Pub Date : 2024-07-25DOI: 10.3390/foundations4030023
A. Vatsala, Govinda Pageni
Computation of the solution of the nonlinear Caputo fractional differential equation is essential for using q, which is the order of the derivative, as a parameter. The value of q can be determined to enhance the mathematical model in question using the data. The numerical methods available in the literature provide only the local existence of the solution. However, the interval of existence is known and guaranteed by the natural upper and lower solutions of the nonlinear differential equations. In this work, we develop monotone iterates, together with lower and upper solutions that converge uniformly, monotonically, and quadratically to the unique solution of the Caputo nonlinear fractional differential equation over its entire interval of existence. The nonlinear function is assumed to be the sum of convex and concave functions. The method is referred to as the generalized quasilinearization method. We provide a Caputo fractional logistic equation as an example whose interval of existence is [0,∞).
{"title":"Generalized Quasilinearization Method for Caputo Fractional Differential Equations with Initial Conditions with Applications","authors":"A. Vatsala, Govinda Pageni","doi":"10.3390/foundations4030023","DOIUrl":"https://doi.org/10.3390/foundations4030023","url":null,"abstract":"Computation of the solution of the nonlinear Caputo fractional differential equation is essential for using q, which is the order of the derivative, as a parameter. The value of q can be determined to enhance the mathematical model in question using the data. The numerical methods available in the literature provide only the local existence of the solution. However, the interval of existence is known and guaranteed by the natural upper and lower solutions of the nonlinear differential equations. In this work, we develop monotone iterates, together with lower and upper solutions that converge uniformly, monotonically, and quadratically to the unique solution of the Caputo nonlinear fractional differential equation over its entire interval of existence. The nonlinear function is assumed to be the sum of convex and concave functions. The method is referred to as the generalized quasilinearization method. We provide a Caputo fractional logistic equation as an example whose interval of existence is [0,∞).","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"28 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141802920","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}
Pub Date : 2024-07-08DOI: 10.3390/foundations4030021
P. Ojeda-May, Alexander Vergara
The intracellular environment displays complex dynamics influenced by factors such as molecular crowding and the low Reynolds number of the cytoplasm. Enzymes exhibiting active matter properties further heighten this complexity which can lead to memory effects. Molecular simulations often neglect these factors, treating the environment as a “thermal bath” using the Langevin equation (LE) with white noise. One way to consider these factors is by using colored noise instead within the generalized Langevin equation (GLE) framework, which allows for the incorporation of memory effects that have been observed in experimental data. We investigated the structural and dynamic differences in Shikimate kinase (SK) using LE and GLE simulations. Our results suggest that GLE simulations, which reveal significant changes, could be utilized for assessing conformational motions’ impact on catalytic reactions.
受分子拥挤和细胞质低雷诺数等因素的影响，细胞内环境呈现出复杂的动态变化。表现出活性物质特性的酶进一步加剧了这种复杂性，可能导致记忆效应。分子模拟通常会忽略这些因素，使用带有白噪声的朗格文方程（LE）将环境视为 "热浴"。考虑这些因素的一种方法是在广义朗温方程（GLE）框架内使用彩色噪声，这样就可以将实验数据中观察到的记忆效应纳入其中。我们使用 LE 和 GLE 模拟研究了莽草酸激酶（SK）的结构和动态差异。我们的结果表明，GLE 模拟能揭示显著的变化，可用于评估构象运动对催化反应的影响。
{"title":"Effects of Colored Noise in the Dynamic Motions and Conformational Exploration of Enzymes","authors":"P. Ojeda-May, Alexander Vergara","doi":"10.3390/foundations4030021","DOIUrl":"https://doi.org/10.3390/foundations4030021","url":null,"abstract":"The intracellular environment displays complex dynamics influenced by factors such as molecular crowding and the low Reynolds number of the cytoplasm. Enzymes exhibiting active matter properties further heighten this complexity which can lead to memory effects. Molecular simulations often neglect these factors, treating the environment as a “thermal bath” using the Langevin equation (LE) with white noise. One way to consider these factors is by using colored noise instead within the generalized Langevin equation (GLE) framework, which allows for the incorporation of memory effects that have been observed in experimental data. We investigated the structural and dynamic differences in Shikimate kinase (SK) using LE and GLE simulations. Our results suggest that GLE simulations, which reveal significant changes, could be utilized for assessing conformational motions’ impact on catalytic reactions.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"114 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141667886","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}
Pub Date : 2024-07-04DOI: 10.3390/foundations4030020
E. Ballico
We study the multiviews of algebraic space curves X from n pin-hole cameras of a real or complex projective space. We assume the pin-hole centers to be known, i.e., we do not reconstruct them. Our tools are algebro-geometric. We give some general theorems, e.g., we prove that a projective curve (over complex or real numbers) may be reconstructed using four general cameras. Several examples show that no number of badly placed cameras can make a reconstruction possible. The tools are powerful, but we warn the reader (with examples) that over real numbers, just using them correctly, but in a bad way, may give ghosts: real curves which are images of the emptyset. We prove that ghosts do not occur if the cameras are general. Most of this paper is devoted to three important cases of space curves: unions of a prescribed number of lines (using the Grassmannian of all lines in a 3-dimensional projective space), plane curves, and curves of low degree. In these cases, we also see when two cameras may reconstruct the curve, but different curves need different pairs of cameras.
