Yue Xiang, Jingjing Guo, Zhengyan Mao, Chao Jiang, Mandan Liu
This paper presents a novel algorithm named Five-element Cycle Integrated Mutation Optimization (FECOIMO) for solving the Traveling Thief Problem (TTP). The algorithm introduces a five-element cycle structure that integrates various mutation operations to enhance both global exploration and local exploitation capabilities. In experiments, FECOIMO was extensively tested on 39 TTP instances of varying scales and compared with five common metaheuristic algorithms: Enhanced Simulated Annealing (ESA), Improved Grey Wolf Optimization Algorithm (IGWO), Improved Whale Optimization Algorithm (IWOA), Genetic Algorithm (GA), and Profit-Guided Coordination Heuristic (PGCH). The experimental results demonstrate that FECOIMO outperforms the other algorithms across all instances, particularly excelling in large-scale instances. The results of the Friedman test show that FECOIMO significantly outperforms other algorithms in terms of average solution, maximum solution, and solution standard deviation. Additionally, although FECOIMO has a longer execution time, its complexity is comparable to that of other algorithms, and the additional computational overhead in solving complex optimization problems translates into better solutions. Therefore, FECOIMO has proven its effectiveness and robustness in handling complex combinatorial optimization problems.
{"title":"Five-Element Cycle Optimization Algorithm Based on an Integrated Mutation Operator for the Traveling Thief Problem","authors":"Yue Xiang, Jingjing Guo, Zhengyan Mao, Chao Jiang, Mandan Liu","doi":"10.3390/sym16091153","DOIUrl":"https://doi.org/10.3390/sym16091153","url":null,"abstract":"This paper presents a novel algorithm named Five-element Cycle Integrated Mutation Optimization (FECOIMO) for solving the Traveling Thief Problem (TTP). The algorithm introduces a five-element cycle structure that integrates various mutation operations to enhance both global exploration and local exploitation capabilities. In experiments, FECOIMO was extensively tested on 39 TTP instances of varying scales and compared with five common metaheuristic algorithms: Enhanced Simulated Annealing (ESA), Improved Grey Wolf Optimization Algorithm (IGWO), Improved Whale Optimization Algorithm (IWOA), Genetic Algorithm (GA), and Profit-Guided Coordination Heuristic (PGCH). The experimental results demonstrate that FECOIMO outperforms the other algorithms across all instances, particularly excelling in large-scale instances. The results of the Friedman test show that FECOIMO significantly outperforms other algorithms in terms of average solution, maximum solution, and solution standard deviation. Additionally, although FECOIMO has a longer execution time, its complexity is comparable to that of other algorithms, and the additional computational overhead in solving complex optimization problems translates into better solutions. Therefore, FECOIMO has proven its effectiveness and robustness in handling complex combinatorial optimization problems.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.
与纯升压和纯三维旋转相对应的 4×4 洛伦兹变换矩阵的明确公式已广为人知。但对于具有任意非零升压和旋转参数的一般洛伦兹变换的明确公式，则鲜为人知。我们通过介绍两种不同的推导来重温这个更一般的公式。第一种推导（比以前文献中出现的推导简单一些）是对 4×4 实矩阵 A 的指数进行求值，其中 A 是对角矩阵 diag(+1,-1,-1,-1) 与任意 4×4 实非对称矩阵的乘积。expA 公式只取决于 A 的特征值，并利用了拉格朗日内插多项式。第二种推导利用了旋量积η†σ¯μχ变换为洛伦兹四矢量的观察结果，其中χ和η是双分量旋量。后一种推导的优势在于，一般洛伦兹变换Λ的相应公式简化为计算 2×2 矩阵乘积的迹。这两种计算方法都能得到等效的Λ表达式。
{"title":"Explicit form for the Most General Lorentz Transformation Revisited","authors":"Howard E. Haber","doi":"10.3390/sym16091155","DOIUrl":"https://doi.org/10.3390/sym16091155","url":null,"abstract":"Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To address the symmetry-related resilience issues of stations and lines in urban rail transit networks, we propose a two-stage robust optimization-based approach for urban rail transit network planning. In this context, resilience is conceptualized as the ability of the network to maintain its operational symmetry under normal and disruptive conditions. Firstly, we used passenger flow distributions as decision variables to construct a two-stage symmetry-based urban rail transit network planning model, aiming to simultaneously minimize the total cost