A simple method for finding all characteristic curves of piecewise-linear resistive circuits using an integer programming solver

2016 ◽  
Author(s):  
Kiyotaka Yamamura ◽  
Ryota Watanabe
Keyword(s):  
Integer Programming ◽  
Piecewise Linear ◽  
Simple Method ◽  
Characteristic Curves

scholarly journals Typical representatives of free homotopy classes in multi-punctured plane

2019 ◽  
Vol 11 (03) ◽  
pp. 623-659
Author(s):  
Maxim Arnold ◽  
Yuliy Baryshnikov ◽  
Yuriy Mileyko
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Probability Measure ◽  
Homotopy Class ◽  
Piecewise Linear ◽  
Homotopy Classes ◽  
Simple Method ◽  
Monte Carlo Techniques ◽  
Free Homotopy Class

We show that a uniform probability measure supported on a specific set of piecewise linear loops in a nontrivial free homotopy class in a multi-punctured plane is overwhelmingly concentrated around loops of minimal lengths. Our approach is based on extending Mogulskii’s theorem to closed paths, which is a useful result of independent interest. In addition, we show that the above measure can be sampled using standard Markov Chain Monte Carlo techniques, thus providing a simple method for approximating shortest loops.

scholarly journals An Assessment of Suitability of a SIMPLE VOF/PLIC-CSF Multiphase Flow Model for Rising Bubble Dynamics

2012 ◽  
Vol 4 (1) ◽  
pp. 65-83 ◽  
Author(s):  
S. Senthil Kumar ◽  
Y. M. C. Delauré
Keyword(s):  
Bubble Dynamics ◽  
Stokes Equations ◽  
Piecewise Linear ◽  
Navier Stokes ◽  
Simple Type ◽  
Two Phase ◽  
Simple Method ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Fluid Properties

A Volume of Fluid (VOF) – Youngs' model for the solution of an incompressible immiscible two-phase flows is presented. The solver computes the flow field by solving the family of Navier Stokes equations on a fixed (Eulerian) Staggered Cartesian grid using the Finite Volume formulation of Semi-Implicit Pressure Linked Equation (SIMPLE) method and tracks the position of interface between two fluids with different fluid properties by Piecewise Linear Interface Construction (PLIC) Method. The suitability of the SIMPLE type implementation is assessed by investigating the dynamics of free rising bubbles for different fluid properties and flow parameters. The results obtained with the present numerical method for rising bubbles in viscous liquids are compared with reported numerical and experimental results.

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