Related papers: Lagrangian Descriptors: A Method for Revealing Pha…
Traffic flow prediction is a typical spatio-temporal prediction problem and has a wide range of applications. The core challenge lies in modeling the underlying complex spatio-temporal dependencies. Various methods have been proposed, and…
Linear time-periodic (LTP) dynamical systems frequently appear in the modeling of phenomena related to fluid dynamics, electronic circuits, and structural mechanics via linearization centered around known periodic orbits of nonlinear…
Trajectory design in highly-perturbed environments like binary asteroids is challenging. It typically requires using realistic, non-autonomous dynamical models in which periodic solutions derived in autonomous systems vanish. In this work,…
We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations. All these models have classical unique solutions, at…
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the non-linear evolution of…
In many applications of finance, biology and sociology, complex systems involve entities interacting with each other. These processes have the peculiarity of evolving over time and of comprising latent factors, which influence the system…
A key aspect of fluid dynamics is the correct definition of the \textit{% phase-space} Lagrangian dynamics which characterizes arbitrary fluid elements of an incompressible fluid. Apart being an unsolved theoretical problem of fundamental…
A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two-…
This paper focuses on developing a new paradigm motivated by investigating the consensus problem of networked Lagrangian systems with time-varying delay and switching topologies. We present adaptive controllers with piecewise continuous or…
In this article, we argue that two distinct types of time should be taken into account in relativistic physics: a geometric time, which emanates from the structure of spacetime and its metrics, and a causal time, indicating the flow from…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
This manuscript studies the unsupervised change point detection problem in time series of graphs using a decoder-only latent space model. The proposed framework consists of learnable prior distributions for low-dimensional graph…
This paper proposes a new methodology in linear time-periodic (LTP) system identification. In contrast to previous methods that totally separate dynamics at different tag times for identification, the method focuses on imposing appropriate…
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of…
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles…
We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field…
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…
We introduce a modal representation for Lagrangian trajectories in turbulence, termed Lagrangian Proper Orthogonal Decomposition (LPOD). An ensemble of particle trajectories is used to construct velocity time series, which are normalized…
This paper presents a novel approach for the identification of linear time-periodic (LTP) systems in continuous time. This method is based on harmonic modeling and consists in converting any LTP system into an equivalent LTI system with…
Deep learning (DL) algorithms are often defined in terms of temporal relationships: a tensor at one timestep may depend on tensors from earlier or later timesteps. Such dynamic dependencies (and corresponding dynamic tensor shapes) are…