scholarly journals A Phase-Field Perspective on Mereotopology

2021 ◽  
Author(s):  
Georg J. Schmitz
Keyword(s):  
Phase Field ◽  
Mathematical Physics ◽  
Geometric Shape ◽  
Triple Junctions ◽  
Analytical Philosophy ◽  
First Order ◽  
Materials Engineering ◽  
Introductory Overview ◽  
Contact Algebra ◽  
Field Perspective

Mereotopology is a concept rooted in analytical philosophy. The phase-field concept is based on mathematical physics and finds applications in materials engineering. The two concepts seem to be disjoint at a first glance. While mereotopology qualitatively describes static relations between things like x isConnected y (topology) or x isPartOf y (mereology) by first order logic and Boolean algebra, the phase-field concept describes the geometric shape of things and its dynamic evolution by drawing on a scalar field. The geometric shape of any thing is defined by its boundaries to one or more neighboring things. The notion and description of boundaries thus provides a bridge between mereotopology and the phase-field concept. The present article aims to relate phase-field expressions describing boundaries and especially triple junctions to their Boolean counterparts in mereotopology and contact algebra. An introductory overview on mereotopology is followed by an introduction to the phase-field concept already indicating first relations to mereo- topology. Mereotopological axioms and definitions are then discussed in detail from a phase-field perspective. A dedicated section introduces and discusses further notions of the isConnected relation emerging from the phase-field perspective like isSpatiallyConnected, isTemporallyConnected, isPhysicallyConnected, isPathConnected and wasConnected. Such relations introduce dynamics and thus physics into mereotopology as transitions from isDisconnected to isPartOf can be described.

scholarly journals Plastic strain-induced evolution of CSL boundaries at elevated temperature for Ni-base superalloy: experimental and phase-field perspective

2020 ◽  
Vol 9 (2) ◽  
pp. 2535-2544
Author(s):  
Xiaoqing Song ◽  
Liying Tang ◽  
Yongxin Wang ◽  
Rongcan Zhou ◽  
Jing Zhang ◽  
...  
Keyword(s):  
Elevated Temperature ◽  
Plastic Strain ◽  
Phase Field ◽  
Field Perspective ◽  
Base Superalloy

scholarly journals On Bers Generating Functions for First Order Systems of Mathematical Physics

2010 ◽  
Vol 21 (3) ◽  
pp. 547-559 ◽  
Author(s):  
Vladislav V. Kravchenko ◽  
Marco P. Ramirez T.
Keyword(s):  
Generating Functions ◽  
Mathematical Physics ◽  
First Order

Discursive Psychology and the Boundaries of Sense

2004 ◽  
Vol 25 (8) ◽  
pp. 1435-1453 ◽  
Author(s):  
Rom Harré
Keyword(s):  
A Priori ◽  
Psychological Research ◽  
Natural Sciences ◽  
Raw Material ◽  
Human Beings ◽  
Discursive Psychology ◽  
Discursive Practices ◽  
Analytical Philosophy ◽  
First Order ◽  
Psychological Phenomena

There are problems in applying the methodology of the natural sciences to problems in psychology. This has led to a rethinking of psychology as the study of discursive practices, including the semantics of working vocabularies and the rules governing orderly thought and action. This has an affinity with analytical philosophy. At the same time it suggests a reinterpretation of older psychological research. First-order experiments study psychological phenomena, but second-order experiments, now very common, study how people describe imaginary situations, and their reactions to them, so that it is essentially a study of discursive practices. Wittgenstein’s use of the word ‘grammar’ suggests a convenient term for clusters of working rules. Philosophers have identified similar clusters of propositions, as a priori but synthetic propositions, expressing principles of order imposed on raw material by human beings. Psychologists have identified contingent universals which have such an ordering function. The revelation of the historical and cultural variability of such grammars opens up the possibility of richer self-understanding and of the repatterning of life systems.

