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Search results for: richards equation
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Subcritical bifurcation of free elastic shell of biological cluster
PublicationIn 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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Structural Stability of Nonautonomous Systems
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Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: II
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A Criterion for Conditional Instability by the First Approximation for Solutions of Differential Systems
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Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: I
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Water need of energy crops - one of the environmental problems in Poland
PublicationPraca przedstawia politykę państwa polskiego dotyczącą energetyki odnawialnej, wraz z instrumentami prawnymi i finansowymi. Polityka energetyczna musi być skoordynowana z gospodarką wodną. Potrzeby wodne roślin energetycznych są wprawdzie 2-3 krotnie niższe niż w Europie Południowej, tym niemniej co najmniej 600 mm w sezonie wegetacyjnym jest wymagane do wzrostu i plonowania roślin energetycznych, a więc zasilanie z opadów atmosferycznych...
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Water needs of production of biomass for energy in Poland
PublicationPrzedstawiono polskie zamierzenia polityczne dotyczące rozwoju produkcji biomasy do celów energetycznych. Produkcja biomasy wymagać będzie zwiększonego zużycia wody przez rośliny. Wprawdzie w Polsce potrzeby wodne roślin energetycznych będą 2-3 krotnie niższe niż w krajach śródziemnomorskich, tym niemniej opady atmosferyczne w Polsce będą niewystarczające i potrzeby wodne wymagać będą nawodnień na poziomie 50% aktualnych opadów...
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Potrzeby wodne roślin energetycznych jako problem oddziaływania na środowisko w Polsce
PublicationPraca przedstawia strategię rozwoju odnawialnych źródeł energii w Polsce, ze szczególnym uwzględnieniem biomasy. Wskazuje się zwłaszcza na instrumenty prawne i finansowe. Produkcja biomasy wymagać będzie znacznych ilości wody w rolnictwie nie-żywnościowym, a więc konieczne będzie skoordynowanie strategii rozwoju energetyki ze strategia gospodarowania woda w Polsce. Z obliczeń wynika, że potrzeby wodne roślin energetycznych będą...
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Potrzeby wodne roślin energetycznych jako problem oddziaływania na środowisko w Polsce
PublicationPraca przedstawia strategię rozwoju odnawialnych źródeł energii w Polsce, ze szczególnym uwzględnieniem biomasy. Wskazuje się zwłaszcza na instrumenty prawne i finansowe. Produkcja biomasy wymagać będzie znacznych ilości wody w rolnictwie nie-żywnościowym, a więc konieczne będzie skoordynowanie strategii rozwoju energetyki ze strategia gospodarowania woda w Polsce. Z obliczeń wynika, że potrzeby wodne roślin energetycznych będą...
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Free Convection Heat Transfer from Horizontal Cylinders
PublicationThe results of experimental investigation of free convection heat transfer in a rectangular container are presented. The ability of the commonly accepted correlation equations to reproduce present experimental data was tested as well. It was assumed that the examined geometry fulfils the requirement of no-interaction between heated cylinder and bounded surfaces. In order to check this assumption recently published correlation equations...
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Symmetry-Breaking Bifurcation for Free Elastic Shell of Biological Cluster, Part 2
PublicationWe will be concerned with a two-dimensional mathematical model for a free elastic shell of biological cluster. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of the shell of biological cluster may be found as solutions of a certain nonlinear functional-differential equation with several physical parameters. For each multiparameter this...
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Interaction of Acoustic and Thermal Modes in the Vibrationally Relaxing Gases. Acoustic Cooling
PublicationThe dynamic equation which governs an excess temperature associated with the thermal mode in vibrationally relaxing gas is derived. The nonlinear transfer of acoustic energy to the energy of the thermal mode in a relaxing gas causes slow variation of temperature with time. The nal dynamic equation is instantaneous. All types of sound, including aperiodic, may be considered as an acoustic source of corresponding heating or cooling....
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Calculations of labyrinth seals with and without diagnostic extraction in fluid-flow machines
PublicationLabyrinth seals are essential components of steam turbine unit constructions. Two types of labyrinth seals can be named, the first of which is the seal without diagnostic steam extraction, and the second – with extraction. The distribution of flow parameters along the packing is affected remarkably by the average seal clearance. The presence of diagnostic extraction leads to the equation system which is determinable and can be...
