Non-adiabatic radiative collapse of a relativistic star under different initial conditions

We examine the role of space-time geometry in the non-adiabatic collapse of a star dissipating energy in the form of radial heat flow, studying its evolution under different initial conditions. The collapse of a star filled with a homogeneous perfect fluid is compared with that of a star filled with inhomogeneous imperfect fluid under anisotropic pressure. Both the configurations are spherically symmetric. However, in the latter case, the physical space t?=?constant of the configurations endowed with spheroidal or pseudospheroidal geometry is assumed to be inhomogeneous. It is observed that as long as the collapse is shear-free, its evolution depends only on the mass and size of the star at the onset of collapse.     

Majorana Representation and Mean Field Approach for Interacting-Boson System

The Majorana representation, which represents a quantum state by stars on the Bloch sphere, provides us an intuitive tool to study the quantum evolution in high dimensional Hilbert space. In this work, we investigate the second quantized model and the mean-field model for the interacting-boson system in the Majorana representation. It is shown that the motions of states in the two models are same in the linear case. Furthermore, the contribution of the nonlinear interaction to the star motions in the second quantized model can be expressed by a single star part which is equal to the nonlinear part of the equation for the star in mean-field model under large boson number limit and an extra part caused by the correlation between stars. These differences and relations can not only be reflected by the population differences between the two boson modes in the two models, but also lie with the differences between the continuous changes of the second quantized evolution with the nonlinear interacting strength and the critical behavior of the mean-field evolution which related to the self-trapping effect. The reason of the difference between the two models is also discussed by an effective Hamiltonian.     

Nonlinear stability of pulsational mode of gravitational collapse in self-gravitating hydrostatically bounded dust molecular cloud

The pulsational mode of gravitational collapse (PMGC) in a hydrostatically bounded dust molecular cloud is responsible for the evolution of tremendous amount of energy during star formation. The source of free energy for this gravito-electrostatic instability lies in the associated self-gravity of the dispersed phase of relatively huge dust grains of solid matter over the gaseous phase of background plasma. The nonlinear stability of the same PMGC in an infinite dusty plasma model (plane geometry approximation for large wavelength fluctuation in the absence of curvature effects) is studied in a hydrostatic kind of homogeneous equilibrium configuration. By the standard reductive perturbation technique, a Korteweg–de Vries (KdV) equation for investigating the nonlinear evolution of the lowest order perturbed self-gravitational potential is developed in a time-stationary (steady-state) form, which is studied analytically as well as numerically. Different nonlinear structures (soliton-like and soliton chain-like) are found to exist in different situations. Astrophysical situations, relevant to it, are briefly discussed.     

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以磁流体理论为基础,采用基于有限体积法的通量差分分裂格式数值求解具有双曲保守律形式的电阻磁流体方程组.编写C++程序对平板几何位形下的等离子体双撕裂模进行了长时间数值模拟,得到双撕裂模不稳定性的演化图景,捕捉到了双撕裂模非线性发展过程中磁场重联的几个典型阶段,讨论了等离子体电阻和两个有理面之间的距离对双撕裂模不稳定性非线性发展的影响.为研究磁流体动力学提供了一种可行的高精度数值算法.     

Vortex rings and solitary waves in trapped Bose–Einstein condensates

We discuss nonlinear excitations in an atomic Bose–Einstein condensate which is trapped in a harmonic potential. We focus on axially symmetric solitary waves propagating along a cylindrical condensate. A quasi one-dimensional dark soliton is the only nonlinear mode for a condensate with weak interactions. For sufficiently strong interactions of experimental interest solitary waves are hybrids of one-dimensional dark solitons and three-dimensional vortex rings. The energy-momentum dispersion of these solitary waves exhibits characteristics similar to a mode proposed sometime ago by Lieb in a strictly 1D model, as well as some rotonlike features. We subsequently discuss interactions between solitary waves. Head-on collisions between dark solitons are elastic. Slow vortex rings collide elastically but faster ones form intermediate structures during collisions before they lose energy to the background fluid. Solitary waves and their interactions have been observed in experiments. However, some of their intriguing features still remain to be experimentally identified.     

