scholarly journals A second order local minimality criterion for the triple junction singularity of the Mumford-Shah functional

2018 ◽  
Vol 24 (1) ◽  
pp. 401-435
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Triple Point ◽  
Triple Junction ◽  
Second Order ◽  
Second Variation ◽  
Point Configurations ◽  
Variation Approach ◽  
Local Minimality ◽  
Ongoing Project

This paper is the first part of an ongoing project aimed at providing a local minimality criterion, based on a second variation approach, for the triple point configurations of the Mumford-Shah functional.

scholarly journals Triple Junction at the Triple Point Resolved on the Individual Particle Level

2017 ◽  
Vol 119 (12) ◽  
Author(s):  
M. Chaudhuri ◽  
E. Allahyarov ◽  
H. Löwen ◽  
S. U. Egelhaaf ◽  
D. A. Weitz
Keyword(s):  
Triple Point ◽  
Triple Junction ◽  
Individual Particle ◽  
Particle Level ◽  
The Individual

scholarly journals GEOMETRIC VARIATIONS OF THE BOLTZMANN ENTROPY

2008 ◽  
Vol 22 (15) ◽  
pp. 1447-1454
Author(s):  
NIKOS KALOGEROPOULOS
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Second Order ◽  
Second Variation ◽  
Boltzmann Entropy ◽  
Constant Energy ◽  
The Stability ◽  
The Second Variation

We perform a calculation of the first and second order infinitesimal variations, with respect to energy, of the Boltzmann entropy of constant energy hypersurfaces of a system with a finite number of degrees of freedom. We comment on the stability interpretation of the second variation in this framework.

Local minimality of the ball for the Gaussian perimeter

2019 ◽  
Vol 12 (2) ◽  
pp. 193-210 ◽  
Author(s):  
Domenico Angelo La Manna
Keyword(s):  
Local Minimizer ◽  
Small Radius ◽  
Second Variation ◽  
Local Minimizers ◽  
Local Minimality ◽  
The Second Variation

AbstractWe prove that balls centered at the origin and with small radius are stable local minimizers of the Gaussian perimeter among all symmetric sets. Precisely, using the second variation of the Gaussian perimeter, we show that if the radius is smaller than{\sqrt{n+1}}, then the ball is a local minimizer, while if it is larger, the ball is not a local minimizer.

scholarly journals Second order infinitesimal bending of curves

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4127-4137 ◽  
Author(s):  
Marija Najdanovic ◽  
Ljubica Velimirovic
Keyword(s):  
Vector Fields ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Second Order ◽  
Dimensional Euclidean Space ◽  
Second Variation ◽  
Explicit Formulas ◽  
Infinitesimal Bending ◽  
Necessary And Sufficient ◽  
The Second Variation

We investigate a second order infinitesimal bending of curves in a three-dimensional Euclidean space in this paper. We give the necessary and sufficient conditions for the vector fields to be infinitesimal bending fields of the corresponding order, as well as explicit formulas which determine these fields. We examine the first and the second variation of some geometric magnitudes which describe a curve, specially a change of the curvature. Two illustrative examples (a circle and a helix) are studied not only analytically but also by drawing curves using computer program Mathematica.

scholarly journals Stability of equilibrium configurations for elastic films in two and three dimensions

2015 ◽  
Vol 8 (2) ◽  
pp. 117-153 ◽  
Author(s):  
Marco Bonacini
Keyword(s):  
Epitaxial Growth ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Variational Model ◽  
Second Variation ◽  
Strict Positivity ◽  
Equilibrium Configurations ◽  
Local Minimality ◽  
Nonlinear Elastic ◽  
The Second Variation

AbstractWe establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.

scholarly journals Minimality via second variation for microphase separation of diblock copolymer melts

2017 ◽  
Vol 2017 (729) ◽  
Author(s):  
Vesa Julin ◽  
Giovanni Pisante
Keyword(s):  
Diblock Copolymers ◽  
Microphase Separation ◽  
Isoperimetric Problem ◽  
Second Order ◽  
Minimality Condition ◽  
Second Variation ◽  
Local Minimizers ◽  
Critical Configurations ◽  
Copolymer Melts ◽  
Non Local

AbstractWe consider a non-local isoperimetric problem arising as the sharp interface limit of the Ohta–Kawasaki free energy introduced to model microphase separation of diblock copolymers. We perform a second order variational analysis that allows us to provide a quantitative second order minimality condition. We show that critical configurations with positive second variation are indeed strict local minimizers of the problem. Moreover, we provide, via a suitable quantitative inequality of isoperimetric type, an estimate of the deviation from minimality for configurations close to the minimum in the

The total curvature of knots under second-order infinitesimal bending

2019 ◽  
Vol 28 (01) ◽  
pp. 1950005
Author(s):  
Marija S. Najdanović ◽  
Svetozar R. Rančić ◽  
Louis H. Kauffman ◽  
Ljubica S. Velimirović
Keyword(s):  
Total Curvature ◽  
Second Order ◽  
Second Variation ◽  
Infinitesimal Bending ◽  
The Second Variation

In this paper, we consider infinitesimal bending of the second-order of curves and knots. The total curvature of the knot during the second-order infinitesimal bending is discussed and expressions for the first and the second variation of the total curvature are given. Some examples aimed to illustrate infinitesimal bending of knots are shown using figures. Colors are used to illustrate curvature values at different points of bent knots and the total curvature is numerically calculated.

scholarly journals The total torsion of knots under second order infinitesimal bending

2020 ◽  
pp. 35-35
Author(s):  
Marija Najdanovic ◽  
Ljubica Velimirovic ◽  
Svetozar Rancic
Keyword(s):  
Second Order ◽  
Second Variation ◽  
Infinitesimal Bending ◽  
The Second Variation ◽  
Total Torsion

In this paper we consider infinitesimal bending of the second order of curves and knots. The total torsion of the knot during the second order infinitesimal bending is discussed and expressions for the first and the second variation of the total torsion are given. Some examples aimed to illustrate infinitesimal bending of knots are shown using figures. Colors are used to illustrate torsion values at different points of bent knots and the total torsion is numerically calculated.

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