Relations Between Helicity Coupling Amplitude and L—S Coupling Amplitude

Relations between helicity coupling amplitude and L-S coupling amplitude are discussed.The equivalence condition for these two kinematic analysis methods and the limitations of the L-S coupling amplitude are also studied in this paper.     

Correlation Renormalized and Induced Spin-Orbit Coupling

Interplay of spin-orbit coupling(SOC) and electron correlation generates a bunch of emergent quantum phases and transitions, especially topological insulators and topological transitions. We find that electron correlation will induce extra large SOC in multi-orbital systems under atomic SOC and change ground state topological properties. Using the Hartree–Fock mean field theory, phase diagrams of px/py orbital ionic Hubbard model on honeycomb lattice are well studied. In general, correction of s...     

Non-Local Coupling and Partial Synchronization in Chaotic Systems

Partial synchronization （PaS） on regular networks with a few non-local couplings are studied. The criterion that PaS can emerge in any given network and some relevant phenomena about Lyapunov exponents are found. Theoretical and numerical analysis show that the non-local coupling is the key mechanism of the emergence of PaS.     

Exchange Coupling and Stability of SmCo7-xHfx

Electronic structure of SmCo7-xHfx compound is calculated by using the multi-scattering Xα method. It is shown that a few of electrons can transfer to the Sm 5d orbital due to orbital hybridization between Sm and Co atoms. The 3d-5d coupling is stronger, which is the main reason to result in the long-range ferromagnetic order between Sm and Co atoms in SmCo7-xHfx. According to the Stoner criterion, the result of spin-unpolarized calculation for the Sm5Co32Hf2 duster could lead to a better understanding of why the ferromagnetic SmCo7-xHfx is a stable phase. For the Sm5Co32Hf2 duster the Fermi level is situated at the overall maximum of the density of states. Moreover the duster wavefunctions at EF are antibonding and hence highly localized in real space, which would lead to a large value for the duster Stoner integral. Thus a rationalization for the magnetic stability of SmCo7-xHfx has been obtained.     

Investigation and Modification of Coupling of Photonic Crystal Defects

We investigate the coupling of photonic crystal (PC) defects by using coupled-mode theory. The PC molecules formed by the coupling of two identical PC atoms are the focus of our study. It is revealed that the flatness of the transmission spectra of the PC molecules is determined uniquely by the phase shift of the travelling wave between the two coupled PC atoms. By properly adjusting the distance between the two constitutional PC atoms, we are able to modify the transmission spectrum of the resulting PC molecule. Theoretical analyses based on the coupled-mode theory are in good agreement with the simulation results obtained by the transfer matrix method and the finite-difference time-domain technique.     

Effects of Inhomogeneous Spin Coupling and Anisotropy on Thermal Entanglement

We study the thermal entanglement properties of a simple system that includes three spins inhomogeneously coupled between them with additional anisotropy in their couplings. The main result is the systematic analysis of the concurrence evolution as functions of inhomogeneity, anisotropy and temperature. By adjusting proportional factor of the interaction J and anisotropy parameter △, the comparison between concurrences C₁₂ andC₁₃ is also presented.     

Cosmological Models with Time Dependent G and Λ Coupling Scalars

A cosmological model in which the universe has its critical density and gravitational constants generalized as coupling scalars in Einstein's theory is considered. A general method of solving the field equations is given. An exact solution for matter distribution in cosmological models satisfying G=G₀(R/R₀)ⁿ is presented. Corresponding physical interpretations of the cosmological solutions are also discussed.     

Coupling of two-dimensional atomistic and continuum models for dynamic crack

A concurrent multiscale method of coupling atomistic and continuum models is presented in the two-dimensional system. The atomistic region is governed by molecular dynamics while the continuum region is represented by construct- ing the mass and stiffness matrix dependent on the coarsening of the grids, which ensures that they merge seamlessly. The low-pass phonon filter embedded in the handshaking region is utilized to effectively eliminate the spurious reflection of high-frequency phonons, while keeping the low-frequency phonons transparent. These schemes are demonstrated by numerically calculating the reflection and transmission coefficient, and by the further application of dynamic crack propa- gation subjected to mode-I tensile loading.     