我们研究从实射或复射空间的 n 个针孔摄像机拍摄的代数空间曲线 X 的多视图。我们假定针孔中心是已知的，也就是说，我们不重建针孔中心。我们的工具是代数几何工具。我们给出了一些一般性定理，例如，我们证明了一条投影曲线（在复数或实数上）可以用四台普通相机来重构。几个例子表明，任何数量的相机都不可能重建曲线。这些工具都很强大，但我们要提醒读者（用例子说明），在实数上，如果只是正确地使用这些工具，但使用方法不当，可能会出现鬼影：实曲线是空集的图像。我们证明，如果摄像机是通用的，就不会出现重影。本文的大部分篇幅都用来讨论空间曲线的三种重要情况：规定数量的线段的联合（使用三维投影空间中所有线段的格拉斯曼）、平面曲线和低度曲线。在这些情况下，我们还可以看到两台摄像机可以重建曲线，但不同的曲线需要不同的摄像机对。
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Pub Date : 2024-06-11DOI: 10.3390/foundations4020018
Csaba Bús, B. Kutus, Á. Ágoston, László Janovák, Pál Sipos
Alkaline–surfactant–polymer (ASP) flooding by means of which alkali additives, surfactant and polymer are inserted as the same slug is one of the most favourable worldwide focuses of Chemical Enhanced Oil Recovery (cEOR) research and field trials, due to the individual synergy of the three chemical components. To develop efficient oil recovery chemicals, it is essential to fully understand the mechanism behind ASP flooding. Nonetheless, there are hardly any studies reporting a systematic characterization of the ASP process. Thus, the present paper focuses on modelling this process in a laboratory by the use of an anionic surfactant—sodium dodecyl sulphate (SDS) in alkaline–polymer media—which is composed of a commercial water-soluble polymer (Flopaam AN125SH®, SNF Floerger, Andrézieux-Bouthéon, France) and alkali compounds (NaOH and Na2CO3). The samples were characterized using rheometry, dynamic light scattering (DLS), infrared spectroscopy (IR) and measurement of inferfacial tension (IFT) between the samples and rapeseed oil. In accordance with the experimental results, surprisingly lower IFT values were recorded between the alkaline–polymer solutions and rapeseed oil than the samples which contained SDS. Increasing polymer and sodium chloride concentration caused a decrease (from 0.591 mN/m to 0.0486 mN/m) in IFT between the surfactant containing samples and rapeseed oil. The IR measurements confirmed that the surfactant was not detected in the oil phase in the absence of NaOH and Na2CO3. The effects of SDS on the viscosity of the mixtures were also investigated, as viscosity is a considerably important parameter in processes using polymers.
