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Search Results (1,973)

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10 pages, 645 KiB  
Article
Theoretical Investigation of Electric Polarizability in Porphyrin–Zinc and Porphyrin–Zinc–Thiazole Complexes Using Small Property-Oriented Basis Sets
by Arkadiusz Kuziemski, Krzysztof Z. Łączkowski and Angelika Baranowska-Łączkowska
Int. J. Mol. Sci. 2024, 25(20), 11044; https://doi.org/10.3390/ijms252011044 - 14 Oct 2024
Abstract
Porphyrin complexes are of great importance due to their possible applications as sensors, solar cells and photocatalysts, as well as their ability to bind additional ligands. A valuable source of knowledge on their nature is their electric properties, which can be evaluated employing [...] Read more.
Porphyrin complexes are of great importance due to their possible applications as sensors, solar cells and photocatalysts, as well as their ability to bind additional ligands. A valuable source of knowledge on their nature is their electric properties, which can be evaluated employing density functional theory (DFT) methods, supporting the experimental research. The present work aims at the application of small property-oriented basis sets in calculation of electric properties in transition metals, their oxides and test coordination complexes. Firstly, the existing polarized ZPol basis set for the first-row transition metals is modified in order to improve atomic polarizability results. For this purpose, optimization of the f-type polarization function exponent is carried out with respect to the value of average atomic polarizability of investigated metals. Next, both the original and the modified basis sets are employed in finite field CCSD(T) calculation of transition metal oxides’ dipole moments, as well as DFT calculation of polarizabilities in porphyrin–zinc and porphyrin–zinc–thiazole complexes. The obtained results show that the ZPol and ZPol-A basis sets can be successfully employed in the calculation of linear electric properties in large systems. The optimization procedure used in the present work can be employed for other source basis sets and elements, leading to new efficient polarized basis sets. Full article
(This article belongs to the Special Issue Molecular Modeling: Latest Advances and Applications)
23 pages, 6263 KiB  
Article
Lateral-Stability-Oriented Path-Tracking Control Design for Four-Wheel Independent Drive Autonomous Vehicles with Tire Dynamic Characteristics under Extreme Conditions
by Zhencheng Yu, Rongchen Zhao and Tengfei Yuan
World Electr. Veh. J. 2024, 15(10), 465; https://doi.org/10.3390/wevj15100465 - 13 Oct 2024
Viewed by 271
Abstract
This paper proposes a lateral-stability-oriented path-tracking controller for four-wheel independent drive (4WID) autonomous vehicles. The proposed controller aims to maintain vehicle stability under extreme conditions while minimizing lateral deviation. Firstly, a tiered control framework comprising upper-level and lower-level controllers is introduced. The upper-level [...] Read more.
This paper proposes a lateral-stability-oriented path-tracking controller for four-wheel independent drive (4WID) autonomous vehicles. The proposed controller aims to maintain vehicle stability under extreme conditions while minimizing lateral deviation. Firstly, a tiered control framework comprising upper-level and lower-level controllers is introduced. The upper-level controller is a lateral stability path-tracking controller that incorporates tire dynamic characteristics, developed using model predictive control (MPC) theory. This controller dynamically updates the tire lateral force constraints in real time to account for variations in tire dynamics under extreme conditions. Additionally, it enhances lateral stability and reduces path-tracking errors by applying additional yaw torque based on minimum tire utilization. The lower-level controllers execute the required steering angles and yaw moments through the appropriate component equipment and torque distribution. The joint simulation results from CarSim and MATLAB/Simulink show that, compared to the traditional MPC controller with unstable sideslip, this controller can maintain vehicle lateral stability under extreme conditions. Compared to the MPC controller, which only considers lateral force constraints, this controller can significantly reduce lateral tracking errors, with an average yaw rate reduction of 31.62% and an average sideslip angle reduction of 40.21%. Full article
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<p>The proposed path-tracking control system utilizes a hierarchical control architecture.</p>
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<p>Seven-degree vehicle dynamics model.</p>
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<p>A simplified vehicle model with two degrees of freedom.</p>
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<p>Co-simulation block diagram.</p>
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<p>Comparison results: (<b>a</b>) global path; (<b>b</b>) front wheel angle.</p>
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<p>Comparison results: (<b>a</b>) lateral error; (<b>b</b>) yaw rate; (<b>c</b>) sideslip angle.</p>
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<p>Control outputs: (<b>a</b>) additional yaw moment; (<b>b</b>) wheel torque of controller C.</p>
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<p>Comparison results: (<b>a</b>) Global path; (<b>b</b>) Front wheel angle.</p>
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<p>Comparison results: (<b>a</b>) lateral error; (<b>b</b>) yaw rate; (<b>c</b>) sideslip angle.</p>
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<p>Control outputs: (<b>a</b>) additional yaw moment; (<b>b</b>) wheel torque of controller C.</p>
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<p>Comparison results of simulation scenario 3: (<b>a</b>) global path; (<b>b</b>) lateral error; (<b>c</b>) front wheel angle; (<b>d</b>) sideslip angle.</p>
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<p>Comparison results of simulation scenario 4: (<b>a</b>) global path; (<b>b</b>) lateral error; (<b>c</b>) front wheel angle; (<b>d</b>) sideslip angle.</p>
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<p>Controller calculation time: (<b>a</b>) scenario 1; (<b>b</b>) scenario 2.</p>
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31 pages, 3615 KiB  
Article
Urban Emergency Evacuation Path Optimization Based on Uncertain Environments to Enhance Response for Symmetric and Asymmetric Evacuation Problems
by Jia Mao, Yanzhi Zhou, Yu Zhou and Xi Wang
Symmetry 2024, 16(10), 1356; https://doi.org/10.3390/sym16101356 - 13 Oct 2024
Viewed by 220
Abstract
Background: Serious secondary disasters caused by extreme natural weather conditions occur frequently, making it essential to establish a scientific and efficient modern emergency management system to maximize life-saving efforts. Methods: This study focuses on the uncertain environment of urban road networks and employs [...] Read more.
Background: Serious secondary disasters caused by extreme natural weather conditions occur frequently, making it essential to establish a scientific and efficient modern emergency management system to maximize life-saving efforts. Methods: This study focuses on the uncertain environment of urban road networks and employs fuzzy theory to construct a 0–1 integer programming model for emergency evacuation paths that minimizes the average expected travel time. Results: We enhanced the neighborhood search strategy of the traditional ACO_time by incorporating the 2-opt and 3-opt perturbation mechanisms from the SA algorithm. Additionally, we utilized improved ant-volume and ant-perimeter models, along with their combinations, in the pheromone-updating mechanism of the basic ACO. The heuristic principles of the A* algorithm were integrated, introducing the joint influence of path and time into the heuristic function of the ACO algorithm. Conclusions: The IACO3 algorithm was tested on the Sioux Falls network and the Berlin Heisenheimer Center network. The computation time of the improved IACO3 algorithm was reduced by up to 20% compared to the original IACO3 algorithm in relation to the SA algorithm, with only a 4–5% increase in computation time compared to the ACO_time algorithm, which translates to an increase of merely 4–5 s. This demonstrates the superior solution efficiency of the IACO3 algorithm. Full article
20 pages, 283 KiB  
Review
EU Environmental Protection in Regard to Sustainable Development: Myth or Reality?
by Ivana Špelić and Alka Mihelić-Bogdanić
Standards 2024, 4(4), 176-195; https://doi.org/10.3390/standards4040010 (registering DOI) - 12 Oct 2024
Viewed by 338
Abstract
According to conclusions agreed to in the 1995 Report of the World Summit for Social Development and the 2015 Sustainable Development Summit, seventeen sustainable development goals (SDGs) have been ratified and published as the 2030 Agenda for Sustainable Development. In 2022, the 8th [...] Read more.