基于有限体积法数值模拟双撕裂模非线性演化

以磁流体理论为基础,采用基于有限体积法的通量差分分裂格式数值求解具有双曲保守律形式的电阻磁流体方程组。编写C++程序对平板几何位形下的等离子体双撕裂模进行了长时间数值模拟,得到双撕裂模不稳定性的演化图景,捕捉到了双撕裂模非线性发展过程中磁场重联的几个典型阶段,讨论了等离子体电阻和两个有理面之间的距离对双撕裂模不稳定性非线性发展的影响。为研究磁流体动力学提供了一种可行的高精度数值算法。     

The role of magnetic damping in the r-mode evolution of accreting neutron stars

The magnetic damping rate was introduced in the evolution equations of r-modes,which shows that r-modes can generate strong toroidal magnetic fields in the core of accreting millisecond pulsars inducing by differential rotation.With consideration of the coupling evolution of r-modes,spin and thermal evolution,we investigated the influence of the magnetic damping on the differential rotation of nonlinear r-modes of accreting neutron stars.We derived the coupling evolution equations of the star involving the magnetic damping rate in the framework of second-order r-mode theory.The numerical results show that the magnetic damping suppressed the nonlinear evolution of r-modes since the saturation amplitude is reduced to a great extent.In particular,because of the presence of the generated toroidal magnetic field,the spin-down of the stars is terminated and the viscous heating effects are also weakened.Moreover,we could obtain a stronger generated toroidal magnetic field in the second-order r-mode theory.The gravitational radiation may be detected by the advanced laser interferometer detector LIGO if the amount of differential rotation is small when the r-mode instability becomes active and the accretion rate is not very high.     

Ion velocity distribution function investigated inside an unstable magnetized plasma exhibiting a rotating nonlinear structure

The frequent situation where a strongly nonlinear rotating structure develops in a linear magnetized plasma column is investigated experimentally with emphasis on the ion velocity distribution function (IVDF). Most often, a mode m=2 appears exhibiting a large density and potential perturbation with angular frequency slightly above the ion cyclotron frequency. For the first time the spatiotemporal evolution of the IVDF is studied using time-resolved laser induced fluorescence to explore the ion's interaction with the nonlinear wave propagating inside the column and at the origin of plasma transport outside the limiter. The ion fluid exhibits an alternance from azimuthal to radial velocity due to the electric field inside the rotating structure. A fluid model also allows us to locally reconstruct the self-consistent electric field evolution which contradicts all existing theories.     

A numerical formulation for nonlinear ultrasonic waves propagation in fluids

A finite-difference algorithm is developed for analysing the nonlinear propagation of pulsed and harmonic ultrasonic waves in fluid media. The time domain model allows simulations from linear to strongly nonlinear plane waves including weak shock. Effects of absorption are included. All the harmonic components are obtained from only one solving process. The evolution of any original signal can be analysed. The nonlinear solution is obtained by the implicit scheme via a fast linear solver. The numerical model is validated by comparison to analytical data. Numerical experiments are presented and commented. The effect of the initial pulse shape on the evolution of the pressure waveform is especially analysed.     

Density fluctuation spectrum in whistler turbulence

We develop a nonlinear two-dimensional fluid model of whistler turbulence that includes effect of electron fluid density perturbations. The latter is coupled nonlinearly with wave magnetic field. This coupling leads essentially to finite compressibility effects in whistler turbulence model. We find from our simulations that despite strong compressibility effects, the density fluctuations follow the evolution of the wave magnetic field fluctuations. In a characteristic regime where large scale whistlers are predominant, the coupled density fluctuations are found to follow a Kolmogorov-like phenomenology in the inertial range turbulence. Consequently, the turbulent energy is dominated by the large scale (compared to electron inertial length) eddies and it follows a Kolmogorov-like k−7/3 spectrum, where k is a characteristic wavenumber.     

