Large transverse field tunnel splittings in the Fe_8 spin Hamiltonian

The spin Hamiltonian that describes the molecular magnet Fe$_8$ has biaxial symmetry with mutually perpendicular easy, medium, and hard magnetic axes. Previous calculations of the ground state tunnel splittings in the presence of a magnetic field along the hard axis are extended, and the meaning of the previously discovered oscillation of this splitting is further clarified

Diabolical points in the magnetic spectrum of Fe_8 molecules

The magnetic molecule Fe_8 has been predicted and observed to have a rich pattern of degeneracies in its spectrum as an external magnetic field is varied. These degeneracies have now been recognized to be diabolical points. This paper analyzes the diabolicity and all essential properties of this system using elementary perturbation theory. A variety of arguments is gievn to suggest that an earlier semiclassical result for a subset of these points may be exactly true for arbitrary spinComment: uses europhys.sty package; 3 embedded ps figure

Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach

Certain spin Hamiltonians that give rise to tunnel splittings that are viewed in terms of interfering instanton trajectories, are restudied using a discrete WKB method, that is more elementary, and also yields wavefunctions and preexponential factors for the splittings. A novel turning point inside the classically forbidden region is analysed, and a general formula is obtained for the splittings. The result is appled to the \Fe8 system. A previous result for the oscillation of the ground state splitting with external magnetic field is extended to higher levels.Comment: RevTex, one ps figur

Integrated flight/propulsion control design for a STOVL aircraft using H-infinity control design techniques

Results are presented from an application of H-infinity control design methodology to a centralized integrated flight propulsion control (IFPC) system design for a supersonic Short Takeoff and Vertical Landing (STOVL) fighter aircraft in transition flight. The emphasis is on formulating the H-infinity control design problem such that the resulting controller provides robustness to modeling uncertainties and model parameter variations with flight condition. Experience gained from a preliminary H-infinity based IFPC design study performed earlier is used as the basis to formulate the robust H-infinity control design problem and improve upon the previous design. Detailed evaluation results are presented for a reduced order controller obtained from the improved H-infinity control design showing that the control design meets the specified nominal performance objectives as well as provides stability robustness for variations in plant system dynamics with changes in aircraft trim speed within the transition flight envelope. A controller scheduling technique which accounts for changes in plant control effectiveness with variation in trim conditions is developed and off design model performance results are presented

A modified approach to controller partitioning

The idea of computing a decentralized control law for the integrated flight/propulsion control of an aircraft by partitioning a given centralized controller is investigated. An existing controller partitioning methodology is described, and a modified approach is proposed with the objective of simplifying the associated controller approximation problem. Under the existing approach, the decentralized control structure is a variable in the partitioning process; by contrast, the modified approach assumes that the structure is fixed a priori. Hence, the centralized controller design may take the decentralized control structure into account. Specifically, the centralized controller may be designed to include all the same inputs and outputs as the decentralized controller; then, the two controllers may be compared directly, simplifying the partitioning process considerably. Following the modified approach, a centralized controller is designed for an example aircraft mode. The design includes all the inputs and outputs to be used in a specified decentralized control structure. However, it is shown that the resulting centralized controller is not well suited for approximation by a decentralized controller of the given structure. The results indicate that it is not practical in general to cast the controller partitioning problem as a direct controller approximation problem

Quenched Spin Tunneling and Diabolical Points in Magnetic Molecules: II. Asymmetric Configurations

The perfect quenching of spin tunneling first predicted for a model with biaxial symmetry, and recently observed in the magnetic molecule Fe_8, is further studied using the discrete phase integral (or Wentzel-Kramers-Brillouin) method. The analysis of the previous paper is extended to the case where the magnetic field has both hard and easy components, so that the Hamiltonian has no obvious symmetry. Herring's formula is now inapplicable, so the problem is solved by finding the wavefunction and using connection formulas at every turning point. A general formula for the energy surface in the vicinity of the diabolo is obtained in this way. This formula gives the tunneling apmplitude between two wells unrelated by symmetry in terms of a small number of action integrals, and appears to be generally valid, even for problems where the recursion contains more than five terms. Explicit results are obtained for the diabolical points in the model for Fe_8. These results exactly parallel the experimental observations. It is found that the leading semiclassical results for the diabolical points appear to be exact, and the points themselves lie on a perfect centered rectangular lattice in the magnetic field space. A variety of evidence in favor of this perfect lattice hypothesis is presented.Comment: Revtex; 4 ps figures; follow up to cond-mat/000311

Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) Instantons

Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the Fe8 molecular solid. It is shown that such paths are essential to a proper understanding of the phenomenon of quenched spin tunneling in these molecules. In the Fe8 problem, such paths are shown to arise as soon as a fourth order anisotropy term in the energy is turned on, making this term a singular perturbation from the semiclassical point of view. The instanton approximation is shown to quantitatively explain the magnetic field dependence of the tunnel splitting, as well as agree with general rules for the number of quenching points allowed for a given value of spin. An accurate approximate formula for the spacing between quenching points is derived

Greedy Algorithms for Steiner Forest

In the Steiner Forest problem, we are given terminal pairs $\{s_i, t_i\}$, and need to find the cheapest subgraph which connects each of the terminal pairs together. In 1991, Agrawal, Klein, and Ravi, and Goemans and Williamson gave primal-dual constant-factor approximation algorithms for this problem; until now, the only constant-factor approximations we know are via linear programming relaxations. We consider the following greedy algorithm: Given terminal pairs in a metric space, call a terminal "active" if its distance to its partner is non-zero. Pick the two closest active terminals (say $s_i, t_j$), set the distance between them to zero, and buy a path connecting them. Recompute the metric, and repeat. Our main result is that this algorithm is a constant-factor approximation. We also use this algorithm to give new, simpler constructions of cost-sharing schemes for Steiner forest. In particular, the first "group-strict" cost-shares for this problem implies a very simple combinatorial sampling-based algorithm for stochastic Steiner forest