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23 pages, 3719 KB  
Article
An Adaptive Dynamic Defense Strategy for Microservices Based on Deep Reinforcement Learning
by Yuanbo Li, Yuanmou Li, Guoqiang Wang and Hongchao Hu
Electronics 2025, 14(20), 4096; https://doi.org/10.3390/electronics14204096 - 19 Oct 2025
Viewed by 225
Abstract
Aiming at the problem that it is difficult to balance security defense and quality of service in a dynamic cloud-native environment, an adaptive dynamic defense strategy (AD2S) for microservices based on deep reinforcement learning is proposed. First, a microservice attack graph model is [...] Read more.
Aiming at the problem that it is difficult to balance security defense and quality of service in a dynamic cloud-native environment, an adaptive dynamic defense strategy (AD2S) for microservices based on deep reinforcement learning is proposed. First, a microservice attack graph model is constructed to extract security threats from multiple dimensions. Combined with queuing theory, the relationships among security performance, quality of service, cleaning cycle, and replica quantity are established to quantitatively model the effectiveness of defense. Subsequently, an adaptive defense framework is designed, which includes state monitoring, policy deployment, and optimization algorithms based on deep reinforcement learning, providing a rapid update solution for the optimal system configuration of microservices under dynamic traffic requests. The experimental results show that under dynamic traffic requests, compared with the existing DSEOM and OADSF strategies, AD2S improves the defense effectiveness by 34.38% and 10.29%, respectively, while ensuring the quality of service, significantly enhancing the system’s security adaptive ability. Full article
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32 pages, 5781 KB  
Article
Mechanistic Insights into 5-Fluorouracil Adsorption on Clinoptilolite Surfaces: Optimizing DFT Parameters for Natural Zeolites, Part II
by Lobna Saeed and Michael Fischer
Appl. Sci. 2025, 15(17), 9535; https://doi.org/10.3390/app15179535 - 29 Aug 2025
Viewed by 713
Abstract
Even though clinoptilolite mineral is the most important natural zeolite for technical applications, the molecular-level insights and detailed knowledge of their true local structures and adsorption behavior are largely lacking. An experimental determination of their surface structures, in particular, could be very challenging [...] Read more.
Even though clinoptilolite mineral is the most important natural zeolite for technical applications, the molecular-level insights and detailed knowledge of their true local structures and adsorption behavior are largely lacking. An experimental determination of their surface structures, in particular, could be very challenging due to the sensitivity of some facets to temperature and impurities. In this study, we present a robust multiscale modeling framework to investigate the adsorption of 5-fluorouracil, an anticancer drug, on dispersion-corrected density functional theory (DFT-D3)-optimized Na-clinoptilolite surfaces. Using a combination of interface force field and polymer consistent force field-based molecular dynamics with simulated annealing and parallel replica sampling, followed by DFT-D3 optimizations, we explore a wide configurational space of surface–molecule interactions. Our results show that Na-clinoptilolite surfaces support very strong adsorption, with adsorption energies ranging from −430.0 to −174.4 kJ/mol. Surface models with exposed Na cations consistently exhibit stronger binding, in contrast to their known steric hindrance effects in bulk environments. Furthermore, cation-free surfaces displayed relatively weaker interactions, yet configurations exposing the 8-membered rings (8 MR) demonstrated more favorable adsorption than those exposing 10 MR channels due to enhanced hydrogen bonding and spatial and entropic confinement effects. These findings reveal the importance of surface composition, local geometry, and configurational sampling in determining adsorption performance and lay the groundwork for future studies on cation-specific and multicationic clinoptilolite systems. Full article
(This article belongs to the Special Issue Development and Application of Computational Chemistry Methods)
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26 pages, 1484 KB  
Article
Digital Twin-Enhanced Programming Education: An Empirical Study on Learning Engagement and Skill Acquisition
by Ming Lu and Zhongyi Hu
Computers 2025, 14(8), 322; https://doi.org/10.3390/computers14080322 - 8 Aug 2025
Cited by 1 | Viewed by 1411
Abstract
As an introductory core course in computer science and related fields, “Fundamentals of Programming” has always faced many challenges in stimulating students’ interest in learning and cultivating their practical coding abilities. The traditional teaching model often fails to effectively connect theoretical knowledge with [...] Read more.
