Benchmark problems

The outlined scheme is shown to yield stable solutions for non-zero Weissenberg number flows in a number of benchmark problems (Swarbric and Nassehi, 1992b). However, the extension of this scheme to more complex problems may involve modifications such as increasing of elemental subdivisions for stress calculations from 3 x 3 to 9 x 9 and/or the discretization of the stress field by biquadratic rather than bi-linear sub-elements. It should also be noted that satisfaction of the BB condition in viscoelastic flow simulations that use mixed formulations is not as clear as the case of purely viscous regimes. 

On the subject of comparing iterative methods a word of caution is in order. Clearly in any quantitative comparison, the termination criteria should be comparable and the benchmark problems should be run on the same computer. Yet even for simple problems and methods, these two requirements prove to be difficult to enforce and insufficient to ensure meaningful comparisons. To allow for the fact that different methods do not terminate at exactly the same point even when the same termination criterion is used, Broyden (B13) introduced a mean convergence rate, R, which is... 

Figure 10.7 shows the extended RTN formulated for the benchmark problem. The production process includes diverging and converging material flows, flexible proportions of output goods (task Tj), cyclic material flows (recycling of output from task T3 into state Si), intermediate products which cannot be stored (state nodes S5, S9, S10, S12), and blending of products in task Ti 5. All processing tasks are operated batch-wise with lower and upper bounds on batch sizes. Batch sizes are... 

Sparacino, G. and Cobelli, C., Deconvolution of physiological and pharmacokinetic data comparison of algorithms on benchmark problems, in Modeling and Control in Biomedical Systems, Linkens, D.A. and Carson, E., Eds., Elsevier, Oxford, 1997, pp. 151-153. 

The goal of this chapter is twofold. First we wish to critically compare—from both a conceptional and a practical point of view—various classical and mixed quantum-classical strategies to describe non-Born-Oppenheimer dynamics. To this end. Section II introduces five multidimensional model problems, each representing a specific challenge for a classical description. Allowing for exact quantum-mechanical reference calculations, aU models have been used as benchmark problems to study approximate descriptions. In what follows, Section III describes in some detail the mean-field trajectory method and also discusses its connection to time-dependent self-consistent-field schemes. The surface-hopping method is considered in Section IV, which discusses various motivations of the ansatz as well as several variants of the implementation. Section V gives a brief account on the quantum-classical Liouville description and considers the possibility of an exact stochastic realization of its equation of motion. 

M. Witczak, J. Patton, and J. Korbicz. Fault detection with observers and genetic programming application to the DAMADICS benchmark problem. In Proceedings of the 5th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes, pages 1203-1208, 2003. 

Reitsma, F. (2004), PBMR-268 Neutronics and Transient Benchmark Problem, PBMR Ltd., South Africa. 

Seker, V., T.J. Downar (2005), Analysis of the OECD/NEA PBMR-268 Transient Benchmark Problem with the PARCS Neutronics Code , American Nuclear Society TRANSACTIONS, 92, 697-699. 

Accident scenarios initiated in the PBMR plant have been described and thoroughly modelled as benchmark problems (Reitsma, 2004). While modelling these scenarios in a coupled nuclear reactor/ chemical plant scheme is interesting, it should be noted that in most of these scenarios the nuclear... 

The widespread adoption by the simulation community of a specific benchmark problem to gauge both the effectiveness and scalability of emerging algorithms, and the suitability of different machine architectures, is to be applauded. 

The MHE and PF frameworks will be demonstrated separately for a simpler problem involving the well studied nonlinear benchmark problem of the Van der Vusse scheme [10] a feed stream of feedstock A enters a reactor and reacts to form the desired product, B. The model assumes a first order reaction for the conversion of A into B, with two competing reactions B C and 2A D. Temperature-dependent Arrhenius reaction rates are assumed. The model has four states concentration of A, concentration of B, reactor temperature, and cooling jacket temperature. 

It is noteworthy that the JG operator has also been successfully incorporated into a Multi-objective Simulated Annealing technique (Sankararao and Gupta, 2007 see Chapter 4 in this book). The performance assessment of this algorithm was done on three well-known test (benchmark) problems commonly used in the evolutionary MOO field. This algorithm was then employed for the MOO of an industrial fluidized-bed catalytic cracking unit. 

Application of the Jumping Gene Adaptations of NSGA-II and MOSA to Three Benchmark Problems... 

The performance of the different JG adaptations of NSGA-II is studied using three benchmark problems, ZDT4, ZDT2 and ZDT3 (Deb, 2001). Similarly, the performance of MOSA and its JG adaptations (only JG and... 

The use of the jumping gene operator (any of the adaptations) increases the randomness/diversity and, thus, usually gives better results. Among the various JG adaptations discussed above, the sJG adaptation is found to be better for the benchmark problems studied here. But the choice of a particular adaptation is problem-specific, e.g., in froth flotation circuits the mJG adaptation (Guria et al., 2005b) is found to be better. 

In 2009, an experimental paper [115] and a related short comment [116] on the issue of the precise characteristics of the PEC of the Be2 E+ state were published in the journal SCIENCE. In their experimental report, whose results resolved previous uncertainties, Merritt, Bondybey and Heaven [115] review and explain briefly the long-held interest in this 70 year-old problem. They note that "The sensitivity of the Be2 PEC to the level of theory has made analysis of this molecule a benchmark problem for quantum mechanics and a critical test for new theoretical models and procedures. At present, more than... 

The constructed algorithm for the inverse analysis was then also validated for this same benchmark problem with Bi = co, from a theoretical perspective, assuming the fluid temperature at the wall to be measurable. Simulated experimental results were produced with 50 terms in the eigenfunction expansion provided in Ref. [6], and the direct problem solution in the inverse analysis was implemented with just 10 terms in the expansion here proposed to avoid the so called inverse crime [28]. A total of 1,000 measurements are provided, with white noise considered normally distributed... 

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