Algebraic design techniques for reliable stabilization

In this paper we study two problems in feedback stabilization. The first is the simultaneous stabilization problem, which can be stated as follows. Given plantsG_{0}, G_{1},..., G_{l}, does there exist a single compensatorCthat stabilizes all of them? The second is that of stabilization by a stable compensator, or more generally, a "least unstable" compensator. Given a plantG, we would like to know whether or not there exists a stable compensatorCthat stabilizesG; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have? We show that the two problems are equivalent in the following sense. The problem of simultaneously stabilizingl + 1plants can be reduced to the problem of simultaneously stabilizinglplants using a stable compensator, which in turn can be stated as the following purely algebraic problem. Given2lmatricesA_{1}, ..., A_{l}, B_{1}, ..., B_{l}, whereA_{i}, B_{i}are right-coprime for alli, does there exist a matrixMsuch thatA_{i} + MB_{i}, is unimodular for alli?Conversely, the problem of simultaneously stabilizinglplants using a stable compensator can be formulated as one of simultaneously stabilizingl + 1plants. The problem of determining whether or not there exists anMsuch thatA + BMis unimodular, given a right-coprime pair (A, B), turns out to be a special case of a question concerning a matrix division algorithm in a proper Euclidean domain. We give an answer to this question, and we believe this result might be of some independent interest. We show that, given twon times mplantsG_{0} and G_{1}we can generically stabilize them simultaneously provided eithernormis greater than one. In contrast, simultaneous stabilizability, of two single-input-single-output plants, g0and g1, is not generic.

Proline ring conformations corresponding to a bistable jump model from 13C spin-lattice relaxation times

A formalism for extracting the conformations of a proline ring based on the bistable jump model of R. E. London [(1978) J. Am. Chem. Soc. 100, 2678-2685] from 13C spin-lattice relaxation times (T1) is given. The method is such that the relaxation data are only partially used to generate the conformations; these conformations are constrained to satisfy the rest of the relaxation data and to yield acceptable ring geometry. An alternate equation for T1 of 13C nuclei to that of London is given. The formalism is illustrated through an example.

Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes

Random walk models are often used to interpret experimental observations of the motion of biological cells and molecules. A key aim in applying a random walk model to mimic an in vitro experiment is to estimate the Fickian diffusivity (or Fickian diffusion coefficient),D. However, many in vivo experiments are complicated by the fact that the motion of cells and molecules is hindered by the presence of obstacles. Crowded transport processes have been modeled using repeated stochastic simulations in which a motile agent undergoes a random walk on a lattice that is populated by immobile obstacles. Early studies considered the most straightforward case in which the motile agent and the obstacles are the same size. More recent studies considered stochastic random walk simulations describing the motion of an agent through an environment populated by obstacles of different shapes and sizes. Here, we build on previous simulation studies by analyzing a general class of lattice-based random walk models with agents and obstacles of various shapes and sizes. Our analysis provides exact calculations of the Fickian diffusivity, allowing us to draw conclusions about the role of the size, shape and density of the obstacles, as well as examining the role of the size and shape of the motile agent. Since our analysis is exact, we calculateDdirectly without the need for random walk simulations. In summary, we find that the shape, size and density of obstacles has a major influence on the exact Fickian diffusivity. Furthermore, our results indicate that the difference in diffusivity for symmetric and asymmetric obstacles is significant.

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

Size effect on the lattice parameter of KCl during mechanical milling

The size effect on the lattice parameter of ionic KCl nanocrystals was studied systematically during mechanical milling of Pure KCl powder under vacuum. The results suggest anomalous lattice expansion, with the lattice parameter increasing from 6.278 angstrom at d = 6 mu m to 6.30307 angstrom at d = 85 mn. The defects generated during ball milling of KCl and surface stress are deemed to be responsible for this lattice parameter expansion. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Proton Spin-Lattice Relaxation in Sodium Ammonium Selenate Dihydrate:NaNHaSeOa.2He0

Proton spin-lattice relaxation studies in sodium ammonium selenate dihydrate carried out in the temperature range 130 to 300 K at 10 MHz show a continuous change in T, at T, indicating a second order phase transition. This compound is a typical case of a highly hindered solid wherein the thermally activated reorientations of ammonium ions freeze well above 77 K, as seen by NMR.Untersuchimgen der Protonen-Spin-Gitter-Relaxation in Natriuni-Ammoniumselenat-Dihydrat bei 10 MHz im Temperaturbereich 130 bis 300 K zeigen eine kontinuierliche Andernng in TI bei T, und ergeben einen Phasenubergang zweiter Art. Diese Verbindung ist ein typischer Fall eines stark ,,behinderten" Festkarpers, in dein die thermisch aktivierten Reorientierungen der Ammoniumionen weit oberhalb 77 H einfrieren, wie die NMR-Ergebnisse zeigen.

