有界噪声激励下Josephson系统的混沌运动

利用随机Melnikov方法分析了有界噪声激励下Josephson系统的运动,并运用均方准则得到了系统产生混沌的临界值。结果表明:有界噪声对系统混沌行为的产生起到了加速的作用;且有界噪声的强度越大,混沌吸引子的发散程度就越大。最后利用数值模拟得到系统的庞加莱映射,分析了在不同参数组合下系统庞加莱映射的特征。结果显示:当有界噪声中的一个参数发生改变,系统的庞加莱映射也会发生相应的改变;特别是有界噪声的激励强度增大时,系统庞加莱映射的发散程度也会随之增大。这从侧面验证了理论结果的正确性。     

Noise-induced chaos in the elastic forced oscillators with real-power damping force

The chaotic behavior of the elastic forced oscillators with real-power exponents of damping and restoring force terms under bounded noise is investigated. By using random Melnikov method, a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system. The results show that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity of the random frequency increases, and decrease as the real-power exponent of damping term increase. The threshold of bounded noise amplitude for the onset of chaos is determined by the numerical calculation via the largest Lyapunov exponents. The effects of bounded noise and real-power exponent of damping term on bifurcation and Poincaré map are also investigated. Our results may provide a valuable guidance for understanding the effect of bounded noise on a class of generalized double well system.     

On the stability of plane parallel viscoelastic shear flows in the limit of infinite Weissenberg and Reynolds numbers

Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. We study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet.The equation for stability is derived and solved numerically using the spectral Chebyshev collocation method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability.     

应用SBFEM研究波浪与薄板的相互作用问题

应用比例边界有限元法(SBFEM)求解了频域下波浪与刚性薄板防波堤相互作用问题。求解中将整个计算区域分为薄板周围的有限子域和直到无限远处的无限子域。有限子域的比例中心设置在薄板的下端,这时薄板的两侧为侧边面,而无限子域的比例中心设置在无限子域与有限子域的交界上,同时将水底和自由水面做为平行侧边面。应用加权余量法在每个子域内推导出比例边界有限元方程,然后在有限子域与无限子域交界上匹配求解。通过与解析解的对比,证明了这种方法的精确性,而后对不同类型的薄板防波堤进行了计算,并给出了反射和透射系数的变化规律。     

The Uniqueness of Nondecaying Solutions for the Navier-Stokes Equations

The uniqueness of solutions of the Navier-Stokes equations in the whole space is established when the velocity field is bounded and the pressure field is a BMO-valued locally integrable-in-time function for bounded initial data. Here the velocity field may not decay at space infinity. Although there are a few results concerning uniqueness without the decay assumption, our result is new and applicable for solutions constructed by solving the integral equations.     

BOUNDEDNESS AND UNIFORM BOUNDEDNESS RESULTS FOR CERTAIN NON-AUTONOMOUS DIFFERENTIAL EQUATIONS OF FOURTH ORDER

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A new method for computing the upper and lower bounds on frequencies of structures with interval parameters

In this paper, we will investigate the method for computing the upper and lower bounds on frequencies of structures with bounded uncertain (or interval) parameters. The stiffness matrix and the mass matrix of structures, whose elements have the initial errors, are unknown except for the fact that they belong to given bounded matrix sets. The set of possible matrices can be described by the interval matrix. By means of the stationary condition of Rayleigh Qutient and the minimax theorem of eigenvalues, the generalized eigenvalue problem of structures with bounded uncertain parameters can be transformed into two different generalized eigenvalue problems. The numerical results indicate that the proposed method is effective.     

A generalization of the method of averaging for systems with two time scales

In this paper we shall consider systems of the form x = ? f(t, ?t, x, y, ?), y = g(t,?t, x, y,?), where x and y are vectors of finite dimensions, f and g are assumed to be bounded for all t, and ? is a real parameter. Sufficient conditions are obtained for the existence of certain solutions which are bounded for all t. These solutions are shown to approach special solutions of a derived simpler averaged system of equations as ? → 0. Moreover, it is shown that there exists only one such bounded solution in the neighborhood of each special solution. In the special case when y is not present, it is shown that if a special solution is stable, solutions starting in nonlocal neighborhoods of this special solution approach the bounded solutions adjacent to it as t → ∞. These results generalize most of the existing work for systems of the type discussed here. Finally, we employ our results to study some problems of physical importance.     

