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.     

Machine-learning-driven on-demand design of phononic beams

The development of phononic crystals, especially their interaction with topological insulators, allows exploration of the anomalous properties of acoustic/elastic waves for various applications. However, rapidly and inversely exploring the geometry of specific targets remains a major challenge. In this work, we show how machine learning can address this challenge by studying phononic crystal beams using two different inverse design schemes. We first develop the theory of phononic beams using the transfer matrix method. Then, we use the reinforcement learning algorithm to effectively and inversely design the structural parameters to maximize the bandgap width. Furthermore, we employ the tandem-architecture neural network to solve the training-difficulty problem caused by inconsistent data and complete the task of inverse structure design with the targeted topological properties. The two inverse-design schemes have different adaptabilities, and both are characterized by high efficiency and stability. This work provides deep insights into the combination of machine learning, topological property,and phononic crystals and offers a reliable platform for rapidly and inversely designing complex material and structure properties.     

Mitigation and prediction of disruption on the HL-2A Tokamak

Injection of high-Z impurities into plasma has been proved to be able to reduce the localized thermal load and mechanical forces on the in-vessel components and the vacuum vessel, caused by disruptions in Tokamaks. An advanced prediction and mitigation system of disruption is implemented in HL-2A to safely shut down plasmas by using the laser ablation of high-Z impurities with a perturbation real-time measuring and processing system. The injection is usually triggered by the amplitude and frequency of the MHD perturbation field which is detected with a Mirnov coil and leads to the onset of a mitigated disruption within a few milliseconds. It could be a simple and potential approach to significantly reducing the plasma thermal energy and magnetic energy before a disruption, thereby achieving safe plasma termination. The plasma response to impurity injection, a mechanism for improving plasma thermal and current quench in major disruptions, the design of the disruption prediction warner, and an evaluation of the mitigation success rate are discussed in the present paper.     

Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations

Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented.The concepts of Lie symmetry and higher order adiabatic invariants of Poincar\'{e} equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.     

Perturbation to Mei Symmetry and Noether Adiabatic Invariants for Birkhoffian Systems

Based on the concept of adiabatic invariant, the perturbation to Mei symmetry and Noether adiabatic invariants for Birkhoffian systems are studied. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the Noether adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.     

Theoretical Calculations of Opacity for Non-Local-Thermodynamic-Equilibrium Plasmas

A method is presented to calculate the spectral-resolved opacity for non-local-thermodynamic-equilibrium plasmas. With the present method, the configuration population is obtained by solving the rate equations within the framework of configuration-averaged approximation in which the cross sections are calculated based on the first-order perturbation theory. The transition properties are calculated by using the unresolved transition array model. As the illustration, the frequency-dependent opacities of AI and Au plasmas are calculated and compared with the simulation results of the super configuration collisional radiative code. General agreements are obtained and there are some discrepancies for opacity of high-Z elements.     

Generalized Supersymmetric Perturbation Theory

Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.     

Perturbation to Mei symmetry and adiabatic invariants for Hamilton systems

Based on the concept of adiabatic invariant, this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.     

Effect of Magnetohydrodynamic Perturbations on the Orbit Loss of Alpha Particles in Tokamak Plasma

We investigate the orbit loss of alpha particles under helical magnetic perturbation in a tokamak.The results show that low-frequency and low-mode number magnetic perturbation can cause stochastic loss of alpha particles.This effect is significant for those particles close to the boundary between the transit zone and the trapped zone.The particle loss is sensitive to the phase of the magnetic perturbation,indicating the modulation of the particle loss with respect to magnetic perturbation.It is also found that the precession of the particle banana orbit can even further enhance the particle loss.     

CORE POLARIZATION CORRECTIONS FOR THE PHOTOIONIZATION OF SODIUM

Many-body perturbation theory with an effective operator is applied to the calculations of photoionization of sodium by consistently including the static and dynamic core polarization. The cross section for the transition (2p→kd+ ks) is obtained by taking into account the dipole and quadrupole core polarization. The results are compared with the many-body perturbation results and measurements.     

Comparison of XYZ Model Fitting Functions for 111Cd in In3La

The XYZ model describes the interaction between nuclear probes and an electric field gradient that fluctuates among three orthogonal directions. The model presents a means to calculate the perturbation function that represents spectra obtained using perturbed angular correlation spectroscopy. Three analytic approximations of the perturbation function have been developed previously, and they are evaluated in the present paper in the context of Cd jumping among In-lattice sites in In₃La.     

Pionic and electromagnetic decays ofb-hadrons

The chiral perturbation theory has been used to calculate pionic and radiative decays ofb-hadrons. These particles are being studied and their decays have been predicted.     

