scholarly journals A comparison of the modern Lie scaling method to classical scaling techniques

2016 ◽  
Vol 20 (7) ◽  
pp. 2669-2678 ◽  
Author(s):  
James Polsinelli ◽  
M. Levent Kavvas

Abstract. In the past 2 decades a new modern scaling technique has emerged from the highly developed theory on the Lie group of transformations. This new method has been applied by engineers to several problems in hydrology and hydraulics, including but not limited to overland flow, groundwater dynamics, sediment transport, and open channel hydraulics. This study attempts to clarify the relationship this new technology has with the classical scaling method based on dimensional analysis, non-dimensionalization, and the Vaschy–Buckingham-Π theorem. Key points of the Lie group theory, and the application of the Lie scaling transformation, are outlined and a comparison is made with two classical scaling models through two examples: unconfined groundwater flow and contaminant transport. The Lie scaling method produces an invariant scaling transformation of the prototype variables, which ensures the dynamics between the model and prototype systems will be preserved. Lie scaling can also be used to determine the conditions under which a complete model is dynamically, kinematically, and geometrically similar to the prototype phenomenon. Similarities between the Lie and classical scaling methods are explained, and the relative strengths and weaknesses of the techniques are discussed.

2015 ◽  
Vol 12 (10) ◽  
pp. 10197-10219 ◽  
Author(s):  
J. Polsinelli ◽  
M. L. Kavvas

Abstract. In the past two decades a new modern scaling technique has emerged from the highly developed theory on the Lie group of transformations. This new method has been applied by engineers to several problems in hydrology and hydraulics including but not limited to groundwater dynamics, sediment transport, and open channel hydraulics. This study attempts to clarify the relationship this new technology has with the classical scaling method based on dimensional analysis, non dimensionalization, and the Buckingham Π theorem. Key points of the Lie group theory, and the application of the Lie scaling transformation, are outlined and a comparison is done with two classical scaling models through two examples: unconfined groundwater flow and contaminant transport. The Lie scaling method produces an invariant scaling transformation of the prototype variables which ensures the dynamics between the model and prototype systems will be preserved. Lie scaling can also be used to determine the conditions under which a complete model is dynamically, kinematically, and geometrically similar to the prototype phenomenon. Similarities between the Lie and classical scaling methods are explained, and the relative strengths and weaknesses of the techniques are discussed.


Author(s):  
Linda Mora Siregar

The purpose of this study is to design a performance appraisal model more effectively in accordance with the company's vision and mission, namely by combining management methods based on objectives (management by objective) and graph scaling methods. In the preparation of performance appraisal models with management methods based on objectives (management by objective) and graph scaling methods, carried out with several stages, namely the first stage is planning the making of performance appraisal models, the second is job analysis, third is the preparation of management methods based on objectives (management by objective), the fourth is the preparation of the scaling method and the fifth is the preparation of the performance appraisal form. The making of this performance appraisal design will use a questionnaire method, observation and also interviews to obtain and collect information and data.  Keywords: Performance Appraisal, Management Methods, Graph Scaling.   Tujuan penelitian ini adalah untuk merancang model penilaian kinerja secara lebih efektif sesuai dengan visi dan misi perusahaan, yaitu dengan menggabungkan metode manajemen berdasarkan sasaran (management by objective) dan metode penskalaan grafik. Dalam penyusunan model penilaian kinerja dengan metode manajemen berdasarkan sasaran (management by objective) dan metode penskalaan grafik, dilakukan dengan beberapa tahapan yaitu tahap pertama adalah perencanaan pembuatan model penilaian kinerja, kedua analisis jabatan, ketiga penyusunan metode manajemen berdasarkan sasaran (management by objective), keempat penyusunan metode penskalaan grafik dan kelima adalah penyusunan formulir penilaian kinerja. Pembuatan rancangan penilaian kinerja ini akan menggunakan metode kuesioner, observasi dan juga wawancara untuk mendapatkan dan mengumpulkan informasi dan data.   Kata Kunci: Penilaian kinerja, Metode Manajemen, Penskalaan Grafik.