and total operating time of the network while preserving its functional symmetry. Secondly, we designed a hybrid evolutionary algorithm with chromosomes having a two-layer encoding structure, where the Niched Pareto Genetic Algorithm served as the main algorithmic framework, and a Large Neighborhood Search mechanism was designed to optimize the connectivity gene layer of individuals, ensuring the symmetry of network connectivity. Finally, we conducted computational verification on randomly generated instances to confirm the effectiveness of the model and algorithm. The experimental results demonstrated that our method could find two sets of Pareto optimal solutions for cost preference and time preference, thereby preserving the operational symmetry of the network under normal and damaged conditions, as well as reducing the total operating time. This effectively improved the overall efficiency and resilience of the network. Our designed hybrid evolutionary algorithm converged to satisfactory objective values in the early iterations, exhibiting strong search and optimization performance and effectively solving the two-stage symmetry-based urban rail transit network planning model.
{"title":"Symmetry-Based Urban Rail Transit Network Planning Using Two-Stage Robust Optimization","authors":"Zhaoguo Huang, Changxi Ma","doi":"10.3390/sym16091149","DOIUrl":"https://doi.org/10.3390/sym16091149","url":null,"abstract":"To address the symmetry-related resilience issues of stations and lines in urban rail transit networks, we propose a two-stage robust optimization-based approach for urban rail transit network planning. In this context, resilience is conceptualized as the ability of the network to maintain its operational symmetry under normal and disruptive conditions. Firstly, we used passenger flow distributions as decision variables to construct a two-stage symmetry-based urban rail transit network planning model, aiming to simultaneously minimize the total cost and total operating time of the network while preserving its functional symmetry. Secondly, we designed a hybrid evolutionary algorithm with chromosomes having a two-layer encoding structure, where the Niched Pareto Genetic Algorithm served as the main algorithmic framework, and a Large Neighborhood Search mechanism was designed to optimize the connectivity gene layer of individuals, ensuring the symmetry of network connectivity. Finally, we conducted computational verification on randomly generated instances to confirm the effectiveness of the model and algorithm. The experimental results demonstrated that our method could find two sets of Pareto optimal solutions for cost preference and time preference, thereby preserving the operational symmetry of the network under normal and damaged conditions, as well as reducing the total operating time. This effectively improved the overall efficiency and resilience of the network. Our designed hybrid evolutionary algorithm converged to satisfactory objective values in the early iterations, exhibiting strong search and optimization performance and effectively solving the two-stage symmetry-based urban rail transit network planning model.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Noor Alam, Shahid Ahmad Wani, Waseem Ahmad Khan, Fakhredine Gassem, Anas Altaleb
The primary objective of this research is to introduce and investigate novel polynomial variants termed Δh Laguerre polynomials. This unique polynomial type integrates the monomiality principle alongside operational rules. Through this innovative approach, the study delves into uncharted territory, unveiling fresh insights that build upon prior research endeavours. Notably, the Δh Laguerre polynomials exhibit significant utility in the realm of quantum mechanics, particularly in the modelling of entropy within quantum systems. The research meticulously unveils explicit formulas and elucidates the fundamental properties of these polynomials, thereby forging connections with established polynomial categories. By shedding light on the distinct characteristics and functionalities of the Δh Laguerre polynomials, this study contributes significantly to their comprehension and application across diverse mathematical and scientific domains.
