Construction of triply periodic minimal surfaces

No abstract is available for this paper.

• Publication year

  1996

• Venue

  Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences

• Publication date

  1996-09-01

• Fields of study

  Materials Science, Mathematics, Physics

• Identifiers
  DOI 10.1098/rsta.1996.0093
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Construction of higher genus minimal surfaces with one end and finite total curvature

  1996cited by this paper
• Computing Discrete Minimal Surfaces and Their Conjugates

  1993cited by this paper
• Lectures on Minimal Surfaces.

  1991cited by this paper
• Geometric Data for Triply Periodic Minimal Surfaces in Spaces of Constant Curvature

  1991cited by this paper
• New periodic minimal surfaces in H^3

  1991cited by this paper
• Bonnet transformation of infinite periodic minimal surfaces with hexagonal symmetry

  1990cited by this paper
• THE THEORY OF TRIPLY PERIODIC MINIMAL-SURFACES

  1990cited by this paper
• The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions

  1989cited by this paper
• New minimal surfaces in $S^3$

  1988cited by this paper
• On 3-periodic minimal surfaces

  1987cited by this paper
• Gesammelte mathematische Abhandlungen

  1970cited by this paper
• Infinite periodic minimal surfaces without self-intersections

  1970cited by this paper
• Über ein verallgemeinertes Dirichletsches Problem für die Minimalflächengleichung und hebbare Unstetigkeiten ihrer Lösungen

  1965cited by this paper
• Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen.

  year unknowncited by this paper

• A Genus-tuning Design on Minimal Surfaces for Open-cell Mechanical Metamaterials

  2026cites this paper
• Comparative Mechanical and Energy Absorption Performance of 3D Printed Bioinspired Bovine Bone and Hybrid TPMS Structures

  2025cites this paper
• The chiral gyrating H'-T surface family: construction from the dual qtz--qzd nets and existence proof using a toroidal Weierstrass method

  2025cites this paper
• Triply periodic surfaces based on metal-organic frameworks

  2025cites this paper
• Tileable Surfaces

  2025cites this paper
• Numerical Investigation of 2D Ordered Pillar Array Columns: An Algorithm of Unit-Cell Automatic Generation and the Corresponding CFD Simulation

  2025cites this paper
• Asymptotic analysis and design of shell-based thermal lattice metamaterials

  2025influential citation
• AI-aided process intensification of structures

  2025cites this paper
• Trigonally and hexagonally symmetric TPMS metamaterials under compressive loading

  2025cites this paper
• Free vibration of functionally graded TPMS porous quadrilateral plates reinforced with graphene nanoplatelets

  2025cites this paper
• DualMS: Implicit Dual-Channel Minimal Surface Optimization for Heat Exchanger Design

  2025cites this paper
• Design and numerical simulation of direct cooling evaporators for chip thermal test based on triply periodic minimal surfaces

  2025cites this paper
• Asymmetric Mechanical Behavior and pre-osteoblast differentiation in Ti-6Al-4V Minimal-Surface Bone-Analogues: The Role of Pore Topology.

  2025cites this paper
• An efficient NURBS-based reconstruction approach to isogeometric analysis of triply periodic minimal surface structures

  2025cites this paper
• Parametric design and performance evaluation of a hybrid triple-periodic minimal surface

  2025cites this paper
• Topology optimization of differentiable microstructures

  2024cites this paper
• Flame-front tracking in Porous Media Burners

  2024cites this paper
• Sandwich structures with TPMS core and printed circuit board faces

  2024cites this paper
• Crystal-Inspired Cellular Metamaterials and Triply Periodic Minimal Surfaces

  2024cites this paper
• Evaluation of the energy absorbing capacity of the two combinations of TPMS structure subjected to different compressive strain rates

  2024cites this paper
• Impact energy absorption in 3D printed bio-inspired PLA structures

  2024cites this paper
• Optimization of porous structures via machine learning for solar thermochemical fuel production

  2024cites this paper
• Design methodology of functionally graded cellular materials: Manipulating design parameters of triply periodic minimal surfaces through three-dimensional density distributions

  2024cites this paper
• Analysis on the convective heat transfer process and performance evaluation of Triply Periodic Minimal Surface (TPMS) based on Diamond, Gyroid and Iwp

