Related papers: Two Dimensional Discrete Dynamics of Integral Valu…
In this paper we develop two models for the steady states and evolution of two dimensional isothermal self gravitating and rotating incompressible gas which are based on the hydrodynamic equations for stratified fluid. The first model is…
Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some…
The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble…
A framework analogous to path integrals in quantum physics is set up for abstract dynamical systems in a W*-algebraic setting. We consider spaces of evolutions, defined in a specific way, of a W*-algebra A as an analogue of spaces of…
We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…
In this article, we develop a systematic approach of the invariant subspace method combined with variable transformation to find the generalized separable exact solutions of the nonlinear two-component system of time-fractional PDEs…
Starting from the Ashtekar Hamiltonian variables for general relativity, the self-dual Einstein equations (SDE) may be rewritten as evolution equations for three divergence free vector fields given on a three dimensional surface with a…
A system's invariance under Galilean transformation implies three locally conserved densities. Including them as variables, the thermodynamics is rendered explicitly frame independent, dissipative mass currents are shown to vanish, and…
We study a quasi-two-dimensional electrostatic drift kinetic system as a model for near-marginal ion temperature gradient (ITG) driven turbulence. A proof is given of the nonlinear stability of this system under conditions of linear…
A neutron star in an inspiraling binary system is tidally deformed by its companion, and the effect leaves a measurable imprint on the emitted gravitational waves. While the tidal interaction falls within the regime of static tides during…
Discovering non-linear dynamical models from data is at the core of science. Recent progress hinges upon sparse regression of observables using extensive libraries of candidate functions. However, it remains challenging to model hidden…
We describe a possible general and simple paradigm in a classical thermal setting for discrete time crystals (DTCs), systems with stable dynamics which is subharmonic to the driving frequency thus breaking discrete time-translational…
We report on recently performed simulations of Causal Dynamical Triangulations (CDT) in 2+1 dimensions aimed at studying its effective dynamics in the continuum limit. Two pieces of evidence from completely different measurements are…
Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
Dynamic invariants are often estimated from experimental time series with the aim of differentiating between different physical states in the underlying system. The most popular schemes for estimating dynamic invariants are capable of…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
We consider all possible dynamical theories which evolve two transverse vector fields out of a three-dimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant…
There still remains an extreme performance gap between Vision Transformers (ViTs) and Convolutional Neural Networks (CNNs) when training from scratch on small datasets, which is concluded to the lack of inductive bias. In this paper, we…