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Keywords = non-perturbative corrections

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17 pages, 1194 KB  
Article
Impact of Induced Forward Leg Movements on Kinematics and Kinetics During Quiet Standing in Healthy Young Right-Leg-Dominant Women: A Quasi-Experimental Study
by Michalina Gulatowska, Michalina Błażkiewicz, Anatolii Tsos and Jacek Wąsik
Appl. Sci. 2025, 15(19), 10764; https://doi.org/10.3390/app151910764 - 6 Oct 2025
Viewed by 281
Abstract
Background: Postural control in healthy young adults involves complex neuromuscular processes; however, the kinematic and kinetic consequences of small, forward leg perturbations in a defined population are not fully described. This study aimed to characterize the kinematic and kinetic consequences of forward leg [...] Read more.
Background: Postural control in healthy young adults involves complex neuromuscular processes; however, the kinematic and kinetic consequences of small, forward leg perturbations in a defined population are not fully described. This study aimed to characterize the kinematic and kinetic consequences of forward leg perturbations during quiet standing. Methods: This investigation used a quasi-experimental repeated-measures design. Sixteen healthy young women (20.1 ± 0.7 years), all right-leg dominant, were tested using the Gait Real-Time Analysis Interactive Laboratory (GRAIL) system. Forward treadmill perturbations were applied to each limb during quiet standing, and joint angles, ground reaction forces, and torques were measured across baseline, perturbation, and response phases. As the data were non-normally distributed, paired comparisons were conducted using the Wilcoxon test, with significance set at p < 0.05 (Bonferroni corrected) and effect sizes (r) reported. Results: Joint angles remained symmetrical between limbs (no significant differences after correction). In contrast, kinetic measures showed clear asymmetries: at baseline, the dominant limb produced greater knee torque (p = 0.0003, r = 0.73), ankle torque (p = 0.0003, r = 0.76), and medio-lateral GRF (p = 0.0003, r = 0.87). During perturbation, it again generated higher knee (p = 0.0036, r = 0.43) and ankle torques (p = 0.0003, r = 0.53), with larger medio-lateral GRF (p = 0.0003, r = 0.87). In the response phase, the dominant limb showed greater hip torque (p = 0.0033, r = 0.43) and a small dorsiflexion shift at the ankle (p = 0.0066, r = 0.41). Anterior–posterior GRF changes were minor and non-significant after correction. Conclusions: Induced forward leg movements caused limb-specific kinetic adjustments while maintaining overall kinematic symmetry. The dominant leg contributed more actively to balance recovery, highlighting its role in stabilizing posture under small perturbations. These findings are specific to the studied demographic and should not be generalized to males, older adults, left-dominant individuals, or clinical populations without further research. Full article
(This article belongs to the Special Issue Applied Biomechanics: Sports Performance and Rehabilitation)
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18 pages, 3973 KB  
Article
Identification and Characterization of Static Craniofacial Defects in Pre-Metamorphic Xenopus laevis Tadpoles
by Emilie Jones, Jay Miguel Fonticella and Kelly A. McLaughlin
J. Dev. Biol. 2025, 13(3), 26; https://doi.org/10.3390/jdb13030026 - 25 Jul 2025
Viewed by 1025
Abstract
Craniofacial development is a complex, highly conserved process involving multiple tissue types and molecular pathways, with perturbations resulting in congenital defects that often require invasive surgical interventions to correct. Remarkably, some species, such as Xenopus laevis, can correct some craniofacial abnormalities during [...] Read more.
