scholarly journals Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface

2021 ◽  
Vol 23 (1) ◽  
pp. 103-158
Author(s):  
Yuan Gao ◽  
Jian-Guo Liu
Keyword(s):  
Numerical Method ◽  
Rough Surface ◽  
Contact Line ◽  
Mean Curvature ◽  
Gradient Flow ◽  
Second Order ◽  
Motion By Mean Curvature ◽  
Contact Line Dynamics

scholarly journals Second order threshold dynamics schemes for two phase motion by mean curvature

2020 ◽  
Vol 410 ◽  
pp. 109404
Author(s):  
Alexander Zaitzeff ◽  
Selim Esedoḡlu ◽  
Krishna Garikipati
Keyword(s):  
Mean Curvature ◽  
Second Order ◽  
Threshold Dynamics ◽  
Two Phase ◽  
Motion By Mean Curvature ◽  
Phase Motion

Determination of rate constants of redox reactions of second order from current-less potential-time curves by a simplified graphical-numerical method

1983 ◽  
Vol 48 (5) ◽  
pp. 1358-1367 ◽  
Author(s):  
Antonín Tockstein ◽  
František Skopal
Keyword(s):  
Numerical Method ◽  
Explicit Form ◽  
Rate Constant ◽  
Optimization Algorithm ◽  
Rate Constants ◽  
Redox Reactions ◽  
Second Order ◽  
Wide Region ◽  
Recurrent Formula

A method for constructing curves is proposed that are linear in a wide region and from whose slopes it is possible to determine the rate constant, if a parameter, θ, is calculated numerically from a rapidly converging recurrent formula or from its explicit form. The values of rate constants and parameter θ thus simply found are compared with those found by an optimization algorithm on a computer; the deviations do not exceed ±10%.

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

scholarly journals A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

scholarly journals Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics

2015 ◽  
Vol 115 (3) ◽  
Author(s):  
Amir Alizadeh Pahlavan ◽  
Luis Cueto-Felgueroso ◽  
Gareth H. McKinley ◽  
Ruben Juanes
Keyword(s):  
Thin Films ◽  
Contact Line ◽  
Partial Wetting ◽  
Internal Selection ◽  
Selection Of ◽  
Contact Line Dynamics
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