arXiv subjects

Andrey Romanov

Publications and source records attributed to Andrey Romanov.

6 recordsLinked to original sources

arXiv2025

Nonlinear constrained optimization of Schur test functions

We apply the iterative nonlinear programming method, previously proposed in our earlier work, to optimize Schur test functions and thereby provide refined upper bounds for the norms of integral operators. As an illustration, we derive such bounds for transfer operators associated with twofold additive compound operators that arise in the study of delay equations. This is related to the verification of frequency inequalities that guarantee the global stability of nonlinear delay equations through the generalized Bendixson criterion.

math.OC↗

arXiv2025

Robust upper estimates for topological entropy via nonlinear constrained optimization over adapted metrics

We present an analytical-numerical method providing robust upper estimates for the topological entropy or, more generally, uniform volume growth exponents of differentiable mappings. By introducing varying metrics, we simplify the analysis at the cost of generally rougher bounds, but keeping the prospect of choosing more relatable metrics to refine the estimates. With any covering of an invariant set by a finite number of cubes, we associate a graph describing overlaps (edges) of the cubes (vertices) under iterates of the mapping. Weighing vertices according to a given metric, we reduce the problem to finding simple cycles with maximal relative weights. Then we develop an algorithm concerned with iterative resolving nonlinear programming problems for optimization of maximal relative weights in general smooth families of metrics which may involve interpolation or neural networks models. We describe applications of the algorithm to compute the largest uniform Lyapunov exponent and uniform Lyapunov dimension for the H\'{e}non and Rabinovich systems justifying the Eden conjecture at stationary and periodic points respectively.

math.DS↗

arXiv2024

Near-Isotropic Sub-{\AA}ngstrom 3D Resolution Phase Contrast Imaging Achieved by End-to-End Ptychographic Electron Tomography

Three-dimensional atomic resolution imaging using transmission electron microscopes is a unique capability that requires challenging experiments. Linear electron tomography methods are limited by the missing wedge effect, requiring a high tilt range. Multislice ptychography can achieve deep sub-{\AA}ngstrom resolution in the transverse direction, but the depth resolution is limited to 2 to 3 nanometers. In this paper, we propose and demonstrate an end-to-end approach to reconstructing the electrostatic potential volume of the sample directly from the 4D-STEM datasets. End-to-end multi-slice ptychographic tomography recovers several slices at each tomography tilt angle and compensates for the missing wedge effect. The algorithm is initially tested in simulation with a Pt@$\mathrm{Al_2O_3}$ core-shell nanoparticle, where both heavy and light atoms are recovered in 3D from an unaligned 4D-STEM tilt series with a restricted tilt range of 90 degrees. We also demonstrate the algorithm experimentally, recovering a Te nanoparticle with sub-{\AA}ngstrom resolution.

physics.comp-ph↗

arXiv2023

High-resolution 3D phase-contrast imaging beyond the depth of field limit via ptychographic multi-slice electron tomography

Resolving single atoms in large-scale volumes has been a goal for atomic resolution microscopy for a long time. Electron microscopy has come close to this goal using a combination of advanced electron optics and computational imaging algorithms. However, atomic-resolution 3D imaging in volumes larger than the depth of field limit of the electron optics has so far been out of reach. Electron ptychography, a computational imaging method allowing to solve the multiple-scattering problem from position- and momentum-resolved measurements, provides the opportunity to surpass this limit. Here, we experimentally demonstrate atomic resolution three-dimensional phase-contrast imaging in a volume surpassing the depth of field limits using multi-slice ptychographic electron tomography. We reconstruct tilt-series 4D-STEM measurements of a Co3O4 nanocube, yielding 1.75 {\AA} resolution in a reconstructed volume of (18.2nm)^3.

cond-mat.mtrl-sci↗

arXiv2023

Frequency conditions for the global stability of nonlinear delay equations with several equilibria

In our adjacent work, we developed a spectral comparison principle for compound cocycles generated by delay equations. It allows to derive frequency inequalities for the uniform exponential stability of such cocycles by means of their comparison with stationary problems. Such inequalities are hard to verify purely analytically, and in this work we develop approximation schemes to verify some of the arising frequency inequalities. Besides some general theoretical results, in applications we stick to the case of scalar equations. By means of the Suarez-Schopf delayed oscillator and the Mackey-Glass equations, we demonstrate applications of the theory to reveal regions in the space of parameters where the absence of closed invariant contours can be guaranteed. Since the frequency inequalities are robust, so close systems also satisfy them, we expect the method to actually imply the global stability, as in known finite-dimensional results utilizing variants of the closing lemma, which is still awaiting developments in infinite dimensions.

math.DS↗

arXiv2021

Hidden and unstable periodic orbits as a result of homoclinic bifurcations in the Suarez-Schopf delayed oscillator and the irregularity of ENSO

We revisit the classical Suarez-Schopf delayed oscillator. Special attention is paid to the region of linear stability in the space of parameters. By means of the theory of inertial manifolds developed in our adjacent papers, we provide analytical-numerical evidence for the existence of two-dimensional inertial manifolds in the model. This allows to suggest a complete qualitative description of the dynamics in the region of linear stability. We show that there are two subregions corresponding to the existence of hidden or self-excited periodic orbits. These subregions must be separated by a curve on which homoclinic "figure eights", bifurcating into a single one or a pair of unstable periodic orbits, should exist. We relate the observed hidden oscillations and homoclinics to the irregularity theories of ENSO and provide numerical evidence that chaotic behavior may appear if a small periodic forcing is applied to the model. We also use parameters from the Suarez-Schopf model to discover hidden and self-excited asynchronous periodic regimes in a ring array of coupled lossless transmission lines studied by J. Wu and H. Xia.

math.DS↗