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Search results for: NONLINEAR EIGENVALUE PROBLEMS
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Analysis of nonlinear eigenvalue problems for guides and resonators in microwave and terahertz technology
PublicationThis dissertation presents developed numerical tools for investigating waveguides and resonators' properties for microwave and terahertz technology. The electromagnetics analysis requires solving complex eigenvalue problems, representing various parameters such as resonant frequency or propagation coefficient. Solving equations with eigenvalue boils down to finding the roots of the determinant of the matrix. At the beginning, one...
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Comments on ''An innovative fast powerful method for tackling electromagnetic eigenvalue problems for multistrip transmission lines''
PublicationPraca stanowi komentarz do publikacji Casanuevy i Garcii dotyczącej techniki szybkiego obliczania charakterystyk dyspersyjnych falowodów z niejednorodnym wypełnieniem. Zwrócono uwagę na niepotrzebną komplikację zagadnienia poprzez zastosowanie techniki rozkładu na wartości szczególne.
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On nonlinear two-point boundary value problems for impulsive differential-algebraic problems [online]
PublicationSformułowano warunki dostateczne na istnienie ekstremalnych rozwiązań dla zagadnień brzegowych dla równań różniczkowo-algebraicznych z impulsami. Badano też nierówności różniczkowo-algebraiczne z impulsami przy odpowiednich warunkach brzegowych. Na przykładzie zilustrowano otrzymane wyniki.
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Efficient and Systematic Solution of Real and Complex Eigenvalue Problems Employing Simplex Chain Vertices Searching Procedure
PublicationW artykule zaprezentowano nowatorską metodę, pozwalającą w bardzo efektywny sposób rozwiązywać rzeczywiste i zespolone zagadnienia własne (które przekształcić można w równania nieliniowe) często spotykane w elektrodynamice obliczeniowej. Idea metody oparta jest o śledzenie miejsc zerowych otrzymanego równania nieliniowego. W proponowanej technice zastosowano regularne wielościany, budując z nich łańcuch (ścieżkę) poszukiwanych...
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Solving nonlinear programming problems by using O&G software.
PublicationPraca opisuje pakiet optymalizacyjny oprogramowania O&G. Umożliwia on rozwiązywanie problemów programowania nieliniowego. Użytkownik może w wygodny sposób formułować rozwiązywane zadanie i dobierać metody obliczeniowe używając interaktywnego interfejsu.
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Degenerated isoparametric finite elements in nonlinear analysis of 2D-problems
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Inverse Nonlinear Eigenvalue Problem Framework for the Synthesis of Coupled-Resonator Filters With Nonresonant Nodes and Arbitrary Frequency-Variant Reactive Couplings
PublicationA novel, general circuit-level description of coupledresonator microwave filters is introduced in this article. Unlike well-established coupling-matrix models based on frequency-invariant couplings or linear frequency-variant couplings (LFVCs), a model with arbitrary reactive frequencyvariant coupling (AFVC) networks is proposed. The engineered formulation is more general than prior-art ones—with the only restriction that the coupling...
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A GPU Solver for Sparse Generalized Eigenvalue Problems with Symmetric Complex-Valued Matrices Obtained Using Higher-Order FEM
PublicationThe paper discusses a fast implementation of the stabilized locally optimal block preconditioned conjugate gradient (sLOBPCG) method, using a hierarchical multilevel preconditioner to solve nonHermitian sparse generalized eigenvalue problems with large symmetric complex-valued matrices obtained using the higher-order finite-element method (FEM), applied to the analysis of a microwave resonator. The resonant frequencies of the low-order...
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Nonlinear multipoint boundary value problems for second order differential equtions
PublicationPraca dotyczy problemow brzegowych dla rownan rozniczkowych rzedu drugiego z odchylonymi argumentami zaleznymi od rozwiazania. Podano warunki dostateczne na istnienie ekstremalnych rozwiazan. Poroblem istnienia jedynego rozwiazania tez byl przedmiotem badan. Podano dwa przyklady ilustrujace otrzymane wyniki.
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First-order functional difference equations with nonlinear boundary value problems
PublicationDyskutowano problem brzegowy dla równań różnicowych z opóźnionym argumentem. Nierówności różnicowe związane z w/w problem też były przedmiotem badań. Stosując metodę iteracji monotonicznych, sformułowano warunki dostateczne na istnienie ekstremalnych rozwiązań problemów brzegowych z opóźnionymi argumentami. Podano dwa przykłady ilustrujące otrzymane wyniki.