{"title":"Characterization of the Solution Properties of Sodium Dodecylsulphate Containing Alkaline–Surfactant–Polymer Flooding Media","authors":"Csaba Bús, B. Kutus, Á. Ágoston, László Janovák, Pál Sipos","doi":"10.3390/foundations4020018","DOIUrl":"https://doi.org/10.3390/foundations4020018","url":null,"abstract":"Alkaline–surfactant–polymer (ASP) flooding by means of which alkali additives, surfactant and polymer are inserted as the same slug is one of the most favourable worldwide focuses of Chemical Enhanced Oil Recovery (cEOR) research and field trials, due to the individual synergy of the three chemical components. To develop efficient oil recovery chemicals, it is essential to fully understand the mechanism behind ASP flooding. Nonetheless, there are hardly any studies reporting a systematic characterization of the ASP process. Thus, the present paper focuses on modelling this process in a laboratory by the use of an anionic surfactant—sodium dodecyl sulphate (SDS) in alkaline–polymer media—which is composed of a commercial water-soluble polymer (Flopaam AN125SH®, SNF Floerger, Andrézieux-Bouthéon, France) and alkali compounds (NaOH and Na2CO3). The samples were characterized using rheometry, dynamic light scattering (DLS), infrared spectroscopy (IR) and measurement of inferfacial tension (IFT) between the samples and rapeseed oil. In accordance with the experimental results, surprisingly lower IFT values were recorded between the alkaline–polymer solutions and rapeseed oil than the samples which contained SDS. Increasing polymer and sodium chloride concentration caused a decrease (from 0.591 mN/m to 0.0486 mN/m) in IFT between the surfactant containing samples and rapeseed oil. The IR measurements confirmed that the surfactant was not detected in the oil phase in the absence of NaOH and Na2CO3. The effects of SDS on the viscosity of the mixtures were also investigated, as viscosity is a considerably important parameter in processes using polymers.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"8 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141360460","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}
Pub Date : 2024-06-04DOI: 10.3390/foundations4020017
S. Innamorati
In the present work, we classify sets of type (4,n) in PG(3,q). We prove that PG(3,q), apart from the planes of PG(3,3), contains only sets of type (4,n) with standard parameters. Thus, somewhat surprisingly, we conclude that there are no sets of type (4,n) in PG(3,q), q ≠ 3, with non-standard parameters.
{"title":"Classifying Sets of Type (4,n) in PG(3,q)","authors":"S. Innamorati","doi":"10.3390/foundations4020017","DOIUrl":"https://doi.org/10.3390/foundations4020017","url":null,"abstract":"In the present work, we classify sets of type (4,n) in PG(3,q). We prove that PG(3,q), apart from the planes of PG(3,3), contains only sets of type (4,n) with standard parameters. Thus, somewhat surprisingly, we conclude that there are no sets of type (4,n) in PG(3,q), q ≠ 3, with non-standard parameters.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141388178","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}
Pub Date : 2024-05-20DOI: 10.3390/foundations4020015
Sean P. Rigby
This work reviews a range of fundamental theoretical considerations in pore structural characterisation. The pore concept is essential for providing a better understanding of physical processes arising within porous media than purely phenomenological approaches. The notion of a pore structure is found to be independently valid and invariant during theory change concerning said physical processes, even for structural models obtained via indirect methods. While imaging methods provide a more direct characterisation of porous solids, there is often a surfeit of information beyond that which can be wielded with current computing power to predict processes sufficiently accurately. Unfortunately, the pore network model extraction methods cannot decide in advance the level of simplification necessary to obtain the optimum minimal idealisation for a given physical process. Pore network models can be obtained with differing geometrical and topological properties, but similar mass transfer rates, for reasons that are often not clear. In contrast, the ‘pore-sifting’ strategy aims to explicitly identify the key feature of the void space that controls a mass transport process of interest.
