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Wyniki wyszukiwania dla: KINETIC CONSTITUTIVE EQUATIONS
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Action-reaction based synthesis of acoustic wavefield equations
PublikacjaThe analysis of acoustic fields is usually based on the well-known mathematics of second order partial differential equations called wave equations. The author explores the duality and symmetry of linear fluid mechanics and develops two distinct equations of acoustics on the basis of a causal approach to local small-scale phenomena. Wavefields that are solutions of these equations have different composition, the spherical pressure...
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Update a simple hypoplastic constitutive model
PublikacjaW artykule omówiono uproszczona formę hipoplastycznego konstytutywnego prawa materiałowego do opisu zachowania się materiałów granulowanych. Wykonano symulacje testów elementów i porównano wyniki z doświadczeniami.
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On neutral differential equations and the monotone iterative method
PublikacjaThe application of the monotone iterative method to neutral differential equations with deviating arguments is considered in this paper. We formulate existence results giving sufficient conditions which guarantee that such problems have solutions. This approach is new and to the Authors' knowledge, this is the first paper when the monotone iterative method is applied to neutral first-order differential equations with deviating...
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Hydraulic equations for vortex separators dimensioning
PublikacjaThe paper presents a set of hydraulic expressions developed to design vortex separators. These devices are used for gravitational removal of suspensions from wastewater. Measurements and theoretical considerations allowed the authors to formulate a mathematically simple velocity field model. Than, equations describing particle motion in the separator were derived. Finally, a technical procedure for hydraulic design of vortex separators...
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Method of lines for Hamilton-Jacobi functional differential equations.
PublikacjaInitial boundary value problems for nonlinear first order partial functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A method of quasi linearization is adopted. Suffcient conditions for the convergence of the method of lines and error estimates for approximate solutions are presented. The proof of the stability of the diffrential difference...
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PROPERTIES OF ONE DIMENSIONAL OPEN-CHANNEL STEADY FLOW EQUATIONS
PublikacjaIn this paper properties of discrete forms of one dimensional steady gradually varied flow equations are discussed. Such forms of flow equations are obtained as a result of approximation of their differential forms, which is required to solve them numerically. For such purpose explicit or implicit numerical approximation schemes for ordinary differential equations can be applied. It turns out that dependently on the chosen approximation...
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Effective sonophotocatalytic degradation of tetracycline in water: Optimization, kinetic modeling, and degradation pathways
PublikacjaHybrid advanced oxidation processes (AOPs) are gaining interest in degradation of variety of recalcitrant compounds for water and wastewater treatment, due to possible synergistic effects. The present study systematically evaluated the degradation of tetracycline (TC) with a sonophotocatalytic process combining acoustic cavitation (sonocavitation) and photocatalysis based on N-doped TiO2 catalyst. The TC degradation rate constant...
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Utopian Kinetic Structures and Their Impact on the Contemporary Architecture
PublikacjaThis paper delves into relationships between twentieth century utopian concepts of movable structures and the kinematic solutions implemented in contemporary architectural projects. The reason for conducting this study is to determine the impact of early architectural conceptions on today's solutions. This paper points out close links that stem from the imagination of artists and architects working in 1960s and 70s and the solutions...
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublikacjaIn this paper, fundamental properties of solutions to fractional-order (FO) Maxwell's equations are analysed. As a starting point, FO Maxwell's equations are introduced in both time and frequency domains. Then, we introduce and prove the fundamental properties of electromagnetic field in FO electromagnetics, i.e. energy conservation, uniqueness of solutions, and reciprocity. Furthermore, the algorithm of the plane wave simulation...
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Inverse Flood Routing Using Simplified Flow Equations
PublikacjaThe paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve...
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Multimode systems of nonlinear equations: derivation, integrability, and numerical solutions
PublikacjaWe consider the propagation of electromagnetic pulses in isotropic media taking a third-order nonlinearityinto account. We develop a method for transforming Maxwell's equations based on a complete set ofprojection operators corresponding to wave-dispersion branches (in a waveguide or in matter) with thepropagation direction taken into account. The most important result of applying the method is a systemof equations describing the...