As an introductory core course in computer science and related fields, “Fundamentals of Programming” has always faced many challenges in stimulating students’ interest in learning and cultivating their practical coding abilities. The traditional teaching model often fails to effectively connect theoretical knowledge with practical applications, resulting in a low retention rate of students’ learning and a weak ability to solve practical problems. Digital twin (DT) technology offers a novel approach to addressing these challenges by creating dynamic, virtual replicas of physical systems with real-time, interactive capabilities. This study explores DT integration in programming teaching and its impact on learning engagement (behavioral, cognitive, emotional) and skill acquisition (syntax, algorithm design, debugging). A quasi-experimental design was employed to study 135 first-year undergraduate students, divided into an experimental group (n = 90) using a DT-based learning environment and a control group (n = 45) receiving traditional instruction. Quantitative data analysis was conducted on participation surveys, planning evaluations, and qualitative feedback. The results showed that, compared with the control group, the DT group exhibited a higher level of sustained participation (p < 0.01) and achieved better results in actual coding tasks (p < 0.05). Students with limited coding experience showed the most significant progress in algorithmic thinking. The findings highlight that digital twin technology significantly enhances engagement and skill acquisition in introductory programming, particularly benefiting novice learners through immersive, theory-aligned experiences. This study establishes a new paradigm for introductory programming education by addressing two critical gaps in digital twin applications: (1) differential effects on students with varying prior knowledge (engagement/skill acquisition) and (2) pedagogical mechanisms in conceptual visualization and authentic context creation. Full article
(This article belongs to the Special Issue Future Trends in Computer Programming Education)
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26 pages, 12914 KB  
Article
Copy/Past: A Hauntological Approach to the Digital Replication of Destroyed Monuments
by Giovanni Lovisetto
Heritage 2025, 8(7), 255; https://doi.org/10.3390/heritage8070255 - 27 Jun 2025
Viewed by 1508
Abstract
This article offers a critical analysis of two ‘replicas’ of monuments destroyed by ISIL in 2015: the Institute for Digital Archaeology’s Arch of Palmyra (2016) and the lamassu from Nimrud, exhibited in the Rinascere dalle Distruzioni exhibition (2016). Drawing on Jacques Derrida’s formulation [...] Read more.
This article offers a critical analysis of two ‘replicas’ of monuments destroyed by ISIL in 2015: the Institute for Digital Archaeology’s Arch of Palmyra (2016) and the lamassu from Nimrud, exhibited in the Rinascere dalle Distruzioni exhibition (2016). Drawing on Jacques Derrida’s formulation of hauntology and Umberto Eco’s theory of forgery, this study examines the ontological, ethical, and ideological stakes of digitally mediated replication. Rather than treating digital and physical ‘copies’ as straightforward reproductions of ancient ‘originals’, the essay reframes them as specters: material re-appearances haunted by loss, technological mediation, and political discourses. Through a close analysis of production methods, rhetorical framings, media coverage, and public reception, it argues that presenting such ‘replicas’ as faithful restorations or acts of cultural resurrection collapses a hauntological relationship into a false ontology. The article thus shows how, by concealing the intermediary, spectral role of digital modeling, such framings enable the symbolic use of these ‘replicas’ as instruments of Western technological triumphalism and digital colonialism. This research calls for a critical approach that recognizes the ontological peculiarities of such replicas, foregrounds their reliance on interpretive rather than purely mechanical processes, and acknowledges the ideological weight they carry. Full article
(This article belongs to the Special Issue Past for the Future: Digital Pathways in Cultural Heritage)
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29 pages, 1299 KB  
Article
Towards Trustworthy Energy Efficient P2P Networks: A New Method for Validating Computing Results in Decentralized Networks
by Fernando Rodríguez-Sela and Borja Bordel
Computers 2025, 14(6), 216; https://doi.org/10.3390/computers14060216 - 2 Jun 2025
Viewed by 774
Abstract
Decentralized P2P networks have emerged as robust instruments to execute computing tasks, with enhanced security and transparency. Solutions such as Blockchain have proved to be successful in a large catalog of critical applications such as cryptocurrency, intellectual property, etc. However, although executions are [...] Read more.