Craniofacial development is a complex, highly conserved process involving multiple tissue types and molecular pathways, with perturbations resulting in congenital defects that often require invasive surgical interventions to correct. Remarkably, some species, such as Xenopus laevis, can correct some craniofacial abnormalities during pre-metamorphic stages through thyroid hormone-independent mechanisms. However, the full scope of factors mediating remodeling initiation and coordination remain unclear. This study explores the differential remodeling responses of craniofacial defects by comparing the effects of two pharmacological agents, thioridazine-hydrochloride (thio) and ivermectin (IVM), on craniofacial morphology in X. laevis. Thio-exposure reliably induces a craniofacial defect that can remodel in pre-metamorphic animals, while IVM induces a permanent, non-correcting phenotype. We examined developmental changes from feeding stages to hindlimb bud stages and mapped the effects of each agent on the patterning of craniofacial tissue types including: cartilage, muscle, and nerves. Our findings reveal that thio-induced craniofacial defects exhibit significant consistent remodeling, particularly in muscle, with gene expression analysis revealing upregulation of key remodeling genes, matrix metalloproteinases 1 and 13, as well as their regulator, prolactin.2. In contrast, IVM-induced defects show no significant remodeling, highlighting the importance of specific molecular and cellular factors in pre-metamorphic craniofacial correction. Additionally, unique neuronal profiles suggest a previously underappreciated role for the nervous system in tissue remodeling. This study provides novel insights into the molecular and cellular mechanisms underlying craniofacial defect remodeling and lays the groundwork for future investigations into tissue repair in vertebrates. Full article
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14 pages, 281 KB  
Article
Leading Logarithm Quantum Gravity
by S. P. Miao, N. C. Tsamis and R. P. Woodard
Universe 2025, 11(7), 223; https://doi.org/10.3390/universe11070223 - 4 Jul 2025
Cited by 10 | Viewed by 383
Abstract
The continual production of long wavelength gravitons during primordial inflation endows graviton loop corrections with secular growth factors. During a prolonged period of inflation, these factors eventually overwhelm the small loop-counting parameter of GH2, causing perturbation theory to break down. [...] Read more.
The continual production of long wavelength gravitons during primordial inflation endows graviton loop corrections with secular growth factors. During a prolonged period of inflation, these factors eventually overwhelm the small loop-counting parameter of GH2, causing perturbation theory to break down. A technique was recently developed for summing the leading secular effects at each order in non-linear sigma models, which possess the same kind of derivative interactions as gravity. This technique combines a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. Generalizing the technique to quantum gravity is a two-step process, the first of which is the determination of the gauge fixing condition that will allow this summation to be realized; this is the subject of this paper. Moreover, we briefly discuss the second step, which shall obtain the Langevin equation, in which secular changes in gravitational phenomena are driven by stochastic fluctuations of the graviton field. Full article
13 pages, 1632 KB  
Article
Cosmological Simulations with Massive Neutrinos: Efficiency and Accuracy
by Bing-Hang Chen, Jun-Jie Zhao, Hao-Ran Yu, Yu Liu, Jian-Hua He and Yipeng Jing
Universe 2025, 11(7), 212; https://doi.org/10.3390/universe11070212 - 26 Jun 2025
Viewed by 529
Abstract
Constraining neutrino mass through cosmological observations relies on precise simulations to calibrate their effects on large scale structure, while these simulations must overcome computational challenges like dealing with large velocity dispersions and small intrinsic neutrino perturbations. We present an efficient N-body implementation [...] Read more.
Constraining neutrino mass through cosmological observations relies on precise simulations to calibrate their effects on large scale structure, while these simulations must overcome computational challenges like dealing with large velocity dispersions and small intrinsic neutrino perturbations. We present an efficient N-body implementation with semi-linear neutrino mass response which gives accurate power spectra and halo statistics. We explore the necessity of correcting the expansion history caused by massive neutrinos and the transition between relativistic and non-relativistic components. The above method of including neutrino masses is built into the memory-, scalability-, and precision-optimized parallel N-body simulation code CUBE 2.0. Through a suite of neutrino simulations, we precisely quantify the neutrino mass effects on the nonlinear matter power spectra and halo statistics. Full article
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26 pages, 3938 KB  
Article
Multifractal Carbon Market Price Forecasting with Memory-Guided Adversarial Network
by Na Li, Mingzhu Tang, Jingwen Deng, Liran Wei and Xinpeng Zhou
Fractal Fract. 2025, 9(7), 403; https://doi.org/10.3390/fractalfract9070403 - 23 Jun 2025
Viewed by 729
Abstract
Carbon market price prediction is critical for stabilizing markets and advancing low-carbon transitions, where capturing multifractal dynamics is essential. Traditional models often neglect the inherent long-term memory and nonlinear dependencies of carbon price series. To tackle the issues of nonlinear dynamics, non-stationary characteristics, [...] Read more.
