Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet

The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations （ODEs） are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles ~, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.

Carreau fluid flow due to nonlinearly stretching sheet with thermal radiation, heat flux, and variable conductivity

A sophisticated theoretical and mathematical model is proposed.It is verified that this model can estimate and monitor the detailed behavior for the steady Carreau fluid flow past a nonlinear stretching surface and the predicted phenomena due to the presence of heat flux,thermal radiation,and viscous dissipation.Despite the fact that some properties of the fluid do not depend on the temperature,the fluid thermal conductivity is assumed to depend on the temperature.Based on accelerating the fluid elements,some of the kinetic energy for the fluid can be turned to the internal heating energy in the form of viscous dissipation phenomena.The contribution in this study is that a similar solution is obtained,in spite of the high nonlinearity of the Carreau model,especially,with the heat flux,variable conductivity,and viscous dissipation phenomena.Some of the major significant findings of this study can be observed from the reduction in the fluid velocity with enhancing the Weissenberg number.Likewise,the increase in the sheet temperature is noted with increasing the Eckert number while the reverse behavior is observed for increasing both the radiation parameter and the conductivity parameter.Finally,the accuracy and trust in the proposed numerical method are validated after benchmarking for our data onto the earlier results.

A Robust D-Stability of Polynomials with Nonlinearly Dependent Perturbations

ＡＲｏｂｕｓｔＤ－ＳｔａｂｉｌｉｔｙｏｆＰｏｌｙｎｏｍｉａｌｓｗｉｔｈＮｏｎｌｉｎｅａｒｌｙＤｅｐｅｎｄｅｎｔＰｅｒｔｕｒｂａｔｉｏｎｓＮＩＮＧＹｏｎｇｃｈｅｎＸＩＥＳｈｅｎｇＺＨＡＮＧＦｕｅｎＹｕＤｅｙｕａｎ宁永臣，谢升，张福恩，于德元（Ｄｅｐｔ．...

STRONGLY RESONANT BIFURCATIONS OF NONLINEARLY COUPLED VAN DER POL-DUFFING OSCILLATOR

In this paper, the strongly resonant bifurcations of a nonlinearly coupled Van der Pol-Duffing Oscillator by the classical multi-scale method are studied. It is shown that there exist periodic motions of a single oscillator, frequency-looking and quasi-periodic motions of two oscillators when the parameters vary. Meanwhile, some numerical results are given to test the theoretical ones.

Phase synchronization between nonlinearly coupled Rssler systems

Phase synchronization between nonlinearly coupled systems with 1：1 and 1：2 resonances is investigated. By introducing a concept of phase for a chaotic motion, it is demonstrated that for different internal resonances, with relatively small parameter epsilon, the difference between the mean frequencies of the two sub-oscillators approaches zero. This implies that phase synchronization can be achieved for weak interaction between the two oscillators. With the increase in coupling strength, fluctuations of the frequency difference can be observed, and for the primary resonance, the amplitudes of the fluctuations of the difference seem much smaller compared to the case with frequency ratio 1：2, even with the weak coupling strength. Unlike the enhanced effect on synchronization for linear coupling, the increase in nonlinear coupling strength results in the transition from phase synchronization to a non-synchronized state. Further investigation reveals that the states from phase synchronization to non-synchronization are related to the critical changes of the Lyapunov exponents, which can also be explained with the diffuse clouds.

Adaptive Iterative Learning Control for Nonlinearly Parameterized Systems with Unknown Time-varying Delay and Unknown Control Direction

This paper proposes a new adaptive iterative learning control approach for a class of nonlinearly parameterized systems with unknown time-varying delay and unknown control direction.By employing the parameter separation technique and signal replacement mechanism,the approach can overcome unknown time-varying parameters and unknown time-varying delay of the nonlinear systems.By incorporating a Nussbaum-type function,the proposed approach can deal with the unknown control direction of the nonlinear systems.Based on a Lyapunov-Krasovskii-like composite energy function,the convergence of tracking error sequence is achieved in the iteration domain.Finally,two simulation examples are provided to illustrate the feasibility of the proposed control method.

