The effect of the biquadratic exchange interaction on the curie temperature of the mixed ising ferromagnet

For the mixed Ising ferromagnet with S = 1 and $\text{S =}\text{1}\text{2}$, the effect of the biquadratic exchange interaction J′ on the Curie temperature has been calculated by the use of the Bethe-Peierls approximation and its effect is shown to be large for J′ > 0.     

Ordered spin structure of FeI2

The antiferromagnetic spin structure found in FeI₂ is investigated theoretically. Up to the third neighbor exchange interactions are necessary to explain the structure of the hexagonal layer and the relations among the interaction constants are derived.     

Pseudo duality in mathematical programming: Unconstrained problems and problems with equality constraints

In this work non-convex programs are analyzed via Legendre transform. The first part includes definitions and the classification of programs that can be handled by the transformation. It is shown that differentiable functions that are represented as a sum of strictly concave and convex functions belong to this class. Conditions under which a function may have such representation are given. Pseudo duality is defined and the pseudo duality theorem for non linear programs with equality constraints is proved.The techniques described are constructive ones, and they enable tocalculate explicitly a pseudo dual once the primal program is given. Several examples are included. In the convex case these techniques enable the explicit calculation of the dual even in cases where direct calculation was not possible.     

A graphical method for a closer study of Richardson's annular effect

Zusammenfassung Ein polares Vektordiagramm ermöglicht eine genauere Studie der Geschwindigkeitsverteilung in Flüssigkeitssäulen kreisrunden Querschnitts, die in laminarem Regime schwingen. Die Kennzahl dient hierbei als Parameter. Kleine Werte vonz haben nur geringen Einfluss auf die Verteilung der Geschwindigkeitsamplituden, führen dagegen schon zu beträchtlichen Voreilwinkeln der Phasenverschiebung, die beiz6,1 einen oberen Grenzwert von 51,8° erreichen, um dann gegen den asymptotischen Endwert von 45° wieder abzunehmen. Die übliche Charakterisierung des Richardsonschen Annulareffekts durch ein Maximum der Amplituden ausserhalb der Achse und durchgängige Phasenvoreilung gegenüber der Geschwindigkeit in der Achse, mit einem Maximum an der Wand, erweist sich als Annäherung. Theoretisch weisen die Verteilungskurven, sowohl der Amplituden als auch der Phasenwinkel bei genügend grossen Werten vonz noch weitere Halbwellen abwechselnden Vorzeichens auf. Die Amplituden dieser Welligkeit sind jedoch so klein, dass die Möglichkeit ihres direkten experimentellen Nachweises zweifelhaft erscheint.     

The magnetic susceptibility of spin-one Ising and Heisenberg ferromagnets with biquadratic exchange and uniaxial anisotropy

For spin-one Ising and Heisenberg ferromagnets with biquadratic exchange interaction J' and uniaxial anisotropy D, the magnetic susceptibility has been calculated by the use of the pair model approximation and its dependences on J' and D are discussed in comparative way.     

Effects of the uniaxial anisotropy on the Curie temperature of the anisotropic Heisenberg ferromagnet with mixed spins S = 12 and S = 1

With the use of the pair model approximation, the effects of the D-term on the Curie temperature of the anisotropic Heisenberg ferromagnet with mixed spins $\text{S =}\text{1}\text{2}$ have been investigated and shown to be significant for D > 0.     

Binary neutron stars: Equilibrium models beyond spatial conformal flatness

Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: the full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the 4-metric and an extrinsic curvature whose time derivative vanishes in a comoving frame. Two independent numerical codes are developed, and solution sequences that model inspiraling binary neutron stars during the final several orbits are successfully computed. The binding energy of the system near its final orbit deviates from earlier results of third post-Newtonian and of spatially conformally flat calculations. The new solutions may serve as initial data for merger simulations and as members of quasiequilibrium sequences to generate gravitational-wave templates, and may improve estimates of the gravitational-wave cutoff frequency set by the last inspiral orbit.     

An efficiency measurement framework for multi-stage production systems

We develop an efficiency measurement framework for systems composed of two subsystems arranged in series that simultaneously computes the efficiency of the aggregate system and each subsystem. Our approach expands the technology sets of each subsystem by allowing each to acquire resources from the other in exchange for delivery of the appropriate (intermediate or final) product, and to form composites from both subsystems. Managers of each subsystem will not agree to ‘`vertical integration’' initiatives unless each subsystem will be more efficient than what each can achieve by separately applying conventional efficiency analysis. A Pareto Efficient frontier characterizes the acceptable set of efficiencies of each subsystem from which the managers will negotiate to select the final outcome. Three proposals for the choice for the Pareto efficient point are discussed: the one that achieves the largest equiproportionate reduction in the classical efficiencies; the one that achieves the largest equal reduction in efficiency; and the one that maximizes the radial contraction in the aggregate consumption of resources originally employed before integration. We show how each choice for the Pareto efficient point determines a derived measure of aggregate efficiency. An extensive numerical example is used to illustrate exactly how the 2 subsystems can significantly improve their operational efficiencies via integration beyond what would be predicted by conventional analysis.     

Effects of biquadratic-exchange in antiferromagnets

The effects of the biquadratic-exchange interaction on magnetic specific heat and sublattice magnetization are studied for antiferromagnets. At the critical ratio of the biquadratic-exchange to the Heisenberg interaction, the spin structure changes abruptly and magnetic properties are affected significantly.     

Magnetic specific heat of the honeycomb lattice of spin one-half with anisotropic Heisenberg exchange by a new method

The magnetic specific heat of the honeycomb lattice of $\text{S =}\text{1}\text{2}$ Heisenberg spin with anisotropic exchange is calculated by using the new approximation method reported in a previous paper. In the spin system with the anisotropy parameter |γ|<1 (Ising-Heisenberg system), the specific heat shows a similar divergence as that of the pure Ising spin system, namely a logarithmic divergence at the critical temperature. The same approximation is also applied to the spin system with |γ|>1 (Heisenberg XY system), showing a divergence of the same kind.