Related papers: Averaging of time-periodic systems without a small…

The calculation of observable averages in non-equilibrium regimes is one of the most important problems in statistical physics. Using the Hamiltonian approach of nonlinear response theory, we obtain a series expansion of the average excess…

We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…

This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse…

In the framework of Lie transform and the global method of averaging, the normal forms of a multidimensional slow-fast Hamiltonian system are studied in the case when the flow of the unperturbed (fast) system is periodic and the induced…

Nonlinear Hamiltonian systems describing the abstract Vlasov and Hartree equations are considered in the framework of algebraic Poissonian theory. The concept of uniformization is introduced; it generalizes the method of second quantization…

When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order "guiding system", placing the time dependence at higher orders. Recent research focused on…

Floating offshore structures often exhibit low-frequency oscillatory motions in the horizontal plane, with amplitudes in the same order as their characteristic dimensions and larger than the corresponding wave-frequency responses, making…

Multivariate time series forecasting with hierarchical structure is pervasive in real-world applications, demanding not only predicting each level of the hierarchy, but also reconciling all forecasts to ensure coherency, i.e., the forecasts…

We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…

This note is devoted to inverse spectral problems for canonical Hamiltonian systems on the half-line. An approach to inverse spectral problems based on the use of truncated Toeplitz operators has been especially effective in the case when…

Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…

Time series analysis finds wide applications in fields such as weather forecasting, anomaly detection, and behavior recognition. Previous methods attempted to model temporal variations directly using 1D time series. However, this has been…

We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…

The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…

We present a new method for the nonlinear approximation of the solution manifolds of parameterized nonlinear evolution problems, in particular in hyperbolic regimes with moving discontinuities. Given the action of a Lie group on the…

For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…

This work provides a systematic recipe for computing accurate high order Fourier expansions of quasiperiodic invariant circles in area preserving maps. The recipe requires only a finite data set sampled from the quasiperiodic circle. Our…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…