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19 pages, 25394 KiB  
Article
Rotational Motion Compensation for ISAR Imaging Based on Minimizing the Residual Norm
by Xiaoyu Yang, Weixing Sheng, Annan Xie and Renli Zhang
Remote Sens. 2024, 16(19), 3629; https://doi.org/10.3390/rs16193629 (registering DOI) - 28 Sep 2024
Abstract
In inverse synthetic aperture radar (ISAR) systems, image quality often suffers from the non-uniform rotation of non-cooperative targets. Rotational motion compensation (RMC) is necessary to perform refocused ISAR imaging via estimated rotational motion parameters. However, estimation errors tend to accumulate with the estimated [...] Read more.
In inverse synthetic aperture radar (ISAR) systems, image quality often suffers from the non-uniform rotation of non-cooperative targets. Rotational motion compensation (RMC) is necessary to perform refocused ISAR imaging via estimated rotational motion parameters. However, estimation errors tend to accumulate with the estimated processes, deteriorating the image quality. A novel RMC algorithm is proposed in this study to mitigate the impact of cumulative errors. The proposed method uses an iterative approach based on a novel criterion, i.e., the minimum residual norm of the signal phases, to estimate different rotational parameters independently to avoid the issue caused by cumulative errors. First, a refined inverse function combined with interpolation is proposed to perform the RMC procedure. Then, the rotation parameters are estimated using an iterative procedure designed to minimize the residual norm of the compensated signal phases. Finally, with the estimated parameters, RMC is performed on signals in all range bins, and focused images are obtained using the Fourier transform. Furthermore, this study utilizes simulated and real data to validate and evaluate the performance of the proposed algorithm. The experimental results demonstrate that the proposed algorithm shows dominance in the aspects of estimation accuracy, entropy values, and focusing characteristics. Full article
16 pages, 1666 KiB  
Article
Ecological Security Evaluation and Prediction for Coal Resource Cities Based on the PSR Model: A Case Study of Xuzhou, China
by Zhihui Song, Nan Zhu, Dejun Yang and Dan He
Sustainability 2024, 16(19), 8461; https://doi.org/10.3390/su16198461 (registering DOI) - 28 Sep 2024
Abstract
The rapid development of urbanization has led to population growth, increased resource consumption, and intensified environmental pollution. Consequently, urban ecological security has increasingly become a key factor constraining the sustainable development of socio-economic systems. This study constructed an urban ecological security evaluation system [...] Read more.
The rapid development of urbanization has led to population growth, increased resource consumption, and intensified environmental pollution. Consequently, urban ecological security has increasingly become a key factor constraining the sustainable development of socio-economic systems. This study constructed an urban ecological security evaluation system based on the Pressure-State-Response (PSR) model and used Xuzhou, a typical coal resource city, as a case study to apply and validate the model. Specifically, the analytic hierarchy process and entropy weight method were used to determine the index weights, and the ecological security index was used to evaluate the ecological security status of each system in Xuzhou from 2006 to 2022. Finally, the grey prediction GM (1,1) model was used to predict the ecological security status of Xuzhou in the next five years. The results show that the “disposal capacity of waste gas treatment facilities”, “per capita disposable income”, and “agricultural fertilizer application intensity” occupy a large weight in the whole evaluation system. The pressure index generally showed a fluctuating upward trend, and the state index fluctuated around 0.12. There is a simultaneous upward trend in the response index and the composite index. The ecological security level of the composite index has increased from “unsafe” in 2006 to “relatively safe” in 2022 and will continue to improve to “ideal security” in the future. This study provides a scientific basis for the formulation of sustainable development policies in Xuzhou and also provides a reference for the ecological safety management and assessment of other similar cities. Full article
15 pages, 430 KiB  
Article
Crystallization Kinetics of Tacrolimus Monohydrate in an Ethanol–Water System
by Suoqing Zhang, Jixiang Zhao, Ming Kong, Jiahui Li, Mingxuan Li, Miao Ma, Li Tong, Tao Li and Mingyang Chen
Crystals 2024, 14(10), 849; https://doi.org/10.3390/cryst14100849 (registering DOI) - 28 Sep 2024
Abstract
Nucleation and growth during the crystallization process are crucial steps that determine the crystal structure, size, morphology, and purity. A thorough understanding of these mechanisms is essential for producing crystalline products with consistent properties. This study investigates the solubility of tacrolimus (FK506) in [...] Read more.
