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Wyniki wyszukiwania dla: shallow water equations
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Parabolic Equations with Functional Dependence
PublikacjaWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence and prove theorems on the existence of solutions to parabolic differential-functional equations.
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Impact of climate change on groundwater recharge in shallow young glacial aquifers in northern Poland
PublikacjaWe investigated the influence of climate change in the period 1951–2020 on shallow aquifers in the Brda and Wda outwash plains (Pomeranian Region, Northern Poland). There was a significant temperature rise (0.3 °C/10 years), which accelerated after 1980 (0.66 °C/10 years). Precipitation became increasingly irregular – extremely rainy years occurred right after or before extremely dry years, and intensive rainfall events became...
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Analiza porównawcza procesów tłumienia i wygładzania fali ciśnienia w trakcie nieustalonego przepływu w rurociągach wykonanych z różnych materiałów.
PublikacjaUderzenie hydrauliczne jest uważane za jeden z najważniejszych problemów nieustalonego przepływu w przewodach, dlatego nadal stanowi obiekt badań wielu naukowców. To zagadnienie może być badane na dwóch poziomach: praktycznym i teoretycznym. W artykule zaprezentowane zostały wyniki badań doświadczalnych przeprowadzonych na stanowisku pomiarowym nieustalonego przepływu, funkcjonującym w Laboratorium Hydraulicznym Wydziału Inżynierii...
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Analysis of Methods for Determining Shallow Waterbody Depths Based on Images Taken by Unmanned Aerial Vehicles
PublikacjaHydrographic surveys enable the acquisition and processing of bathymetric data, which after being plotted onto nautical charts, can help to ensure safety of navigation, monitor changes in the coastal zone, and assess hydro-engineering structure conditions. This study involves the measurement of waterbody depth, identification of the seabed shape and geomorphology, the coastline course, and the location of underwater obstacles....
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An analytical four-layer horizontal electric current dipole model for analysing underwater electric potential in shallow seawater
PublikacjaThe paper presents a new analytical four‑layer (air–water–bottom–non‑conductive layer) horizontal electric dipole model which allows an accurate approximation of ship’s Underwater Electric Potential (UEP) from a sufficient depth in shallow coastal marine waters. The numerical methods, usually Finite Element Method (FEM) or Boundary Elements Method (BEM), are typically used to estimate the electric field and the distribution of...
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Some aspects of noise generated by a small ship in the shallow sea
PublikacjaThe passing and underwater moving objects produce the noises of variable intensity, which significantly increase the overall level of noise in the sea. This applies to both the sonic and ultrasonic range. The excessive levels of underwater noise adversely affects the so-called underwater acoustic climate and is the reason why this phenomenon is intensively investigated from the number of years. The results of experimental work...
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Analysis of the process of water entry of an amphibious vehicle
PublikacjaThe paper presents a method of computational and experimental analysis of the process of water entry of an amphibious vehicle. The computational method is based on the Reynolds Averaged Navier-Stokes Equations (RANSE) solver and the xperiment was carried out in the towing tank at Ship Design and Research Centre S.A. with the use of a scale model. The analysis was focused on the safety of water entry, i.e. the maximum pitch and...
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Systems of Nonlinear Fractional Differential Equations
PublikacjaUsing 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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GENERAL DYNAMIC PROJECTING OF MAXWELL EQUATIONS
PublikacjaA complete – system of Maxwell equations is splitting into independent subsystems by means of a special dynamic projecting technique. The technique relies upon a direct link between field components that determine correspondent subspaces. The explicit form of links and corresponding subspace evolution equations are obtained in conditions of certain symmetry, it is illustrated by examples of spherical and quasi-one-dimensional waves.
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Concept of an Innovative Autonomous Unmanned System for Bathymetric Monitoring of Shallow Waterbodies (INNOBAT System)
PublikacjaBathymetry is a subset of hydrography, aimed at measuring the depth of waterbodies and waterways. Measurements are taken inter alia to detect natural obstacles or other navigational obstacles that endanger the safety of navigation, to examine the navigability conditions, anchorages, waterways and other commercial waterbodies, and to determine the parameters of the safe depth of waterbodies in the vicinity of ports, etc. Therefore,...
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Functional delay fractional equations
PublikacjaIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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Methodology for Performing Bathymetric Measurements of Shallow Waterbodies Using an UAV, and their Processing Based on the SVR Algorithm
PublikacjaState-of-art methods of bathymetric measurements for shallow waterbodies use Global Navigation Satellite System (GNSS) receiver, bathymetric Light Detection and Ranging (LiDAR) sensor or satellite imagery. Currently, photogrammetric methods with the application of Unmanned Aerial Vehicles (UAV) are gathering great importance. This publication aims to present step-by-step methodology for carrying out the bathymetric measurements...
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Methodology for Performing Bathymetric Measurements of Shallow Waterbodies Using an UAV, and their Processing Based on the SVR Algorithm
PublikacjaState-of-art methods of bathymetric measurements for shallow waterbodies use Global Navigation Satellite System (GNSS) receiver, bathymetric Light Detection and Ranging (LiDAR) sensor or satellite imagery. Currently, photogrammetric methods with the application of Unmanned Aerial Vehicles (UAV) are gathering great importance. This publication aims to present step-by-step methodology for carrying out the bathymetric measurements...
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Boundary problems for fractional differential equations
PublikacjaIn 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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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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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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Transmission properties of a shallow hydroacoustic channel.
PublikacjaWielokrotne odbicia fali akustycznej od granic ośrodka są przyczyną poważnych ograniczeń możliwości transmisyjnych w płytkich kanałach hydroakustycznych. Zastosowanie modelu BNM kanału, należącego do rezultatów międzynarodowego projektu PROSIM tworzonego w ramach inicjatywy MAST-III, pozwoliło obliczyć funkcje odpowiedzi impulsowych kanału i przeprowadzić symulację transmisji sygnału cyfrowego. Artykuł prezentuje wyniki transmisji...
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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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Effect of shallow traps on admittance spectra of the system carrying SCLC and on values of charge carrier mobility extracted from susceptance
PublikacjaThe work concerns small-signal spectra of space-charge-limited current below threshold frequency (ft) of shallow traps. It is shown that below ft the small-signal concentration of trapped charge carriers is proportional to and in phase with small-signal concentration of free charge carriers, so there is no room for “slow shallow traps”. Conductance can be reduced by the traps, however no change in the range of real capacitance...
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The effect of using jug-type water filters on selected metals concentration in tap water – a case study
PublikacjaIn this study, the effect of the filtration process on Na, K, Mg, Ca, Fe and Zn concentration in water, using filters from one of the leading European manufacturers, was investigated. The increase in Na (up to 300%) and K concentration (up to 320%) at the beginning of jug filter usage was reported. A decrease in Ca, Fe and Zn concentration was observed. Standard filters remove 80–90% of Mg from tap water at the beginning of the...
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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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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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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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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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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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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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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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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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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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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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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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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.