Multi-time scale analysis applied to long time simulation of power systems

The results are presented of applying multi-time scale analysis using the singular perturbation technique for long time simulation of power system problems. A linear system represented in state-space form can be decoupled into slow and fast subsystems. These subsystems can be simulated with different time steps and then recombined to obtain the system response. Simulation results with a two-time scale analysis of a power system show a large saving in computational costs.

Time Scale Separated Nonlinear Partial Integrated Guidance and Control of Interceptors in the Terminal Phase

The paper proposes a time scale separated partial integrated guidance and control of an interceptor for engaging high speed targets in the terminal phase. In this two loop design, the outer loop is an optimal control formulation based on nonlinear model predictive spread control philosophies. It gives the commanded pitch and yaw rates whereas necessary roll-rate command is generated from a roll-stabilization loop. The inner loop tracks the outer loop commands using the dynamicinversion philosophy. However, unlike conventional designs, in both the loops the Six degree of freedom (Six-DOF) interceptor model is used directly. This intelligent manipulation preserves the inherent time scale separation property between the translational and rotational dynamics, and hence overcomes the deficiency of current IGC designs, while preserving its benefits. Six-DOF simulation studies have been carried out accounting for three dimensional engagement geometry. Different comparison studies were also conducted to measure the performance of the algorithm.

Sensitivity of the simulated precipitation to changes in convective relaxation time scale

The paper describes the sensitivity of the simulated precipitation to changes in convective relaxation time scale (TAU) of Zhang and McFarlane (ZM) cumulus parameterization, in NCAR-Community Atmosphere Model version 3 (CAM3). In the default configuration of the model, the prescribed value of TAU, a characteristic time scale with which convective available potential energy (CAPE) is removed at an exponential rate by convection, is assumed to be 1 h. However, some recent observational findings suggest that, it is larger by around one order of magnitude. In order to explore the sensitivity of the model simulation to TAU, two model frameworks have been used, namely, aqua-planet and actual-planet configurations. Numerical integrations have been carried out by using different values of TAU, and its effect on simulated precipitation has been analyzed. The aqua-planet simulations reveal that when TAU increases, rate of deep convective precipitation (DCP) decreases and this leads to an accumulation of convective instability in the atmosphere. Consequently, the moisture content in the lower-and mid-troposphere increases. On the other hand, the shallow convective precipitation (SCP) and large-scale precipitation (LSP) intensify, predominantly the SCP, and thus capping the accumulation of convective instability in the atmosphere. The total precipitation (TP) remains approximately constant, but the proportion of the three components changes significantly, which in turn alters the vertical distribution of total precipitation production. The vertical structure of moist heating changes from a vertically extended profile to a bottom heavy profile, with the increase of TAU. Altitude of the maximum vertical velocity shifts from upper troposphere to lower troposphere. Similar response was seen in the actual-planet simulations. With an increase in TAU from 1 h to 8 h, there was a significant improvement in the simulation of the seasonal mean precipitation. The fraction of deep convective precipitation was in much better agreement with satellite observations.

The actor-critic algorithm as multi-time-scale stochastic approximation

The actor-critic algorithm of Barto and others for simulation-based optimization of Markov decision processes is cast as a two time Scale stochastic approximation. Convergence analysis, approximation issues and an example are studied.

Comparison of the ultrafast to slow time scale dynamics of three liquid crystals in the isotropic phase

The dynamics of three liquid crystals, 4'(pentyloxy)-4-biphenylcarbonitrile (5-OCB), 4'-pentyl-4-biphenylcarbonitrile (5-CB), and 1-isothiocyanato-(4-propylcyclohexyl)benzene (3-CHBT), are investigated from very short time (similar to1 ps) to very long time (>100 ns) as a function of temperature using optical heterodyne detected optical Kerr effect experiments. For all three liquid crystals, the data decay exponentially only on the longest time scale (> several ns). The temperature dependence of the long time scale exponential decays is described well by the Landau-de Gennes theory of the randomization of pseudonematic domains that exist in the isotropic phase of liquid crystals near the isotropic to nematic phase transition. At short time, all three liquid crystals display power law decays. Over the full range of times, the data for all three liquid crystals are fit with a model function that contains a short time power law. The power law exponents for the three liquid crystals range between 0.63 and 0.76, and the power law exponents are temperature independent over a wide range of temperatures. Integration of the fitting function gives the empirical polarizability-polarizability (orientational) correlation function. A preliminary theoretical treatment of collective motions yields a correlation function that indicates that the data can decay as a power law at short times. The power law component of the decay reflects intradomain dynamics. (C) 2002 American Institute of Physics.