According to conclusions agreed to in the 1995 Report of the World Summit for Social Development and the 2015 Sustainable Development Summit, seventeen sustainable development goals (SDGs) have been ratified and published as the 2030 Agenda for Sustainable Development. In 2022, the 8th Environment Action Programme was legally agreed upon, following the six European Green Deal priorities. These SDGs serve as a constant reminder of the importance of globally coordinated actions in compliance with the theory of sustainable development. However, more than a constant reminder, this international agreement should become the foundation for necessary change. On 22 July 2024, the daily global average temperature reached a new record high. The EU treaties signed between 1951 and 2007 laid the foundation for the creation of EU environmental policy. However, those EU treaties, along with environmental policy, form merely a non-binding and minimum set of priorities without any sanctions imposed for illegal practices. In 2021, EU member countries adopted the European Climate Law as the first legally binding document seeking to achieve goals set by the Paris Agreement and the European Green Deal. Any further EU sustainable development policies are dependent on global cooperation as a key element of survival. With the EU’s dependent on the rest of the world for its energy, the forcing of any obligatory change will be hard to achieve. This proves the importance of the 17th SDG, agreed in 2015. Only global partnership for sustainable development can prevent further damage to our ecosystem and achieve priorities set by the EU and UN agendas. The review aims to present the connection between sustainable development (SD) goals defined by the European Commission, for which the most important aspects are the need to meet the environmental requirements to protect future needs in the long run, and to confront the shortcomings of European law-making practices, in which most crucial reforms are presented as non-binding legal acts. Finally, in 2024 members of the European Parliament established an extended list of environmental crimes to be regarded as punishable offences and replaced the Environmental Crime Directive, making criminal activities and offences potentially legally punishable; however, it is yet to be seen how this initiative will be incorporated within the national legislations of each EU member country and to what extent. Full article
(This article belongs to the Special Issue Sustainable Development Standards)
22 pages, 2403 KiB  
Article
MDSA: A Dynamic and Greedy Approach to Solve the Minimum Dominating Set Problem
by Fatih Okumuş and Şeyda Karcı
Appl. Sci. 2024, 14(20), 9251; https://doi.org/10.3390/app14209251 - 11 Oct 2024
Viewed by 335
Abstract
The graph theory is one of the fundamental structures in computer science used to model various scientific and engineering problems. Many problems within the graph theory are categorized as NP-hard and NP-complete. One such problem is the minimum dominating set (MDS) problem, which [...] Read more.
The graph theory is one of the fundamental structures in computer science used to model various scientific and engineering problems. Many problems within the graph theory are categorized as NP-hard and NP-complete. One such problem is the minimum dominating set (MDS) problem, which seeks to identify the minimum possible subsets in a graph such that every other node in the subset is directly connected to a node in this subset. Due to its inherent complexity, developing an efficient polynomial-time method to address the MDS problem remains a significant challenge in graph theory. This paper introduces a novel algorithm that utilizes a centrality measure known as the Malatya Centrality to effectively address the MDS problem. The proposed algorithm, called the Malatya Dominating Set Algorithm (MDSA), leverages centrality values to identify dominating sets within a graph. It extends the Malatya centrality by incorporating a second-level centrality measure, which enhances the identification of dominating nodes. Through a systematic and algorithmic approach, these centrality values are employed to pinpoint the elements of the dominating set. The MDSA uniquely integrates greedy and dynamic programming strategies. At each step, the algorithm selects the most optimal (or near-optimal) node based on the centrality values (greedy approach) while updating the neighboring nodes’ criteria to influence subsequent decisions (dynamic programming). The proposed algorithm demonstrates efficient performance, particularly in large-scale graphs, with time and space requirements scaling proportionally with the size of the graph and its average degree. Experimental results indicate that our algorithm outperforms existing methods, especially in terms of time complexity when applied to large datasets, showcasing its effectiveness in addressing the MDS problem. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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<p>The influential area of the first Malatya centrality values.</p>
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<p>The influential area of the second Malatya centrality values.</p>
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<p>A grid of size 5 × 6.</p>
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<p>Application steps of Malatya Dominating Set Algorithm to grid of sizes 5 × 6. Red nodes represent the nodes included in the dominating set. Gray nodes are nodes that are neighbors to a dominating set node. Blue nodes indicate nodes that have not yet been visited.</p>
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<p>Banana tree.</p>
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<p>Results of the algorithm’s first iteration on banana tree. (<b>a</b>) The raw output of the graph generated by the algorithm (<b>b</b>) Readable visualization of the graph.</p>
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<p>The resultant graphs of second (<b>a</b>) and third (<b>b</b>) iterations.</p>
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24 pages, 9787 KiB  
Article
Impact of the Source Material Gradation on the Disaster Mechanism of Underground Debris Flows in Mines
by Rujun Tuo, Haiyong Cheng, Shunchuan Wu, Jiayang Zou, Deng Liu, Weihua Liu, Jing Zhang, Guanzhao Jiang and Wei Sun
Sustainability 2024, 16(20), 8788; https://doi.org/10.3390/su16208788 - 11 Oct 2024
Viewed by 351
Abstract
In mines where the natural caving method is used, the frequent occurrence of underground debris flows and the complex mine environments make it difficult to prevent and control underground debris flows. The source is one of the critical conditions for the formation of [...] Read more.
In mines where the natural caving method is used, the frequent occurrence of underground debris flows and the complex mine environments make it difficult to prevent and control underground debris flows. The source is one of the critical conditions for the formation of debris flows, and studying the impact of source material gradation on underground debris-flow disasters can effectively help prevent and control these occurrences. This paper describes a multiscale study of underground debris flows using physical model experiments and the discrete-element method (PFC3D) to understand the impact of the source material gradation on the disaster mechanism of underground debris flows from macroscopic and microscopic perspectives. Macroscopically, an increase in content of medium and large particles in the gradation will enhance the instantaneous destructive force. Large particles can more easily cause disasters than medium and fine particles with the same content, but the disaster-causing ability is minimized when the contents of medium and large particles exceed 50% and 60%, respectively. With increasing fine particle content, the long-distance disaster-causing ability and duration is increased. On the microscopic level, the source-level pairs affect the initial flow mode, concentration area of the force chain, average velocity, average runout distance, and change in energy of the underground debris flow. Among them, the proportion of large particles in the gradation significantly affects the change in kinetic energy, change in dissipative energy, time to reach the peak kinetic energy, and time of coincidence of dissipative energy and gravitational potential energy. The process of underground debris flow can be divided into a “sudden stage”, a “continuous impact stage”, and a “convergence and accumulation stage”. This work reveals the close relationship between source material gradation and the disaster mechanism of underground debris flows and highlights the necessity of considering the source material gradation in the prevention and control of underground debris flows. It can provide an important basic theory for the study of environmental and urban sustainable development. Full article
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<p>Experimental device: (<b>A</b>) on-site experimental equipment and (<b>B</b>) experimental model design drawing.</p>
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<p>Moraine materials of different particle sizes: (<b>a</b>) &lt;8 mm, (<b>c</b>) 8–20 mm, and (<b>c</b>) 20–40 mm.</p>
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<p>Particle size distribution (PSD) of the moraine samples: (<b>a</b>) particle size frequency curve and (<b>b</b>) particle size accumulation curve.</p>
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<p>Changes in vibration acceleration with time.</p>
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<p>Impact pressure–time relationship curves of G1–G6 in S1S2.</p>
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<p>Components of the linear model of the rolling resistance of the adhesive.</p>
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<p>Numerical simulation device and initial deposition of particles.</p>
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<p>Comparison of the model experiment and numerical simulation experiment results. Among them, (<b>a1</b>–<b>a5</b>) are the results of debris flow movement of physical experiments at five time points; the (<b>b1</b>–<b>b5</b>) are the results of the debris flow movement of the numerical experiment at five time points.</p>
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<p>Experimental and numerical simulation results of the final impact distance of the debris flow.</p>
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<p>Spatial distribution of the initial velocity of the particle column.</p>
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<p>Changes in the initial flow contact force chain of the particle column. Among them, (<b>a1</b>–<b>a3</b>), (<b>b1</b>–<b>b3</b>), (<b>c1</b>–<b>c3</b>), (<b>d1</b>–<b>d3</b>), (<b>e1</b>–<b>e3</b>) and (<b>f1</b>–<b>f3</b>) are the force chain structure of the initial movement of debris flow under the source gradation of 3:1:2, 5:1:2, 3:3:2, 3:5:2, 3:1:4 and 3:1:6 respectively.</p>
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<p>Motion characteristics of particles at different times.</p>
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<p>Changes in average velocity of underground debris flows with different source gradations over time.</p>
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<p>Changes in average runout distance of underground debris flows with time for different source gradations.</p>
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<p>The evolution characteristics of kinetic energy, potential energy, and loss energy with time when underground debris flow occurs in the original gradation, G1 (3:1:2); fine particle group, G2 (5:1:2); medium particle groups, G3 (3:3:2) and G4 (3:5:2); and large particle groups, G5 (3:1:4) and G6 (3:1:6).</p>
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18 pages, 4857 KiB  
Article
Mean Droplet Size Prediction of Twin Swirl Airblast Nozzle at Elevated Operating Conditions
by Jiaming Miao, Bo Wang, Guangming Ren and Xiaohua Gan
Energies 2024, 17(20), 5027; https://doi.org/10.3390/en17205027 - 10 Oct 2024
Viewed by 282
Abstract
This study introduces a novel predictive model for atomization droplet size, developed using comprehensive data collected under elevated temperature and pressure conditions using a twin swirl airblast nozzle. The model, grounded in flow instability theory, has been meticulously parameterized using the Particle Swarm [...] Read more.
