scholarly journals On two curvature-driven problems in Riemann–Finsler geometry

2019 ◽  
Author(s):  
David Bao
Keyword(s):  
Finsler Geometry ◽  
Curvature Driven

NUMERICAL SIMULATIONS OF MEAN CURVATURE FLOW IN THE PRESENCE OF A NONCONVEX ANISOTROPY

1998 ◽  
Vol 08 (04) ◽  
pp. 573-601 ◽  
Author(s):  
FRANCESCA FIERRO ◽  
ROBERTA GOGLIONE ◽  
MAURIZIO PAOLINI
Keyword(s):  
Numerical Simulations ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Finsler Geometry ◽  
Vertical Motion ◽  
Reaction Diffusion ◽  
Curvature Flow ◽  
Reaction Diffusion Equation ◽  
Curvature Driven ◽  
Anisotropic Mean Curvature

In this paper we present and discuss the results of some numerical simulations in order to investigate the mean curvature flow problem in the presence of a nonconvex anisotropy. Mathematically, nonconvexity of the anisotropy leads to the ill-posedness of the evolution problem, which becomes forward–backward parabolic. Simulations presented here refer to two different settings: curvature driven vertical motion of graphs (nonparametric setting) and motion in the normal direction by anisotropic mean curvature of surfaces (parametric setting). In the latter we first relax the problem via an Allen–Cahn type reaction-diffusion equation, in the context of Finsler geometry (diffused interface approximation). Our results suggest three main points. A nonconvex anisotropy and its convexification give rise, for both settings and the discretizations considered, to different evolutions. Wrinkled regions seem to appear only in correspondence to locally concave parts of the anisotropy. Moreover, locally convex regions (interior to the convexification of the so-called Frank diagram) seem to play an important role.

Image inpainting algorithm based on double-cross curvature-driven diffusion model

2013 ◽  
Vol 33 (12) ◽  
pp. 3536-3539
Author(s):  
Donghai ZHAI ◽  
Wenjie ZUO ◽  
Weixia DUAN ◽  
Jiang YU ◽  
Tongliang LI
Keyword(s):  
Diffusion Model ◽  
Image Inpainting ◽  
Curvature Driven ◽  
Double Cross

scholarly journals 2D‐Berry‐Curvature‐Driven Large Anomalous Hall Effect in Layered Topological Nodal‐Line MnAlGe

2021 ◽  
pp. 2006301
Author(s):  
Satya N. Guin ◽  
Qiunan Xu ◽  
Nitesh Kumar ◽  
Hsiang‐Hsi Kung ◽  
Sydney Dufresne ◽  
...  
Keyword(s):  
Hall Effect ◽  
Anomalous Hall Effect ◽  
Nodal Line ◽  
Berry Curvature ◽  
Curvature Driven

scholarly journals Finsler geometry modeling of complex fluids: reduction in viscous resistance

2021 ◽  
Vol 1730 (1) ◽  
pp. 012036
Author(s):  
Masahiko Okumura ◽  
Ippei Homma ◽  
Shuta Noro ◽  
Hiroshi Koibuchi
Keyword(s):  
Complex Fluids ◽  
Finsler Geometry ◽  
Viscous Resistance ◽  
Geometry Modeling

scholarly journals Finsler geometry modeling for anisotropic diffusion in Turing patterns

2021 ◽  
Vol 1730 (1) ◽  
pp. 012035
Author(s):  
Hiroshi Koibuchi ◽  
Masahiko Okumura ◽  
Shuta Noro
Keyword(s):  
Anisotropic Diffusion ◽  
Finsler Geometry ◽  
Turing Patterns ◽  
Geometry Modeling

scholarly journals Finsler Geometry for Two-Parameter Weibull Distribution Function

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Emrah Dokur ◽  
Salim Ceyhan ◽  
Mehmet Kurban
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Cumulative Probability ◽  
Two Dimensional ◽  
Energy Potential ◽  
Two Parameter

To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape (k) and scale (c) parameters in two-dimensional Finsler space is realized using a different approach by Finsler geometry. In addition, new probability and cumulative probability density functions based on Finsler geometry are proposed which can be used in many real world applications. For future studies, it is aimed at proposing more accurate models by using this novel approach than the models which have two-parameter Weibull probability density function, especially used for determination of wind energy potential of a region.

Experimental study of curvature‐driven flute instability in the gas‐dynamic trap*

1994 ◽  
Vol 1 (5) ◽  
pp. 1529-1535 ◽  
Author(s):  
A. A. Ivanov ◽  
A. V. Anikeev ◽  
P. A. Bagryansky ◽  
V. N. Bocharov ◽  
P. P. Deichuli ◽  
...  
Keyword(s):  
Experimental Study ◽  
Flute Instability ◽  
Gas Dynamic ◽  
Curvature Driven

scholarly journals Curvature-driven foam coarsening on a sphere: A computer simulation

2016 ◽  
Vol 93 (5) ◽  
Author(s):  
Shawn D. Ryan ◽  
Xiaoyu Zheng ◽  
Peter Palffy-Muhoray
Keyword(s):  
Computer Simulation ◽  
Curvature Driven
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