Related papers: Dynamics under Geometric Dissipation
The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold. We focus on the case of spherical systems, which are…
In this paper, we study the stabilization problem for a hyperbolic type Stokes system posed on a bounded domain. We show that when the damping effects are restricted to a subdomain satisfying the geometrical control condition the system…
We study axisymmetric accretion of slowly rotating matter onto a gravitation center. The process of the flow restructuring is presented as the angular velocity of accreting gas approaches the Keplerian velocity. For spherically-symmetric…
Novel criteria for global asymptotic stability of nonlinear uncertain finite-dimensional systems are presented. The results are obtained by a combination of the "discretization approach" and the ideas contained in the proof of the original…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
A theory of dissipative generalized continuum mechanics is presented in the framework of weakly nonlocal non-equilibrium thermodynamics. The evolution equation of microdeformation is obtained by thermodynamic principles. Conditions of…
We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and…
The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant $\Lambda$ is zero. The resulting framework lies at the foundation of research in diverse…
Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out…
We show that the dynamical symmetry exists in dissipative quantum many-body systems. Under constraints on both Hamiltonian and dissipation parts, the time evolution of particular observables can be symmetric between repulsive and attractive…
The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the…
Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle…
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…
A geometric formulation for stabilization of systems with one degree of underactuation which fully solves the energy shaping problem for these system is given. The results show that any linearly controllable simple mechanical system with…
When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics…
Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…