Structural dependence of exciton in carbon nanotubes

The binding energies and sizes of excitons, and energy splitting of the bright-dark excitons in single-walled carbon nanotubes have been calculated using the nonorthogonal tight-binding model, supplemented by the long-range Coulomb interaction. It is found that the binding energies and the sizes of excitons not only depend on tube's diameter d, but also its chirality. However, the splitting of the bright-dark excitons mostly depends on 1/d². Our obtained results show that the curvature effect is very important for the exciton excitations in the SWNTs, especially in the smaller diameter ones.     

Variational calculations of ionized-donor-bound excitons in GaAs-Al x Ga 1 - x As quantum wells

Using a two-parameter wave function, we calculate variationally the binding energy of an exciton bound to an ionized donor impurity (D^+,X) in GaAs-Al_xGa_1-xAs quantum wells for the values of the well width from 10 to 300 ?, when the dopant is located in the center of the well and at the edge of the well. The theoretical results confirm that the previous experimental speculation proposed by Reynolds et al. [Phys. Rev. B 40, 6210 (1989)] is the binding energy of D^+,X for the dopant at the edge of the well. In addition, we also calculate the center-of-mass wave function of the exciton and the average interparticle distances. The results are discussed in detail. Received 17 July 2000 and Received in final form 13 November 2000     

ANTI-PERIODIC BOUNDARY VALUE PROBLEM FOR FIRST ORDER DELAY DIFFERENTIAL EQUATIONS

The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results on the existence and uniqueness of the solution for anti-periodic boundary value problem of delay differential equations.     

Coupling effect of surface plasmon polaritons in single-negative lamellar heterostructure

Propagation characteristics of surface plasmon polaritons (SPPs) in the lamellar heterostructure, which is actually a SPP waveguide array, constructed by two kinds of single negative (SNG) material layers stacked alternatively are investigated. Based on the finite element method (FEM), the negative-refraction (NR) property is demonstrated when the electromagnetic wave penetrates through free space into such SNG lamellar structure. A clear view of the underlying physics of NR is presented qualitatively that is mainly related to the coupled SPPs. The strong coupling effect leads to the novel SPP dispersion curves and then the anomalous propagation characteristics.     

Frontier orbitals analysis and density-functional energetics for metal-substituted fullerene C58Fe2

The formation mechanism, geometric structures, and electronic properties of a metal-substituted fullerene C₅₈Fe₂ have been studied using frontier orbital theory (FOT) and density functional theory (DFT). FOT predicts that two Fe atoms prefer to substitute the two carbons of a [6,6] double bond of C₆₀ yielding a structure denoted as C₅₈Fe₂-3, which is different from the two equivalent substitution sites, i.e., the sites on the opposite of C₆₀ cage or in the nearest neighboring sites of a pentagonal ring for C₅₈X₂ (X=N and B), and also different from the cross sites of a hexagonal ring for C₅₈Si₂. Five possible structures of C₅₈Fe₂ are optimized using DFT to see whether FOT works. The DFT calculations support the prediction of FOT. The Mulliken charge of Fe atom in C₅₈Fe₂-3 shows that the two Fe atoms of C₅₈Fe₂-3 lose 0.70 electron to the carbons of the cage, and the net spin populations of Fe atom indicate that each Fe atom has 1.11 μ_B magnetic moments, while each of the four nearest neighboring carbons has magnetic moments. Thus, the two Fe atoms have ferromagnetic interaction with each other, and have weak antiferromagnetic interaction with their four nearest neighboring carbons, leaving 2.0 μ_B magnetic moments for the molecule.     

Remarks on some families of fractional-order differential equations

The main purpose of this note is to draw the reader's attention towards some errors and omissions in a recent work involving solutions of some families of fractional-order differential equations, which was published in this Journal (see, for details, [Tomovski ?, Hilfer R, Srivastava HM. Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions. Integral Transforms Spec Funct. 2010;21:797–814]). Several relevant remarks and observations on some other related recent developments on this subject are also presented.     

Preparation, magnetoresistance and magnetocaloric effect of two-layered perovskite La 2.5- x K 0.5+ x Mn 2 O 7+δ

Polycrystalline two-layered perovskite La_2.5-xK_0.5+xMn₂O _{7 + δ} (0 < x < 0.5) samples have been prepared by a modified sol-gel method and their magnetoresistance and magnetocaloric effects have been studied. A large deviation between the metal-insulator (MI) transition temperature (T _ρ ) and the magnetic transition temperature (T_C) is observed. Large magnetoresistance (MR) effects with Δρ/ρ of ∼40% at 12 kOe are obtained in wide temperature ranges. The maximum of the magnetic entropy change peaks at its Curie temperature (T_C), far above its MI transition temperature (T _ρ ). The large magnetic entropy change (∼1.4 J/kg.K) is obtained in the sample La_2.5-xK_0.5+xMn₂O _{7 + δ} (x = 0.35) upon 10 kOe applied magnetic field. Received 2 May 2002 / Received in final form 1st October 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: wzhong@ufp.nju.edu.cn     

Local field dynamics in a resonant quantum tunneling system of magnetic molecules

We observed non-exponential relaxation for a quantum tunneling molecular magnetic system at very low temperatures and argue that it results from evolving intermolecular dipole fields. At the very beginning of the relaxation, the magnetization follows a square-root time dependence. A simple model is developed for the intermediate time range that is in good agreement with the data over 4 decades in time. Detailed numerical calculations as well as measurements are presented which indicate unusual correlation effects in these systems. Received: 15 May 1998 / Revised: 10 July 1998 / Accepted: 11 July 1998     

Sound scattering from partially water-filled elastic spherical shell with an internal elastic plate

According to the equation of motion in the elastic medium and integral equation of target scattering, the sound scattering from the partially water-filled elastic spherical shells with and without an inner plate is studied using the finite element and boundary element method, and the scattering normalized form functions of the shell filled with different volume of water are computed and the mechanism of resonance scattering is analyzed. The results show that the resonance of the shell with partially water-filled and without the plate is mainly related to the volume of water, and the resonance is produced by inner water and the spherical shell. The resonance characteristics of partially water-filled elastic shell with the plate are similar to that of empty structured elastic spherical shell, and the sound field in inner water is weaker which indicates the main resonance characteristics are decided by spherical shell and the plate. In addition, the scattering characteristics of spherical shell with plate and one side full water-filled are greatly different from the partially water-filled ones.