Multiple Time-scale Model Research Articles

A Multiple Time-Scale Model for Heat Transfer in Turbulent Shear Flows.

This paper reports a multiple time-scale turbulence model for a thermal field in shear flows. The model is based on the concept of the three divided thermal fluctuation spectra. The spectrum in the highest wavenumber region is modeled using an algebraic relation concerned with the molecular Prandtl number, and the remaining two other regions are modeled with four differential equations. Comparisons with the DNS data indicate that the present model works well for the predictions of thermal fields not only in wall shear flows under varions Prandtl numbers but in homogeneous shear flows with a mean thermal gradient.

Phase synchronization in two coupled chaotic neurons

Chaotically-spiking dynamics of Hindmarsh–Rose neurons are discussed based on a flexible definition of phase for chaotic flow. The phase synchronization of two coupled chaotic neurons is in fact the spike synchronization. As a multiple time-scale model, the coupled HR neurons have quite different behaviors from the Rössler oscillators only having single time-scale mechanism. Using such a multiple time-scale model, the phase function can detect synchronization dynamics that cannot be distinguished by cross-correlation. Moreover, simulation results show that the Lyapunov exponents cannot be used as a definite criterion for the occurrence of chaotic phase synchronization for such a system. Evaluation of the phase function shows its utility in analyzing nonlinear neural systems.

TIME, TRACE, MEMORY

Objections to a trace hypothesis for interval timing do not apply to the multiple‐time‐scale (MTS) theory, which incorporates a dynamic trace tuned by the system history and can easily accommodate interval timing over a 1,000:1 range. The MTS model can also account for Weber's law as well as systematic deviations from it. Contrary to our critics, we contend that patterns of variance in interval timing experiments are not fully described by scalar expectancy theory, and that attempting to understand timing by assigning variance to different elements of a flexible model that lacks inductive support is a flawed strategy, because the attempt may be successful even if the model is wrong. We further argue that biological plausibility is an unreliable guide to the development of behavioral theory, that prediction is not the same as test, that induction should precede deduction, and that a rat is not a clock.

Transport process of turbulence energy in particle-laden turbulent flow

The interactions between dispersed particles and fluid turbulence have been investigated experimentally and numerically in a fully developed downflow channel in water. Particle velocities and fluid velocities in the presence of 340 μm and 500 μm glass beads and 420 μm cellulose particles were measured by digital particle image velocimetry. In the presence of particles slightly greater than the Kolmogorov lengthscale of flow and with a large particle time constant, turbulence energy was augmented in the streamwise direction, which means that the energy was transported by means of particle concentration fluctuations. The dissipation rate in the equation of streamwise component of the Reynolds stress was also increased. Cellulose particles with a small particle time constant dissipated the turbulence energy in the streamwise and transverse directions due to particle drag. A multiple time-scale model in which the effect of particle concentration fluctuations on large scales of turbulent motion was reflected can present both turbulence attenuation and augmentation by particles. The particle concentration fluctuations increase the turbulence energy in the production range, which induces increasing the energy transport from the production range to the transfer range and yields finally enhancing the dissipation.