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Wyniki wyszukiwania dla: SHALLOW WATER EQUATIONS
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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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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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FURTHER REMARKS ON THE NEO-CLASSICAL NAVIER-STOKES EQUATIONS
PublikacjaThe seminal Navier-Stokes equations have been stated yet before creation of principles of thermodynamics and the first and second laws. In the literature there is the common opinion that the Navier-Stokes equations cannot be taken as a thermodynamically correct model of “working fluid” which is able to describe transformation of “ heat” into “work” and vice versa. Therefore, in the paper, a new exposition of thermodynamically...
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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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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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Multiobjective Water Distribution Systems Control of Pumping Cost, Water Quality, and Storage-Reliability Constraints
PublikacjaThis work describes a multiobjective model for trading-off pumping cost and water quality for water distribution systems operation. Constraints are imposed on flows and pressures, on periodical tanks operation, and on tanks storage. The methodology links the multiobjective SPEA2 algorithm with EPANET, and is applied on two example applications of increasing complexity, under extended period simulation conditions and variable energy...
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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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Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks
PublikacjaIn this article, we formulate and solve the representation problem for diffusion equations: giving a discretization of the Laplace transform of a diffusion equation under a space discretization over a space scale determined by an increment h > 0, can we construct a continuous in h family of Cauer ladder networks whose constitutive equations match for all h > 0 the discretization. It is proved that for a finite differences discretization...
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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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The Application of a Mobile Unmanned Device for Monitoring Water and Sediment Pollution in the Port of Gdynia
PublikacjaPollution in the Port of Gdynia can encompass various types of substances and contaminants that affect the quality of water and sediment in this region. Ships entering and leaving the port can release pollutants such as oil, fuel, waste, and chemicals into the water. Controlling and monitoring these pollutants is a crucial part of environmental stewardship. In recent years, uncrewed units have been increasingly in use for in situ...
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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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Water Treatment 2022/2023
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WATER TREATMENT 2023/2024
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WATER TREATMENT 2024/2025
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Water Resources Management 2023
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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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The shallow sea experiment with usage of linear hydrophone array
PublikacjaPurpose of this article is to present designed and made linear hydrophone array and the results obtained during in situ trails on Gulf of Gdańsk. The measuring system allowed to localize hydrophones in the selected points and perform measurements in both the horizontal antenna positioning and vertical. Made in this way recordings allow creating accurate 3D imaging of sound intensity/propagation. During research three floating objects...
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Modular impedance tomograph for shallow soil subsurface investigation.
PublikacjaW pracy przedstawiono konstrukcję i procedury pomiarowe konfigurowalnego systemu pomiarowego. Konstrukcja systemu oparta jest idei tzw. elektrody aktywnej, która zbudowana jest z wykorzystaniem mikrokontrolera ADuC 812.
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Sessile droplet contact angle of water–Al2O3, water–TiO2 and water–Cu nanofluids
PublikacjaThis work presents measurements of the contact angle of sessile droplets for three nanofluids, i.e. water–Al2O3, water–TiO2 and water–Cu. The plates made of glass, anodized aluminium and stainless steel of different roughness served as substrates. Ultrasonic vibration was used for 30–60 min in order to stabilise the dispersion of the nanoparticles. Nanoparticles were tested at the concentration of 0.01%, 0.1%, and 1% by weight....
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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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Neoclassical Navier–Stokes Equations Considering the Gyftopoulos–Beretta Exposition of Thermodynamics
PublikacjaThe seminal Navier-Stokes equations were stated even before the creation of the foundations of thermodynamics and its first and second laws. There is a widespread opinion in the literature on thermodynamic cycles that the Navier-Stokes equations cannot be taken as a thermodynamically correct model of a local "working fluid", which would be able to describe the conversion of "heating" into "working" (Carnot's type cycles) and vice...
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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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Runoff Water
PublikacjaThis entry summarizes the current state of knowledge on the role of atmospheric pollutants' transport to the surface and transformations of wet deposition on contact with various surfaces. Runoff waters are one of the forms in which precipitation reaches the groundwater and surface water. They are formed when rain or melting snow washes the surfaces of roofs, highways, agricultural areas, or tree canopies. Pollutants present in...
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Systems, Environments, and Soliton Rate Equations: Toward Realistic Modeling
PublikacjaIn order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: (1) find a ‘Lax representation’ where all the kinetic variables are combined into a single matrix ρ, all the kinetic constants are encoded in a matrix H; (2) find a Darboux–Bäcklund dressing transformation for the Lax representation iρ˙=[H,f(ρ)], where f models a time-dependent environment; (3) find...
