Dynamic Scale Model Research Articles

Dynamic scaling of the critical mixture perfluoromethylcyclohexane–carbon tetrachloride

Ultrasonic attenuation, specific heats at constant pressure, static and dynamic light scattering as well as shear viscosity data of the perfluoromethylcyclohexane–carbon tetrachloride critical system have been re-evaluated in the light of the Bhattacherjee–Ferrell dynamic scaling model. The experimental sonic attenuation coefficients yield the theoretical form of the scaling function if a noncritical relaxation term is assumed to contribute to the total spectra in addition to the critical contribution. Evidence from noncritical ultrasonic spectra suggests the noncritical relaxation to be due to rotational isomerization of the perfluoromethylcyclohexane molecule. The amplitudes in the power laws of the fluctuation correlation length, the mutual diffusion coefficient and the relaxation rate of concentration fluctuations are ξ0 = (0.228 ± 0.021) nm, D0 = (1.24 ± 0.04) × 109 m2 s−1, and Γ0 = (47.5 ± 13) × 109 s−1, respectively. The amplitude of the critical term in the heat capacity is Cpc = (0.093 ± 0.002) J g−1 K−1 and the adiabatic coupling constant results as g = 0.126.

A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation

Large-eddy simulations of incompressible Newtonian fluid flows with approximate deconvolution models based on the van Cittert method are reported. The Legendre spectral element method is used for the spatial discretization to solve the filtered Navier–Stokes equations. A novel variant of approximate deconvolution models blended with a mixed scale model using a dynamic evaluation of the subgrid-viscosity constant is proposed. This model is validated by comparing the large-eddy simulation with the direct numerical simulation of the flow in a lid-driven cubical cavity, performed at a Reynolds number of 12,000. Subgrid modeling in the case of a flow with coexisting laminar, transitional and turbulent zones such as the lid-driven cubical cavity flow represents a challenging problem. Moreover, the coupling with the spectral element method having very low numerical dissipation and dispersion builds a well suited framework to analyze the efficiency of a subgrid model. First- and second-order statistics obtained using this new model are showing very good agreement with the direct numerical simulation. Filtering operations rely on an invertible filter applied in a modal basis and preserving the C 0-continuity across elements. No clipping on dynamic parameters was needed to preserve numerical stability.

SPACSYS: Integration of a 3D root architecture component to carbon, nitrogen and water cycling—Model description

It is an ongoing challenge to develop and demonstrate management practices that increase the sustainability of agricultural systems. Soil carbon and nitrogen dynamics directly affect soil quality, crop productivity and environmental impacts. Root systems are central to the acquisition of water and nutrients by plants, but are also a major pathway for the inputs of carbon and nutrients to soil. The complexity of both biotic and abiotic interactions, combined with stochastic changes in root architecture, makes it difficult to understand below-ground dynamics on the basis of experimentation alone. The integration of dynamic models of above-ground growth, three-dimensional root system demography, and interactions between plants and the environment, into one single model is a major challenge because of the complexity of the systems. In order to understand the interaction between a plant and the environment, it is advantageous to develop a model framework to integrate submodels that simulate various plant and environmental components. The objective of this paper is to outline a mechanistic and process-based model, which is capable of simulating interactions among environmental conditions around plants, plant growth and development, nitrogen and carbon cycles, with a three-dimensional root system submodel as an interface. The model presented in this paper is a mixed dimensional, multi-layer, field scale, weather-driven and daily time-step dynamic simulation model. The current version includes a plant growth and development component, a nitrogen cycling component, a carbon cycling component, plus a soil water component that includes representation of water flow to field drains as well as downwards through the soil layers, together with a heat transfer component. The components themselves and linkage among components are designed using object-oriented techniques, which makes the model robust, understandable and reusable. The components are implemented in the C++ programming language, and inputs and outputs of all components are organised as a database in either Microsoft ® SQL Server 2000, Access 2000 or MySQL5.0. Root architecture is visualised by using the OpenGL graphics system. Preliminary validation with two separate experimental datasets shows that the model can reasonably simulate root systems, nitrogen cycling, water movement and plant growth.