Joule–Thomson expansion of higher dimensional nonlinearly AdS black hole with power Maxwell invariant source

In this paper,the Joule–Thomson expansion of the higher dimensional nonlinearly anti-de Sitter(Ad S)black hole with power Maxwell invariant source is investigated.The results show the Joule–Thomson coefficient has a zero point and a divergent point,which coincide with the inversion temperature Tiand the zero point of the Hawking temperature,respectively.The inversion temperature increases monotonously with inversion pressure.For the high-pressure region,the inversion temperature decreases with the dimensionality D and the nonlinearity parameter s,whereas it increases with the charge Q.However,Tifor the low-pressure region increase with D and s,while it decreases with Q.The ratioηBHbetween the minimum inversion temperature and the critical temperature does not depend on Q,it recovers the higher dimensional Reissner–N?rdstrom Ad S black hole case when s=1.However,for s>1,it becomes smaller and smaller as D increases and approaches a constant when D→∞.Finally,we found that an increase of mass M and s,or reducing the charge Q and D can enhance the isenthalpic curve,and the effect of s on the isenthalpic curve is much greater than other parameters.

Enhanced continuous-variable entanglement by a pair of nonlinearly coupled waveguides

We seek to analyze a three-level cascade laser with a pair of nonlinearly coupled waveguides inside the cavity. Applying the pertinent master equation, we investigate the squeezing and entanglement properties intracavity produced by our system. It is shown that with the help of nonlinearly coupled waveguides highly squeezed as well as macroscopic entangled light with high intensity can be achieved.

A Fastly Convergent Directly Feasible Directions Method for Nonlinearly Inequality Constrained Optimization

In this paper, a new superlinearly convergent algorithm for nonlinearly constrained optimization problems is presented. The search directions are directly computed by a few formulas, and neither quadratic programming nor linear equation need to be sovled. Under mild assumptions, the new algorithm is shown to possess global and superlinear convergence.

Robust adaptive output feedback control of nonlinearly parameterized systems

The ideas of adaptive nonlinear damping and changing supply functions were used to counteract the effects of parameter and nonlinear uncertainties,unmodeled dynamics and unknown bounded disturbances.The high-gain observer was used to estimate the state of the system.A robust adaptive output feedback control scheme was proposed for nonlinearly parameterized systems represented by input-output models.The scheme does not need to estimate the unknown parameters nor add a dynamical signal to dominate the effects of unmodeled dynamics.It is proven that the proposed control scheme guarantees that all the variables in the closed-loop system are bounded and the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately.Simulation results have illustrated the effectiveness of the proposed robust adaptive control scheme.

Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics

Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties.How to con-trol such systems effectively is one of the most chal-lenging problems.This paper presents a robust adaptive controller for a significant class of nonlinearly param-eterized systems.The controller can be used in cases where there exist parameter and nonlinear uncertainties,unmodeled dynamics and unknown bounded distur-bances.The design of the controller is based on the control Lyapunov function method.A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics,nonlinear uncertainties and unknown bounded distur-bances.The backstepping procedure is employed to overcome the complexity in the design.With the pro-posed method,the estimation of the unknown parame-ters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are.It is proved theoretically that the proposed robust adap-tive control scheme guarantees the stability of nonline-arly parameterized system.Furthermore,all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately.Simula-tion results illustrate the effectiveness of the proposed robust adaptive controller.

Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays

An observer-based adaptive iterative learning control （AILC） scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality （LMI） method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative （PID） feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function （CEF）, we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.

Stability analysis of radial inflation of incompressible compositerubber tubes

The inflation mechanism is examined for a composite cylindrical tube composed of two incompressible rubber materials, and the inner surface of the tube is subjected to a suddenly applied radial pressure. The mathematical model of the problem is formulated, and the corresponding governing equation is reduced to a second-order ordinary differential equation by means of the incompressible condition of the material, the boundary conditions, and the continuity conditions of the radial displacement and the radial stress of the cylindrical tube. Moreover, the first integral of the equation is obtained. The qualitative analyses of static inflation and dynamic inflation of the tube are presented. Particularly, the effects of material parameters, structure parameters, and the radial pressure on radial inflation and nonlinearly periodic oscillation of the tube are discussed by combining numerical examples.

