On the Classification of 3D Periodic Polyhedral Cellular Systems

2008 ◽  
Vol 589 ◽  
pp. 341-348
Author(s):  
Tamás Réti ◽  
Enikő Bitay
Keyword(s):  
Materials Science ◽  
Cellular Systems ◽  
Combinatorial Structure ◽  
Space Filling ◽  
Shape Factors ◽  
3D Space ◽  
Triply Periodic ◽  
Combinatorial Classification ◽  
Periodic Space

In several fields of materials science space-filling polyhedral systems are generally used for modeling and characterizing the microstructure of polycrystalline and cellular materials. In this paper a simple quantitative method designated to classify 3D triply periodic, space-filling, cellular systems is outlined. The concept of the proposed method is based on the known analogy between the combinatorial structure of 3D space-filling polyhedral systems and of 4D polytopes. For classification purposes various topological shape indices are defined and tested. It is demonstrated that using two appropriately selected shape factors (asymmetry and compactness coefficients) a global combinatorial classification of cellular systems can be performed.

Quadratic-monomial generated domains from mixed signed, directed graphs

2019 ◽  
Vol 29 (02) ◽  
pp. 279-308
Author(s):  
Michael A. Burr ◽  
Drew J. Lipman
Keyword(s):  
Directed Graphs ◽  
Complete Characterization ◽  
Combinatorial Structure ◽  
Signed Directed Graph ◽  
Odd Cycle ◽  
Combinatorial Classification ◽  
Special Case ◽  
Text Condition

Determining whether an arbitrary subring [Formula: see text] of [Formula: see text] is a normal or Cohen-Macaulay domain is, in general, a nontrivial problem, even in the special case of a monomial generated domain. We provide a complete characterization of the normality, normalizations, and Serre’s [Formula: see text] condition for quadratic-monomial generated domains. For a quadratic-monomial generated domain [Formula: see text], we develop a combinatorial structure that assigns, to each quadratic monomial of the ring, an edge in a mixed signed, directed graph [Formula: see text], i.e. a graph with signed edges and directed edges. We classify the normality and the normalizations of such rings in terms of a generalization of the combinatorial odd cycle condition on [Formula: see text]. We also generalize and simplify a combinatorial classification of Serre’s [Formula: see text] condition for such rings and construct non-Cohen–Macaulay rings.

scholarly journals Multiplicity-Free Schubert Calculus

2010 ◽  
Vol 53 (1) ◽  
pp. 171-186 ◽  
Author(s):  
Hugh Thomas ◽  
Alexander Yong
Keyword(s):  
Algebraic Geometry ◽  
Schubert Calculus ◽  
Chow Ring ◽  
Free Products ◽  
Linear Basis ◽  
Combinatorial Classification ◽  
Schubert Classes ◽  
Multiplicity Free

AbstractMultiplicity-free algebraic geometry is the study of subvarieties Y ⊆ X with the “smallest invariants” as witnessed by a multiplicity-free Chow ring decomposition of [Y] ∈ A*(X) into a predetermined linear basis.This paper concerns the case of Richardson subvarieties of the Grassmannian in terms of the Schubert basis. We give a nonrecursive combinatorial classification of multiplicity-free Richardson varieties, i.e., we classify multiplicity-free products of Schubert classes. This answers a question of W. Fulton.

scholarly journals Combinatorial classification of quantum lens spaces

2018 ◽  
Vol 297 (2) ◽  
pp. 339-365
Author(s):  
Peter Jensen ◽  
Frederik Klausen ◽  
Peter Rasmussen
Keyword(s):  
Lens Spaces ◽  
Combinatorial Classification

Assistance for Telepresence by Stereovision-Based Augmented Reality and Interactivity in 3D Space

2002 ◽  
Vol 11 (5) ◽  
pp. 525-535 ◽  
Author(s):  
Philippe Fuchs ◽  
Fawzi Nashashibi ◽  
Didier Maman
Keyword(s):  
Image Analysis ◽  
Augmented Reality ◽  
Mixed Reality ◽  
Vision System ◽  
Geometric Model ◽  
Interactive Approach ◽  
3D Space ◽  
Nuclear Plants ◽  
3D Positioning

In this paper, we describe some use of mixed reality as a new assistance for performing teleoperation tasks in remote scenes. We will start by a brief classification of augmented reality. This paper then describes the principle of our mixed reality system in teleoperation. It tackles the problem of scene registration using a man–machine cooperative and multisensory vision system. The system provides the operator with powerful sensorial feedback as well as appropriate tools to build (and update automatically) the geometric model of the perceived scene. We describe a new interactive approach combining image analysis and mixed reality techniques for assisted 3D geometric and semantic modeling. At the end of this paper, we describe applications in nuclear plants with results in 3D positioning.

scholarly journals Multifunctional DNA Nanomaterials for Biomedical Applications

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
Dick Yan Tam ◽  
Pik Kwan Lo
Keyword(s):  
Targeted Delivery ◽  
Materials Science ◽  
Drug Loading ◽  
Dna Nanotechnology ◽  
Control Release ◽  
Structural Features ◽  
Cellular Systems ◽  
Triggered Release ◽  
Self Assembled

The rapidly emerging DNA nanotechnology began with pioneer Seeman’s hypothesis that DNA not only can carry genetic information but also can be used as molecular organizer to create well-designed and controllable nanomaterials for applications in materials science, nanotechnology, and biology. DNA-based self-assembly represents a versatile system for nanoscale construction due to the well-characterized conformation of DNA and its predictability in the formation of base pairs. The structural features of nucleic acids form the basis of constructing a wide variety of DNA nanoarchitectures with well-defined shapes and sizes, in addition to controllable permeability and flexibility. More importantly, self-assembled DNA nanostructures can be easily functionalized to construct artificial functional systems with nanometer scale precision for multipurposes. Apparently scientists envision artificial DNA-based nanostructures as tool for drug loading andin vivotargeted delivery because of their abilities in selective encapsulation and stimuli-triggered release of cargo. Herein, we summarize the strategies of creating multidimensional self-assembled DNA nanoarchitectures and review studies investigating their stability, toxicity, delivery efficiency, loading, and control release of cargos in addition to their site-specific targeting and delivery of drug or cargo molecules to cellular systems.

