Related papers: Momentum Map and Action-Angle Variables for Nambu …
A dynamic factor model with factor series following a VAR$(p)$ model is shown to have a VARMA$(p,p)$ model representation. Reduced-rank structures are identified for the VAR and VMA components of the resulting VARMA model. It is also shown…
We propose a novel method for motion planning and illustrate its implementation on several canonical examples. The core novel idea underlying the method is to define a metric for which a path of minimal length is an admissible path, that is…
Base inertial parameters constitute a minimal inertial parametrization of mechanical systems that is of interest, for example, in parameter estimation and model reduction. Numerical and symbolic methods are available to determine their…
Various fluid mechanical systems enjoy a hidden, higher-dimensional dynamical Poincare symmetry, which arises owing to their descent from a Nambu-Goto action. Also, for the same reason, there are equivalence transformations between…
Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is…
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display…
A geometric approach to derive the Nambu brackets for ideal two-dimensional (2D) hydrodynamics is suggested. The derivation is based on two-forms with vanishing integrals in a periodic domain, and with resulting dynamics constrained by an…
We will consider here some dynamics of the tangent map, weaker than hyperbolicity, and we will discuss if these structures are rich enough to provide a good description of the dynamics from a topological and geometrical point of view. This…
Patterns and waves are basic and important phenomena that govern the dynamics of physical and biological systems. A common theme in investigating such systems is to identify the intrinsic factors responsible for such self-organization. The…
We study the drift of slow variables in a slow-fast Hamiltonian system with several fast and slow degrees of freedom. For any periodic trajectory of the fast subsystem with the frozen slow variables we define an action. For a family of…
I describe a generalization of the hybrid Monte Carlo (HMC) algorithm in which the molecular dynamics (MD) steps utilize Nambu generalized Hamiltonian dynamics. Characterized by multiple Hamiltonian functions, this formalism allows me to…
Damped-driven systems are ubiquitous in engineering and science. Despite the diversity of physical processes observed in a broad range of applications, the underlying instabilities observed in practice have a universal characterization…
Recent developments on three body systems have revealed that dynamics of trajectories passing through collinear configurations can be easily adopted. We analyse the reduction procedure in order to detect the points where collinear…
Geometric mechanics provides valuable insights into how biological and robotic systems use changes in shape to move by mechanically interacting with their environment. In high-friction environments it provides that the entire interaction is…
Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the…
The motion of a mechanical system can be defined as a path through its configuration space. Computing such a path has a computational complexity scaling exponentially with the dimensionality of the configuration space. We propose to reduce…
This paper presents entropy maps, an approach to describing and visualising uncertainty among alternative potential movement intentions in pedestrian simulation models. In particular, entropy maps show the instantaneous level of randomness…
Driving a quantum system periodically in time can profoundly alter its long-time dynamics and trigger topological order. Such schemes are particularly promising for generating non-trivial energy bands and gauge structures in quantum-matter…
Microorganisms often perform chemotaxis, (i.e., sensing and moving toward a region with a higher concentration of an attractive chemical) by changing the rate of tumbling for random walk. We studied several models with internal adaptive…
We consider the dynamics of a Hamiltonian particle forced by a rapidly oscillating potential in $\dim$-dimensional space. As alternative to the established approach of averaging Hamiltonian dynamics by reformulating the system as…