Nucleation and growth during the crystallization process are crucial steps that determine the crystal structure, size, morphology, and purity. A thorough understanding of these mechanisms is essential for producing crystalline products with consistent properties. This study investigates the solubility of tacrolimus (FK506) in an ethanol–water system (1:1, v/v) and examines its crystallization kinetics using batch crystallization experiments. Initially, the solubility of FK506 was measured, and classical nucleation theory was employed to analyze the induction period to determine interfacial free energy () and other nucleation parameters, including the critical nucleus radius (), critical free energy (), and the molecular count of the critical nucleus (). Crystallization kinetics under seeded conditions were also measured, and the parameters of the kinetic model were analyzed to understand the effects of process states such as temperature on the crystallization process. The results suggested that increasing temperature and supersaturation promotes nucleation. The surface entropy factor () indicates that the tacrolimus crystal growth mechanism is a two-dimensional nucleation growth. The growth process follows the particle size-independent growth law proposed by McCabe. The estimated kinetic parameters reveal the effects of supersaturation, temperature, and suspension density on the nucleation and growth rates. Full article
(This article belongs to the Special Issue Crystallization Process and Simulation Calculation, Third Edition)
17 pages, 349 KiB  
Article
Information Properties of Consecutive Systems Using Fractional Generalized Cumulative Residual Entropy
by Mohamed Kayid and Mansour Shrahili
Fractal Fract. 2024, 8(10), 568; https://doi.org/10.3390/fractalfract8100568 (registering DOI) - 28 Sep 2024
Abstract
We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system’s lifetime and explore its preservation properties in [...] Read more.
We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system’s lifetime and explore its preservation properties in terms of established stochastic orders. Additionally, we obtain useful bounds. To aid practical applications, we propose two nonparametric estimators for the fractional generalized cumulative residual entropy in these systems. The efficiency and performance of these estimators are illustrated using simulated and real datasets. Full article
27 pages, 6721 KiB  
Article
A Lightweight Multi-Mental Disorders Detection Method Using Entropy-Based Matrix from Single-Channel EEG Signals
by Jiawen Li, Guanyuan Feng, Jujian Lv, Yanmei Chen, Rongjun Chen, Fei Chen, Shuang Zhang, Mang-I Vai, Sio-Hang Pun and Peng-Un Mak
Brain Sci. 2024, 14(10), 987; https://doi.org/10.3390/brainsci14100987 (registering DOI) - 28 Sep 2024
Abstract
Background: Mental health issues are increasingly prominent worldwide, posing significant threats to patients and deeply affecting their families and social relationships. Traditional diagnostic methods are subjective and delayed, indicating the need for an objective and effective early diagnosis method. Methods: To [...] Read more.