{"title":"Do Pores Exist?—Foundational Issues in Pore Structural Characterisation","authors":"Sean P. Rigby","doi":"10.3390/foundations4020015","DOIUrl":"https://doi.org/10.3390/foundations4020015","url":null,"abstract":"This work reviews a range of fundamental theoretical considerations in pore structural characterisation. The pore concept is essential for providing a better understanding of physical processes arising within porous media than purely phenomenological approaches. The notion of a pore structure is found to be independently valid and invariant during theory change concerning said physical processes, even for structural models obtained via indirect methods. While imaging methods provide a more direct characterisation of porous solids, there is often a surfeit of information beyond that which can be wielded with current computing power to predict processes sufficiently accurately. Unfortunately, the pore network model extraction methods cannot decide in advance the level of simplification necessary to obtain the optimum minimal idealisation for a given physical process. Pore network models can be obtained with differing geometrical and topological properties, but similar mass transfer rates, for reasons that are often not clear. In contrast, the ‘pore-sifting’ strategy aims to explicitly identify the key feature of the void space that controls a mass transport process of interest.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"45 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141118960","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}
Pub Date : 2024-05-14DOI: 10.3390/foundations4020014
Andrew Peplow, Bilong Liu
This paper introduces an efficient computational procedure for analyzing the propagation of harmonic waves in layered elastic media. This offers several advantages, including the ability to handle arbitrary frequencies, depths, and the number of layers above an elastic half-space, and efforts to follow dispersion curves and flag up possible singularities are investigated. While there are inherent limitations in terms of computational accuracy and capacity, this methodology is straightforward to implement for studying free or forced vibrations and obtaining relevant response data. We present computations of wavenumber dispersion diagrams, phase velocity plots, and response data in both the frequency and time domains. These computational results are provided for two example cases: plane strain and axisymmetry. Our methodology is grounded in a well-conditioned dynamic stiffness approach specifically tailored for deep-layered strata analysis. We introduce an innovative method for efficiently computing wavenumber dispersion curves. By tracking the slope of these curves, users can effectively manage continuation parameters. We illustrate this technique through numerical evidence of a layer resonance in a real-life case study characterized by a fold in the dispersion curves. Furthermore, this framework is particularly advantageous for engineers addressing problems related to ground-borne vibrations. It enables the analysis of phenomena such as zero group velocity (ZGV), where a singularity occurs, both in the frequency and time domains, shedding light on the unique characteristics of such cases. Given the reduced dimension of the problem, this formulation can considerably aid geophysicists and engineers in areas such as MASW or SASW techniques.
{"title":"Minimal Conditioned Stiffness Matrices with Frequency-Dependent Path Following for Arbitrary Elastic Layers over Half-Spaces","authors":"Andrew Peplow, Bilong Liu","doi":"10.3390/foundations4020014","DOIUrl":"https://doi.org/10.3390/foundations4020014","url":null,"abstract":"This paper introduces an efficient computational procedure for analyzing the propagation of harmonic waves in layered elastic media. This offers several advantages, including the ability to handle arbitrary frequencies, depths, and the number of layers above an elastic half-space, and efforts to follow dispersion curves and flag up possible singularities are investigated. While there are inherent limitations in terms of computational accuracy and capacity, this methodology is straightforward to implement for studying free or forced vibrations and obtaining relevant response data. We present computations of wavenumber dispersion diagrams, phase velocity plots, and response data in both the frequency and time domains. These computational results are provided for two example cases: plane strain and axisymmetry. Our methodology is grounded in a well-conditioned dynamic stiffness approach specifically tailored for deep-layered strata analysis. We introduce an innovative method for efficiently computing wavenumber dispersion curves. By tracking the slope of these curves, users can effectively manage continuation parameters. We illustrate this technique through numerical evidence of a layer resonance in a real-life case study characterized by a fold in the dispersion curves. Furthermore, this framework is particularly advantageous for engineers addressing problems related to ground-borne vibrations. It enables the analysis of phenomena such as zero group velocity (ZGV), where a singularity occurs, both in the frequency and time domains, shedding light on the unique characteristics of such cases. Given the reduced dimension of the problem, this formulation can considerably aid geophysicists and engineers in areas such as MASW or SASW techniques.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"7 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140981823","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}
Pub Date : 2024-05-11DOI: 10.3390/foundations4020013
David Ellerman
There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on logical entropy) are shown to start with the quantitative versions of subsets and partitions. Some basic universal mapping properties in the category of Sets are developed that precede the abstract duality of category theory. But by far the main application is to the clarification and interpretation of quantum mechanics. Since classical mechanics illustrates the Boolean worldview of full distinctness, it is natural that quantum mechanics would be based on the indefiniteness of its characteristic superposition states, which is modeled at the set level by partitions (or equivalence relations). This approach to interpreting quantum mechanics is not a jury-rigged or ad hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences.