Carbon market price prediction is critical for stabilizing markets and advancing low-carbon transitions, where capturing multifractal dynamics is essential. Traditional models often neglect the inherent long-term memory and nonlinear dependencies of carbon price series. To tackle the issues of nonlinear dynamics, non-stationary characteristics, and inadequate suppression of modal aliasing in existing models, this study proposes an integrated prediction framework based on the coupling of gradient-sensitive time-series adversarial training and dynamic residual correction. A novel gradient significance-driven local adversarial training strategy enhances immunity to volatility through time step-specific perturbations while preserving structural integrity. The GSLAN-BiLSTM architecture dynamically recalibrates historical–current information fusion via memory-guided attention gating, mitigating prediction lag during abrupt price shifts. A “decomposition–prediction–correction” residual compensation system further decomposes base model errors via wavelet packet decomposition (WPD), with ARIMA-driven dynamic weighting enabling bias correction. Empirical validation using China’s carbon market high-frequency data demonstrates superior performance across key metrics. This framework extends beyond advancing carbon price forecasting by successfully generalizing its “multiscale decomposition, adversarial robustness enhancement, and residual dynamic compensation” paradigm to complex financial time-series prediction. Full article
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19 pages, 22225 KB  
Article
Integrated Correction of Nonlinear Dynamic Drift in Terrestrial Mobile Gravity Surveys: A Comparative Study Based on the Northeastern China Gravity Monitoring Network
by Zhaohui Chen and Jinzhao Liu
Remote Sens. 2025, 17(12), 2025; https://doi.org/10.3390/rs17122025 - 12 Jun 2025
Viewed by 694
Abstract
The Northeastern China Gravity Monitoring Network (NCGMN; 40–50°N), a pioneering time-variable gravity monitoring system in high-latitude cold-temperate environments, serves as a critical infrastructure for geodynamic investigations of the Songliao Basin, Changbai Mountain volcanic zone, and northern Tan-Lu Fault Zone. To address the data [...] Read more.
The Northeastern China Gravity Monitoring Network (NCGMN; 40–50°N), a pioneering time-variable gravity monitoring system in high-latitude cold-temperate environments, serves as a critical infrastructure for geodynamic investigations of the Songliao Basin, Changbai Mountain volcanic zone, and northern Tan-Lu Fault Zone. To address the data reliability challenges posed by nonlinear dynamic drifts in spring-type relative gravimeters during mobile surveys, this study quantifies—for the first time—the non-smooth normal distribution characteristics of such drifts using the inaugural 2015 dataset from two CG-5 instruments. Results demonstrate a 7–15% reduction in mean dynamic drift rates compared to static conditions, with spatiotemporal variability governed by multi-physics field coupling (terrain undulation, thermal fluctuation, and barometric perturbation). A comprehensive correction framework—integrating a gravimetric line drift rate computation, multi-model validation, and absolute datum cross-validation—reveals gravity value discrepancies up to ±10 μGal across models. The innovative hybrid scheme combines local drift preprocessing (initial-point modeling, line fitting, variance-sum optimization) with global adjustment optimization, achieving the significant suppression of nonlinear drift errors. The variance-sum optimal and Bayesian adjustment hybrid synergizes local variance minimization and global temporal correlation priors, delivering the following: (1) 34% and 29% reductions in segment self-difference standard deviations versus classical and Bayesian adjustments; (2) 24% and 14% decreases in segment residual standard deviations; (3) 12% and 6% improvements in absolute datum cross-validation precision. This study establishes a foundation for the reliable extraction of μGal-level gravity signals, advancing high-precision gravity monitoring of seismicity, volcanic unrest, and fault zone deformation in complex terrains. By harmonizing local-scale accuracy with network-wide consistency, the framework sets a new benchmark for time-variable gravity studies in challenging environments. Full article
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17 pages, 4951 KB  
Article
A 3-D Defect Profile Inversion Method Based on the Continuity Correction Strategy
by Chenlin Wang, Jianhua Tang, Yicheng Duan, Senxiang Lu and Hao Wen
Machines 2025, 13(6), 446; https://doi.org/10.3390/machines13060446 - 23 May 2025
Viewed by 544
Abstract
Magnetic flux leakage (MFL) detection is widely used in the non-destructive testing of pipelines. Inversion is a key step in MFL detection, and iterative inversion based on an optimization algorithm is an effective method for constructing the 3-D profile of defects in pipelines. [...] Read more.
