Article
Physics, Multidisciplinary
Han Yan, Feng Zhang, Jin Wang
Summary: This work introduces a non-equilibrium thermodynamic and dynamical framework for studying critical transitions in complex systems based on thermodynamic quantities and time-reversal symmetry breaking which detects transitions much earlier than previous works based on nonlinear dynamics and bifurcation theory, providing a practical way for predicting transitions.
COMMUNICATIONS PHYSICS
(2023)
Article
Multidisciplinary Sciences
Georgios Margazoglou, Tobias Grafke, Alessandro Laio, Valerio Lucarini
Summary: Two independent data analysis methodologies were applied to identify stable climate states in an intermediate complexity climate model, revealing a third intermediate stable state in addition to the well-known warm and snowball earth states. The approaches showed remarkable agreement and demonstrated the interplay between the identified multistable climate states.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Computer Science, Interdisciplinary Applications
Nathan T. Boyd, Steven A. Gabriel, George Rest, Tom Dumm
Summary: This paper investigates the game theory of resource-allocation situations where the first come, first serve heuristic creates inequitable, asymmetric benefits to the players. Specifically, this problem is formulated as a Generalized Nash Equilibrium Model where the players are arranged sequentially along a directed line graph. The goal of the model is to reduce the asymmetric benefits among the players using a policy instrument. It serves as a more realistic, alternative approach to the line-graph models considered in the cooperative game-theoretic literature. An application-oriented formulation is also developed for water resource systems. The players in this model are utilities who withdraw water and are arranged along a river basin from upstream to downstream. This model is applied to a stylized, three-node model as well as a test bed in the Duck River Basin in Tennessee, USA. Based on the results, a non-cooperative, water-release market can be an acceptable policy instrument according to metrics traditionally used in cooperative game theory.
COMPUTERS & OPERATIONS RESEARCH
(2023)
Article
Physics, Mathematical
Tushar Das, Feliks Przytycki, Giulio Tiozzo, Mariusz Urbanski, Anna Zdunik
Summary: This study focuses on a class of dynamical systems called weakly coarse expanding, which is a generalization to expanding Thurston maps in the postcritically infinite case and is closely related to coarse expanding conformal systems. The paper proves the existence and uniqueness of equilibrium states for a wide class of potentials, as well as statistical laws such as central limit theorem, law of iterated logarithm, exponential decay of correlations and a large deviation principle. Furthermore, all these results are proven even in the presence of periodic (repelling) branch points when the system is defined on the 2-sphere.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Thermodynamics
R. Sujith, Vishnu R. Unni
Summary: Unsteady flow fields in combustion systems can lead to inherent instabilities, requiring tools from nonlinear dynamics and complex systems theory for analysis and control. Understanding and characterizing these dynamics is crucial for ensuring the safe and reliable operation of high efficiency combustion systems.
PROCEEDINGS OF THE COMBUSTION INSTITUTE
(2021)
Article
Mathematics, Applied
Kaiyin Huang, Shaoyun Shi, Shuangling Yang
Summary: The Morales-Ramis theory provides an effective and powerful non-integrability criterion for complex analytic Hamiltonian systems via the differential Galoisian obstruction. In this paper, we give a new Morales-Ramis type theorem on the meromorphic Jacobi non-integrability of general analytic dynamical systems. The key point is to show that the existence of Jacobian multipliers of a nonlinear system implies the existence of common Jacobian multipliers of Lie algebra associated with the identity component. In addition, we apply our results to the polynomial integrability of Karabut systems for stationary gravity waves in finite depth.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Physics, Multidisciplinary
Sebastiano Peotta, Fredrik Brange, Aydin Deger, Teemu Ojanen, Christian Flindt
Summary: Dynamical phase transitions extend the concept of criticality to nonstationary settings, involving sudden changes in the macroscopic properties of time-evolving quantum systems. The research combines symmetry, topology, and nonequilibrium physics, utilizing Loschmidt cumulants to determine critical times of interacting many-body systems. Experimental prospects include predicting the first critical time of a quantum many-body system by measuring energy fluctuations in the initial state, with potential implementation on near-term quantum computers with a limited number of qubits.
