Sigmoid generalized complementary equation for evaporation over wet surfaces: A nonlinear modification of the Priestley–Taylor equation

2021 ◽  
Author(s):  
Songjun Han ◽  
Fuqiang Tian ◽  
Wei Wang ◽  
Liming Wang
Keyword(s):  
Complementary Equation

scholarly journals Getting the Best of Both Worlds? Developing Complementary Equation-Based and Agent-Based Models

2017 ◽  
Vol 53 (2) ◽  
pp. 763-782 ◽  
Author(s):  
Claudius Gräbner ◽  
Catherine S. E. Bale ◽  
Bernardo Alves Furtado ◽  
Brais Alvarez-Pereira ◽  
James E. Gentile ◽  
...  
Keyword(s):  
Agent Based Models ◽  
Agent Based ◽  
Complementary Equation

scholarly journals Construct Linear Polynomial Complementary Transformation for NP-Completeness Using Parallel Genetic Algorithm

2016 ◽  
Author(s):  
Tarik Eltaeib ◽  
Julius Dichter
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Parallel Genetic Algorithm ◽  
Algorithm Optimization ◽  
Parallel Genetic Algorithms ◽  
Np Completeness ◽  
Linear Polynomial ◽  
Optimization Function ◽  
Speed Up ◽  
Complementary Equation

This paper examines the correlation between numbers of computer cores in parallel genetic algorithms. The objective to determine the linear polynomial complementary equation in order represent the relation between number of parallel processing and optimum solutions. Model this relation as optimization function (f(x)) which able to produce many simulation results. F(x) performance is outperform genetic algorithms. Compression results between genetic algorithm and optimization function is done. Also the optimization function give model to speed up genetic algorithm. Optimization function is a complementary transformation which maps a TSP given to linear without changing the roots of the polynomials.

Linear Complementary Equation Method Applied in the Load Response of Cable-Strut Systems

1998 ◽  
Vol 13 (1) ◽  
pp. 35-40 ◽  
Author(s):  
B-B. Wang ◽  
S-Z. Xu ◽  
X-L. Liu
Keyword(s):  
Iteration Method ◽  
Step Length ◽  
Newton Iteration ◽  
Load Response ◽  
Computation Process ◽  
Novel Method ◽  
Newton Iteration Method ◽  
Complementary Equation ◽  
The Given ◽  
Derivation Process

In this paper, the drawbacks of the Newton iteration method are analyzed. Then the Linear Complementary Equation (LCE) method is introduced into the cable-strut system to cope with the “retiring” problem of elements under load. The corresponding variants of the function of zero-stress and the flow factor of zero-stress are invented to represent the characteristics of cables and struts retiring from functioning. The derivation process is given in detail and its efficiency is proved by case studies. The LCE method has overcome all the drawbacks of the iteration method, because its computation process is non-conditionally stable, and its step length can be determined at about 1/5 of the given load value for all cases to ensure accuracy. It is novel method for studying the load response of cable-strut systems.

Dynamic Behavior of a Clamped Plastic Beam With Cracks at Supporting Ends Under Impact

1999 ◽  
Vol 121 (4) ◽  
pp. 406-412 ◽  
Author(s):  
F. L. Chen ◽  
T. X. Yu
Keyword(s):  
Axial Force ◽  
Complete Solution ◽  
Bending Moment ◽  
Deformation Energy ◽  
Failure Behavior ◽  
J Integral ◽  
Rigid Plastic ◽  
The Stability ◽  
Complementary Equation ◽  
Initial Cracks

This paper examines a projectile impact on a rigid-plastic beam with cracks at the fully clamped ends. By assuming the cracked sections yield immediately after impact, a three-hinge/two-hinge mechanism for the response process is constructed so that a complete solution considering the interaction between bending moment M and axial force N is derived. The key of the formulation is to find a complementary equation concerning the axial force N. To predict accurately the stability of the initial cracks, the J-integral criterion is extended to involve the contribution of the axial force. All the governing equations are nondimensionalized and rearranged, ready for Runge-Kutta integration procedure. The numerical results demonstrate that the mass ratio and the axial force have significant influence on the final deformation, energy partition, and the value of J-integral near the crack tip. The J-integral is not very sensitive to the depth of the initial cracks, but the presence of initial cracks in a beam may alter the failure behavior of the beam after impact, that is, from a strength-type failure to a fracture-type failure.