A k-Space Analysis of MR Tagging

We present a k-space approximation that directly relates a pulse sequence to its residual pattern of z-directed magnetization M_z, in a manner akin to the k-space approximation for small tip-angle excitation. Our approximation is particularly useful for the analysis and design of tagging sequences, in which M_z is the important quantity—as opposed to the transverse magnetization components M_x and M_y considered in selective excitation. We demonstrate that our approximation provides new insights into tagging, can be used to design novel tag patterns, and, more generally, may be applied to selective presaturation sequences for purposes other than tagging.     

应变Ge/Si1-xGex 价带色散模型

基于k·p微扰理论, 通过引入应变哈密顿量作为微扰, 建立了双轴应变Ge/Si_1-xGe_x价带色散关系模型. 模型适于任意晶向弛豫Si_1-xGe_x虚衬底上的应变Ge价带结构, 通过该模型可获得任意k方向应变Ge的价带结构和空穴有效质量. 模型的Matlab模拟结果显示, 应变Ge/Si_1-xGe_x价带带边空穴有效质量随Ge组分的增加而减小, 其各向异性比弛豫Ge更加显著. 本文研究成果对Si基应变Ge MOS器件及集成电路的沟道应力与晶向的设计有参考价值.     

Linear free‐energy relationships in semiquinone species and their Mn(II) and Cu(II) complexes

Linear free‐energy relationships for a series of functionalized semiquinone ligands and their Mn^II‐ and Cu^IIhydro‐tris(3‐cumenyl‐5‐methylpyrazolyl) borate complexes were examined. Quinone–semiquinone cycle half‐wave reduction potentials and semiquinone hydrogen hyperfine coupling constants (a_H) were determined and their correlation with Hammett σ parameters reported. A new σ parameter, σ_aH, has been proposed. Mn^II and Cu^II metal complex metal–ligand charge transfer and n → π* UV transitions were found to be modulated by substituents. Satisfactory Hammett correlations between UV transitions and various σ values have been determined and compared in a number of instances. Copyright © 2011 John Wiley & Sons, Ltd.     

High pressure behavior of alkaline earth tellurides

We have predicted high pressure structural behavior and elastic properties of alkaline earth tellurides (AETe; AE = Ca, Sr, Ba) by using two body interionic potential approach with modified ionic charge (Z _m e). This method has been found quite satisfactory in case of the rare earth compounds. The equation of state curve, structural phase transition pressure from NaCl (B1) to CsCl (B2) phase and associated volume collapse at transition pressure of alkaline earth tellurides (AETe) obtained from this approach, so have been compared with experimentally measured data reveal good agreement. We have also investigated bulk modulus, second and third order elastic constants and pressure derivatives of second order elastic constants at ambient pressure which shows predominantly ionic nature of these compounds. First time, we have calculated the Poisson ratio, Young and Shear modulus of these compounds.      

Time reversal for systems with internal symmetry

Wigner time reversal implemented by antiunitary transformations on the wavefunctions is to be refined if we are to deal with systems with internal symmetry. The necessary refinements are formulated. Application to a number of physical problems is made with some unexpected revelations about some popular models.This paper is presented in felicitation of Jean-Pierre Vigier with pleasant recollections of his infectious enthusiasm. This work is supported in part by DOE Grant No. DE-FG03-93ER40757. The authors thank Iwo Bialynicki-Birula and J. Bruce French for sharing their insights, and Luis J. Boya for discussions.     

On the solution of some vertex models using factorizableS matrices

The intimate connection between factorizableS matrices and some vertex models in two dimensions (to be reviewed here) is exploited to show that the knowledge of theS matrix not only allows us to define a solvable vertex modelá la Zamolodchikov, but often to write down the free energy by inspection. The prototype for discussion is Baxter's eight-vertex model generated by Zamolodchikov's Z₄ S matrix. The method is then applied to a hitherto unsolved 19-vertex model, based on the isospin-1S matrix of Zamolidchikov and Fateev, and agreement is checked to fourth order in a perturbation series. The possibility of molding other problems like theq-state Potts model into this framework is considered.Research supported in part by NSF grant No. INT 8117361.     

Noisy nonlinear coupled equations—Some new insights

We discuss the use of coupled nonlinear stochastic differential equations to model the dynamics of complex systems, and present some analytical insights into their critical behaviour. These concern in particular the role of infrared divergences which show up in a self-consistent resummation of perturbation theory (mode-coupling approximation), and their effects on critical exponents obtained in earlier work.     

Rotational analysis of the 0–9, 0–10 and 0–11 bands of theA 2II u -X 2II g band system of (16O18O)+

High-resolution spectra of the 0–9, 0–10 and 0–11 bands of theA ²II _u —X ²II _g system of (¹⁶O¹⁸O)⁺ ion have been studied for their rotational structure. This study enables a direct determination of the Λ-doubling parameters of theA ²II _u andX ²II _g states. The model of ‘pure precession’ explains, though not entirely, the Λ-doubling of theX ²II _a state as arising out of its interaction with theB ² Σ _g ⁻ state. The Λ-doubling in theA ²II _u state was found insignificant.