This study introduces a novel predictive model for atomization droplet size, developed using comprehensive data collected under elevated temperature and pressure conditions using a twin swirl airblast nozzle. The model, grounded in flow instability theory, has been meticulously parameterized using the Particle Swarm Optimization (PSO) algorithm. Through rigorous analysis, including analysis of variance (ANOVA), the model has demonstrated robust reliability and precision, with a maximum relative error of 19.3% and an average relative error of 6.8%. Compared to the classical atomization model by Rizkalla and Lefebvre, this model leverages theoretical insights and incorporates a range of interacting variables, enhancing its applicability and accuracy. Spearman correlation analysis reveals that air pressure and the air pressure drop ratio significantly negatively impact droplet size, whereas the fuel–air ratio (FAR) shows a positive correlation. Experimental validation at ambient conditions shows that the model is applicable with a reliability threshold of We1/Re1 ≥ 0.13 and highlights the predominance of the pressure swirl mechanism over aerodynamic atomization at higher fuel flow rates (q > 1.25 kg/h). This research effectively bridges theoretical and practical perspectives, offering critical insights for the optimization of airblast nozzle design. Full article
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<p>The experiment system schematic diagram.</p>
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<p>Detail structure of twin swirl airblast nozzle.</p>
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<p>The effects of swirling air characterized by <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>e</mi> <mo>=</mo> <msub> <mi>ρ</mi> <mi>a</mi> </msub> <msubsup> <mi>U</mi> <mi>a</mi> <mn>2</mn> </msubsup> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>/</mo> <mi>σ</mi> </mrow> </semantics></math>: (<b>a</b>) The scatter plot SMD-<span class="html-italic">We</span>. (<b>b</b>) The scatter plot after linearization <span class="html-italic">ln</span>(<span class="html-italic">SMD</span>)-<span class="html-italic">ln</span>(<span class="html-italic">We</span>); Pearson’s correlation coefficient <span class="html-italic">r</span> = −0.882.</p>
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<p>Analytical evaluation figures for the regression model: (<b>a</b>) the normal probability plot of residuals with 0.95 confidence interval; (<b>b</b>) the test of the influence of run order on residuals; (<b>c</b>) the plot of residual variance; (<b>d</b>) the distribution of predicted <span class="html-italic">SMD</span> values with relative error 19.3% and average relative error 6.8%.</p>
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<p>The test of the model’s ability to generalize.</p>
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<p>The residual distribution plots for the three models discussed.</p>
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<p>“R-L” model’s normal probability plots of residuals with 0.95 confidence interval.</p>
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<p>Comparison of two prediction models: (<b>a</b>) the distribution of predicted SMD values for the two models discussed; (<b>b</b>)the distribution of relative errors for the two models discussed.</p>
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<p>Spearman analysis of SMD for experimental variables.</p>
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<p>The comparison of measured and predicted SMD values with swirler pressure drop ratios of 3% and 5% at ambient temperature and pressure.</p>
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<p>The relationship between the SMD and fuel flow rate q with swirler pressure drop ratios of 1%, 3%, and 5% at ambient temperature and pressure.</p>
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19 pages, 17495 KiB  
Article
Study on the Design Method of High-Resolution Volume-Phase Holographic Gratings
by Shuo Wang, Lei Dai, Chao Lin, Long Wang, Zhenhua Ji, Yang Fu, Quyouyang Gao and Yuquan Zheng
Sensors 2024, 24(19), 6493; https://doi.org/10.3390/s24196493 - 9 Oct 2024
Viewed by 349
Abstract
Volume-phase holographic gratings are suitable for use in greenhouse gas detection imaging spectrometers, enabling the detection instruments to achieve high spectral resolution, high signal-to-noise ratios, and high operational efficiency. However, when utilized in the infrared wavelength band with high dispersion requirements, gratings struggle [...] Read more.
Volume-phase holographic gratings are suitable for use in greenhouse gas detection imaging spectrometers, enabling the detection instruments to achieve high spectral resolution, high signal-to-noise ratios, and high operational efficiency. However, when utilized in the infrared wavelength band with high dispersion requirements, gratings struggle to meet the demands for low polarization sensitivity due to changes in diffraction performance caused by phase delays in the incidence of light waves with distinct polarization states, and current methods for designing bulk-phase holographic gratings require a large number of calculations that complicate the balance of diffraction properties. To overcome this problem, a design method for transmissive bulk-phase holographic gratings is proposed in this study. The proposed method combines two diffraction theories (namely, Kogelnik coupled-wave theory and rigorous coupled-wave theory) and establishes a parameter optimization sequence based on the influence of design parameters on diffraction characteristics. Kogelnik coupled-wave theory is employed to establish the initial Bragg angle range, ensuring that the diffraction efficiency and phase delay of the grating thickness curve meet the requirements for incident light waves in various polarization states. Utilizing rigorous coupled-wave theory, we optimize grating settings based on criteria such as a center wavelength diffraction efficiency greater than 95%, polarization sensitivity less than 10%, maximum bandwidth, and spectral diffraction efficiency exceeding 80%. The ideal grating parameters are ultimately determined, and the manufacturing tolerances for various grating parameters are analyzed. The design results show that the grating stripe frequency is 1067 lines per millimeter, and the diffraction efficiencies of TE and TM waves are 96% and 99.89%, respectively. The diffraction efficiency of unpolarized light is more than 88% over the whole spectral range with an average efficiency of 94.49%, an effective bandwidth of 32 nm, and a polarization sensitivity of less than 7%. These characteristics meet the performance requirements for dispersive elements based on greenhouse gas detection, the spectral resolution of the detection instrument is up to 0.1 nm, and the signal-to-noise ratio and working efficiency are improved by increasing the transmittance of the instrument. Full article
(This article belongs to the Section Optical Sensors)
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<p>(<b>a</b>) Structure of the VPHG; (<b>b</b>) transmissive VPHG recording; (<b>c</b>) reflective VPHG recording.</p>
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<p>Bragg diffraction principle. (Blue arrows represent the incident and diffracted light, and black arrows represent the grating vector).</p>
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<p>K-vector circle: (<b>a</b>) grating recording; (<b>b</b>) grating Bragg diffraction and diffraction deviating from Bragg conditions; (<b>c</b>) wavelength-shifted reconstruction principle.</p>
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<p>(<b>a</b>) Diagram of the principle of diffraction theory calculation; (<b>b</b>) types of refractive index modulation within the grating.</p>
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<p>Comparison of the two theories for different grating periods.</p>
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<p>Comparison of the two theories for different grating thicknesses.</p>
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<p>Comparison of the two theories for different refractive index modulations.</p>
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<p>Comparison of the diffraction performance of the two types of gratings: (<b>a</b>) wavelength selectivity curves for different polarization states of the transmission-type VPHG; (<b>b</b>) angular selectivity curves for different polarization states of the transmission-type VPHG; (<b>c</b>) wavelength selectivity curves for different polarization states of the reflection-type VPHG; (<b>d</b>) angular selectivity curves for different polarization states of the reflection-type VPHG.</p>
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<p>(<b>a</b>) The relationship between diffraction efficiency and grating thickness for different polarization states when Δ<span class="html-italic">n</span> = 0.045. (<b>b</b>) The relationship between diffraction efficiency and grating thickness for different polarization states when Δ<span class="html-italic">n</span> = 0.05. (<b>c</b>) The relationship between diffraction efficiency and refractive index modulation for different polarization states when <span class="html-italic">d</span> = 25 μm. (<b>d</b>) The relationship between diffraction efficiency and refractive index modulation for different polarization states when <span class="html-italic">d</span> = 30 μm.</p>
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<p>(<b>a</b>) The effect of d and Δ<span class="html-italic">n</span> on diffraction efficiency for TE wave incidence. (<b>b</b>) The effect of d and Δ<span class="html-italic">n</span> on diffraction efficiency for TM wave incidence.</p>