The Doubly Nonlinear Limit Load Analysis of Space Grid Structure

2012 ◽  
Vol 166-169 ◽  
pp. 144-149
Author(s):  
Cao Xi ◽  
Yun Hong Hao
Keyword(s):  
Limit Load ◽  
Grid Structure ◽  
Limit Loads ◽  
Load Increment ◽  
Mechanics Model ◽  
Space Grid ◽  
Calculated Load ◽  
Doubly Nonlinear ◽  
Load Analysis ◽  
Complementary Equation

This paper first adopts variational inequation—the method of linear complementary equation. We use this method to analyses the elastoplastic limit load of space grid structure. This is a way to resolve the nonlinear question. Adopting this method to resolve the limit load of space grid structure avoid some drawback caused by adopting iteration method. We only need do some limited compute to a load-increment then we can obtain consequence, which fit in with all condition. Particularly, though adopting the method of linear complementary equation, we can control the value of limit load, make the calculated load can not exceed the limit load. Once exceeding, computer can decrease load- increment automatically and load again till getting the limit load of structure. Based on elastoplastic limit load analysis, this paper has considered big deformation impact on the limit load of bspace grid structure. We have made analysis of doubly nonlinear limit loads under the condition of coupling out of elastoplastic big deformation. The method and theory of this paper can combine with all kinds of single rod mechanics model.

An Improved Analytical Solution of Population Balance Equation Involving Aggregation and Breakage via Fibonacci and Lucas Approximation Method

2018 ◽  
Vol 17 (5) ◽  
Author(s):  
Zehra Pınar ◽  
Abhishek Dutta ◽  
Mohammed Kassemi ◽  
Turgut Öziş
Keyword(s):  
Analytical Solution ◽  
Approximation Method ◽  
Balance Equation ◽  
Population Balance ◽  
Travelling Wave ◽  
Population Balance Equation ◽  
Auxiliary Equation ◽  
Auxiliary Equation Method ◽  
Analytical Approaches ◽  
Complementary Equation

AbstractThis study presents a novel analytical solution for the Population Balance Equation (PBE) involving particulate aggregation and breakage by making use of the appropriate solution(s) of the associated complementary equation of a nonlinear PBE via Fibonacci and Lucas Approximation Method (FLAM). In a previously related study, travelling wave solutions of the complementary equation of the PBE using Auxiliary Equation Method (AEM) with sixth order nonlinearity was taken to be analogous to the description of the dynamic behavior of the particulate processes. However, in this study, the class of auxiliary equations is extended to Fibonacci and Lucas type equations with given transformations to solve the PBE. As a proof-of-concept for the novel approach, the general case when the number of particles varies with respect to time is chosen. Three cases i. e. balanced aggregation and breakage and when either aggregation or breakage can dominate are selected and solved for their corresponding analytical solution and compared with the available analytical approaches. The solution obtained using FLAM is found to be closer to the exact solution and requiring lesser parameters compared to the AEM and thereby being a more robust and reliable framework.

scholarly journals Speeds and stance of titanosaur sauropods: analysis of Titanopodus tracks from the Late Cretaceous of Mendoza, Argentina

2011 ◽  
Vol 83 (1) ◽  
pp. 279-290 ◽  
Author(s):  
Bernardo J. González Riga
Keyword(s):  
South America ◽  
Late Cretaceous ◽  
The South ◽  
Dynamic Similarity ◽  
Neuquen Basin ◽  
Neuquén Basin ◽  
Walking Speeds ◽  
Complementary Equation

