Related papers: Dynamical symmetries and well-localized hydrogenic…
This paper discusses dynamical systems for disk-covering and sphere-packing problems. We present facility location functions from geometric optimization and characterize their differentiable properties. We design and analyze a collection of…
A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation…
The morphology of a mixture made of a polar active gel immersed in an isotropic passive fluid is studied numerically. Lattice Boltzmann method is adopted to solve the Navier-Stokes equation and coupled to a finite-difference scheme used to…
The quantum dynamical evolution of atomic and molecular aggregates, from their compact to their fragmented states, is parametrized by a single collective radial parameter. Treating all the remaining particle coordinates in d dimensions…
A complete classification of integrable conservative hydrodynamic chains is presented. These hydrodynamic chains are written via special coordinates -- moments, such that right hand sides of these infinite component systems depend linearly…
We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our…
We consider optical high harmonic generation in a hydrogen atom confined in a breathing spherical box by considering atomic nucleus as fixed at the center of sphere. In such spherically symmetric, dynamical trap, the high harmonic…
A method of calculating a new class of symmetries is presented for partial differential equations. The method give a new dynamical solution for an isothermal and cylindrically symmetric hydrodynamics equations under self-gravity. The…
We present two methods for computing the dynamic structure factor for warm dense hydrogen without invoking either the Born-Oppenheimer approximation or the Chihara decomposition, by employing a wave-packet description that resolves the…
This exploration of solutions for the orbits of Local Group galaxies under the cosmological initial condition of growing peculiar velocities and fitted to measured distances, redshifts, and proper motions reveals a considerable variety of…
Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within…
We show how to generate robust self-sustained clusters of soliton bullets-spatiotemporal (optical or matter-wave) solitons. The clusters carry an orbital angular momentum being supported by competing nonlinearities. The "atoms" forming the…
By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One…
In this paper we present a full general relativistic one-dimensional hydro-code which incorporates a modern high-resolution shock-capturing algorithm, with an approximate Riemann solver, for the correct modelling of formation and…
Finding constrained saddle points on Riemannian manifolds is significant for analyzing energy landscapes arising in physics and chemistry. Existing works have been limited to special manifolds that admit global regular level-set…
We have developed the formalism necessary to employ the discontinuous-Galerkin approach in general-relativistic hydrodynamics. The formalism is firstly presented in a general 4-dimensional setting and then specialized to the case of…
The static and dynamical properties of a one-dimensional quantum system described by a non-Hermitian Hamiltonian of the so-called Hatano-Nelson type; a tight-binding model with asymmetric (or non-reciprocal) hopping, are studied. The static…
Dynamical System has been widely used for encoding trajectories from human demonstration, which has the inherent adaptability to dynamically changing environments and robustness to perturbations. In this paper we propose a framework to…