Dielectric relaxation in compressed glassy and orientationally disordered mixed crystals

Results of isobaric and isothermal studies of dielectric relaxation in a vitrifying orientationally disordered crystal ${[{(\mathrm{C}{\mathrm{H}}_{3})}_{3}\mathrm{C}(\mathrm{C}{\mathrm{H}}_{2}\mathrm{O}\mathrm{H})]}_{0.70}{[{(\mathrm{C}{\mathrm{H}}_{3})}_{2}\mathrm{C}{(\mathrm{C}{\mathrm{H}}_{2}\mathrm{O}\mathrm{H})}_{2}]}_{0.30}$ under pressures reaching $P=1.8\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ are discussed. The application of the linearized derivative-based analysis made it possible to detect validity domains of the Vogel-Fulcher-Tammann $\ensuremath{\tau}={\ensuremath{\tau}}_{0}^{\mathit{VFT}}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}({D}_{T}{T}_{0}∕T\ensuremath{-}{T}_{0})$ relation, the critical-like $\ensuremath{\tau}(T)\ensuremath{\propto}{(T\ensuremath{-}{T}_{X})}^{\ensuremath{-}g}$ dependence as well as their pressure counterparts. The agreement with predictions of the dynamical scaling model (DSM) is worth stressing. This suggests that the decoupling of translational and orientational degrees of freedom may be the key mechanism responsible for the validity of the DSM description for glassy systems. The application of high pressures led to the emergence of a phase transition, absent in studies under atmospheric pressure. The parametrization of the pressure evolution of the phase transition temperature $[{T}_{\mathit{tr}}(P)]$ via the extended Simon-Glatzel-type relation suggests the possible maximum of ${T}_{\mathit{tr}}(P)$ at extreme pressures. It is concluded that the nontypical increase of the fragility strength coefficient $({D}_{T})$ noted on cooling in studies under atmospheric pressure [A. Drozd-Rzoska et al., Phys. Rev. B 73, 224205 (2006)] may be due to approaching the phase transition hidden under compression.

Solution Structure and Dynamics of Cartilage Aggrecan

We studied the structure and dynamics of porcine laryngeal aggrecan in solution using a range of noninvasive techniques: dynamic light scattering (DLS), small-angle neutron scattering (SANS), video particle tracking (VPT) microrheology, and diffusing wave spectroscopy (DWS). The data are analyzed within the framework of a combined static and dynamic scaling model, and evidence is found for reptation of the comb backbones with unentangled side-chain dynamics. Small-angle neutron scattering indicated standard polyelectrolyte scaling of the mesh size (xi) with concentration (c) in semidilute solutions for the whole aggrecan aggregate, xi = Ac(-0.47+/-0.04), with the prefactor (A) implying there is on average 60 nm between the aggrecan subunits along the backbone. VPT demonstrated large exponents for the power law dependence of the intrinsic viscosity (eta) on the polymer concentration in the semidilute concentration regime, eta approximately c(alpha); with alpha equal to 2.04 +/- 0.06 and 1.95 +/- 0.08 for the assembled and disassembled aggrecan aggregates, respectively. DWS at high frequencies (10(4)-10(5) Hz) gave evidence for internal Rouse modes of the aggrecan monomers, independent of the degree of self-assembly of the molecules.

Dynamic scaling of the critical binary mixture methanol-hexane

Acoustical attenuation spectrometry, dynamic light scattering, shear viscosity, density, and heat capacity measurements of the methanol/n-hexane mixture of critical composition have been performed. The critical part in the sonic attenuation coefficients nicely fits to the empirical scaling function of the Bhattacharjee-Ferrell [Phys. Rev. A 24, 1643 (1981)] dynamic scaling model if the theoretically predicted scaled half-attenuation frequency Omega(12) (BF)=2.1 is used. The relaxation rates of order parameter fluctuations, as resulting from the acoustical spectra, within the limits of experimental error agree with those from a combined evaluation of the light scattering and shear viscosity measurements. Both series of data display power law with amplitude Gamma(0)=44x10(9) s(-1). The amplitude of the fluctuation correlation length follows as xi(0)=0.33 nm from the light scattering data and as xi(0)=0.32 nm from the amplitude of the singular part of the heat capacity if the two-scale factor universality relation is used. The adiabatic coupling constant g=0.11 results from the amplitude of the critical contribution to the acoustical spectrum near the critical point, in conformity with g=0.12 as following from the variation of the critical temperature with pressure along the critical line and the thermal expansion coefficient.

