On the connection between different noise structures for LPV-SS models

Different representations to describe noise processes and finding connections or equivalence between them have been part of active research for decades, in particular for linear time-invariant case. In this paper the linear parameter-varying (LPV) setting is addressed; starting with the connection between an LPV state-space (SS) representation with a general noise structure and the LPV-SS model in an innovation structure, i.e., the Kalman filter. More specifically, the considered LPV-SS representation with general noise structure has static, affine dependence on the scheduling signal; however, we show that its companion innovation structure has a dynamic, rational dependency structure. Following, we would like to highlight the consequences of approximating this Kalman gain by a static, affine dependency structure. To this end, firstly, we use the "fading memory" effect of the Kalman filter to reason how the Kalman gain can be approximated to depend only on a partial trajectory of the scheduling signal. This effect is shown by proving an asymptotically decreasing error upper bound on the covariance matrix associated to the innovation structure in case the covariance matrix is subjected to an incorrect initialization or disturbance. Secondly, we show by an example that an LPV-SS representation that has dynamical, rational dependency on the scheduling signal can be transformed into static, affinely dependent representation by introducing additional states. Therefore, an approximated Kalman gain can, in some cases, be represented by a static, affine Kalman gain at the cost of additional states.Comment: 6 page

Affine parameter-dependent Lyapunov functions for LPV systems with affine dependence

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, which are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for L2-gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables.</p

Bayesian identification of LPV-BJ models : a multidimensional kernel approach

poster, no abstract available

Anderson-Yuval approach to the multichannel Kondo problem

We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant level model. Limiting cases in which the equivalent resonant level model is solvable are identified. The solution correctly captures the properties of the two channel Kondo model, and also allows an analytic description of the cross-over from the non Fermi liquid to the Fermi liquid behavior caused by the channel anisotropy.Comment: 23 pages, ReVTeX, 4 figures av. on reques

Topological (Sliced) Doping of a 3D Peierls System: Predicted Structure of Doped BaBiO3

At hole concentrations below x=0.4, Ba_(1-x)K_xBiO_3 is non-metallic. At x=0, pure BaBiO3 is a Peierls insulator. Very dilute holes create bipolaronic point defects in the Peierls order parameter. Here we find that the Rice-Sneddon version of Peierls theory predicts that more concentrated holes should form stacking faults (two-dimensional topological defects, called slices) in the Peierls order parameter. However, the long-range Coulomb interaction, left out of the Rice-Sneddon model, destabilizes slices in favor of point bipolarons at low concentrations, leaving a window near 30% doping where the sliced state is marginally stable.Comment: 6 pages with 5 embedded postscript figure

A recent rebuilding of most spirals ?

Re-examination of the properties of distant galaxies leads to the evidence that most present-day spirals have built up half of their stellar masses during the last 8 Gyr, mostly during several intense phases of star formation during which they took the appearance of luminous infrared galaxies (LIRGs). Distant galaxy morphologies encompass all of the expected stages of galaxy merging, central core formation and disk growth, while their cores are much bluer than those of present-day bulges. We have tested a spiral rebuilding scenario, for which 75+/-25% of spirals have experienced their last major merger event less than 8 Gyr ago. It accounts for the simultaneous decreases, during that period, of the cosmic star formation density, of the merger rate, of the number densities of LIRGs and of compact galaxies, while the densities of ellipticals and large spirals are essentially unaffected.Comment: (1) GEPI, Obs. Meudon, France ;(2)Max-Planck Institut fuer Astronomie, Germany (3) National Astronomical Observatories, CAS, China. Five pages, 1 figure. To be published in "Starbursts: From 30 Doradus to Lyman Break Galaxies", held in Cambridge, ed. R. de Grijs & R. M. Gonzalez Delgado (Dordrecht: Kluwer

Multi-Channel Kondo Necklace

A multi--channel generalization of Doniach's Kondo necklace model is formulated, and its phase diagram studied in the mean--field approximation. Our intention is to introduce the possible simplest model which displays some of the features expected from the overscreened Kondo lattice. The $N$ conduction electron channels are represented by $N$ sets of pseudospins \vt_{j}, $j=1, ... , N$, which are all antiferromagnetically coupled to a periodic array of |\vs|=1/2 spins. Exploiting permutation symmetry in the channel index $j$ allows us to write down the self--consistency equation for general $N$. For $N>2$, we find that the critical temperature is rising with increasing Kondo interaction; we interpret this effect by pointing out that the Kondo coupling creates the composite pseudospin objects which undergo an ordering transition. The relevance of our findings to the underlying fermionic multi--channel problem is discussed.Comment: 29 pages (2 figures upon request from [email protected]), LATEX, submitted for publicatio

Quantum phase transition in a two-channel-Kondo quantum dot device

We develop a theory of electron transport in a double quantum dot device recently proposed for the observation of the two-channel Kondo effect. Our theory provides a strategy for tuning the device to the non-Fermi-liquid fixed point, which is a quantum critical point in the space of device parameters. We explore the corresponding quantum phase transition, and make explicit predictions for behavior of the differential conductance in the vicinity of the quantum critical point

Charge-density wave formation in Sr_{14}Cu_{24}O_{41}

The electrodynamic response of the spin-ladder compound Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ ($x=0, 3, 9$) has been studied from radiofrequencies up to the infrared. At temperatures below 250 K a pronounced absorption peak appears around 12 cm$^{-1}$ in Sr$_{14}$Cu$_{24}$O$_{41}$ for the radiation polarized along the chains/ladders (${\bf E}\parallel {\bf c}$). In addition a strongly temperature dependent dielectric relaxation is observed in the kHz - MHz range. We explain this behavior by a charge density wave which develops in the ladders sub-system and produces a mode pinned at 12 cm$^{-1}$. With increasing Ca doping the mode shifts up in frequency and eventually disappears for $x=9$ because the dimensionality of the system crosses over from one to two dimensions, giving way to the superconducting ground state under pressure.Comment: One name added to author list 4 pages, 2 figures, email: [email protected]

The Local Bubble and Interstellar Material Near the Sun

The properties of interstellar matter (ISM) at the Sun are regulated by our location with respect to the Local Bubble (LB) void in the ISM. The LB is bounded by associations of massive stars and fossil supernovae that have disrupted natal ISM and driven intermediate velocity ISM into the LB interior void. The Sun is located in such a driven ISM parcel. The Local Fluff has a bulk velocity of 19 km/s in the LSR, and an upwind direction towards the center of the gas and dust ring formed by the Loop I supernova remnant interaction with the LB. When the ram pressure of the LIC is included in the total LIC pressure, and if magnetic thermal and cosmic ray pressures are similar, the LIC appears to be in pressure equilibrium with the local hot bubble plasma.Comment: Proceedings of Symposium on the Composition of Matter, honoring Johannes Geiss on the occasion of his 80th birthday. Space Science Reviews (in press