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<p>(<b>a</b>) Wavelength selectivity curves for different values of Δ<span class="html-italic">n</span> and <span class="html-italic">d</span> when Δ<span class="html-italic">n·d</span> is constant. (<b>b</b>) Angular selectivity curves for different values of Δ<span class="html-italic">n</span> and <span class="html-italic">d</span> when Δ<span class="html-italic">n·d</span> is constant.</p>
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<p>Thickness and diffraction efficiency curves for different periods and Bragg angles: (<b>a</b>) Λ = 1.0757 μm, <span class="html-italic">θ<sub>B</sub></span> = 30°; (<b>b</b>) Λ = 1.0141 μm, <span class="html-italic">θ<sub>B</sub></span> = 32.03°; (<b>c</b>) Λ = 0.9377 μm, <span class="html-italic">θ<sub>B</sub></span> = 35°; (<b>d</b>) Λ = 0.8367 μm, <span class="html-italic">θ<sub>B</sub></span> = 40°.</p>
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<p>Four scenarios where the diffraction efficiency at the intersection points of the thickness and diffraction efficiency curves for different polarization states is equal to 0.95.</p>
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<p>Analysis of the designed VPHG diffraction’s performance: (<b>a</b>) wavelength selectivity curves for different polarization states; (<b>b</b>) angular selectivity curves for different polarization states; (<b>c</b>) polarization sensitivity; (The red line indicates the value of polarization sensitivity.) (<b>d</b>) wavelength selectivity curve for non-polarized light. (The red line indicates the value of diffraction efficiency of unpolarized light).</p>
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<p>Diffraction performance analysis of VPHG designed using Kogelnik theory: (<b>a</b>) wavelength selectivity curves for different polarization states; (<b>b</b>) angular selectivity curves for different polarization states; (<b>c</b>) polarization sensitivity; (The red line indicates the value of polarization sensitivity). (<b>d</b>) wavelength selectivity curve for non-polarized light. (The red line indicates the value of diffraction efficiency of unpolarized light).</p>
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<p>Diffraction performance analysis of VPHG designed using RCWA theory: (<b>a</b>) wavelength selectivity curves for different polarization states; (<b>b</b>) angular selectivity curves for different polarization states; (<b>c</b>) polarization sensitivity; (The red line indicates the value of polarization sensitivity). (<b>d</b>) wavelength selectivity curve for non-polarized light. (The red line indicates the value of diffraction efficiency of unpolarized light).</p>
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<p>Results of tolerance analysis for different parameters of VPHG: (<b>a</b>) Analysis results of grating period accuracy; (<b>b</b>) Bragg Angle accuracy analysis results; (<b>c</b>) Accuracy analysis results of grating thickness; (<b>d</b>) Accuracy analysis results of the index modulation system.</p>
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33 pages, 3482 KiB  
Review
Literature Review on Thermodynamic and Kinetic Limitations of Thermal Decomposition of Methane
by Andrzej Mianowski, Mateusz Szul, Tomasz Radko, Aleksander Sobolewski and Tomasz Iluk
Energies 2024, 17(19), 5007; https://doi.org/10.3390/en17195007 - 8 Oct 2024
Viewed by 405
Abstract
The state of the art in methane pyrolysis does not yet provide a definitive answer as to whether the concept of an elementary reaction is universally applicable to the apparently simple process of methane dissociation. Similarly, the literature currently lacks a comprehensive and [...] Read more.
The state of the art in methane pyrolysis does not yet provide a definitive answer as to whether the concept of an elementary reaction is universally applicable to the apparently simple process of methane dissociation. Similarly, the literature currently lacks a comprehensive and unambiguous description of the methane pyrolysis process and, in particular, a single model that would well represent its course at both the micro and macro scales. Given the wide range of conditions under which this reaction can occur—whether thermal or thermo-catalytic, in solid or fluidized bed reactors—it is crucial to evaluate the usefulness of different kinetic models and their compatibility with basic thermodynamic principles and design assumptions. To address these research gaps, the authors analysed the thermodynamic and kinetic dependencies involved in the thermal decomposition of methane, using the synthesis of methane from its elemental components and its reversibility as a basis for exploring suitable kinetic models. Using experimental data available in the literature, a wide range of kinetic models have been analysed to determine how they all relate to the reaction rate constant. It was found that regardless of whether the process is catalytic or purely thermal, for temperatures above 900 °C the reversibility of the reaction has a negligible effect on the hydrogen yield. This work shows how the determined kinetic parameters are consistent with the Kinetic Compensation Effect (KCE) and, by incorporating elements of Transition State Theory (TST), the possibility of the existence of Entropy–Enthalpy Compensation (EEC). The indicated correspondence between KCE and EEC is strengthened by the calculated average activation entropy at isokinetic temperature (SB=275.0 J·(mol·K)1). Based on these results, the authors also show that changes in the activation energy (E=20421 kJ·mol1) can only serve as an estimate of the optimal process conditions, since the isoconversion temperature (Tiso=12001450 K>Teq) is shown to depend not only on thermodynamic principles but also on the way the reaction is carried out, with temperature (T) and pressure (P) locally compensating each other. Full article
(This article belongs to the Section J: Thermal Management)
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<p>Change in heat capacity of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">α</mi> <mo>−</mo> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">e</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">γ</mi> <mo>−</mo> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">e</mi> </mrow> </semantics></math> vs. temperature.</p>
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<p>The free energy as a function of temperature for the reactions 1–7 given in <a href="#energies-17-05007-t001" class="html-table">Table 1</a>.</p>
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<p>Transformation of the experimental results from [<a href="#B82-energies-17-05007" class="html-bibr">82</a>,<a href="#B108-energies-17-05007" class="html-bibr">108</a>] to the form of Equation (39) further simplified to the linear relation of Equation (43), <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">C</mi> <msub> <mrow> <mi mathvariant="normal">H</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> <mo>_</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Graphical representation of the kinetic equations <math display="inline"><semantics> <mrow> <mi>g</mi> <mfenced separators="|"> <mrow> <mi>α</mi> </mrow> </mfenced> <mo>=</mo> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mi>t</mi> </mrow> </semantics></math> for the data shown in [<a href="#B57-energies-17-05007" class="html-bibr">57</a>], <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>800</mn> <mo> </mo> <mo>°</mo> <mi mathvariant="normal">C</mi> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">C</mi> <msub> <mrow> <mi mathvariant="normal">H</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> <mo>_</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Experimental data for nickel catalyst; data shown in [<a href="#B38-energies-17-05007" class="html-bibr">38</a>] <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>750</mn> <mo> </mo> <mo>°</mo> <mi mathvariant="normal">C</mi> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">C</mi> <msub> <mrow> <msub> <mrow> <mi mathvariant="normal">H</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Parameters of the Arrhenius equation according to literature data in the form of KCE, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>i</mi> <mi>s</mi> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mn>1335.0</mn> <mo> </mo> <mi mathvariant="normal">K</mi> </mrow> </semantics></math>.</p>
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<p>KCE converted to thermodynamic activation functions according to EEC. <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mn>815.2</mn> <mo> </mo> <mi mathvariant="normal">K</mi> <mo>,</mo> </mrow> </semantics></math> the point marked in red is outside of the range of correlation shown in <a href="#energies-17-05007-f006" class="html-fig">Figure 6</a>. The point highlighted in red was taken from [<a href="#B62-energies-17-05007" class="html-bibr">62</a>].</p>
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22 pages, 7173 KiB  
Article
An Automated Clubbed Fingers Detection System Based on YOLOv8 and U-Net: A Tool for Early Prediction of Lung and Cardiovascular Diseases
by Wen-Shin Hsu, Guan-Tsen Liu, Su-Juan Chen, Si-Yu Wei and Wei-Hsun Wang
Diagnostics 2024, 14(19), 2234; https://doi.org/10.3390/diagnostics14192234 - 7 Oct 2024
Viewed by 528
Abstract
Background/Objectives: Lung and cardiovascular diseases are leading causes of mortality worldwide, yet early detection remains challenging due to the subtle symptoms. Digital clubbing, characterized by the bulbous enlargement of the fingertips, serves as an early indicator of these diseases. This study aims [...] Read more.
