Sensitivity Coefficients Utilized in Nonlinear Estimation With Small Parameters in a Heat Transfer Problem

1970 ◽  
Vol 92 (2) ◽  
pp. 215-221 ◽  
Author(s):  
J. V. Beck
Keyword(s):  
Model Building ◽  
Transfer Problem ◽  
Nonlinear Estimation ◽  
Transient Heat Conduction ◽  
Computer Time ◽  
Sensitivity Coefficients ◽  
Yield Information ◽  
Small Parameters ◽  
The Difference ◽  
Building Identification

The method of nonlinear estimation for determining parameters in differential equations is extended to treat more efficiently the problem of determining dominant and small parameters. Using the sensitivity coefficients, it is shown how to determine the dominant parameters first using nonlinear estimation and then using linear least squares to find the small parameters. This procedure can save a considerable amount of computer time. Even more important is the application to model-building (identification). The residuals for the difference of the temperatures calculated, assuming the small parameters are zero, and the measured temperatures are shown to yield information for discriminating between alternate mathematical models. A transient heat-conduction example is given to illustrate some of the concepts developed.

Ontogeny and heterochrony in the ostracode Cavellina Coryell from Lower Permian rocks in Kansas

Paleobiology ◽  
1986 ◽  
Vol 12 (3) ◽  
pp. 290-301 ◽  
Author(s):  
Peter N. Schweitzer ◽  
Roger L. Kaesler ◽  
G. P. Lohmann
Keyword(s):  
Life Histories ◽  
Morphological Difference ◽  
Structural Difference ◽  
Lower Permian ◽  
Closely Related Species ◽  
Know How ◽  
Taxonomic Level ◽  
Yield Information ◽  
Structural Differences ◽  
The Difference

Animals evolve by changing their form and by changing the rate at which they develop. Since evolution of development through time may be directly related to the adaptation of their life histories, study of ontogeny in fossils may yield information about the ecology of extinct animals. We need to know how to measure animals' ontogeny and at what taxonomic level structural differences overshadow differences in development. Two closely related species of the Permian ostracode Cavellina were compared to determine how much of the morphological difference between them is due to differences in their ontogenies. Most of the difference is not related to ontogeny. They also differ in a way that could be explained by heterochrony, although this difference is secondary in importance to the structural difference. These findings suggest that ecological adaptation might best be studied by examining the changes in development that occur within species through time and space.

scholarly journals A New Approach for the Construction of Long-Periodic Perturbations

1978 ◽  
Vol 41 ◽  
pp. 57-64
Author(s):  
Rudolf Dvorak
Keyword(s):  
Analytical Method ◽  
Specific Problem ◽  
Computer Time ◽  
Lagrange Equations ◽  
New Approach ◽  
Precise Method ◽  
Periodic Perturbations ◽  
Small Parameters ◽  
New Form ◽  
Specific Formulation

AbstractThe aim of this work is to study perturbations of planets of a period of some thousands of years. The use of an analytical method allows us to separate all different influences, e.g. near resonances and is combined with the very precise method of the numerical integration. The truncation to low orders can be avoided which is made by analytical methods in using developments with respect to the small parameters inclinations and eccentricities. For this purpose a special form of the Lagrange Equations is used where the terms containing the inverse distancefrom the planet to the perturbing one are separated as it is the most difficult to compute. To develop this a specific formulation has been found where the short periodic terms can precisely be determined. Although the development seems to be of a certain complexity the small numbers of quantities used can be tabulated once and for all in a specific problem. It should be possible to integrate the new form of the Lagrange Equations within a reasonable computer-time to determine the long periodic perturbations.

scholarly journals Interval Model of the Efficiency of the Functioning of Information Web Resources for Services on Ecological Expertise

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2116
Author(s):  
Mykola Dyvak ◽  
Oleksandr Papa ◽  
Andrii Melnyk ◽  
Andriy Pukas ◽  
Nataliya Porplytsya ◽  
...  
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Model Building ◽  
Experimental Studies ◽  
Discrete Models ◽  
Model Parameters ◽  
Incorrect Choice ◽  
Web Resources ◽  
Web Resource ◽  
The Difference

Mathematical models of the efficiency dynamics of information web resources are considered in this paper. The application of interval discrete models in the form of difference equations is substantiated and the approach to estimation of the model parameters is proposed. The proposed approach is based on the artificial bee colony algorithm (ABCA). A number of experimental studies have been carried out based on data on the functioning of web resources related to environmental monitoring services. The indicator of an information web resource user’s activity has been investigated. Three cases of model building in the form of difference equations as interval discrete models (IDM) have been considered. They vary in the general kind of expression. As a result of the computational experiments, it is shown that the adequacy of a model depends on the expression of the difference equation. In the case of its incorrect choice, the proposed method of parameters’ identification may be ineffective. The obtained interval discrete model in the difference equation form, which describes the efficiency of a web resource, makes it possible to optimize business processes in an organization that uses this web resource, as well as optimally allocate organizational resources and the workload of employees of the administrative service center. Based on the conducted experiments, the efficiency of the proposed model’s application is confirmed.

