Invariant Equilibrium

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Ruderman Michael - One of the best experts on this subject based on the ideXlab platform.

  • Stick-slip and convergence of feedback-controlled systems with Coulomb friction
    'Wiley', 2021
    Co-Authors: Ruderman Michael
    Abstract:

    An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an Invariant Equilibrium set, is proved to be always reachable and globally attractive. It is shown that only asymptotic convergence can be achieved, with at least one but mostly an infinite number of consecutive stick-slip cycles, independent of the initial conditions. Theoretical developments are supported by a number of numerical results with dedicated convergence examples.publishedVersionPaid Open AccessUNIT agreemen

  • Stick-slip and convergence of feedback-controlled systems with Coulomb friction
    2021
    Co-Authors: Ruderman Michael
    Abstract:

    An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an Invariant Equilibrium set, is proved to be always reachable and globally attractive. It is shown that only asymptotic convergence can be achieved, with at least one but mostly an infinite number of consecutive stick-slip cycles, independent of the initial conditions. Theoretical developments are supported by a number of numerical results with dedicated convergence examples.Comment: 14 pages, 8 figure

  • Stick-slip and convergence of feedback-controlled systems with Coulomb friction
    2020
    Co-Authors: Ruderman Michael
    Abstract:

    An analysis of stick-slip behavior and trajectory convergence in feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an Invariant Equilibrium set, is proved to be always reachable and globally attractive. It is shown that only asymptotic convergence can be achieved, with at least one but mostly an infinite number of consecutive stick-slip cycles, independent of the initial conditions. Theoretical developments are supported by a number of numerical results with dedicated convergence examples.Comment: 9 pages, 8 figure

Alexei A Starobinsky - One of the best experts on this subject based on the ideXlab platform.

  • Equilibrium state of a self interacting scalar field in the de sitter background
    Physical Review D, 1994
    Co-Authors: Alexei A Starobinsky, Junichi Yokoyama
    Abstract:

    The behavior of a weakly self-interacting scalar field with a small mass in the de Sitter background is investigated using the stochastic approach (including the case of a double-well interaction potential). The existence of the de Sitter-Invariant Equilibrium quantum state of the scalar field in the presence of the interaction is shown for any sign of the mass term. The stochastic approach is further developed to produce a method of calculating an arbitrary anomalously large correlation function of the scalar field in the de Sitter background, and expressions for the two-point correlation function in the Equilibrium state, correlation time, and spatial physical correlation radius are presented. The latter does not depend on time, which implies that the characteristic size of domains with positive and negative values of the scalar field remains the same on average in the Equilibrium state in spite of the expansion of the t=const hypersurface of the de Sitter space-time.

Junichi Yokoyama - One of the best experts on this subject based on the ideXlab platform.

  • Equilibrium state of a self interacting scalar field in the de sitter background
    Physical Review D, 1994
    Co-Authors: Alexei A Starobinsky, Junichi Yokoyama
    Abstract:

    The behavior of a weakly self-interacting scalar field with a small mass in the de Sitter background is investigated using the stochastic approach (including the case of a double-well interaction potential). The existence of the de Sitter-Invariant Equilibrium quantum state of the scalar field in the presence of the interaction is shown for any sign of the mass term. The stochastic approach is further developed to produce a method of calculating an arbitrary anomalously large correlation function of the scalar field in the de Sitter background, and expressions for the two-point correlation function in the Equilibrium state, correlation time, and spatial physical correlation radius are presented. The latter does not depend on time, which implies that the characteristic size of domains with positive and negative values of the scalar field remains the same on average in the Equilibrium state in spite of the expansion of the t=const hypersurface of the de Sitter space-time.

I K Garkushin - One of the best experts on this subject based on the ideXlab platform.

  • systems of fluorides and bromides of lithium sodium and cesium with mono and Invariant monotectic equilibria
    Russian Journal of Inorganic Chemistry, 2013
    Co-Authors: G E Egortsev, M A Istomova, I K Garkushin
    Abstract:

    Phase diagram with mono- and Invariant Equilibrium were studied by differential thermal analysis by the example of a system of fluorides and bromides of group 1 s-block elements (lithium, sodium, and cesium). Bordering elements were studied, the quaternary reciprocal system Li,Na,Cs∥F,Br was partitioned into simplexes, and a tree of phases was constructed. The liquidi of the systems LiF-NaBr-CsBr and LiF-NaF-CsBr were constructed, the T-x diagrams of polythermal sections passing through phase separation regions were built, and phases being in Equilibrium under specific thermodynamic conditions were described.

A Saccone - One of the best experts on this subject based on the ideXlab platform.

  • the mg zn si system constitutional properties and phase formation during mechanical alloying
    Intermetallics, 2010
    Co-Authors: S De Negri, M Skrobanska, S Delfino, A Saccone
    Abstract:

    Abstract The isothermal section of the Mg–Zn–Si system at 300 °C was determined through the characterization of annealed samples by means of scanning electron microscopy, electron probe microanalysis and X-ray powder diffraction. No ternary phases have been detected in this system at 300 °C. The Mg 2 Si phase was found to dissolve about 2 at.% Zn, changing its lattice parameter from a  = 0.6347(4) nm to a  = 0.6335(4) nm; the other binary phases do not form detectable solid solutions with the third element. Based on the results obtained on samples subjected to different thermal treatments a U-type Invariant Equilibrium is proposed to occur in the solid state at 350  T Mg–Zn–Si powder blends of two different compositions were mechanically alloyed in a planetary ball mill. In both cases the milling process promoted solid state reactions between the constituent elements, leading to the formation of multiphase samples containing crystalline Mg–Si and Mg–Zn binary phases.