7,206 research outputs found

    Potential and kinetic shaping for control of underactuated mechanical systems

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    This paper combines techniques of potential shaping with those of kinetic shaping to produce some new methods for stabilization of mechanical control systems. As with each of the techniques themselves, our method employs energy methods and the LaSalle invariance principle. We give explicit criteria for asymptotic stabilization of equilibria of mechanical systems which, in the absence of controls, have a kinetic energy function that is invariant under an Abelian group

    Density Functional Study of Ternary Topological Insulator Thin Films

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    Using an ab-initio density functional theory based electronic structure method with a semi-local density approximation, we study thin-film electronic properties of two topological insulators based on ternary compounds of Tl (Thallium) and Bi (Bismuth). We consider TlBiX2_2 (X=Se, Te) and Bi2_2XX_2Y(X,Y=Se,Te)compoundswhichprovidebetterDiraccones,comparedtothemodelbinarycompoundsBiY (X,Y= Se,Te) compounds which provide better Dirac cones, compared to the model binary compounds Bi_2XX_3$ (X=Se, Te). With this property in combination with a structurally perfect bulk crystal, the latter ternary compound has been found to have improved surface electronic transport in recent experiments. In this article, we discuss the nature of surface states, their locations in the Brillouin zone and their interactions within the bulk region. Our calculations suggest a critical thin film thickness to maintain the Dirac cone which is significantly smaller than that in binary Bi-based compounds. Atomic relaxations or rearrangements are found to affect the Dirac cone in some of these compounds. And with the help of layer-projected surface charge densities, we discuss the penetration depth of the surface states into the bulk region. The electronic spectrum of these ternary compounds agrees very well with the available experimental results.Comment: 9 pages, 11 figures, 1 table, Accepted for publication in Physical Review

    Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

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    For pt.I, see ibid., vol.45, p.2253-70 (2000). We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline

    Investigation of Structural Dynamics of Enzymes and Protonation States of Substrates Using Computational Tools.

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    This review discusses the use of molecular modeling tools, together with existing experimental findings, to provide a complete atomic-level description of enzyme dynamics and function. We focus on functionally relevant conformational dynamics of enzymes and the protonation states of substrates. The conformational fluctuations of enzymes usually play a crucial role in substrate recognition and catalysis. Protein dynamics can be altered by a tiny change in a molecular system such as different protonation states of various intermediates or by a significant perturbation such as a ligand association. Here we review recent advances in applying atomistic molecular dynamics (MD) simulations to investigate allosteric and network regulation of tryptophan synthase (TRPS) and protonation states of its intermediates and catalysis. In addition, we review studies using quantum mechanics/molecular mechanics (QM/MM) methods to investigate the protonation states of catalytic residues of β-Ketoacyl ACP synthase I (KasA). We also discuss modeling of large-scale protein motions for HIV-1 protease with coarse-grained Brownian dynamics (BD) simulations

    SIRT1 Mediates Central Circadian Control in the SCN by a Mechanism that Decays with Aging

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    SummarySIRT1 is a NAD+-dependent protein deacetylase that governs many physiological pathways, including circadian rhythm in peripheral tissues. Here, we show that SIRT1 in the brain governs central circadian control by activating the transcription of the two major circadian regulators, BMAL1 and CLOCK. This activation comprises an amplifying circadian loop involving SIRT1, PGC-1α, and Nampt. In aged wild-type mice, SIRT1 levels in the suprachiasmatic nucleus are decreased, as are those of BMAL1 and PER2, giving rise to a longer intrinsic period, a more disrupted activity pattern, and an inability to adapt to changes in the light entrainment schedule. Young mice lacking brain SIRT1 phenocopy these aging-dependent circadian changes, whereas mice that overexpress SIRT1 in the brain are protected from the effects of aging. Our findings indicate that SIRT1 activates the central pacemaker to maintain robust circadian control in young animals, and a decay in this activity may play an important role in aging

    Asymptotic stabilization of Euler-Poincaré mechanical systems

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    Stabilization of mechanical control systems by the method of controlled Lagrangians and matching is used to analyze asymptotic stabilization of systems whose underlying dynamics are governed by the Euler-Poincar´e equations. In particular, we analyze asymptotic stabilization of a satellite
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