The Experts below are selected from a list of 243 Experts worldwide ranked by ideXlab platform

Oliver Sawodny - One of the best experts on this subject based on the ideXlab platform.

  • the glansdorff Prigogine stability criterion for biochemical reaction networks
    Automatica, 2011
    Co-Authors: Michael Ederer, Ernst Dieter Gilles, Oliver Sawodny
    Abstract:

    Local stability analysis of steady states in mathematical models of biochemical reaction networks is an important tool for systems biology. The second variation of the Gibbs energy around a steady state is a positive definite function and a candidate for a Lyapunov function. A sufficient condition for the local stability is the local negative definiteness of the time derivative of this function. This is expressed by the Glansdorff-Prigogine stability criterion. Previously, the criterion was criticized to be overly conservative and difficult to check. Here, we derive an easily testable form of the criterion for models of biochemical networks. The criterion can be evaluated with incomplete knowledge of the parameters. For ideal mass-action kinetics, it depends only on the steady state fluxes. For reaction systems in ideal solutions, the Glansdorff-Prigogine criterion is overly conservative and we give a tighter criterion that depends on the same subset of the parameters as the Glansdorff-Prigogine criterion. Whenever these criteria are indefinite, there exist parameter values such that the steady state is unstable. By means of simple example systems we explore these aspects and discuss the possible uses of the criteria for systems biology.

Alexandros Sopasakis - One of the best experts on this subject based on the ideXlab platform.

  • Developments in the theory of the Prigogine-Herman kinetic equation of vehicular traffic
    2020
    Co-Authors: Alexandros Sopasakis
    Abstract:

    The nonlinear kinetic equation of Prigogine and Herman is examined in regards to existence and uniqueness of solutions. The solution exists and is unique in the Banach space of bounded continuous functions over a particular subspace Ω. The equilibrium solution of the kinetic equation of Prigogine and Herman is used to derive asymptotic type series expansions in the form of Hilbert or Chapman and Enskog for concentrations (c ) corresponding to the stable flow regime of traffic (0 < c < c crit ). As expected the conservation of mass equation, the Lighthill-Whitham-Richards model, can be obtained from these expansions. We use the Chapman-Enskog expansion to obtain hydrodynamic-like equations equivalent to the Euler, Navier-Stokes or Burnett equations of fluid flow, depending on the order of the series expansions we used. The zeroth and first order hydrodynamic-like partial differential equations are solved using appropriate conservative numerical schemes. Analogous continuum approximations up to order one are obtained from the Hilbert expansion. Last a zeroth-order (extended Lighthill-Whitham-Richards) model is obtained for unstable flow at sufficiently high concentrations. (Less)

  • the Prigogine herman kinetic model predicts widely scattered traffic flow data at high concentrations
    Transportation Research Part B-methodological, 1998
    Co-Authors: Paul Nelson, Alexandros Sopasakis
    Abstract:

    The classical derivation of a traffic stream model (e.g. speed/concentration relation) from the equilibrium solutions of the Prigogine-Herman kinetic equation invokes the nontrivial assumption that the underlying distribution of desired speeds is nonzero for vanishingly small speeds. In this paper we investigate the situation when this assumption does not hold. It is found that the Prigogine-Herman kinetic equation has a one-parameter family of equilibrium solutions, and hence an associated traffic stream model, only for traffic concentrations below some critical value; at higher concentrations there is a two-parameter family of solutions, and hence a continuum of mean velocities for each concentration. This result holds for both constant values of the passing probability and the relaxation time, and for values that depend on concentration in the manner assumed by Prigogine and Herman. It is hypothesized that this result reflects the well-known tendency toward substantial scatter in observational data of traffic flow at high concentrations.

Mati Meron - One of the best experts on this subject based on the ideXlab platform.