Background/Objectives: Lung and cardiovascular diseases are leading causes of mortality worldwide, yet early detection remains challenging due to the subtle symptoms. Digital clubbing, characterized by the bulbous enlargement of the fingertips, serves as an early indicator of these diseases. This study aims to develop an automated system for detecting digital clubbing using deep-learning models for real-time monitoring and early intervention. Methods: The proposed system utilizes the YOLOv8 model for object detection and U-Net for image segmentation, integrated with the ESP32-CAM development board to capture and analyze finger images. The severity of digital clubbing is determined using a custom algorithm based on the Lovibond angle theory, categorizing the condition into normal, mild, moderate, and severe. The system was evaluated using 1768 images and achieved cloud-based and real-time processing capabilities. Results: The system demonstrated high accuracy (98.34%) in real-time detection with precision (98.22%), sensitivity (99.48%), and specificity (98.22%). Cloud-based processing achieved slightly lower but robust results, with an accuracy of 96.38%. The average processing time was 0.15 s per image, showcasing its real-time potential. Conclusions: This automated system provides a scalable and cost-effective solution for the early detection of digital clubbing, enabling timely intervention for lung and cardiovascular diseases. Its high accuracy and real-time capabilities make it suitable for both clinical and home-based health monitoring. Full article
(This article belongs to the Section Machine Learning and Artificial Intelligence in Diagnostics)
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<p>Architecture of the proposed system for detecting clubbed fingers, used for preliminary identification of clubbed fingers.</p>
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<p>Architecture of the YOLOv8-based model.</p>
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<p>Architecture of the U-Net-based model.</p>
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<p>Diagram illustrating the proposed CFSA algorithm.</p>
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<p>The three feature points required for the Lovibond angle measurement are marked as follows: Point A is the nail base, Point B is the first phalanx nail fold, and Point C is the nail plate.</p>
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<p>The angle formed by the lines connecting the three points—nail base, first phalanx nail fold, and nail plate—is described as follows: Point A is the nail base, Point B is the first phalanx nail fold, and Point C is the nail plate. The vector <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>A</mi> <mi>B</mi> </mrow> <mo>⃑</mo> </mover> </mrow> </semantics></math> represents the direction from the nail base to the first phalanx nail fold, and the vector <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>A</mi> <mi>C</mi> </mrow> <mo>⃑</mo> </mover> </mrow> </semantics></math> represents the direction from the nail base to the nail plate.</p>
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<p>ESP32-CAM development board.</p>
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<p>Before inputting the annotated image into YOLOv8 (<b>left</b> image) and after YOLOv8 recognition (<b>right</b> image).</p>
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<p>The annotated image before inputting into U-Net (<b>left</b> image) and the output after U-Net segmentation (<b>right</b> image).</p>
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27 pages, 729 KiB  
Article
Selection of Green Recycling Suppliers for Shared Electric Bikes: A Multi-Criteria Group Decision-Making Method Based on the Basic Uncertain Information Generalized Power Weighted Average Operator and Basic Uncertain Information-Based Best–Middle–Worst TOPSIS Model
by Limei Liu, Fei Shao and Chen He
Sustainability 2024, 16(19), 8647; https://doi.org/10.3390/su16198647 - 6 Oct 2024
Viewed by 562
Abstract
This study introduces a novel multi-criteria group evaluation approach grounded in the theory of basic uncertain information (BUI) to facilitate the selection of green recycling suppliers for shared electric bikes. Firstly, a comprehensive index system of green recycling suppliers is established, encompassing recycling [...] Read more.
This study introduces a novel multi-criteria group evaluation approach grounded in the theory of basic uncertain information (BUI) to facilitate the selection of green recycling suppliers for shared electric bikes. Firstly, a comprehensive index system of green recycling suppliers is established, encompassing recycling capacity, environmental sustainability, financial strength, maintenance capabilities, and policy support, to provide a solid foundation for the scientific selection process. Secondly, the basic uncertain information generalized power weighted average (BUIGPWA) operator is proposed to aggregate group evaluation information with BUI pairs, and some related properties are investigated. Furthermore, the basic uncertain information-based best–middle–worst TOPSIS (BUI-BMW-TOPSIS) model incorporating the best, middle, and worst reference points to enhance decision-making accuracy is proposed. Ultimately, by integrating the BUIGPWA operator for group information aggregation with the BUI-BMW-TOPSIS model to handle multi-criteria decision information, a novel multi-criteria group decision-making (MCGDM) method is constructed to evaluate green recycling suppliers for shared electric bikes. Case analyses and comparative analyses demonstrate that compared with the BUIWA operator, the BUIGPWA operator yields more reliable results because of its consideration of the degree of support among decision-makers. Furthermore, in contrast to the traditional TOPSIS method, the BUI-BMW-TOPSIS model incorporates the credibility of information provided by decision-makers, leading to more trustworthy outcomes. Notably, variations in attribute weights significantly impact the decision-making results. In summary, our methods excel in handling uncertain information and complex multi-criteria group decisions, boosting scientific rigor and reliability, and supporting optimization and sustainability of shared electric bike green recycling suppliers. Full article
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<p>Illustrative process of the MCGDM approach.</p>
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13 pages, 2699 KiB  
Article
Insight into the Reversible Hydrogen Storage of Titanium-Decorated Boron-Doped C20 Fullerene: A Theoretical Prediction
by Zhiliang Chai, Lili Liu, Congcong Liang, Yan Liu and Qiang Wang
Molecules 2024, 29(19), 4728; https://doi.org/10.3390/molecules29194728 - 6 Oct 2024
Viewed by 539
Abstract
Hydrogen storage has been a bottleneck factor for the application of hydrogen energy. Hydrogen storage capacity for titanium-decorated boron-doped C20 fullerenes has been investigated using the density functional theory. Different boron-doped C20 fullerene absorbents are examined to avoid titanium atom clustering. [...] Read more.