Article
Engineering, Aerospace
Rajib Mia, Bangaru Rama Prasadu, Elbaz I. Abouelmagd
Summary: In this study, the modified elliptic restricted three-body problem is used to study the dynamical motion of infinitesimal bodies by considering additional perturbed forces. Semi-analytical solutions are obtained for the locations of non-collinear equilibrium points. The model is applied to real astronomical systems, and the locations and stability of these points are numerically and graphically estimated.
Article
Mathematics, Applied
Miguel A. Prado Reynoso, Marcus W. Beims
Summary: Oseledec's theorem provides necessary conditions for the existence of Oseledec's splitting and the formal definition of Lyapunov exponents. By introducing the concept of R-domination and R-non-domination, we propose three quantifiers that can be used to study the complex dynamics of physical systems. Numerical results demonstrate that regions near hyperbolic periodic points have larger Oseledec R-domination compared to regions around islands of regularity.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Operations Research & Management Science
Pankaj Gautam, Daya Ram Sahu, Avinash Dixit, Tanmoy Som
Summary: This paper analyzes a new framework regarding the inclusion problem and dynamical systems, discussing the uniqueness and convergence of generated trajectories and introducing a new dynamical system with the essence of non-self-adjoint linear operators. The research results extend traditional dynamical systems in the framework of variable metrics and can be applied to compute a generalized Nash equilibrium in monotone games.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2021)
Article
Automation & Control Systems
Fangfang Dong, Dong Jin, Xiaomin Zhao, Jiang Han, Wei Lu
Summary: A robust control method with tunable parameters is proposed to address time-varying bounded uncertainty in mechanical systems, ensuring system stability. Fuzzy set theory is used to describe uncertainty, and parameters of the control are optimized based on non-cooperative game theory. The effectiveness of the optimized control method is demonstrated in trajectory tracking control for an omnidirectional mobile platform.
Article
Computer Science, Interdisciplinary Applications
S. Baars, D. Castellana, F. W. Wubs, H. A. Dijkstra
Summary: In this paper, a modified method, Trajectory-Adaptive Multilevel Sampling (TAMS), has been developed to compute probabilities of rapid transitions in stochastic nonlinear dynamical systems. The key innovation of a projected time-stepping approach significantly reduces computational costs and memory usage, enabling its application to high-dimensional systems. The performance of this new implementation of TAMS is studied through an example of the collapse of the Atlantic Ocean Circulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics
Diana T. Pham, Zdzislaw E. Musielak
Summary: Non-standard Lagrangians, which lack discernible energy-like terms, are found to produce the same equations of motion as standard Lagrangians, which contain identifiable energy-like terms. A novel method is developed for deriving non-standard Lagrangians for second-order nonlinear differential equations with damping, and the limitations of this method are explored. It is demonstrated that these limitations only exist for nonlinear dynamical systems that can be converted into linear ones. The derived results are then applied to selected population dynamics models to derive non-standard Lagrangians, their corresponding null Lagrangians, and gauge functions, and to discuss their roles in population dynamics.
Article
Mathematics, Applied
Steven L. Brunton, Marko Budisic, Eurika Kaiser, J. Nathan Kutz
Summary: The field of dynamical systems is undergoing a transformation due to the emergence of mathematical tools and algorithms from modern computing and data science. Data-driven approaches that use operator-theoretic or probabilistic frameworks are replacing first-principles derivations and asymptotic reductions. The Koopman spectral theory, which represents nonlinear dynamics using an infinite-dimensional linear operator, has the potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. However, a challenge remains in obtaining finite-dimensional coordinate systems and embeddings that approximately linearize the dynamics. The success of Koopman analysis is attributed to its rigorous theoretical connections, measurement-based approach suitable for leveraging big data and machine learning techniques, and the development of simple yet powerful numerical algorithms.
Review
Mechanics
R. A. S. Frantz, J. -Ch. Loiseau, J. -Ch. Robinet
Summary: In fluid dynamics, predicting and characterizing bifurcations, from the onset of unsteadiness to the transition to turbulence, is crucial. This review presents a concise theoretical and numerical framework for computing and analyzing stability of high-dimensional systems. The methods discussed are implemented in an open-source toolbox, nekStab, and their accuracy and performance are demonstrated using standard benchmarks.
APPLIED MECHANICS REVIEWS
(2023)