基于信息熵的变星光谱快速识别方法

变星对人类研究宇宙的起源与发展具有重要意义,对于变星研究的困难首先源于对变星的筛选和识别,即如何从海量恒星光谱数据中有效识别变星光谱。传统的异常数据定义试图通过不同的方式寻找异常数据与一般模式之间的偏差,进而予以定量分析和筛选。然而,这种方法的时间复杂度过大,且结果存在不可理解和无法解释的问题。文章利用熵可以反映系统有序程度与稳定程度的特性,引入信息熵作为衡量数据集一般模式的标准,提出了基于信息熵的变星光谱快速识别方法。该方法显著降低了算法的时间复杂度,有效地消除了人为主观因素对识别结果的影响。采用国家天文台提供的Sloan数字巡天数据实验验证了该方法的可行性和有效性。     

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term,an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tensionwas introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important.However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.     

Acoustic heating produced in the thermoviscous flow of a Bingham plastic

This study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic’s viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation governing acoustic heating, and to retain those belonging to the thermal mode. The nonlinear terms of the final equation are a result of interaction between sounds and the thermal mode. In the field of intense sound, the resulting nonlinear acoustic terms form a driving force for the heating. The final governing dynamic equation of the thermal mode is valid in a weakly nonlinear flow. It is instantaneous, and does not imply that sounds be periodic. The equations governing the dynamics of both sounds and the thermal mode depend on sign of the shear rate. An example of the propagation of a bipolar initially acoustic pulse and the evolution of the heating induced by it is illustrated and discussed.     

Neutron-Capture Elements in the Double-Enhanced Star HE 1305-0007： a New s- and r-Process Paradigm

The star HE 1305-0007 is a metal-poor double-enhanced star with metallicity [Fe/H] = -2.0, which is just at the upper limit of the metallicity for the observed double-enhanced stars. Using a parametric model, we find that almost all s-elements were made in a single neutron exposure. This star should be a member of a post-commonenvelope binary. After the s-process material has experienced only one neutron exposure in the nucleosynthesis region and is dredged-up to its envelope, the AGB evolution is terminated by the onset of common-envelope evolution. Based on the high radial-velocity of HE 1305-0007, we speculate that the star could be a runaway star from a binary system, in which the AIC event has occurred and produced the r-process elements.     

Reentrant behavior of the phase stiffness in Josephson junction arrays

The phase diagram of a 2D Josephson junction array with large substrate resistance, described by a quantum XY model, is studied by means of Fourier path-integral Monte Carlo. A genuine Berezinskii-Kosterlitz-Thouless transition is found up to a threshold value g( small star, filled ) of the quantum coupling, beyond which no phase coherence is established. Slightly below g( small star, filled ) the phase stiffness shows a reentrant behavior with temperature, in connection with a low-temperature disappearance of the superconducting phase, driven by strong nonlinear quantum fluctuations.     

Strongly nonlinear beats in the dynamics of an elastic system with a strong local stiffness nonlinearity: Analysis and identification

We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong nonlinear stiffness at its free end.     

Neutronization and Protonization of Nuclei: Two Possible Ways of the Evolution of Astrophysical Objects and the Laboratory Electron-Nucleus Collapse

