相关论文: Advances in Cislunar Periodic Solutions via Taylor…

Describing general quantum many-body dynamics is a challenging task due to the exponential growth of the Hilbert space with system size. The time-dependent variational principle (TDVP) provides a powerful tool to tackle this task by…

Learning complex physical dynamics purely from data is challenging due to the intrinsic properties of systems to be satisfied. Incorporating physics-informed priors, such as in Hamiltonian Neural Networks (HNNs), achieves high-precision…

The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors…

We present a Lohner-type algorithm for rigorous integration of systems of Delay Differential Equations (DDEs) with multiple delays and its application in computation of Poincar\'e maps to study the dynamics of some bounded, eternal…

Designing spacecraft trajectories remains challenging in the presence of stochastic effects such as maneuver execution errors and observation uncertainties. Although covariance control and belief-space planning provide useful tools for…

We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor-Hoenselaers-Perj\'es procedure, we perform an expansion in the mass potential of a static…

The problem of orbital stabilization of underactuated mechanical systems with one passive degree-of-freedom (DOF) is revisited. Virtual holonomic constraints are enforced using a continuous controller; this results in a dense set of closed…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

This paper presents a novel approach for constructing neural networks which model charged particle beam dynamics. In our approach, the Taylor maps arising in the representation of dynamics are mapped onto the weights of a polynomial neural…

An ever-growing observational aggregate of extrasolar planets has revealed that systems of planets that reside in or near mean-motion resonances are relatively common. While the origin of such systems is attributed to protoplanetary…

We present a combinatorial approach to rigorously show the existence of fixed points, periodic orbits, and symbolic dynamics in discrete-time dynamical systems, as well as to find numerical approximations of such objects. Our approach…

In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider a model for spin-orbital motion: orbital…

We develop a class of mixed virtual volume methods for elliptic problems on polygonal/polyhedral grids. Unlike the mixed virtual element methods introduced in \cite{brezzi2014basic,da2016mixed}, our methods are reduced to symmetric,…

Low density plasmas in curved spacetimes, such as those found in accretion flows around black holes, are challenging to model from first principles, owing to the large scale separation between the characteristic scales of the microscopic…

We present a diffusion mechanism for time-dependent perturbations of autonomous Hamiltonian systems introduced in [25]. This mechanism is based on shadowing of pseudo-orbits generated by two dynamics: an `outer dynamics', given by…

In the planar three-body problem, we study solutions with zero initial velocity (brake orbits). Following such a solution until the three masses become collinear (syzygy), we obtain a continuous, flow-induced Poincar\'e map. We study the…

We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…

Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…

We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…

A method for ray-tracing through n-body simulations has been recently proposed. It is based on a periodic universe covered by simulation boxes. Photons move along appropriate directions to avoid periodicity effects. Here, an improved…