Applications of control theory

Applications of control theory are considered in the areas of decoupling and wake steering control of submersibles, a method of electrohydraulic conversion with no moving parts, and socio-economic system modelling

Analysis of OD Flows (Raw Data)

In a recent paper, Structural Analysis of Network Traffic Flows, we analyzed the set of Origin Destination traffic flows from the Sprint-Europe and Abilene backbone networks. This report presents the complete set of results from analyzing data from both networks. The results in this report are specific to the Sprint-1 and Abilene datasets studied in the above paper. The following results are presented here: 1 Rows of Principal Matrix (V) 2 1.1 Sprint-1 Dataset ................................ 2 1.2 Abilene Dataset.................................. 9 2 Set of Eigenflows 14 2.1 Sprint-1 Dataset.................................. 14 2.2 Abilene Dataset................................... 21 3 Classifying Eigenflows 26 3.1 Sprint-1 Dataset.................................. 26 3.2 Abilene Datase.................................... 44Centre National de la Recherche Scientifique (CNRS) France; Sprint Labs; Office of Naval Research (N000140310043); National Science Foundation (ANI-9986397, CCR-0325701

Spin dynamics of quantum and classical Heisenberg dimers

Analytical solutions for the time-dependent autocorrelation function of the classical and quantum mechanical spin dimer with arbitrary spin are presented and compared. For large spin quantum numbers or high temperature the classical and the quantum dimer become more and more similar, yet with the major difference that the quantum autocorrelation function is periodic in time whereas the classical is not.Comment: 10 pages, 4 postscript figures, uses 'epsfig.sty'. Submitted to Physica A. More information available at http://www.physik.uni-osnabrueck.de/makrosysteme

Hamiltonian type Lie bialgebras

We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.Comment: LaTeX, 16 page

Model Exact Low-Lying States and Spin Dynamics in Ferric Wheels; Fe6_6 to Fe12_{12}

Using an efficient numerical scheme that exploits spatial symmetries and spin-parity, we have obtained the exact low-lying eigenstates of exchange Hamiltonians for ferric wheels up to Fe$_{12}$. The largest calculation involves the Fe$_{12}$ ring which spans a Hilbert space dimension of about 145 million for M$_s$=0 subspace. Our calculated gaps from the singlet ground state to the excited triplet state agrees well with the experimentally measured values. Study of the static structure factor shows that the ground state is spontaneously dimerized for ferric wheels. Spin states of ferric wheels can be viewed as quantized states of a rigid rotor with the gap between the ground and the first excited state defining the inverse of moment of inertia. We have studied the quantum dynamics of Fe$_{10}$ as a representative of ferric wheels. We use the low-lying states of Fe$_{10}$ to solve exactly the time-dependent Schr\"odinger equation and find the magnetization of the molecule in the presence of an alternating magnetic field at zero temperature. We observe a nontrivial oscillation of magnetization which is dependent on the amplitude of the {\it ac} field. We have also studied the torque response of Fe$_{12}$ as a function of magnetic field, which clearly shows spin-state crossover.Comment: Revtex, 24 pages, 8 eps figure

Butterfly hysteresis loop at non-zero bias field in antiferromagnetic molecular rings: cooling by adiabatic magnetization

At low temperatures, the magnetization of the molecular ferric wheel NaFe$_6$ exhibits a step at a critical field $B_c$ due to a field-induced level-crossing. By means of high-field torque magnetometry we observed a hysteretic behavior at the level-crossing with a characteristic butterfly shape which is analyzed in terms of a dissipative two-level model. Several unusual features were found. The non-zero bias field of the level-crossing suggests the possibility of cooling by adiabatic magnetization.Comment: 4 pages, 5 figures, REVTEX4, to appear in PR

Lie bialgebras of generalized Witt type

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra $W$ of generalized Witt type, all Lie bialgebras on $W$ are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group $H^1(W,W \otimes W)$ is trivial.Comment: 14 page

Proton NMR for Measuring Quantum-Level Crossing in the Magnetic Molecular Ring Fe10

The proton nuclear spin-lattice relaxation rate 1/T1 has been measured as a function of temperature and magnetic field (up to 15 T) in the molecular magnetic ring Fe10. Striking enhancement of 1/T1 is observed around magnetic field values corresponding to a crossing between the ground state and the excited states of the molecule. We propose that this is due to a cross-relaxation effect between the nuclear Zeeman reservoir and the reservoir of the Zeeman levels of the molecule. This effect provides a powerful tool to investigate quantum dynamical phenomena at level crossing.Comment: Four pages, to appear in Phys.Rev.Let

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Rotational modes in molecular magnets with antiferromagnetic Heisenberg exchange

In an effort to understand the low temperature behavior of recently synthesized molecular magnets we present numerical evidence for the existence of a rotational band in systems of quantum spins interacting with nearest-neighbor antiferromagnetic Heisenberg exchange. While this result has previously been noted for ring arrays with an even number of spin sites, we find that it also applies for rings with an odd number of sites as well as for all of the polytope configurations we have investigated (tetrahedron, cube, octahedron, icosahedron, triangular prism, and axially truncated icosahedron). It is demonstrated how the rotational band levels can in many cases be accurately predicted using the underlying sublattice structure of the spin array. We illustrate how the characteristics of the rotational band can provide valuable estimates for the low temperature magnetic susceptibility.Comment: 14 pages, 7 figures, to be published in Phys. Rev.