Optimal micropatterns in transport networks

DOI10.1137/15M1050227zbMath1394.49044arXiv1511.08467OpenAlexW3105839379MaRDI QIDQ2960390

Alessio Brancolini, Benedikt Wirth

Publication date: 9 February 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.08467

zbMATH Keywords

irrigationWasserstein distanceoptimal transportbranched transportoptimal networksurban planningenergy scaling lawsmicropatterns

Mathematics Subject Classification ID

Deterministic network models in operations research (90B10) Variational problems in a geometric measure-theoretic setting (49Q20) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (8)

General transport problems with branched minimizers as functionals of 1-currents with prescribed boundary ⋮ A branched transport limit of the Ginzburg-Landau functional ⋮ Optimal Shapes for Tree Roots ⋮ Optimal micropatterns in 2D transport networks and their relation to image inpainting ⋮ Self-similar minimizers of a branched transport functional ⋮ A 2-dimensional shape optimization problem for tree branches ⋮ Asymptotic self-similarity of minimizers and local bounds in a model of shape-memory alloys ⋮ Energy scaling law for a singularly perturbed four-gradient problem in helimagnetism

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equivalent formulations for the branched transport and urban planning problems
• Interpolation inequalities in pattern formation
• Fractal regularity results on optimal irrigation patterns
• On the Hölder regularity of the landscape function
• The structure of branched transportation networks
• Optimal transportation networks. Models and theory
• Optimal urban networks via mass transportation
• Functional analysis, Sobolev spaces and partial differential equations
• Domain branching in uniaxial ferromagnets: A scaling law for the minimum energy
• A variational model of irrigation patterns
• Energy minimization and flux domain structure in the intermediate state of a type-I superconductor
• Traffic plans
• Branched Microstructures in the Ginzburg--Landau Model of Type-I Superconductors
• Synchronic and Asynchronic Descriptions of Irrigation Problems
• Sets of Finite Perimeter and Geometric Variational Problems
• Optimal Fine-Scale Structures in Compliance Minimization for a Shear Load
• Optimal networks for mass transportation problems
• Nucleation barriers at corners for a cubic-to-tetragonal phase transformation
• Synchronized traffic plans and stability of optima
• Surface energy and microstructure in coherent phase transitions
• Nucleation Barriers for the Cubic‐to‐Tetragonal Phase Transformation
• Blister Patterns and Energy Minimization in Compressed Thin Films on Compliant Substrates
• Energy scaling and branched microstructures in a model for shape-memory alloys with SO(2) invariance
• Wrinkles as the Result of Compressive Stresses in an Annular Thin Film
• Scaling Law and Reduced Models for Epitaxially Strained Crystalline Films
• Ground state energy scaling laws during the onset and destruction of the intermediate state in a type I superconductor
• Optimal Transport

This page was built for publication: Optimal micropatterns in transport networks