2010 ◽  
Vol 7 (2) ◽  
pp. 2157-2186 ◽  
Author(s):  
Y. Lin ◽  
G. X. Wang

Abstract. Finding an effective method to upscale or downscale hydrological processes is the central concern in hydrological research. The aim of this paper is to investigate a powerful, regulated relationship between runoff and catchment area, and establish the runoff scale transfer model for Gongga Mountain in China. We chose a series of catchments in which the contributing areas ranged from 0.41 km2 to 80.5 km2 to monitor the hydrological processes and meteorological conditions since 1990. To identify the nature and causes of variation in the runoff response to the size of catchments, a two-stage scaling method was proposed to describe the processes of runoff scaling. The results indicated that runoff had a different statistical relationship in different seasons and the related parameters were also different. The scaling models indicated a higher simulation efficiency and precision between the observed runoff and the calculated runoff, and they also provided a practical way for upscaling or downscaling in an alpine mountain watershed. For alpine mountain catchments, the results showed that the vegetation type and cover might be important factors for the runoff response to the scale effective.


2006 ◽  
Vol 129 (2) ◽  
pp. 312-317 ◽  
Author(s):  
Changduk Kong ◽  
Jayoung Ki

In order to estimate the gas turbine engine performance precisely, the component maps containing their own performance characteristics should be used. Because the components map is an engine manufacturer’s propriety obtained from many experimental tests with high cost, they are not provided to the customer generally. Some scaling methods for gas turbine component maps using experimental data or data partially given by engine manufacturers had been proposed in a previous study. Among them the map generation method using experimental data and genetic algorithms had showed the possibility of composing the component maps from some random test data. However not only does this method need more experimental data to obtain more realistic component maps but it also requires some more calculation time to treat the additional random test data by the component map generation program. Moreover some unnecessary test data may introduced to generate inaccuracy in component maps. The map generation method called the system identification method using partially given data from the engine manufacturer (Kong and Ki, 2003, ASME J. Eng. Gas Turbines Power, 125, 958–979) can improve the traditional scaling methods by multiplying the scaling factors at design point to off-design point data of the original performance maps, but some reference map data at off-design points should be needed. In this study a component map generation method, which may identify the component map conversely from some calculation results of a performance deck provided by the engine manufacturer using the genetic algorithms, was newly proposed to overcome the previous difficulties. As a demonstration example for this study, the PW206C turbo shaft engine for the tilt rotor type smart unmanned aerial vehicle which has been developed by Korea Aerospace Research Institute was used. In order to verify the proposed method, steady-state performance analysis results using the newly generated component maps were compared with them performed by the Estimated Engine Performance Program deck provided by the engine manufacturer. The performance results using the identified maps were also compared with them using the traditional scaling method. In this investigation, it was found that the newly proposed map generation method would be more effective than the traditional scaling method and the methods explained above.


Author(s):  
Changduk Kong ◽  
Jayoung Ki ◽  
Myoungcheol Kang

A scaling method for characteristics of gas turbine components using experimental data or partially given data from engine manufacturers was newly proposed. In case of currently used traditional scaling methods, the predicted performance around the on-design point may be well agreed with the real engine performance, but the simulated performance at off-design points far away from the on-design point may not be well agreed with the real engine performance generally. It would be caused that component scaling factors, which were obtained at on-design point, is also used at all other operating points and component maps are derived from different known engine components. Therefore to minimize the analyzed performance error in the this study, firstly component maps are constructed by identifying performances given by engine manufacturers at some operating conditions, then the simulated performance using the identified maps is compared with performances using currently used scaling methods. In comparison, the analyzed performance using the currently used traditional scaling method was well agreed with the real engine performance at the on-design point but had maximum 12% error at off design points within the flight envelope of a calculation example turboprop engine. However the performance result using the newly proposed scaling method had maximum 6% reasonable error even at all flight envelope.


Blood ◽  
2015 ◽  
Vol 125 (7) ◽  
pp. 1180-1188 ◽  
Author(s):  
Christoph J. Hofbauer ◽  
Shawn F. J. Whelan ◽  
Maria Hirschler ◽  
Peter Allacher ◽  
Frank M. Horling ◽  
...  

Key Points A new technology is presented to assess apparent affinities of FVIII-specific antibodies, differentiated for isotypes and IgG subclasses. Affinities of FVIII-specific antibodies in patients with FVIII inhibitors are up to 100-fold higher than in patients without inhibitors.


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