  2023cites this paper
• ASSESSMENT OF THE USE OF TRIPLY PERIODIC MINIMAL SURFACES AS HEAT SINKS FOR MW/M²-HEAT FLUX CLASS COMPONENTS

  2023cites this paper
• Effective elastic and strength properties of triply periodic minimal surfaces lattice structures by numerical homogenization

  2023cites this paper
• Evaluation of the mechanical behavior of 3D printed cellular metamaterials with special geometries

  2023cites this paper
• New families of triply periodic minimal surface-like shell lattices

  2023cites this paper
• Inverse Designing Surface Curvatures by Deep Learning

  2023cites this paper
• Design, development and fluidic behavior analysis of triply periodic minimal surface (TPMS) based scaffolds for bone-applications

  2023cites this paper
• Metal Fused Filament Fabrication: Distortion Compensation Co2 Electrochemical Reduction

  2023cites this paper
• Improving the thermal response flexibility of 2- and 3-phase composite phase change materials by metallic triply periodic minimal surface structures

  2023cites this paper
• Procedural Metamaterials: A Unified Procedural Graph for Metamaterial Design

  2023cites this paper
• Biomimetic Scaffolds Using Triply Periodic Minimal Surface-Based Porous Structures for Biomedical Applications.

  2023cites this paper
• Additively Manufactured Multi-Morphology Bone-like Porous Scaffolds: Experiments and Micro-Computed Tomography-Based Finite Element Modeling Approaches

  2022cites this paper
• Graph Based Metamaterials: Deep Learning of Structure-Property Relations

  2022cites this paper
• A comprehensive characterization of fracture in unit cell open foams generated from Triply Periodic Minimal Surfaces

  2022cites this paper
• Structural Integrity of Additively Manufactured Materials

  2022cites this paper
• On the Effect of Lattice Topology on Mechanical Properties of SLS Additively Manufactured Sheet-, Ligament-, and Strut-Based Polymeric Metamaterials

  2022cites this paper
• BYU ScholarsArchive BYU ScholarsArchive Minimal graphs in R3 over convex domains Minimal graphs in R3 over convex domains

  2022cites this paper
• Discrete Minimal Nets with Symmetries

  2021cites this paper
• On in-plane drill rotations for Cosserat surfaces

  2021cites this paper
• Geometrical Degrees of Freedom for Cellular Structures Generation: A New Classification Paradigm

  2021cites this paper
• Additively manufactured mechanical metamaterials based on triply periodic minimal surfaces: Performance, challenges, and application

  2021cites this paper
• Design analysis of the “Schwartz D” based heat exchanger: A numerical study

  2021cites this paper
• Mechanical behavior of polymeric selective laser sintered ligament and sheet based lattices of triply periodic minimal surface architectures

  2020cites this paper
• Effective Anisotropic Elastic and Plastic Yield Properties of Periodic Foams Derived from Triply Periodic Schoen’s I-WP Minimal Surface

  2020cites this paper
• Minimal surfaces on mirror-symmetric frames: a fluid dynamics analogy

  2020cites this paper
• Diseño digital y fabricación de grupos de superficies arquitectónicas complejas, eficientes y continuas = Digital Design and Fabrication of Clusters of Complex, Efficient and Continuous Architectural Surfaces

  2020influential citation
• A Gyroidal MOF with Unprecedented Interpenetrating utc-c Network Exhibiting Exceptional Thermal Stability and Ultrahigh CO2 Affinity.

  2019cites this paper
• Two new embedded triply periodic minimal surfaces of genus 4

  2018cites this paper
• Design of Three-Dimensional, Triply Periodic Unit Cell Scaffold Structures for Additive Manufacturing

  2018cites this paper
• Opérateur de Laplace-Beltrami discret sur les surfaces digitales. (Discrete Laplace-Beltrami Operator on digital surfaces)

  2018cites this paper
• A chiral family of triply-periodic minimal surfaces derived from the quartz network

  2018influential citation
• Triply Periodic Minimal Surfaces Sheet Scaffolds for Tissue Engineering Applications: An Optimization Approach toward Biomimetic Scaffold Design.

  2018cites this paper
• Na+ and solute diffusion in aqueous channels of Myverol bicontinuous cubic phase: PGSE NMR and computer modelling

  2017cites this paper
• Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties.

