LOCALIZED FAMILIES OF BENDING WAVES IN A THIN MEDIUM-LENGTH CYLINDRICAL SHELL UNDER PRESSURE

The initial-boundary-value problem for the equations describing motion of a thin, medium-length, non-circular cylindrical shell is examined. The shell edges are not necessarily plane curves, with the conditions of a joint support, a rigid clamp or a free edge being considered as the boundary conditions. The shell is supposed to experience normal internal (or external) dynamic pressure which may be non-uniform in the circumferential direction. It is assumed that the initial displacements and velocities of the points at the shell middle surface are functions decreasing rapidly away from some generatrix. Using the complex WKB method the asymptotic solution of the governing equations is constructed by superimposing localized families (wave packets) of bending waves running in the circumferential direction. The dependence of frequencies, group velocities, amplitudes and other dynamic characteristics upon variable pressure and geometrical parameters of the shell are studied. As an example, the wave forms of motion of a circular cylindrical shell with sloping edges under growing dynamic pressure are considered. The effect of localization of bending vibrations near the longest generator as well as the effects of reflection, focusing and increasing amplitude in the running wave packets are revealed.     

Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays

A delay-differential equation modelling a bidirectional associative memory (BAM) neural network with three neurons is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold reduction. Numerical simulation results are given to support the theoretical predictions.     

On simultaneous linear extensions of partial (pseudo)metrics

We consider the question of simultaneous extension of (pseudo) metrics defined on nonempty closed subsets of a compact metrizable space. The main result is a counterpart of the result due to Künzi and Shapiro for the case of extension operators of partial continuous functions and includes, as a special case, Banakh's theorem on linear regular operators extending (pseudo)metrics.

     

Control of adiabatic two-phase dielectric fluid flow distribution with EHD conduction pumping

Electrohydrodynamic (EHD) conduction pumping is associated with the heterocharge layers of finite thickness in the vicinity of the electrodes, which are based on the process of dissociation of the neutral electrolytic species and recombination of the generated ions. This paper presents the successful control of dielectric liquid/vapor flow distribution between two parallel branch lines utilizing an EHD conduction pump at a select mass flux level under adiabatic condition.     

Density viscous continuum traffic flow model

A new traffic flow model called density viscous continuum model is developed to describe traffic more reasonably. The two delay time scales are taken into consideration, differing from the model proposed by Xue and Dai [Phys. Rev. E 68 (2003) 066123]. Moreover the relative density is added to the motion equation from which the viscous term can be derived, so we obtain the macroscopic continuum model from microscopic car following model successfully. The condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg-de-Vries (KdV) equation, and the soliton solution is derived. The results show that local cluster effects can be obtained from the new model and are consistent with the diverse nonlinear dynamical phenomena observed in the freeway traffic.     

Sub-Riemannian geometry of the coefficients of univalent functions

We consider coefficient bodies Mn for univalent functions. Based on the Löwner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a representation of the Virasoro algebra. Then Mn are defined as sub-Riemannian manifolds. Given a Lie-Poisson bracket they form a grading of subspaces with the first subspace as a bracket-generating distribution of complex dimension two. With this sub-Riemannian structure we construct a new Hamiltonian system to calculate regular geodesics which turn to be horizontal. Lagrangian formulation is also given in the particular case M₃.     

Inducing or suppressing chaos in a double-well Duffing oscillator by time delay feedback

The chaotic behavior of a double-well Duffing oscillator with both delayed displacement and velocity feedbacks under a harmonic excitation is investigated. By means of the Melnikov technique, necessary condition for onset of chaos resulting from homoclinic bifurcation is derived analytically. The analytical results reveal that for negative feedback the presence of time delay lowers the threshold and enlarges the possible chaotic domain in parameter space; while for positive feedback the presence of time delay enhances the threshold and reduces the possible chaotic domain in parameter space, which are further verified numerically through Poincare maps of the original system. Furthermore, the effect of the control gain parameters on the chaotic motion of the original system is studied in detail.