arXiv subjects

Sergii Skurativskyi

Publications and source records attributed to Sergii Skurativskyi.

9 recordsLinked to original sources

arXiv2025

Cluster analysis of earthquake hypocenters in Azerbaijan and surrounding territories

The research focuses on seismic events that occurred in Azerbaijan and adjacent territories, regions known for strong seismic activity. We analyze a catalog of recorded earthquakes between 2010 and 2023, extracting the locations of the earthquake hypocenters for study purposes. Using statistical methods and cluster analysis tools, we developed a procedure for partitioning hypocenter clusters. The procedure begins with estimates of the Morisita Index, which is suitable for preliminary assessments of the statistical properties of hypocenter sets. Analysis of the Morisita Index indicates that the spatial distribution of hypocenters is heterogeneous, containing denser domains referred to as clusters. The next stage involves identifying spatial clusters using the DBSCAN and HDBSCAN algorithms. Due to the strong dependence of results on the algorithm's parameters, we selected several partitions with 5-8 clusters that provided maximal or near-maximal Silhouette Index values. The final stage assesses the similarity of the resulting partitions, using the Adjusted Rand Index to identify partitions with a specified degree of similarity. The final set of partitions was compared to the fault network of the region. Based on the selected partition, the earthquake depth distributions were studied. Specifically, approximate probability density functions were constructed in the form of mixtures of normal distributions, leading to the identification of several bimodal distributions.

physics.geo-ph↗

arXiv2025

Approximation of Invariant Solutions to the Nonlinear Filtration Equation by Modified Pade Approximants

This paper deals with a mathematical model for oil filtration in a porous medium and its self-similar and traveling wave regimes. The model consists of the equation for conservation mass and dependencies for porosity, permeability, and oil density on pressure. The oil viscosity is considered to be the experimentally expired parabolic relationship on pressure. To close the model, two types of Darcy law are used: the classic one and the dynamic one describing the relaxation processes during filtration. In the former case, self-similar solutions are studied, while in the latter case, traveling wave solutions are the focus. Using the invariant solutions, the initial model is reduced to the nonlinear ordinary differential equations possessing the trajectories vanishing at infinity and representing the moving liquid fronts in porous media. To approximate these solutions, we elaborate the semi-analytic procedure based on modified Pade approximants. In fact, we calculate sequentially Pade approximants up to 3d order for a two-point boundary value problem on the semi-infinite domain. A good agreement of evaluated Pade approximants and numerical solutions is observed. The approach provides relatively simple quasi-rational expressions of solutions and can be easily adapted for other types of model's nonlinearity.

math-ph↗

arXiv2025

Cluster and statistical analysis of spatial earthquake patterns in the South Caucasus region

The Caucasus region is characterized by heterogeneous and strong seismicity as a result of collision between Arabian and Eurasian tectonic plates. A rich variety of seismic events also distinguishes Azerbaijan, located in its south part. In this research, we consider the earthquakes, specifically spatial earthquake patterns that occurred in Azerbaijan and adjacent areas from 2010 to 2023. Applying density-based clustering algorithms to the earthquake catalog, the proper partitions of spatial earthquake distributions were obtained. The statistical properties of the catalog's partition into 7 clusters are studied in more detail. In particular, we consider the random variable, which is the distance from the fixed point of the earth's surface to earthquake epicenters. The analytical approximation of the cumulative distribution function is constructed for the case when the fixed point coincides with the cluster center and epicenters in the cluster are distributed by the bi-variate normal distribution. For comparison, the numerical distribution functions are evaluated on the basis of Johnson curves and good agreement is observed. Another case is also considered when the fixed point lies outside of a cluster. Under the assumption that a cluster is a circle and epicenters in it are distributed uniformly, the cumulative and probability distribution functions are derived. Applying these functions to the approximation of histograms for the distances from the Shamkir hydroelectric power station to the clusters shows that satisfactory agreement can be achieved. These results are promising for performing the seismic risk assessment for the Shamkir station or other objects of Azerbaijan's critical infrastructure.

physics.geo-ph↗

arXiv2019

On the spectral stability of soliton-like solutions to a non-local hydrodynamic-type model