We consider the peculiarities of the fundamental nuclear transformations running both in the shell of a heavy star compressed by the strong gravitational field and during the laboratory electron-nucleus collapse where the compression occurs at the expense of the electron-nucleus interaction in a volume occupied by a degenerate electron gas, define their analogs, and analyze the differences. It is shown that the account of relativistic and nonlinear corrections to the Coulomb electron-nucleus interaction gives the possibility to realize two alternative ways for the evolution of the star matter which depend on both the rate of compression upon the gravitational collapse and the initial isotope composition of a star on the stage preceding the collapse. Upon the relatively slow compression of a heavy star in the process of gravitational collapse after the attainment of the threshold electron density, there occur the stage-by-stage neutronization of nuclei and the formation of a neutron star with a great concentration of neutrons and a low concentration of protons and electrons. This process is characterized by the presence of a bounded interval of the density of a relativistic degenerate gas of electrons (“the neutronization corridor”), in the scope of which the neutronization runs with a decrease in the Fermi energy and the release of energy in the form of fast neutrinos. At a higher electron density, the process of protonization becomes energy-gained. In this case, an increase in both the charge of nuclei and the concentration of degenerate electrons causes the continuous increase in the binding energy of electrons and nuclei which turns out to be more significant than the increase in the Fermi energy of electrons. The transition of nuclei through “the neutronization corridor” into “the protonization zone”, which ranges up to the nuclear density of a substance, is possible only in the case of a very fast compression of a heavy star. Such a process leads to the possibility of the formation of proton stars with a very small residual concentration of neutrons and a great (nuclear) concentration of protons and electrons. It is shown that analogous effects can be realized during the laboratory electron-nucleus collapse. Due to a microscopic size of the collapse zone, a great velocity of its formation, and a relatively low rate of neutronization, the passage of the electron-nucleus substance through “the neutronization corridor” weakly affects its state. In this case, the main mechanism of transformations is the process of protonization with a simultaneous increase in the concentration of degenerate electrons.     

可压流体Rayleigh-Taylor不稳定性的离散Boltzmann模拟

使用离散Boltzmann模型模拟了可压流体系统中多模初始情况下的Rayleigh-Taylor不稳定性.该离散Boltzmann模型等效于一个Navier-Stokes模型外加一个关于热动非平衡行为的粗粒化模型.通过模拟Riemann问题:Sod激波管、冲击波碰撞和热Couette流问题验证模型的有效性,所得数值结果与解析解一致.利用该模型对界面间断随机多模初始扰动的可压Rayleigh-Taylor不稳定性进行数值模拟研究,得到不稳定性界面演化过程的基本图像.由于黏性和热传导共同作用,一开始扰动界面被"抹平",演化较慢;随着模式互相耦合而减少,演化开始加速,并经历非线性小扰动阶段和不规则非线性阶段,而后发展成典型的"蘑菇状",后期进入湍流混合阶段.由于扰动模式的耦合与发展,轻重流体的重力势能、压缩能与动能相互转化,系统先是趋于热动平衡态,而后偏离热动平衡态以线性形式增长,接着再次趋于热动平衡态,最后慢慢远离热动平衡态.     

Effect of Tidal Torques on Rotational Mixing in Close Binaries

The effect of tidal torques on rotational mixing in close binaries is investigated. It is found that spin angular momentum can attain a high value due to a strong tidal torque. Nitrogen and helium enrichment occurs early in the binary system that is triggered by tides. The stellar radius can reach a high value in the single star model with high initial velocities at the early stage of the evolution, but efficient rotational mixing can inhibit stellar expanding at the subsequent evolution. Central compactness is increased by the centrifugal force at the early stage of evolution but is reduced by rotational mixing induced by strong tides. The binary models with weak tides have high values of central temperature and stellar radius. Rotational mixing in single stars can slow down the shrinkage of convective cores, while convective cores can be expanded by strong tides in the binary system.Efficient rotational mixing induced by tides can cause the star to evolve towards high temperature and luminosity.     

Boson Nebulae Charge

We use the first-order approximate solutions to the nonlinear system of Klein-Gordon-Maxwell-Einstein equations describing the minimally coupled charged spin-less field to a spherically symmetric spacetime to analyze a becoming boson star. In the far future and long-range approximation, we derive an analytical time-dependent charge which allows us to point out several significant moments in the evolution of the boson nebula.