  • x ray reflectivity studies of atomic level surface segregation in a liquid eutectic alloy of ausn
    arXiv: Materials Science, 2007
    Co-Authors: Venkatachalapathy S K Balagurusamy, Reinhard Streitel, Oleg Shpyrko, Peter S Pershan, Mati Meron
    Abstract:

    X-ray reflectivity studies reveal atomic-level surface-segregation at the free surface of the eutectic Au71Sn29 liquid alloy. The surface-segregation extends up to three layers, in which the top layer is almost a pure monolayer of Sn, the second layer is almost a pure monolayer of Au and the third layer appears to be slightly enhanced in Au. Although the surface-segregation concentration profiles can be qualitatively accounted for by the theories of Defay-Prigogine and Strohl-King, they cannot satisfactorily account for the measured surface tension. PACS numbers: 61.20.-p, 61.10.-i, 68.03.-g

  • x ray reflectivity studies of atomic level surface segregation in a liquid eutectic alloy of ausn
    Physical Review B, 2007
    Co-Authors: Venkatachalapathy S K Balagurusamy, Reinhard Streitel, Oleg Shpyrko, Peter S Pershan, Mati Meron
    Abstract:

    X-ray reflectivity studies reveal atomic-level surface-segregation at the free surface of the eutectic Au{sub 71}Sn{sub 29} liquid alloy. The surface-segregation extends up to three layers, in which the top layer is almost a pure monolayer of Sn, the second layer is almost a pure monolayer of Au and the third layer appears to be slightly enhanced in Au. Although the surface-segregation concentration profiles can be qualitatively accounted for by the theories of Defay-Prigogine and Strohl-King, they cannot satisfactorily account for the measured surface tension.

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

  • the glansdorff Prigogine stability criterion for biochemical reaction networks
    Automatica, 2011
    Co-Authors: Michael Ederer, Ernst Dieter Gilles, Oliver Sawodny
    Abstract:

    Local stability analysis of steady states in mathematical models of biochemical reaction networks is an important tool for systems biology. The second variation of the Gibbs energy around a steady state is a positive definite function and a candidate for a Lyapunov function. A sufficient condition for the local stability is the local negative definiteness of the time derivative of this function. This is expressed by the Glansdorff-Prigogine stability criterion. Previously, the criterion was criticized to be overly conservative and difficult to check. Here, we derive an easily testable form of the criterion for models of biochemical networks. The criterion can be evaluated with incomplete knowledge of the parameters. For ideal mass-action kinetics, it depends only on the steady state fluxes. For reaction systems in ideal solutions, the Glansdorff-Prigogine criterion is overly conservative and we give a tighter criterion that depends on the same subset of the parameters as the Glansdorff-Prigogine criterion. Whenever these criteria are indefinite, there exist parameter values such that the steady state is unstable. By means of simple example systems we explore these aspects and discuss the possible uses of the criteria for systems biology.

Venkatachalapathy S K Balagurusamy - One of the best experts on this subject based on the ideXlab platform.

  • x ray reflectivity studies of atomic level surface segregation in a liquid eutectic alloy of ausn
    arXiv: Materials Science, 2007
    Co-Authors: Venkatachalapathy S K Balagurusamy, Reinhard Streitel, Oleg Shpyrko, Peter S Pershan, Mati Meron
    Abstract:

    X-ray reflectivity studies reveal atomic-level surface-segregation at the free surface of the eutectic Au71Sn29 liquid alloy. The surface-segregation extends up to three layers, in which the top layer is almost a pure monolayer of Sn, the second layer is almost a pure monolayer of Au and the third layer appears to be slightly enhanced in Au. Although the surface-segregation concentration profiles can be qualitatively accounted for by the theories of Defay-Prigogine and Strohl-King, they cannot satisfactorily account for the measured surface tension. PACS numbers: 61.20.-p, 61.10.-i, 68.03.-g

  • x ray reflectivity studies of atomic level surface segregation in a liquid eutectic alloy of ausn
    Physical Review B, 2007
    Co-Authors: Venkatachalapathy S K Balagurusamy, Reinhard Streitel, Oleg Shpyrko, Peter S Pershan, Mati Meron
    Abstract:

    X-ray reflectivity studies reveal atomic-level surface-segregation at the free surface of the eutectic Au{sub 71}Sn{sub 29} liquid alloy. The surface-segregation extends up to three layers, in which the top layer is almost a pure monolayer of Sn, the second layer is almost a pure monolayer of Au and the third layer appears to be slightly enhanced in Au. Although the surface-segregation concentration profiles can be qualitatively accounted for by the theories of Defay-Prigogine and Strohl-King, they cannot satisfactorily account for the measured surface tension.