{"title":"Exploring Properties and Applications of Laguerre Special Polynomials Involving the Δh Form","authors":"Noor Alam, Shahid Ahmad Wani, Waseem Ahmad Khan, Fakhredine Gassem, Anas Altaleb","doi":"10.3390/sym16091154","DOIUrl":"https://doi.org/10.3390/sym16091154","url":null,"abstract":"The primary objective of this research is to introduce and investigate novel polynomial variants termed Δh Laguerre polynomials. This unique polynomial type integrates the monomiality principle alongside operational rules. Through this innovative approach, the study delves into uncharted territory, unveiling fresh insights that build upon prior research endeavours. Notably, the Δh Laguerre polynomials exhibit significant utility in the realm of quantum mechanics, particularly in the modelling of entropy within quantum systems. The research meticulously unveils explicit formulas and elucidates the fundamental properties of these polynomials, thereby forging connections with established polynomial categories. By shedding light on the distinct characteristics and functionalities of the Δh Laguerre polynomials, this study contributes significantly to their comprehension and application across diverse mathematical and scientific domains.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mingzhi Tang, Wenfeng Zhou, Yanchao Hu, Gang Wang, Yanguang Yang
A novel decomposition method that adheres to both local time translation symmetry and spatial rotational symmetry is proposed in this study, thereby extending the limitations of existing methods, which are typically restricted to quasi-two-dimensional configurations. Grounded in the FIK and RD identities, this method provides a clear physical and reliable interpretation suitable for arbitrary-curvature profiles. Utilizing this method, an analysis of the aerothermodynamic characteristics of the bistable states of curved compression ramp flows was conducted. The results reveal that the generation of undisturbed and peak Cf is dominated by viscous dissipation. Specifically, flow separation happens when all of the energy input from the work exerted by the adverse pressure gradient (APG) is insufficient to be entirely converted into local viscous dissipation and kinetic energy. Furthermore, the propensity for flow separation at higher wall temperatures is firstly elucidated quantitatively from the perspective of the work by the APG. The peak heat flux is predominantly triggered by the work of viscous stress, with the secondary contribution from energy transport playing a more significant role in the generation of the peak heat flux of the separation state than that of the attachment state.
本研究提出了一种既遵守局部时间平移对称性又遵守空间旋转对称性的新型分解方法，从而扩展了现有方法的局限性，因为现有方法通常仅限于准二维配置。该方法以 FIK 和 RD 特性为基础，提供了适用于任意曲率剖面的清晰可靠的物理解释。利用这种方法，对弯曲压缩斜坡流双稳态的空气热力学特性进行了分析。结果表明，未扰动和峰值 Cf 的产生是由粘性耗散主导的。具体来说，当逆向压力梯度（APG）做功输入的所有能量不足以完全转化为局部粘性耗散和动能时，就会发生流动分离。此外，我们还首次从逆压力梯度做功的角度定量阐明了在较高壁温条件下发生流体分离的倾向。峰值热通量主要是由粘性应力做功引发的，在分离状态的峰值热通量产生过程中，能量传输的次要贡献比附着状态的贡献更为重要。
{"title":"Local-Energy-Conservation-Based Decomposition Method for Wall Friction and Heat Flux","authors":"Mingzhi Tang, Wenfeng Zhou, Yanchao Hu, Gang Wang, Yanguang Yang","doi":"10.3390/sym16091147","DOIUrl":"https://doi.org/10.3390/sym16091147","url":null,"abstract":"A novel decomposition method that adheres to both local time translation symmetry and spatial rotational symmetry is proposed in this study, thereby extending the limitations of existing methods, which are typically restricted to quasi-two-dimensional configurations. Grounded in the FIK and RD identities, this method provides a clear physical and reliable interpretation suitable for arbitrary-curvature profiles. Utilizing this method, an analysis of the aerothermodynamic characteristics of the bistable states of curved compression ramp flows was conducted. The results reveal that the generation of undisturbed and peak Cf is dominated by viscous dissipation. Specifically, flow separation happens when all of the energy input from the work exerted by the adverse pressure gradient (APG) is insufficient to be entirely converted into local viscous dissipation and kinetic energy. Furthermore, the propensity for flow separation at higher wall temperatures is firstly elucidated quantitatively from the perspective of the work by the APG. The peak heat flux is predominantly triggered by the work of viscous stress, with the secondary contribution from energy transport playing a more significant role in the generation of the peak heat flux of the separation state than that of the attachment state.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Emily C. Marcinowski, George F. Michel, Eliza L. Nelson
