painlevé waves. In this paper, taking the Kadomtsev–Petviashvili (KP) equation as an illustration model, a new method is established to find interactions among different types of nonlinear waves. The nonlocal symmetries related to the Darboux transformation (DT) of the KP equation is localized after embedding the original system to an enlarged one. Then the DT is used to find the corresponding group invariant solutions. It is shown that the essential and unique role of the DT is to add an additional soliton on a Boussinesq-type wave or a KdV-type wave, which are two basic reductions of the KP equation.     

On the steady solitary-wave solution of the Green–Naghdi equations of different levels

The steady-state solitary wave solution of high-level Green–Naghdi (GN) equations is obtained by use of the Newton–Raphson method. Four aspects of solitary waves are studied: the wave speed, wave profile, velocity field and particle trajectory. A convergence study is performed for each individual case. Results of the converged model are compared with the existing laboratory experiments and other theoretical solutions for an inviscid and incompressible fluid, including the solutions of the Euler equations. Particle trajectories, predicted by the GN model, show close agreement with the laboratory measurements and provide a new approach to understanding the movement of the particles under a solitary wave. It is further shown that high-level GN equations can predict the solitary wave of the highest height.     

Fluid–structure interaction approaches on fixed grids based on two different domain decomposition ideas

This paper presents two domain decomposition techniques for fixed grid fluid–structure interaction simulations that can be applied to the interaction of general structures with incompressible flows. One approach is based on an overlapping domain decomposition idea while the other uses non-overlapping domains. The first technique combines a fixed grid Chimera approach with arbitrary Lagrangean Eulerian based methods, the second one is based on an eXtended Finite Element Method (XFEM) strategy. Both techniques are used in a partitioned and strong coupling fluid–structure framework. The usage of such fixed-grid methods considerably increases the range of possible applications. Several test examples demonstrate key features of both methods.     

Gas transfer at the air–water interface: experiments with different turbulence forcing mechanisms

Most environmentally important gases (such as oxygen or carbon dioxide) have low solubility. The transfer process of such gases across the air–water interface is controlled by molecular diffusion and turbulence, concentrated within a very thin layer in the water side. A challenge for a better understanding of the problem is to be able to elucidate the transport processes happening within this thin layer. We used non-invasive measurement techniques to study the interaction between the gas transfer process and the hydrodynamic condition in the water phase with two different turbulence forcing mechanisms, namely grid-stirred and buoyant-convective turbulence. The experimental setup for the turbulence generation and the measurement techniques are described. The different dominating turbulent transport mechanisms of the two cases were discussed, and a comparison of the different measured scales between the two cases is also presented.     

Adaptive synchronization of different Cohen–Grossberg chaotic neural networks with unknown parameters and time-varying delays

In this paper, an adaptive linear feedback controller is presented to study the synchronization problem of different Cohen–Grossberg neural networks with unknown parameters and time-varying delays. Lyapunov stability theory and Barbalat’s lemma are used to guarantee the response system can be synchronized with the drive system. The synchronization criteria of this paper which do not solve any linear matrix inequality are easily verified. These results remove some restrictions on amplification functions and activation functions. Finally, numerical simulations are carried out to illustrate the effectiveness of the obtained results.     

Effects of polydispersity on the micro–macro behavior of granular assemblies under different deformation paths

The micromechanical and macromechanical behavior of idealized granular assemblies, made by linearly elastic, frictionless, polydisperse spheres, are studied in a periodic, triaxial box geometry, using the discrete element method. Emphasis is put on the effect of polydispersity under purely isotropic loading and unloading, deviatoric(volume conserving), and uniaxial compression paths.We show that scaled pressure, coordination number and fraction of rattlers behave in a very similar fashion as functions of volume fraction, irrespective of the deformation path applied. Interestingly, they show a systematic dependence on the deformation mode and polydispersity via the respective jamming volume fraction. This confirms that the concept of a single jamming point has to be rephrased to a range of variable jamming points, dependent on microstructure and history of the sample, making the jamming volume fraction a state-variable.This behavior is confirmed when a simplified constitutive model involving structural anisotropy is calibrated using the purely isotropic and deviatoric simulations. The basic model parameters are found to depend on the polydispersity of the sample through the different jamming volume fractions. The predictive power of the calibrated model is checked by comparison with an independent test, namely uniaxial compression. The important features of the uniaxial experiment are captured and a qualitative prediction for the evolution of stress and fabric is shown involving a "softening" regime in both stress and fabric – stronger for the latter – that was not prescribed into the model a priori.     

