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2 results

  • 6 - Dynamics and Dynamical Properties

  • Claudio Zannoni
  • Book:
    Liquid Crystals and their Computer Simulations
    Published online:
    21 July 2022
    Print publication:
    28 July 2022, pp 288-331

  • Summary

    The dynamic evolution of a classic molecular system is first introduced formally via Liouville equation. Then, single-particle time correlation functions and their general properties (like short and long time limits) for orientational correlation functions (OCF) in liquid crystals are discussed and translational and orientational diffusion coefficients are introduced. The link between OCFs, obtainable from computer simulations, and experiments is established with Linear Response theory and examples from dielectric relaxation, ionic and thermal conductivity, viscosities are presented, with reference to the literature. The rotational diffusion equation in an anisotropic fluid, normally employed to analyze experiments is also introduced, with explicit expressions derived for Fluorescence Depolarization.

  • THE DYNAMIC PROPERTIES OF ENDOGENOUS GROWTH MODELS

  • Norman Sedgley, Bruce Elmslie
  • Journal:
    Macroeconomic Dynamics / Volume 17 / Issue 5 / July 2013
    Published online by Cambridge University Press:
    11 March 2013, pp. 1118-1134

  • This paper explores the dynamics of semiendogenous versus fully endogenous growth models in “lab equipment” specifications of the models with expanding sectors. Capital is allowed to accumulate and is used, together with other inputs, to produce new knowledge. The stability of the steady state path is found to be determined by the inequality and/or knife-edge restrictions needed to produce steady state growth. This paper takes the ratio of the shadow price of capital to knowledge and the level of consumption as jump variables. Semiendogenous growth models lead to a 4 × 4 dynamic system where the sign of the coefficient matrix of the log linearized dynamic system is indefinite, leading to a potential for both stable and unstable equilibria. The knife-edge restrictions needed to generate policy influences on growth are shown to be restrictions that reduce the system to 3 × 3 with a positive definite coefficient matrix, thereby guaranteeing a globally stable equilibrium. Implications for empirical testing are addressed.