Magnetic flux leakage (MFL) detection is widely used in the non-destructive testing of pipelines. Inversion is a key step in MFL detection, and iterative inversion based on an optimization algorithm is an effective method for constructing the 3-D profile of defects in pipelines. However, conventional inversion algorithms suffer from weak convergence ability and are prone to local optima, which can lead to significant errors in the results. To improve the algorithm’s convergence and result accuracy, this paper proposes a “continuity correction” strategy based on geometric features of defects, which examines the relative depth value of each depth point and corrects the values of implausible points. On this basis, this paper combines the secretary bird optimization algorithm (SBOA) with the differential evolution strategy and the perturbation strategy to enhance the search capability. Through an accuracy experiment and a robustness experiment on an experimental platform, it is demonstrated that the method outperforms conventional algorithms in terms of accuracy and robustness against interference when constructing the 3-D profile of defects. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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17 pages, 18705 KB  
Article
A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory
by Meng Wang and Chenyang Li
Molecules 2025, 30(9), 2082; https://doi.org/10.3390/molecules30092082 - 7 May 2025
Cited by 1 | Viewed by 745
Abstract
We present an economical approach to treat spin–orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian is then augmented with the Breit–Pauli Hamiltonian [...] Read more.
We present an economical approach to treat spin–orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian is then augmented with the Breit–Pauli Hamiltonian and diagonalized using spin-pure reference states to obtain the SOC-corrected energy spectrum. The spin–orbit mean-field approximation is also assumed to reduce the cost associated with the two-electron spin–orbit integrals. The resulting method is termed BP1-SA-DSRG-PT2c, and it possesses the same computational scaling as the non-relativistic counterpart, where only the one- and two-body density cumulants are required to obtain the vertical transition energy. The accuracy of BP1-SA-DSRG-PT2c is assessed on a few atoms and small molecules, including main-group diatomic molecules, transition-metal atoms, and actinide dioxide cations. Numerical results suggest that BP1-SA-DSRG-PT2c performs comparably to other internally contracted multireference perturbation theories with SOC treated using the state interaction scheme. Full article
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24 pages, 14371 KB  
Article
An Enhanced Transportation System for People of Determination
by Uma Perumal, Fathe Jeribi and Mohammed Hameed Alhameed
Sensors 2024, 24(19), 6411; https://doi.org/10.3390/s24196411 - 3 Oct 2024
Cited by 5 | Viewed by 1489
Abstract
Visually Impaired Persons (VIPs) have difficulty in recognizing vehicles used for navigation. Additionally, they may not be able to identify the bus to their desired destination. However, the bus bay in which the designated bus stops has not been analyzed in the existing [...] Read more.
