scholarly journals A Coordinate-Free Approach to Tracing the Coupler Curves of Pin-Jointed Linkages

2011 ◽  
Author(s):  
Nicola´s Rojas ◽  
Federico Thomas
Keyword(s):  
High Order ◽  
Step Method ◽  
Surjective Mapping ◽  
Predictor Corrector

In general, high-order coupler curves of plane mechanisms cannot be properly traced by standard predictor-corrector algorithms due to drifting problems and the presence of singularities. Instead of focusing on finding better algorithms for tracing curves, a simple coordinate-free method that first traces these curves in a distance space and then maps them onto the mechanism workspace is proposed. Tracing a coupler curve in the proposed distance space is much simpler because (a) the equation of this curve in this space can be straightforwardly obtained from a sequence of bilaterations; and (b) the curve in this space naturally decomposes into branches in which the signs of the oriented areas of the triangles involved in the aforementioned bilaterations remain constant. A surjective mapping permits to map the thus traced curves onto the workspace of the mechanism. The advantages of this two-step method are exemplified by tracing the coupler curves of a double butterfly linkage, curves that can reach order 48.

Research on Coupling Scheme of Monte Carlo Burnup Calculation in RMC

2018 ◽  
Author(s):  
Wanlin Li ◽  
Kan Wang ◽  
Ganglin Yu ◽  
Yaodong Li
Keyword(s):  
Monte Carlo ◽  
Neutron Flux ◽  
Cross Section ◽  
Neutron Transport ◽  
Effective Cross Section ◽  
High Order ◽  
Step Method ◽  
Step Approximation ◽  
Predictor Corrector ◽  
Burnup Calculation

Monte Carlo (MC) burnup calculation method, implemented through coupling neutron transport and point depletion solvers, is widely used in design and analysis of nuclear reactor. Burnup calculation is generally solved by dividing reactor lifetime into steps and modeling geometry into numbers of burnup areas where neutron flux and one group effective cross sections are treated as constant during each burnup step. Such constant approximation for neutron flux and effective cross section will lead to obvious error unless using fairly short step. To yield accuracy and efficiency improvement, coupling schemes have been researched in series of MC codes. In this study, four coupling schemes, beginning of step approximation, predictor-corrector methods by correcting nuclide density and flux-cross section as well as high order predictor-corrector with sub-step method were researched and implemented in RMC. Verification and comparison were performed by adopting assembly problem from VERA international benchmark. Results illustrate that high order coupled with sub-step method is with notable accuracy compared to beginning of step approximation and traditional predictor-corrector, especially for calculation in which step length is fairly long.

scholarly journals Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages1

2013 ◽  
Vol 5 (2) ◽  
Author(s):  
Nicolás Rojas ◽  
Federico Thomas
Keyword(s):  
Configuration Space ◽  
Distance Geometry ◽  
High Order ◽  
Degree Of Freedom ◽  
Step Method ◽  
Simple Method ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Planar Linkages ◽  
Predictor Corrector

In general, high-order coupler curves of single-degree-of-freedom plane linkages cannot be properly traced by standard predictor–corrector algorithms due to drifting problems and the presence of singularities. Instead of focusing on finding better algorithms for tracing curves, a simple method that first traces the configuration space of planar linkages in a distance space and then maps it onto the mechanism workspace, to obtained the desired coupler curves, is proposed. Tracing the configuration space of a linkage in the proposed distance space is simple because the equation that implicitly defines this space can be straightforwardly obtained from a sequence of bilaterations, and the configuration space embedded in this distance space naturally decomposes into components corresponding to different combinations of signs for the oriented areas of the triangles involved in the bilaterations. The advantages of this two-step method are exemplified by tracing the coupler curves of a double butterfly linkage.

A high-order predictor-corrector method for solving nonlinear differential equations of fractional order

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Thien Binh Nguyen ◽  
Bongsoo Jang
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Prediction Method ◽  
High Order ◽  
New Class ◽  
Accuracy Order ◽  
Predictor Corrector ◽  
Uniform Accuracy

AbstractAn accurate and efficient new class of predictor-corrector schemes are proposed for solving nonlinear differential equations of fractional order. By introducing a new prediction method which is explicit and of the same accuracy order as that of the correction stage, the new schemes achieve a uniform accuracy order regardless of the values of fractional order

scholarly journals New Predictor-Corrector Methods with High Efficiency for Solving Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Nonlinear Systems ◽  
Iterative Methods ◽  
Order Of Convergence ◽  
High Efficiency ◽  
Numerical Test ◽  
Efficiency Index ◽  
High Order ◽  
The Other ◽  
Predictor Corrector ◽  
Theoretical Results

A new set of predictor-corrector iterative methods with increasing order of convergence is proposed in order to estimate the solution of nonlinear systems. Our aim is to achieve high order of convergence with few Jacobian and/or functional evaluations. Moreover, we pay special attention to the number of linear systems to be solved in the process, with different matrices of coefficients. On the other hand, by applying the pseudocomposition technique on each proposed scheme we get to increase their order of convergence, obtaining new efficient high-order methods. We use the classical efficiency index to compare the obtained procedures and make some numerical test, that allow us to confirm the theoretical results.

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