Multiple Transitions to Chaos in a Damped Parametrically Forced Pendulum

We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying $\omega_0$ (the natural frequency of the pendulum) and $A$ (the amplitude of the external driving force). As $A$ is increased, the SP will restabilize after its instability, destabilize again, and so {\it ad infinitum} for any given $\omega_0$. Its destabilizations (restabilizations) occur via alternating supercritical (subcritical) period-doubling bifurcations (PDB's) and pitchfork bifurcations, except the first destabilization at which a supercritical or subcritical bifurcation takes place depending on the value of $\omega_0$. For each case of the supercritical destabilizations, an infinite sequence of PDB's follows and leads to chaos. Consequently, an infinite series of period-doubling transitions to chaos appears with increasing $A$. The critical behaviors at the transition points are also discussed.Comment: 20 pages + 7 figures (available upon request), RevTex 3.

Quantum mechanical analysis of the equilateral triangle billiard: periodic orbit theory and wave packet revivals

Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by $T_{rev} = 9 \mu a^2/4\hbar \pi$ where $a$ and $\mu$ are the length of one side and the mass of the point particle respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral ($60^{\circ}-60^{\circ}-60^{\circ}$) triangle, such as the half equilateral ($30^{\circ}-60^{\circ}-90^{\circ}$) triangle and other `foldings', which have related energy spectra and revival structures.Comment: 34 pages, 9 embedded .eps figure

Supermassive Binaries and Extragalactic Jets

Some quasars show Doppler shifted broad emission line peaks. I give new statistics of the occurrence of these peaks and show that, while the most spectacular cases are in quasars with strong radio jets inclined to the line of sight, they are also almost as common in radio-quiet quasars. Theories of the origin of the peaks are reviewed and it is argued that the displaced peaks are most likely produced by the supermassive binary model. The separations of the peaks in the 3C 390.3-type objects are consistent with orientation-dependent "unified models" of quasar activity. If the supermassive binary model is correct, all members of "the jet set" (astrophysical objects showing jets) could be binaries.Comment: 31 pages, PostScript, missing figure is in ApJ 464, L105 (see http://www.aas.org/ApJ/v464n2/5736/5736.html

The Physics of Star Cluster Formation and Evolution

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00689-4.Star clusters form in dense, hierarchically collapsing gas clouds. Bulk kinetic energy is transformed to turbulence with stars forming from cores fed by filaments. In the most compact regions, stellar feedback is least effective in removing the gas and stars may form very efficiently. These are also the regions where, in high-mass clusters, ejecta from some kind of high-mass stars are effectively captured during the formation phase of some of the low mass stars and effectively channeled into the latter to form multiple populations. Star formation epochs in star clusters are generally set by gas flows that determine the abundance of gas in the cluster. We argue that there is likely only one star formation epoch after which clusters remain essentially clear of gas by cluster winds. Collisional dynamics is important in this phase leading to core collapse, expansion and eventual dispersion of every cluster. We review recent developments in the field with a focus on theoretical work.Peer reviewe

Radioactive ion beam research at LLNL

In this paper we discuss efforts underway at LLNL to develop the technology for the measurement of proton and alpha-particle reactions with unstable nuclei which are necessary for understanding the nucleosynthesis and energy generation in hot hydrogen-burning environments. 16 refs., 5 figs

Laser-induced forward transfer of focussed ion beam pre-machined donors

In this paper we report femtosecond laser-induced forward transfer (LIFT) of pre-machined donor films. 1 µm thick zinc oxide (ZnO) films were first machined using the focussed ion beam (FIB) technique up to a depth of 0.8 µm. Debris-free micro-pellets of ZnO with extremely smooth edges and surface uniformity were subsequently printed from these pre-machined donors using LIFT. Printing results of non-machined ZnO donor films and films deposited on top of a polymer dynamic release layer (DRL) are also presented for comparison, indicating the superior quality of transfer achievable and utility of this pre-machining technique

Some nuclear data needs in astrophysics

In this paper we discuss a number of astrophysical environments and how improved nuclear data could facilitate a better understanding of them. One area of interest includes proton and alpha-particle reactions with unstable nuclei which are necessary for understanding the nucleosynthesis and energy generation in hot hydrogen-burning environments. Efforts underway at LLNL and elsewhere to develop the technology for the measurement of these reaction rates are discussed. Heavy-element nucleosynthesis in the late stages of red-giant stars and supernovae requires a complete network of neutron capture rates and beta-decay rates for nuclei near and far from stability. Experimental and theoretical efforts at LLNL to supply the input data and to model the nucleosynthetic environments will be outlined. Suggestions are made as to which nuclear data are most critical for the various scenarios. 42 refs., 11 figs., 1 tab