Chaotic scattering in the restricted three-body problem I. The Copenhagen problem

We consider the scattering motion of the planar restricted three-body problem with two equal masses on a circular orbit. Using the methods of chaotic scattering we present results on the structure of scattering functions. Their connection with primitive periodic orbits and the underlying chaotic saddle are studied. Numerical evidence is presented which suggests that in some intervals of the Jacobi integral the system is hyperbolic. The Smale horseshoe found there is built from a countable infinite number of primitive periodic orbits, where the parabolic orbits play a fundamental role.     

One more explanation of superluminal motion

The occurrence of superluminal motion in extragalactic radio sources is believed to be quite common. Among others, the geometrical scattering of radio radiation can also cause superluminal expansion and or motion and halo formation, In this paper, the effectiveness of the stimulated Raman scattering in producing these features is investigated. The scattering medium is a plasma whose position, density and temperature decide the rate and angle of scattering. When the radiation from a stationary and constant source gets scattered from a stationary plasma, a halo is formed around the source. However, the scattering of a rotating radiation beam does produce superluminal motion of the virtual source. It is found that the plasma should have the characteristics of the emission-line regions and the intercloud medium in order to Raman scatter the radiation. Since the scattering is polarization dependent, it is possible to estimate the rotation of the electric vector along the direction of the apparent motion of a radio source.     

Formation of the radio profile components of the Crab pulsar

The induced Compton scattering of radio emission off the particles of the ultrarelativistic electron–positron plasma in the open field line tube of a pulsar is considered. We examine the scattering of a bright narrow radio beam into the background over a wide solid angle and specifically study the scattering in the transverse regime, which holds in a moderately strong magnetic field and gives rise to the scattered component nearly antiparallel to the streaming velocity of the scattering particles. Making use of the angular distribution of the scattered intensity and taking into account the effect of rotational aberration in the scattering region, we simulate the profiles of the backscattered components as applied to the Crab pulsar. It is suggested that the interpulse (IP), the high-frequency interpulse (IP') and the pair of so-called high-frequency components (HFC1 and HFC2) result from the backward scattering of the main pulse (MP), precursor (PR) and low-frequency component (LFC), respectively. The components of the high-frequency profiles, the IP' and HFCs, are interpreted for the first time. The HFC1 and HFC2 are argued to be a single component split by the rotational aberration close to the light cylinder. It is demonstrated that the observed spectral and polarization properties of the profile components of the Crab pulsar as well as the giant pulse phenomenon outside the MP can be explained in terms of our model.     

Scattered emission from a relativistic outflow and its application to gamma-ray bursts

We investigate a scenario of photon scattering by electrons within a relativistic outflow. The outflow is composed of discrete shells with different speeds. One shell emits radiation for a short duration. Some of this radiation is scattered by the shell(s) behind. We calculate in a simple two-shell model the observed scattered flux density as a function of the observed primary flux density, the normalized arrival time delay between the two emission components, the Lorentz factor ratio of the two shells and the scattering shell's optical depth. Thomson scattering in a cold shell and inverse Compton scattering in a hot shell are both considered. The results of our calculations are applied to the gamma-ray bursts and the afterglows. We find that the scattered flux from a cold slower shell is small and likely to be detected only for those bursts with very weak afterglows. A hot scattering shell could give rise to a scattered emission as bright as the X-ray shallow decay component detected in many bursts, on a condition that the isotropically equivalent total energy carried by the hot electrons is large, ∼10⁵²–10⁵⁶ erg. The scattered emission from a faster shell could appear as a late short γ-ray/MeV flash or become part of the prompt emission depending on the delay of the ejection of the shell.     

基于逆散射理论的介质参数与其地震响应的尺度对应关系研究

在反演过程中进行频带控制是多尺度反演的重要策略,但数据频率成分与要反演的参数之间的尺度对应关系尚不清晰。本文利用Kormendi论文中的测井曲线模型,基于逆散射理论将地下介质参数的扰动分解为0-0-9-11 Hz、9-11-18-22 Hz、18-22-36-44 Hz和36-44-80-90 Hz共4个尺度,并利用反射率正演模拟方法生成4个尺度扰动成分的地震响应。通过对比地下介质参数不同尺度的扰动及其地震响应的频带成分,发现二者在4个扰动尺度上均具有一致性,由此得出介质参数与其地震响应具有定量尺度对应关系的结论。据此从介质扰动的尺度概念引申出反射系数的尺度概念,从逆散射理论角度探讨实验结果的理论依据,并对其在指导反演分频参数选取及薄互层解释等方面的应用展望进行讨论。