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

Magnetization Process of Nanoscale Iron Cluster

Low-temperature magnetization process of the nanoscale iron cluster in linearly sweeped fields is investigated by a numerical analysis of time-dependent Schr$\ddot{\rm o}$dinger equation and the quantum master equation. We introduce an effective basis method extracting important states, by which we can obtain the magnetization process effectively. We investigate the structure of the field derivative of the magnetization. We find out that the antisymmetric interaction determined from the lattice structure reproduces well the experimental results of the iron magnets and that this interaction plays an important role in the iron cluster. Deviations from the adiabatic process are also studied. In the fast sweeping case, our calculations indicate that the nonadiabatic transition dominantly occurs at the level crossing for the lowest field. In slow sweeping case, due to the influence of the thermal environment to the spin system, the field derivative of the magnetization shows an asymmetric behavior, the magnetic F$\ddot{\rm o}$hn effect, which explains the substructure of the experimental results in the pulsed field.Comment: 5 pages of text and 2 pages of 6 figures. To appear in J. Phys. Soc. Jp

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

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.

Anisotropy of graphite optical conductivity

The graphite conductivity is evaluated for frequencies between 0.1 eV, the energy of the order of the electron-hole overlap, and 1.5 eV, the electron nearest hopping energy. The in-plane conductivity per single atomic sheet is close to the universal graphene conductivity $e^2/4\hbar$ and, however, contains a singularity conditioned by peculiarities of the electron dispersion. The conductivity is less in the $c-$direction by the factor of the order of 0.01 governed by electron hopping in this direction.Comment: 3 pages, 3 figure

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

Ferromagnetic coupling and magnetic anisotropy in molecular Ni(II) squares

We investigated the magnetic properties of two isostructural Ni(II) metal complexes [Ni4Lb8] and [Ni4Lc8]. In each molecule the four Ni(II) centers form almost perfect regular squares. Magnetic coupling and anisotropy of single crystals were examined by magnetization measurements and in particular by high-field torque magnetometry at low temperatures. The data were analyzed in terms of an effective spin Hamiltonian appropriate for Ni(II) centers. For both compounds, we found a weak intramolecular ferromagnetic coupling of the four Ni(II) spins and sizable single-ion anisotropies of the easy-axis type. The coupling strengths are roughly identical for both compounds, whereas the zero-field-splitting parameters are significantly different. Possible reasons for this observation are discussed.Comment: 7 pages, 7 figure

Identifiability of flow distributions from link measurements with applications to computer networks

We study the problem of identifiability of distributions of flows on a graph from aggregate measurements collected on its edges. This is a canonical example of a statistical inverse problem motivated by recent developments in computer networks. In this paper (i) we introduce a number of models for multi-modal data that capture their spatio-temporal correlation, (ii) provide sufficient conditions for the identifiability of nth order cumulants and also for a special class of heavy tailed distributions. Further, we investigate conditions on network routing for the flows that prove sufficient for identifiability of their distributions (up to mean). Finally, we extend our results to directed acyclic graphs and discuss some open problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58107/2/ip7_5_004.pd

An online healthy relationship tool and safety decision aid for women experiencing intimate partner violence (I-DECIDE): a randomised controlled trial

Background Evidence for online interventions to help women experiencing intimate partner violence is scarce. We assessed whether an online interactive healthy relationship tool and safety decision aid (I-DECIDE) would increase women's self-efficacy and improve depressive symptoms compared with an intimate partner violence information website. Methods In this two-group pragmatic randomised controlled trial, we enrolled women who had screened positive for any form of intimate partner violence or fear of a partner in the 6 months before recruitment. Women aged 16–50 years currently residing in Australia, who had safe access to a computer and an internet connection, and who answered positively to one of the screening questions in English were eligible for inclusion. Participants were randomly assigned (1:1) by computer to receive either the intervention or control website. The intervention website consisted of modules on healthy relationships, abuse and safety, and relationship priority setting, and a tailored action plan. The control website was a static intimate partner violence information website. As the initial portion of the website containing the baseline questions was identical for both groups, there was no way for women to tell which group they had been allocated to, and the research team were also masked to participant allocation until after analysis of the 12-month data. Data were collected at baseline, immediately after completion of the website, at 6 months, and 12 months. Primary outcomes were mean general self-efficacy score (immediately after website completion, and at 6 months and 12 months) and mean depression score (at 6 months and 12 months). Data analyses were done according to intention-to-treat principles, accounting for missing data, and adjusted for outcome baseline scores. This trial was registered with the Australian New Zealand Clinical Trials Registry, ACTRN 12614001306606. Findings Between Jan 16, and Aug 28, 2015, 584 patients registered for the study and were assessed for eligibility. 422 eligible participants were randomly allocated to the intervention group (227 patients) or control group (195 patients). 179 (79%) participants in the intervention group and 156 (80%) participants in the control group completed 12-month follow-up. Mean self-efficacy at 6 months and 12 months was lower for participants in the intervention group than for participants in the control group, although this did not meet the prespecified mean difference (6 months: 27·5 [SD 5·1] vs 28·1 [4·4], imputed mean difference 1·3 [95% CI 0·3 to 2·3]; 12 months: 27·8 [SD 5·4] vs 29·0 [5·0], imputed mean difference 1·6 [95% CI 0·5 to 2·7]). We found no difference between groups in depressive symptoms at 6 months or 12 months (6 months: 22·5 [SD 17·1] vs 24·2 [17·2], imputed mean difference −0·3 [95% CI −3·5 to 3·0]; 12 months: 21·9 [SD 19·3] vs 21·5 [19·3], imputed mean difference −1·9 [95% CI −5·6 to 1·7]). Qualitative findings indicated that participants found the intervention supportive and a motivation for action. Interpretation Our findings highlight the need for further research, development, and refinement of online interventions for women experiencing intimate partner violence, particularly into the duration needed for interventions. Although we detected no meaningful differences between groups, our qualitative results indicated that some women find an online tool a helpful source of motivation and support

Predicting a Gapless Spin-1 Neutral Collective Mode branch for Graphite

Using the standard tight binding model of 2d graphite with short range electron repulsion, we find a gapless spin-1, neutral collective mode branch {\em below the particle-hole continuum} with energy vanishing linearly with momenta at the $\Gamma$ and $K$ points in the BZ. This spin-1 mode has a wide energy dispersion, 0 to $\sim 2 eV$ and is not Landau damped. The `Dirac cone spectrum' of electrons at the chemical potential of graphite generates our collective mode; so we call this `spin-1 zero sound' of the `Dirac sea'. Epithermal neutron scattering experiments, where graphite single crystals are often used as analyzers (an opportunity for `self-analysis'!), and spin polarized electron energy loss spectroscopy (SPEELS) can be used to confirm and study our collective mode.Comment: 4 pages of LaTex file, 3 eps figure file