The magnetic properties of one-dimensional spin-1 ferromagnetic Heisenberg model in a magnetic field within Callen approximation

The effect of magnetic field h on the magnetic properties of the one-dimensional spin-1 ferromagnetic Heisenberg model is studied by the double-time Green’s function method. The magnetization and susceptibility are obtained within the Callen approximation. The zero-field susceptibility is as a decreasing function of the temperature T. The magnetization m increases in the whole field region, but the susceptibility maximum χ(T_m) decreases. The position T_m of the susceptibility maximum is both solved analytically and fits well to be a power law T_m∼h^γ at low fields and to be linear increasing at high fields. The height χ(T_m) decreases as a power law χ(T_m)∼h^−β with h increasing. The exponents (γ,β) obtained in our results agree with the other theoretical results. Our results are roughly in agreement with the results obtained in the experiment of Ni(OH)(NO₃)H₂O.     

Effects of doping on the surface energies of nanocrystals and evidence from studies at high pressure

Zn_1−XMn_XS (X=0.85% and 1.26%) nanoparticles have been synthesized using a specially designed equipment and we have studied the influence of doping Mn²⁺ on the surface energy of ZnS. The high pressure behaviors of ZnS nanocrystals with different dopant contents have been investigated using angle-dispersive synchrotron X-ray powder diffraction up to 45.1 GPa. Theoretical calculations show that doping with Mn²⁺ increases the surface energy of the nanocrystals. The theoretical result has been further corroborated by our experimental observation of an increase in the phase transition pressure of Mn²⁺ doped ZnS nanocrystals in diamond-anvil-cell studies.     

Freudenthal duality and generalized special geometry

Freudenthal duality, introduced in Borsten et al. (2009) [1] and defined as an anti-involution on the dyonic charge vector in d=4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential.Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N>2 supergravities, as well as N=2 generic special geometry, not necessarily having a coset space structure.     

Study of high-coercivity sintered NdFeB magnets

Magnetic powders for sintered NdFeB magnets have been prepared by using an advanced processing method including strip casting, hydrogen decrepitation, jet milling and rubber isotropic press. The effects of Dy, Ga and Co addition on the microstructure and magnetic properties of sintered magnets have been investigated. By adopting a suitable component ratio and adjusting proper technological parameters, we have prepared high-coercivity sintered NdFeB magnets with hard magnetic properties of _jH_c=25.6 kOe, B_r=13.2 kG and (BH)_max=39.9 MGOe. The temperature coefficient of coercivity of the magnets (between 20 and 150 °C) is –0.53%/°C. The magnetic properties at high temperature satisfy the needs of permanent magnet motors.     

An orbifold relative index theorem

In this paper we prove a relative index theorem for pairs of generalized Dirac operators on orbifolds which are the same at infinity. This generalizes to orbifolds a celebrated theorem of Gromov and Lawson.     

Dijkgraaf–Witten invariants of surfaces and projective representations of groups

We compute the Dijkgraaf–Witten invariants of surfaces in terms of projective representations of groups. As an application we prove that the complex Dijkgraaf–Witten invariants of surfaces of positive genus are positive integers.     

Finite-gap Solutions of the Fuchsian Equations

We find a new class of Fuchsian equations, with algebro-geometric solutions associated to a hyperelliptic curve. A method for calculating its arithmetic genus and branching points is suggested. Numerous examples are given.     

Spin-glass behavior and magnetocaloric effect in melt-spun TbCuAl alloys

Magnetic properties and magnetocaloric effects of amorphous and crystalline TbCuAl ribbons are investigated by measuring their ac susceptibilities including a nonlinear term and dc magnetizations. The in-phase third harmonic ac susceptibility is found to be negative. It can be well fitted by the expression at high temperatures, indicating a spin-glass behavior in amorphous TbCuAl alloy. ΔT_f(ω)/[T_f(ω)Δlog₁₀ω], a possible distinguishing criterion to judge the presence of a spin-glass behavior is ∼0.011. The frequency-dependent data can be well fitted by the conventional critical slowing down law and the spin-glass transition temperature is obtained to be 20.1 K. The maximum of magnetic entropy change reaches 4.5 J kg⁻¹ K⁻¹ for a field change of 0-50 000 Oe, while the crystalline TbCuAl compound experiences a simple ferromagnetic-to-paramagnetic phase transition. The peak value of magnetic entropy change is obtained at the Curie temperature and reaches 14.4 J kg⁻¹ K⁻¹ for the same field change, which is much larger than that of amorphous TbCuAl alloy.     

Fractal localized structures related to Jacobian elliptic functions in the higher-order Broer－Kaup system

This work reveals a novel phenomenon—that the localized coherent structures of a (2﹢1)﹣dimensional physical model possesses fractal behaviours. To clarify the interesting phenomenon, we take the (2﹢1)﹣dimensional higher-order Broer－Kaup system as a concrete example. Starting from a B?cklund transformation, we obtain a linear equation, and then a general solution of the system is derived. From this some special localized excitations with fractal behaviours are obtained by introducing some types of lower-dimensional fractal patterns that related to Jacobian elliptic functions.     

Numerical study of nonlinear Schrödinger and coupled Schrödinger equations by differential transformation method

This paper presents the coupled version of a previous work on nonlinear Schrödinger equation [23]. It focuses on the construction of approximate solutions of nonlinear Schrödinger equations. In this paper, we applied the differential transformation method (DTM) to solving coupled Schrödinger equations. The obtained results show that the technique suggested here is accurate and easy to apply.