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The Lost Kinetic Architecture and How to Reintroduce it in the Landscape – The Case Study of the Drainage Windmills in the Vistula Delta
PublikacjaRecreating the lost kinetic landscape of the Vistula Delta is a considerable challenge. The study aims to propose a method for reproducing windmills and their effect on the landscape. The paper suggests a method based on the transposition of the forms of movement from windmills historically present in the region to modern forms. The method is based on a series of analyses starting with the study of the region and its history followed...
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Boundary value problems for first-order dynamic equations
PublikacjaPraca dotyczy zagadnień związanych z istnieniem rozwiązań (ekstremalnych i jednego) dla problemów brzegowych dla równań dynamicznych pierwszego rzędu z opóźnionymi argumentami. Dyskutowane są również odpowiednie nierówności dynamiczne związane z zagadnieniami brzegowymi. Liczne przykłady ilustrują otrzymane wyniki.
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Balance errors in numerical solutions of shallow water equations
PublikacjaThe analysis of the conservative properties of the shallow water equations is presented in the paper. The work focuses on the consistency of numerical solution of these equations with the conservation laws of mass and momentum. The investigations involve two different conservative forms which are solved by an implicit box scheme. The theoretical analysis supported by numerical experiments is carried out for rectangular channel...
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A coupled constitutive model for fracture in plain concrete based on continuum theory with non-local softening and eXtended Finite Element Method
PublikacjaThe paper presents a constitutive model for concrete which combines a continuous and discontinuous fracture description. In a continuum regime, two different constitutive laws were used. First, a plasticity model with a Rankine failure criterion and an associated fl ow rule was used. Second, a constitutive law based on isotropic damage mechanics was formulated. In order to capture the width of a localized zone and to obtain mesh-independent...
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Kinetic analysis of the reduction of a ternary system of Bi, Sb and Te oxides by hydrogen for BiSbTe3 synthesis
PublikacjaReduction in a hydrogen atmosphere of Bi2O3, Sb2O3 and TeO2 mixes oxides for the synthesis of BiSbTe3 was analysed. The reduction reactions of Sb2O3 and Sb2O4 oxides, as well as Bi2O3+Sb2O3 and Sb2O3+3TeO2 mix- tures, were also evaluated. The reduction of Sb2O4 is investigated for the first time. The reactions of the mixed oxides systems also were not the subject of research so far despite being used for synthesis of the (Bi,Sb)2Te3...
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Systems of boundary value problems of advanced differential equations
PublikacjaThis paper considers the existence of extremal solutions to systems of advanced differential equations with corresponding nonlinear boundary conditions. The monotone iterative method is applied to obtain the existence results. An example is provided for illustration.
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DIFFERENTIAL EQUATIONS
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Coupled nonlinear Schrödinger equations in optic fibers theory
PublikacjaIn this paper a detailed derivation and numerical solutions of CoupledNonlinear Schr¨odinger Equations for pulses of polarized electromagnetic wavesin cylindrical fibers has been reviewed. Our recent work has been compared withsome previous ones and the advantage of our new approach over other methods hasbeen assessed. The novelty of our approach lies is an attempt to proceed withoutloss of information within the frame of basic...
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Existence of solutions with an exponential growth for nonlinear differential-functional parabolic equations
PublikacjaWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence.We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.
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Kinetic analysis of the stage for a high speed steam turbine
PublikacjaThis article analyzes possibilites of resonances within a control stage for a high speed steam turbine. This stage hase been based on assembling of a single blade to a rotating disk and increasing of rigidity of the system by using of a bandage. In the analysis will be nd a possiblity of resonance frequency, and mistuning by showing safety working ranges. The calculations have bean used the3D modal and harmonic analysis by the...
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Experimental methods in thermodynamic and kinetic studies on photocatalytic materials
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Implicit difference methods for first order partial differential functional equations
PublikacjaKlasyczne rozwiązania problemów początkowo brzegowych przybliżane są rozwiązaniami uwikłanych metod różnicowych. Wykazana została zbieżność i stabilność uwikłanych schematów. Dowód stabilności opiera się na technice porównawczej z nieliniowym oszacowaniem typu Perrona dla funkcji danych.
