This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights from their eigenvalue density, as a promising avenue for chaos monitoring. Inspired by a technique originally designed for detecting phase transitions in spin systems, we successfully adapted and applied it to identify analogous transformative patterns in the context of the Chirikov standard map. Leveraging the precision previously demonstrated in localizing critical points within magnetic systems in our prior research, our method accurately pinpoints the Chirikov resonance overlap criterion for the chaos boundary at K≈2.43, reinforcing its effectiveness. Additionally, we verified our findings by employing a combined approach that incorporates Lyapunov exponents and bifurcation diagrams. Lastly, we demonstrate the adaptability of our technique to other maps, establishing its capability to capture the transition to chaos, as evidenced in the logistic map.
{"title":"Exploring Transition from Stability to Chaos through Random Matrices","authors":"Roberto da Silva, Sandra Denise Prado","doi":"10.3390/dynamics3040042","DOIUrl":"https://doi.org/10.3390/dynamics3040042","url":null,"abstract":"This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights from their eigenvalue density, as a promising avenue for chaos monitoring. Inspired by a technique originally designed for detecting phase transitions in spin systems, we successfully adapted and applied it to identify analogous transformative patterns in the context of the Chirikov standard map. Leveraging the precision previously demonstrated in localizing critical points within magnetic systems in our prior research, our method accurately pinpoints the Chirikov resonance overlap criterion for the chaos boundary at K≈2.43, reinforcing its effectiveness. Additionally, we verified our findings by employing a combined approach that incorporates Lyapunov exponents and bifurcation diagrams. Lastly, we demonstrate the adaptability of our technique to other maps, establishing its capability to capture the transition to chaos, as evidenced in the logistic map.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136351490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marija Mitrović Dankulov, Bosiljka Tadić, Roderick Melnik
The essence of the stochastic processes behind the empirical data on infection and fatality during pandemics is the complex interdependence between biological and social factors. Their balance can be checked on the data of new virus outbreaks, where the population is unprepared to fight the viral biology and social measures and healthcare systems adjust with a delay. Using a complex systems perspective, we combine network mapping with K-means clustering and multifractal detrended fluctuations analysis to identify typical trends in fatality rate data. We analyse global data of (normalised) fatality time series recorded during the first two years of the recent pandemic caused by the severe acute respiratory syndrome coronavirus 2 as an appropriate example. Our results reveal six clusters with robust patterns of mortality progression that represent specific adaptations to prevailing biological factors. They make up two significant groups that coincide with the topological communities of the correlation network, with stabilising (group g1) and continuously increasing rates (group g2). Strong cyclic trends and multifractal small-scale fluctuations around them characterise these patterns. The rigorous analysis and the proposed methodology shed more light on the complex nonlinear shapes of the pandemic’s main characteristic curves, which have been discussed extensively in the literature regarding the global infectious diseases that have affected humanity throughout its history. In addition to better pandemic preparedness in the future, the presented methodology can also help to differentiate and predict other trends in pandemics, such as fatality rates, caused simultaneously by different viruses in particular geographic locations.
{"title":"Robust Global Trends during Pandemics: Analysing the Interplay of Biological and Social Processes","authors":"Marija Mitrović Dankulov, Bosiljka Tadić, Roderick Melnik","doi":"10.3390/dynamics3040041","DOIUrl":"https://doi.org/10.3390/dynamics3040041","url":null,"abstract":"The essence of the stochastic processes behind the empirical data on infection and fatality during pandemics is the complex interdependence between biological and social factors. Their balance can be checked on the data of new virus outbreaks, where the population is unprepared to fight the viral biology and social measures and healthcare systems adjust with a delay. Using a complex systems perspective, we combine network mapping with K-means clustering and multifractal detrended fluctuations analysis to identify typical trends in fatality rate data. We analyse global data of (normalised) fatality time series recorded during the first two years of the recent pandemic caused by the severe acute respiratory syndrome coronavirus 2 as an appropriate example. Our results reveal six clusters with robust patterns of mortality progression that represent specific adaptations to prevailing biological factors. They make up two significant groups that coincide with the topological communities of the correlation network, with stabilising (group g1) and continuously increasing rates (group g2). Strong cyclic trends and multifractal small-scale fluctuations around them characterise these patterns. The rigorous analysis and the proposed methodology shed more light on the complex nonlinear shapes of the pandemic’s main characteristic curves, which have been discussed extensively in the literature regarding the global infectious diseases that have affected humanity throughout its history. In addition to better pandemic preparedness in the future, the presented methodology can also help to differentiate and predict other trends in pandemics, such as fatality rates, caused simultaneously by different viruses in particular geographic locations.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135137648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Effectively identifying and characterizing the various dynamics present in complex and chaotic systems is fundamental for chaos control, chaos classification, and behavior-transition forecasting, among others. It is a complicated task that becomes increasingly difficult as systems involve more dimensions and parameters. Here, we extend methods inspired in ordinal patterns to analyze 2D iterative maps to unveil underlying approximate symmetries of their dynamics. We distinguish different families of chaos within the systems, find similarities among chaotic maps, identify approximate temporal and dynamical symmetries, and anticipate sharp transitions in dynamics. We show how this methodology displays the evolution of the spatial correlations in a dynamical system as the control parameter varies. We prove the power of these techniques, which involve simple quantifiers as well as combinations of them, in extracting relevant information from the complex dynamics of 2D systems, where other techniques are less informative or more computationally demanding.