Background: Mental health issues are increasingly prominent worldwide, posing significant threats to patients and deeply affecting their families and social relationships. Traditional diagnostic methods are subjective and delayed, indicating the need for an objective and effective early diagnosis method. Methods: To this end, this paper proposes a lightweight detection method for multi-mental disorders with fewer data sources, aiming to improve diagnostic procedures and enable early patient detection. First, the proposed method takes Electroencephalography (EEG) signals as sources, acquires brain rhythms through Discrete Wavelet Decomposition (DWT), and extracts their approximate entropy, fuzzy entropy, permutation entropy, and sample entropy to establish the entropy-based matrix. Then, six kinds of conventional machine learning classifiers, including Support Vector Machine (SVM), k-Nearest Neighbors (kNN), Naive Bayes (NB), Generalized Additive Model (GAM), Linear Discriminant Analysis (LDA), and Decision Tree (DT), are adopted for the entropy-based matrix to achieve the detection task. Their performances are assessed by accuracy, sensitivity, specificity, and F1-score. Concerning these experiments, three public datasets of schizophrenia, epilepsy, and depression are utilized for method validation. Results: The analysis of the results from these datasets identifies the representative single-channel signals (schizophrenia: O1, epilepsy: F3, depression: O2), satisfying classification accuracies (88.10%, 75.47%, and 89.92%, respectively) with minimal input. Conclusions: Such performances are impressive when considering fewer data sources as a concern, which also improves the interpretability of the entropy features in EEG, providing a reliable detection approach for multi-mental disorders and advancing insights into their underlying mechanisms and pathological states. Full article
20 pages, 996 KiB  
Article
Entity Linking Model Based on Cascading Attention and Dynamic Graph
by Hongchan Li, Chunlei Li, Zhongchuan Sun and Haodong Zhu
Electronics 2024, 13(19), 3845; https://doi.org/10.3390/electronics13193845 (registering DOI) - 28 Sep 2024
Abstract
The purpose of entity linking is to connect entity mentions in text to real entities in the knowledge base. Existing methods focus on using the text topic, entity type, linking order, and association between entities to obtain the target entities. Although these methods [...] Read more.
The purpose of entity linking is to connect entity mentions in text to real entities in the knowledge base. Existing methods focus on using the text topic, entity type, linking order, and association between entities to obtain the target entities. Although these methods have achieved good results, they ignore the exploration of candidate entities, leading to insufficient semantic information among entities. In addition, the implicit relationship and discrimination within the candidate entities also affect the accuracy of entity linking. To address these problems, we introduce information about candidate entities from Wikipedia and construct a graph model to capture implicit dependencies between different entity decisions. Specifically, we propose a cascade attention mechanism and develop a novel local entity linkage model termed CAM-LEL. This model leverages the interaction between entity mentions and candidate entities to enhance the semantic representation of entities. Furthermore, a global entity linkage model termed DG-GEL based on a dynamic graph is established to construct an entity association graph, and a random walking algorithm and entity entropy are used to extract the implicit relationships within entities to increase the differentiation between entities. Experimental results and in-depth analyses of multiple datasets show that our model outperforms other state-of-the-art models. Full article
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18 pages, 1298 KiB  
Article
Adsorption, Adhesion, and Wettability of Commercially Available Cleansers at Dental Polymer (PMMA) Surfaces
by Stanisław Pogorzelski, Paulina Janowicz, Krzysztof Dorywalski, Katarzyna Boniewicz-Szmyt and Paweł Rochowski
Materials 2024, 17(19), 4755; https://doi.org/10.3390/ma17194755 - 27 Sep 2024
Viewed by 187
Abstract
This study aims to evaluate the adsorptive, adhesive, and wetting energetic properties of five commercially available cleansers in contact with model dental polymer (PMMA). It was assumed that the selected parameters allow for determining the optimal concentration and place of key component accumulation [...] Read more.
This study aims to evaluate the adsorptive, adhesive, and wetting energetic properties of five commercially available cleansers in contact with model dental polymer (PMMA). It was assumed that the selected parameters allow for determining the optimal concentration and place of key component accumulation for antibacterial activity in the bulk liquid phase and prevention of oral plaque formation at the prosthetic material surface. The adsorptive (Gibbs’ excesses ΓLV, critical micellar concentration) and thermal (entropy and enthalpy) surface characteristics originated from surface tension γLV(T) and γLV(C) dependences. The surface wetting properties were quantified upon the contact angle hysteresis formalism on the advancing ΘA, receding ΘR contact angles, and γLV as the input data, which yield a set of wettability parameters: 2D adsorptive film pressure, surface free energy with its dispersive and polar components, work of adhesion, and adhesional tension, considered as interfacial interaction indicators. In particular, molecular partitioning Kp and ΓLV are indicators of the efficiency of particular active substance accumulation in the volume phase, while γSV, a = ΓSL/ΓLV, and WA point to the degree of its accumulation at the immersed polymer surface. Finally, the liquid penetration coefficient PC and the Marangoni temperature gradient-driven liquid flow speed were estimated. Full article
21 pages, 2129 KiB  
Article
A Novel Approach to Enhancing the Determination of Primary Indicators in Non-Idealised Absorption Chillers
by Gábor L. Szabó
Energies 2024, 17(19), 4858; https://doi.org/10.3390/en17194858 - 27 Sep 2024
Viewed by 175
Abstract
The accurate optimisation of absorption chillers is often impeded by idealised models that overlook system interactions and machine complexities. This study introduces a validated mathematical description for predicting the primary indicators of non-idealised absorption chillers, accounting for factors such as the electrical work [...] Read more.
