Brake Orbits of First Order Convex Hamiltonian Systems with Particular Anisotropic Growth

Combining the dual least action principle with Mountain-pass lemma,we obtain the existence of brake orbits for first-order convex Hamiltonian systems with particular anisotropic growth.     

Carlsson's rank conjecture and a conjecture on square-zero upper triangular matrices

Let k be an algebraically closed field and A the polynomial algebra in r variables with coefficients in k. In case the characteristic of k is 2, Carlsson [9] conjectured that for any DG-A-module M of dimension N as a free A-module, if the homology of M is nontrivial and finite dimensional as a k-vector space, then $2^r\le N$. Here we state a stronger conjecture about varieties of square-zero upper triangular $N\times N$ matrices with entries in A. Using stratifications of these varieties via Borel orbits, we show that the stronger conjecture holds when $N<8$ or $r<3$ without any restriction on the characteristic of k. As a consequence, we obtain a new proof for many of the known cases of Carlsson's conjecture and give new results when $N>4$ and $r=2$.     

Periodic,breather and rogue wave solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid dynamics

Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Periodic wave solutions are constructed by virtue of the Hirota–Riemann method. Based on the extended homoclinic test approach, breather and rogue wave solutions are obtained. Moreover, through the symbolic computation, the relationship between the one-periodic wave solutions and one-soliton solutions has been analytically discussed, and it is shown that the one-periodic wave solutions approach the one-soliton solutions when the amplitude $\eta \to 0$.     

Generic diffeomorphisms with measure-expansive homoclinic classes

We prove that for C¹ generic diffeomorphisms, every measure-expansive locally maximal homoclinic class is hyperbolic.     

Sensitivity analysis for a type of statically stable sailcrafts

Two types of sensitivities are proposed for statically stable sailcrafts.One type is the sensitivities of solar-radiation-pressure force with respect to position of the center of mass,and the other type is the sensitivities of solar-radiation-pressure force with respect to attitude.The two types of sensitivities represent how the solar-radiationpressure force changes with the position of mass center and the attitude.Sailcrafts with larger sensitivities undergo larger error of the solar-radiation-pressure force,leading to larger orbit error,as demonstrated by simulation.Then as a case study,detailed formulas are derived to calculate the sensitivities for sailcrafts with four triangular sails.According to these formulas,in order to reduce both types of sensitivities,the angle between opposed sails should not be too large,and the center of mass should be as close to the axis of symmetry of the four sails as possible and as far away from the center of pressure of the sailcraft as possible.     

Electron transport of a quantum wire with spatially periodic spin–orbit coupling

Electron transport properties of an ideal one-dimensional (1D) quantum wire are studied including spatially periodic Rashba spin–orbit coupling (SOC) and Dresselhaus SOC. By comparing with the previous work [S.J. Gong, Z.Q. Yang, J. Phys. Condens. Matter 19 (2007) 446209], two transmission gaps appear in the transmission probability of electrons and their widths are also broadened dramatically. Moreover, it is found that their widths are sensitive not only to the strength of SOCs but also to the length ratio of SOCs segment and non-SOCs segment. In addition, a ‘circle-type’ transmission behavior has been found by tuning the strength of SOCs continuously. Our results may extend the previous work and provide an more effective method to manipulate the current in nanoelectric devices.     

Application of the multireference equation of motion coupled cluster method,including spin–orbit coupling,to the atomic spectra of Cr,Mn, Fe and Co

The recently introduced multireference equation of motion (MR-EOM) approach is combined with a simple treatment of spin–orbit coupling, as implemented in the ORCA program. The resulting multireference equation of motion spin–orbit coupling (MR-EOM-SOC) approach is applied to the first-row transition metal atoms Cr, Mn, Fe and Co, for which experimental data are readily available. Using the MR-EOM-SOC approach, the splittings in each L-S multiplet can be accurately assessed (root mean square (RMS) errors of about 70 cm^?1). The RMS errors for J-specific excitation energies range from 414 to 783 cm^?1 and are comparable to previously reported J-averaged MR-EOM results using the ACESII program. The MR-EOM approach is highly efficient. A typical MR-EOM calculation of a full spin–orbit spectrum takes about 2 CPU hours on a single processor of a 12-core node, consisting of Intel XEON 2.93 GHz CPUs with 12.3 MB of shared cache memory.     

Theoretical study of electronic structure of rhodium mononitride and interpretation of experimental spectra

Potential energy curves of 22 electronic states of RhN have been calculated by the complete active space second‐order perturbation theory method. The X¹Σ₀⁺ is assigned as the ground state, and the first excited state a³Π₀+ is 978 cm^?1 higher. The ¹Δ(I) and B¹Σ⁺ states are located at 9521 and 13,046 cm^?1 above the ground state, respectively. The B¹Σ⁺ state should be the excited state located 12,300 cm^?1 above the ground state in the experimental study. Moreover, two excited states, C¹Π and b³Σ⁺, are found 14,963 and 15,082 cm^?1 above the X¹Σ⁺ state, respectively. The transition C¹Π₁–X¹Σ₀⁺ may contribute to the experimentally observed bands headed at 15,071 cm^?1. There are two excited states, D¹Δ and E¹Σ⁺, situate at 20,715 and 23,145 cm^?1 above the X¹Σ⁺ state. The visible bands near 20,000 cm^?1 could be generated by the electronic transitions D¹Δ₂–a³Π₁ and E¹Σ⁺₀–X¹Σ⁺₀ because of the spin–orbit coupling effect. © 2013 Wiley Periodicals, Inc.