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wszystkich: 910
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Wyniki wyszukiwania dla: NONLINEAR
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Subcritical bifurcation of free elastic shell of biological cluster
PublikacjaIn this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublikacjaIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Boundary value problems with causal operators
PublikacjaPraca dotyczy istnienia rozwiązań dla równań różniczkowych z nieliniowymi dwu-punktowymi warunkami brzegowymi. Podano warunki dostateczne na istnienie rozwiązań takich zagadnień stosując metodę iteracji monotonicznych. Dyskutowano też nierówności różniczkowe rzędu pierwszego z dodatnimi operatorami liniowymi oraz problem rozwiązań ekstremalnych.
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublikacjaQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ1 space. It turns out that in principle most of the results can be carried over to the L1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic...
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The smoothness test for a density function
PublikacjaThe problem of testing hypothesis that a density function has no more than μ derivatives versus it has more than μ derivatives is considered. For a solution, the L2 norms of wavelet orthogonal projections on some orthogonal ‘‘differences’’ of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution,...
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Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions
PublikacjaIn this paper we investigate integral boundary value problems for fourth order differentialequations with deviating arguments.Wediscuss our problem both for advanced or delayedarguments. We establish sufficient conditions under which such problems have positivesolutions. To obtain the existence of multiple (at least three) positive solutions, we use afixed point theorem due to Avery and Peterson. An example is also included to...
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Comparision principles for parabolic differential - functional initial - value problems.
PublikacjaBadamy paraboliczne równania z zależnością funkcyjną i podajemy kryteria jednoznaczności przy warunkach porównawczych typu Perrona i Lipschitza dla nieliniowej prawej strony. W przypadku gdy zależność funkcyjna dotyczy również pochodnej funkcji niewiadomej, to stosujemy nierówności typu Henry'ego.
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Boundary value problems for first order differential equations of mixed type
PublikacjaPraca dotyczy równań różniczkowo-całkowych z nieliniowymi warunkami brzegowymi. Podano warunki dostateczne na istnienie jedynego rozwiązania oraz rozwiązań ekstremalnych takich problemów. Dyskutowane są nierówności różniczkowo-całkowe. Podano przykłady ilustrujące otrzymane wyniki teoretyczne.
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Nonnegative solutions to nonlocal boundary value problems for systems of second-order differential equations dependent on the first-order derivatives
PublikacjaStosując tw. Avery-Petersona o punkcie stałym, podano warunki dostateczne na istnienie nieujemnych rozwiązań dla układów równań różniczkowych rzędu drugiego z argumentami opóźnionymi i wyprzedzonymi oraz warunkami brzegowymi zawierającymi całki Stieltjesa. Praca zawiera wiele przykładów.
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The equivariant spectral flow and bifurcation of periodic solutions of Hamiltonian systems
PublikacjaWe define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This G-equivariant spectral flow shares all common properties of the integer valued classical spectral flow, and it can be non-trivial even if the classical spectral flow vanishes. Our main theorem uses the G-equivariant spectral flow...
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An absorbing set for the Chialvo map
PublikacjaThe classical Chialvo model, introduced in 1995, is one of the most important models that describe single neuron dynamics. In order to conduct effective numerical analysis of this model, it is necessary to obtain a rigorous estimate for the maximal bounded invariant set. We discuss this problem, and we correct and improve the results obtained by Courbage and Nekorkin (2010). In particular, we provide an explicit formula for an...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublikacjaIn this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell’s equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of...
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Clarke duality for Hamiltonian systems with nonstandard growth
PublikacjaWe consider the existence of periodic solutions to Hamiltonian systems with growth conditions involving G-function. We introduce the notion of symplectic G-function and provide relation for the growth of Hamiltonian in terms of certain constant CG associated to symplectic G-function G. We discuss an optimality of this constant for some special cases. We also provide applications to the Φ-laplacian type systems.
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Electromagnetic-based derivation of fractional-order circuit theory
PublikacjaIn this paper, foundations of the fractional-order circuit theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order...
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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublikacjaThe purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use...
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Bifurcation of equilibrium forms of a gas column rotating with constant speed around its axis of symmetry
PublikacjaWe will be concerned with the problem of deformation of the lateral surface of a column that rotates with constant speed around its axis of symmetry. The column is filled by a gas and our goal is to investigate the deformation of the lateral surface depending on the pressure of the gas.
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Signal propagation in electromagnetic media described by fractional-order models
PublikacjaIn this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced....