Hydrogen storage has been a bottleneck factor for the application of hydrogen energy. Hydrogen storage capacity for titanium-decorated boron-doped C20 fullerenes has been investigated using the density functional theory. Different boron-doped C20 fullerene absorbents are examined to avoid titanium atom clustering. According to our research, with three carbon atoms in the pentagonal ring replaced by boron atoms, the binding interaction between the Ti atom and C20 fullerene is stronger than the cohesive energy of titanium. The calculated results revealed that one Ti atom can reversibly adsorb four H2 molecules with an average adsorption energy of −1.52 eV and an average desorption temperature of 522.5 K. The stability of the best absorbent structure with a gravimetric density of 4.68 wt% has been confirmed by ab initio molecular dynamics simulations. These findings suggest that titanium-decorated boron-doped C20 fullerenes could be considered as a potential candidate for hydrogen storage devices. Full article
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<p>(<b>a</b>) Top and side views of C<sub>20</sub>. (<b>b</b>) Top and side views of the adsorbent B123 model. (<b>c</b>) Binding energy of different amounts of boron doping, where brown, green and blue represent carbon, boron and titanium atoms respectively. (<b>d</b>) Changes in energy and bond length in the ab initio molecular dynamics simulation (300 K, 5 ps) of the B123 model.</p>
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<p>Hydrogen adsorption on the B123 model, where brown, green, blue and white represent carbon, boron, titanium and hydrogen atoms respectively.</p>
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<p>Desorption temperature as a function of pressure in the B123 model.</p>
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<p>(<b>a</b>) Relative energy as a function of temperature under a given pressure in the B123 model. (<b>b</b>) Relative energy as a function of pressure under a given temperature in the B123 model.</p>
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<p>Total density of states of C<sub>20</sub> fullerene and B123 model.</p>
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<p>Partial density of states for (<b>a</b>) C 2p orbital of C<sub>20</sub>; (<b>b</b>) C 2p orbital of B123; (<b>c</b>) B 2p orbital of isolated B; (<b>d</b>) Ti 3d orbital of isolated Ti; (<b>e</b>) B 2p orbital of B123; and (<b>f</b>) Ti 3d orbital of B123.</p>
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<p>Partial density of states for the (<b>a</b>) H 1s orbital of isolated H<sub>2</sub>; (<b>b</b>) H 1s orbital of C<sub>20</sub> fullerene + H<sub>2</sub>; (<b>c</b>) H 1s orbital of B123 + H<sub>2</sub>; (<b>d</b>) Ti 3d orbital of B123; and (<b>e</b>) Ti 3d orbital of B123 + H<sub>2</sub>. Fermi level is set to zero energy.</p>
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<p>Charge density difference for the (<b>a</b>) B123 system; (<b>b</b>) B123 + H<sub>2</sub> system. Yellow and blue colors represent charge-gained and charge-lost regions, respectively.</p>
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27 pages, 2445 KiB  
Review
From Geometry of Hamiltonian Dynamics to Topology of Phase Transitions: A Review
by Giulio Pettini, Matteo Gori and Marco Pettini
Entropy 2024, 26(10), 840; https://doi.org/10.3390/e26100840 - 5 Oct 2024
Viewed by 416
Abstract
In this review work, we outline a conceptual path that, starting from the numerical investigation of the transition between weak chaos and strong chaos in Hamiltonian systems with many degrees of freedom, comes to highlight how, at the basis of equilibrium phase transitions, [...] Read more.
In this review work, we outline a conceptual path that, starting from the numerical investigation of the transition between weak chaos and strong chaos in Hamiltonian systems with many degrees of freedom, comes to highlight how, at the basis of equilibrium phase transitions, there must be major changes in the topology of submanifolds of the phase space of Hamiltonian systems that describe systems that exhibit phase transitions. In fact, the numerical investigation of Hamiltonian flows of a large number of degrees of freedom that undergo a thermodynamic phase transition has revealed peculiar dynamical signatures detected through the energy dependence of the largest Lyapunov exponent, that is, of the degree of chaoticity of the dynamics at the phase transition point. The geometrization of Hamiltonian flows in terms of geodesic flows on suitably defined Riemannian manifolds, used to explain the origin of deterministic chaos, combined with the investigation of the dynamical counterpart of phase transitions unveils peculiar geometrical changes of the mechanical manifolds in correspondence to the peculiar dynamical changes at the phase transition point. Then, it turns out that these peculiar geometrical changes are the effect of deeper topological changes of the configuration space hypersurfaces v=VN1(v) as well as of the manifolds {Mv=VN1((,v])}vR bounded by the ∑v. In other words, denoting by vc the critical value of the average potential energy density at which the phase transition takes place, the members of the family {v}v<vc are not diffeomorphic to those of the family {v}v>vc; additionally, the members of the family {Mv}v>vc are not diffeomorphic to those of {Mv}v>vc. The topological theory of the deep origin of phase transitions allows a unifying framework to tackle phase transitions that may or may not be due to a symmetry-breaking phenomenon (that is, with or without an order parameter) and to finite/small N systems. Full article
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<p><math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>ϵ</mi> <mo>)</mo> </mrow> </mrow> </mstyle> </semantics></math> computed with Equation (<a href="#FD42-entropy-26-00840" class="html-disp-formula">42</a>) at <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>128</mn> </mrow> </mstyle> </semantics></math> is represented by full circles ad computed at <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>256</mn> </mrow> </mstyle> </semantics></math> by full triangles. The largest Lyapunov exponent <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>ϵ</mi> <mo>)</mo> </mrow> </mrow> </mstyle> </semantics></math> computed with Equation (<a href="#FD50-entropy-26-00840" class="html-disp-formula">50</a>) is represented by open circles (<math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>256</mn> </mrow> </mstyle> </semantics></math>) and open squares (<math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>2000</mn> </mrow> </mstyle> </semantics></math>). The solid line is the analytic prediction for <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>ϵ</mi> <mo>)</mo> </mrow> </mrow> </mstyle> </semantics></math> as discussed in the following section.</p>
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<p>Pictorial representation of how two geodesics—<math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mi>γ</mi> <mn>1</mn> </msub> </mstyle> </semantics></math> and <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mi>γ</mi> <mn>2</mn> </msub> </mstyle> </semantics></math>, issuing respectively from the close points <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>A</mi> </mstyle> </semantics></math> and <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>B</mi> </mstyle> </semantics></math>—separate on a 2D “bumpy” manifold where the variations of curvature activate parametric instability.</p>
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<p>Lyapunov exponent <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>λ</mi> </mstyle> </semantics></math> vs. energy density <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>ε</mi> </mstyle> </semantics></math> for the FPU <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>β</mi> </mstyle> </semantics></math> model with <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </mstyle> </semantics></math>. The continuous line is the theoretical computation according to Equation (<a href="#FD56-entropy-26-00840" class="html-disp-formula">56</a>), while the circles and squares are the results of numerical simulations with <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>N</mi> </mstyle> </semantics></math> respectively equal to 256 and 2000. From [<a href="#B31-entropy-26-00840" class="html-bibr">31</a>].</p>
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<p>Lyapunov exponent <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>λ</mi> </mstyle> </semantics></math> vs. energy density <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>ϵ</mi> </mstyle> </semantics></math> for the 1d-<math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>X</mi> <mi>Y</mi> </mrow> </mstyle> </semantics></math> model with <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </mstyle> </semantics></math>. The continuous line is the theoretical computation according to (<a href="#FD56-entropy-26-00840" class="html-disp-formula">56</a>), while full circles, squares, and triangles are the results of numerical simulations with <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>N</mi> </mstyle> </semantics></math>, respectively, equal to 150, 1000, and 1500. The dotted line is the theoretical result, where the value of <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mi>k</mi> <mn>0</mn> </msub> </mstyle> </semantics></math> has been corrected to account for an excess of negative values of <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mi>k</mi> <mi>R</mi> </msub> </mstyle> </semantics></math> in an intermediate interval of <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>ϵ</mi> </mstyle> </semantics></math> values.</p>
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<p><b>Left panel</b>: Lyapunov exponent <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>λ</mi> </mstyle> </semantics></math> vs. the temperature <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>T</mi> </mstyle> </semantics></math> for the three-dimensional <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>X</mi> <mi>Y</mi> </mrow> </mstyle> </semantics></math> model, defined in (<a href="#FD61-entropy-26-00840" class="html-disp-formula">61</a>), numerically computed on an <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>10</mn> <mo>×</mo> <mn>10</mn> <mo>×</mo> <mn>10</mn> </mrow> </mstyle> </semantics></math> lattice (solid circles) and on an <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>15</mn> <mo>×</mo> <mn>15</mn> <mo>×</mo> <mn>15</mn> </mrow> </mstyle> </semantics></math> lattice (solid squares). The critical temperature of the phase transition is <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msub> <mi>T</mi> <mi mathvariant="normal">c</mi> </msub> <mo>≈</mo> <mn>2.15</mn> </mrow> </mstyle> </semantics></math>. From [<a href="#B7-entropy-26-00840" class="html-bibr">7</a>]. <b>Right panel</b>: Fluctuations of the Ricci curvature (Eisenhart metric), for the same model. Here, <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>10</mn> <mo>×</mo> <mn>10</mn> <mo>×</mo> <mn>10</mn> </mrow> </mstyle> </semantics></math>. The critical temperature of the phase transition is marked by a vertical dotted line.</p>