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Flexural buckling and post-buckling of columns made of aluminium alloy
PublicationThe paper concerns flexural buckling and initial post-buckling of axially compressed columns made of aluminium alloy described by the Ramberg-Osgood relationship. The non-linear differential equation of the problem is derived using the stationary total energy principle and the assumptions of classical beam theory within a finite range. The approximate analytical solution of the equation leading to the buckling loads and initial...
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Buckling and initial post-local buckling behaviour of cold-formed channel member flange
PublicationThe initial post-buckling behaviour of a cold-formed channel member flange after its local buckling is investigated. An axially compressed column or beam subjected to pure bending is considered. The member material is assumed to follow a linear stress-strain relationship. The governing non-linear differential equation of the problem is derived using the minimum total potential energy principle. An approximate solution for the equation...
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Automatic Regularization by Quantization in Reducible Representations of CCR: Point-Form Quantum Optics with Classical Sources
PublicationElectromagnetic fields are quantized in a manifestly covariant way by means ofa class of reducible "center-of-mass N-representations" of the algebra of canonical commutationrelations (CCR). The four-potential Aa(x) transforms in these representations as aHermitian four-vector field in Minkowski four-position space (without change of gauge), butin momentum space it splits into spin-1 massless photons and two massless scalars. Whatwe...
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Investigations On Water Circulation in Animal Sea-Water Basins – On the Example of Seals′ Breeding Pools
PublicationThis paper presents general comments concerning investigations on water circulation in animal breeding pools containing sea water. As an example are given results of computer simulation of water circulation in seals’ breeding pools situated in Marine Station at Hel, belonging to Oceanographic Institute, Gdansk University. A mathematical model of three main pools was prepared with taking into account their inflow and outflow water...
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Water uptake in protective organic coatings and its reflection in measured coating impedance
PublicationWater uptake in commercially available epoxy coating on mild steel using impedance spectroscopy and gravimetry was studied. The water content in the coating was determined using the Brasher-Kingsbury equation and various methods of coating capacitance calculation used in the literature. The obtained results were compared with reference gravimetric data. An overestimation of values obtained from impedance data in relation to gravimetric...
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Low Cost Method for Location Service in the WCDMA System
PublicationA new and low cost method for a location service (LCS) in the Wideband Code Division Multiple Access (WCDMA) system is outlined. This method, which is called TDOA + RTT, enables calculation of the geographical position of a mobile station (MS) without knowledge of relative time differences (RTDs) between base stations (BSs). The TDOA+RTT method is based on the measurement of round trip times (RTTs) between the MS and the serving...
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Signal propagation in electromagnetic media described by fractional-order models
PublicationIn 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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Directed pulse dynamics
PublicationIntroducing a projection method into a one-dimensional model of a pulse propagation in isotropic media, we derive and investigate a system of equation describing dynamics ultrashort pulses of opposite directions ofpropagation and ones with interaction of directed pulses with different polarization.
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One-Dimensional Modeling of Flows in Open Channels
PublicationIn this chapter, modeling of the unsteady open channel flow using one-dimensional approach is considered. As this question belongs to the well-known and standard problems of open channel hydraulic engineering, comprehensively presented and described in many books and publications, our attention is focused on some selected aspects only. As far as the numerical solution of the governing equations is considered, one can find out that...
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Experimental investigation of two-phase thermosyphon heat exchanger charged with acetone
PublicationThis paper presents thermal characteristics of prototype of a two-phase thermosyphon heat exchanger (TPTHEx) charged with acetone as a working fluid. The TPTHEx consists of two horizontal cylindrical vessels connected by two risers and a downcomer. Tube bundles placed in the lower and upper cylinders work as an evaporator and a condenser, respectively. The tested TPTHEx operates in a vacuum. Therefore, the working liquid is boiled...
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Local buckling of thin-walled channel member flange made of aluminum alloy
PublicationThe paper deals with local stability of the thin-walled compressed flange of channel columns and beams made of aluminum alloy. The aim of paper is to find critical stress of local buckling of the flange member taking into account the web-flange interaction in linear and nonlinear elastic range of the member material. The governing differential equation of the problem is derived with aid of the principle of stationary total potential...
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Parametric method applicable in assessing breakout force and time for lifting slender bodies from seabed
PublicationThe article presents a parametric method applicable in assessing the suction force of a slender body to the seabed, and prognosing the body extrication time. Along with the body weight in water, the information on the suction force is essential for assessing the force needed to lift the object from the seabed. Based on the Foda theory and the resulting integral equation, which relates the maximum suction force with basic parameters...