{"title":"Unveiling Dynamical Symmetries in 2D Chaotic Iterative Maps with Ordinal-Patterns-Based Complexity Quantifiers","authors":"Benjamin S. Novak, Andrés Aragoneses","doi":"10.3390/dynamics3040040","DOIUrl":"https://doi.org/10.3390/dynamics3040040","url":null,"abstract":"Effectively identifying and characterizing the various dynamics present in complex and chaotic systems is fundamental for chaos control, chaos classification, and behavior-transition forecasting, among others. It is a complicated task that becomes increasingly difficult as systems involve more dimensions and parameters. Here, we extend methods inspired in ordinal patterns to analyze 2D iterative maps to unveil underlying approximate symmetries of their dynamics. We distinguish different families of chaos within the systems, find similarities among chaotic maps, identify approximate temporal and dynamical symmetries, and anticipate sharp transitions in dynamics. We show how this methodology displays the evolution of the spatial correlations in a dynamical system as the control parameter varies. We prove the power of these techniques, which involve simple quantifiers as well as combinations of them, in extracting relevant information from the complex dynamics of 2D systems, where other techniques are less informative or more computationally demanding.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Olefins are crucial building blocks for petrochemical industry, serving as raw materials for the production of various products such as plastics, synthetic fibers, detergents, solvents, and other chemicals. In FCC, heavy petroleum feedstocks are injected into a catalytic cracking unit, where they are mixed with a catalyst. The catalyst aids in breaking down the large hydrocarbon molecules into smaller fragments, including olefins like Propylene and Ethylene. These polymerization reactions occur at high temperatures. They demand that heat removal occurs as quickly as possible in order to control the reactor temperature and to avoid “hot spots” in the Regenerator or localized oxidation reactions (and to avoid creep rupture of the regenerator steel cladding). The cooling of the regenerator cladding surface can be achieved by impinging water droplets (spray), ejected from a spray nozzle. Spray cooling can provide uniform cooling and handle high heat fluxes in both a single phase and two phases. This research provides a thermal hydraulic design of regenerator spray cooling systems. In the framework of this research, Fire Dynamics Simulator (FDS) software was applied in order to simulate the temperature field and the water vapor mass fraction. A COMSOL Multiphysics finite element code was used in order to calculate the temperature field inside the regenerator cladding. The calculated surface temperatures and heat transfer convective coefficient, obtained using FDS software, were validated successfully against COMSOL numerical results and previous results in the literature. The numerical simulations were carried out for two cases. The first case was carried out at a distance of 0.5 m, and the second case was carried out at a distance of 0.2 m. A grid sensitivity study was carried out on the FDS model. Numerical integrations were carried out over time in order to calculate the average temperatures. The difference between these four average temperatures, calculated by applying different grids, is less than 7.4%. The calculated surface temperatures and heat transfer convective coefficient were validated successfully against COMSOL numerical results and previous research. It was shown that the calculated temperatures decrease in the second case. The water spray system managed to cool the steel wall more effectively as the water spray system approaches the steel cladding.