Decentralized P2P networks have emerged as robust instruments to execute computing tasks, with enhanced security and transparency. Solutions such as Blockchain have proved to be successful in a large catalog of critical applications such as cryptocurrency, intellectual property, etc. However, although executions are transparent and P2P are resistant against common cyberattacks, they tend to be untrustworthy. P2P nodes typically do not offer any evidence about the quality of their resolution of the delegated computing tasks, so trustworthiness of results is threatened. To mitigate this challenge, in usual P2P networks, many different replicas of the same computing task are delegated to different nodes. The final result is the one most nodes reached. But this approach is very resource consuming, especially in terms of energy, as many unnecessary computing tasks are executed. Therefore, new solutions to achieve trustworthy P2P networks, but with an energy efficiency perspective, are needed. This study addresses this challenge. The purpose of the research is to evaluate the effectiveness of an audit-based and score-based approach is assigned to each node instead of performing identical tasks redundantly on different nodes in the network. The proposed solution employs probabilistic methods to detect the malicious nodes taking into account parameters like number of executed tasks and number of audited ones giving a value to the node, and game theory which consider that all nodes play with the same rules. Qualitative and quantitative experimental methods are used to evaluate its impact. The results reveal a significant reduction in network energy consumption, minimum a 50% comparing to networks in which each task is delivered to different nodes considering the task is delivered to a pair of nodes, supporting the effectiveness of the proposed approach. Full article
(This article belongs to the Section Blockchain Infrastructures and Enabled Applications)
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20 pages, 824 KB  
Communication
Oxidation Potential of 2,6-Dimethyl-1,4-dihydropyridine Derivatives Estimated by Structure Descriptors
by Lorentz Jäntschi
Symmetry 2024, 16(10), 1320; https://doi.org/10.3390/sym16101320 - 7 Oct 2024
Viewed by 2001
Abstract
Linear relationships, expressing the electrochemical properties of molecules as functions of structure, give insight into the associated electrochemical process and are a tool for prediction. Many biological activities rely on water-based dissociation, making electrochemical properties a bridge between structure and activity. Motivated by [...] Read more.
Linear relationships, expressing the electrochemical properties of molecules as functions of structure, give insight into the associated electrochemical process and are a tool for prediction. Many biological activities rely on water-based dissociation, making electrochemical properties a bridge between structure and activity. Motivated by a previous study, a replica is made here on a different dataset in order to validate/invalidate the previously reported results. There are several methods for obtaining structure-based descriptors. Some of the methods have been devised to account for molecular topology, some to account for molecular geometry, and others to account for both. Two methods are involved here to derive structure-based descriptors and further obtain structure–property relationships (FMPI and ChPE). In order to express structure descriptors, both FMPI and ChPE express first the topology of the molecule, using the heavy atoms identity matrix and the heavy atoms adjacency matrix, both square symmetric matrices in the belief that symmetry is one major factor of molecular stability. A set of 2,6-dimethyl-1,4-dihydropyridine derivatives with oxidation peak potentials and coulometrically determined number of electrons experimental data is subjected to the search for structure–activity relationships. Even if the 2,6-dimethyl-1,4-dihydropyridine is a symmetric compound (of Cs point group), their derivatives are generally not symmetric (9 out of 24 are asymmetric). The dataset is subjected to descriptive and inferential statistics in order to filter out the most relevant structure–activity relationship. The geometry is built using three levels of theory (one from molecular mechanics and two others from density functionals, of which one accounts for the interaction with water as solvent). One challenge of picking one out of two reported measured values is dealt with by calculating the likelihood associated with the two choices. Relevant structure–activity models are extracted and discussed. The use of in vivo (in water, SM8 model) models in geometry optimization (from MMFF94 and B3LYP and to M06 + Water SM8) results in a precision gain, but this is, in most of the cases, not statistically significant, and this can be considered a negative result. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry of Molecules Related to Biological Activity)
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17 pages, 953 KB  
Article
From Sensory Experience to Revisit Intentions: An Embodied Cognition Perspective on Replica Tourism
by Yang Liu and Kazumitsu Minamikawa
Sustainability 2024, 16(18), 8030; https://doi.org/10.3390/su16188030 - 13 Sep 2024
Cited by 3 | Viewed by 4572
Abstract
This study explores the impact of sensory experiences on tourists’ experiences at replica destinations, aiming to clarify the intrinsic influence mechanisms between sensory experiences, perceived authenticity, well-being, and the intention to revisit. Utilizing embodied cognition theory, this study empirically tested its application through [...] Read more.
