Search

We study the evolution of the longitudinal release wave that is generated by induced tensile fracture as it propagates through solid rectangular Polymethylmethacrylate (PMMA) bars of different constant cross section. High speed multi-point photoelasticity is used to register the strain wave. In all cases, oscillations develop at the bottom of the release wave that exhibit the qualitative features of an undular bore. The pre-strain, post-strain, strain rate of the release wave and the cross section dimensions determine the evolution of the oscillations. From the wave speed and strain rate close to the fracture site, we estimate the strain rate of the release wave as well as the growth of the amplitude and duration of the leading oscillation away from the fracture site on using formulae derived from the simple analytical solution [1] of the linearised Gardner equation (linearised near the pre-strain level at fracture), developed in our earlier work . Our estimates are then compared to experimental data, where qualitative and good semi-quantitative agreements are established.

Undular bores, or dispersive shock waves, are non-stationary waves propagating as oscillatory transitions between two basic states, in which the oscillatory structure gradually expands and grows in amplitude with distance travelled. We demonstrate for the first time, using high-speed pointwise photoelasticity, the generation of undular bores in solid (polymethylmethacrylate) pre-strained bars by natural and induced tensile fracture. For the distances relevant to our experiments, the viscoelastic extended Korteweg - de Vries (veKdV) equation is shown to provide very good agreement with the key observed experimental features for suitable choice of material parameters, while some local features at the front of the bore are also captured reasonably well by the linearisation near the nonzero pre-strain level. The experimental and theoretical approaches presented open new avenues and analytical tools for the study and application of dispersive shock waves in solids., Comment: 16 pages, 10 figures

We consider the structure of a galactic nucleus in which a compact supermassive object (e.g., a black hole or spinar) is embedded. The surrounding stars are assumed to satisfy a polytropic or isothermal equation of state. The density distribution of these loaded polytropes has a sharp central spike in which the time scale for stellar collisions can be short. Other properties of loaded polytropes, such as their masses, radii, projected density distribution, relaxation times, and stability, can also differ significantly from those of normal polytropes.

A series of two-dimensional numerical experiments is performed in order to test the response of an isothermal, self-gravitating gas disk to a uniformly rotating, barlike gravitational potential. The barlike potential is an equilibrium stellar model from the n-body calculations of Miller and Smith (1979). In the bar-dominated, central regions of the disk, a gas bar whose phase depends primarily on the location of principal resonances in the disk is formed. This response can be understood in terms of orbit-crowding effects. In the gas-dominated outer regions of the disk, two-armed trailing spiral waves are formed. The local pitch angle of these waves increases with increasing fractional gas mass. These self-gravitating gas waves are not self-sustaining. They are driven from the ends of equilibrium stellar bars, and their phase does not depend on the location of resonances in the disk. The relevance of these self-gravitating waves to observations and models of barred spiral galaxies is discussed. It is concluded that these waves and their associated ringlike structures may be consistent with the morphological distribution of gas features in barred spiral galaxies.

Steady-state gasdynamical studies, previously limited to tightly wound normal spiral galaxies, are extended to models of barred spirals with a 5% to 10% perturbing potential. The models show that a strong wave manifestation is an important constituent of the bar structure in many barred spirals and that a density-wave shock wave can form a bar structure as pronounced as the narrow bars often evident in optical photographs of barred spirals. The dark narrow dust lanes often observed along the leading edges of bar structures are identified as tracers of shocks, and it is found that strong shocks along a bar structure during even a small part of a galaxy's lifetime might easily deplete a large enough proportion of the gas to cause a lack of gas in the inner annuli encompassing the bar by the time of the present epoch. It is emphasized that even moderate-amplitude barlike perturbations in the disk can drive large noncircular gas motions, typically 50 to 150 km/s.

Line-of-sight gas velocities calculated from a numerical hydrodynamical model of a barred spiral galaxy are compared with the observations and models made by Peterson, Rubin, Ford, and Thonnard of the gas flow in NGC 5383. The hydrodynamical model provides a somewhat better fit to the observations of NGC 5383 than does their symmetric, warped-disk model. It is argued that the basic model appropriate to understanding the gas motions in barred spiral galaxies is not circular rotation but rather a characteristic elliptical pattern of flow.

The response of rotating disks of gas to barlike perturbations in galactic gravitational fields is investigated. In particular, two-dimensional time-dependent numerical hydrodynamical calculations have been performed in order to determine the steady-state response of disks of gas to rotating barlike perturbations. Two types of barlike perturbations are considered: oval distortions in the axisymmetric gravitational field of the disk, and heterogeneous prolate spheroids. The calculations reveal that in the absence of gaseous self-gravity, a viscous differentially rotating disk of gas responds to a rotating barlike perturbation by forming a central gas bar with two trailing spiral waves. The local phase of the gas response is primarily a function of the number and spacing of the principal resonances in the disk. This result may be understood in terms of particle orbit theory. The gas response to barlike perturbations also depends on the relative strength and the effective axial ratio of the bar. In these calculations strong narrow bars produce offset shocks in the central gas bar. These shocks correspond in position to the long narrow dust lanes observed in many barred spiral galaxies.