The accurate optimisation of absorption chillers is often impeded by idealised models that overlook system interactions and machine complexities. This study introduces a validated mathematical description for predicting the primary indicators of non-idealised absorption chillers, accounting for factors such as the electrical work of the Solution Circulation Pump, entropy changes within the refrigerant cycle, and exergy losses. Validation against 13 years of data (2008–2021) from the University of Debrecen’s absorption chiller indicated close agreement, with deviations within acceptable limits. The use of a solution heat exchanger shifted cooling indicators towards their minima. Sensitivity analyses indicated that a 2.5% reduction in condenser temperature increased COP by 41.3% and Cooling Exergetic Efficiency by 15.5%, while a 2.5% reduction in the Heat Fraction Factor improved both by 34%. Adjusting absorber temperature and Heat Fraction Factor down by 2.5%, alongside a 2.5% rise in generator temperature, resulted in a 100.8% increase in COP and a 52.8% boost in Cooling Exergetic Efficiency. These insights provide a solid foundation for future optimisation strategies in real-life absorption chiller systems. Full article
(This article belongs to the Section K: State-of-the-Art Energy Related Technologies)
8 pages, 2738 KiB  
Communication
Predictions of Lattice Parameters in NiTi High-Entropy Shape-Memory Alloys Using Different Machine Learning Models
by Tu-Ngoc Lam, Jiajun Jiang, Min-Cheng Hsu, Shr-Ruei Tsai, Mao-Yuan Luo, Shuo-Ting Hsu, Wen-Jay Lee, Chung-Hao Chen and E-Wen Huang
Materials 2024, 17(19), 4754; https://doi.org/10.3390/ma17194754 - 27 Sep 2024
Viewed by 201
Abstract
This work applied three machine learning (ML) models—linear regression (LR), random forest (RF), and support vector regression (SVR)—to predict the lattice parameters of the monoclinic B19′ phase in two distinct training datasets: previously published ZrO2-based shape-memory ceramics (SMCs) and NiTi-based high-entropy [...] Read more.
This work applied three machine learning (ML) models—linear regression (LR), random forest (RF), and support vector regression (SVR)—to predict the lattice parameters of the monoclinic B19′ phase in two distinct training datasets: previously published ZrO2-based shape-memory ceramics (SMCs) and NiTi-based high-entropy shape-memory alloys (HESMAs). Our findings showed that LR provided the most accurate predictions for ac, am, bm, and cm in NiTi-based HESMAs, while RF excelled in computing βm for both datasets. SVR disclosed the largest deviation between the predicted and actual values of lattice parameters for both training datasets. A combination approach of RF and LR models enhanced the accuracy of predicting lattice parameters of martensitic phases in various shape-memory materials for stable high-temperature applications. Full article
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21 pages, 1341 KiB  
Article
A Machine Learning-Based Sustainable Energy Management of Wind Farms Using Bayesian Recurrent Neural Network
by Aisha Blfgeh and Hanadi Alkhudhayr
Sustainability 2024, 16(19), 8426; https://doi.org/10.3390/su16198426 - 27 Sep 2024
Viewed by 227
Abstract
The sustainable management of energy sources such as wind plays a crucial role in supplying electricity for both residential and industrial purposes. For this, accurate wind data are essential to bring sustainability in energy output estimations for wind stations. The choice of an [...] Read more.
