The possibility of a shock wave recovery at a discrete closed interface with a heated gas has been investigated. A two-dimensional model applied to conditions of optical discharges featuring spherical, elliptical, and drop-like configurations demonstrated that non-symmetry in the shock refraction contributes to the specific mechanism of recovery other than simply its compensation. Even though the full restoration of the hypersonic flow state does not occur in a strict sense of it, clear reverse changes toward the initial shape of the shock front eventually take place, thus creating an appearance of a full recovery seen in experiments. From analysis of different interface symmetries, the factors determining the recovery dynamics are identified. The results are directly applicable to the problem of energy deposition into a hypersonic flow; however, it can be useful anywhere else where the flow modifications following the interaction are important. The dimensionless form of the equations allows applications on any scale other than that demonstrated for the optical discharges.
{"title":"Non-Symmetry in the Shock Refraction at a Closed Interface as a Recovery Mechanism","authors":"A. Markhotok","doi":"10.3390/dynamics4010004","DOIUrl":"https://doi.org/10.3390/dynamics4010004","url":null,"abstract":"The possibility of a shock wave recovery at a discrete closed interface with a heated gas has been investigated. A two-dimensional model applied to conditions of optical discharges featuring spherical, elliptical, and drop-like configurations demonstrated that non-symmetry in the shock refraction contributes to the specific mechanism of recovery other than simply its compensation. Even though the full restoration of the hypersonic flow state does not occur in a strict sense of it, clear reverse changes toward the initial shape of the shock front eventually take place, thus creating an appearance of a full recovery seen in experiments. From analysis of different interface symmetries, the factors determining the recovery dynamics are identified. The results are directly applicable to the problem of energy deposition into a hypersonic flow; however, it can be useful anywhere else where the flow modifications following the interaction are important. The dimensionless form of the equations allows applications on any scale other than that demonstrated for the optical discharges.","PeriodicalId":507568,"journal":{"name":"Dynamics","volume":"49 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139441291","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}
The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling parameters, calculate an infinite number of renormalization constants, identify a plane of fixed points in the infinite dimensional space of coupling parameters, discuss their stability and critical scaling in the model, and formulate a simple law relating the asymptotic size of an avalanche to a model exponent quantifying the time-scale separation between the slow energy injection and fast avalanche relaxation processes.
{"title":"Multiplicative Renormalization of Stochastic Differential Equations for the Abelian Sandpile Model","authors":"Dimitri Volchenkov","doi":"10.3390/dynamics4010003","DOIUrl":"https://doi.org/10.3390/dynamics4010003","url":null,"abstract":"The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling parameters, calculate an infinite number of renormalization constants, identify a plane of fixed points in the infinite dimensional space of coupling parameters, discuss their stability and critical scaling in the model, and formulate a simple law relating the asymptotic size of an avalanche to a model exponent quantifying the time-scale separation between the slow energy injection and fast avalanche relaxation processes.","PeriodicalId":507568,"journal":{"name":"Dynamics","volume":"59 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139386813","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}
Yangyang Liu, Ziying Zhang, Hua Zhang, Yaguang Liu
In this work, the explicit boundary-condition-enforced immersed boundary method (EIBM) and the lattice Boltzmann flux solver (LBFS) are integrated into OpenFOAM to efficiently solve incompressible flows with complex geometries and moving boundaries. The EIBM applies the explicit technique to greatly improve the computational efficiency of the original boundary-condition-enforced immersed boundary method. In addition, the improved EIBM inherits the accurate interpretation of the no-slip boundary condition and the simple implementation from the original one. The LBFS uses the finite volume method to discretize the recovered macroscopic governing equations from the lattice Boltzmann equation. It enjoys the explicit relationship between the pressure and density, which avoids solving the pressure Poisson equation and thus saves much computational cost. Another attractive feature of the LBFS lies in its simultaneous evaluation of the inviscid and viscous fluxes. OpenFOAM, as an open-source CFD platform, has drawn increasing attention from the CFD community and has been proven to be a powerful tool for various problems. Thus, implementing the EIBM and LBFS into such a popular platform can advance the practical application of these two methods and may provide an effective alternative for complicated incompressible flow problems. The performance of the integrated solver in OpenFOAM is comprehensively assessed by comparing it with the widely used numerical solver in OpenFOAM, namely, the Pressure-Implicit with Splitting of Operators (PISO) algorithm with the IBM. A series of representative test cases with stationary and moving boundaries are simulated. Numerical results confirm that the present method does not have any streamline penetration and achieves the second-order accuracy in space. Therefore, the present method implemented in the open-source platform OpenFOAM may have good potential and can serve as a powerful tool for practical engineering problems.
