On the nonlinear dynamics of a single degree of freedom oscillator with a time-varying mass

In this paper the forced vibrations of an undamped single degree of freedom oscillator with a time varying mass will be studied. An initial value problem for an oscillator equation with a Rayleigh type of nonlinearity will be formulated, and by applying a straight-forward perturbation method the problem will be solved approximately. The approximations of the solutions will be used to construct a map. By using this map the stability properties of the solutions can be determined. The stability properties of the nonlinear problem will be compared to those for the linear problem, which have been studied earlier in the literature. The instability regions in the parameter space and some phase-space figures for the nonlinear problem will be computed numerically. It will also be shown how the behaviour of the solutions changes when the instability regions in the parameter space are crossed.     

sdg Interacting boson model: hexadecupole degree of freedom in nuclear structure

Thesdg interacting boson model (sdgIBM), which includes monopole (s), quadrupole (d) and hexadecupole (g) degrees of freedom, enables one to analyze hexadecupole (E4) properties of atomic nuclei. Various aspects of the model, both analytical and numerical, are reviewed emphasizing the symmetry structures involved. A large number of examples are given to provide understanding and tests, and to demonstrate the predictiveness of thesdg model. Extensions of the model to include proton-neutron degrees of freedom and fermion degrees of freedom (appropriate for odd mass nuclei) are briefly described. A comprehensive account ofsdgIBM analysis of all the existing data on hexadecupole observables (mainly in the rare-earth region) is presented, includingβ ₄ (hexadecupole deformation) systematics,B(IS4; 0 _GS ⁺ →4 _γ ⁺ ) systematics that give information about hexadecupole component in γ-vibration,E4 matrix elements involving few low-lying 4⁺ levels,E4 strength distributions and hexadecupole vibrational bands in deformed nuclei. The survey of literature for this review was concluded in December 1991.     

Pairing with a delta interaction in the energy density nuclear mass formula

The variations of the average pairing strength in the (N, Z) plane are studied with a δ-interaction in the frame of the self-consistent energy density formalism. It is found that the same δ-interaction with constant strength can be used for protons and neutrons in spherical nuclei near the stability line. This interaction is used to study the extrapolation of the average pairing strength to deformed nuclei, to the superheavy region and to the regions of the drip lines. The consequences of the results for the stability of superheavy nuclei and for magic numbers far from the stability region are examined.     

Effective mass overshoot in single degree of freedom mechanical systems with a particle damper

We study the response of a single degree of freedom mechanical system composed of a primary mass, M, a linear spring, a viscous damper and a particle damper. The particle damper consists in a prismatic enclosure of variable height that contains spherical grains (total mass m_p). Contrary to what it has been discussed in previous experimental and simulation studies, we show that, for small containers, the system does not approach the fully detuned mass limit in a monotonous way. Rather, the system increases its effective mass up and above M+m_p before reaching this expected limiting value (which is associated with the immobilization of the particles due to a very restrictive container). Moreover, we show that a similar effect appears in the tall container limit where the system reaches effective masses below the expected asymptotic value M. We present a discussion on the origin of these overshoot responses and the consequences for industrial applications.     

Spin degree of freedom in the nu=1 bilayer electron system investigated by nuclear spin relaxation

The nuclear-spin-relaxation rate 1/T(1) has been measured in a bilayer electron system at and around total Landau level filling factor nu=1. The measured 1/T(1), which probes electron spin fluctuations, is found to increase gradually from the quantum Hall (QH) state at low fields through a phase transition to the compressible state at high fields. Furthermore, 1/T(1) in the QH state shows a noticeable increase away from nu=1. These results demonstrate that, as opposed to common assumption, the electron spin degree of freedom is not completely frozen either in the QH or the compressible states.     

Reflection asymmetry in the calculations of nuclear mass parameters in terms of the modified oscillator model

The cranking model has been adapted to the four dimentional (?₂, ?₃, ?₄, ?₅) nuclear shape parametrization of the Nilsson model. Some advantages of the nuclear shape parametrization in terms of Legendre polynomials are pointed out. The most characteristic properties of the mass parameters and their dependence upon the shell structure are illustrated and discussed for some actinide nuclei.     

Nucleon exchange mechanism of mass asymmetry relaxation in fission and other binary nuclear reactions

Mass asymmetry relaxation as manifested in fission and heavy ion-induced binary reactions is reviewed. In fission, the dynamics is characteristic of a fully damped case and is well described by a stochastic theory. In heavy ion deep inelastic collisions and quasi-fission, on the other hand, the relaxation is incomplete giving rise to the possibility of studying its time evolution.     