How infants engage with objects changes dramatically over the first year of life. While some infants exhibit a consistent hand preference for acquiring objects during this period, others have no identifiable preference. The goal of this study was to test whether lateralization confers an advantage in the development of early object management skills. We examined whether lateralized infants show different rates of growth in how they interact with multiple objects as compared to infants without a hand preference. In a longitudinal study consisting of seven monthly visits from 6 to 12 months, 303 infants were assessed for their hand preference and object management skill (i.e., holding up to three objects). Group-Based Trajectory Modeling (GBTM) identified the following three hand preference trajectory groups: Left, Right, and No Preference (NP). A Hierarchical Generalized Linear Model (HGLM) with the NP infants as the reference group for statistical comparisons revealed that while all the infants showed similar trends in their object management skills over time, the lateralized infants had an advantage over the non-lateralized infants. The infants in the Right and Left groups transitioned from holding one to two objects more quickly relative to the NP infants. Further research is needed to determine if this early object skill advantage cascades to a more complex handling of multiple objects.
{"title":"Object Skill Advantage in Infants with a Hand Preference","authors":"Emily C. Marcinowski, George F. Michel, Eliza L. Nelson","doi":"10.3390/sym16091148","DOIUrl":"https://doi.org/10.3390/sym16091148","url":null,"abstract":"How infants engage with objects changes dramatically over the first year of life. While some infants exhibit a consistent hand preference for acquiring objects during this period, others have no identifiable preference. The goal of this study was to test whether lateralization confers an advantage in the development of early object management skills. We examined whether lateralized infants show different rates of growth in how they interact with multiple objects as compared to infants without a hand preference. In a longitudinal study consisting of seven monthly visits from 6 to 12 months, 303 infants were assessed for their hand preference and object management skill (i.e., holding up to three objects). Group-Based Trajectory Modeling (GBTM) identified the following three hand preference trajectory groups: Left, Right, and No Preference (NP). A Hierarchical Generalized Linear Model (HGLM) with the NP infants as the reference group for statistical comparisons revealed that while all the infants showed similar trends in their object management skills over time, the lateralized infants had an advantage over the non-lateralized infants. The infants in the Right and Left groups transitioned from holding one to two objects more quickly relative to the NP infants. Further research is needed to determine if this early object skill advantage cascades to a more complex handling of multiple objects.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abedel-Karrem Alomari, Wael Mahmoud Mohammad Salameh, Mohammad Alaroud, Nedal Tahat
This research focuses on finding multiple solutions (MSs) to nonlinear fractional boundary value problems (BVPs) through a new development, namely the predictor Laplace fractional power series method. This method predicts the missing initial values by applying boundary or force conditions. This research provides a set of theorems necessary for deriving the recurrence relations to find the series terms. Several examples demonstrate the efficacy, convergence, and accuracy of the algorithm. Under Caputo’s definition of the fractional derivative with symmetric order, the obtained results are visualized numerically and graphically. The behavior of the generated solutions indicates that altering the fractional derivative parameters within their domain symmetrically changes these solutions, ultimately aligning them with the standard derivative. The results are compared with the homotopy analysis method and are presented in various figures and tables.