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Solution of coupled integral equations for quantum scattering in the presence of complex potentials
PublikacjaIn this paper, we present a method to compute solutions of coupled integral equations for quantum scattering problems in the presence of a complex potential. We show how the elastic and absorption cross sections can be obtained from the numerical solution of these equations in the asymptotic region at large radial distances.
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Existence of unbounded solutions to parabolic equations with functional dependence
PublikacjaThe Cauchy problem for nonlinear parabolic differential-functional equations is considered. Under natural generalized Lipschitz-type conditions with weights, the existence and uniqueness of unbounded solutions is obtained in three main cases: (i) the functional dependence u(·); (ii) the functional dependence u(·) and ∂xu(·); (iii) the functional dependence u(·)and the pointwise dependence ∂xu(t,x).
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Application of the numerical-analytic method for systems of differential equations with parameter
PublikacjaThe numerical-analytic method is applied to systems of differential equations with parameter under the assumption that the corresponding functions satisfy the Lipschitz conditions in matrix notation. We also obtain several existence results for problems with deviations of an argument
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Certain family of analytical solutions of nonlinear von Neumann equations
PublikacjaIn this paper we present a slight generalization of certain type of Darboux transformation, that may be used sub-sequently in a convenient way. This method allows to obtain families of solutions of nonlinear von Neumann equations, that are used in particular in DNA modeling.
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Viscoplastic constitutive laws and their implementation it the finite element method
PublikacjaW pracy przedstawiono zasady formułowania i zastosowania w metodzie elementów skończonych lepkoplastycznych praw konstytutywnych. Podano skrótowo sposób identyfikacji parametrów i omówiono pewne szczególne założenia, które muszą być przyjęte aby można było dane prawo zastosować w obliczeniach numerycznych.
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublikacjaIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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Examination of advanced isotropic constitutive laws under complex stress states in plain and reinforced concrete specimens
PublikacjaThe performance of advanced isotropic constitutive laws under complex stress states in plain and reinforced concrete specimens is investigated. Three different formulations are chosen: original Mazars model, Mazars mi model and model proposed by Pereira and coworkers. The degradation of the material in all formulations is described via a single variable, but a strain/stress state is taken into account via quite sophisticated relationships....
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Few-Layer Black Phosphorus/Chitosan Nanocomposite Electrodes via Controlled Electrodeposition for Enhanced Electrochemical Kinetic Performance
PublikacjaThis study presents the preparation and characterization of few-layer black phosphorus (FLBP) chitosan electrodes by controlled electrochemical deposition of chitosan nanoparticles on FLBP-modified glassy carbon electrodes. FLBP was prepared by solvent-assisted exfoliation of bulk BP and was further modified with chitosan forming together a nanocomposite, including easy cross-linking with nanomaterials and film-forming properties....
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Method of lines for nonlinear first order partial functional differential equations.
PublikacjaClassical 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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Existence and uniqueness for neutral equations with state dependent delays
PublikacjaW pracy w celu wykazania istnienia i jednoznaczności rozwiązania równania została zaprezentowana metoda porównawcza.
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Positive solutions to boundary value problems for impulsive second-order differential equations
PublikacjaIn this paper, we discuss four-point boundary value problems for impulsive second-order differential equations. We apply the Krasnoselskii's fixed point theorem to obtain sufficient conditions under which the impulsive second-order differential equations have positive solutions. An example is added to illustrate theoretical results.
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Application of Pierson-Moskowitz wave spectrum to solution differential equations of multihull vessel
PublikacjaMotion of a dynamic system can be generated by different external or internal factors. At mathematical modelling external excitation factors of the most significant effect on the system, are selected. Such external factors are usually called excitations. Response of the system to given excitations is mathematically characterized by a definite transformation called operator of a system. For a broad class of dynamic systems the...
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Monotone iterative method for first-order differential equations at resonance
PublikacjaThis paper concerns the application of the monotone iterative technique for first-order differential equations involving Stieltjes integrals conditions. We discuss such problems at resonance when the measure in the Stieltjes integral is positive and also when this measure changes the sign. Sufficient conditions which guarantee the existence of extremal, unique and quasi-solutions are given. Three examples illustrate the results.