The sustainable management of energy sources such as wind plays a crucial role in supplying electricity for both residential and industrial purposes. For this, accurate wind data are essential to bring sustainability in energy output estimations for wind stations. The choice of an appropriate distribution function significantly affects the actual wind data, directly influencing the estimated energy output. While the Weibull function is commonly used to describe wind speed at various locations worldwide, the variability of weather information across wind sites varies significantly. Probabilistic forecasting offers comprehensive probability information for renewable generation and load, assisting decision-making in power systems under uncertainty. Traditional probabilistic forecasting techniques based on machine learning (ML) rely on prediction uncertainty derived from previous distributional assumptions. This study utilized a Bayesian Recurrent Neural Network (BNN-RNN), incorporating prior distributions for weight variables in the RNN network layer and extending the Bayesian networks. Initially, a periodic RNN processes data for wind energy prediction, capturing trends and correlation characteristics in time-series data to enable more accurate and reliable energy production forecasts. Subsequently, the wind power meteorological dataset was analyzed using the reciprocal entropy approach to reduce dimensionality and eliminate variables with weak connections, thereby simplifying the structure of the prediction model. The BNN-RNN prediction model integrates inputs from RNN-transformed time-series data, dimensionality-reduced weather information, and time categorization feature data. The Winkler index is lower by 3.4%, 32.6%, and 7.2%, respectively, and the overall index of probability forecasting pinball loss is reduced by 51.2%, 22.3%, and 10.7%, respectively, compared with all three approaches. The implications of this study are significant, as they demonstrate the potential for more accurate wind energy forecasting through Bayesian optimization. These findings contribute to more precise decision-making and bring sustainability to the effective management of energy systems by proposing a Bayesian Recurrent Neural Network (BNN-RNN) to improve wind energy forecasts. The model further enhances future estimates of wind energy generation, considering the stochastic nature of meteorological data. The study is crucial in increasing the understanding and application of machine learning by establishing how Bayesian optimization significantly improves probabilistic forecasting models that would revolutionize sustainable energy management. Full article
(This article belongs to the Special Issue Renewable Energy, Electric Power Systems and Sustainability)
15 pages, 7008 KiB  
Article
Radiation Resistance of High-Entropy Alloys CoCrFeNi and CoCrFeMnNi, Sequentially Irradiated with Kr and He Ions
by Bauyrzhan Amanzhulov, Igor Ivanov, Vladimir Uglov, Sergey Zlotski, Azamat Ryskulov, Alisher Kurakhmedov, Asset Sapar, Yerulan Ungarbayev, Mikhail Koloberdin and Maxim Zdorovets
Materials 2024, 17(19), 4751; https://doi.org/10.3390/ma17194751 - 27 Sep 2024
Viewed by 202
Abstract
This work studied the effect of sequential irradiation by krypton and helium ions at room temperature on the composition and structure of CoCrFeNi and CoCrFeMnNi high-entropy alloys (HEAs). Irradiation of the HEAs by 280 keV Kr14+ ions up to a fluence of [...] Read more.
