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29 pages, 13960 KiB  
Article
Blockchain in Smart Grids: A Bibliometric Analysis and Scientific Mapping Study
J 2024, 7(1), 19-47; https://doi.org/10.3390/j7010002 - 06 Jan 2024
Viewed by 624
Abstract
To achieve sustainability and fulfill sustainable development goals, the digitalization of the power sector is vital. This study aims to examine how blockchain can be integrated into and enrich smart grids. In total, 10 research questions are explored. Scopus and Web of Science [...] Read more.
To achieve sustainability and fulfill sustainable development goals, the digitalization of the power sector is vital. This study aims to examine how blockchain can be integrated into and enrich smart grids. In total, 10 research questions are explored. Scopus and Web of Science (WoS) were used to identify documents related to the topic. The study involves the analysis of 1041 scientific documents over the period 2015–2022. The related studies are analyzed from different dimensions including descriptive statistics, identification of the most common keywords and most widely used outlets, examination of the annual scientific production, the analysis of the most impactful and productive authors, countries, and affiliations. The advancement of the research focus and the most popular topics are also examined. Additionally, the results are analyzed, the main findings are discussed, open issues and challenges are presented, and suggestions for new research directions are provided. Based on the results, it was evident that blockchain plays a vital role in securing smart grids and realizing power sector digitalization, as well as in achieving sustainability and successfully meeting sustainable development goals. Full article
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18 pages, 1699 KiB  
Review
An Overview of Mathematical Methods Applied in the Biomechanics of Foot and Ankle–Foot Orthosis Models
J 2024, 7(1), 1-18; https://doi.org/10.3390/j7010001 - 22 Dec 2023
Viewed by 451
Abstract
Ankle–foot orthoses (AFOs) constitute medical instruments designed for patients exhibiting pathological gait patterns, notably stemming from conditions such as stroke, with the primary objective of providing support and facilitating rehabilitation. The present research endeavors to conduct a comprehensive review of extant scholarly literature [...] Read more.
Ankle–foot orthoses (AFOs) constitute medical instruments designed for patients exhibiting pathological gait patterns, notably stemming from conditions such as stroke, with the primary objective of providing support and facilitating rehabilitation. The present research endeavors to conduct a comprehensive review of extant scholarly literature focusing on mathematical techniques employed for the examination of AFO models. The overarching aim is to gain deeper insights into the biomechanical intricacies underlying these ankle–foot orthosis models from a mathematical perspective, while concurrently aiming to advance novel models within the domain. Utilizing a specified set of keywords and their configurations, a systematic search was conducted across notable academic databases, including ISI Web of Knowledge, Google Scholar, Scopus, and PubMed. Subsequently, a total of 23 articles were meticulously selected for in-depth review. These scholarly contributions collectively shed light on the utilization of nonlinear optimization techniques within the context of ankle–foot orthoses (AFOs), specifically within the framework of fully Cartesian coordinates, encompassing both kinematic and dynamic dimensions. Furthermore, an exploration of a two-degree-of-freedom AFO design tailored for robotic rehabilitation, which takes into account the interplay between foot and orthosis models, is delineated. Notably, the review article underscores the incorporation of shape memory alloy (SMA) elements in AFOs and overviews the constitutive elastic, viscoelastic, and hyperelastic models. This comprehensive synthesis of research findings stands to provide valuable insights for orthotists and engineers, enabling them to gain a mathematical understanding of the biomechanical principles underpinning AFO models and fostering the development of innovative AFO designs. Full article
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12 pages, 8756 KiB  
Article
A Comparative Study of Finite Element Method and Hybrid Finite Element Method–Spectral Element Method Approaches Applied to Medium-Frequency Transformers with Foil Windings
J 2023, 6(4), 627-638; https://doi.org/10.3390/j6040041 - 13 Dec 2023
Viewed by 715
Abstract
This study aims to improve the computational efficiency of the frequency domain analysis of medium-frequency transformers (MFTs) with the presence of large clearance distances and fine foil windings. The winding loss and magnetic energy in MFTs in the medium-frequency range are calculated utilizing [...] Read more.