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Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein
PublikacjaWe analyse a model of Hes1 gene transcription and protein synthesis with a negative feedback loop. The effect of multiple binding sites in the Hes1 promoter as well as the dimer formation process are taken into account. We consider three, possibly different, time scales connected with: (i) the process of binding to/dissolving from a binding site, (ii) formation and dissociation of dimers, (iii) production and degradation of Hes1...
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Multiresolution analysis and adaptive estimation on a sphere using stereographic wavelets
PublikacjaWe construct an adaptive estimator of a density function on d dimensional unit sphere Sd (d ≥ 2), using a new type of spherical frames. The frames, or as we call them, stereografic wavelets are obtained by transforming a wavelet system, namely Daubechies, using some stereographic operators. We prove that our estimator achieves an optimal rate of convergence on some Besov type class of functions by adapting to unknown smoothness....
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Generalization of Kramers-Krönig relations for evaluation of causality in power-law media
PublikacjaClassical Kramers-Krönig (K–K) relations connect real and imaginary parts of the frequency-domain response of a system. The K–K relations also hold between the logarithm of modulus and the argument of the response, e.g. between the attenuation and the phase shift of a solution to a wave-propagation problem. For square-integrable functions of frequency, the satisfaction of classical K–K relations implies causality in the time domain....
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Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
PublikacjaStarting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
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Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation
PublikacjaWe consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our proof, based on the concept of the Brouwer degree, gives more, namely that from each bifurcation point there branches off a continuum of solutions.
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Equivariant Conley index in Hilbert spaces and applications to strongly indefinite problems
PublikacjaW pracy zdefiniowano teorię indeksu Conley`a w przestrzeni Hilberta z działaniem zwartej grupy Liego. Została ona wykorzystana do szacowania z dołu ilości rozwiązań periodycznych w teorii nieliniowych autonomicznych układów Hamiltona.
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Structure–property relationships and third-order nonlinearities in diketopyrrolopyrrole based D–π–A–π–D molecules
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Influence of nonlinearities on the efficiency and accuracy of FEM calculations on the example of a steel build-up thin-walled column
PublikacjaDue to the increase of computing capabilities of standard processing units, it is possible to perform complex analyses, considering a number of nonlinearities, such as geometric, material and boundary (contact) even on personal computers. In the paper, the authors have analysed the efficiency and accuracy of standard PC’s FEM calculations performed in Abaqus CAE 2017 software on the example of a critical load assessment of a thin-walled...
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Parameter of nonlinearity B/A of three-component systems with separate volumes of liquid, its vapor and a neutral gas
PublikacjaOtrzymane zostało wyrażenie dla zaburzenia entropii substancji o trzech komponentach jako funkcja zaburzeń jej ciśnienia i gęstości. Na podstawie wzoru prędkość i parametru nieliniowosci fali akustycznej zostały wyliczone jako funkcje i ciśnienia i koncentracji pary i powietrza. Rezultaty są przedstawione w postaci wykresów.
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Evaluation of foil capacitor nonlinearities and flucuations during manufacturingoszacowanie nieliniowości i fluktuacji kondensatorów foliowych w procesie produkcyjnym.
PublikacjaPrzedstawiono dwa podejścia do problemów niezawodności elementów elektronicznych. Opisano mierzone przeciwzakłóceniowe kondensatory foliowe produkowane przez MIFLEX (Kutno), zasadę i układ do pomiaru wskaźnika trzeciej harmonicznej sygnału pobudzającego oraz jego zależność od parametrów mierzonego elementu. Przedstawiono wyniki statystyczne pomiaru parametrów funkcjonalnych oraz trzeciej harmonicznej próbek tych kondensatorów przed...
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Evaluation of foil capacitor nonlinearities and fluctuations during manufacturingOszacowanie nieliniowości i fluktuacji kondensatorów foliowych w procesie produkcyjnym
PublikacjaPrzeanalizowano nieliniowości i właściwości szumowe kondensatorów w celu ustalenie kryteriów testowania nieniszczącego i selekcji kondensatorów przeciwzakłóceniowych do różnych klas trwałości i niezawodności. Przedstawiono wybrane wyniki eksperymentalne pomiaru kondensatorów produkowanych przez ZR MIFLEX w Kutnie oraz koncepcję systemu pomiarowego przeznaczonego do implementacji tych pomiarów w procesie produkcyjnym.
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A study on application of Smoothed Particle Hydrodynamics to multi-phase flows
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Numerical Analysis of TB32 Crash Tests for 4-cable Guardrail Barrier System Installed on the Horizontal Convex Curves of Road
PublikacjaHorizontal curves are one of the elements of road infrastructure where statistically a relatively high number of accidents have been reported. In the last ten years in Poland approx. 10% of all road accidents happened on horizontal curves of roads and was responsible for approx. 14% of all fatalities on Polish roads. Thus, this issue is important and requires extensive research and proper road safety treatments. One possible measure...