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<p><b>Left panel</b>: Lyapunov exponent <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>λ</mi> </mstyle> </semantics></math> vs. the energy per particle <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>ε</mi> </mstyle> </semantics></math>, numerically computed for the two-dimensional <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </mstyle> </semantics></math><math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msup> <mi>φ</mi> <mn>4</mn> </msup> </mstyle> </semantics></math> model, with <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>100</mn> </mrow> </mstyle> </semantics></math> (solid circles), <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>400</mn> </mrow> </mstyle> </semantics></math> (open circles), <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>900</mn> </mrow> </mstyle> </semantics></math> (solid triangles), and <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> <mn>2500</mn> </mrow> </mstyle> </semantics></math> (open triangles). The critical energy is marked by a vertical dotted line, and the dashed line is the power law <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msup> <mi>ε</mi> <mn>2</mn> </msup> </mstyle> </semantics></math>. From [<a href="#B9-entropy-26-00840" class="html-bibr">9</a>]. <b>Right panel</b>: Root mean square fluctuation of the Ricci curvature (Eisenhart metric) <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mi>σ</mi> <mi>k</mi> </msub> </mstyle> </semantics></math>, divided by the average curvature <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mi>k</mi> <mn>0</mn> </msub> </mstyle> </semantics></math>, numerically computed for the same model. The inset shows a magnification of the region close to the transition.</p>
Full article ">Figure 7
<p>Here, the function <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>f</mi> </mstyle> </semantics></math> is the height of a point of the bent cylinder with respect to the ground. In <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mi>P</mi> <mn>1</mn> </msub> </mstyle> </semantics></math>, it is <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>d</mi> <mi>f</mi> <mo>=</mo> <mn>0</mn> </mrow> </mstyle> </semantics></math>. The level sets <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msub> <mo>Σ</mo> <mi>u</mi> </msub> <mo>=</mo> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mstyle> </semantics></math> below this critical point are circles, whereas above are the union of two circles. The manifolds <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msub> <mi>M</mi> <mi>u</mi> </msub> <mo>=</mo> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mo>(</mo> <mo>−</mo> <mo>∞</mo> <mo>,</mo> <mi>u</mi> <mo>]</mo> </mrow> <mo>)</mo> </mrow> </mrow> </mstyle> </semantics></math> are disks for <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>u</mi> <mo>&lt;</mo> <msub> <mi>u</mi> <mi>c</mi> </msub> </mrow> </mstyle> </semantics></math> and cylinders for <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>u</mi> <mo>&gt;</mo> <msub> <mi>u</mi> <mi>c</mi> </msub> </mrow> </mstyle> </semantics></math>.</p>
Full article ">Figure 8
<p><b>Left panel</b>: Mean-field <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>X</mi> <mi>Y</mi> </mrow> </mstyle> </semantics></math> model. Plot of <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mo form="prefix">log</mo> <mo>(</mo> <mo>|</mo> <mi>χ</mi> <mo>|</mo> <mrow> <mo>(</mo> <msub> <mi>M</mi> <mi>v</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> <mo>/</mo> <mi>N</mi> </mrow> </mstyle> </semantics></math> as a function of <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>v</mi> </mstyle> </semantics></math>. <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> </mrow> </mstyle> </semantics></math> 50, 200, 800 (from bottom to top) and <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>h</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </mstyle> </semantics></math>; <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msub> <mi>v</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>0.5</mn> <mo>+</mo> <mi mathvariant="script">O</mi> <mrow> <mo>(</mo> <msup> <mi>h</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </mstyle> </semantics></math>. <b>Right panel</b>: Plot of <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mo form="prefix">log</mo> <mo>(</mo> <mo>|</mo> <mi>χ</mi> <mo>|</mo> <mrow> <mo>(</mo> <msub> <mi>M</mi> <mi>v</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> <mo>/</mo> <mi>N</mi> </mrow> </mstyle> </semantics></math> for the one-dimensional <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>X</mi> <mi>Y</mi> </mrow> </mstyle> </semantics></math> model with nearest-neighbor interactions as a function of <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>v</mi> </mstyle> </semantics></math>. <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>N</mi> <mo>=</mo> </mrow> </mstyle> </semantics></math> 50, 200, 800 (from bottom to top).</p>
Full article ">Figure 9
<p>Logarithmic Euler characteristic <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>σ</mi> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> </mstyle> </semantics></math> of the <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mi>M</mi> <mi>v</mi> </msub> </mstyle> </semantics></math> manifolds as a function of the potential energy <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>v</mi> </mstyle> </semantics></math>. The phase transition is signaled as a singularity of the first derivative at <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msub> <mi>v</mi> <mi>c</mi> </msub> <mo>=</mo> <mo>Δ</mo> </mrow> </mstyle> </semantics></math>; the sign of the second derivative around the singular point allows to predict the order of the transition.</p>
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<p>The variance of the scalar curvature of the potential level sets <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mo>Σ</mo> <mi>v</mi> </msub> </mstyle> </semantics></math> is reported versus temperature <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>T</mi> </mstyle> </semantics></math> normalized by the folding temperature <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mi>T</mi> <mi>f</mi> </msub> </mstyle> </semantics></math> for the SH3 and PYP proteins, respectively.</p>
Full article ">Figure 11
<p>The variance in sectional curvatures of the potential level sets <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mo>Σ</mo> <mi>v</mi> </msub> </mstyle> </semantics></math> is reported versus potential energy density <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>v</mi> </mstyle> </semantics></math> for the SH3 and PYP proteins, respectively. Vertical dashed lines correspond to the folding transitions.</p>
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<p><b>Left panel</b>: Second derivative <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msup> <mo>∂</mo> <mn>2</mn> </msup> <mi>S</mi> <mo>/</mo> <mo>∂</mo> <msup> <mi>u</mi> <mn>2</mn> </msup> </mrow> </mstyle> </semantics></math> of the configurational entropy versus the average potential energy per degree of freedom <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>u</mi> </mstyle> </semantics></math>. Lattice dimensions: <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msup> <mi>n</mi> <mn>3</mn> </msup> <mo>=</mo> <mn>6</mn> <mo>×</mo> <mn>6</mn> <mo>×</mo> <mn>6</mn> </mrow> </mstyle> </semantics></math> (rhombs), <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msup> <mi>n</mi> <mn>3</mn> </msup> <mo>=</mo> <mn>8</mn> <mo>×</mo> <mn>8</mn> <mo>×</mo> <mn>8</mn> </mrow> </mstyle> </semantics></math> (squares), <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msup> <mi>n</mi> <mn>3</mn> </msup> <mo>=</mo> <mn>10</mn> <mo>×</mo> <mn>10</mn> <mo>×</mo> <mn>10</mn> </mrow> </mstyle> </semantics></math> (circles), <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msup> <mi>n</mi> <mn>3</mn> </msup> <mo>=</mo> <mn>14</mn> <mo>×</mo> <mn>14</mn> <mo>×</mo> <mn>14</mn> </mrow> </mstyle> </semantics></math> (full circles). The vertical dot-dashed line locates the phase transition point. <b>Right panel</b>: second moment of the total mean curvature of the potential level sets <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <msub> <mo>Σ</mo> <mi>u</mi> </msub> </mstyle> </semantics></math> versus the average potential energy per degree of freedom <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mi>u</mi> </mstyle> </semantics></math>. <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msup> <mi>n</mi> <mn>3</mn> </msup> <mo>=</mo> <mn>6</mn> <mo>×</mo> <mn>6</mn> <mo>×</mo> <mn>6</mn> </mrow> </mstyle> </semantics></math> (rhombs), <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msup> <mi>n</mi> <mn>3</mn> </msup> <mo>=</mo> <mn>8</mn> <mo>×</mo> <mn>8</mn> <mo>×</mo> <mn>8</mn> </mrow> </mstyle> </semantics></math> (squares), <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msup> <mi>n</mi> <mn>3</mn> </msup> <mo>=</mo> <mn>10</mn> <mo>×</mo> <mn>10</mn> <mo>×</mo> <mn>10</mn> </mrow> </mstyle> </semantics></math> (circles). The oblique dashed line is a guide to the eye. The vertical dashed line at <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <mi>u</mi> <mo>≃</mo> <mo>−</mo> <mn>1.32</mn> </mrow> </mstyle> </semantics></math> corresponds to the phase transition point and to the point where the second derivative <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mrow> <msup> <mi>d</mi> <mn>2</mn> </msup> <msub> <mi>σ</mi> <mi>M</mi> </msub> <mo>/</mo> <mi>d</mi> <msup> <mi>u</mi> <mn>2</mn> </msup> </mrow> </mstyle> </semantics></math> jumps from a negative value to zero.</p>
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20 pages, 2913 KiB  
Article
Excess Thermodynamic Properties and FTIR Studies of Binary Mixtures of Toluene with 2-Propanol or 2-Methyl-1-Propanol
by Maria Magdalena Naum and Vasile Dumitrescu
Molecules 2024, 29(19), 4706; https://doi.org/10.3390/molecules29194706 - 4 Oct 2024
Viewed by 377
Abstract
Physical properties of the binary solutions, toluene with 2-propanol and 2-methyl-1-propanol, were measured at T = 293.15, 298.15, 303.15, 308.15, and 313.15 K and P = 100 kPa. The experimental density values were tested with the Emmerling et al. and Gonzalez-Olmos–Iglesias equations. The [...] Read more.