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Geometrically nonlinear analysis of shells - Benchmark problems for Autocad Robot Analysis Professional
PublicationThe aim of this work is to verify the suitability of commercial engineering software for geometrically nonlinear analysis of shells. This paper deals with the static, geometrically nonlinear analysis of shells made of an isotropic material. The Finite Element Method (FEM) is chosen to solve the problem. The results of the commercial software Autocad Robot Structural Analysis Professional (ARSAP) are compared with the litera-ture...
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Nonlinear boundary value problems for second order differential equations with causal operators
PublicationW pracy rozważane są równania różniczkowe rzędu drugiego z nielinowymi warunkami brzegowymi. Prawa strona takich zagadnień zawiera operatory typu ''causal''. Podane zostały warunki dostateczne na istnienie rozwiązań tego typu problemów. Badano też nierówności różniczkowe związane z w/w równaniami różniczkowymi. Podano przykład ilustrujący otrzymane wyniki teoretyczne.
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GPU-Accelerated LOBPCG Method with Inexact Null-Space Filtering for Solving Generalized Eigenvalue Problems in Computational Electromagnetics Analysis with Higher-Order FEM
PublicationThis paper presents a GPU-accelerated implementation of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method with an inexact nullspace filtering approach to find eigenvalues in electromagnetics analysis with higherorder FEM. The performance of the proposed approach is verified using the Kepler (Tesla K40c) graphics accelerator, and is compared to the performance of the implementation based on functions from...
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Application of discrete wavelet transform in seismic nonlinear analysis of soil–structure interaction problems
PublicationSimulation of soil-structure interaction (SSI) effects is a time-consuming and costly process. However, ignoring the influence of SSI on structural response may lead to inaccurate results, especially in the case of seismic nonlinear analysis. In this paper, wavelet transform methodology has been utilized for investigation of the seismic response of soil-structure systems. For this purpose, different storey outrigger braced buildings...
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Inline Microwave Filters With N+1 Transmission Zeros Generated by Frequency-Variant Couplings: Coupling-Matrix-Based Synthesis and Design
PublicationA general coupling-matrix-based synthesis methodology for inline Nth-order microwave bandpass filters (BPFs) with frequency-variant reactive-type couplings that generate N+1 transmission zeros (TZs) is presented in this brief. The proposed approach exploits the formulation of the synthesis problem as three inverse nonlinear eigenvalue problems (INEVPs) so that the coupling matrix is built from their sets of eigenvalues. For this...
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Direct estimation of linear and nonlinear functionals of quantum state
PublicationWe present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator. The network has many potential applications ranging from purity tests and eigenvalue estimations to direct characterization of...
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Modal FEM Analysis of Ferrite Resonant Structures
PublicationThe finite-element method (FEM) is applied for modal analysis of ferrite-loaded spherical resonators. To improve the efficiency of the numerical calculations, the body-of-revolution (BOR) technique is utilized. Due to the frequency-dependent ferrite permeability, FEM leads to a nonlinear eigenvalue problem that is challenging to solve. To this end, Beyn’s method is proposed. The effectiveness of the proposed approach is confirmed...
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Nonlocal Vibration of Carbon/Boron-Nitride Nano-hetero-structure in Thermal and Magnetic Fields by means of Nonlinear Finite Element Method
PublicationHybrid nanotubes composed of carbon and boron-nitride nanotubes have manifested as innovative building blocks to exploit the exceptional features of both structures simultaneously. On the other hand, by mixing with other types of materials, the fabrication of relatively large nanotubes would be feasible in the case of macroscale applications. In the current article, a nonlinear finite element formulation is employed to deal with...
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Frequency-Variant Double-Zero Single-Pole Reactive Coupling Networks for Coupled-Resonator Microwave Bandpass Filters
PublicationIn this work, a family of frequency-variant reactive coupling (FVRC) networks is introduced and discussed as new building blocks for the synthesis of coupled-resonator bandpass filters with real or complex transmission zeros (TZs). The FVRC is a type of nonideal frequency-dependent inverter that has nonzero elements on the diagonal of the impedance matrix, along with a nonlinear frequency-variation profile of its transimpedance...
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Nieliniowa statyka 6-parametrowych powłok sprężysto plastycznych. Efektywne obliczenia MES
PublicationGłównym zagadnieniem omawianym w monografii jest sformułowanie sprężysto-plastycznego prawa konstytutywnego w nieliniowej 6-parametrowej teorii powłok. Wyróżnikiem tej teorii jest występujący w niej w naturalny sposób tzw. stopień 6 swobody, czyli owinięcie (drilling rotation). Podstawowe założenie pracy to przyjęcie płaskiego stanu naprężenia uogólnionego na ośrodek typu Cosseratów. Takie podejście stanowi oryginalny aspekt opracowania....