Leaf N, P Stoichiometry and Nutrient Resorption in Phosphorus-Enriched Soils in a Mountainous Region of the Dianchi Lake Watershed

2014 ◽  
Vol 955-959 ◽  
pp. 3687-3690
Author(s):  
Kai Yan ◽  
Changqun Duan ◽  
Long Zhang ◽  
Xin Xv ◽  
Change Liu ◽  
...  
Keyword(s):  
Model Building ◽  
Ecological Model ◽  
Nutrient Resorption ◽  
Dianchi Lake ◽  
Resorption Efficiency ◽  
Fresh Leaf ◽  
The Difference ◽  
Leaf P ◽  
Plant Forms ◽  
Leaf N

Understanding the leaf N, P concentrations and nutrient resorption of plants growing in phosphorus–enriched soil (PES) can provide new data for ecostoichiometric research and ecological model building. In this study, 117 green leaves and 53 senesced leaves of dominant plants in PES in the Dianchi Lake watershed, SW China, were sampled. Plants in PES had high fresh leaf P (4.60mg/g), senesced leaf P (2.70mg/g), and low fresh leaf N: P (4.41), senesced leaf N: P (3.21). P resorption efficiency (PRE) (25.09%) was significantly lower than N resorption efficiency (NRE) (52.68%). Forbs had the highest P content in fresh (5.35mg/g) and senesced leaf (3.25mg/g) among plants forms. Although NRE was varied among plant forms, the difference in PRE was not significant. In conclusion, PES has a tremendous impact on the patterns of leaf N, P and nutrient resorption of different plant forms, those results were different from general results.

scholarly journals A Simulation Study of Loess Slope Instability and Damage Under Intensive Seismic Vibration

2021 ◽  
Author(s):  
chaoyu chang ◽  
Jingshan Bo ◽  
WenHao Qi ◽  
feng qiao ◽  
da peng
Keyword(s):  
Principal Stress ◽  
Model Building ◽  
Horizontal Displacement ◽  
Field Investigation ◽  
Slope Instability ◽  
Particle Flow Code ◽  
Seismic Vibration ◽  
Loess Slope ◽  
Damage Process ◽  
The Difference

Abstract The instability and damage of the loess slope under intensive seismic vibration can be a complicated process, involving in sliding, horizontal displacement and rotation, which makes the particle flow code a suitable theory to simulate the instability and damage of the loess slope. In this study, based on both field investigation and indoor experiments, PFC2D program was adopted to simulate the instability and damage process of the loess slope landslide under intensive seismic vibration through the detailed identification of relevant parameters, model building and dynamic input. The analysis has revealed three main findings. Firstly, the volley surface structure dominated in the slope tends to magnify the vibration, resulting in intensive vibration of the soil body on the slide surface and an increased high frequency components of Fourier spectrum. Secondly, under the dynamic forces, the slope first accumulates and damages in the lower part, forming a shear outlet. Under the pulling of the lower particles, the difference between the first principal stress and the third principal stress gradually increases, destroying the inherent cohesive contact between the particles, leading to the instability damage. Thirdly, the upper soil body experiences tensile damage, forming a through slide face which causes the instability damage of the whole slope. The sliding face demonstrates in a oval shape, with a deeper arch as the vibration lasts longer.

The paper describes methods of studying the texture properties of rocks from photographs of a whole core using variograms and matrices of co-occurrence. The practical goal of our research is to obtain curves based on images of rocks; for example, core photographs, microresistivity formation images (FMI), and X-ray computerized tomography (CT), which make it possible to segment images depending on the difference of textural characteristics of different areas of the image. Such texture attributes—separately or along with color information—can be used in the tasks of automatic lithotyping, as well as in modeling the petrophysical properties of rocks. Our practical experience in building predictive models from core photographs has shown that the use of versatile information improves the quality of modeling. In some cases, the classification of lithotypes and the prediction of reservoir properties is difficult and leads to erroneous results if we do not use all the available information. In practice, UV images of the core are not always available. There are also daylight core photos, when the color characteristics are not very informative. In such cases, including imaging types such as X-ray CT, texture attributes can be of great help in predictive model building

2021 ◽  
Author(s):  
I.A. Seleznev ◽  
D.O. Makienko ◽  
V.V. Abashkin ◽  
A.A. Chertova ◽  
A.F. Samokhvalov
Keyword(s):  
Model Building ◽  
Practical Experience ◽  
Color Information ◽  
Reservoir Properties ◽  
X Ray ◽  
The Difference ◽  
Available Information ◽  
Texture Attributes

Study on the Airflow Level Posture Sensor Based on Fluid-Solid Coupling

2011 ◽  
Vol 268-270 ◽  
pp. 636-639
Author(s):  
Ming Ming Ji ◽  
Lin Hua Piao ◽  
Bai Hua Li
Keyword(s):  
Tilt Angle ◽  
Model Building ◽  
Three Dimensional ◽  
Three Dimensional Model ◽  
Three Dimensional Modeling ◽  
Equation Solving ◽  
Dimensional Modeling ◽  
Element Simulation ◽  
Hermetic Chamber ◽  
The Difference

Using ANSYS program, the finite element simulation based on Fluid-Solid coupling is conducted by a series of procedures, such as three-dimensional model building of airflow level posture sensor according to the actual size of the proportion, network modifying, loads applying and equation solving. The flow field in three-dimensional hermetic chamber of sensitive element of airflow level posture sensor is calculated. The numerical results show that: 1) The velocity difference of air flow at two heat source changes with the tilt angle, the difference between airflow velocity increases with the increase of the tilt angle. 2)Compared with two-dimensional modeling, the simulation result of three-dimensional modeling and fluid-solid analysis methods are more comprehensive and accurate, which provides more reliable basis for practical research of the airflow level posture sensor.

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