Self-sustained Motion Research Articles

Nonlinear resonance study of the periodic motion of the explosive crystallization front in glasses.

The theoretical treatment of self-sustained periodic motion of the explosive crystallization ~EC! front in a thin amorphous film is presented. The main attention is given to the study of nonlinear resonance phenomena occurring due to the presence of a small external periodic perturbation with the frequency being in the vicinity of the ordinary or parametric resonance. Weakly anharmonic oscillations of the EC front velocity are considered with the Van der Pole method, and the expressions for the limit cycle amplitude in the case of free and forced oscillations are derived. Depending on the values of kinetic and thermophysical parameters of the model, different kinds of resonance curves ~i.e., front oscillation amplitudes versus frequency detuning ! are obtained and analyzed. Our predictions may be tested experimentally by monitoring the explosive growth rate using the modulation of laser intensity or employing amorphous films with thickness periodicity. It is also shown that inclusion of the results of dynamic stability analysis changes the steady-state EC stability diagram in the ( Ts ,d) plane ~Ts is the substrate temperature and d the film thickness! so that the region of stable EC regimes becomes substantially more limited.

Hypersonic flow past open cavities

The hypersonic flow over a cavity is investigated. The time-dependent compressible Navier-Stokes equations, in terms of mass averaged variables, are numerically solved. An implicit algorithm, with a subiteration procedure to recover time-accuracy, is used to perform the time-accurate computations. The objective of the study is to investigate the effects of Reynolds number and cavity dimensions. The comparison of the computations with available experimental data, in terms of time mean static pressure, heat transfer, and Mach number show good agreement. In the computations large vortex structures, which adversely affect the cavity flow characteristics, are observed at the rear of the cavity. A self-sustained oscillatory motion occurs within the cavity over a range of Reynolds number and cavity dimensions. The frequency spectra of the oscillations show good agreement with a modified semi-empirical relation.

Dynamics and Bifurcations of Pursuit Guidance for Vehicle Path Keeping in the Dive Plane

The problem of dynamic interactions between an orientation control law and pure pursuit guidance law for dive plane response of underwater vehicles is analyzed. A complete stability analysis is performed in order to evaluate regions of stable vehicle operations. It is shown that loss of stability can occur in either a static or dynamic way. In the first, a linearly increasing path deviation is observed, whereas in the second the loss of stability is accompanied by the generation of self-sustained oscillatory motions around the commanded path. Nonlinear analysis reveals the occurrence of both static and Poincaré-Andronov-Hopf bifurcations. Numerical experiments support the analytic predictions of the bifurcation analysis.

Transonic buffet on a supercritical aerofoil

The buffet characteristics of a supercritical aerofoil were investigated in the High Reynolds Number Two-Dimensional Test Facility of the National Aeronautical Establishment (NAE). The test was performed quite deep into the buffet régime. The buffet onset boundary was determined from the divergence of the unsteady balance normal force. Steady and unsteady pressure measurements were obtained for shock-induced separation with reattachment as well as fully separated flows. For flow conditions where discrete shock wave oscillations occurred, ensemble-averaging of the unsteady pressures determined the propagation velocity of the pressure wave induced by periodic shock motion. A model of the self-sustained oscillatory shock motion due to shock-boundary layer interaction was formulated. Broad-band cross-correlations of the pressure field determined the downstream convection velocities of the turbulent eddies of separated flows.

An electric dipole in self-accelerated transverse motion

It is shown that the equations of classical electrodynamics for an electric dipole possess a solution in which the dipole moves in self-sustained motion with constant proper acceleration in a direction perpendicular to its moment.

Geometrical structure of torsional and rotational degrees of freedom in defect systems

The geometrical and physical significance of the translational and rotational degrees of freedom of a dislocation in two-dimensional (2-D) systems is established. It is shown that the phase space accessible to the non-conservative translational motion of dislocations, in the presence of point defects, can also be realized by means of their conservative motion described by a set of torsion angles. This leads to the concept of torsional degrees of freedom providing wandering type slow motion in phase space and glass type behavior. The equation of motion of a N-particle torsional oscillator is derived and qualitatively discussed. Transitions between its rotational states being mediated by dislocation reaction processes, and its point defect generation regime leading to self-sustained non-conservative motion is studied. Physical consequences of the intricate geometry of the phase space for the melting transition are worked out. The three-dimensional (3-D) problem is studied in lesser detail.