This study aims to improve the computational efficiency of the frequency domain analysis of medium-frequency transformers (MFTs) with the presence of large clearance distances and fine foil windings. The winding loss and magnetic energy in MFTs in the medium-frequency range are calculated utilizing a finite element method (FEM) using common triangular and alternative rectilinear mesh elements. Additionally, in order to improve the computational efficiency of the calculations, a spectral element method (SEM) is coupled with a FEM, thus creating a hybrid FEM–SEM formulation. In such a hybrid approach, the FEM is used to calculate the current density distribution in the two-dimensional (2D) cross-section of the foil conductors to achieve reliable accuracy, and the SEM is adopted in the nonconducting clearance distances of the winding window to reduce the system of equations. The comparative analysis of the calculated resistance and reactance of the under-study models showed that the FEM with rectilinear mesh elements and the FEM–SEM model outperformed the FEM with triangular mesh elements in terms of accuracy and computational cost. The hybrid FEM–SEM model enables a reduced system of equations for modeling the electromagnetic behavior of MFTs. This research provides valuable insights into both the computational approaches and meshing challenges in the analysis of MFTs and offers a foundation for future research on the design and optimization of MFTs. Full article
(This article belongs to the Section Engineering)
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22 pages, 2499 KiB  
Article
Relationship between Plasma Lipopolysaccharide Concentration and Health Status in Healthy Subjects and Patients with Abnormal Glucose Metabolism in Japan: A Preliminary Cross-Sectional Study
J 2023, 6(4), 605-626; https://doi.org/10.3390/j6040040 - 30 Nov 2023
Viewed by 592
Abstract
Lipopolysaccharides are components of Gram-negative bacteria. The relationship between blood lipopolysaccharide levels and health status has mainly been investigated in Europe, and there is a lack of information about Asia, particularly Japan. This study aimed to investigate the relationship between blood lipopolysaccharide levels [...] Read more.
Lipopolysaccharides are components of Gram-negative bacteria. The relationship between blood lipopolysaccharide levels and health status has mainly been investigated in Europe, and there is a lack of information about Asia, particularly Japan. This study aimed to investigate the relationship between blood lipopolysaccharide levels and health status in the Japanese. We conducted two cross-sectional studies in 36 healthy subjects (Study 1) and 36 patients with abnormal glucose metabolism (AGM; Study 2). The plasma lipopolysaccharide concentration in healthy subjects was positively correlated with body mass index. The plasma lipopolysaccharide concentration in AGM patients was obviously higher than that in healthy subjects. Furthermore, in AGM patients, the plasma lipopolysaccharide concentration was positively correlated with C-peptide, fasting plasma glucose levels, triglycerides, and stage of diabetic nephropathy. The plasma lipopolysaccharide concentration was also negatively correlated with 20/(C-peptide × fasting plasma glucose), an indicator of insulin resistance, and high-density lipoprotein cholesterol. In particular, the correlation between plasma lipopolysaccharide concentration and triglycerides in AGM patients was maintained in multiple regression analyses adjusted for age, sex, or body mass index. These results suggest a possible role of lipopolysaccharides in obesity in healthy subjects and in the deterioration of triglyceride metabolism in AGM patients in the Japanese population. Full article
(This article belongs to the Section Public Health & Healthcare)
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13 pages, 785 KiB  
Article
Antioxidant Activity of Selected Medicinal Plants Used by Traditional Herbal Practitioners to Treat Cancer in Malawi
J 2023, 6(4), 592-604; https://doi.org/10.3390/j6040039 - 20 Nov 2023
Viewed by 1168
Abstract
This study evaluated the phytochemical composition and antioxidant activity of Piliostigma thonningii (Schumach.) Milne-Redh, Psorospermum febrifugum Spach, Inula glomerata Oliv. and Hiern, Zanthoxylum chalybeum Engl. and Monotes africanus A.DC., claimed to treat cancer by Malawian traditional herbal practitioners. Ground and dried plant extracts [...] Read more.