Visually Impaired Persons (VIPs) have difficulty in recognizing vehicles used for navigation. Additionally, they may not be able to identify the bus to their desired destination. However, the bus bay in which the designated bus stops has not been analyzed in the existing literature. Thus, a guidance system for VIPs that identifies the correct bus for transportation is presented in this paper. Initially, speech data indicating the VIP’s destination are pre-processed and converted to text. Next, utilizing the Arctan Gradient-activated Recurrent Neural Network (ArcGRNN) model, the number of bays at the location is detected with the help of a Global Positioning System (GPS), input text, and bay location details. Then, the optimal bay is chosen from the detected bays by utilizing the Experienced Perturbed Bacteria Foraging Triangular Optimization Algorithm (EPBFTOA), and an image of the selected bay is captured and pre-processed. Next, the bus is identified utilizing a You Only Look Once (YOLO) series model. Utilizing the Sub-pixel Shuffling Convoluted Encoder–ArcGRNN Decoder (SSCEAD) framework, the text is detected and segmented for the buses identified in the image. From the segmented output, the text is extracted, based on the destination and route of the bus. Finally, regarding the similarity value with respect to the VIP’s destination, a decision is made utilizing the Multi-characteristic Non-linear S-Curve-Fuzzy Rule (MNC-FR). This decision informs the bus conductor about the VIP, such that the bus can be stopped appropriately to pick them up. During testing, the proposed system selected the optimal bay in 247,891 ms, which led to deciding the bus stop for the VIP with a fuzzification time of 34,197 ms. Thus, the proposed model exhibits superior performance over those utilized in prevailing works. Full article
(This article belongs to the Section Intelligent Sensors)
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22 pages, 3190 KB  
Article
Sustainable Impact of Stance Attribution Design Cues for Robots on Human–Robot Relationships—Evidence from the ERSP
by Dong Lv, Rui Sun, Qiuhua Zhu, Jiajia Zuo and Shukun Qin
Sustainability 2024, 16(17), 7252; https://doi.org/10.3390/su16177252 - 23 Aug 2024
Cited by 1 | Viewed by 1469
Abstract
With the development of large language model technologies, the capability of social robots to interact emotionally with users has been steadily increasing. However, the existing research insufficiently examines the influence of robot stance attribution design cues on the construction of users’ mental models [...] Read more.
With the development of large language model technologies, the capability of social robots to interact emotionally with users has been steadily increasing. However, the existing research insufficiently examines the influence of robot stance attribution design cues on the construction of users’ mental models and their effects on human–robot interaction (HRI). This study innovatively combines mental models with the associative–propositional evaluation (APE) model, unveiling the impact of the stance attribution explanations of this design cue on the construction of user mental models and the interaction between the two types of mental models through EEG experiments and survey investigations. The results found that under the influence of intentional stance explanations (compared to design stance explanations), participants displayed higher error rates, higher θ- and β-band Event-Related Spectral Perturbations (ERSPs), and phase-locking value (PLV). Intentional stance explanations trigger a primarily associatively based mental model of users towards robots, which conflicts with the propositionally based mental models of individuals. Users might adjust or “correct” their immediate reactions caused by stance attribution explanations after logical analysis. This study reveals that stance attribution interpretation can significantly affect users’ mental model construction of robots, which provides a new theoretical framework for exploring human interaction with non-human agents and provides theoretical support for the sustainable development of human–robot relations. It also provides new ideas for designing robots that are more humane and can better interact with human users. Full article
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15 pages, 11142 KB  
Article
Inertial Methodology for the Monitoring of Structures in Motion Caused by Seismic Vibrations
by Julio C. Rodríguez-Quiñonez, Jorge Alejandro Valdez-Rodríguez, Moises J. Castro-Toscano, Wendy Flores-Fuentes and Oleg Sergiyenko
Infrastructures 2024, 9(7), 116; https://doi.org/10.3390/infrastructures9070116 - 19 Jul 2024
Cited by 1 | Viewed by 1839
Abstract
This paper presents a non-invasive methodology for structural health monitoring (SHM) integrated with inertial sensors and signal conditioning techniques. The proposal uses the signal of an IMU (inertial measurement unit) tri-axial accelerometer and gyroscope to continuously measure the displacements of a structure in [...] Read more.