This study explores the impact of sensory experiences on tourists’ experiences at replica destinations, aiming to clarify the intrinsic influence mechanisms between sensory experiences, perceived authenticity, well-being, and the intention to revisit. Utilizing embodied cognition theory, this study empirically tested its application through data collected via an online survey of tourists who visited a well-known replica destination, Window of the World in Shenzhen, within three months prior to completing the survey. The findings reveal that tourists’ sensory experiences, except for smell and taste, are directly related to the intention to revisit. Positive sensory experiences influence perceived authenticity and well-being, subsequently leading to an increased intention to revisit. By providing empirical evidence on tourists’ sensory experiences at replica destinations in different cultural contexts, this study enriches the existing body of research and broadens the scope of replica tourism studies. In addition, an increasing number of replica tourism destinations play an important role in protecting traditional tourist destinations, especially historical sites. This study provides valuable insights for the future development of replica tourism destinations in promoting sustainable tourism. At the same time, this study extends the application of embodied cognition theory to replica tourism, contributing to theoretical development and offering new insights into the role of sensory experiences in shaping tourist behavior. Full article
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16 pages, 5675 KB  
Article
Development of Replica Molding Processes for Hypervariable Microstructural Components
by Yung-Jin Weng, Yu-Zhe Gao and Yu-Ming Chen
Processes 2024, 12(9), 1968; https://doi.org/10.3390/pr12091968 - 13 Sep 2024
Cited by 1 | Viewed by 3653
Abstract
The current study investigates the development of a replica molding process for hypervariable microstructures. Initially, the mold deformation theory for these hypervariable microstructures was derived. Based on this theory, a metal material with magnetic properties was selected as the structural material to create [...] Read more.
The current study investigates the development of a replica molding process for hypervariable microstructures. Initially, the mold deformation theory for these hypervariable microstructures was derived. Based on this theory, a metal material with magnetic properties was selected as the structural material to create a negative Poisson’s ratio (NPR) geometric structure. The experimental results, obtained by fabricating the NPR geometric mold layer with a metal material with adjustable magnetic properties and controlling microstructure deformation indirectly, validate the deformation theory and its predictions. These results demonstrate that the developed molding process, integrated with the magnetic NPR regulation system, exhibits excellent stability and replication capability. In this study, at the zero height (z = 0) position on the interface between the NPR geometric structure layer and the Polydimethylsiloxane (PDMS), the variation becomes more pronounced with increasing distance from the center of the microstructure. Furthermore, the tendency of the function curve varies accordingly. The primary cause is the lack of constraints on the free ends of both sides and the excessive constraints on the intermediate parts. Under the conditions in this study, the maximum ratio of its influence on the radial diameter thickness was 2.1%. This innovative process facilitates the rapid imprinting of microstructural components and offers the advantage of efficient molding. Full article
(This article belongs to the Special Issue Low-Carbon Design and Manufacturing Processes)
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18 pages, 934 KB  
Article
Hilbert Space Delocalization under Random Unitary Circuits
by Xhek Turkeshi and Piotr Sierant
Entropy 2024, 26(6), 471; https://doi.org/10.3390/e26060471 - 29 May 2024
Cited by 12 | Viewed by 1761
Abstract
The unitary dynamics of a quantum system initialized in a selected basis state yield, generically, a state that is a superposition of all the basis states. This process, associated with the quantum information scrambling and intimately tied to the resource theory of coherence, [...] Read more.