{"title":"Predictor Laplace Fractional Power Series Method for Finding Multiple Solutions of Fractional Boundary Value Problems","authors":"Abedel-Karrem Alomari, Wael Mahmoud Mohammad Salameh, Mohammad Alaroud, Nedal Tahat","doi":"10.3390/sym16091152","DOIUrl":"https://doi.org/10.3390/sym16091152","url":null,"abstract":"This research focuses on finding multiple solutions (MSs) to nonlinear fractional boundary value problems (BVPs) through a new development, namely the predictor Laplace fractional power series method. This method predicts the missing initial values by applying boundary or force conditions. This research provides a set of theorems necessary for deriving the recurrence relations to find the series terms. Several examples demonstrate the efficacy, convergence, and accuracy of the algorithm. Under Caputo’s definition of the fractional derivative with symmetric order, the obtained results are visualized numerically and graphically. The behavior of the generated solutions indicates that altering the fractional derivative parameters within their domain symmetrically changes these solutions, ultimately aligning them with the standard derivative. The results are compared with the homotopy analysis method and are presented in various figures and tables.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We herein study the circular orbit stability of a static black hole system composed of multiple Reissner–Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black holes at different spacetime, we find that the continuity of their stable circular orbits changes, i.e., the peaks of the effective potentials are transformed from single-peaked to bi-peaked, and that the distance a between the black holes is the main reason for this change. This characteristic is completely different from the continuity of the stable circular orbit interval of any kind of single black hole in the past. After calculation, we obtain several critical values that lead to the change in circular orbit stability. The three fundamental frequencies (orbital frequency, radial local frequency, and vertical local frequency) are derived and compared for two different spacetimes of double and three black holes. We also analyse the effect of the black hole distance a on the three fundamental frequencies of circular orbits.
我们在此研究由多个赖斯纳-诺德斯特伦（RN）黑洞组成的静态黑洞系统的圆轨道稳定性。通过比较两个静态黑洞、三个静态黑洞（TBHs）、四个静态黑洞和五个静态黑洞在不同时空的圆轨道，我们发现它们的稳定圆轨道的连续性发生了变化，即有效势的峰值从单峰变成了双峰，而黑洞之间的距离a是导致这种变化的主要原因。这一特征与过去任何一种单黑洞的稳定圆轨道区间的连续性完全不同。经过计算，我们得到了导致圆轨道稳定性变化的几个临界值。我们得出了三个基本频率（轨道频率、径向局部频率和垂直局部频率），并对双黑洞和三黑洞的两种不同时空进行了比较。我们还分析了黑洞距离 a 对圆轨道三个基本频率的影响。
{"title":"Stability Analysis of Stable Circular Orbit in Multi-Static Black Hole Spacetime","authors":"Zefang Fan, Yu Wang, Xianggao Wang","doi":"10.3390/sym16091140","DOIUrl":"https://doi.org/10.3390/sym16091140","url":null,"abstract":"We herein study the circular orbit stability of a static black hole system composed of multiple Reissner–Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black holes at different spacetime, we find that the continuity of their stable circular orbits changes, i.e., the peaks of the effective potentials are transformed from single-peaked to bi-peaked, and that the distance a between the black holes is the main reason for this change. This characteristic is completely different from the continuity of the stable circular orbit interval of any kind of single black hole in the past. After calculation, we obtain several critical values that lead to the change in circular orbit stability. The three fundamental frequencies (orbital frequency, radial local frequency, and vertical local frequency) are derived and compared for two different spacetimes of double and three black holes. We also analyse the effect of the black hole distance a on the three fundamental frequencies of circular orbits.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mary G. Thoubaan, Dheia G. Salih Al-Khafajy, Abbas Kareem Wanas, Daniel Breaz, Luminiţa-Ioana Cotîrlă
This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey’s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters.
