Closed loop identification based on quantization

This paper proposes a new closed-loop identification scheme for a single-input-single-output control loop. It is based upon a quantizer inserted into the feedback path. The quantizer can be used to generate an equivalent persistently exciting signal with which the well known two-stage and/or two-step method can be used directly. Simulation examples and an experimental demonstration are used to illustrate the proposed scheme

Systemic risk in dynamical networks with stochastic failure criterion

Complex non-linear interactions between banks and assets we model by two time-dependent Erd\H{o}s Renyi network models where each node, representing bank, can invest either to a single asset (model I) or multiple assets (model II). We use dynamical network approach to evaluate the collective financial failure---systemic risk---quantified by the fraction of active nodes. The systemic risk can be calculated over any future time period, divided on sub-periods, where within each sub-period banks may contiguously fail due to links to either (i) assets or (ii) other banks, controlled by two parameters, probability of internal failure $p$ and threshold $T_h$ ("solvency" parameter). The systemic risk non-linearly increases with $p$ and decreases with average network degree faster when all assets are equally distributed across banks than if assets are randomly distributed. The more inactive banks each bank can sustain (smaller $T_h$), the smaller the systemic risk---for some $T_h$ values in I we report a discontinuity in systemic risk. When contiguous spreading becomes stochastic (ii) controlled by probability $p_2$---a condition for the bank to be solvent (active) is stochastic---the systemic risk decreases with decreasing $p_2$. We analyse asset allocation for the U.S. banks.Comment: 7 pages, 7 figure

Remark on approximation in the calculation of the primordial spectrum generated during inflation

We re-examine approximations in the analytical calculation of the primordial spectrum of cosmological perturbation produced during inflation. Taking two inflation models (chaotic inflation and natural inflation) as examples, we numerically verify the accuracy of these approximations.Comment: 10 pages, 6 figures, to appear in PR

Reduced magnetohydrodynamic theory of oblique plasmoid instabilities

The three-dimensional nature of plasmoid instabilities is studied using the reduced magnetohydrodynamic equations. For a Harris equilibrium with guide field, represented by \vc{B}_o = B_{po} \tanh (x/\lambda) \hat{y} + B_{zo} \hat{z}, a spectrum of modes are unstable at multiple resonant surfaces in the current sheet, rather than just the null surface of the polodial field $B_{yo} (x) = B_{po} \tanh (x/\lambda)$, which is the only resonant surface in 2D or in the absence of a guide field. Here $B_{po}$ is the asymptotic value of the equilibrium poloidal field, $B_{zo}$ is the constant equilibrium guide field, and $\lambda$ is the current sheet width. Plasmoids on each resonant surface have a unique angle of obliquity $\theta \equiv \arctan(k_z/k_y)$. The resonant surface location for angle $\theta$ is x_s = - \lambda \arctanh (\tan \theta B_{zo}/B_{po}), and the existence of a resonant surface requires $|\theta| < \arctan (B_{po} / B_{zo})$. The most unstable angle is oblique, i.e. $\theta \neq 0$ and $x_s \neq 0$, in the constant-$\psi$ regime, but parallel, i.e. $\theta = 0$ and $x_s = 0$, in the nonconstant-$\psi$ regime. For a fixed angle of obliquity, the most unstable wavenumber lies at the intersection of the constant-$\psi$ and nonconstant-$\psi$ regimes. The growth rate of this mode is $\gamma_{\textrm{max}}/\Gamma_o \simeq S_L^{1/4} (1-\mu^4)^{1/2}$, in which $\Gamma_o = V_A/L$, $V_A$ is the Alfv\'{e}n speed, $L$ is the current sheet length, and $S_L$ is the Lundquist number. The number of plasmoids scales as $N \sim S_L^{3/8} (1-\mu^2)^{-1/4} (1 + \mu^2)^{3/4}$.Comment: 9 pages, 8 figures, to be published in Physics of Plasma

First-principles study of symmetry lowering in relaxed BaTiO3/SrTiO3 superlattices