This study evaluated the phytochemical composition and antioxidant activity of Piliostigma thonningii (Schumach.) Milne-Redh, Psorospermum febrifugum Spach, Inula glomerata Oliv. and Hiern, Zanthoxylum chalybeum Engl. and Monotes africanus A.DC., claimed to treat cancer by Malawian traditional herbal practitioners. Ground and dried plant extracts were analyzed for total phenolic content (TPC), total flavonoid content (TFC), total alkaloid content (TAC), ferric reducing antioxidant power (FRAP) and 2,2-Diphenyl-1-Picrylhydrazyl (DPPH) using standard assays. The TPC, TFC, and TAC ranged from 539 ± 2.70 to 4602 ± 32 mg GAE/g DW, 6.18 ± 0.03 to 64.04 ± 0.16 mg QE/g DW and 19.25 ± 0.07 to 76.05 ± 0.36 mg CE/g DW, respectively, and the variations were significant, p < 0.05. FRAP values ranged from 82.15 ± 0.7 to 687.28 ± 0.71 mg TEAC/g DW and decreased in the following order: P. thoningii (Schumach.) Milne-Redh > P. febrifugum Spach > M. africanus A.DC > Z. chalybeum Engl > I. glomerata Oliv. and Hiern. The scavenging activity (SA50) of the extracts ranged from 0.09 ± 0.01 to 1.57 ± 0.01 μg/mL of extract with P. thonningii (Schumach.) Milne-Redh showing the lowest value. Based on the levels of phenolic compounds and their antioxidant activity, the plants in this study could be considered for use as medicinal agents and sources of natural bioactive compounds and antioxidants. Full article
(This article belongs to the Special Issue Herbal Medicines: Current Advances and Clinical Prospects)
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13 pages, 288 KiB  
Article
Improving ISOMAP Efficiency with RKS: A Comparative Study with t-Distributed Stochastic Neighbor Embedding on Protein Sequences
J 2023, 6(4), 579-591; https://doi.org/10.3390/j6040038 - 31 Oct 2023
Viewed by 790
Abstract
Data visualization plays a crucial role in gaining insights from high-dimensional datasets. ISOMAP is a popular algorithm that maps high-dimensional data into a lower-dimensional space while preserving the underlying geometric structure. However, ISOMAP can be computationally expensive, especially for large datasets, due to [...] Read more.
Data visualization plays a crucial role in gaining insights from high-dimensional datasets. ISOMAP is a popular algorithm that maps high-dimensional data into a lower-dimensional space while preserving the underlying geometric structure. However, ISOMAP can be computationally expensive, especially for large datasets, due to the computation of the pairwise distances between data points. The motivation behind this study is to improve efficiency by leveraging an approximate method, which is based on random kitchen sinks (RKS). This approach provides a faster way to compute the kernel matrix. Using RKS significantly reduces the computational complexity of ISOMAP while still obtaining a meaningful low-dimensional representation of the data. We compare the performance of the approximate ISOMAP approach using RKS with the traditional t-SNE algorithm. The comparison involves computing the distance matrix using the original high-dimensional data and the low-dimensional data computed from both t-SNE and ISOMAP. The quality of the low-dimensional embeddings is measured using several metrics, including mean squared error (MSE), mean absolute error (MAE), and explained variance score (EVS). Additionally, the runtime of each algorithm is recorded to assess its computational efficiency. The comparison is conducted on a set of protein sequences, used in many bioinformatics tasks. We use three different embedding methods based on k-mers, minimizers, and position weight matrix (PWM) to capture various aspects of the underlying structure and the relationships between the protein sequences. By comparing different embeddings and by evaluating the effectiveness of the approximate ISOMAP approach using RKS and comparing it against t-SNE, we provide insights on the efficacy of our proposed approach. Our goal is to retain the quality of the low-dimensional embeddings while improving the computational performance. Full article
15 pages, 2303 KiB  
Article
Photocatalytic Reduction of Cr(VI) and Pb(II) with Biogenically Synthesized Copper Oxide Nanoparticles Using an Extract of the Myriophyllum spicatum Plant
J 2023, 6(4), 564-578; https://doi.org/10.3390/j6040037 - 31 Oct 2023
Viewed by 859
Abstract
The biogenic synthesis of copper oxide nanoparticles was explored using the Myriophyllum spicatum plant through a process involving co-precipitation and was utilized as an effective photocatalyst for the reduction of Cr(VI) and Pb(II) ions in an aqueous solution. The plant-mediated CuO nanoparticles were [...] Read more.
