Integrable potentials with cubic and quartic invariants

The necessary general form for a two-dimensional integrable potential to admit an invariant of the type: I=(xp_y-yp_x)ⁿ+ lower order terms, is obtained and an explicit construction is carried out at n = 3,4. A generalization is made to other similar types of the invariant.     

Exact invariants and adiabatic invariants of the singular Lagrange system

Based on the theory of symmetries and conserved quantities of the singular Lagrange system, the perturbations to the symmetries and adiabatic invariants of the singular Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the singular Lagrange system is proposed. Then, the conditions for the existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.     

Exact invariants and adiabatic invariants of dynamical system of relative motion

Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of a dynamical system of relative motion are studied. The perturbation to symmetries for the dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.     

准坐标下完整系统的精确不变量与绝热不变量

基于对称性与不变量理论，研究了准坐标下完整系统的精确不变量与绝热不变量。研究了在小扰动作用下准坐标完整系统的对称性摄动。提出了高阶绝热不变量的概念，给出了精确不变量与绝热不变量存在的形式与条件。然后研究了相应的逆问题。     

约束哈密顿系统在相空间中的精确不变量与绝热不变量

研究小干扰力作用下约束哈密顿系统对称性的摄动问题.建立了非保守约束哈密顿系统的正则方程,在增广相空间中研究了系统的对称性与精确不变量.基于力学系统的高阶绝热不变量的概念,给出了系统的各阶绝热不变量的形式及存在条件,并建立了绝热不变量与对称变换之间的对应关系 关键词： 约束哈密顿系统 对称性 摄动 不变量     

Packing of elastic wires in spherical cavities

We investigate the morphologies and maximum packing density of thin wires packed into spherical cavities. Using simulations and experiments, we find that ordered as well as disordered structures emerge, depending on the amount of internal torsion. We find that the highest packing densities are achieved in low torsion packings for large systems, but in high torsion packings for small systems. An analysis of both situations is given in terms of energetics and comparison is made to analytical models of DNA packing in viral capsids.     

Lagrange系统对称性的摄动与Hojman型绝热不变量

研究Lagrange系统对称性的摄动与绝热不变量.列出未受扰Lagrange系统的Lie对称性导致的Hojman守恒量；基于力学系统的高阶绝热不变量的定义，研究在小扰动作用下Lagrange系统Lie对称性的摄动，得到了系统的一类Hojman形式的绝热不变量.并举例说明结果的应用. 关键词： Lagrange系统 对称性 摄动 绝热不变量     

Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions

In this paper,the least square fitting method with the cubic B-spline basis hmctioas is derived to reduce the influence of statistical fluctuations in the gamma ray spectra.The derived procedure is simple and automatic.The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.     

Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions

In this paper, the least square fitting method with the cubic B-spline basis lunctions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and automatic. The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.     

事件空间中完整系统的Lie对称性与绝热不变量

研究事件空间中完整力学系统Lie对称性的摄动与绝热不变量.基于力学系统的高阶绝热不变量的概念，研究在小扰动作用下系统Lie对称性的摄动，得到了事件空间中完整力学系统的一类Hojman形式的高阶绝热不变量，给出了绝热不变量存在的条件及形式.并举例说明结果的应用. 关键词： 事件空间 对称性 摄动 绝热不变量     

Enhancement and inhibition of acoustic radiation in spherical cavities

Acoustic radiation from a source located inside layered cavities is studied using the transfer matrix method. It is shown that the radiation can be either enhanced or inhibited, depending on the characteristics and the material composition of the cavities. The analysis predicts well-defined spectral peaks and nodes in some cavities. It is found that significant enhancement and inhibition are possible by varying acoustic parameters. The results also show that the strength of the radiating source can be significantly modified due to the presence of layered structures. The link to the similar phenomena in the optical cavities is discussed.     

Exact invariants and adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system

The exact invariants and the adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher-order adiabatic invariant of a mechanical system under the action of a small perturbation, the forms of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.     

