Existence of a homoclinic point for the Hénon map

We prove analytically that for the Hénon map of the plane into itself (s, t)(t+1–1.4a ², 0.3s), there exists a transversal homoclinic point.     

Conditions for thermal stabilization of the superconductor’s critical state

Conditions for thermal stabilization of the electrodynamic states of a superconductor are studied. The macroscopic states are simulated in the nonisothermal approximation by numerically solving a set of the Fourier and Maxwell equations with the magnetic flux penetration boundary unknown. Stability criteria for the critical state described by the viscous flow model are formulated. The results are compared with those following from the isothermal theory. It is shown that errors inherent in the isothermal approximation are significant for a thermally insulated superconductor. Therefore, the well-known adiabatic criterion of stability formulated in the isothermal approximation limits the domain of stable states, since a correct determination of conditions for the superconducting-normal state transition must take into account the thermal history of the stable superconducting state formation. On the whole, the error of loss calculation in the isothermal approximation increases when the heat transfer coefficient decreases or an external magnetic field sweep and the size of the superconductor’s cross section increases. On the other hand, nonisothermal stability conditions expand the variety of allowable states, since they include conditions that links the currently developed theory of thermomagnetic instability, the theory of losses, and the theory of a superconductor’s thermal stabilization.     

Experimental determination of the conditions for the transition of Jupiter’s atmosphere to the conducting state

The intensity of optical radiation and resistance of a hydrogen-helium layer with He mass fraction Y=m_He/(m_He+m_H)?0.24, which corresponds to the composition of the outer layers of Jupiter’s atmosphere [2], were simultaneously measured under multiple shock compression up to 164 GPa in plane geometry. The initial pressure and temperature of the mixture were equal to 8 MPa and 77.4 K, respectively, and the velocity of steel strikers was equal to 6.2 km/s. These conditions allowed the generation of the final compressed curve close to the adiabatic states of Jupiter’s atmosphere according to the models proposed in [2, 3]. The conditions for the appearance of the conducting phase in the compression process and the achieved level of electrical conductivity were determined. The experimental data were compared with the one-dimensional fluid-dynamic simulation of the compression process using the equation of state for the mixture in a model similar to the one proposed in [3, 8]. The experimental data were also compared with the behavior of pure components having the same initial density as in the mixture and compressed to the same final pressure.     

Quantum diffusion of light particles in the vortex state of type‐II superconductors

The paper investigates the modification of the quasiparticle excitation spectrum of type‐II superconductors caused by the formation of a flux‐line lattice and its effects on the tunnelling rate of light positively charged interstitial particles. It is shown that near the upper critical field B_c2 the BCS–Gorkov equations predict for the spectral density J(\omega) (giving the probability of an energy exchange \hbar\omega between particle and the electron system) “superohmic” behaviour \propto \omega^3/2 at low frequencies with a prefactor that depends on the position of the tunnelling centre relative to the flux‐line lattice and on the angle between jump vector and the flux‐lines. As in normal‐conducting metals, at higher frequencies J(\omega)=2K_el\omega, is predicted. At low temperatures T the superohmic J(\omega) leads to hopping rates \nu \propto T^-2. At higher temperatures a crossover to the Kondo law ( ) is expected. This revised version was published online in August 2006 with corrections to the Cover Date.     

Singular temperature dependence of the equation of state of superconductors with spin–orbit interaction in the low-temperature region

The equation of state is investigated for a thin superconducting film in a longitudinal magnetic field and with strong spin-orbit interaction at the critical point. As a first step, the state with the maximal value of the magnetic field for a given value of spin–orbit interaction at T = 0 is chosen. This state is investigated in the low-temperature region. The temperature contribution to the equation of state is weakly singular.     

The enhanced volume source boundary point method for the calculation of acoustic radiation problem

The Volume Source Boundary Point Method(VSBPM) is greatly improved so that it will speed up the VSBPM‘s solution of the acoustic radiation problem caused by the vibrating body.The fundamental solution provided by Helmholtz equation is enforced in a weighted residual sense over a tetrahedron located on the normal line of the boundary node to replace the coefficient matrices of the system equation.Through the enhanced volume source boundary point analysis of various examples and the sound field of a vibrating rectangular box in a semi-anechoic chamber,it has revealed that the calculating speed of the EVSBPM is more than 10 times faster than that of the VSBPM while it workss on the aspects of its calculating precision and stability,adaptation to geometric shape of vibrating body as well as its ability to overcome the non-uniqueness problem.     

The effect of the superconducting–normal proximity on the Josephson tunneling of high-Tc superconductors

The Josephson coupling between two identical high-temperature superconductors was studied theoretically based on a superconducting–normal (SN) bilayer model with s+id-wave pairing in the S layer. It is indicated that due to the proximity effect between S and N layers as the interlayer hopping t_⊥ decreases, the product of the tunneling current through the junction and the normal-state resistance of the junction can be substantially reduced from the value described by the Ambegaokar–Baratoff (AB) theory. Our theoretical result is in good agreement with the experiments.     