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Selected problems of sensitivity and reliability of a jack-up platform
PublicationThe paper deals with sensitivity and reliability applications to numerical studies of an off-shore platform model. Structural parameters and sea conditions are referred to the Baltic jack-up drilling platform. The study aims at the influence of particular basic variables on static and dynamic response as well as the probability of failure due to water waves and wind loads. The paper presents the sensitivity approach to a generalized...
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Method of lines for nonlinear first order partial functional differential equations.
PublicationClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
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Nonlinear Properties of Seawater as a Factor Determining Nonlinear Wave Propagation
PublicationTaking practical advantage of nonlinear acoustical interactions occurring in seawater [1, 2] requires knowledge of the parameter of nonlinearity B=A of this medium. The literature does not offer much reports on B=A parameter value for seawater. In the few papers concerning that address the issue, results concerning ocean waters with high salinity and at large depths are given [3], while studies concerning seawater with low salinity...
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Nonlinear Viscoelastic Properties of Polyurethane Nanocomposites
PublicationIn recent years, the nonlinear viscoelastic behaviors of elastomeric nanocomposites have been examined, especially for a wide range of rubbery composite (including natural rubber) materials. This chapter describes the influence of fillers and nanofillers on the nonlinear viscoelastic properties of elastomeric polyurethane systems. These filled elastomers (similar to the classic natural rubber reinforced elastomers), also exhibit...
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Eigenvalue approach to synthesis of prototype filters with source/load coupling
PublicationArtykuł przedstawia nową, szybko zbieżną, technikę syntezy macierzy sprzężeń filtrów o charaktrystyce Czebyszewa. Synteza opiera się na zastosowaniu metody najmniejszych kwadratów w odniesieniu do wartości własnych macierzy sprzężeń oraz jej podmacierzy.
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Nonlinear properties of the Gotland Deep – Baltic Sea
PublicationThe properties of the nonlinear phenomenon in water, including sea water, have been well known for many decades. The feature of the non homogeneous distribution of the speed of sound along the depth of the sea is very interesting from the physical and technical point of view. It is important especially in the observation of underwater area by means of acoustical method ( Grelowska et al ., 2013; 2014). The observation of the underwater...
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Rheological Problems of Technical Fabirc
PublicationW pracy przedstawiono wyniki identyfikacji modeli Chaboche'a i Schapery dla tkaniny technicznej Panama.
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Fractional problems with advanced arguments
PublicationThis paper concerns boundary fractional differential problems with advanced arguments. We investigate the existence of initial value problems when the initial point is given at the end point of an interval. Nonhomogeneous linear fractional differential equations are also studied. The existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using...
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The nonlinear effects of sound in a liquid with relaxation losses
PublicationThe nonlinear effects of sound in electrolyte with a chemical reaction are examined. The dynamic equations that govern non-wave modes in the field of intense sound are derived, and acoustic forces of vortex, entropy, and relaxation modes are determined in the cases of low-frequency sound and high-frequency sound. The difference in the nonlinear effects of sound in electrolyte and in a gas with excited vibrational degrees of molecules,...
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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublicationIn this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...
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A Nonlinear Model of a Mesh Shell
PublicationFor a certain class of elastic lattice shells experiencing finite deformations, a continual model using the equations of the so-called six-parameter shell theory has been proposed. Within this model, the kinematics of the shell is described using six kinematically independent scalar degrees of freedom — the field of displacements and turns, as in the case of the Cosserat continuum, which gives reason to call the model under consideration...
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Generation and Propagation of Nonlinear Waves in a Towing Tank
PublicationThe paper presents the results of the research focused on linear and nonlinear wave generation and propagation in a deepwater towing tank equipped with a single flap-type wavemaker of variable draft. The problem of wave generation and propagation has been theoretically formulated and solved by applying an analytical method; linear and nonlinear solutions were obtained. The linear solution has been verified experimentally. The...
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Investigation of Vibro-Acoustical Properties Using Eigenvalue Problem Solution and Wavelets
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Systems of Nonlinear Fractional Differential Equations
PublicationUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.
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Dimensionally Consistent Nonlinear Muskingum Equation
PublicationAlthough the Muskingum equation was proposed nearly 75 years ago, it is still a subject of active research. Despite of its simple form, the real properties of this equation have not been comprehensively explained. This paper proposes a new interpretation of the linear McCarthy’s relation. This relation can be interpreted only together with the storage equation, whereas the Muskingum equation can be derived directly from the system...
