Fundamental and subharmonic resonances in a system with a ‘1-1’ internal resonance

The fundamental and subharmonic resonances of a two degree-of-freedom oscillator with cubic stiffness nonlinearities and linear viscous damping are examined using a multiple-seales averaging analysis. The system is in a 1–1 internal resonance, i.e., it has two equal linearized eigenfrequencies, and it possesses nonlinear normal modes. For weak coupling stiffnesses the internal resonance gives rise to a Hamiltonian Pitchfork bifurcation of normal modes which in turn affects the topology of the fundamental and subharmonic resonance curves. It is shown that the number of resonance branches differs before and after the mode bifurcation, and that jump phenomena are possible between forced modes. Some of the steady state solutions were found to be very sensitive to damping: a whole branch of fundamental resonances was eliminated even for small amounts of viscous damping, and subharmonic steady state solutions were shifted by damping to higher frequencies. The analytical results are verified by a numerical integration of the equations of motion, and a discussion of the effects of the mode bifurcation on the dynamics of the system is given.     

泡沫流体的剪应力与法向应力差

本文在同时考虑表面张力与粘性力的情况下,以三维模型—长菱形十二面体及泡沫的应力张量表达式为基础,得出了泡沫的剪应力及法向应力差表达式,并通过计算机进行了求解,讨论了泡沫粘度、泡沫大小等因素对剪应力及法向应力差的影响。 实验使用了 RMS-605 大型流交仪、RV-2 流变仪及毛细管流变仪测定泡沫流变特性。消除了表面滑移影响后得到的剪应力与法向应力表数据与理论结果较接近,说明理论模型具有一定的实用价值。     

推导粒子数态波函数的厄米多项式算符法

引入厄米多项式算符并用其正规乘积展开式推导出了粒子数态|n〉在坐标表象和动量表象下的波函数,并由此得出了坐标和动量本征态的福克(Fock)表示形式,这是一个简洁而全新的推导方法.     

Fine structure of the isoscalar giant quadrupole resonance in Ca due to Landau damping?

The fragmentation of the Isoscalar Giant Quadrupole Resonance (ISGQR) in ⁴⁰Ca has been investigated in high energy-resolution experiments using proton inelastic scattering at Ep=200 MeV$E_{\mathrm{p}}=200\text{MeV}$. Fine structure is observed in the region of the ISGQR and its characteristic energy scales are extracted from the experimental data by means of a wavelet analysis. The experimental scales are well described by Random Phase Approximation (RPA) and second-RPA calculations with an effective interaction derived from a realistic nucleon–nucleon interaction by the Unitary Correlation Operator Method (UCOM). In these results characteristic scales are already present at the mean-field level pointing to their origination in Landau damping, in contrast to the findings in heavier nuclei and also to SRPA calculations for ⁴⁰Ca based on phenomenological effective interactions, where fine structure is explained by the coupling to two-particle–two-hole (2p–2h) states.     

n模耦合谐振子量子系统的精确波函数

利用不变本征算符法研究了n模耦合谐振子量子系统的简正频率及其对应的简正坐标与共轭动量,并对系统的哈密顿量进行了退耦合,得到了系统的明显的简正频率解析解.推导出坐标表象中系统的精确波函数的解析解.并对不同情形的耦合系数进行了讨论,认识到n模动量耦合谐振子体系和n模坐标耦合谐振子体系是本文所研究的体系的特例.     

A monotone version of the Sokolov property and monotone retractability in function spaces

We introduce the monotone Sokolov property and show that it is dual to monotone retractability in the sense that X   is monotonically retractable if and only if _Cp(X)$C_p(X)$ is monotonically Sokolov. Besides, a space X   is monotonically Sokolov if and only if _Cp(X)$C_p(X)$ is monotonically retractable. Monotone retractability and monotone Sokolov property are shown to be preserved by R$\mathbb{R}$-quotient images and _Fσ$F_{\sigma }$-subspaces. Furthermore, every monotonically retractable space is Sokolov so it is collectionwise normal and has countable extent. We also establish that if X   and _Cp(X)$C_p(X)$ are Lindelöf Σ-spaces then they are both monotonically retractable and have the monotone Sokolov property. An example is given of a space X   such that _Cp(X)$C_p(X)$ has the Lindelöf Σ-property but neither X   nor _Cp(X)$C_p(X)$ is monotonically retractable. We also establish that every Lindelöf Σ-space with a unique non-isolated point is monotonically retractable. On the other hand, each Lindelöf space with a unique non-isolated point is monotonically Sokolov.     

Parameter space of the Rulkov chaotic neuron model

The parameter space of the two dimensional Rulkov chaotic neuron model is taken into account by using the qualitative analysis, the co-dimension 2 bifurcation, the center manifold theorem, and the normal form. The goal is intended to clarify analytically different dynamics and firing regimes of a single neuron in a two dimensional parameter space. Our research demonstrates the origin that there exist very rich nonlinear dynamics and complex biological firing regimes lies in different domains and their boundary curves in the two dimensional parameter plane. We present the parameter domains of fixed points, the saddle-node bifurcation, the supercritical/subcritical Neimark–Sacker bifurcation, stability conditions of non hyperbolic fixed points and quasiperiodic solutions. Based on these parameter domains, it is easy to know that the Rulkov chaotic neuron model can produce what kinds of firing regimes as well as their transition mechanisms. These results are very useful for building-up a large-scale neuron network with different biological functional roles and cognitive activities, especially in establishing some specific neuron network models of neurological diseases.