Critical fluctuations of the micellar triethylene glycol monoheptyl ether-water system

Using the equal volume criterion and also the pseudospinodal conception the critical demixing point of the triethylene glycol monoheptyl ether/water system (C7E3H2O) has been determined as Ycrit=0.1 and Tcrit=296.46 K (Y, mass fraction of surfactant). From density measurements the critical micelle concentration (cmc) followed as Ycmc=0.007 at 288.15 K and Ycmc=0.0066 at 298.15 K. The (static) shear viscosity etas and the mutual diffusion coefficient D of the C7E3H2O mixture of critical composition have been evaluated to yield their singular and background parts. From a combined treatment of both quantities the relaxation rate Gamma of order parameter fluctuations has been derived. Gamma follows power law with universal critical exponent and amplitude Gamma0=3.1 x 10(9) s(-1). Broadband ultrasonic spectra of C7E3H2O mixtures exhibit a noncritical relaxation, reflecting the monomer exchange between micelles and the suspending phase, and a critical term due to concentration fluctuations. The former is subject to a relaxation time distribution that broadens when approaching the critical temperature. The latter can be well represented with the aid of the dynamic scaling model by Bhattacharjee and Ferrell (BF) [Phys. Rev. A. 31, 1788 (1985)]. The half-attenuation frequency in the scaling function of the latter model is noticeably smaller (Omega12 (BF) approximately 1) than the theoretically predicted value Omega12 (BF)=2.1. This result has been taken as an indication of a coupling between the fluctuations in the local concentration and the kinetics of micelle formation, in correspondence with the idea of a fluctuation controlled monomer exchange [T. Telgmann and U. Kaatze, Langmuir 18, 3068 (2002)].

Critical Dynamics of the Binary System Nitroethane/3-Methylpentane: Relaxation Rate and Scaling Function

Shear viscosity and dynamic light scattering measurements as well as ultrasonic spectrometry studies of the nitroethane/3-methylpentane mixture of critical composition have been performed at various temperatures near the critical temperature, T(c). A combined evaluation of the shear viscosity and mutual diffusion coefficient data yielded the amplitude, xi(0), of the fluctuation correlation length, xi, assumed to follow power law, and the relaxation rate, Gamma, or order parameter fluctuations. The latter was found to follow power law with the theoretical universal exponent. The amplitudes xi(0) = 0.23 +/- 0.02 nm and Gamma(0) = (125 +/- 5) x 10(9) s(-1) nicely agree with literature values. Using the relaxation rates resulting from the viscosity and diffusion coefficient data, the scaling function has been calculated assuming the ultrasonic spectra to be composed of a critical part and a noncritical background contribution. The experimental scaling function fits well to the predictions of the Bhattacharjee-Ferrell dynamic scaling model with scaled half-attenuation frequency, Omega(BF)1/2= 2.1. The amplitude of the sonic spectra yields the amount |g| = 0.26 of the adiabatic coupling constant, g, in fair agreement with -0.29 from another thermodynamic relation.

The microrheology of polystyrene sulfonate combs in aqueous solution

Video particle tracking (VPT) and diffusing wave spectroscopy were used to characterize the microrheology of polystyrene sulfonate combs in aqueous solutions. At low frequencies VPT demonstrated predominantly viscous behavior. The manner in which the viscosity scaled as a function of monomer concentration was a sensitive function of the comb architecture. Densely branched combs or combs with long side chains demonstrated entangled polyelectrolyte scaling above the overlap concentration, whereas sparsely branched combs had unentangled polyelectrolyte scaling. A dynamic scaling model was developed for the viscosity of unentangled semidilute solutions of comb polyelectrolytes. Diffusing wave spectroscopy demonstrated Rouse modes (G' approximately G" approximately omega12) for the high-frequency dynamics of the semidilute comb solutions. The form of the high-frequency viscoelasticity was independent of the chain architecture and the modulus scaled as expected for linear flexible polyelectrolytes.

Sound attenuation, shear viscosity, and mutual diffusivity behavior in the nitroethane-cyclohexane critical mixture.

The shear viscosity eta(s), mutual diffusion coefficient D, and ultrasonic attenuation spectra of the nitroethane-cyclohexane mixture of critical composition have been measured at various temperatures near the critical temperature T(c). The relaxation rate of order parameter fluctuations resulting from a combined evaluation of the eta(s) and D data follows power law behavior with the theoretical exponent and with the large amplitude Gamma(o)=(156+/-2)x10(9) s(-1). The ultrasonic spectra have been evaluated in terms of a critical contribution and a noncritical background contribution. The amplitude of the former exhibits a temperature dependence, in conformity with a temperature dependence in the adiabatic coupling constant (|g| = 0.064 near T(c) and 0.1 at T-T(c)=3 K). If the variation of the critical amplitude with T is taken into account the experimental attenuation coefficient data display a scaling function which nicely fits to the theoretical prediction from the Bhattacharjee-Ferrell dynamic scaling model [R. A. Ferrell and J. K. Bhattacharjee, Phys. Rev. A 31, 1788 (1985)].