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THE USE OF MORPHOLOGICAL FILTERS AND GRANULOMETRIC METHOD TO ANALYZE THE MOVEMENT OF THE MOLECULES IN THE SEA WATER OF THE SOUTHERN BALTIC SEA
PublikacjaModern granulometry opens a new way of analysing images by means of morphological filters. In this paper a closer look has been presented on the problem of interpreting information about the features and conditions of marine environment from images taken at the sea coast and shallow water. Using this method allows for example selection of the objects on the image according to the differences in shape. Processes occurring in the...
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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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Characterization of PVDF/Graphene Nanocomposite Membranes for Water Desalination with Enhanced Antifungal Activity
PublikacjaSeawater desalination is a worldwide concern for the sustainable production of drinking water. In this regard, membrane distillation (MD) has shown the potential for effective brine treatment. However, the lack of appropriate MD membranes limits its industrial expansion since they experience fouling and wetting issues. Therefore, hydrophobic membranes are promising candidates to successfully deal with such phenomena that are typical...
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Model of Nutrient and Pesticide Outflow with Surface Water to Puck Bay (Southern Baltic Sea)
PublikacjaCoastal basins are particularly exposed to the adverse impact of anthropogenic stress. In many places, despite only the seasonal increase in the number of residents, progressive urbanization and associated changes in the catchment characteristics are noticeable. Puck Bay is part of the Gulf of Gdansk and belongs to the Baltic Sea. Although the area of Puck Bay is covered by the Natura 2000 Network, this has not saved it from eutrophication...
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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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Aneta Łuczkiewicz prof. dr hab. inż.
OsobyProwadzę badania nad zdolnościami adaptacyjnymi mikroorganizmów oraz możliwością ich wykorzystania do wspomagania procesów technologicznych. Łączę inżynierię środowiska z elementami inżynierii biomedycznej i materiałowej. Interesują mnie nowatorskie metody detekcji mikroorganizmów istotnych klinicznie w środowisku wodnym (tzw. epidemiologia oparta na ściekach) oraz zaawansowane i praktyczne rozwiązania w sektorze gospodarki wodnej....
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Why the solvation water around proteins is more dense than bulk water
PublikacjaThe main aim of this work is to propose a rational explanation of commonly observed phenomenon of increasing water density within solvation shell of proteins. We have observed that geometry of the water-water hydrogen bond network within solvation layer differs from the one in bulk water and it is the effect of interactions of water molecules with protein surface. Altered geometry of the network reflects changes in the structure...
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Why the Solvation Water around Proteins Is More Dense than Bulk Water
PublikacjaThe main aim of this work is to propose a rational explanation of the commonly observed phenomenon of increasing water density within solvation shell of proteins. We have observed that the geometry of the water–water hydrogen bond network within solvation layer differs from the one in bulk water, and it is the result of interactions of water molecules with protein surface. Altered geometry of the network reflects changes in the...
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Advanced Oxidation Processes for Degradation of Water Pollutants—Ambivalent Impact of Carbonate Species: A Review
PublikacjaAdvanced oxidation processes (AOPs) hold great promise in the removal of organic contaminants. Reactive oxygen species (ROS) produced in AOPs react with target pollutants to initially form several intermediate compounds that finally undergo complete mineralization. Such observations are reported, especially for laboratory-scale experiments performed in pure water. On the other hand, while considering real contaminated wastewater...
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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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Nonlinear principal component analysis of the tidal dynamics in a shallow sea
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Limit States of Shallow Bridge Foundations With Sheet Piling Covers
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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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A graphical approach to yield and boundary surfaces of selected hypoplastic constitutive equations
PublikacjaThe article describes how to identify the boundary and yield surface for hypoplastic constitutive equations proposed by Wu, Gudehus and Bauer. It is shown how to identify and plot the surfaces for any equation in this class. Calculation errors are analyzed characteristic for appleid set of numerical formulas. In the paper there are computer links to the source code prepared in the MATLAB system, based on istructions in the article....
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An Experimental and Numerical Analysis of Water Hammer Phenomenon in Slurries
PublikacjaThe analysis of slurry transportation in pressure pipelines is important both from practical and theoretical point of view. Due to the nature of the medium, the number of problems arising in the course of design, operation, measurements and mathematical modeling is much higher compared to the cases where the flowing liquid is homogeneous. The equations describing the flow are more complex, and higher number of the parameters is...