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<title>Non-linear glasses and metaglasses for photonics, a review: Part II. Kerr nonlinearity and metaglasses of positive and negative refraction</title>
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Quantitative hyperbolicity estimates in one-dimensional dynamics
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Abstract DNA-type systems
PublikacjaAbstrakcyjny system typu DNA jest definiowany przez zestaw nieliniowych kinetycznych równań z wielomianowymi nieliniowościami, które przyjmują rozwiązania solitonowe związane z geometrią helis. Zestaw równań pozwala na dwie różne reprezentacje Laxa: forma von Neumanna i Darboux-kowariantna para Laxa. Wyjaśniamy dlaczego nie-Kolmogorowskie modele prawdopodobieństwa pojawiające się w kinetyce solitonowej są naturalnie związane z...
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Towards a classification of networks with asymmetric inputs
PublikacjaCoupled cell systems associated with a coupled cell network are determined by (smooth) vector fields that are consistent with the network structure. Here, we follow the formalisms of Stewart et al (2003 SIAM J. Appl. Dyn. Syst. 2, 609–646), Golubitsky et al (2005 SIAM J. Appl. Dyn. Syst. 4, 78–100) and Field (2004 Dyn. Syst. 19, 217–243). It is known that two non-isomorphic n-cell coupled networks can determine the same sets of...
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Unusual streaming in chemically reacting gases
PublikacjaNonlinear stimulation of the vorticity mode caused by losses in the momentum of sound in the chemically reacting gas, is considered. The instantaneous dynamic equation which describes the nonlinear generation of the vorticity mode, is derived. It includes a quadratic nonlinear acoustic source. Both periodic and aperiodic sound may be considered as the origin of the vorticity flow. In the non-equilibrium regime of the chemical reaction,...
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The equations for interactions of polarization modes in optical fibres including the kerr effect
PublikacjaWe have derived coupled nonlinear Schro¨ dinger equations (CNLSE) for arbitrary polarized light propagation in a single-mode fibre employing electromagnetic field complete description. We used a basis of transverse eigenmodes with appropriate projecting; hence, the nonlinear constants depend on the waveguide geometry. Accounting for a weak nonlinearity, which is connected to the Kerr effect, we have given explicit expressions for...
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On the correspondence between two- and three-dimensional Eshelby tensors
PublikacjaWe consider both three-dimensional (3D) and two-dimensional (2D) Eshelby tensors known also as energy–momentum tensors or chemical potential tensors, which are introduced within the nonlinear elasticity and the resultant nonlinear shell theory, respectively. We demonstrate that 2D Eshelby tensor is introduced earlier directly using 2D constitutive equations of nonlinear shells and can be derived also using the throughthe-thickness...
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Non-Wave Variations in Temperature Caused by Sound in a Chemically Reacting Gas
PublikacjaA weakly nonlinear generation of non-acoustic modes in the field of sound in a gas is considered. An exotericchemical reaction of A->B type, which takes place in a gas, may be reversible or not. Two types of sound areconsidered, low-frequency and high-frequency as compared with the characteristic time of a chemical reaction.For both these cases, the governing equations of non-acoustic modes are derived and conclusions of the efficiencyof...
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Magnetoacoustic Heating in Nonisentropic Plasma Caused by Different Kinds of Heating-Cooling Function
PublikacjaThe nonlinear phenomena which associate with magnetoacoustic waves in a plasma are analytically studied. A plasma is an open system with external inflow of energy and radiation losses. A plasma’s flow may be isentropically stable or unstable. The nonlinear phenomena occur differently in dependence on stability or instability of a plasma’s flow. The nonlinear instantaneous equation which describes dynamics of nonwave entropy mode...
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approximation of photonic crystal fibres with large air holes by the step index fibre model
PublikacjaAn equivalent step index fibre with a silica core and air cladding is used to model photonic crystal fibres with large air holes. We model this fibre for linear polarisation (we focus on the lowest few transverse modes of the electromagnetic field). The equivalent step index radius is obtained by equating the lowest two eigenvalues of the model to those calculated numerically for the photonic crystal fibres. The step index parameters...
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Interaction between acoustic and non-acoustic mode in bubbly liquid
PublikacjaThe nonlinear interaction of acoustic and entropy modes in a bubbly liquid is the subject of investigation. Thedynamic equation governing an excess density of the entropy mode is derived. Nonlinearity and dispersion are the reasons forexcitation of the entropy mode. The nonlinear interaction of modes as a reason for bubble to grow due to sound, is discovered.Some numerical examples of the modes interactions are made.
