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We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with…
This paper presents a nonlinear approach to measurements a general framework for dealing with variations of environmental conditions. My method may prove promising to extensions beyond classical physics, economics, and other sciences. I…
We extend the approximate residual balancing (ARB) framework to nonlinear models, answering an open problem posed by Athey et al. (2018). Our approach addresses the challenge of estimating average treatment effects in high-dimensional…
The first-principles-based effective Hamiltonian scheme provides one of the most accurate modeling technique for large-scale structures, especially for ferroelectrics. However, the parameterization of the effective Hamiltonian is…
We present a method that formally calculates \emph{exact} frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary…
The sensitivity of long-time averages of a hyperbolic chaotic system to parameter perturbations can be determined using the shadowing direction, the uniformly-bounded-in-time solution of the sensitivity equations. Although its existence is…
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging…
Following arXiv:2303.02992, we develop an approach to the Hamiltonian theory of normal forms based on continuous averaging. We concentrate on the case of normal forms near an elliptic singular point, but unlike arXiv:2303.02992 we do not…
The application of the collective variables method to the study of the behaviour of nonuniversal characteristics of the system in the critical region is illustrated by an example of the order parameter. Explicit expressions for the order…
We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…
This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…
We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
This paper proposes a recursive interval-valued estimation framework for identifying the parameters of linearly parameterized systems which may be slowly time-varying. It is assumed that the model error (which may consist in measurement…
The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential…
Hamiltonian Truncation Effective Theory is a framework that aims to improve the results of Hamiltonian truncation in a systematic, order-by-order fashion using Effective Field Theory methodology. The result is a truncated effective…
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…