An algebraic algorithm for the design and analysis of linear dynamical systems

In an earlier paper [1], it has been shown that velocity ratio, defined with reference to the analogous circuit, is a basic parameter in the complete analysis of a linear one-dimensional dynamical system. In this paper it is shown that the terms constituting velocity ratio can be readily determined by means of an algebraic algorithm developed from a heuristic study of the process of transfer matrix multiplication. The algorithm permits the set of most significant terms at a particular frequency of interest to be identified from a knowledge of the relative magnitudes of the impedances of the constituent elements of a proposed configuration. This feature makes the algorithm a potential tool in a first approach to a rational design of a complex dynamical filter. This algorithm is particularly suited for the desk analysis of a medium size system with lumped as well as distributed elements.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

An algebraic approach to the restoration of images

Two different matrix algorithms are described for the restoration of blurred pictures. These are illustrated by numerical examples.

Pyrrolidine ring conformations in prolyl peptides from 13C spin-lattice relaxation times

A method was developed in the framework of a bistable jump model to obtain the pyrrolidine ring conformations in proline peptides from 13C spin-lattice relaxation times. Equations are presented expressing the ring torsions in terms of the 13C spin-lattice relaxation times of the ring carbons. This method was applied to 26 pyrrolidine ring systems and acceptable conformations were obtained.

Large Low-Frequency Fluctuations in the Velocity of a Driven Vortex Lattice in a Single Crystal of 2H-NbSe2 Superconductor

The driven state of a well-ordered flux line lattice in a single crystal of 2H-NbSe2 in the time domain has revealed the presence of substantial fluctuations in velocity, with large and distinct time periods (similar to seconds). A superposition of a periodic drive in the driven vortex lattice causes distinct changes in these fluctuations. We propose that prior to the onset of the peak effect there exists a heretofore unexplored regime of coherent dynamics, with unexpected behavior in velocity fluctuations.

Origin of activation of Lattice Oxygen and Synergistic Interaction in Bimetal-Ionic Ce0.89Fe0.1Pd0.01O2-delta Catalyst

Flourite-type nanocrystalline Ce0.9Fe0.1O2-delta and Ce0.89Fe0.1Pd0.01O2-delta solid solutions have been synthesized by solution combustion method,'.which show higher oxygen storage/release property (OSC) compared to CeO2 and Ce0.8Zr0.2O2. Temperature programmed reduction an XPS study reveal that the presence of Pd ion in Ce0.9Fe0.1O2-delta facilitates complete reduction of Fe3+ to Fe2+ state and partial reduction of Ce4+ to Ce3+ state at.temperatures as low as 105 degrees C compared to 400 degrees C for monometal-ionic Ce0.9Fe0.1O2-delta. Fe3+ ion is reduced to Fe2+ and not to Feo due to favorable redox potential for Ce4+ + Fe2+ -> Ce3+ + Fe3+ reaction. Using first-principles density functional theory calculation we determine M-O (M = Pd, Fe, Ce) bond lengths, and find that bond lengths vary from shorter (2.16 angstrom) to longer (2.9 angstrom) bond distances compared to mean Ce-O bond distance of 2.34 angstrom. for CeO2. Using these results in bond valence analysis, we show that oxygen with bond valences as low as -1.55 are created, leading to activation of lattice oxygen in the bimetal ionic catalyst. Temperatures of CO oxidation and NO reduction by CO/H-2 are lower with the bimetalionic Ce0.89Fe0.1Pd0.01O2-delta catalyst compared to monometal-ionic Ce0.9Fe0.1O2-delta and Ce0.99Pd0.01O2-delta catalysts. From XPS studies of Pd impregnated on CeO2 and Fe2O3 oxides, we show that the synergism leading to low temperature activation of lattice oxygen in bimetal-ionic catalyst Ce0.89Fe0.1Pd0.01O2-delta is due to low-temperature reduction of Pd2+ to Pd-0, followed by Pd-0 + 2Fe(3+) -> Pd2+ + 2Fe(2+), Pd-0 + 2Ce(4+) -> Pd2+ + 2Ce(3+) redox reaction.

Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method

Purpose - The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid-driven flow in a three-dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two-dimensional (2D) cavity. Design/methodology/approach - The second-order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25-4) and Reynolds numbers (0.01-1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier-Stokes (NS) equations and with available experimental data. Findings - The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side-walls in transverse direction (in 3D), due to which the vorticity in the core-region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry-plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid-motion are observed; these are weak at low. Reynolds numbers, but become quite strong at high Reynolds numbers. Originality/value - The findings will be useful in the study of variety of enclosed fluid flows.