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Magnetoacoustic heating in a quasi-isentropic magnetic gas
PublikacjaThe nonlinear heating of a plasma which associates with the transfer of energy of magnetoacoustic waves into that of the entropy mode, is analytically studied. A plasma is uniform and motionless at equilibrium. Perturbations in a plasma are described by a system of ideal magnetohydrodynamic equations. The equilibrium straight magnetic strength and the wave vector form a constant angle which varies from 0 to π/2. There exist four...
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Interaction of Acoustic and Thermal Modes in the Gas with Nonequilibrium Chemical Reactions: Possibilities of Acoustic Cooling
PublikacjaNonlinear generation of thermal mode during propagation of dominative sound in a chemically reacting gas is considered. The dynamic equation of excess temperature associated with the thermal mode is derived. It is instantaneous and includes quadratic nonlinear acoustic source reflecting the nonlinear character of interaction between acoustic and non-acoustic types of gas motion. Both periodic and aperiodic sound may be considered...
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Sensorless Multiscalar Control of Five-Phase Induction Machine with Inverter Output Filter
PublikacjaThe paper presents a complete solution for speed sensorless control system for five-phase induction motor with voltage inverter, LC filter and nonlinear control of combined fundamental and third harmonic flux distribution. The control principle, also known as multiscalar control, nonlinear control or natural variables control, is based on a use of properly selected scalar variables in control feedback to linearize controlled system....
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Control of mass concentration of reagents by sound in a gas with nonequilibrium chemical reactions
PublikacjaThe weakly nonlinear dynamics of a chemically reacting gas is studied. Nonlinear interaction of acoustic and nonacoustic types of motion are considered. We decompose the base equations using the relationships of the gas-dynamic perturbations specific for every type of motion. The governing equation for the mass fraction of a reagent influenced by dominating sound is derived and discussed. The conclusions concern the equilibrium...
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Robust output prediction of differential – algebraic systems – application to drinking water distribution system
PublikacjaThe paper presents the recursive robust output variable prediction algorithm, applicable for systems described in the form of nonlinear algebraic-differential equations. The algorithm bases on the uncertainty interval description, the system model, and the measurements. To improve the algorithm efficiency, nonlinear system models are linearised along the nominal trajectory. The effectiveness of the algorithm is demonstrated on...
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Dynamiczne wyznaczanie parametrów elektrycznego obwodu szeregowego
PublikacjaPo załączeniu napięcia na skutek istnienia inercji prąd w obwodzie zaczyna narastać od wartości zerowej do znamionowej. W tym czasie narastają spadki napięć na rezystancjach (impedancjach obwodu) do chwili spełnienia prawa Kirchhoffa. Można utworzyć układ ze sprzężeniem zwrotnym (układ regulacji stałowartościowej bądź nadążnej), który poszukuje parametrów obwodu spełniających prawa Kirchhoffa – elementy nie muszą być liniowe. W...
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Self-refraction of acoustic pulses with shock fronts in some nonequilibrium media
PublikacjaThe nonlinear self-refraction of acoustic pulsed beams, which include shock fronts, is studied. The medium of sound propagation is a gas where thermodynamically nonequilibrium processes take place, such as exothermic chemical reaction or excitation of vibrational degrees of a molecule’s freedom. Comparative analysis of the features of sound propagation over gases where pure nonlinear attenuation of the shock wave occurs, and gases...
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Zastosowanie odcinków nieliniowej krzywizny w torze zwrotnym rozjazdu kolejowego
PublikacjaW pracy została przedstawiona analityczna metoda kształtowania toru zwrotnego rozjazdu kolejowego posiadającego na swojej długości odcinki nieliniowej krzywizny. Odcinki te służą łagodzeniu wykresu krzywizny w skrajnych strefach rozjazdu W omawianej metodzie dokonano identyfikacji problemu rozkładu krzywizny za pomocą równań różniczkowych. Uzyskane rozwiązania mają charakter uniwersalny; m. in. pozwalają na przyjmowanie dowolnych...
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A Review of Hyperelastic Constitutive Models for Dielectric Elastomers
PublikacjaDielectric elastomers are smart materials that are essential components in soft systems and structures. The core element of a dielectric elastomer is soft matter, which is mainly rubber-like and elastomeric. These soft materials show a nonlinear behaviour and have a nonlinear strain-stress curve. The best candidates for modelling the nonlinear behaviour of such materials are hyperelastic strain energy functions. Hyperelastic functions...