International demand and liquidity shocks in a SVAR model of the Australian economy

A structural vector autoregressive model of the Australian economy that allows for international shocks from the USA, Japan as well as world commodity prices is specified and estimated for the period 1979–1999. A block exogenous structure linking the three countries is imposed. The international linkages are modelled using a factor structure to circumvent problems from estimating large scale dynamic models. The factors are estimated recursively using a Kalman filter and are found to represent aggregate demand and liquidity shocks for the USA and Japan respectively. The key empirical result is the USA shocks are the dominant source of international shocks on the Australian economy with the Japanese economy having a dampening effect on the USA shocks. The empirical results also show that Australian monetary policy responds to domestic conditions rather than international monetary policy.

Turbulent Flow: Analysis, Measurement, and Prediction

Preface. Acknowledgments. 1. Preliminaries. 2. Overview of Turbulent Flow Physics and Equations. 3. Experimental and Numerical Methods. 4. Properties of Bounded Turbulent Flows. 5. Properties of Turbulent Free Shear Flows. 6. Turbulent Transport. 7. Theory of Idealized Turbulent Flows. 8. Turbulence Modeling. 9. Applications of Turbulence Modeling. 10. Large Eddy Simulations. 11. Analysis of Turbulent Scalar Fields. 12. Turbulence Theory. Author Index. Subject Index.

Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models

This article studies the local robustness of estimators and tests for the conditional location and scale parameters in a strictly stationary time series model. We first derive optimal bounded-influence estimators for such settings under a conditionally Gaussian reference model. Based on these results, we obtain optimal bounded-influence versions of the classical likelihood-based tests for parametric hypotheses. We propose a feasible and efficient algorithm for the computation of our robust estimators, which uses analytical Laplace approximations to estimate the auxiliary recentering vectors, ensuring Fisher consistency in robust estimation. This strongly reduces the computation time by avoiding the simulation of multidimensional integrals, a task that typically must be addressed in the robust estimation of nonlinear models for time series. In some Monte Carlo simulations of an AR(1)–ARCH(1) process, we show that our robust procedures maintain a very high efficiency under ideal model conditions and at the same time perform very satisfactorily under several forms of departure from conditional normality. In contrast, classical pseudo–maximum likelihood inference procedures are found to be highly inefficient under such local model misspecifications. These patterns are confirmed by an application to robust testing for autoregressive conditional heteroscedasticity.

Scale Free and Dynamic Models of Developement of the Hub and Spokes Networks in the Mediterranean

This paper puts forward an analysis suggesting a parallelism between hub and spokes networks in maritime transport and complex networks (such as the world-wide web, www). This possible parallelism is then used to explain the way networks in the Mediterranean may evolve. Since there is at present an on-going process in the Mediterranean involving interaction among countries bordering on the Mediterranean, with the aim of creating a trade area, and since this will result in a different intensity and typology of trade, the paper investigates how this transformation may affect currently existing maritime networks. We believe there is a strong similarity between the development models of scale free networks and hub and spokes transport systems. We thus conclude that the transformations arising from the process of Mediterranean integration will not adversely affect the development of newly integrated countries on the southern shores of the Mediterranean, and may even enhance their expansion. In this context, measures enacted by policy makers are advisable only if they are coherent with and boost spontaneous trends.

Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models

This paper studies the local robustness of estimators and tests for the conditional location and scale parameters in a strictly stationary time series model. We first derive optimal bounded-influence estimators for such settings under a conditionally Gaussian reference model. Based on these results, optimal bounded-influence versions of the classical likelihood-based tests for parametric hypotheses are obtained. We propose a feasible and efficient algorithm for the computation of our robust estimators, which makes use of analytical Laplace approximations to estimate the auxiliary recentering vectors ensuring Fisher consistency in robust estimation. This strongly reduces the necessary computation time by avoiding the simulation of multidimensional integrals, a task that has typically to be addressed in the robust estimation of nonlinear models for time series. In some Monte Carlo simulations of an AR 1)-ARCH(1) process we show that our robust procedures maintain a very high efficiency under ideal model conditions and at the same time perform very satisfactorily under several forms of departure from conditional normality. On the contrary, classical Pseudo Maximum Likelihood inference procedures are found to be highly inefficient under such local model misspecifications. These patterns are confirmed by an application to robust testing for ARCH.