The unitary dynamics of a quantum system initialized in a selected basis state yield, generically, a state that is a superposition of all the basis states. This process, associated with the quantum information scrambling and intimately tied to the resource theory of coherence, may be viewed as a gradual delocalization of the system’s state in the Hilbert space. This work analyzes the Hilbert space delocalization under the dynamics of random quantum circuits, which serve as a minimal model of the chaotic dynamics of quantum many-body systems. We employ analytical methods based on the replica trick and Weingarten calculus to investigate the time evolution of the participation entropies which quantify the Hilbert space delocalization. We demonstrate that the participation entropies approach, up to a fixed accuracy, their long-time saturation value in times that scale logarithmically with the system size. Exact numerical simulations and tensor network techniques corroborate our findings. Full article
(This article belongs to the Section Quantum Information)
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30 pages, 879 KB  
Article
Replica Field Theory for a Generalized Franz–Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation
by Hiroshi Frusawa
Entropy 2024, 26(3), 241; https://doi.org/10.3390/e26030241 - 8 Mar 2024
Cited by 1 | Viewed by 1983
Abstract
On approaching the dynamical transition temperature, supercooled liquids show heterogeneity over space and time. Static replica theory investigates the dynamical crossover in terms of the free energy landscape (FEL). Two kinds of static approaches have provided a self-consistent equation for determining this crossover, [...] Read more.
On approaching the dynamical transition temperature, supercooled liquids show heterogeneity over space and time. Static replica theory investigates the dynamical crossover in terms of the free energy landscape (FEL). Two kinds of static approaches have provided a self-consistent equation for determining this crossover, similar to the mode coupling theory for glassy dynamics. One uses the Morita–Hiroike formalism of the liquid state theory, whereas the other relies on the density functional theory (DFT). Each of the two approaches has advantages in terms of perturbative field theory. Here, we develop a replica field theory that has the benefits from both formulations. We introduce the generalized Franz–Parisi potential to formulate a correlation functional. Considering fluctuations around an inhomogeneous density determined by the Ramakrishnan–Yussouf DFT, we find a new closure as the stability condition of the correlation functional. The closure leads to the self-consistent equation involving the triplet direct correlation function. The present field theory further helps us study the FEL beyond the mean-field approximation. Full article
(This article belongs to the Section Statistical Physics)
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25 pages, 622 KB  
Article
On Minimal Entanglement Wedge Cross Section for Holographic Entanglement Negativity
by Jaydeep Kumar Basak, Vinay Malvimat, Himanshu Parihar, Boudhayan Paul and Gautam Sengupta
Universe 2024, 10(3), 125; https://doi.org/10.3390/universe10030125 - 5 Mar 2024
Cited by 35 | Viewed by 2154
Abstract
We demonstrate the equivalence of two different conjectures in the literature for the holographic entanglement negativity in AdS3/CFT2, modulo certain constants. These proposals involve certain algebraic sums of bulk geodesics homologous to specific combinations of subsystems, and the entanglement [...] Read more.
We demonstrate the equivalence of two different conjectures in the literature for the holographic entanglement negativity in AdS3/CFT2, modulo certain constants. These proposals involve certain algebraic sums of bulk geodesics homologous to specific combinations of subsystems, and the entanglement wedge cross section (EWCS) backreacted by a cosmic brane for the conical defect geometry in the bulk gravitational path integral. It is observed that the former conjectures reproduce the field theory replica technique results in the large central charge limit whereas the latter involves constants related to the Markov gap. In this context, we establish an alternative construction for the EWCS of a single interval in a CFT2 at a finite temperature to resolve an issue for the latter proposal involving thermal entropy elimination for holographic entanglement negativity. Our construction for the EWCS correctly reproduces the corresponding field theory results modulo the Markov gap constant in the large central charge limit. Full article
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21 pages, 3122 KB  
Review
Multiscale Methods Framework with the 3D-RISM-KH Molecular Solvation Theory for Supramolecular Structures, Nanomaterials, and Biomolecules: Where Are We Going?