This work studied the effect of sequential irradiation by krypton and helium ions at room temperature on the composition and structure of CoCrFeNi and CoCrFeMnNi high-entropy alloys (HEAs). Irradiation of the HEAs by 280 keV Kr14+ ions up to a fluence of 5 × 1015 cm–2 and 40 keV He2+ ions up to a fluence of 2 × 1017 cm–2 did not alter their elemental distribution and constituent phases. Blisters formed on the nickel surface after sequential irradiation, where large blisters had an average diameter of 3.8 μm. The lattice parameter of the (Co, Cr, Fe and Ni) and (Co, Cr, Fe, Mn and Ni) solid solutions increased by 0.17% and 0.37% after sequential irradiation, respectively. Irradiation by Kr ions led to a decrease in tensile macrostresses in the HEAs in the region of krypton ion implantation (Region I) and the formation of compressive macrostresses in the region behind the peak of implanted krypton (Region II). Sequential irradiation formed large compressive stresses in Ni and HEAs equal to −131.5 MPa, −300 MPa and −613.5 MPa in Ni, CoCrFeNi and CoCrFeMnNi, respectively, in the Region II. Irradiation by krypton ions decreased the dislocation density by 1.6–2.3 times, and irradiation with helium ions increased it by 11–15 times relative to unirradiated samples for CoCrFeNi and CoCrFeMnNi, respectively. Sequentially irradiated CoCrFeMnNi HEA had higher macrostresses and dislocation density than CoCrFeNi. Full article
(This article belongs to the Special Issue Advanced Science and Technology of High Entropy Materials)
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18 pages, 12338 KiB  
Article
Effects of Mo Addition on Microstructure and Corrosion Resistance of Cr25-xCo25Ni25Fe25Mox High-Entropy Alloys via Directed Energy Deposition
by Han-Eol Kim, Jae-Hyun Kim, Ho-In Jeong, Young-Tae Cho, Osama Salem, Dong-Won Jung and Choon-Man Lee
Micromachines 2024, 15(10), 1196; https://doi.org/10.3390/mi15101196 - 27 Sep 2024
Viewed by 262
Abstract
Highly entropy alloys (HEAs) are novel materials that have great potential for application in aerospace and marine engineering due to their superior mechanical properties and benefits over conventional materials. NiCrCoFe, also referred to as Ni-based HEA, has exceptional low-temperature strength and microstructural stability. [...] Read more.
Highly entropy alloys (HEAs) are novel materials that have great potential for application in aerospace and marine engineering due to their superior mechanical properties and benefits over conventional materials. NiCrCoFe, also referred to as Ni-based HEA, has exceptional low-temperature strength and microstructural stability. However, HEAs have limited corrosion resistance in some environments, such as a 3.5 wt% sodium chloride (NaCl) solution. Adding corrosion-resistant elements such as molybdenum (Mo) to HEAs is expected to increase their corrosion resistance in a variety of corrosive environments. Metal additive manufacturing reduces production times compared to casting and eliminates shrinkage issues, making it ideal for producing homogeneous HEA. This study used directed energy deposition (DED) to create Cr25-xCo25Ni25Fe25Mox (x = 0, 5, 10%) HEAs. Tensile strength and potentiodynamic polarization tests were used to assess the materials’ mechanical properties and corrosion resistance. The mechanical tests revealed that adding 5% Mo increased yield strength (YS) by 20.1% and ultimate tensile strength (UTS) by 9.5% when compared to 0% Mo. Adding 10% Mo led to a 32.5% increase in YS and a 20.4% increase in UTS. Potentiodynamic polarization tests were used to assess corrosion resistance in a 3.5-weight percent NaCl solution. The results showed that adding Mo significantly increased initial corrosion resistance. The alloy with 5% Mo had a higher corrosion potential (Ecorr) and a lower current density (Icorr) than the alloy with 0% Mo, indicating improved initial corrosion resistance. The alloy containing 10% Mo had the highest corrosion potential and the lowest current density, indicating the slowest corrosion rate and the best initial corrosion resistance. Finally, Cr25-xCo25Ni25Fe25Mox (x = 0, 5, 10%) HEAs produced by DED exhibited excellent mechanical properties and corrosion resistance, which can be attributed to the presence of Mo. Full article
(This article belongs to the Special Issue Future Prospects of Additive Manufacturing)
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19 pages, 3747 KiB  
Article
Ductility Index for Refractory High Entropy Alloys
by Ottó K. Temesi, Lajos K. Varga, Nguyen Quang Chinh and Levente Vitos
Crystals 2024, 14(10), 838; https://doi.org/10.3390/cryst14100838 - 27 Sep 2024
Viewed by 160
Abstract
The big advantage of refractory high entropy alloys (RHEAs) is their strength at high temperatures, but their big disadvantage is their brittleness at room temperature, which prevents their machining. There is a great need to classify the alloys in terms of brittle-ductile (B-D) [...] Read more.
