On a Class of Ordinary Differential Equations of Various Orders on a Graph

Mathematical Notes -     

Routes to chaos and mode-locking in interferometers with nematic film inserts

The influence of time-dependent periodic optical drive in the Fabry-Perot interferometer system has been investigated using a theoretical model equation. A variety of features such as different routes to chaos, multiperiodic oscillations, coexistence of multiple attractors and mode-locking with devil’s staircase are found to occur for a certain range of parametric values.     

Mathematical study of the small oscillations of an incompressible and inviscid liquid under zero gravity in a container of revolution with elastic bottom and anchored edge

In this paper, the Authors study the small oscillations of an inviscid liquid under zero gravity in a container of revolution with elastic bottom, considered as a membrane or a plate, and anchored edge. They obtain the equations of the displacements of the free surface and the bottom and they reduce these equations to a functional equation in a suitable Hilbert space. By using the methods of Functional Analysis the Authors prove the existence of the small oscillations. Research partially supported by GNFM, MURST (Italy).     

Interference and interactions in mesoscopic rings

We consider a mesoscopic ring connected to external reservoirs by tunnel junctions. The ring is capacitively coupled to an external gate electrode and may be pierced by a magnetic field. Due to strong electron–electron interactions within the ring the conductance shows Coulomb blockade oscillations as a function of the gate voltage, while Aharonov–Bohm interference effects lead to a dependence on the magnetic flux. The Hamiltonian of the ring is given by a Luttinger model that allows for an exact treatment of both interaction and interference effects. We conclude that the positions of conductance maxima as a function the external parameters can be used to determine the interaction parameter , and the shapes of conductance peaks are strongly affected by electron correlations within the ring.     

Ion acoustic soliton propagation in a magnetized relativistic plasma

Summary The Korteweg-de Vries equation for ion acoustic waves in the presence of weakly relativistic ion streaming velocity is derived in a magnetic plasma. It is found that relativistic effects are important in the solitary wave propagation for both fast and slow modes. Earlier results are reconfirmed. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Wave Motions in a Two-Layer Fluid Driven by Small Oscillations of a Cylinder Intersecting the Interface

The plane problem of steady-state small oscillations of a horizontal cylinder located at the interface between two fluids of different densities and indefinite depth is considered in the linear formulation. Boundary integral equations for the surface source distribution are derived. The behavior of the distributed singularities at points of intersection of the body contour and the interface is investigated. The problem of oscillations of a circular cylinder is solved by the multipole expansion method. The apparent mass and damping coefficients of the radiation problem and the reflection coefficient of the problem of scattering of an impinging wave by a floating body are calculated.     

Global classical solutions to the compressible micropolar viscous fluids with large oscillations and vacuum

In this paper, we consider the three dimensional Cauchy problem of the compressible micropolar viscous flows. We prove the existence of unique global classical solution for smooth initial data with small initial energy but possibly large oscillations and the initial density may allowed to contain the interior and far field vacuum states. Furthermore, the large time behavior of the solution is obtained as well.     

Multiphonon Bundle Emission in a Strong-Coupling Cavity Optomechanical System

Nonclassical effects in mesoscopic systems have attracted much attention recently. In this paper, it is shown that multiphonon bundle emission can be observed in a strong-coupling cavity optomechanical system. Theoretical analysis shows that when the driving field is adjusted to nth-order sideband excitation, the coupling between the cavity mode and the vibrational mode leads to super-Rabi oscillations, and finally results in an n-phonon bundles emission. Based on the current technology, this process can work in a wide range of parameters. Numerical simulation confirms the validity of the derivation. It is thought that this physical mechanism broadens the applications of cavity optomechanical system in realm of quantum phononics, such as in quantum metrology and phonon laser.     

Oscillatory behavior of supersonic impinging jet flows

Oscillatory flows of a choked underexpanded supersonic impinging jet issuing from a convergent nozzle have been computed using the axisymmetric unsteady Navier--Stokes system. This paper focuses on the oscillatory flow features associated with the variation of the nozzle-to-plate distance and nozzle pressure ratio. Frequencies of the surface pressure oscillation and flow structural changes from computational results have been analyzed. Staging behavior of the oscillation frequency has been observed for both cases of nozzle-to-plate distance variation and pressure ratio variation. However, the staging behavior for each case exhibits different features. These two distinct staging behaviors of the oscillation frequency are found to correlate well if the frequency and the distance are normalized by the length of the shock cell. It is further found that the staging behavior is strongly correlated with the change of the pressure wave pattern in the jet shear layer, but not with the shock cell structure. Communicated by K. Takayama PACS 02.60.Cb; 47.40.−x; 47.40.Nm; 47.35.+I; 47.15.−x     

1／2亚谐共振──主参数共振情况下非线性振动系统的余维2退化分叉

本文应用Normal Form理论和退化向量场的普适开折理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,用Melnikov方法讨论了全局分叉的存在性.