Related papers: Reverse-engineering invariant manifolds with asymp…
Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between…
Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been…
This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…
Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transformations. Their macroscopic response--including energy dissipation during impact,…
We analytically compute asymptotic expansions of a 1-dimensional sub-manifold of stable and unstable manifolds in a 4-dimensional symplectic mapping by using the method called asymptotic expansions beyond all orders. This method enables us…
We propose a new method for constructing partially hyperbolic diffeomorphisms on closed manifolds. As a demonstration of the method we show that there are simply connected closed manifolds that support partially hyperbolic diffeomorphisms.
Designing complex physical systems, including photonic structures, is typically a tedious trial-and-error process that requires extensive simulations with iterative sweeps in multi-dimensional parameter space. To circumvent this…
We present a method to construct a symplecticity preserving renormalization group map of a chain of weakly nonlinear symplectic maps and obtain a general reduced symplectic map describing its long-time behaviour. It is found that the…
In this paper we obtain an almost sure invariance principle for convergent sequences of either Anosov diffeomorphisms or expanding maps on compact Riemannian manifolds and prove an ergodic stability result for such sequences. The sequences…
A robotic platform for mobile manipulation needs to satisfy two contradicting requirements for many real-world applications: A compact base is required to navigate through cluttered indoor environments, while the support needs to be large…
Robotic laparoscopic grasper is a surgical tool with minimal invasion. In this robot, achieve goals like precise tracking, stability and disturbance rejection are very important. In this paper, first the stages of modeling and simulating of…
In this paper, we derive high-dimensional asymptotic properties of the Moore-Penrose inverse and, as a byproduct, of various ridge-type inverses of the sample covariance matrix. In particular, the analytical expressions of the asymptotic…
Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic…
Two generically different but universal dynamical quantum many-body behaviors are discovered by probing the stability of trapped fragmented bosonic systems with strong repulsive finite/long range inter-particle interactions. We use…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…
We obtain general results on the dynamics of exactly conical geometries, where we use the notion of boundaries at infinity to characterize asymptotic behavior. As we demonstrate in examples, these notions also apply to smooth geometries…
An internal model of the own body can be assumed a fundamental and evolutionary-early representation as it is present throughout the animal kingdom. Such functional models are, on the one hand, required in motor control, for example solving…
We show that the standard method for constructing closed hyperbolic manifolds of arbitrary dimension possessing reflective symmetries typically produces reflections whose fixed point sets are nonseparating.
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
Compared to conventional robots, flexible manipulators offer many advantages, such as faster end-effector velocities and less energy consumption. However, their flexible structure can lead to undesired oscillations. Therefore, the applied…