Enhanced single photon emission in silicon carbide with Bull's eye cavities

The authors demonstrate a Bull's eye cavity design that is composed of circular Bragg gratings and micropillar optical cavity in 4H silicon carbide (4H-SiC) for single photon emission. Numerical calculations are used to investigate and optimize the emission rate and directionality of emission. Thanks to the optical mode resonances and Bragg reflections, the radiative decay rates of a dipole embedded in the cavity center is enhanced by 12.8 times as compared to that from a bulk 4H-SiC. In particular, a convergent angular distribution of the emission in far field is simultaneously achieved, which remarkably boost the collection efficiency. The findings of this work provide an alternative architecture to manipulate light—matter interactions for achieving high-efficient SiC single photon sources towards applications in quantum information technologies.     

Shock wave similarity invariants. I. Convergence laws of spherical and cylindrical shock waves in a constant-density gas

Using the similarity and dimensional methods, dimensionless similarity invariants of shock wave similarity are determined, using which convergence laws of strong spherical and cylindrical shock waves in a constant-density gas are determined.     

Conserved quantities and adiabatic invariants of fractional Birkhoffian system of Herglotz type

In order to further study the dynamical behavior of nonconservative systems,we study the conserved quantities and the adiabatic invariants of fractional Brikhoffian systems with four kinds of different fractional derivatives based on Herglotz differential variational principle.Firstly,the conserved quantities of Herglotz type for the fractional Brikhoffian systems based on Riemann-Liouville derivatives and their existence conditions are established by using the fractional Pfaff-Birkhoff-d Alembert principle of Herglotz type.Secondly,the effects of small perturbations on fractional Birkhoffian systems are studied,the conditions for the existence of adiabatic invariants for the Birkhoffian systems of Herglotz type based on Riemann-Liouville derivatives are established,and the adiabatic invariants of Herglotz type are obtained.Thirdly,the conserved quantities and adiabatic invariants for the fractional Birkhoffian systems of Herglotz type under other three kinds of fractional derivatives are established,namely Caputo derivative,Riesz-Riemann-Liouville derivative and Riesz-Caputo derivative.Finally,an example is given to illustrate the application of the results.     

Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres

We propose and demonstrate a "bottom-up" approach to constructing photonic structures for photon manipulation. Supermonodispersive polymer microspheres are used as building blocks and a size uniformity better than 0.05% could be obtained by sorting the spheres using spectroscopic methods. The spheres are positioned in a V groove on a silicon substrate and form a photonic chain with resonant coupling of the optical whispering-gallery modes. Photonic band modes are clearly observed in fluorescence and resonant scattering spectra, and an excellent agreement with a tight-binding model calculation is found. Heavy photon states and a group index as high as 40 are obtained.     

Subsonic non-steady-state gas flows in channels with inner cavities

A set of gasdynamic equations is given in the general form for matter with an arbitrary equation of state in the case when the entropy equation is used instead of the energy equation. In the ideal gas approximation in view of viscosity, a numerical investigation is performed of non-steady-state two-dimensional flows in a channel with a cavity. The calculation results have demonstrated that, given the flow velocity and the geometry of channel and cavity, pressure pulsations arise that are due to the departure of vortices from the cavity into the main flow. The values of the amplitude and frequency of pressure pulsations are determined. If measures are taken aimed at limiting the departure of vortices from the cavity, for example, a baffle is installed to restrict the interaction between the main flow and gas in the cavity, one can considerably increase the flow velocity in the channel, unaffected by the cavity. Such non-steady-state flows may be realized in MHD-generator channels, resonators of gas flow lasers, gas ducts for ventilation and gas transport systems, mufflers, whistles, etc.     

Large velocity capture range and low temperatures with cavities

There are interesting modifications to the Doppler force when atoms strongly couple to an optical cavity. In particular, there is the possibility to increase the velocity capture range while maintaining a final temperature close to the Doppler limit. The mechanism is based on the multiple absorption emissions of each cavity photon. A previously reported counterintuitive Doppler effect is clarified.     

Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system

Based on the theory of symmetries and conserved quantities, the perturbation to the symmetries and adiabatic invariants of a type of nonholonomic singular system are discussed. Firstly, the concept of higher order adiabatic invariants of the system is proposed. Secondly, the conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Thirdly, we study the inverse problems of the perturbation to symmetries of the system. An example is presented to illustrate these results.     

Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems

Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.