scholarly journals Phase Transition as an Emergent Phenomenon Analysed by Violation of Structural Invariant (M, BM)

MENDEL ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 45-50
Author(s):  
Jiri Bila ◽  
Ali H Reshak ◽  
Jan Chysky
Keyword(s):  
Complex System ◽  
Phase Transition ◽  
Main Attention ◽  
Physical Description ◽  
Structural Invariant ◽  
Emergent Phenomenon ◽  
System A ◽  
Emergent Phenomena ◽  
Physical Approach ◽  
Structural Invariants

When modeling complex systems, we usually encounter the following difficulties: partiality, large amounts of data and uncertainty of conclusions. The most common approach used for modeling is the physical approach, sometimes reinforced by statistical procedures. If we assume emergences in the complex system, a physical approach is not appropriate at all. Instead, we build here the approach of structural invariants. In this paper, we show that another plane can be built above the plane of physical description, which is responsible for violation of structural invariants. Main attention is concentrated (in this article) on the invariant matroid and bases of matroid (M, BM) in combination with Ramsey graph theory. In addition, the article introduces a calculus that describes the emergent phenomena using two quantities - the power of the emergent phenomenon and the complexity of the structure of the considered complex system. We show the application of the method for modeling phase transition in chemistry.

scholarly journals Modeling Complex Systems by Structural Invariants Approach

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Jiri Bila ◽  
Ali. H. Reshak ◽  
Jan Chysky
Keyword(s):  
Complex System ◽  
Complex Systems ◽  
Simple Description ◽  
Emergent Phenomenon ◽  
Statistical Procedures ◽  
Qualitative Interpretation ◽  
Physical Approach ◽  
Simple Geometry ◽  
Complicated Geometry ◽  
Structural Invariants

When modeling complex systems, we usually encounter the following difficulties: partiality, large amount of data, and uncertainty of conclusions. It can be said that none of the known approaches solves these difficulties perfectly, especially in cases where we expect emergences in the complex system. The most common is the physical approach, sometimes reinforced by statistical procedures. The physical approach to modeling leads to a complicated description of phenomena associated with a relatively simple geometry. If we assume emergences in the complex system, the physical approach is not appropriate at all. In this article, we apply the approach of structural invariants, which has the opposite properties: a simple description of phenomena associated with a more complicated geometry (in our case pregeometry). It does not require as much data and the calculations are simple. The price paid for the apparent simplicity is a qualitative interpretation of the results, which carries a special type of uncertainty. Attention is mainly focused (in this article) on the invariant matroid and bases of matroid (M, BM) in combination with the Ramsey graph theory. In addition, this article introduces a calculus that describes the emergent phenomenon using two quantities—the power of the emergent phenomenon and the complexity of the structure that is associated with this phenomenon. The developed method is used in the paper for modeling and detecting emergent situations in cases of water floods, traffic jams, and phase transition in chemistry.

On the signature of complex system: A decomposed approach

2018 ◽  
Vol 265 (3) ◽  
pp. 1115-1123 ◽  
Author(s):  
Gaofeng Da ◽  
Ping Shing Chan ◽  
Maochao Xu
Keyword(s):  
Complex System ◽  
System A

scholarly journals External tuning of topological phase transitions induced by interaction driven mass renormalization

2021 ◽  
Author(s):  
Thies Jansen ◽  
Alexander Brinkman
Keyword(s):  
Phase Transition ◽  
Mean Field Theory ◽  
Tight Binding ◽  
Mean Field ◽  
Topological Phase ◽  
Binding Model ◽  
System A ◽  
Topological Phase Transition ◽  
Topological Phases Of Matter ◽  
Electron Interactions

Abstract Electron-electron interactions can be useful for realizing new nontrivial topological phases of matter. Here, we show by means of a tight-binding model and mean field theory how electron-electron interactions can lead to a topological phase transition. By externally adding or removing electrons from the system a band inversion between two bands with dierent parity is induced. This leads to a topological nontrivial phase if spin-orbit coupling is present. Besides the toy-model illustrating this mechanism, we also propose SmB6 as a possible playground for experimentally realizing a topological phase transition by external tuning.

scholarly journals Detection of Emergent Situations in Complex Systems by Structural Invariant (MB, M)

MENDEL ◽  
2017 ◽  
Vol 23 (1) ◽  
pp. 163-170 ◽  
Author(s):  
Jiri Bila ◽  
Martin Novak
Keyword(s):  
Complex System ◽  
Complex Systems ◽  
Detection Method ◽  
Water Cycle ◽  
Ramsey Theorem ◽  
Structural Invariant

The paper introduces complete description of the detection method that uses structural invariant Matroid and its Bases (MB, M). There are recapitulated essential concepts from the used knowledge field as “complex system, emergent situations (A, B, C)”, Ramsey theorem and principal computation variables “power” and “complexity” of emergence phenomenon. The method is explained in details and the demonstration of its application is done by the detection of emergent situation – violation of Short Water Cycle in an ecosystem.

Mechanics of Growing Solids and Phase Transitions

2013 ◽  
Vol 535-536 ◽  
pp. 89-93 ◽  
Author(s):  
Alexander V. Manzhirov
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Mathematical Theory ◽  
Solid Phase ◽  
Phase Growth ◽  
Main Attention ◽  
Transition Processes

Phase transitions can be usually observed in nature and technology which effectively utilize certain types of these transitions. An approach to modeling phase transition processes on the basis of the mathematical theory of growing solids is developed. Liquid-solid and gas-solid phase transitions are under consideration. Main attention is paid to the processes of solid phase growth and deformation.

A Novel Markov Model and its Application to BIT System

2012 ◽  
Vol 239-240 ◽  
pp. 721-725
Author(s):  
Wen Rong Zheng ◽  
Shu Zong Wang
Keyword(s):  
Complex System ◽  
Fault Diagnosis ◽  
Fault Detection ◽  
Markov Model ◽  
False Alarm ◽  
False Alarm Rate ◽  
Detection Rate ◽  
Intermittent Fault ◽  
System A ◽  
Main Factor

Intermittent fault is the main factor for the raise of false alarm during the process of the detection in built-in test (BIT). Two-state Markov model and three-state Markov model for test is built for system fault diagnosis with BIT. According to the application of BIT in some complex system, a comparison of the false alarm rate between two-state Markov model and three-state Markov model is present, which shows we can reduce the false alarm rate (FAR) and improve fault detection rate by using three-state Markov model in BIT.

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