{"title":"Analysis of a Bifurcation and Stability of Equilibrium Points for Jeffrey Fluid Flow through a Non-Uniform Channel","authors":"Mary G. Thoubaan, Dheia G. Salih Al-Khafajy, Abbas Kareem Wanas, Daniel Breaz, Luminiţa-Ioana Cotîrlă","doi":"10.3390/sym16091144","DOIUrl":"https://doi.org/10.3390/sym16091144","url":null,"abstract":"This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey’s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In relativity, the Newtonian concepts of velocity and acceleration are observer-dependent quantities that vary with the chosen frame of reference. It is well established that in the comoving frame, cosmic expansion is currently accelerating; however, in the rest frame, this expansion is actually decelerating. In this paper, we explore the implications of this distinction. The traditional measure of cosmic acceleration, denoted by q, is derived from the comoving frame and describes the acceleration of the scale factor a for a 3D space-like homogeneous sphere. We introduce a new parameter qE representing the acceleration experienced between observers within the light cone. By comparing qE to the traditional q using observational data from Type Ia supernovae (SN) and the radial clustering of galaxies and quasars (BAO)—including the latest results from DESI2024—our analysis demonstrates that qE aligns more closely with these data. The core argument of the paper is that Λ—regardless of its origin—creates an event horizon that divides the manifold into two causally disconnected regions analogous to conditions inside a black hole’s interior, thereby allowing for a rest-frame perspective qE in which cosmic expansion appears to be decelerating and the horizon acts like a friction term. Such a horizon suggests that the universe cannot maintain homogeneity outside. The observed cosmological constant Λ can then be interpreted not as a driver of new dark energy or a modification of gravity but as a boundary term exerting an attractive force, akin to a rubber band, resisting further expansion and preventing event horizon crossings. This interpretation calls for a reconsideration of current cosmological models and the assumptions underlying them.
在相对论中，牛顿的速度和加速度概念是依赖于观察者的量，随所选参照系的不同而变化。众所周知，在运动参照系中，宇宙膨胀目前正在加速；然而，在静止参照系中，这种膨胀实际上正在减速。在本文中，我们将探讨这一区别的意义。宇宙加速度的传统度量（用 q 表示）来自于运动帧，描述的是三维空间类均质球的尺度因子 a 的加速度。我们引入了一个新参数 qE，代表光锥内观测者之间的加速度。通过使用 Ia 型超新星（SN）以及星系和类星体径向聚类（BAO）的观测数据（包括 DESI2024 的最新结果）将 qE 与传统的 q 进行比较，我们的分析表明 qE 与这些数据更加吻合。这篇论文的核心论点是，无论Λ的起源如何，它都会产生一个事件穹界，将流形分成两个因果断开的区域，类似于黑洞内部的状况，从而允许从静止帧的角度看qE，在这个角度中，宇宙膨胀似乎正在减速，而穹界就像一个摩擦项。这样的视界表明，宇宙无法在外部保持均质性。这样，观测到的宇宙学常数Λ就不能被解释为新暗能量的驱动力或引力的改变，而可以被解释为一个施加吸引力的边界项，类似于橡皮筋，抵制进一步膨胀并阻止事件视界的穿越。这种解释要求我们重新考虑当前的宇宙学模型及其所依据的假设。
{"title":"On the Interpretation of Cosmic Acceleration","authors":"Enrique Gaztanaga","doi":"10.3390/sym16091141","DOIUrl":"https://doi.org/10.3390/sym16091141","url":null,"abstract":"In relativity, the Newtonian concepts of velocity and acceleration are observer-dependent quantities that vary with the chosen frame of reference. It is well established that in the comoving frame, cosmic expansion is currently accelerating; however, in the rest frame, this expansion is actually decelerating. In this paper, we explore the implications of this distinction. The traditional measure of cosmic acceleration, denoted by q, is derived from the comoving frame and describes the acceleration of the scale factor a for a 3D space-like homogeneous sphere. We introduce a new parameter qE representing the acceleration experienced between observers within the light cone. By comparing qE to the traditional q using observational data from Type Ia supernovae (SN) and the radial clustering of galaxies and quasars (BAO)—including the latest results from DESI2024—our analysis demonstrates that qE aligns more closely with these data. The core argument of the paper is that Λ—regardless of its origin—creates an event horizon that divides the manifold into two causally disconnected regions analogous to conditions inside a black hole’s interior, thereby allowing for a rest-frame perspective qE in which cosmic expansion appears to be decelerating and the horizon acts like a friction term. Such a horizon suggests that the universe cannot maintain homogeneity outside. The observed cosmological constant Λ can then be interpreted not as a driver of new dark energy or a modification of gravity but as a boundary term exerting an attractive force, akin to a rubber band, resisting further expansion and preventing event horizon crossings. This interpretation calls for a reconsideration of current cosmological models and the assumptions underlying them.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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