The biogenic synthesis of copper oxide nanoparticles was explored using the Myriophyllum spicatum plant through a process involving co-precipitation and was utilized as an effective photocatalyst for the reduction of Cr(VI) and Pb(II) ions in an aqueous solution. The plant-mediated CuO nanoparticles were characterized using microscopic techniques (TEM and SEM), FT-IR, and XRD analyses. The amount of the reduced metal ions was determined by UV–visible and Atomic Absorption (AA) spectrophotometers. The analyses of the functional group present in the leaf extract revealed the type of bioactive molecules that were involved in the formation of copper oxide nanoparticles. The nanoparticles were used in the photo-enhanced reduction of hexavalent Cr and divalent Pb ions, and the impact of solution pH, initial metal concentrations, and photocatalyst dosage was investigated to establish the optimal performance of the CuO nanoparticles. Results revealed a direct association between the reduction of metal ions and catalyst dosage in both cases. A maximum percentage reduction of 89.2% and 79.1% was achieved for Cr(VI) and Pb(II), respectively, using 3 g of the CuO nanoparticles. This confirms that the CuO nanoparticles exhibited higher efficiency for Cr(VI) reduction as compared to Pb(II) reduction and indicates that CuO nanoparticles are a promising photocatalyst that is capable of reducing these metal ions into less toxic products. Full article
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20 pages, 11248 KiB  
Article
Application of AI-Based Techniques on Moody’s Diagram for Predicting Friction Factor in Pipe Flow
J 2023, 6(4), 544-563; https://doi.org/10.3390/j6040036 - 07 Oct 2023
Viewed by 1053
Abstract
The friction factor is a widely used parameter in characterizing flow resistance in pipes and open channels. Recently, the application of machine learning and artificial intelligence (AI) has found several applications in water resource engineering. With this in view, the application of artificial [...] Read more.
The friction factor is a widely used parameter in characterizing flow resistance in pipes and open channels. Recently, the application of machine learning and artificial intelligence (AI) has found several applications in water resource engineering. With this in view, the application of artificial intelligence techniques on Moody’s diagram for predicting the friction factor in pipe flow for both transition and turbulent flow regions has been considered in the present study. Various AI methods, like Random Forest (RF), Random Tree (RT), Support Vector Machine (SVM), M5 tree (M5), M5Rules, and REPTree models, are applied to predict the friction factor. While performing the statistical analysis (root-mean-square error (RMSE), mean absolute error (MAE), squared correlation coefficient (R2), and Nash–Sutcliffe efficiency (NSE)), it was revealed that the predictions made by the Random Forest model were the most reliable when compared to other AI tools. The main objective of this study was to highlight the limitations of artificial intelligence (AI) techniques when attempting to effectively capture the characteristics and patterns of the friction curve in certain regions of turbulent flow. To further substantiate this behavior, the conventional algebraic equation was used as a benchmark to test how well the current AI tools work. The friction factor estimates using the algebraic equation were found to be even more accurate than the Random Forest model, within a relative error of ≤±1%, in those regions where the AI models failed to capture the nature and variation in the friction factor. Full article
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8 pages, 3251 KiB  
Communication
Non-Destructive Discrimination of Blue Inks on Suspected Documents through the Combination of Raman Spectroscopy and Chemometric Analysis
J 2023, 6(4), 536-543; https://doi.org/10.3390/j6040035 - 26 Sep 2023
Viewed by 955
Abstract
Increasingly sophisticated techniques for falsifying and forging legal documents demand non-destructive and accurate analysis methods. Researchers have extensively investigated ink discrimination through an interdisciplinary analysis involving Raman spectroscopy and chemometrics, which is now regarded as a leading forensic document analysis approach. In this [...] Read more.
Increasingly sophisticated techniques for falsifying and forging legal documents demand non-destructive and accurate analysis methods. Researchers have extensively investigated ink discrimination through an interdisciplinary analysis involving Raman spectroscopy and chemometrics, which is now regarded as a leading forensic document analysis approach. In this study, a groundbreaking method was developed to identify the specific origin of blue-ink pens used in written documents. By employing Raman spectroscopy in conjunction with principal component analysis (PCA), we successfully differentiated between 45 different blue-ink pens used on various documents. The Raman spectroscopy analysis provided a visual examination of each blue ink’s unique Raman signature, and PCA was then applied to the processed spectral data. Moreover, we successfully distinguished highly similar ink types in documents through the combined use of Raman spectroscopy, Pearson’s correlation analysis, and a statistical approach (PCA). Full article
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19 pages, 3741 KiB  
Article
Multiplicity Analysis of a Thermistor Problem—A Possible Explanation of Delamination Fracture
J 2023, 6(3), 517-535; https://doi.org/10.3390/j6030034 - 04 Sep 2023
Viewed by 763
Abstract
In the present study, a numerical bifurcation analysis of a PTC thermistor problem is carried out, considering a realistic heat dissipation mechanism due to conduction, nonlinear temperature-dependent natural convection, and radiation. The electric conductivity is modeled as a strongly nonlinear and smooth function [...] Read more.