The study of the binding energy of nuclear matter in the relativistic σ− ω− π model with Δ isobar degree of freedom

The relativistic σ?ω?π model is proposed and used to calculate the binding energy of relativistic nuclear matter. By coupling Δ isobar to the σ meson, the zero-point fluctuation energy of the Δ isobar in the one loop approximation is derived. We calculate the effective mass of nucleon and Δ isobar, exchange and correlation energies, pressure and incompressibility of nuclear matter. The density dependence correction to σNN ωNN coupling constants is a very important mechanism to saturate the binding energy. The pion propagator is nuclear matter is constructed by the relativistic particle-hole, delta-hole and short-range correlation. The pion dispersion relation is calculated we find it’s very sensitive to the effective mass of nucleon and Δ isobar.     

Critical-point behaviour of axially deformed nuclei in the octupole degree of freedom

The evolution of the octupole excitation is investigated along the Th isotope chain. The isotope ²²⁶Th results to be close to the critical point (square-well potential in the octupole amplitude ).Received: 26 October 2002, Published online: 16 March 2004PACS: 21.60.Ev Collective models     

The influence of the entrance channel mass asymmetry on the reaction mechanism

We have tried to investigate the influence of the entrance channel mass asymmetry on the reaction mechanisms associated with heavy ion collisions. Two systems, one very much asymmetric (O+Mo) and the other one almost symmetric (Cr+Fe), were studied in detail by measuring evaporation residues, deep inelastic collision products and fission fragments. An important fraction of the fragments observed in the Cr+Fe system exhibits all the characteristics of fission fragments. The analysis of these data seems to indicate that these fission like products are most likely emitted by a long lived composite system having not reached full statistical equilibrium for all the degrees of freedom. As a consequence, the fusion cross section for this symmetric system is too low as compared to predictions based on a critical distance approach for fusion, whereas the asymmetric system (O+Mo) is well understood in term of the same model.     

核对称轴不同相对取向对熔合动力学的影响

计算了核对称轴不同相对取向时的熔合位垒.基于双核模型观念，考虑了熔合与准裂变的竞争，通过数值法求解主方程，计算了⁷⁶Ge+²⁰⁸Pb，⁴⁸Ca+²⁴⁴Pu核对称轴不同相对取向对熔合概率的影响，探索了最有利于超重元素合成的弹靶相对取向.取向不同时，对熔合反应的影响较大，计算结果表明弹靶碰撞为腰对腰时，更有利于发生熔合反应. 关键词： 超重元素 熔合概率 变形核 方向角度     

Oxidation at the Si/SiO2 interface: influence of the spin degree of freedom

We show, using first-principles spin-polarized total-energy calculations, that depending on the spin configuration of the system, the reaction of an O2 molecule with a Si-Si bond in a suboxidized region might result either in a peroxy linkage defect (for a singlet spin state) or in a perfect Si-O-Si bond plus an interstitial O atom (for a triplet spin state). Even though the singlet has a lower energy than the triplet configuration, we find a rather small probability for triplet to singlet conversion. Therefore, as the O2 in an SiO2 interstitial site has a triplet configuration, this reaction spin dependence may have a strong influence on the high quality of the Si/SiO2 interface.     

The mixing of elementary particles and the mass formula for bosons

The paper deals with the possibility of the existence of — ₂ mixing and the question of the Gell-Mann-Okubo formula (GOF) for bosons.     

熔合反应中入射道质量不对成度效应

The symmetric and asymmetric fusion reaction systems forming the same compound nuclei ^26Al, ^30Si, ^38Ar and ^170Hf are investigated with the frame of improved isospin dependent quantum molecular dynamics model. The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies, the Coulomb barriers and the fusion cross sections. The calculated fusion cross sections agree quantitatively with the experimental data. The results indicate that compound nucleus formation is favorable for the systems with larger mass asymmetry because of the smaller Coulomb contribution to the fusion barrier.     

Effects of the entrance channel mass asymmetry in fusion reactions

The symmetric and asymmetric fusion reaction systems forming the same compound nuclei 26Al,30Si,38Ar and 170Hf are investigated with the frame of improved isospin dependent quantum molecular dynamics model.The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies,the Coulomb barriers and the fusion cross sections.The calculated fusion cross sections agree quantitatively with the experimental data.The results indicate that compound nucleus formation is favorable for the systems with larger mass asymmetry because of the smaller Coulomb contribution to the fusion barrier.     

On the evolution of the mass asymmetry in damped heavy-ion collisions

TotaT kinetic energy vs. fragment mass distributions have been measured in the reactions of⁶⁴Zn projectiles with¹¹⁴Sn,^natAg and¹³⁹La nuclei at incidence energies of 20–50% above the Coulomb barrier. Conclusions are drawn on the possible influence of nuclear structure effects on the energy dissipation and the mass drift behaviour of the present collision systems.     

刚性杆和滑块组成的单自由度非线性振动

用动力学方法,导出了刚性杆和滑块组成的单自由度非线性振动系统的运动微分方程;求出了杆的摆动角速度和角加速度、杆与滑块的相互作用力与杆的摆角间的关系式;给出了系统振动周期的计算公式;借助Matlab软件画出了杆与滑块的相互作用力随角坐标的变化曲线及周期随角振幅的变化曲线．