{"title":"Thermal Hydraulics Simulation of a Water Spray System for a Cooling Fluid Catalytic Cracking (FCC) Regenerator","authors":"Alon Davidy","doi":"10.3390/dynamics3040039","DOIUrl":"https://doi.org/10.3390/dynamics3040039","url":null,"abstract":"Olefins are crucial building blocks for petrochemical industry, serving as raw materials for the production of various products such as plastics, synthetic fibers, detergents, solvents, and other chemicals. In FCC, heavy petroleum feedstocks are injected into a catalytic cracking unit, where they are mixed with a catalyst. The catalyst aids in breaking down the large hydrocarbon molecules into smaller fragments, including olefins like Propylene and Ethylene. These polymerization reactions occur at high temperatures. They demand that heat removal occurs as quickly as possible in order to control the reactor temperature and to avoid “hot spots” in the Regenerator or localized oxidation reactions (and to avoid creep rupture of the regenerator steel cladding). The cooling of the regenerator cladding surface can be achieved by impinging water droplets (spray), ejected from a spray nozzle. Spray cooling can provide uniform cooling and handle high heat fluxes in both a single phase and two phases. This research provides a thermal hydraulic design of regenerator spray cooling systems. In the framework of this research, Fire Dynamics Simulator (FDS) software was applied in order to simulate the temperature field and the water vapor mass fraction. A COMSOL Multiphysics finite element code was used in order to calculate the temperature field inside the regenerator cladding. The calculated surface temperatures and heat transfer convective coefficient, obtained using FDS software, were validated successfully against COMSOL numerical results and previous results in the literature. The numerical simulations were carried out for two cases. The first case was carried out at a distance of 0.5 m, and the second case was carried out at a distance of 0.2 m. A grid sensitivity study was carried out on the FDS model. Numerical integrations were carried out over time in order to calculate the average temperatures. The difference between these four average temperatures, calculated by applying different grids, is less than 7.4%. The calculated surface temperatures and heat transfer convective coefficient were validated successfully against COMSOL numerical results and previous research. It was shown that the calculated temperatures decrease in the second case. The water spray system managed to cool the steel wall more effectively as the water spray system approaches the steel cladding.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136264090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
John G. Rosser, Tyamo Okosun, Orlando J. Ugarte, Chenn Q. Zhou
A continuous iron ore pellet feed system for a direct reduction ironmaking furnace is reportedly jamming in a hopper above the furnace, where a counterflowing gas seals off the furnace flue gas. The conditions that result in jamming are not well understood. The system is computationally modeled utilizing the coupled discrete element method (DEM) and computational fluid dynamics (CFD) technique. The technique is computationally expensive; therefore, the pellet sizing is modified while preserving the key metrics important in jamming. The model is used to study the impact of pellet moisture, heating, and ice formation between pellets in relation to the jamming event. The results indicate that the influence of moisture alone on the bulk shear rate is unlikely to jam the system and that insufficient heat is supplied by the counterflowing gas to raise the temperature of the pellets, which suggests freezing conditions can exist within the hopper. Particle bonding is implemented to replicate wet and icy pellets freezing and breaking up. The results indicate that the system jams in winter conditions when the hopper is charged with a minimum of 15% icy pellets, or 10% icy with 5% wet pellets. These results agree with industry reports of jamming during winter operations.
{"title":"Investigation of Jamming Phenomenon in a Direct Reduction Furnace Pellet Feed System Using the Discrete Element Method","authors":"John G. Rosser, Tyamo Okosun, Orlando J. Ugarte, Chenn Q. Zhou","doi":"10.3390/dynamics3040038","DOIUrl":"https://doi.org/10.3390/dynamics3040038","url":null,"abstract":"A continuous iron ore pellet feed system for a direct reduction ironmaking furnace is reportedly jamming in a hopper above the furnace, where a counterflowing gas seals off the furnace flue gas. The conditions that result in jamming are not well understood. The system is computationally modeled utilizing the coupled discrete element method (DEM) and computational fluid dynamics (CFD) technique. The technique is computationally expensive; therefore, the pellet sizing is modified while preserving the key metrics important in jamming. The model is used to study the impact of pellet moisture, heating, and ice formation between pellets in relation to the jamming event. The results indicate that the influence of moisture alone on the bulk shear rate is unlikely to jam the system and that insufficient heat is supplied by the counterflowing gas to raise the temperature of the pellets, which suggests freezing conditions can exist within the hopper. Particle bonding is implemented to replicate wet and icy pellets freezing and breaking up. The results indicate that the system jams in winter conditions when the hopper is charged with a minimum of 15% icy pellets, or 10% icy with 5% wet pellets. These results agree with industry reports of jamming during winter operations.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136032682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a new formalism for constructing probabilities associated with the causal ordering of events in quantum theory, where an event is defined as the emergence of a measurement record on a detector. We start with constructing probabilities for the causal ordering events in classical physics, where events are defined in terms of worldline coincidences. Then, we show how these notions generalize to quantum systems, where there exists no fundamental notion of trajectory. The probabilities constructed here are experimentally accessible, at least in principle. Our analysis here clarifies that the existence of quantum orderings of events do not require quantum gravity effects: it is a consequence of the quantum dynamics of matter, and it appears in the presence of a fixed background spacetime.