On the role of cloud adjustment time scale in simulating precipitation with Relaxed Arakawa-Schubert convection scheme

The precipitation by Relaxed Arakawa-Schubert cumulus parameterization in a General Circulation Model (GCM) is sensitive to the choice of relaxation parameter or specified cloud adjustment time scale. In the present study, we examine sensitivity of simulated precipitation to the choice of cloud adjustment time scale (tau(adj)) over different parts of the tropics using National Center for Environmental Prediction (NCEP) Seasonal Forecast Model (SFM) during June-September. The results show that a single specified value of tau(adj) performs best only over a particular region and different values are preferred over different parts of the world. To find a relation between tau(adj) and cloud depth (convective activity) we choose six regions over the tropics. Based on the observed relation between outgoing long-wave radiation and tau(adj), we propose a linear cloud-type dependent relaxation parameter to be used in the model. The simulations over most parts of the tropics show improved results due to this newly formulated cloud-type dependent relaxation parameter.

Oscillatory settling in wormlike-micelle solutions: bursts and a long time scale

We study the dynamics of a spherical steel ball falling freely through a solution of entangled wormlike-micelles. If the sphere diameter is larger than a threshold value, the settling velocity shows repeated short oscillatory bursts separated by long periods of relative quiescence. We propose a model incorporating the interplay of settling-induced flow, viscoelastic stress and, as in M. E. Cates, D. A. Head and A. Ajdari, Phys. Rev. E, 2002, 66, 025202(R) and A. Aradian and M. E. Cates, Phys. Rev. E, 2006, 73, 041508, a slow structural variable for which our experiments offer independent evidence.

Climate response to changes in atmospheric carbon dioxide and solar irradiance on the time scale of days to weeks

Recent studies show that fast climate response on time scales of less than a month can have important implications for long-term climate change. In this study, we investigate climate response on the time scale of days to weeks to a step-function quadrupling of atmospheric CO2 and contrast this with the response to a 4% increase in solar irradiance. Our simulations show that significant climate effects occur within days of a stepwise increase in both atmospheric CO2 content and solar irradiance. Over ocean, increased atmospheric CO2 warms the lower troposphere more than the surface, increasing atmospheric stability, moistening the boundary layer, and suppressing evaporation and precipitation. In contrast, over ocean, increased solar irradiance warms the lower troposphere to a much lesser extent, causing a much smaller change in evaporation and precipitation. Over land, both increased CO2 and increased solar irradiance cause rapid surface warming that tends to increase both evaporation and precipitation. However, the physiological effect of increased atmospheric CO2 on plant stomata reduces plant transpiration, drying the boundary layer and decreasing precipitation. This effect does not occur with increased solar irradiance. Therefore, differences in climatic effects from CO2 versus solar forcing are manifested within days after the forcing is imposed.

Role of the cloud adjustment time scale in simulation of the interannual variability of Indian summer monsoon

The simulation of precipitation in a general circulation model relying on relaxed mass flux cumulus parameterization scheme is sensitive to cloud adjustment time scale (CATS). In this study, the frequency of the dominant intra-seasonal mode and interannual variability of Indian summer monsoon rainfall (ISMR) simulated by an atmospheric general circulation model is shown to be sensitive to the CATS. It has been shown that a longer CATS of about 5 h simulates the spatial distribution of the ISMR better. El Nio Southern Oscillation-ISMR relationship is also sensitive to CATS. The equatorial Indian Ocean rainfall and ISMR coupling is sensitive to CATS. Our study suggests that a careful choice of CATS is necessary for adequate simulation of spatial pattern as well as interannual variation of Indian summer monsoon precipitation.

The motion and the core structure of a geostrophic vortex - one-time scale inner solution and the motion of the vortex

By means of the matched asymptotic expansion method with one-time scale analysis we have shown that the inviscid geostrophic vortex solution represents our leading solution away from the vortex. Near the vortex there is a viscous core structure, with the length scale O(a). In the core the viscous stresses (or turbulent stresses) are important, the variations of the velocity and the equivalent height are finite and dependent of time. It also has been shown that the leading inner solutions of the core structure are the same for two different time scales of S/(ghoo)1/2 and S/a (ghoo)1/2. Within the accuracy of O(a) the velocity of a geostrophic vortex center is equal to the velocity of the local background flow, where the vortex is located, in the absence of the vortex. Some numerical examples demonstrate the contributions of these results.