  2017cites this paper
• Mathematical Modeling of 3D Tissue Engineering Constructs

  2017cites this paper
• Mechanical properties of 3D printed interpenetrating phase composites with novel architectured 3D solid-sheet reinforcements

  2016cites this paper
• Construction of Negatively Curved Cubic Carbon Crystals via Standard Realizations

  2016cites this paper
• Finite element prediction of effective elastic properties of interpenetrating phase composites with architectured 3D sheet reinforcements

  2016cites this paper
• Micromechanical finite element predictions of a reduced coefficient of thermal expansion for 3D periodic architectured interpenetrating phase composites

  2015cites this paper
• Evaluation of Cellular Solids Derived from Triply Periodic Minimal Surfaces

  2015influential citation
• Open Source Software for the Automatic Design of Scaffold Structures for Tissue Engineering Applications

  2014cites this paper
• RIEMANNIAN SUBMANIFOLDS: A SURVEY

  2013cites this paper
• Minimalflächen und Seifenblasen

  2010cites this paper
• A CONSTRUCTION METHOD FOR TRIPLY PERIODIC MINIMAL SURFACES

  2010cites this paper
• A limit-method for solving period problems on minimal surfaces

  2009cites this paper
• Ja n 20 03 Bicontinuous surfaces in self-assembling amphiphilic systems

  2008cites this paper
• Mesoscopic simulations of multiphase flows

  2008cites this paper
• Classification of Spatial Polygons that Could Possibly Generate Embedded Triply Periodic Minimal Surfaces

  2008cites this paper
• The Doubly Periodic Scherk-Costa Surfaces

  2008cites this paper
• Triply periodic minimal surfaces bounded by vertical symmetry planes

  2008cites this paper
• Convergence of the Cotangent Formula: An Overview

  2008cites this paper
• D.E.U.S. (Dimension Embedded in Unified Symmetry)

  2007cites this paper
• Triply Periodic Nanostructures

  2007cites this paper
• On the convergence of metric and geometric properties of polyhedral surfaces

  2007cites this paper
• Local v/a variations as a measure of structural packing frustration in bicontinuous mesophases, and geometric arguments for an alternating ${\rm Im}\overline{{\mathsf3}}{\rm m}$ (I-WP) phase in block-copolymers with polydispersity

  2007cites this paper
• Loop Group Methods for Constant Mean Curvature Surfaces

  2006cites this paper
• Chirality and domain growth in the gyroid mesophase

  2006cites this paper
• Mesoscale fluid simulation with the Lattice Boltzmann method

  2005cites this paper
• Skeletons in the labyrinth : medial representations and packing properties of bicontinuous space partitions

  2005cites this paper
• Geometric modeling of space-optimal unit-cell-based tissue engineering scaffolds

  2005cites this paper
• Modeling liquid crystal bilayer structures with minimal surfaces.

  2004cites this paper
• Detection and tracking of defects in the gyroid mesophase

  2004cites this paper
• Infinite periodic discrete minimal surfaces without self-intersections

  2004cites this paper
• Unstable Periodic Discrete Minimal Surfaces

  2003cites this paper
• Isoperimetric inequalities in crystallography

  2003cites this paper
• Bicontinuous Surfaces in Self-assembling Amphiphilic Systems

  2003influential citation
• Periodic Surfaces In Physics, Chemistry And Biology

  2003cites this paper
• Periodic minimal surfaces of cubic symmetry

  2003cites this paper
• Minimal graphs in R3 over convex domains

  2003cites this paper
• The shape of two-dimensional space

  2002cites this paper
• Computational Aspects of Discrete Minimal Surfaces

  2002cites this paper
• Cubic Polyhedra

  2002cites this paper
• Polyhedral Surfaces of Constant Mean Curvature

  2002cites this paper
• A Plateau Problem at Infinity for Properly Immersed Minimal Surfaces with Finite Total Curvature

  2001cites this paper
• Self-intersecting three-periodic minimal surfaces forming one-periodic tubes or finite polyhedra

  2001cites this paper
• Chapter 3 - Riemannian Submanifolds

  2000cites this paper
• Self-intersecting three-periodic minimal surfaces forming two-periodic (flat) labyrinths

  2000cites this paper