Eigenstructure Assignment Based Controllers Applied to Flexible Spacecraft

The objective of this paper is to evaluate the behaviour of a controller designed using a parametric Eigenstructure Assignment method and to evaluate its suitability for use in flexible spacecraft. The challenge of this objective lies in obtaining a suitable controller that is specifically designated to alleviate the deflections and vibrations suffered by external appendages in flexible spacecraft while performing attitude manoeuvres. One of the main problems in these vehicles is the mechanical cross-coupling that exists between the rigid and flexible parts of the spacecraft. Spacecraft with fine attitude pointing requirements need precise control of the mechanical coupling to avoid undesired attitude misalignment. In designing an attitude controller, it is necessary to consider the possible vibration of the solar panels and how it may influence the performance of the rest of the vehicle. The nonlinear mathematical model of a flexible spacecraft is considered a close approximation to the real system. During the process of controller evaluation, the design process has also been taken into account as a factor in assessing the robustness of the system

Exotic Superconducting Phases of Ultracold Atom Mixtures on Triangular Lattices

We study the phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms on a triangular optical lattice, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. We contrast this work with our previous results for a square lattice system in Phys. Rev. Lett. {\bf 97}, 030601 (2006). Using functional renormalization group techniques we show that the phase diagrams for a triangular lattice contain exotic superconducting phases. For spin-1/2 fermions on an isotropic lattice we find a competition of $s$-, $p$-, extended $d$-, and $f$-wave symmetry, as well as antiferromagnetic order. For an anisotropic lattice, we further find an extended p-wave phase. A Bose-Fermi mixture with spinless fermions on an isotropic lattice shows a competition between $p$- and $f$-wave symmetry. These phases can be traced back to the geometric shapes of the Fermi surfaces in various regimes, as well as the intrinsic frustration of a triangular lattice.Comment: 6 pages, 4 figures, extended version, slight modification

Unconventional Spin Density Waves in Dipolar Fermi Gases

The conventional spin density wave (SDW) phase (Overhauser, 1962), as found in antiferromagnetic metal for example (Fawcett 1988), can be described as a condensate of particle-hole pairs with zero angular momentum, $\ell=0$, analogous to a condensate of particle-particle pairs in conventional superconductors. While many unconventional superconductors with Cooper pairs of finite $\ell$ have been discovered, their counterparts, density waves with non-zero angular momenta, have only been hypothesized in two-dimensional electron systems (Nayak, 2000). Using an unbiased functional renormalization group analysis, we here show that spin-triplet particle-hole condensates with $\ell=1$ emerge generically in dipolar Fermi gases of atoms (Lu, Burdick, and Lev, 2012) or molecules (Ospelkaus et al., 2008; Wu et al.) on optical lattice. The order parameter of these exotic SDWs is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half-filling as a function of the dipolar orientation, and discuss how these SDWs arise amidst competition with superfluid and charge density wave phases.Comment: 5 pages, 3 figure

Orbital symmetry fingerprints for magnetic adatoms in graphene

In this paper, we describe the formation of local resonances in graphene in the presence of magnetic adatoms containing localized orbitals of arbitrary symmetry, corresponding to any given angular momentum state. We show that quantum interference effects which are naturally inbuilt in the honeycomb lattice in combination with the specific orbital symmetry of the localized state lead to the formation of fingerprints in differential conductance curves. In the presence of Jahn-Teller distortion effects, which lift the orbital degeneracy of the adatoms, the orbital symmetries can lead to distinctive signatures in the local density of states. We show that those effects allow scanning tunneling probes to characterize adatoms and defects in graphene.Comment: 15 pages, 11 figures. Added discussion about the multi-orbital case and the validity of the single orbital picture. Published versio

Weak dipole moment of τ\tau in e+e−e^+e^- collisions with longitudinally polarized electrons

It is pointed out that certain CP-odd momentum correlations in the production and subsequent decay of tau pairs in $e^+e^-$ collisions get enhanced when the $e^-$ is longitudinally polarized. Analytic expressions for these correlations are obtained for the single-pion decay mode of $\tau$ when $\tau^+\tau^-$ have a ``weak" dipole form factor (WDFF) coupling to $Z$ . For $e^+e^-$ collisions at the $Z$ peak, a sensitivity of about 1-5$\times 10^{-17}$\mbox{$e$ cm} for the $\tau$ WDFF can be reached using a {\em single} $\tau^+\tau^-$ decay channel, with $10^6\, Z$'s likely to be available at the SLC at Stanford with $e^-$ polarization of 62\%-75\%.Comment: 9 pages, Latex, PRL-TH-93/17 (Revised

Thermalization and its Breakdown for a Large Nonlinear Spin

By developing a semi-classical analysis based on the Eigenstate Thermalization Hypothesis, we determine the long time behavior of a large spin evolving with a nonlinear Hamiltonian. Despite integrable classical dynamics, we find the Eigenstate Thermalization Hypothesis for the diagonal matrix elements of observables is satisfied in the majority of eigenstates, and thermalization of long time averaged observables is generic. The exception is a novel mechanism for the breakdown of thermalization based on an unstable fixed point in the classical dynamics. Using the semi-classical analysis we derive how the equilibrium values of observables encode properties of the initial state. This analysis shows an unusual memory effect in which the remembered initial state property is not conserved in the integrable classical dynamics. We conclude with a discussion of relevant experiments and the potential generality of this mechanism for long time memory and the breakdown of thermalization.Comment: 10 page

Anomalous magnetic moment in parity-conserving QED3

In this article we derive the anomalous magnetic moment of fermions in (2+1)-dimensional parity-conserving QED3, in the presence of an externally applied constant magnetic field. We use a spectral representation of the photon propagator to avoid infrared divergences. We also discuss the scaling with the magnetic field intensity in the case of strong external fields, where there is dynamical mass generation for fermions induced by the magnetic field itself (magnetic catalysis). The results of this paper may be of relevance to the physics of high-temperature superconductors.Comment: 27 pages LATEX, three eps figures incorporate

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov's direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology