Dynamics of Order Parameter

Dynamics of Order Parameter 6.5.1 Landau-Khalatnikov Approach... 

J. P. McClymer, P. H. Keyes, Dynamics of order parameter and director fluctuations in the nematic phase of a lyotropic liquid crystal, Phys. Rev. E 1993, 48, 2838-2841. 

Several examples of order parameters are shown in Fig. 2.5. Some of them, e.g., the torsional angles a, are dynamical variables, which means that they can be fully... 

Another apparent difference between the various free energy methods lies in the treatment of order parameters. In the original formulation of a number of methods, order parameters were dynamical variables - i.e., variables that can be expressed in terms of the Cartesian coordinates of the particles - whereas in others, they were parameters in the Hamiltonian. This implies a different treatment of the order parameter in the equations of motion. If one, however, applies the formalism of metadynamics, or extended dynamics, in which any parameter can be treated as a dynamical variable, most conceptual differences between these two cases vanish. 

Abstract. We review the recent development of quantum dynamics for nonequilibrium phase transitions. To describe the detailed dynamical processes of nonequilibrium phase transitions, the Liouville-von Neumann method is applied to quenched second order phase transitions. Domain growth and topological defect formation is discussed in the second order phase transitions. Thermofield dynamics is extended to nonequilibrium phase transitions. Finally, we discuss the physical implications of nonequilibrium processes such as decoherence of order parameter and thermalization. 

With increasing flow rate, the orientational state in the nematic solution should change. Larson [154] solved numerically Eqs. (39) and (40b) with Vscf(a) given by Eq. (41) for a homogeneous system (T[f ] = 0) in the simple shear flow to obtain the time-dependent orientational distribution function f(a t) as a function of k. The non-steady orientational state in the nematic solution can be described in terms of the time-dependent (dynamic) scalar order parameter S[Pg.149]

We now study the characteristics of the order parameter of the superconductivity induced by the attractive interaction between the flu electrons originated in the dynamic Jahn-Teller effect. To this end, we estimate the energy gain per Cgo molecule due to the superconductivity by using a simple consideration of Hint. It is reasonable to expect that there can be three types of order parameter, i.e., those of the Ag, Hg, and TXg symmetries, because flu X qu is reduced to the sum of these three representations. We examine the three possibilities below. 

A. V. Komolkin, Aatto Laaksonen and A. Maliniak, Molecular Dynamics Simulation of a Nematic Liquid Crystal, J. Chem. Phys. 101 (1994) 4103 M. R. Wilson, Determination of Order Parameters in Realistic Atom-Based Models of Liquid Crystal Systems, J. Mol. Liq. 68 (1996) 23 ... 

Genheden S, Diehl C, Akke M, Ryde U (2010) Starting-condition dependence of order parameters derived from molecular dynamics simulations. J Chem Theory Comput 6 2176-2190... 

Idiyatullin D, Daragan VA, Mayo KH (2003) (NH)-N-15 backbone dynamics of protein GB1 comparison of order parameters and correlation times derived using various model-free approaches. J Phys Chem B 107 2602-2609... 

Besides monitoring morphological changes on membranes, wide-line NMR can also report on internal membrane dynamics, i.e. determine the microfluidity of the bilayer core. This is where the concept of order parameter takes place. Order parameters, S, are time and space averages (denoted by angular brackets) of the quantity... 

Models of stochastic dynamics (Chapman-Kolmogorov equation for the probability distributions of order parameters) ... 

H g Powder spectra Quadrupole splitting T,J2 Direct determination of order parameters and bond vectors Measurable in cells and dispersed lipids 7 dominated by fast (ns) motions T2 dominated by slow (ms- ms) motions Low natural abundance Need for selective deutera tion Low sensitivity Ordering properties of phospholipids Dynamic properties of phospholipids... 

For a conserved order parameter, the interface dynamics and late-stage domain growth involve the evapomtion-diffusion-condensation mechanism whereby large droplets (small curvature) grow at tlie expense of small droplets (large curvature). This is also the basis for the Lifshitz-Slyozov analysis which is discussed in section A3.3.4. 

The practical goal of EPR is to measure a stationary or time-dependent EPR signal of the species under scrutiny and subsequently to detemiine magnetic interactions that govern the shape and dynamics of the EPR response of the spin system. The infomiation obtained from a thorough analysis of the EPR signal, however, may comprise not only the parameters enlisted in the previous chapter but also a wide range of other physical parameters, for example reaction rates or orientation order parameters. 

Analytic teclmiques often use a time-dependent generalization of Landau-Ginzburg ffee-energy fiinctionals. The different universal dynamic behaviours have been classified by Hohenberg and Halperin [94]. In the simple example of a binary fluid (model B) the concentration difference can be used as an order parameter m.. A gradient in the local chemical potential p(r) = 8F/ m(r) gives rise to a current j... 

This time development of the order parameter is completely detenninistic when the equilibrium p(r) = const is reached the dynamics comes to rest. Noise can be added to capture the effect of themial fluctuations. This leads to a Langevin dynamics for the order parameter. 

Variation in Verlet order parameter during the equilibration phase of a molecular dynamics simulation of... 

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