Grain boundary-induced premelting and solid ↔ melt phase transformations: effect of interfacial widths and energies and triple junctions at the nanoscale

2021 ◽  
Author(s):  
Anup Basak
Keyword(s):  
Grain Boundary ◽  
Phase Transformations ◽  
Phase Field ◽  
Triple Junction ◽  
Triple Junctions ◽  
Field Approach ◽  
Boundary Width ◽  
Melt Phase

Grain boundary-induced transformations between solid, premelt, and melt are studied using a phase field approach. The effect of grain boundary width and energy and triple junction energy is studied.

scholarly journals Linear-superelastic Ti-Nb nanocomposite alloys with ultralow modulus via high-throughput phase-field design and machine learning

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yuquan Zhu ◽  
Tao Xu ◽  
Qinghua Wei ◽  
Jiawei Mai ◽  
Hongxin Yang ◽  
...  
Keyword(s):  
Machine Learning ◽  
Mechanical Properties ◽  
Martensitic Transformation ◽  
High Throughput ◽  
Phase Field ◽  
Degrees Of Freedom ◽  
Advanced Materials ◽  
First Order ◽  
Advanced Technologies ◽  
First Order Transition

AbstractThe optimal design of shape memory alloys (SMAs) with specific properties is crucial for the innovative application in advanced technologies. Herein, inspired by the recently proposed design concept of concentration modulation, we explore martensitic transformation (MT) in and design the mechanical properties of Ti-Nb nanocomposites by combining high-throughput phase-field simulations and machine learning (ML) approaches. Systematic phase-field simulations generate data of the mechanical properties for various nanocomposites constructed by four macroscopic degrees of freedom. An ML-assisted strategy is adopted to perform multiobjective optimization of the mechanical properties, through which promising nanocomposite configurations are prescreened for the next set of phase-field simulations. The ML-guided simulations discover an optimized nanocomposite, composed of Nb-rich matrix and Nb-lean nanofillers, that exhibits a combination of mechanical properties, including ultralow modulus, linear super-elasticity, and near-hysteresis-free in a loading-unloading cycle. The exceptional mechanical properties in the nanocomposite originate from optimized continuous MT rather than a sharp first-order transition, which is common in typical SMAs. This work demonstrates the great potential of ML-guided phase-field simulations in the design of advanced materials with extraordinary properties.

scholarly journals On modelling harmonic waves in linear micropolar elastic media by four screw fields

2020 ◽  
pp. 27-36
Author(s):  
Юрий Николаевич Радаев
Keyword(s):  
Differential Equations ◽  
Linear Theory ◽  
Harmonic Wave ◽  
Mathematical Physics ◽  
Harmonic Waves ◽  
Micropolar Elasticity ◽  
Alternative Analysis ◽  
First Order ◽  
Physical Fields ◽  
Vector Differential Equation

В статье рассматриваются дифференциальные уравнения для потенциалов, обеспечивающие выполнение связанных векторных дифференциальных уравнений линейной теории микрополярной упругости в случае гармонической зависимости поля перемещений и микровращений от времени. Предложена альтернативная схема расщепления связанных векторных дифференциальных уравнений микрополярной теории упругости для потенциалов на несвязанные уравнения первого порядка. Она основана на пропорциональности с разными масштабными факторами вихревых составляющих перемещений и микровращений одному вихревому винтовому полю. Найдено представление векторов перемещений и микровращений с помощью четырех винтовых векторов, обеспечивающее выполнимость связанных векторных дифференциальных уравнений линейной теории микрополярной упругости. В результате проблема нахождения вихревых составляющих перемещений и микровращений сводится к решению четырех несвязанных между собой векторных винтовых дифференциальных уравнений первого порядка с частными производными. Полученные результаты могут быть использованы в прикладных задачах механики, связанных с распространением гармонических (монохроматических) волн перемещений и микровращений вдоль длинных волноводов. The paper is devoted to study of the coupled vector differential equations of the linear theory of micropolar elasticity formulated in terms of displacements and microrotations in the case of a harmonic dependence of the physical fields on time. An alternative analysis aimed at splitting the coupled vector differential equation of the linear theory of micropolar elasticity into uncoupled equations is given. It is based on a notion of proportionality of the vortex parts of the displacements and microrotations to the single vector, which satisfies the screw equation well known from the mathematical physics. As a result, the problem of finding the vortex parts of the displacements and microrotations fields is reduced to solution of four uncoupled screw differential equations of the first order with partial derivatives. Obtained results are to be used in applied problems of the micropolar elasticity and in particular in studies of harmonic wave propagation along waveguides

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