Generalized Multi-component TC Hierarchy and Its Multi-component Integrable Coupling System

A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra X is presented. Based on the FM, the multi-component integrable coupling system of the generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach.     

Coupling and degenerating modes in longitudinal–torsional step horns

Longitudinal–torsional vibration is used and proposed for a variety of ultrasonic applications including motors, welding, and rock-cutting. To obtain this behavior in an ultrasonic step horn one can either, (i) couple the longitudinal and torsional modes of the horn by incorporating a ring of diagonal slits in the thick base section or, (ii) place helical flutes in the thin stem section to degenerate the longitudinal mode into a modified behavior with a longitudinal–torsional motion. This paper compares the efficacy of these two design approaches using both numerical and experimental techniques.     

Electron—Phonon Coupling in Anion Metallic Solids and Superconducting MgB2

We analyse the Hopfield factor of the newly found superconductor MgB2 using the linear muffin-tin orbital method.Based on a uniform transferred charge density model raised,it is shown from our calculation that the high difference of electronegativity between boron and magnesium favours the high l(l 1) angular momentum hybridization and then the Hopfield factor.Our analysis is consistent with experimental results.Comparisons with cuprate superconductors are also discussed.     

Coupling between velocity and interface perturbations in cylindrical Rayleigh–Taylor instability

Rayleigh–Taylor instability(RTI) in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear(WN) model. When the initial velocity perturbation is comparable to the interface perturbation, the coupling between them plays a significant role. The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small. The effects of the mode number on the first three harmonics are discussed respectively. The low-mode number perturbation leads to large amplitudes of RTI growth. The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly. When the mode number of the perturbation is large enough,the WN results in planar geometry are recovered.     

Competition between Stepwise Polarization Switching and Chirality Coupling in Ferroelectric GeS Nanotubes

Ferroelectricity of group-Ⅳ chalcogenides MX(M = Ge,Sn;X = Se,S) monolayers has been extensively investigated.However,how the ferroelectricity evolves in their one-dimensional nanotubes remains largely unclear.Employing an accurate deep-learning interatomic potential of first-principles precision,we uncover a general stepwise mechanism for polarization switching in zigzag and chiral Ge S nanotubes,which has an energy barrier that is substantially lower than the one associated with the convention...     

On the Coupling of φ Meson to Nucleons and Backward φ Production

Some analyses of the electromagnetic form factors of the nucleon and some analyses of the nucleon-nucleon potential favor a large coupling of the φ meson to nucleons. This is frequently quoted by advocates of a large ss component of the nucleon. It is shown that such large OZI-violating couplings are incompatible with data on φ production in backward direction via nucleon exchange.     

（2＋2）-Dimensional Discrete Soliton Equations and Integrable Coupling System

In this paper, we extend a （2＋2）-dimensional continuous zero curvature equation to （2＋2）-dimensional discrete zero curvature equation, then a new （2＋2）-dimensional cubic Volterra lattice hierarchy is obtained. Fhrthermore, the integrable coupling systems of the （2＋2）-dimensional cubic Volterra lattice hierarchy and the generalized Toda lattice soliton equations are presented by using a Lie algebraic system sl（4）.     

Transitions in a Logistic Growth Model Induced by Noise Coupling and Noise Color

With unified colored noise approximation, the logistic growth model is used to analyze cancer cell population when colored noise is included. It is found that both the coupling between noise terms and the noise color can induce continuous first-order-like and re-entrance-like phase transitions in the system. The coupling and the noise color can also increase tumor cell growth for small number of cell mass and repress tumor cell growth for large number of cell mass. It is shown that the approximate analytic expressions are consistent with the numerical simulations.     

Critical Coupling Constants and Eigenvalue Asymptotics of Perturbed Periodic Sturm–Liouville Operators

Perturbations of asymptotic decay c/r ² arise in the partial-wave analysis of rotationally symmetric partial differential operators. We show that for each end-point λ₀ of the spectral bands of a perturbed periodic Sturm–Liouville operator, there is a critical coupling constant c _crit such that eigenvalues in the spectral gap accumulate at λ₀ if and only if c/c _crit>1. The oscillation theoretic method used in the proof also yields the asymptotic distribution of the eigenvalues near λ₀. Received: 23 September 1999 / Accepted: 21 December 1999