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Pub Date : 2024-04-23DOI: 10.3390/foundations4020012
A. Margellou, Philippos J. Pomonis
In this work we suggest that the common cause for the development of various power laws is the existence of a suitable exchangeable quantity between the agents of a set. Examples of such exchangeable quantities, leading to eponymous power laws, include money (Pareto’s Law), scientific knowledge (Lotka’s Law), people (Auerbach’s Law), and written or verbal information (Zipf’s Law), as well as less common cases like bullets during deadly conflicts, recognition in social networks, heat between the atmosphere and sea-ice floes, and, finally, mass of water vapors between pores in solids. This last case is examined closely in the present article based on extensive experimental data. It is shown that the transferred mass between pores, which eventually grow towards a power law distribution, may be expressed using different parameters, either transferred surface area, or transferred volume, or transferred pore length or transferred pore anisotropy. These distinctions lead to different power laws of variable strength as reflected by the corresponding exponent. The exponents depend quantitatively on the spread of frequency distribution of the examined parameter and tend to zero as the spread of distribution tends to a single order of magnitude. A comparison between the energy and the entropy of different kinds of pore distributions reveals that these two statistical parameters are linearly related, implying that the system poise at a critical state and the exchangeable quantities are the most convenient operations helping to keep this balance.
{"title":"Exchangeable Quantities and Power Laws: Τhe Case of Pores in Solids","authors":"A. Margellou, Philippos J. Pomonis","doi":"10.3390/foundations4020012","DOIUrl":"https://doi.org/10.3390/foundations4020012","url":null,"abstract":"In this work we suggest that the common cause for the development of various power laws is the existence of a suitable exchangeable quantity between the agents of a set. Examples of such exchangeable quantities, leading to eponymous power laws, include money (Pareto’s Law), scientific knowledge (Lotka’s Law), people (Auerbach’s Law), and written or verbal information (Zipf’s Law), as well as less common cases like bullets during deadly conflicts, recognition in social networks, heat between the atmosphere and sea-ice floes, and, finally, mass of water vapors between pores in solids. This last case is examined closely in the present article based on extensive experimental data. It is shown that the transferred mass between pores, which eventually grow towards a power law distribution, may be expressed using different parameters, either transferred surface area, or transferred volume, or transferred pore length or transferred pore anisotropy. These distinctions lead to different power laws of variable strength as reflected by the corresponding exponent. The exponents depend quantitatively on the spread of frequency distribution of the examined parameter and tend to zero as the spread of distribution tends to a single order of magnitude. A comparison between the energy and the entropy of different kinds of pore distributions reveals that these two statistical parameters are linearly related, implying that the system poise at a critical state and the exchangeable quantities are the most convenient operations helping to keep this balance.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"14 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140668288","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}
Pub Date : 2024-02-24DOI: 10.3390/foundations4010009
Ismael Fernández-Osete, David Bermejo, Xavier Ayneto-Gubert, X. Escaler
Nowadays, hydropower plants are being used to compensate for the variable power produced by the new fluctuating renewable energy sources, such as wind and solar power, and to stabilise the grid. Consequently, hydraulic turbines are forced to work more often in off-design conditions, far from their best efficiency point. This new operation strategy increases the probability of erosive cavitation and of hydraulic instabilities and pressure fluctuations that increase the risk of fatigue damage and reduce the life expectancy of the units. To monitor erosive cavitation and fatigue damage, acoustic emissions induced by very-high-frequency elastic waves within the solid have been traditionally used. Therefore, acoustic emissions are becoming an important tool for hydraulic turbine failure detection and troubleshooting. In particular, artificial intelligence is a promising signal analysis research hotspot, and it has a great potential in the condition monitoring of hydraulic turbines using acoustic emissions as a key factor in the digitalisation process. In this paper, a brief introduction of acoustic emissions and a description of their main applications are presented. Then, the research works carried out for cavitation and fracture detection using acoustic emissions are summarised, and the different levels of development are compared and discussed. Finally, the role of artificial intelligence is reviewed, and expected directions for future works are suggested.
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