Study of heat transfer of a helium–xenon mixture in heated channels with different cross-sectional shapes

This paper describes the results of an experimental study of heat transfer in the case of the flow of a helium–xenon mixture with a Prandtl number approximately equal to 0.23 and the flows of pure helium and air in heated tubes of circular or triangular cross sections with a constant density of the heat flow. The region of thermal stability is studied. The law of heat transfer on the stabilized region is compared with known relationships. The approach that helps obtaining an expression for the calculation of heat transfer in heat transfer devices with circular and triangular cross sections, which operate in a mixture heating mode on the initial region, is developed.     

Analysis of a new 3D smooth autonomous system with different wing chaotic attractors and transient chaos

This letter proposes a new 3D quadratic autonomous chaotic system which displays an extremely complicated dynamical behavior over a large range of parameters. The new chaotic system has five real equilibrium points. Interestingly, this system can generate one-wing, two-wing, three-wing and four-wing chaotic attractors and periodic motion with variation of only one parameter. Besides, this new system can generate two coexisting one-wing and two coexisting two-wing attractors with different initial conditions. Furthermore, the transient chaos phenomenon happens in the system. Some basic dynamical behaviors of the proposed chaotic system are studied. Furthermore, the bifurcation diagram, Lyapunov exponents and Poincaré mapping are investigated. Numerical simulations are carried out in order to demonstrate the obtained analytical results. The interesting findings clearly show that this is a special strange new chaotic system, which deserves further detailed investigation.     

2D reduced graphene oxide–titania nanocomposites synthesized under different hydrothermal conditions for treatment of hazardous organic pollutants

Two-dimensional reduced graphene oxide–titania (RGO–TiO₂) composites were prepared using a single-step hydrothermal method under various hydrothermal reaction conditions. The morphological and surface characteristics of the RGO–TiO₂ composites and reference materials were determined. The RGO–TiO₂ composites showed photocatalytic activity for the decomposition of two target pollutants that was superior to both pure TiO₂ and RGO under fluorescent daylight lamp illumination. The photocatalytic activity of the RGO–TiO₂ composite increased as the hydrothermal treatment time increased from 1 to 24 h, but then it decreased as the time increased to 36 h, which indicated the presence of an optimal treatment time. RGO–TiO₂ composites activated by violet light-emitting diodes (LEDs) displayed lower decomposition efficiency than those activated by a daylight lamp, likely because of the lower light intensity of violet LEDs (0.2 mW/cm²) when compared with that of the daylight lamp (1.4 mW/cm²). However, the photocatalytic decomposition of the target pollutants using the RGO–TiO₂ composite was more energy-efficient using the violet LEDs. The photocatalytic reaction rates increased as the residence time decreased, whereas the reverse was true for the decomposition efficiency.     

Multi-component Reynolds-averaged Navier–Stokes simulations of Richtmyer–Meshkov instability and mixing induced by reshock at different times

Turbulent mixing generated by shock-driven acceleration of a perturbed interface is simulated using a new multi-component Reynolds-averaged Navier–Stokes (RANS) model closed with a two-equation $K$ – $\epsilon $ model. The model is implemented in a hydrodynamics code using a third-order weighted essentially non-oscillatory finite-difference method for the advection terms and a second-order central difference method for the gradients in the source and diffusion terms. In the present reshocked Richtmyer–Meshkov instability and mixing study, an incident shock with Mach number $M\!a_{\mathrm{s}}=1.20$ is generated in air and progresses into a sulfur hexafluoride test section. The time evolution of the predicted mixing layer widths corresponding to six shock tube test section lengths are compared with experimental measurements and three-dimensional multi-mode numerical simulations. The mixing layer widths are also compared with the analytical self-similar power-law solution of the simplified model equations prior to reshock. A set of model coefficients and initial conditions specific to these six experiments is established, for which the widths before and after reshock agree very well with experimental and numerical simulation data. A second set of general coefficients that accommodates a broader range of incident shock Mach numbers, Atwood numbers, and test section lengths is also established by incorporating additional experimental data for $M\!a_{\mathrm{s}}=1.24$ , $1.50$ , and $1.98$ with $At=0.67$ and $M\!a_{\mathrm{s}}=1.45$ with $At=-0.67$ and previous RANS modeling. Terms in the budgets of the turbulent kinetic energy and dissipation rate equations are examined to evaluate the relative importance of turbulence production, dissipation and diffusion mechanisms during mixing. Convergence results for the mixing layer widths, mean fields, and turbulent fields under grid refinement are presented for each of the $M\!a_{\mathrm{s}}=1.20$ cases.