scholarly journals The Hénon problem with large exponent in the disc

2020 ◽  
Vol 268 (10) ◽  
pp. 5892-5944 ◽  
Author(s):  
Anna Lisa Amadori ◽  
Francesca Gladiali
Keyword(s):  
Large Exponent

On the Discretization of the Power-Law Hemolysis Model

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Mohammad M. Faghih ◽  
Ahmed Islam ◽  
M. Keith Sharp
Keyword(s):  
Fluid Dynamics ◽  
Power Law ◽  
Velocity Fields ◽  
Radial Expansion ◽  
Complex Flows ◽  
Cfd Simulations ◽  
Large Exponent ◽  
Computer Based ◽  
Computational Fluid Dynamics Cfd ◽  
Simple Flows

Abstract Flow-induced hemolysis remains a concern for blood-contacting devices, and computer-based prediction of hemolysis could facilitate faster and more economical refinement of such devices. While evaluation of convergence of velocity fields obtained by computational fluid dynamics (CFD) simulations has become conventional, convergence of hemolysis calculations is also essential. In this paper, convergence of the power-law hemolysis model is compared for simple flows, including pathlines with exponentially increasing and decreasing stress, in gradually expanding and contracting Couette flows, in a sudden radial expansion and in the Food and Drug Administration (FDA) channel. In the exponential cases, convergence along a pathline required from one to tens of thousands of timesteps, depending on the exponent. Greater timesteps were required for rapidly increasing (large exponent) stress and for rapidly decreasing (small exponent) stress. Example pathlines in the Couette flows could be fit with exponential curves, and convergence behavior followed the trends identified from the exponential cases. More complex flows, such as in the radial expansion and the FDA channel, increase the likelihood of encountering problematic pathlines. For the exponential cases, comparison of converged hemolysis values with analytical solutions demonstrated that the error of the converged solution may exceed 10% for both rapidly decreasing and rapidly increasing stress.

Zero-sum invariants on finite abelian groups with large exponent

2019 ◽  
Vol 342 (12) ◽  
pp. 111617
Author(s):  
Dongchun Han ◽  
Hanbin Zhang
Keyword(s):  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Large Exponent ◽  
Zero Sum
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