{"title":"Implementation and Validation of Explicit Immersed Boundary Method and Lattice Boltzmann Flux Solver in OpenFOAM","authors":"Yangyang Liu, Ziying Zhang, Hua Zhang, Yaguang Liu","doi":"10.3390/dynamics4010002","DOIUrl":"https://doi.org/10.3390/dynamics4010002","url":null,"abstract":"In this work, the explicit boundary-condition-enforced immersed boundary method (EIBM) and the lattice Boltzmann flux solver (LBFS) are integrated into OpenFOAM to efficiently solve incompressible flows with complex geometries and moving boundaries. The EIBM applies the explicit technique to greatly improve the computational efficiency of the original boundary-condition-enforced immersed boundary method. In addition, the improved EIBM inherits the accurate interpretation of the no-slip boundary condition and the simple implementation from the original one. The LBFS uses the finite volume method to discretize the recovered macroscopic governing equations from the lattice Boltzmann equation. It enjoys the explicit relationship between the pressure and density, which avoids solving the pressure Poisson equation and thus saves much computational cost. Another attractive feature of the LBFS lies in its simultaneous evaluation of the inviscid and viscous fluxes. OpenFOAM, as an open-source CFD platform, has drawn increasing attention from the CFD community and has been proven to be a powerful tool for various problems. Thus, implementing the EIBM and LBFS into such a popular platform can advance the practical application of these two methods and may provide an effective alternative for complicated incompressible flow problems. The performance of the integrated solver in OpenFOAM is comprehensively assessed by comparing it with the widely used numerical solver in OpenFOAM, namely, the Pressure-Implicit with Splitting of Operators (PISO) algorithm with the IBM. A series of representative test cases with stationary and moving boundaries are simulated. Numerical results confirm that the present method does not have any streamline penetration and achieves the second-order accuracy in space. Therefore, the present method implemented in the open-source platform OpenFOAM may have good potential and can serve as a powerful tool for practical engineering problems.","PeriodicalId":507568,"journal":{"name":"Dynamics","volume":"47 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139389023","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}
The symmetries of a Riemann surface Σ∖{ai} with n punctures ai are encoded in its fundamental group π1(Σ). Further structure may be described through representations (homomorphisms) of π1 over a Lie group G as globalized by the character variety C=Hom(π1,G)/G. Guided by our previous work in the context of topological quantum computing (TQC) and genetics, we specialize on the four-punctured Riemann sphere Σ=S2(4) and the ‘space-time-spin’ group G=SL2(C). In such a situation, C possesses remarkable properties: (i) a representation is described by a three-dimensional cubic surface Va,b,c,d(x,y,z) with three variables and four parameters; (ii) the automorphisms of the surface satisfy the dynamical (non-linear and transcendental) Painlevé VI equation (or PVI); and (iii) there exists a finite set of 1 (Cayley–Picard)+3 (continuous platonic)+45 (icosahedral) solutions of PVI. In this paper, we feature the parametric representation of some solutions of PVI: (a) solutions corresponding to algebraic surfaces such as the Klein quartic and (b) icosahedral solutions. Applications to the character variety of finitely generated groups fp encountered in TQC or DNA/RNA sequences are proposed.
{"title":"Dynamics of Fricke–Painlevé VI Surfaces","authors":"Michel Planat, David Chester, K. Irwin","doi":"10.3390/dynamics4010001","DOIUrl":"https://doi.org/10.3390/dynamics4010001","url":null,"abstract":"The symmetries of a Riemann surface Σ∖{ai} with n punctures ai are encoded in its fundamental group π1(Σ). Further structure may be described through representations (homomorphisms) of π1 over a Lie group G as globalized by the character variety C=Hom(π1,G)/G. Guided by our previous work in the context of topological quantum computing (TQC) and genetics, we specialize on the four-punctured Riemann sphere Σ=S2(4) and the ‘space-time-spin’ group G=SL2(C). In such a situation, C possesses remarkable properties: (i) a representation is described by a three-dimensional cubic surface Va,b,c,d(x,y,z) with three variables and four parameters; (ii) the automorphisms of the surface satisfy the dynamical (non-linear and transcendental) Painlevé VI equation (or PVI); and (iii) there exists a finite set of 1 (Cayley–Picard)+3 (continuous platonic)+45 (icosahedral) solutions of PVI. In this paper, we feature the parametric representation of some solutions of PVI: (a) solutions corresponding to algebraic surfaces such as the Klein quartic and (b) icosahedral solutions. Applications to the character variety of finitely generated groups fp encountered in TQC or DNA/RNA sequences are proposed.","PeriodicalId":507568,"journal":{"name":"Dynamics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139452514","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}
Robot manipulators possess the capability to autonomously execute complex sequences of actions. Their proficiency in handling challenging and hazardous tasks has led to their widespread adoption across diverse sectors, including industry, business, household appliances, rehabilitation, and many more. However, certain tasks prove to be challenging for individual robots, primarily due to constraints in their structure and limited degrees of freedom. Cooperative robot manipulators (CRMs) emerge as a compelling solution when dealing with large, heavy, or flexible payloads. The utilization of CRMs offers a host of benefits, including enhanced manipulation performance achieved through the synergy of sensing and actuation capabilities or by tapping into increased redundancy. Numerous techniques have been devised for the control and dynamical modeling of CRMs. Nevertheless, the field continues to present technical challenges and scientific inquiries. To inspire and facilitate further research and development in this realm, this review aims to consolidate the current body of knowledge pertaining to CRMs kinematics, dynamics modeling, and various control methodologies used for payload manipulation via CRMs.