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Kinetic Description of the Membrane–Solution Interface for Ion-Selective Electrodes
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Modeling of Ozonation of Reactive Black 5 Through a Kinetic Approach
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Adenylate kinases of thermophilesAquifex aeolicusandGeobacillus stearothermophilus: biochemical and kinetic studies
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Quasi-solutions for generalized second order differential equations with deviating arguments
PublikacjaThis paper deal with boundary value problems for generalized second order differential equations with deviating arguments. Existence of quasi-solutions and solutions are proved by monotone iterative method. Examples with numerical results are added.
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On Von Karman Equations and the Buckling of a Thin Circular Elastic Plate
PublikacjaWe shall be concerned with the buckling of a thin circular elastic plate simply supported along a boundary, subjected to a radial compressive load uniformly distributed along its boundary. One of the main engineering concerns is to reduce deformations of plate structures. It is well known that von Karman equations provide an established model that describes nonlinear deformations of elastic plates. Our approach to study plate deformations...
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Functional differential equations
PublikacjaSformułowano dość ogólne warunki dostateczne na to, aby odpowiednio zdefiniowane ciągi monotoniczne były zbieżne do jedynego, w pewnym segmencie, rozwiązania zagadnienia początkowego dla funkcyjnych równań różniczkowych. Omawiane równanie jest ogólne, a np. zwyczajne równania różniczkowe czy równania różniczkowo-całkowe są jego szczególnymi przypadkami.
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Justyna Signerska-Rynkowska dr inż.
OsobySince 2016 assistant professor at Gdańsk University of Technology, Faculty of Applied Physics and Mathematics, Division of Differential Equations and Mathematics Applications 2021-2024 visiting assistant professor in Dioscuri Centre in Topological Data Analysis (Institute of Mathematics of the Polish Academy of Sciences, IMPAN) Since 2020 - Principal Investigator in "SONATA" grant “Challenges of low-dimensional...
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Some developments in constitutive modelling of soft clays, Keynote lecture
PublikacjaPrzedstawiono przegląd najczęściej stosowanych modeli konstytutywnych dla naturalnych gruntów słabonośnych, takich jak: gliny, namuły lub torfy. Skupiono się przede wszystkim na takich elementach charakterystyki mechanicznej gruntów słabonośnych jak: anizotropia, zjawisko pełzania i relaksacji oraz destrukturyzacja. Artykuł jest podsumowaniem 4-letniego projektu badawczego finansowanego w ramach 5 ramowego projektu Unii Europejskiej:...
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Constitutive models for technical woven fabric state of the art and futuretrends.
PublikacjaPrzedstawiono główne kierunki rozwoju nieliniowych praw konstytutywnych służących do opisu zachowania tkaniny technicznej z uwzględnieniem niesprężystych właściwości wątku i osnowy. Praca zawiera krótki rys historyczny rozwoju praw oraz omówienie typowych prób laboratoryjnych służących do identyfikacji parametrów materiałowych.
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublikacjaWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Systems, environments, and soliton rate equations: A non-Kolmogorovian framework for population dynamics
PublikacjaSoliton rate equations are based on non-Kolmogorovian models of probability and naturally include autocatalytic processes. The formalism is not widely known but has great unexplored potential for applications to systems interacting with environments. Beginning with links of contextuality to non- Kolmogorovity we introduce the general formalism of soliton rate equations and work out explicit examples of subsystems interacting with...
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Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations
PublikacjaThe light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo (MC) algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present implementation...
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Weighted difference schemes for systems of quasilinear first order partial functional differential equations
PublikacjaThe paper deals with initial boundary value problems of the Dirichlet type for system of quasilinear functional differential equations. We investigate weighted difference methods for these problems. A complete convergence analysis of the considered difference methods is given. Nonlinear estimates of the Perron type with respect to functional variables for given functions are assumed. The proof of the stability of difference problems...
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Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space
PublikacjaUsing the Mountain Pass Theorem, we establish the existence of periodic solution for Euler–Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.