Physical properties of the binary solutions, toluene with 2-propanol and 2-methyl-1-propanol, were measured at T = 293.15, 298.15, 303.15, 308.15, and 313.15 K and P = 100 kPa. The experimental density values were tested with the Emmerling et al. and Gonzalez-Olmos–Iglesias equations. The results indicate that the equation by Emmerling et al. is the best to correlate the density for toluene + 2-methyl-1-propanol system, while for toluene + 2-propanol, both proposed equations are proper to correlate the density with composition and temperature. The viscosity results were verified with different models containing two adjustable parameters. The values of viscosity deviation (η), excess molar volume (VE), excess Gibbs energy (ΔG*E), partial molar volumes (V1¯ and V2¯), and apparent molar volume (Vφ,1 and Vφ,2) were calculated. The values of the excess molar volume were positive for both systems, while negative values were obtained for the viscosity deviation and the excess Gibbs energy. The excess properties of the mixtures were adjusted to the Redlich–Kister equation. The values of thermodynamic functions of activation of viscous flow were computed and analyzed. Additionally, the Prigogine–Flory–Patterson (PFP) theory was applied to calculate VE and then compared with experimental values. The values of the percentage absolute average deviation obtained suggest the validity of this theory. The Fourier transform infrared spectroscopy (FTIR) spectra of the binary solutions studied in this work allowed for the understanding of the interactions between the molecules of these systems. Full article
(This article belongs to the Section Applied Chemistry)
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Figure 1

Figure 1
<p>Excess molar volumes (<span class="html-italic">V</span><sup>E</sup>) versus mole fraction for toluene (1) + 2−propanol (2) system at: ■ 293.15 K; ● 298.15 K; ▲ 303.15 K; ▼ 308.15 K; ♦ 313.15 K. The solid curve was determined with R–K equation.</p>
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<p>Excess molar volumes (<span class="html-italic">V</span><sup>E</sup>) versus mole fraction for toluene (1) + 2−methyl−1−propanol (2) system at: ■ 293.15 K; ● 298.15 K; ▲ 303.15 K; ▼ 308.15 K; ♦ 313.15 K. The solid curve was determined with R–K equation.</p>
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<p>Viscosity deviation (Δ<span class="html-italic">η</span>) versus mole fraction for toluene (1) + 2−propanol (2) system at: ■ 293.15 K; ● 298.15 K; ▲ 303.15 K; ▼ 308.15 K; ♦ 313.15 K. The solid curve was determined with R–K equation.</p>
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<p>Viscosity deviation (Δ<span class="html-italic">η</span>) versus mole fraction for toluene (1) + 2−methyl−1−propanol (2) system at: ■ 293.15 K; ● 298.15 K; ▲ 303.15 K; ▼ 308.15 K; ♦ 313.15 K. The solid curve was determined with R–K equation.</p>
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<p>Excess Gibbs energy (Δ<span class="html-italic">G</span><sup>#E</sup>) versus mole fraction for toluene (1) + 2−propanol (2) system at: ■ 293.15 K; ● 298.15 K; ▲ 303.15 K; ▼ 308.15 K; ♦ 313.15 K. The solid curve was determined with R–K equation.</p>
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<p>Excess Gibbs energy (Δ<span class="html-italic">G</span><sup>#E</sup>) versus mole fraction for toluene (1) + 2−methyl−1−propanol (2) system at: ■ 293.15 K; ● 298.15 K; ▲ 303.15 K; ▼ 308.15 K; ♦ 313.15 K. The solid curve was determined with R–K equation.</p>
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<p>FTIR spectra of binary mixture at different mole fraction (x) and at room temperature: (<b>a</b>) toluene (<span class="html-italic">x</span>) − 2-propanol, (<b>b</b>) <span class="html-italic">n</span>-heptane (<span class="html-italic">x</span>) − 2-propanol, (<b>c</b>): toluene (<span class="html-italic">x</span>) − 2-methyl-1-propanol, (<b>d</b>): <span class="html-italic">n</span>-heptane (<span class="html-italic">x</span>) − 2−methyl-1-propanol.</p>
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11 pages, 1600 KiB  
Article
Detection of Alzheimer’s Disease Using Hybrid Meta-ROI of MRI Structural Images
by Xiaoming Zheng and on behalf of the Alzheimer’s Disease Neuroimaging Initiative
Diagnostics 2024, 14(19), 2203; https://doi.org/10.3390/diagnostics14192203 - 2 Oct 2024
Viewed by 525
Abstract
Background: The averaged cortical thickness of meta-ROI is currently being used for the diagnosis and prognosis of Alzheimer’s disease (AD) using structural MRI brain images. The purpose of this work is to present a hybrid meta-ROI for the detection of AD. Methods: The [...] Read more.
Background: The averaged cortical thickness of meta-ROI is currently being used for the diagnosis and prognosis of Alzheimer’s disease (AD) using structural MRI brain images. The purpose of this work is to present a hybrid meta-ROI for the detection of AD. Methods: The AD detectability of selected cortical and volumetric regions of the brain was examined using signal detection theory. The top performing cortical and volumetric ROIs were taken as input nodes to the artificial neural network (ANN) for AD classification. Results: An AD diagnostic accuracy of 91.9% was achieved by using a hybrid meta-ROI consisting of thicknesses of entorhinal and middle temporal cortices, and the volumes of the hippocampus and inferior lateral ventricles. Pairing inferior lateral ventricle dilation with hippocampal volume reduction improves AD detectability by 5.1%. Conclusions: Hybrid meta-ROI, including the dilation of inferior lateral ventricles, outperformed both cortical thickness- and volumetric-based meta-ROIs in the detection of Alzheimer’s disease. Full article
(This article belongs to the Special Issue Neuropathology, Neuroimaging and Biomarkers in Neurological Disease)
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Figure 1
<p>(<b>a</b>) Combined case distributions (histograms) of Alzheimer’s disease (AD) and normal controls (NC) on the entorhinal cortical thickness variable. (<b>b</b>) Cumulative case numbers of Alzheimer’s disease (AD) and normal controls (NC) on the entorhinal cortical thickness variable.</p>
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<p>(<b>a</b>) A coronal slice of a young healthy subject’s T1-weighted MRI image showing the locations of the hippocampus and inferior lateral ventricles. (<b>b</b>) A surface map of the same young healthy subject’s cortical parcellation showing the entorhinal and middle temporal regions.</p>
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<p>(<b>a</b>) ROC curves of AD diagnosis (NC_AD), MCI conversion to AD (MCI_AD), and detection of mild cognitive impairment from normal controls (NC_MCI) using the variable of entorhinal cortical thickness. (<b>b</b>) ROC curves of AD (status = 1) diagnosis and NC (status = 0) identification using artificial neural network (ANN), using hybrid input notes of entorhinal and middle temporal cortical thickness, and hippocampal and inferior lateral ventricle volumes (<a href="#diagnostics-14-02203-f004" class="html-fig">Figure 4</a>a).</p>
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<p>(<b>a</b>) The artificial neural network, using input notes of entorhinal and middle temporal cortical thickness and hippocampal and inferior lateral ventricle volumes, achieved the highest AUC = 0.919. (<b>b</b>) Normalized importance (weighting) of the four input notes of (<b>a</b>).</p>
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