In the present study, a numerical bifurcation analysis of a PTC thermistor problem is carried out, considering a realistic heat dissipation mechanism due to conduction, nonlinear temperature-dependent natural convection, and radiation. The electric conductivity is modeled as a strongly nonlinear and smooth function of the temperature between two limiting values, based on measurements. The temperature field has been resolved for both cases were either the current or the voltage (nonlocal problem) is the controlling parameter. With the aid of an efficient continuation algorithm, multiple steady-state solutions that do not depend on the external circuit have been identified as a result of the inherent nonlinearities. The analysis reveals that the conduction–convection parameter and the type of the imposed boundary conditions have a profound effect on the solution structure and the temperature profiles. For the case of current control, depending on the boundary conditions, a complex and interesting multiplicity pattern appears either as a series of nested cusp points or as enclosed branches emanating from pitchfork bifurcation points. The stability analysis reveals that when the device edges are insulated, only the uniform solutions are stable, namely, one “cold” and one “hot”. A key feature of the “hot” state is that the corresponding temperature is proportional to the input power and its magnitude could be one or even two orders of magnitude higher than the “cold” one. Therefore, the change over from the “cold” to the “hot” state induces a thermal shock and could perhaps be the reason for the mechanical failure (delamination fracture) of PTC thermistors. Full article
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9 pages, 282 KiB  
Article
Effect on Weight Loss of an Oral Supplement Containing Cinnamon Bark (Cinnamomum cassia) and Withania somnifera in Adult Patients with Overweight and Obesity: A Pilot Study
J 2023, 6(3), 508-516; https://doi.org/10.3390/j6030033 - 02 Sep 2023
Viewed by 1642
Abstract
With the prevalence of obesity soaring and the absence of an effective and safe treatment that is low-cost and always feasible, food supplements have gained attention for their potential benefits in the absence of significant safety concerns. Cinnamomum cassia (CC) and Withania somnifera [...] Read more.
With the prevalence of obesity soaring and the absence of an effective and safe treatment that is low-cost and always feasible, food supplements have gained attention for their potential benefits in the absence of significant safety concerns. Cinnamomum cassia (CC) and Withania somnifera (WS) are plant-based supplements reported to be effective in improving metabolic health and body composition, the first mainly acting on insulin resistance and the second on energy expenditure and leptin resistance, as shown in preclinical and some clinical studies. Their combination, which is possibly synergistic given their different mechanisms of action, has never been studied. This was a double-blind placebo-controlled study. Patients with overweight or obesity were prescribed a mildly hypocaloric diet with 300 mg CC plus 150 mg WS tid for 4 weeks in a crossover design; anthropometric parameters and safety outcomes were collected. Forty patients were enrolled, and the combination CC + WS induced significant weight loss compared with placebo (−2.66% vs. −1.28%, respectively; p = 0.0002). No significant adverse events were recorded. Our study demonstrates for the first time that the tested combination is an inexpensive yet effective strategy to enhance weight loss in patients receiving a mildly hypocaloric diet. Further studies are warranted to investigate the mechanisms underlying the weight loss effect of CC/WS in human subjects, as well as to explore potential additional metabolic effects obtained with this treatment. Full article
(This article belongs to the Special Issue Herbal Medicines: Current Advances and Clinical Prospects)
16 pages, 1242 KiB  
Article
Removal of Pathogenic Bacteria in a Horizontally Fed Subsurface Constructed Wetland Hybrid System
J 2023, 6(3), 492-507; https://doi.org/10.3390/j6030032 - 28 Aug 2023
Viewed by 1287
Abstract
The management of effluents and their treatment is a fundamental issue in water management, the removal of different types of contaminants is another relevant issue for public health and the environment. Bacteria are one of the main types of contaminants in untreated water [...] Read more.