This paper presents a non-invasive methodology for structural health monitoring (SHM) integrated with inertial sensors and signal conditioning techniques. The proposal uses the signal of an IMU (inertial measurement unit) tri-axial accelerometer and gyroscope to continuously measure the displacements of a structure in motion due to seismic vibrations. A system, called the “Inertial Displacement Monitoring System” or “IDMS”, is implemented to attenuate the signal error of the IMU with methodologies such as a Kalman filter to diminish the influence of white noise, a Chebyshev filter to isolate the frequency values of a seismic motion, and a correction algorithm called zero velocity observation update (ZVOB) to detect seismic vibrations and diminish the influence of external perturbances. As a result, the IDMS is a methodology developed to measure displacements when a structure is in motion due to seismic vibration and provides information to detect failures opportunely. Full article
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30 pages, 2160 KB  
Article
Isospin QCD as a Laboratory for Dense QCD
by Toru Kojo, Daiki Suenaga and Ryuji Chiba
Universe 2024, 10(7), 293; https://doi.org/10.3390/universe10070293 - 12 Jul 2024
Cited by 10 | Viewed by 1535
Abstract
QCD with the isospin chemical potential μI is a useful laboratory to delineate the microphysics in dense QCD. To study the quark–hadron continuity, we use a quark–meson model that interpolates hadronic and quark matter physics at microscopic level. The equation of state [...] Read more.
QCD with the isospin chemical potential μI is a useful laboratory to delineate the microphysics in dense QCD. To study the quark–hadron continuity, we use a quark–meson model that interpolates hadronic and quark matter physics at microscopic level. The equation of state is dominated by mesons at low density but taken over by quarks at high density. We extend our previous studies with two flavors to the three-flavor case to study the impact of the strangeness, which may be brought by kaons (K+,K0)=(us¯,sd¯) and the UA(1) anomaly. In the normal phase, the excitation energies of kaons are reduced by μI in the same way as hyperons in nuclear matter at the finite baryon chemical potential. Once pions condense, kaon excitation energies increase as μI does. Moreover, strange quarks become more massive through the UA(1) coupling to the condensed pions. Hence, at zero and low temperature, the strange hadrons and quarks are highly suppressed. The previous findings in two-flavor models, sound speed peak, negative trace anomaly, gaps insensitive to μI, persist in our three-flavor model and remain consistent with the lattice results to μI 1 GeV. We discuss the non-perturbative power corrections and quark saturation effects as important ingredients to understand the crossover equations of state measured on the lattice. Full article
(This article belongs to the Special Issue Studies in Neutron Stars)
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18 pages, 741 KB  
Article
Approaching the Conformal Limit of Quark Matter with Different Chemical Potentials
by Connor Brown, Veronica Dexheimer, Rafael Bán Jacobsen and Ricardo Luciano Sonego Farias
Symmetry 2024, 16(7), 852; https://doi.org/10.3390/sym16070852 - 5 Jul 2024
Cited by 2 | Viewed by 1846
Abstract
We study in detail the influence of different chemical potentials (baryon, electric charge, strange, and neutrino) on how and how fast a free gas of quarks in the zero-temperature limit reaches the conformal limit. We discuss the influence of non-zero masses, the inclusion [...] Read more.