Speed estimations from trackways of Titanopodus mendozensis González Riga and Calvo provide information about the locomotion of titanosaurian sauropods that lived in South America during the Late Cretaceous. Titanopodus ichnites were found at Agua del Choique, a newly discovered track site in the Loncoche Formation, Late Campanian-Early Maastrichtian of Mendoza, Argentina. This speed study follows the hypothesis of dynamic similarity proposed by Alexander. As a refinement of this method, a complementary equation is presented here based on an articulated titanosaurian specimen collected in strata that are regarded as correlative to those that have yielded Titanopodus tracks (Allen Formation, Neuquén Basin). This analysis indicates that hip height can be estimated as 4.586 times the length of the pes track in derived titanosaurs. With an estimation of the hip height and the stride measurements, the speed is calculated. The study of two wide-gauge trackways indicates that Titanopodus ichnites were produced by mediumsized titanosaurs (hip height of 211-229 cm) that walked at 4.7-4.9 km/h towards the south and southwest, following, in part, a sinuous pathway. These speeds and some taphonomic features of tracks (prominent rims, distorted elongated shapes)indicate the capacity of derived titanosaurs for walking effectively over a very wet and slippery substrate. In the ichnological record, the walking speeds of Titanopodustrackmakers are somewhat faster than those previously inferred for most sauropods.

scholarly journals Bayesian simultaneous equation models for the analysis of energy intake and partitioning in growing pigs

2012 ◽  
Vol 150 (6) ◽  
pp. 764-774 ◽  
Author(s):  
A. B. STRATHE ◽  
H. JØRGENSEN ◽  
E. KEBREAB ◽  
A. DANFÆR
Keyword(s):  
Energy Intake ◽  
Current Knowledge ◽  
Simultaneous Equation ◽  
Open Circuit ◽  
Growing Pigs ◽  
Metabolizable Energy ◽  
Informative Priors ◽  
Metabolic Scaling ◽  
Complementary Equation ◽  
Simultaneous Equation Models

SUMMARYThe objective of the current study was to develop Bayesian simultaneous equation models for modelling energy intake and partitioning in growing pigs. A key feature of the Bayesian approach is that parameters are assigned prior distributions, which may reflect the current state of nature. In the models, rates of metabolizable energy (ME) intake, protein deposition (PD) and lipid deposition (LD) were treated as dependent variables accounting for residuals being correlated. Two complementary equation systems were used to model ME intake (MEI), PD and LD. Informative priors were developed, reflecting current knowledge about metabolic scaling and partial efficiencies of PD and LD rates, whereas flat non-informative priors were used for the reminder of the parameters. The experimental data analysed originate from a balance and respiration trial with 17 cross-bred pigs of three genders (barrows, boars and gilts) selected on the basis of similar birth weight. The pigs were fed four diets based on barley, wheat and soybean meal supplemented with crystalline amino acids to meet or exceed Danish nutrient requirement standards. Nutrient balances and gas exchanges were measured at c. 25, 75, 120 and 150 kg body weight (BW) using metabolic cages and open circuit respiration chambers. A total of 56 measurements were performed. The sensitivity analysis showed that only the maintenance component was sensitive to the prior specification, and hence the maintenance estimate of 0·91 MJ ME/kg0·60 per day (0·95 credible interval (CrI): 0·78–1·09) should be interpreted with caution. It was shown that boars’ ability to deposit protein was superior to that of barrows and gilts, as these had an estimated maximum PD (PDmax) of 250 g/day (0·95 CrI: 237–263), whereas the barrows and gilts had a PDmax of 210 g/day (0·95 CrI: 198–220). Furthermore, boars reached PDmax at 109 kg BW (0·95 CrI: 93·6–130), whereas barrows and gilts maximized PD at 81·7 kg BW (0·95 CrI: 75·6–89·5). At 25 kg BW, the boars partitioned on average 5–6% more of the ME above maintenance into PD than barrows and gilts, and this was progressively increased to 10–11% more than barrows and gilts at 150 kg BW. The Bayesian modelling framework can be used to further refine the analysis of data from metabolic studies in growing pigs.

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