{"title":"Cooperative Robot Manipulators Dynamical Modeling and Control: An Overview","authors":"Amin Ghorbanpour","doi":"10.3390/dynamics3040045","DOIUrl":"https://doi.org/10.3390/dynamics3040045","url":null,"abstract":"Robot manipulators possess the capability to autonomously execute complex sequences of actions. Their proficiency in handling challenging and hazardous tasks has led to their widespread adoption across diverse sectors, including industry, business, household appliances, rehabilitation, and many more. However, certain tasks prove to be challenging for individual robots, primarily due to constraints in their structure and limited degrees of freedom. Cooperative robot manipulators (CRMs) emerge as a compelling solution when dealing with large, heavy, or flexible payloads. The utilization of CRMs offers a host of benefits, including enhanced manipulation performance achieved through the synergy of sensing and actuation capabilities or by tapping into increased redundancy. Numerous techniques have been devised for the control and dynamical modeling of CRMs. Nevertheless, the field continues to present technical challenges and scientific inquiries. To inspire and facilitate further research and development in this realm, this review aims to consolidate the current body of knowledge pertaining to CRMs kinematics, dynamics modeling, and various control methodologies used for payload manipulation via CRMs.","PeriodicalId":507568,"journal":{"name":"Dynamics","volume":"16 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139184013","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}
Moving animal groups consist of many distinct individuals but can operate and function as one unit when performing different tasks. Effectively evading unexpected predator attacks is one primary task for many moving groups. The current explanation for predator evasion responses in moving animal groups require the individuals in the groups to interact via (velocity) alignment. However, experiments have shown that some animals do not use alignment. This suggests that another explanation for the predator evasion capacity in at least these species is needed. Here we establish that effective collective predator evasion does not require alignment, it can be induced via attraction and repulsion alone. We also show that speed differences between individuals that have directly observed the predator and those that have not influence evasion success and the speed of the collective evasion process, but are not required to induce the phenomenon. Our work here adds collective predator evasion to a number of phenomena previously thought to require alignment interactions that have recently been shown to emerge from attraction and repulsion alone. Based on our findings we suggest experiments and make predictions that may lead to a deeper understanding of not only collective predator evasion but also collective motion in general.
{"title":"An Alignment-Free Explanation for Collective Predator Evasion in Moving Animal Groups","authors":"Daniel Strömbom, Catherine Futterman","doi":"10.3390/dynamics3040043","DOIUrl":"https://doi.org/10.3390/dynamics3040043","url":null,"abstract":"Moving animal groups consist of many distinct individuals but can operate and function as one unit when performing different tasks. Effectively evading unexpected predator attacks is one primary task for many moving groups. The current explanation for predator evasion responses in moving animal groups require the individuals in the groups to interact via (velocity) alignment. However, experiments have shown that some animals do not use alignment. This suggests that another explanation for the predator evasion capacity in at least these species is needed. Here we establish that effective collective predator evasion does not require alignment, it can be induced via attraction and repulsion alone. We also show that speed differences between individuals that have directly observed the predator and those that have not influence evasion success and the speed of the collective evasion process, but are not required to induce the phenomenon. Our work here adds collective predator evasion to a number of phenomena previously thought to require alignment interactions that have recently been shown to emerge from attraction and repulsion alone. Based on our findings we suggest experiments and make predictions that may lead to a deeper understanding of not only collective predator evasion but also collective motion in general.","PeriodicalId":507568,"journal":{"name":"Dynamics","volume":"17 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139273666","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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