{"title":"Quantum Probabilities for the Causal Ordering of Events","authors":"Charis Anastopoulos, Maria-Electra Plakitsi","doi":"10.3390/dynamics3040037","DOIUrl":"https://doi.org/10.3390/dynamics3040037","url":null,"abstract":"We develop a new formalism for constructing probabilities associated with the causal ordering of events in quantum theory, where an event is defined as the emergence of a measurement record on a detector. We start with constructing probabilities for the causal ordering events in classical physics, where events are defined in terms of worldline coincidences. Then, we show how these notions generalize to quantum systems, where there exists no fundamental notion of trajectory. The probabilities constructed here are experimentally accessible, at least in principle. Our analysis here clarifies that the existence of quantum orderings of events do not require quantum gravity effects: it is a consequence of the quantum dynamics of matter, and it appears in the presence of a fixed background spacetime.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136115182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we analyse the classical action as a tool to reveal the phase space structure of Hamiltonian systems simply and intuitively. We construct a scalar field using the values of the action along the trajectories to analyse the phase space. The different behaviours of the trajectories around important geometrical objects like normally hyperbolic invariant manifolds, their stable and unstable manifolds, and KAM structures generate characteristic patterns in the scalar field generated by the action. Also, we present a simple argument based on the conservation of energy and the behaviour of the trajectories to understand the origin of the patterns in this scalar field. As examples, we study the phase space of open Hamiltonian systems with two and three degrees of freedom.
{"title":"The Classical Action as a Tool to Visualise the Phase Space of Hamiltonian Systems","authors":"Francisco Gonzalez Montoya","doi":"10.3390/dynamics3040036","DOIUrl":"https://doi.org/10.3390/dynamics3040036","url":null,"abstract":"In this paper, we analyse the classical action as a tool to reveal the phase space structure of Hamiltonian systems simply and intuitively. We construct a scalar field using the values of the action along the trajectories to analyse the phase space. The different behaviours of the trajectories around important geometrical objects like normally hyperbolic invariant manifolds, their stable and unstable manifolds, and KAM structures generate characteristic patterns in the scalar field generated by the action. Also, we present a simple argument based on the conservation of energy and the behaviour of the trajectories to understand the origin of the patterns in this scalar field. As examples, we study the phase space of open Hamiltonian systems with two and three degrees of freedom.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135855854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article aims to develop a new Adaptive Proportional Integral Derivative (PID) Nonsingular Dual Terminal Sliding Mode Control, designed for tracking the position of robot manipulators under disturbances and uncertainties. Compared with existing PID Nonsingular Fast Terminal Sliding Mode (PIDNFTSM) controllers, this work effectively avoids singularity problems in control while significantly enhancing the convergence speed of errors. An adaptive reaching law is proposed to estimate the bound information of the first derivative of lumped disturbance by regulating itself based on sliding variables. The overall system stability is proven by using the Lyapunov approach. Subsequent simulation results verify the effectiveness of the proposed controller regarding tracking error reduction, energy efficiency enhancements, and singularity avoidance.