by Dipankar Roy and Andriy Kovalenko
Thermo 2023, 3(3), 375-395; https://doi.org/10.3390/thermo3030023 - 2 Jul 2023
Cited by 3 | Viewed by 3593
Abstract
3D-RISM-KH molecular solvation theory based on statistical mechanics has been an engine of the multiscale methods framework, which also includes molecular simulation techniques. Its applications range from the solvation energy of small molecules to the phase behavior of polymers and biomolecules. Molecular solvation [...] Read more.
3D-RISM-KH molecular solvation theory based on statistical mechanics has been an engine of the multiscale methods framework, which also includes molecular simulation techniques. Its applications range from the solvation energy of small molecules to the phase behavior of polymers and biomolecules. Molecular solvation theory predicts and explains the molecular mechanisms and functioning of a variety of chemical and biomolecular systems. This includes the self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), the aggregation of peptides and proteins related to neurodegeneration, the binding of ligands to proteins, and the solvation properties of biomolecules related to their functions. The replica RISM-KH-VM molecular solvation theory predicts and explains the structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous carbon supercapacitor electrodes, and is part of recent research and development efforts. A new quasidynamics protocol couples multiple time step molecular dynamics (MTS-MD) stabilized with an optimized isokinetic Nosé–Hoover (OIN) thermostat driven by 3D-RISM-KH mean solvation forces at gigantic outer time steps of picoseconds, which are extrapolated forward at short inner time steps of femtoseconds with generalized solvation force extrapolation (GSFE). The OIN/3D-RISM-KH/GSFE quasidynamics is implemented in the Amber Molecular Dynamics package. It is validated on miniprotein 1L2Y and protein G in ambient aqueous solution, and shows the rate of sampling 150 times faster than in standard MD simulations on these biomolecules in explicit water. The self-consistent field version of Kohn–Sham DFT in 3D-RISM-KH mean solvation forces is implemented in the Amsterdam Density Functional (ADF) package. Its applications range from solvation thermochemistry, conformational equilibria, and photochemistry to activation barriers of different nanosystems in solutions and ionic liquids. Full article
(This article belongs to the Special Issue Feature Papers of Thermo in 2023)
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26 pages, 488 KB  
Article
Synchronizing Many Filesystems in Near Linear Time
by Elod P. Csirmaz and Laszlo Csirmaz
Future Internet 2023, 15(6), 198; https://doi.org/10.3390/fi15060198 - 30 May 2023
Cited by 2 | Viewed by 2544
Abstract
Finding a provably correct subquadratic synchronization algorithm for many filesystem replicas is one of the main theoretical problems in operational transformation (OT) and conflict-free replicated data types (CRDT) frameworks. Based on the algebraic theory of filesystems, which incorporates non-commutative filesystem commands natively, we [...] Read more.
Finding a provably correct subquadratic synchronization algorithm for many filesystem replicas is one of the main theoretical problems in operational transformation (OT) and conflict-free replicated data types (CRDT) frameworks. Based on the algebraic theory of filesystems, which incorporates non-commutative filesystem commands natively, we developed and built a proof-of-concept implementation of an algorithm suite which synchronizes an arbitrary number of replicas. The result is provably correct, and the synchronized system is created in linear space and time after an initial sorting phase. It works by identifying conflicting command pairs and requesting one of the commands to be removed. The method can be guided to reach any of the theoretically possible synchronized states. The algorithm also allows asynchronous usage. After the client sends a synchronization request, the local replica remains available for further modifications. When the synchronization instructions arrive, they can be merged with the changes made since the synchronization request. The suite also works on filesystems with a directed acyclic graph-based path structure in place of the traditional tree-like arrangement. Consequently, our algorithms apply to filesystems with hard or soft links as long as the links create no loops. Full article
(This article belongs to the Special Issue Software Engineering and Data Science II)
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25 pages, 9385 KB  
Article
Functionality Versus Sustainability for PLA in MEX 3D Printing: The Impact of Generic Process Control Factors on Flexural Response and Energy Efficiency
by Markos Petousis, Nectarios Vidakis, Nikolaos Mountakis, Emmanuel Karapidakis and Amalia Moutsopoulou
Polymers 2023, 15(5), 1232; https://doi.org/10.3390/polym15051232 - 28 Feb 2023
Cited by 53 | Viewed by 3709
Abstract
Process sustainability vs. mechanical strength is a strong market-driven claim in Material Extrusion (MEX) Additive Manufacturing (AM). Especially for the most popular polymer, Polylactic Acid (PLA), the concurrent achievement of these opposing goals may become a puzzle, especially since MEX 3D-printing offers a [...] Read more.