MELTING AND CRYSTALLIZATION BEHAVIOR OFAN AROMATIC POLY (AZOMETHINE ETHER) WITH NON-LINEARLY SHAPED MOLECULAR CONFORMATIONS

The melting and crystallization behavior have been investigated for an aromatic poly (azomethine ether)with non-linearly shaped molecular conformations. This polymer was found to undergo multiple melting processes and its phase transition behavior was influenced sensitively by the thermal history of sample. A significant difference between the polymer chain aggregation abilities of samples cooled from the different states was observed. The possible molecular morphology and aggregation models for describing the structures of this polymer were proposed and discussed. The crystallization behavior of the samples cooled from the partially isotropic state and the influence of cooling rate on it have also been examined with DSC.

A Note on Self-Accelerating Olver and Olver-Gauss Beams

The recent introduction by Belafhal et al. [Opt. and Photon. J. 5, 234-246 (2015)] of mth-order Olver beams as a novel class of self-accelerating nondiffracting solutions to the paraxial equation is a direct contradiction to the seminal work of Berry and Balazs who determined that the infinite-energy Airy wave packet is the only accelerating nondiffracting solution to the (1 + 1)D Schrödinger equation. It is shown in this note that the work of Belafhal et al. is valid only for m=0, which coincides with the Airy solution.

Neural networks-based iterative learning control consensus for periodically time-varying multi-agent systems

In this paper,the problem of adaptive iterative learning based consensus control for periodically time-varying multi-agent systems is studied,in which the dynamics of each follower are driven by nonlinearly parameterized terms with periodic disturbances.Neural networks and Fourier base expansions are introduced to describe the periodically time-varying dynamic terms.On this basis,an adaptive learning parameter with a positively convergent series term is constructed,and a distributed control protocol based on local signals between agents is designed to ensure accurate consensus of the closed-loop systems.Furthermore,consensus algorithm is generalized to solve the formation control problem.Finally,simulation experiments are implemented through MATLAB to demonstrate the effectiveness of the method used.

Adaptive neural control of nonlinear periodic time-varying parameterized mixed-order multi-agent systems with unknown control coefficients

In this paper, we first consider the adaptive leader-following consensus problem for a class of nonlinear parameterized mixedorder multi-agent systems with unknown control coefficients and time-varying disturbance parameters of the same period. Neural networks and Fourier series expansions are used to describe the unknown nonlinear periodic time-varying parameterized function.A distributed control protocol is designed based on adaptive control, matrix theory, and Nussbaum function. The robustness of the distributed control protocol is analyzed by combining the stability analysis theory of closed-loop systems. On this basis, this paper discusses the case of time-varying disturbance parameters with non-identical periods, expanding the application scope of this control protocol. Finally, the effectiveness of the algorithm is verified by a simulation example.

Analysis on a Superlinearly Convergent Augmented Lagrangian Method

The augmented Lagrangian method is a classical method for solving constrained optimization.Recently,the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive sensing and low rank matrix optimization problems.However,most Lagrangian methods use first order information to update the Lagrange multipliers,which lead to only linear convergence.In this paper,we study an update technique based on second order information and prove that superlinear convergence can be obtained.Theoretical properties of the update formula are given and some implementation issues regarding the new update are also discussed.

Nonlinear Shell Models of Kirchhoff-Love Type:Existence Theorem and Comparison with Koiter's Model

We define two nonlinear shell models whereby the deformation of an elastic shell with small thickness minimizes ad hoc functionals over sets of admissible deformations of Kirchhoff-Love type. We establish that both models are close in a specific sense to the well-known nonlinear shell model of W.T. Koiter and that one of them has a solution, by contrast with Koiter's model for which such an existence theorem is yet to be proven.

Immersion and invariance adaptive control of a class of continuous stirred tank reactors

An immersion and invariance （l＆l） manifold based adaptive control algorithm is presented for a class of continuous stirred tank reactors （CSTR） to realize performance-oriented control in this paper. The nonlinear contraction method is combined into the control law design to render the closed-loop CSTR system globally asymptotically stable, firstly. Then, the l＆l method is used to form the adaptation law such that the off-the-manifold coordinate （the parameter estimation error） converges to zero using P-monotone property enforced by selecting tuning function in manifold. As a result, the state of the closed-loop CSTR converges to its desired value asymptotically. The simulation is given to illustrate the effectiveness of the presented algorithm.