Long-Term Simulations

Inefficiency of Direct Simulation Suppose we want to compute the corresponding invariant measure p by direct simulation. Direct long term simulation by symplectic discretization of (1) yields the discrete solution ( ) a )i, ... 

For long term simulations, it turns out that the reproduction of the conservation properties is most important in order to ensure reliable results. 

Long term simulations require structurally stable integrators. Symplec-tic and symmetric methods nearly perfectly reproduce structural properties of the QCMD equations, as, for example, the conservation of the total energy. We introduced an explicit symplectic method for the QCMD model — the Pickaback scheme— and a symmetric method based on multiple time stepping. 

Abstract. The overall Hamiltonian structure of the Quantum-Classical Molecular Dynamics model makes - analogously to classical molecular dynamics - symplectic integration schemes the methods of choice for long-term simulations. This has already been demonstrated by the symplectic PICKABACK method [19]. However, this method requires a relatively small step-size due to the high-frequency quantum modes. Therefore, following related ideas from classical molecular dynamics, we investigate symplectic multiple-time-stepping methods and indicate various possibilities to overcome the step-size limitation of PICKABACK. 

For long-term simulations, it generally proves advantageous to consider numerical integrators which pass the structural properties of the model onto the calculated solutions. Hence, a careful analysis of the conservation properties of QCMD model is required. A particularly relevant constant of motion of the QCMD model is the total energy of the system... 

Ginoux P. Prospero J. and Torres O. (2002). Long-term simulation of dust distribution with the GOCART model Correlation with the North Atlantic Oscillation. In J.A. Lee and T.M. Zobeck (eds.), Proceedings of ICAR5/GCTE-SEN Joint Conference. International Center for Arid and Semiarid Lands Studies, Texas Tech. University, Lubbock, Texas, pp. 241-245. 

The coupled long-term simulation and data assimilation runs are structured as a sequence of coupled runs (6 h in data assimilation, 24 h in forecast mode) because the IFS needs a re-start from a meteorological analysis as often as possible. The CTM provides the tracer initial conditions of the IFS for the first forecasts. There are three modes of how the initial conditions for the GRG-tracers are obtained in the subsequent forecasts (see Fig. 10.2). 

After the optimization, the robustness of the Pareto front has to be assessed. For each final solution of the optimization, a simulation of 609 days is performed with the influent proposed for BSM1 LT. This influent is typical of the events which perturb the WWTPs like rains, storms and holidays. After this long-term simulation, daily means are computed for both objectives. Then, for the evaluation of the robustness, a Principal Components Analysis (PCA) of these 609 daily mean values is performed. This provides the two directions of variations. 10 and 90 percentiles of the projections of... 

In this study, the optimization of a WWTP control law by means of a multi-objectives genetic algorithm proved to be a reliable technique. To be feasible, this optimization however needs to be performed on a limited time horizon (typically two or three sludge retention times). This study showed that the addition of a long term simulation of final optimized settings allows the decision maker to check the quality of the results produced, as well as to have more insight into the performances of the control law. 

Embedded in the circulation model, it provides a coupled physical-biogeochemical model of the Baltic Sea ecosystem as an example application. Several applications of the model system are discussed, covering process studies, such as currents in the western Baltic, river plumes, and sediment transport, but also long-term simulations of the ecosystem dynamics. 

Applications of three-dimensional Baltic Sea circulation models, which encompass both synoptic scales and slowly varying long-term processes, were reported in Lehmann (1995), Lehmann and Hinrichsen (2000), Neumann et al. (2002), Schrum et al. (2003), and Lehmann et al. (2004). Long-term simulations covering the last century have been carried out by Meier... 

The horizontal ice distribution simulated with such a low order ice model resembles the observed distributions of sea ice however, the storage of freshwater in the ice and the formation of a new water mass by freezing with brine release and by melting is neglected. To include these features, the three-level ice model of Winton (2000) is coupled with MOM-3.1 to provide an improved representation of sea ice for long-term simulations. The sea ice is vertically resolved by two ice layers and a snow cover, with different development of thickness and temperature. As shown in Fig. 19.3, this local thermodynamic description yields arealistic simulation of the interannual variation in the thickness and the spatial extent of the ice cover in the Baltic Sea. The transfer of wind momentum to the currents and to surface waves is exponentially damped out if the ice thickness exceeds a critical value, for example, 10 cm, assuming fast ice. 

Another requirement for long-term simulations arises from the restricted water exchange of the B altic Sea with the open ocean leading to long residence times in the order of 30 years (e.g.. Dobs et al., 2004). This implies that long-term simulations, which should describe the response of the whole Baltic Sea to changes in the external forcing, have to cover at least 30 years to include the time span of the residence time. 

The purpose of this paper is to present an assessment exercise of a leaching pesticide using the PRZM model. The assessment begins with a calibration of PRZM for the pesticide aldicarb applied to tobacco in North Carolina and potatoes in Wisconsin. Following these calibrations, long term simulations are performed using these same calibration scenarios. Examination of key PRZM output indicates the "potential" for aldicarb to contaminate ground water in the scenarios modeled. 

The appropriate means to "test" a model is dependent on the biases of the model tester and the purposes of his exercise. Words such as calibration, validation, and verification have been used to describe a model testing procedure. For this study, PRZM was calibrated to three field sites to determine appropriate parameters for longer term simulations. These long term simulations employed the same parameters as the calibration simulations, and their purpose was to examine trends in pesticide leaching as expressed by PRZM output. 

Long term simulations were performed using Identical scenarios as the calibration scenarios. The purpose was to assess trends In aldicarb leaching by examining key PRZM outputs of aldicarb mass and concentration at 2 meters below the soil surface. The results Indicate that there was little to no potential for aldicarb to leach in the sandy loam soils modeled in North Carolina and Wisconsin. 

Patsch, J. and Radach, G. (1997) Long-term simulation of the eutrophication of the North Sea temporal development of nutrients, chlorophyll and primary production in comparison to observations. Journal of Sea Research, 38, 275-310. 

In practice, a low order approximation of Hh is used, such as the truncation to terms of order four or six in the stepsize.) The resulting method substantially exhibits higher accuracy than the standard Collisional Verlet method in long term simulations, including accurate recovery of statistical properties (for example velocity autocorrelation functions). Additional cost is, however, involved in the handling of the collisions. 

Fijany A et al (1998) Novel algorithms for massively parallel, long-term, simulation of molecular dynamics systems. Adv Eng Softw 29(3-6) 441-450... 

However, the most definitive tests for biodegradability of plastics involves the use of " C-labelled plastics in long-term simulated-soil-burial procedures. The procedure has been used in medical research for many years to decipher the intricate pathways of important biological reactions involving... 

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