The big advantage of refractory high entropy alloys (RHEAs) is their strength at high temperatures, but their big disadvantage is their brittleness at room temperature, which prevents their machining. There is a great need to classify the alloys in terms of brittle-ductile (B-D) properties, with easily obtainable ductility indices (DIs) ready to help design these refractory alloys. Usually, the DIs are checked by representing them as a function of fraction strain, ε. The critical values of DI and ε divide the DI—ε area into four squares. In the case of a successful DI, the points representing the alloys are located in the two diagonal opposite squares, well separating the alloys with (B-D) properties. However, due to the scatter of the data, the B-D separation is not perfect, and it is difficult to establish the critical value of DI. In this paper, we solve this problem by replacing the fracture strain parameter with new DIs that scale with the old DIs. These new DIs are based on the force constant and amplitude of thermal vibration around the Debye temperature. All of them are easily available and can be calculated from tabulated data. Full article
(This article belongs to the Special Issue Advances in Processing, Simulation and Characterization of Alloys)
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16 pages, 4835 KiB  
Article
Pressure Effects on the Thermodynamic Properties of MgSiO3 Akimotoite
by Chang Su, Wei Song, Guang Yang, Yonggang Liu and Qingyi Li
Crystals 2024, 14(10), 837; https://doi.org/10.3390/cryst14100837 - 26 Sep 2024
Viewed by 304
Abstract
The thermodynamic properties of MgSiO3 akimotoite at high temperatures and high pressures are important for investigating the phase equilibria of the Earth’s transition zone and the upper part of the lower mantle. In this paper, we present the self-consistent unit-cell volume, elastic [...] Read more.
The thermodynamic properties of MgSiO3 akimotoite at high temperatures and high pressures are important for investigating the phase equilibria of the Earth’s transition zone and the upper part of the lower mantle. In this paper, we present the self-consistent unit-cell volume, elastic properties, and in particular, thermodynamic properties including thermal expansion, heat capacity, entropy, and Grüneisen parameter of MgSiO3 akimotoite at pressures up to 30 GPa and temperatures to 2000 K using an iterative numerical method and available experimental data, which are consistent with the previous studies. The results show that the determined thermal expansion, heat capacity, entropy, and Grüneisen parameter exhibit a nonlinear and negative relationship with increasing pressure. Additionally, the pressure derivatives of these thermodynamic parameters along with the temperature are also presented. Full article
(This article belongs to the Section Mineralogical Crystallography and Biomineralization)
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18 pages, 1333 KiB  
Article
Strain-Rate and Stress-Rate Models of Nonlinear Viscoelastic Materials
by Claudio Giorgi and Angelo Morro
Mathematics 2024, 12(19), 3011; https://doi.org/10.3390/math12193011 - 26 Sep 2024
Viewed by 234
Abstract
The paper is devoted to the modeling of nonlinear viscoelastic materials. The constitutive equations are considered in differential form via relations between strain, stress, and their derivatives in the Lagrangian description. The thermodynamic consistency is established by using the Clausius–Duhem inequality through a [...] Read more.
The paper is devoted to the modeling of nonlinear viscoelastic materials. The constitutive equations are considered in differential form via relations between strain, stress, and their derivatives in the Lagrangian description. The thermodynamic consistency is established by using the Clausius–Duhem inequality through a procedure that involves two uncommon features. Firstly, the entropy production is regarded as a positive-valued constitutive function per se. This view implies that the inequality is in fact an equation. Secondly, this statement of the second law is investigated by using an algebraic representation formula, thus arriving at quite general results for rate terms that are usually overlooked in thermodynamic analyses. Starting from strain-rate or stress-rate equations, the corresponding finite equations are derived. It then emerges that a greater generality of the constitutive equations of the classical models, such as those of Boltzmann and Maxwell, are obtained as special cases. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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