On the Topological Characterization of 3-D Polyhedral Microstrutures

2007 ◽  
Vol 537-538 ◽  
pp. 563-570 ◽  
Author(s):  
Tamás Réti ◽  
Agnes Csizmazia ◽  
Imre Felde
Keyword(s):  
Single Phase ◽  
Cellular Systems ◽  
Convex Polyhedra ◽  
Quantitative Characterization ◽  
Topological Characterization ◽  
Shape Factors ◽  
3 Dimensional ◽  
Cellular Models ◽  
Finite Set

To characterize topologically the polycrystalline microstructure of single-phase alloys computer simulations are performed on 3-dimensional cellular models. These infinite periodic cellular systems are constructed from a finite set of space filling convex polyhedra (grains). It is shown that the appropriately selected topological shape factors can be successfully used for the quantitative characterization of computer-simulated microstructures of various types.

scholarly journals Strain and interface energy of ellipsoidal inclusions subjected to volumetric eigenstrains: shape factors

2022 ◽  
Author(s):  
H. J. Böhm ◽  
G. A. Zickler ◽  
F. D. Fischer ◽  
J. Svoboda
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
Materials Science ◽  
Elastic Strain Energy ◽  
Transformation Strain ◽  
Interface Energy ◽  
Shape Factors ◽  
Computational Materials Science ◽  
The Matrix ◽  
Computational Materials

AbstractThermodynamic modeling of the development of non-spherical inclusions as precipitates in alloys is an important topic in computational materials science. The precipitates may have markedly different properties compared to the matrix. Both the elastic contrast and the misfit eigenstrain may yield a remarkable generation of elastic strain energy which immediately influences the kinetics of the developing precipitates. The relevant thermodynamic framework has been mostly based on spherical precipitates. However, the shapes of actual particles are often not spherical. The energetics of such precipitates can be met by adapting the spherical energy terms with shape factors. The well-established Eshelby framework is used to evaluate the elastic strain energy of inclusions with ellipsoidal shapes (described by the axes a, b, and c) that are subjected to a volumetric transformation strain. The outcome of the study is two shape factors, one for the elastic strain energy and the other for the interface energy. Both quantities are provided in the form of easy-to-use diagrams. Furthermore, threshold elastic contrasts yielding strain energy shape factors with the value 1.0 for any ellipsoidal shape are studied.

scholarly journals Development of regulatory framework in field of restoration materials

2020 ◽  
Vol 164 ◽  
pp. 14022
Author(s):  
Jurij Pukharenko ◽  
Irina Aubakirova
Keyword(s):  
Building Materials ◽  
Materials Science ◽  
Regulatory Framework ◽  
International Standards ◽  
Future Generations ◽  
Historical Objects ◽  
Technical Properties ◽  
Further Development ◽  
Cultural Monuments

The restoration of historical objects allows you to save and recreate cultural monuments for the present and future generations. The work provides information on the restoration process, restoration materials, principles of scientific restoration. Based on the example of dry building mixes and ceramic decor, the classification of restoration materials is given and the main technical properties are highlighted, the need for standardization of these materials with the involvement of specialists in the field of building materials science is shown. It is shown that general construction quality indicators do not fully reflect the requirements of restoration materials in terms of reproducing the authenticity of material and technology. A review of the regulatory framework in the field of restoration, including federal laws, codes of restoration rules, interstate, national and international standards, is given. The features and directions of the further development of standardization in the field of restoration materials are highlighted.

scholarly journals Scaffold Techniques and Designs in Tissue Engineering Functions and Purposes: A Review

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Abdalla Eltom ◽  
Gaoyan Zhong ◽  
Ameen Muhammad
Keyword(s):  
Tissue Engineering ◽  
Materials Science ◽  
Clinical Medicine ◽  
Cellular Systems ◽  
Scaffold Design ◽  
Design Assessment ◽  
Scaffold Fabrication ◽  
Definition Of ◽  
Manufacturing Technologies ◽  
Almost All

In this review paper, the definition of the tissue engineering (TE) was comprehensively explored towards scaffold fabrication techniques and applications. Scaffold properties and features in TE, biological aspects, scaffold material composition, scaffold structural requirements, and old and current manufacturing technologies were reported and discussed. In almost all the reviewed reports, the TE definition denotes renewal, development, and repairs of damaged tissues caused by various factors such as disease, injury, or congenital disabilities. TE is multidisciplinary that combines biology, biochemistry, clinical medicine, and materials science whose application in cellular systems such as organ transplantation serves as a delivery vehicle for cells and drug. According to the previous literature and this review, the scaffold fabrication techniques can be classified into two main categories: conventional and modern techniques. These TE fabrication techniques are applied in the scaffold building which later on are used in tissue and organ structure. The benefits and drawbacks of each of the fabrication techniques have been described in conjunction with current areas of research devoted to deal with some of the challenges. To figure out, the highlighted aspects aimed to define the advancements and challenges that should be addressed in the scaffold design for tissue engineering. Additionally, this study provides an excellent review of original numerical approaches focused on mechanical characteristics that can be helpful in the scaffold design assessment in the analysis of scaffold parameters in tissue engineering.

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