A212 LARGE EDDY SIMULATION OF FLOWFIELDS AROUND NACA 0012 AND WIND TURBINE AIRFOILS AT HIGH ANGLE OF ATTACK

In the paper, the large eddy simulation of the flow fields around the NACA0012 airfoils and the MEL053 wind turbine airfoils developed by Mechanical Engineering Laboratory (MEL), Japan, is to be presented and discussed, with a special emphasis on the airfoil characteristics at the high angles of attack. As the subgrid scale models, the (conventional) Smagorinsky or dynamic subgrid scale model is used, and the numerical results are compared with the experiments. At high angles of attack, the quantitative agreement with the experiments is observed when the dynamic subgrid scale model is used. One the other hand, the Smagorinsky subgrid scale model over-predicts the subgrid stresses near the leading edge of the suction surface, poorly predicts the location of the re-attachment of the flow, and thus poorly predicts the static pressure on the airfoil. The difference in the numerical results between the Smagorinsky and dynamic subgrid scale models is less conspicuous for the MEL053 airfoils since the EML053 airfoils have more tendency to stall near the trailing edge.

Large Eddy Simulation of Flow and Scalar Transport in a Round Jet

Large eddy simulation (LES) was performed for a spatially developing round jet and its scalar transport at four steps of Reynolds number set between 1 200 and 1 000 000. Simulated domain, which extends 30 times nozzle diameter, includes initial, transitional and established stage of jet. Modified convection outflow condition was proposed in order to minimize effect of downstream boundary. Tested were two kinds of subgrid scale (SGS) models, Smagorinsky model (SM) and dynamic Smagorinsky model (DSM). In the former model parameters are kept at empirically deduced constants, while in the latter they are calculated using different levels of space filtering. Data analysis based on decay law of jet clearly presented performance of SGS models. Simulated results by SM and DSM compared favorably with existing measurements of jet and its scalar transport and however quantitative accuracy of DSM was better than SM at transitional stage of flow field. Computed parameters by DSM, coefficient for SGS stresses, CR, and SGS eddy diffusivity ratio, ГSGS, were not far from empirical constants of SM. Optimization of model coefficient was suggested in DSM so that coefficient CR was nearly equal in established stage of jet but it reduced in low turbulence close to the jet nozzle.

Two-time scale controller design for a high speed planar parallel manipulator with structural flexibility

Planar parallel manipulators, with potential applications in high speed, high acceleration tasks such as electronic component placement, would be subject to mechanical vibration due to high inertial forces acting on the linkages and other components. To achieve high throughput capability, such motion induced vibration would have to be damped quickly, to reduce settling time of the platform position and orientation. This paper develops a two-time scale dynamic model of a three-degree-of-freedom planar parallel manipulator with structurally flexible linkages. Based on the two-time scale model, a composite controller, consisting of a computed torque controller for the slow time-scale or rigid body subsystem dynamics, and a linear-quadratic state-feedback regulator for the fast time-scale flexible dynamic subsystem, is designed. Simulation results show that the composite control scheme permits the parallel manipulator platform to follow a given desired trajectory, while damping structural vibration arising due to excitation from inertial forces.

Two-time scale controller design for a high speed planar parallel manipulator with structural flexibility

SummaryPlanar parallel manipulators, with potential applications in high speed, high acceleration tasks such as electronic component placement, would be subject to mechanical vibration due to high inertial forces acting on the linkages and other components. To achieve high throughput capability, such motion induced vibration would have to be damped quickly, to reduce settling time of the platform position and orientation. This paper develops a two-time scale dynamic model of a three-degree-of-freedom planar parallel manipulator with structurally flexible linkages. Based on the two-time scale model, a composite controller, consisting of a computed torque controller for the slow time-scale or rigid body subsystem dynamics, and a linear-quadratic state-feedback regulator for the fast time-scale flexible dynamic subsystem, is designed. Simulation results show that the composite control scheme permits the parallel manipulator platform to follow a given desired trajectory, while damping structural vibration arising due to excitation from inertial forces.

Temperature dependence of relaxation times and the length scale of cooperative motion for glass-forming liquids

When considered in the framework of a dynamic scaling model, the length scale of cooperative motion of all glass-forming liquids appears to have a universal temperature dependence. This model also predicts relaxation times with a system-specific temperature dependence, as the product of the universal cooperative length scale raised to the sixth power and a non-universal thermally activated process. In the glassy state, the length scale for cooperative motion can become temperature-independent, so the model predicts relaxation times to have an Arrhenius temperature dependence. As expected by the model, the same activation energy is observed both above and below the glass transition. At sufficiently high temperatures the model ceases to apply to relaxation times, and the crossover to a high- T Arrhenius temperature dependence provides an experimental estimate of the caging temperature. We also report an approximate power law relation between the fragility index and the cooperative length scale at the glass transition.