Process sustainability vs. mechanical strength is a strong market-driven claim in Material Extrusion (MEX) Additive Manufacturing (AM). Especially for the most popular polymer, Polylactic Acid (PLA), the concurrent achievement of these opposing goals may become a puzzle, especially since MEX 3D-printing offers a variety of process parameters. Herein, multi-objective optimization of material deployment, 3D printing flexural response, and energy consumption in MEX AM with PLA is introduced. To evaluate the impact of the most important generic and device-independent control parameters on these responses, the Robust Design theory was employed. Raster Deposition Angle (RDA), Layer Thickness (LT), Infill Density (ID), Nozzle Temperature (NT), Bed Temperature (BT), and Printing Speed (PS) were selected to compile a five-level orthogonal array. A total of 25 experimental runs with five specimen replicas each accumulated 135 experiments. Analysis of variances and reduced quadratic regression models (RQRM) were used to decompose the impact of each parameter on the responses. The ID, RDA, and LT were ranked first in impact on printing time, material weight, flexural strength, and energy consumption, respectively. The RQRM predictive models were experimentally validated and hold significant technological merit, for the proper adjustment of process control parameters per the MEX 3D-printing case. Full article
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13 pages, 893 KB  
Article
Entanglement Renyi Entropy of Two Disjoint Intervals for Large c Liouville Field Theory
by Jun Tsujimura and Yasusada Nambu
Entropy 2022, 24(12), 1758; https://doi.org/10.3390/e24121758 - 30 Nov 2022
Viewed by 1687
Abstract
Entanglement entropy (EE) is a quantitative measure of the effective degrees of freedom and the correlation between the sub-systems of a physical system. Using the replica trick, we can obtain the EE by evaluating the entanglement Renyi entropy (ERE). The ERE is a [...] Read more.
Entanglement entropy (EE) is a quantitative measure of the effective degrees of freedom and the correlation between the sub-systems of a physical system. Using the replica trick, we can obtain the EE by evaluating the entanglement Renyi entropy (ERE). The ERE is a q-analogue of the EE and expressed by the q replicated partition function. In the semi-classical approximation, it is apparently easy to calculate the EE because the classical action represents the partition function by the saddle point approximation and we do not need to perform the path integral for the evaluation of the partition function. In previous studies, it has been assumed that only the minimal-valued saddle point contributes to the EE. In this paper, we propose that all the saddle points contribute comparably but not necessarily equally to the EE by dealing carefully with the semi-classical limit and then the q1 limit. For example, we numerically evaluate the ERE of two disjoint intervals for the large c Liouville field theory with q1. We exploit the BPZ equation with the four twist operators, whose solution is given by the Heun function. We determine the ERE by tuning the behavior of the Heun function such that it becomes consistent with the geometry of the replica manifold. We find the same two saddle points as previous studies for q1 in the above system. Then, we provide the ERE for the large but finite c and the q1 in case that all the saddle points contribute comparably to the ERE. In particular, the ERE is the summation of these two saddle points by the same weight, due to the symmetry of the system. Based on this work, it shall be of interest to reconsider EE in other semi-classical physical systems with multiple saddle points. Full article
(This article belongs to the Section Astrophysics, Cosmology, and Black Holes)
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