A model of nonlinear elastic medium with internal structure is considered. The medium is assumed to contain cavities, microcracks or blotches of substances that differ sharply in physical properties from the base material. To describe the wave processes in such a medium, the averaged values of physical fields are used. This leads to nonlinear evolutionary PDEs, differing from the classical balance equations. The system under consideration possesses a family of invariant soliton-like solutions. These solutions are shown to be spectrally stable under certain restrictions on the parameters.

nlin.PS↗

arXiv2019

Solitary wave dynamics governed by the modified FitzHugh-Nagumo equation

The paper deals with the studies of the nonlinear wave solutions supported by the modified FitzHugh-Nagumo (mFHN) system. It was proved in our previous work that the model, under certain conditions, possesses a set of soliton-like traveling wave (TW) solutions. In this paper we show that the model has two solutions of the soliton type differing in propagation velocity. Their location in parametric space, and stability properties are considered in more details. Numerical results accompanied by the application of the Evans function technique prove the stability of fast solitary waves and instability of slow ones. A possible way of formation and annihilation of localized regimes in question is studied therein too.

nlin.PS↗

arXiv2019

Existence of the solitary wave solutions supported by the hyperbolic modification of the FitzHugh-Nagumo system

We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh-Nagumo system, describing the nerve impulse propagation in axon. The modeling system is shown to possesses soliton-like solutions under certain restrictions on the parameters. The results of theoretical studies are backed by the direct numerical simulation.

nlin.PS↗

arXiv2019

Properties of impact events in the model of forced impacting oscillator: experimental and numerical investigations

The paper deals with the studies of forced impacting oscillator when are taken into account the dry and viscous resistance, as well as the generalized Hertz contact law during an impact. The numerical treatments of mathematical model are accompanied with the validations on the base of experimental rig. To study the solutions of the mathematical model, we construct the sequences of impacts, when the system is evolved in periodic and chaotic modes. The statistical properties of chaotic impact events are considered in more details. In particular, we analyze the successive iterations of impact map, autocorrelation function and coefficient of variation for the impact train, the histograms for the inter-impact intervals and values of obstacle penetrations. It is revealed that the impact sequence is stationary but non-Poissonian and contains temporal scales which do not relate to the external stimulus. This sequence can be described by a bimodal distribution. These findings are confirmed by the analysis of experimental data.

nlin.CD↗

arXiv2015

Solitary waves in one-dimensional pre-stressed lattice and its continual analog

One of the most interesting phenomena occuring in nonlinear media models is the existence of wave patterns, such as kinks, solitons, compactons, peakons and many others. There are known numerous nonlinear evolutionary PDEs, supporting soliton (multi-soliton) and compacton traveling wave (TW) solutions. Unfortunately, the vast majority of the models, with the exception of completely integrable ones, do not enable to analyze the properties of solitary waves interaction using only qualitative methods. Therefore it is instructive, when dealing with the non-integrable PDEs, to combine the qualitative treatment with numerical simulations. In this report we are going to present the results of studying compacton solutions in the continual models for granular pre-stressed chains. The model is shown to possess a pair of compacton TW solutions which are the bright and dark compactons. First we consider the stability properties of the compacton solutions and show that both the bright and the dark compactons pass the stability test. Next we analyze the dynamics of the compactons, simulating numerically the temporal evolution of a single compacton, a well as the interection of pairs of compactons, including bright-bright, dark-dark and bright-dark pairs. To be able to simulate the evolutin of interacting compactons, we have modified the numerical scheme built by J. de Frutos, M. A. Lopez-Marcos, and J. M. Sanz-Serna. Results of simulations are compared with that of evolution of corresponding impulse in the granular pre-stressed chain.

nlin.PS↗

arXiv2015

On the dynamics of solitary wave solutions supported by the model of mutually penetrating continua

The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators. These equations of motion are closed by the cubic constitutive equation for the carrying medium. Studying the wave solutions we reduce this model to a plane dynamical system of Hamiltonian type. This allows us to derive the relation describing the homoclinic trajectory going through the origin and obtain the solitary wave with infinite support. Moreover, there exist a limiting solitary wave with finite support, i.e. compacton. To model the solitary waves dynamics, we construct the three level finite-difference numerical scheme and study its stability. We are interested in the interaction of the pair of solitary waves. It turns out that the collisions of solitary waves have non-elastic character but the shapes of waves after collisions are preserved.

nlin.PS↗