The management of effluents and their treatment is a fundamental issue in water management, the removal of different types of contaminants is another relevant issue for public health and the environment. Bacteria are one of the main types of contaminants in untreated water discharged to receiving bodies. The objective of this research was to evaluate the removal efficiency of pathogenic bacteria in a horizontal feeding subsurface artificial wetland that treats wastewater originated from the Boca de Río Technological Institute, Veracruz, Mexico. A hybrid system composed of seven cells with three types of substrates and ornamental type vegetation was designed; the indicators evaluated were the concentration of total and fecal coliforms and the efficiency of bacterial removal in the stages of the system. The artificial wetland system demonstrated a significant reduction (p < 0.05) between the different cells of the system. The values of pathogenic bacteria removal obtained in the wetland were higher than 99% in the cells of the system and times. In conclusion, it was identified that the interaction of the components of this system and its operation under the climatic seasons of the site influenced the removal efficiency of pathogenic bacteria, allowing optimal removal efficiency. Full article
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15 pages, 1818 KiB  
Review
Mapping the Glymphatic Pathway Using Imaging Advances
J 2023, 6(3), 477-491; https://doi.org/10.3390/j6030031 - 08 Aug 2023
Cited by 1 | Viewed by 1466
Abstract
The glymphatic system is a newly discovered waste-clearing system that is analogous to the lymphatic system in our central nervous system. Furthermore, disruption in the glymphatic system has also been associated with many neurodegenerative disorders (e.g., Alzheimer’s disease), traumatic brain injury, and subarachnoid [...] Read more.
The glymphatic system is a newly discovered waste-clearing system that is analogous to the lymphatic system in our central nervous system. Furthermore, disruption in the glymphatic system has also been associated with many neurodegenerative disorders (e.g., Alzheimer’s disease), traumatic brain injury, and subarachnoid hemorrhage. Thus, understanding the function and structure of this system can play a key role in researching the progression and prognoses of these diseases. In this review article, we discuss the current ways to map the glymphatic system and address the advances being made in preclinical mapping. As mentioned, the concept of the glymphatic system is relatively new, and thus, more research needs to be conducted in order to therapeutically intervene via this system. Full article
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17 pages, 2703 KiB  
Article
Three-Dimensional Unsteady Axisymmetric Viscous Beltrami Vortex Solutions to the Navier–Stokes Equations
J 2023, 6(3), 460-476; https://doi.org/10.3390/j6030030 - 05 Aug 2023
Viewed by 832
Abstract
This paper is aimed at eliciting consistency conditions for the existence of unsteady incompressible axisymmetric swirling viscous Beltrami vortices and explicitly constructing solutions that obey the conditions as well as the Navier–Stokes equations. By Beltrami flow, it is meant that vorticity, i.e., the [...] Read more.
This paper is aimed at eliciting consistency conditions for the existence of unsteady incompressible axisymmetric swirling viscous Beltrami vortices and explicitly constructing solutions that obey the conditions as well as the Navier–Stokes equations. By Beltrami flow, it is meant that vorticity, i.e., the curl of velocity, is proportional to velocity at any local point in space and time. The consistency conditions are derived for the proportionality coefficient, the velocity field and external force. The coefficient, whose dimension is of [length−1], is either constant or nonconstant. In the former case, the well-known exact nondivergent three-dimensional unsteady vortex solutions are obtained by solving the evolution equations for the stream function directly. In the latter case, the consistency conditions are given by nonlinear equations of the stream function, one of which corresponds to the Bragg–Hawthorne equation for steady inviscid flow. Solutions of a novel type are found by numerically solving the nonlinear constraint equation at a fixed time. Time dependence is recovered by taking advantage of the linearity of the evolution equation of the stream function. The proportionality coefficient is found to depend on space and time. A phenomenon of partial restoration of the broken scaling invariance is observed at short distances. Full article
(This article belongs to the Section Physical Sciences)
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23 pages, 417 KiB  
Article
On Multivariate Picard–Fuchs Systems and Equations
J 2023, 6(3), 437-459; https://doi.org/10.3390/j6030029 - 04 Aug 2023
Viewed by 879
Abstract
In this paper, we studied the Picard–Fuchs systems and equations which appear in the theory of Gauss–Manin systems and connections associated with deformations of isolated singularities. Among other things, we describe some interesting properties of such systems and relationships between them. Then we [...] Read more.
In this paper, we studied the Picard–Fuchs systems and equations which appear in the theory of Gauss–Manin systems and connections associated with deformations of isolated singularities. Among other things, we describe some interesting properties of such systems and relationships between them. Then we show how to calculate the fundamental solutions to the Gauss–Manin system for Aμ-singularities and to the corresponding generalized Legendre equations in terms of the multidimensional Horn’s hypergeometric functions. In conclusion, some important questions concerning basic properties of the local and global Picard–Fuchs systems of Pfaffian type, involving integrability conditions and commuting relations, are discussed in some detail. Full article
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