{"title":"Adaptive Proportional Integral Derivative Nonsingular Dual Terminal Sliding Mode Control for Robotic Manipulators","authors":"Hiep Dai Le, Tamara Nestorović","doi":"10.3390/dynamics3040035","DOIUrl":"https://doi.org/10.3390/dynamics3040035","url":null,"abstract":"This article aims to develop a new Adaptive Proportional Integral Derivative (PID) Nonsingular Dual Terminal Sliding Mode Control, designed for tracking the position of robot manipulators under disturbances and uncertainties. Compared with existing PID Nonsingular Fast Terminal Sliding Mode (PIDNFTSM) controllers, this work effectively avoids singularity problems in control while significantly enhancing the convergence speed of errors. An adaptive reaching law is proposed to estimate the bound information of the first derivative of lumped disturbance by regulating itself based on sliding variables. The overall system stability is proven by using the Lyapunov approach. Subsequent simulation results verify the effectiveness of the proposed controller regarding tracking error reduction, energy efficiency enhancements, and singularity avoidance.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135141524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ricardo A. Calix, Orlando Ugarte, Tyamo Okosun, Hong Wang
Computational fluid dynamics (CFD)-based simulation has been the traditional way to model complex industrial systems and processes. One very large and complex industrial system that has benefited from CFD-based simulations is the steel blast furnace system. The problem with the CFD-based simulation approach is that it tends to be very slow for generating data. The CFD-only approach may not be fast enough for use in real-time decisionmaking. To address this issue, in this work, the authors propose the use of machine learning techniques to train and test models based on data generated via CFD simulation. Regression models based on neural networks are compared with tree-boosting models. In particular, several areas (tuyere, raceway, and shaft) of the blast furnace are modeled using these approaches. The results of the model training and testing are presented and discussed. The obtained R2 metrics are, in general, very high. The results appear promising and may help to improve the efficiency of operator and process engineer decisionmaking when running a blast furnace.
{"title":"Machine Learning-Based Regression Models for Ironmaking Blast Furnace Automation","authors":"Ricardo A. Calix, Orlando Ugarte, Tyamo Okosun, Hong Wang","doi":"10.3390/dynamics3040034","DOIUrl":"https://doi.org/10.3390/dynamics3040034","url":null,"abstract":"Computational fluid dynamics (CFD)-based simulation has been the traditional way to model complex industrial systems and processes. One very large and complex industrial system that has benefited from CFD-based simulations is the steel blast furnace system. The problem with the CFD-based simulation approach is that it tends to be very slow for generating data. The CFD-only approach may not be fast enough for use in real-time decisionmaking. To address this issue, in this work, the authors propose the use of machine learning techniques to train and test models based on data generated via CFD simulation. Regression models based on neural networks are compared with tree-boosting models. In particular, several areas (tuyere, raceway, and shaft) of the blast furnace are modeled using these approaches. The results of the model training and testing are presented and discussed. The obtained R2 metrics are, in general, very high. The results appear promising and may help to improve the efficiency of operator and process engineer decisionmaking when running a blast furnace.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135197489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Computational complexity reduction is at the basis of a new formulation of many-body quantum states according to tensor network ansatz, originally framed in one-dimensional lattices. In order to include long-range entanglement characterizing phase transitions, the multiscale entanglement renormalization ansatz (MERA) defines a sequence of coarse-grained lattices, obtained by targeting the map of a scale-invariant system into an identical coarse-grained one. The quantum circuit associated with this hierarchical structure includes the definition of causal relations and unitary extensions, leading to the definition of ground subspaces as stabilizer codes. The emerging error correcting codes are referred to logical indices located at the highest hierarchical level and to physical indices yielded by redundancy, framed in the AdS-CFT correspondence as holographic quantum codes with bulk and boundary indices, respectively. In a use-case scenario based on errors consisting of spin erasure, the correction is implemented as the reconstruction of a bulk local operator.
{"title":"Multiscale Entanglement Renormalization Ansatz: Causality and Error Correction","authors":"Domenico Pomarico","doi":"10.3390/dynamics3030033","DOIUrl":"https://doi.org/10.3390/dynamics3030033","url":null,"abstract":"Computational complexity reduction is at the basis of a new formulation of many-body quantum states according to tensor network ansatz, originally framed in one-dimensional lattices. In order to include long-range entanglement characterizing phase transitions, the multiscale entanglement renormalization ansatz (MERA) defines a sequence of coarse-grained lattices, obtained by targeting the map of a scale-invariant system into an identical coarse-grained one. The quantum circuit associated with this hierarchical structure includes the definition of causal relations and unitary extensions, leading to the definition of ground subspaces as stabilizer codes. The emerging error correcting codes are referred to logical indices located at the highest hierarchical level and to physical indices yielded by redundancy, framed in the AdS-CFT correspondence as holographic quantum codes with bulk and boundary indices, respectively. In a use-case scenario based on errors consisting of spin erasure, the correction is implemented as the reconstruction of a bulk local operator.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135202891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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