Point-to-point trajectory planning of wheeled mobile manipulators with stability constraint. Extension of the random-profile approach

We propose a flexible stochastic scheme for point-to-point trajectory planning of nonholonomic wheeled mobile manipulators subjected to move in a structured workspace. The problem is known to be complex, particularly if obstacles are present and if dynamic stability constraint is considered. The proposed method consists of extending to wheeled mobile manipulators the random-profile approach recently applied to wheeled platforms. This versatile method handles constraints on: (i) geometry (obstacle avoidance, bounded joint positions and path curvature); (ii) kinematics (bounded velocities and accelerations); (iii) dynamics (bounded torques, stability condition). It may be applied using various forms of cost functions involving travel time, efforts and power. Solutions are presented for planar and spatial nonholonomic wheeled mobile manipulators undertaking, in a constrained workspace, a point-to-point task defined either in generalized or operational coordinates.     

On the scattering of H-polarized electromagnetic field by an ideally conductive cylindrical body of a trapping type

We consider a two-dimensional analog of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency which is the limit of poles generated by both the bounded component of the resonator and the narrow connecting channel. Under the assumption that the limit eigenfrequency is a simple eigenfrequency of the bounded component, the asymptotics of two poles converging to this eigenfrequency are constructed by using the method of matching asymptotic expansions. Explicit formulas for the leading terms of the asymptotics of poles and of the solution of the scattering problem are obtained.     

On the Existence of a Smooth Bounded Semiinvariant Manifold for a Degenerate Nonlinear System of Difference Equations in the Space m

Using the Green–Samoilenko function, we construct a bounded Frechét-differentiable semiinvariant manifold for a nonlinear system of difference equations in a Banach space of bounded number sequences.     

On Admissibility Criteria for Weak Solutions of the Euler Equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper, we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct, in more than one space dimension, we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique.     

On the use of perfectly matched layers in the presence of long or backward propagating guided elastic waves

An efficient method to compute the scattering of a guided wave by a localized defect, in an elastic waveguide of infinite extent and bounded cross section, is considered. It relies on the use of perfectly matched layers (PML) to reduce the problem to a bounded portion of the guide, allowing for a classical finite element discretization. The difficulty here comes from the existence of backward propagating modes, which are not correctly handled by the PML. We propose a simple strategy, based on finite-dimensional linear algebra arguments and using the knowledge of the modes, to recover a correct approximation to the solution with a low additional cost compared to the standard PML approach. Numerical experiments are presented in the two-dimensional case involving Rayleigh–Lamb modes.     

Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term简

This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.     

Effect of localized imperfections on the critical loads of ribbed shells

A numerical approach to the assessment of the critical stresses for imperfect ribbed shells is developed. Initial deflections occupying a part of the shell surface (they are circumferentially bounded) are considered. The couple stresses and nonlinearity of the precritical state are taken into account. Numerical examples are given     

Bounded noise enhanced stability and resonant activation

We investigate the escape problem of a Brownian particle over a potential barrier driven by bounded noise, which is different form the common unbounded noise. Some novel stochastic phenomena and results are founded. For weak frequency of bounded noise, the mean first passage time (MFPT) shows a non-monotonic dependence on the intensity of white noise. One remarkable behavior is the phenomenon of co-occurrence of noise-enhanced stability and resonant activation. Another novel finding is that the position of minimum of MFPT about frequency shows monotone non-decreasing or non-increasing function with the variation of amplitude of bounded noise, while the minimum of MFPT monotonously depends on the amplitude of bounded noise. More important, we uncover the relationship of the parameters of bounded noise which induce the occurrence of the phenomenon of resonant activation. Besides, resonant activation can also be induced by simplified bounded noise, called sine-Wiener noise. The behaviors presented in our work driven by bounded noise show distinctive features compared with the ones inspired by the common noise.     

Moment Lyapunov exponent of three-dimensional system under bounded noise excitation

In the present paper,the moment Lyapunov exponent of a codimensional two-bifurcation system is evaluted,which is on a three-dimensional central manifold and subjected to a parametric excitation by the ...     

ON THE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF CERTAIN FIFTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS

The sufficient conditions are given for all solutions of certain non- autonomous differential equation to be uniformly bounded and convergence to zero as t →∞ ?. The result given includes and improves that result obtained by Abou-El-Ela & Sadek .     

Control Problems for the Steady-State Equations of Magnetohydrodynamics of a Viscous Incompressible Fluid

Control problems for a steady-state model of the magnetohydrodynamics of a viscous incompressible fluid in a bounded domain with an impermeable, perfectly conducting boundary are formulated. The resolvability of the problems is studied, the use of the Lagrange principle is justified, and optimality systems are analyzed.     

On the sliding mode control of mechanical systems

We consider the control of mechanical systems based on sliding mode control techniques. Recently developed simplex control methods are shown to converge in a finite time when applied to nonlinear systems under bounded deterministic uncertainty. Applications are considered to the control of mechanical systems in which the control action is provided by monodirectional devices.