The ground state of the Frenkel–Kontorova model

The continual approximation of the ground state of the discrete Frenkel–Kontorova model is tested using a symmetric algorithm of numerical simulation. A “kaleidoscope effect” is found, which means that the curves representing the dependences of the relative extension of an N-atom chain vary periodically with increasing N. Stairs of structural transitions for N ? 1 are analyzed by the channel selection method with the approximation N = ∞. Images of commensurable and incommensurable structures are constructed. The commensurable–incommensurable phase transitions are stepwise.     

Magnetization of type-ii superconductors in the range of fields H c 1 ≤ H ≤ H c 2Variational Method

A variational method is proposed to find the magnetic field dependence of the magnetization of type-II superconductors in the mixed state by a self-consistent technique. This model allows for suppression of the order parameter to zero at the centers of Abrikosov vortices and also for the magnetic field dependence of the order parameter. The results can be applied to the entire range of fields H _c 1 ≤ H ≤ H _c 2 for any values of the Ginzburg-Landau parameter $\kappa > 1/\sqrt 2$ . It is shown that in weak fields where κ ? 1 the behavior of the magnetization can be described exactly in the London approximation provided that the correct value of H _c 1 is used. Near the second critical field this dependence shows good agreement with the well-known Abrikosov result. It is also shown that using the concept of isolated vortices and applying the principle of superposition of the fields and currents generated by these vortices to calculate the magnetization gives inaccurate quantitative results even in fairly weak fields. By going beyond these concepts, it was possible to allow more accurately for the influence of the vortex cores on the magnetization behavior in the intermediate range of fields H _c 1 ?H ? H _c 2 and to identify the range of validity of various approximations used widely in the literature.     

The theoretical study on the potential energy curve for X~3△ state of TiO molecule

This paper applies the density functional theory method to optimise the structure for X ³Δ state of TiO molecule with the basis sets 6-31G, 6-31++G and 6-311G^**. Comparing the attained results with the experiments, it obtains the conclusion that the basis set 6-31++G is most suitable for the optimal structure calculations of X ³Δ state of TiO molecule. The whole potential energy curve for the electronic state is further scanned by using B3P86/6-31++G method for the ground state, then it uses a least square fitted to Murrell--Sorbie functions, at last it calculates the spectroscopic constants and force constants, which are in better agreement with the experimental data.     

Probability distribution and Bell’s inequality for the quantum qubit state

The problem of Bell’s inequality violation for a particle with spin 1/2 is studied within the tomographic approach. Two possible methods for constructing the distribution functions associated with the qubit quantum state are presented. The Bell parameter maximum is studied for each proposed distribution.     

Dynamics of the normal–superconductor phase transition and the puzzle of the Meissner effect

The analysis of Pippard (1950) for the growth of the normal phase into the superconducting phase in the presence of a magnetic field H>H_c$H>H_c$ is applied in reverse to the case H<H_c$H<H_c$ (H_c=$H_c=$ critical magnetic field). We carry out the analysis both for a planar and a cylindrical geometry. As the superconducting phase grows into the normal phase, a supercurrent is generated at the superconductor–normal phase boundary that flows in direction opposite to the Faraday electric field resulting from the moving phase boundary. This supercurrent motion is in direction opposite to what is dictated by the Lorentz force on the current carriers, and in addition requires that mechanical momentum of opposite sign be transferred to the system as a whole to ensure momentum conservation. In the cylindrical geometry case, a macroscopic torque of unknown origin acts on the body as a whole as the magnetic field is expelled. We argue that the conventional BCS-London theory of superconductivity cannot explain these facts, and that as a consequence the Meissner effect remains unexplained within the conventional theory of superconductivity. We propose that the Meissner effect can only be understood by assuming that there is motion of charge in direction perpendicular to the normal–superconductor phase boundary and point out that the unconventional theory of hole superconductivity describes this physics.     

Mechanical effects in the n → s transition of work-hardened metal and alloy superconductors

In the superconducting transitions, the dissolution of filamentary forms of intermediate phase, retained at edge-type dislocations to temperatures somewhat below (ns) and above (sn) the critical temperature, induces (+ or –) thermal spikes at the dislocation cores. In a recent model, these have been shown to trigger transients in creep, and to give rise to yield-point effects in tensile tests, such as are observed in the ns transition in metals and undeformed alloys. The model is now extended to cover corresponding observations in type I work-hardened metal and alloy superconductors.     

The MACQM Calculation for the BInding Energy of the Equilateral Triangle Structure of H3^— Cluster

Considering that the equilateral triangle structure of H3^- cluster can be formed from the interaction of H^- with two hydrogen atoms,a modified arrangement channel quantum mechanics method has been used to calculate the total energy curve for this structure,The result shows that the cureve has a minimal energy-1.6672 a.u.at an internuclear distance of 1.77a0,so its dissociation energy(binding energy)is D(H^- H H)=0.1395,a.u.This means that the cluster H3^- may be formed in an equilateral triangle structure with a bond length of 1.77α0.     

Calculation of the lowest 1 S resonance state of the H− anion by the stabilization method

By the example of the lowest resonance state of the H^? system, two versions of the stabilization method are considered: with introduction of an external potential into the Hamiltonian and with enlargement of the single-particle function basis. A comparison of the results suggests the possibility of applying these methods to calculating the resonance parameters in many-electron systems.