The crystal structure and local spontaneous polarization of (BaTiO3)m/(SrTiO3)n superlattices is calculated using a first-principles density functional theory method. The in-plane lattice constant is 1% larger than the SrTiO3 substrate to imitate the relaxed superlattice structure and the symmetry is lowered to monoclinic space group Cm which allows polarization to develop along the [110] and [001] directions. The polarization component in the [110] direction is found to develop only in the SrTiO3 layers and falls to zero in the BaTiO3 layers, whereas the polarization in the [001] direction is approximately uniform throughout the superlattice. These findings are consistent with recent experimental data and first-principles results for epitaxially strained BT and ST.Comment: 4 pages, 2 figure

Dust-to-gas ratio, XCOX_{\rm CO} factor and CO-dark gas in the Galactic anticentre: an observational study

We investigate the correlation between extinction and H~{\sc i} and CO emission at intermediate and high Galactic latitudes (|b|>10\degr) within the footprint of the Xuyi Schmidt Telescope Photometric Survey of the Galactic anticentre (XSTPS-GAC) on small and large scales. In Paper I (Chen et al. 2014), we present a three-dimensional dust extinction map within the footprint of XSTPS-GAC, covering a sky area of over 6,000\,deg$^2$ at a spatial angular resolution of 6\,arcmin. In the current work, the map is combined with data from gas tracers, including H~{\sc i} data from the Galactic Arecibo L-band Feed Array H~{\sc i} survey and CO data from the Planck mission, to constrain the values of dust-to-gas ratio $DGR=A_V/N({\rm H})$ and CO-to-$\rm H_2$ conversion factor $X_{\rm CO}=N({\rm H_2})/W_{\rm CO}$ for the entire GAC footprint excluding the Galactic plane, as well as for selected star-forming regions (such as the Orion, Taurus and Perseus clouds) and a region of diffuse gas in the northern Galactic hemisphere. For the whole GAC footprint, we find $DGR=(4.15\pm0.01) \times 10^{-22}$\,$\rm mag\,cm^{2}$ and $X_{\rm CO}=(1.72 \pm 0.03) \times 10^{20}$\,$\rm cm^{-2}\,(K\,km\,s^{-1})^{-1}$. We have also investigated the distribution of "CO-dark" gas (DG) within the footprint of GAC and found a linear correlation between the DG column density and the $V$-band extinction: $N({\rm DG}) \simeq 2.2 \times 10^{21} (A_V - A^{c}_{V})\,\rm cm^{-2}$. The mass fraction of DG is found to be $f_{\rm DG}\sim 0.55$ toward the Galactic anticentre, which is respectively about 23 and 124 per cent of the atomic and CO-traced molecular gas in the same region. This result is consistent with the theoretical work of Papadopoulos et al. but much larger than that expected in the $\rm H_2$ cloud models by Wolfire et al.Comment: 11 pages, 7 figures, accepted for publication in MNRA

Interaction-Free All-Optical Switching via Quantum-Zeno Effect

We propose a novel interaction-free scheme for all-optical switching which does not rely on the physical coupling between signal and control waves. The interaction-free nature of the scheme allows it to overcome the fundamental photon-loss limit imposed by the signal-pump coupling. The same phenomenon protects photonic-signal states from decoherence, making devices based on this scheme suitable for quantum applications. Focusing on $\chi^{(2)}$ waveguides, we provide device designs for traveling-wave and Fabry-Perot switches. In both designs, the performance is optimal when the signal switching is induced by coherent dynamical evolution. In contrast, when the switching is induced by a rapid dissipation channel, it is less efficient.Comment: 14 pages, 14 figures, submitted to Physical Review

Degenerate Fermi gas in a combined harmonic-lattice potential

In this paper we derive an analytic approximation to the density of states for atoms in a combined optical lattice and harmonic trap potential as used in current experiments with quantum degenerate gases. We compare this analytic density of states to numerical solutions and demonstrate its validity regime. Our work explicitly considers the role of higher bands and when they are important in quantitative analysis of this system. Applying our density of states to a degenerate Fermi gas we consider how adiabatic loading from a harmonic trap into the combined harmonic-lattice potential affects the degeneracy temperature. Our results suggest that occupation of excited bands during loading should lead to more favourable conditions for realizing degenerate Fermi gases in optical lattices.Comment: 11 pages, 9 figure