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Single and Dual-GPU Generalized Sparse Eigenvalue Solvers for Finding a Few Low-Order Resonances of a Microwave Cavity Using the Finite-Element Method
PublicationThis paper presents two fast generalized eigenvalue solvers for sparse symmetric matrices that arise when electromagnetic cavity resonances are investigated using the higher-order finite element method (FEM). To find a few loworder resonances, the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm with null-space deflation is applied. The computations are expedited by using one or two graphical processing...
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On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution
PublicationAmong various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In...
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On the geometrically nonlinear vibration of a piezo-flexomagnetic nanotube
PublicationIn order to describe the behavior of thin elements used in MEMS and NEMS, it is essential to study a nonlinear free vibration of nanotubes under complicated external fields such as magnetic environment. In this regard, the magnetic force applied to the conductive nanotube with piezo-flexomagnetic elastic wall is considered. By the inclusion of Euler-Bernoulli beam and using Hamilton’s principle, the equations governing the system...
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Boundary problems for differential equations with advanced arguments
PublicationDyskutowane są zagadnienia brzegowe dla równań różniczkowych z wyprzedzonymi argumentami. Przedstawione są warunki dostateczne istnienia quasirozwiązań i rozwiązań rozważanych zagadnień.
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Identification of nonlinear viscoelastic properties of the ''Panama'' fabric
PublicationTkanina techniczna Panama wytwarzana przez firmę Sattler (Niemcy)wykazuje cechy nieliniowe w tym właściwości lepkosprężyste w czasie testów długoterminowych. Na podstawie jednoosiowych testów płynięcia i regeneracji przeprowadzonych dla pięciu poziomów obciążenia przeprowadzono identyfikacje nieliniowych lepkosprężystych właściwości tkaniny. Do opisu zależności konstytutywnych użyto całkowego modelu Schapery'ego. Zastosowano funkcję...
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The application of nonlinear curvature sections in the turnout diverging track
PublicationThe paper presents the analytical method of modelling the diverging track of railway turnout with nonlinear curvature sections. These sections were used for smoothing the graph of curvature in the extreme areas of turnout. The problem of the curvature distribution was identified with the use of differential equations. The resulting solutions are of universal nature for example the ability of assuming any values of curvature at...
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On nonlinear dilatational strain gradient elasticity
PublicationWe call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the...
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Acceleration waves in the nonlinear micromorphic continuum
PublicationWithin the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortion tensor may undergo jump discontinuities. Here we obtain the acoustic tensor for...
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Features of Nonlinear Sound Propagation in Vibrationally Excited Gases
PublicationWeakly nonlinear sound propagation in a gas where molecular vibrational relaxation takes place is studied. New equations which govern the sound in media where the irreversible relaxation may take place are derived and discussed. Their form depends on the regime of excitation of oscillatory degrees of freedom, equilibrium (reversible) or non-equilibrium (irreversible), and on the comparative frequency of the sound in relation to...
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Boundary problems for fractional differential equations
PublicationIn this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.
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Nonlinear Influence of Sound on the Vibrational Energy of Molecules in a Relaxing Gas
PublicationDynamics of a weakly nonlinear and weakly dispersive flow of a gas where molecular vibrational relaxation takes place is studied. Variations in the vibrational energy in the field of intense sound is considered. These variations are caused by a nonlinear transfer of the acoustic energy into energy of vibrational degrees of freedom in a relaxing gas. The final dynamic equation which describes this is instantaneous, it includes a...
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Nonlinear phenomena of small-scale sound in a gas with exponential stratification
PublicationThe nonlinear dynamics of perturbations, quickly varying in space, with comparatively large characteristic wavenumbers k: k>1/H, is considered. H is the scale of density and pressure reduction in unperturbed gas, as the coordinate (H is the so-called height of the uniform equilibrium gas). Coupling nonlinear equations which govern the sound and the entropy mode in a weakly nonlinear flow are derived. They describe the dynamics...
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Problems and Solutions of Software Design in Scrum Projects
PublicationThe aim of the paper is to identify the problems and solutions of the software design in Scrum project as well as to analyze the effectiveness of the solutions. Through a series of workshops with 4 experts from IT industry and academia we have identified 52 problems and 99 unique solutions. In this paper we present a list of 10 common problems and 5 solutions for each problem selected by the number of sources. The effectiveness...
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Comparison of Optimization Techniques for Coupling Matrix Synthesis Using Eigenvalue Based Approach
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A Novel Approach to Fully Nonlinear Mathematical Modeling of Tectonic Plates
PublicationThe motion of the Earth's layers due to internal pressures is simulated in this research with an efficient mathematical model. The Earth, which revolves around its axis of rotation and is under internal pressure, will change the shape and displacement of the internal layers and tectonic plates. Applied mathematical models are based on a new approach to shell theory involving both two and three-dimensional approaches. It is the...