Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEscape distribution for an inclined billiard
132
0
0.0
(
0
)
Added by
Nikolaos Georgakarakos Ph.D.
Publication date
2014
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
H${acute{e}}$non [8] used an inclined billiard to investigate aspects of chaotic scattering which occur in satellite encounters and in other situations. His model consisted of a piecewise mapping which described the motion of a point particle bouncing elastically on two disks. A one parameter family of orbits, named h-orbits, was obtained by starting the particle at rest from a given height. We obtain an analytical expression for the escape distribution of the h-orbits, which is also compared with results from numerical simulations. Finally, some discussion is made about possible applications of the h-orbits in connection with Hills problem.
rate research
Read More
In this paper, we examine the level spacing distribution $P(S)$ of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed $P(S)$ is a new type, which is quite different from the previous conclusion. Even in the strong coupling limit, the Poisson-like behavior rather than Wigner-like is seen for $S>1$, although the level repulsion still remains in the small $S$ region. The difference from the previous works is analyzed in detail.
We develop an original apparatus of the granular impact experiment by which the incident angle of the solid projectile and inclination angle of the target granular layer can be systematically varied. Whereas most of the natural cratering events occur on inclined surfaces with various incident angles, there have not been any experiments on oblique impacts on an inclined target surface. To perform systematic impact experiments, a novel experimental apparatus has to be developed. Therefore, we build an apparatus for impact experiments where both the incident angle and the inclination angle can be independently varied. The projectile-injection unit accelerates a plastic ball (6~mm in diameter) up to $v_isimeq 100$~m~s$^{-1}$ impact velocity. The barrel of the injection unit is made with a three-dimensional printer. The impact dynamics is captured by high-speed cameras to directly measure the impact velocity and incident angle. The rebound dynamics of the projectile (restitution coefficient and rebound angle) is also measured. The final crater shapes are measured using a line-laser profiler mounted on the electric stages. By scanning the surface using this system, a three-dimensional crater shape (height map) can be constructed. From the measured result, we can define and measure the characteristic quantities of the crater. The analyzed result on the restitution dynamics is presented as an example of systematic experiments using the developed system.
The Greens functions of the two and three-dimensional relativistic Aharonov-Bohm (A-B) systems are given by the path integral approach. In addition the exact radial Greens functions of the spherical A-B quantum billiard system in two and three-dimensional are obtained via the perturbation techanique of $delta $-function.
Although a large number of astronomical craters are actually produced by the oblique impacts onto inclined surfaces, most of the laboratory experiments mimicking the impact cratering have been performed by the vertical impact onto a horizontal target surface. In previous studies on the effects of oblique impact and inclined terrain, only one of the impact angle $varphi$ or target inclination angle $theta$ has been varied in the experiments. Therefore, we perform impact-cratering experiments by systematically varying both $varphi$ and $theta$. A solid projectile of diameter $D_{rm i}=6$~mm is impacted onto a sand surface with the range of impact velocity $v_{rm i}=7$--$97$~m~s$^{-1}$. From the experimental result, we develop scaling laws for the crater dimensions on the basis of $Pi$-group scaling. As a result, the crater dimensions such as cavity volume, diameter, aspect ratio, and depth-diameter ratio can be scaled by the factors $sin varphi$ and $cos theta$ as well as the usual impact parameters ($v_{rm i}$, $D_{rm i}$, density of projectile, and surface gravity). Finally, we consider the possible application of the obtained scaling laws to the estimate of impact conditions (e.g., impact speed and impact angle) in natural crater records.
We extended a previous qualitative study of the intermittent behaviour of a chaotical nucleonic system, by adding a few quantitative analyses: of the configuration and kinetic energy spaces, power spectra, Shannon entropies, and Lyapunov exponents. The system is regarded as a classical nuclear billiard with an oscillating surface of a 2D Woods-Saxon potential well. For the monopole and dipole vibrational modes we bring new arguments in favour of the idea that the degree of chaoticity increases when shifting the oscillation frequency from the adiabatic to the resonance stage of the interaction. The order-chaos-order-chaos sequence is also thoroughly investigated and we find that, for the monopole deformation case, an intermittency pattern is again found. Moreover, coupling between one-nucleon and collective degrees of freedom is proved to be essential in obtaining chaotic states.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