We study in detail the influence of different chemical potentials (baryon, electric charge, strange, and neutrino) on how and how fast a free gas of quarks in the zero-temperature limit reaches the conformal limit. We discuss the influence of non-zero masses, the inclusion of leptons, and different constraints, such as charge neutrality, zero-net strangeness, and fixed lepton fraction. We also investigate for the first time how the symmetry energy of the system under some of these conditions approaches the conformal limit. We find that the inclusion of all quark masses (even the light ones) can produce different results depending on the chemical potential values or constraints assumed. A positive or negative deviation of 10% from the pressure of free massless quarks with the same chemical potential was found to take place as low as μB=77 to as high as 48,897 MeV. This illustrates the fact that the “free” or conformal limit is not a unique description. Finally, we briefly discuss what kind of corrections are expected from perturbative QCD as one goes away from the conformal limit. Full article
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18 pages, 8503 KB  
Article
Effects of Two Quantum Correction Parameters on Chaotic Dynamics of Particles near Renormalized Group Improved Schwarzschild Black Holes
by Junjie Lu and Xin Wu
Universe 2024, 10(7), 277; https://doi.org/10.3390/universe10070277 - 26 Jun 2024
Cited by 6 | Viewed by 1846
Abstract
A renormalized group improved Schwarzschild black hole spacetime contains two quantum correction parameters. One parameter γ represents the identification of cutoff of the distance scale, and another parameter Ω stems from nonperturbative renormalization group theory. The two parameters are constrained by the data [...] Read more.
A renormalized group improved Schwarzschild black hole spacetime contains two quantum correction parameters. One parameter γ represents the identification of cutoff of the distance scale, and another parameter Ω stems from nonperturbative renormalization group theory. The two parameters are constrained by the data from the shadow of M87* central black hole. The dynamics of electrically charged test particles around the black hole are integrable. However, when the black hole is immersed in an external asymptotically uniform magnetic field, the dynamics are not integrable and may allow for the occurrence of chaos. Employing an explicit symplectic integrator, we survey the contributions of the two parameters to the chaotic dynamical behavior. It is found that a small change of the parameter γ constrained by the shadow of M87* black hole has an almost negligible effect on the dynamical transition of particles from order to chaos. However, a small decrease in the parameter Ω leads to an enhancement in the strength of chaos from the global phase space structure. A theoretical interpretation is given to the different contributions. The term with the parameter Ω dominates the term with the parameter γ, even if the two parameters have same values. In particular, the parameter Ω acts as a repulsive force, and its decrease means a weakening of the repulsive force or equivalently enhancing the attractive force from the black hole. On the other hand, there is a positive Lyapunov exponent that is universally given by the surface gravity of the black hole when Ω0 is small and the external magnetic field vanishes. In this case, the horizon would influence chaotic behavior in the motion of charged particles around the black hole surrounded by the external magnetic field. This point can explain why a smaller value of the renormalization group parameter would much easily induce chaos than a larger value. Full article
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16 pages, 622 KB  
Article
Casimir Energy in (2 + 1)-Dimensional Field Theories
by Manuel Asorey, Claudio Iuliano and Fernando Ezquerro
Physics 2024, 6(2), 613-628; https://doi.org/10.3390/physics6020040 - 17 Apr 2024
Cited by 3 | Viewed by 1870
Abstract
We explore the dependence of vacuum energy on the boundary conditions for massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the simplest geometrical setup given by a two-dimensional space bounded by two homogeneous parallel wires in order to compare it with [...] Read more.
We explore the dependence of vacuum energy on the boundary conditions for massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the simplest geometrical setup given by a two-dimensional space bounded by two homogeneous parallel wires in order to compare it with the non-perturbative behaviour of the Casimir energy for non-Abelian gauge theories in (2 + 1) dimensions. Our results show the existence of two types of boundary conditions which give rise to two different asymptotic exponential decay regimes of the Casimir energy at large distances. The two families are distinguished by the feature that the boundary conditions involve or not interrelations between the behaviour of the fields at the two boundaries. Non-perturbative numerical simulations and analytical arguments show such an exponential decay for Dirichlet boundary conditions of SU(2) gauge theories. The verification that this behaviour is modified for other types of boundary conditions requires further numerical work. Subdominant corrections in the low-temperature regime are very relevant for numerical simulations, and they are also analysed in this paper. Full article
(This article belongs to the Special Issue 75 Years of the Casimir Effect: Advances and Prospects)
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