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Projecting procedure for meta-material fiber
PublicationWe would like to show new way of derivation evolution equation for short pulses in dielectric waveguide including one model of metamaterial waveguide. This derivation model rely on projecting to the orthogonal basis. In our case to orthogonal basis for cylindrical waveguide.
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Three-dimensional modeling and automatic analysis of the human nasal cavity and paranasal sinuses using the computational fluid dynamics method
PublicationPurpose The goal of this study was to develop a complete workflow allowing for conducting computational fluid dynam- ics (CFD) simulation of airflow through the upper airways based on computed tomography (CT) and cone-beam computed tomography (CBCT) studies of individual adult patients. Methods This study is based on CT images of 16 patients. Image processing and model generation of the human nasal cavity and paranasal sinuses...
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Verification of the method of reconstructing convective velocity fields on the basis of temperature fields in vertical, differential and equally heated, open and closed channels
PublicationThis paper describes a method of reconstructing velocity fields, i.e. a numerical reconstruction procedure (NRP) that involves the numerical processing of experimentally measured temperature distributions in free convection heat transfer. The NRP consists in solving only the continuity and Navier–Stokes equations with an additional source term. This term is proportional to a known temperature (e.g. from a thermal imaging camera)...
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Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect
PublicationIn recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This...
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Path integrals formulations leading to propagator evaluation for coupled linear physics in large geometric models
PublicationReformulating linear physics using second kind Fredholm equations is very standard practice. One of the straightforward consequences is that the resulting integrals can be expanded (when the Neumann expansion converges) and probabilized, leading to path statistics and Monte Carlo estimations. An essential feature of these algorithms is that they also allow to estimate propagators for all types of sources, including initial conditions....
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A Generalized Framework Towards Structural Mechanics of Three-layered Composite Structures
PublicationThree-layered composite structures find a broad application. Increasingly, composites are being used whose layer thicknesses and material properties diverge strongly. In the perspective of structural mechanics, classical approaches to analysis fail at such extraordinary composites. Therefore, emphasis of the present approach is on arbitrary transverse shear rigidities and structural thicknesses of the individual layers. Therewith...
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Verification of algorithms determining wave loads on support structure of wind turbine
PublicationThe offshore wind turbines require determination of wave loads on their support structure. This structure is fixed and, therefore, this problem is reduced to solving only the diffraction problem, which is determined by Laplace equation and conditions on the following boundaries: on the support structure, on the sea free surface and on its bottom, and at infinity on free surface. The linear problem was applied to determine the wave...
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Alternative convolution approach to friction in unsteady pipe flow
PublicationIn the paper some aspects of the unsteady friction in pipe flow expressed by the convolution are analyzed. This additional term introduced into the motion equation involves the accelerations of fluid occurring in the past and a weighting function. The essence of such approach is to assume the appropriate form of weighting function. However, until now no fully reliable formula for this function has been found. To avoid some inconveniences...
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Determination of t8/5 cooling times for underwater local dry welding of steel
PublicationKnowledge of thermal history is the basic condition for studying the structure - properties of welded joints. The determinant of thermal history is the thermal cycle, whose in-situ measurements are still a big challenge. Water as the welding environment complicates this issue even more. The article presents a method to determine an equation for calculating t8/5 cooling times for underwater gas metal arc welding of unalloyed steels...
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Fractional problems with advanced arguments
PublicationThis paper concerns boundary fractional differential problems with advanced arguments. We investigate the existence of initial value problems when the initial point is given at the end point of an interval. Nonhomogeneous linear fractional differential equations are also studied. The existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using...
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Numerical Investigation of Nuclear Reactor Kinetic and Heat Transfer Fractional Model with Temperature Feedback
PublicationAbstract—In the paper, the numerical results concerning the kinetics and proposed heat exchange models in nuclear reactor based on fractional calculus are presented for typical inputs. Two fractional models are proposed and compared with the model based on ordinary derivative. The first fractional model is based on one of the generalized Cattaneo equations. The second one is based on replacing the ordinary to fractional order of...
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On Nonlinear Dynamic Theory of Thin Plates with Surface Stresses
PublicationWe discuss the modelling of dynamics of thin plates considering surface stresses according to Gurtin–Murdoch surface elasticity. Taking into account the surface mass density we derive the two-dimensional (2D) equations of motion. For the reduction of the three-dimensional (3D) motion equations to the 2D ones we use the trough-the-thickness integration procedure. As a result, the 2D dynamic parameters of the plate depend not only...
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Thermo-resonance analysis of an excited graphene sheet using a new approach
PublicationForced vibration of graphene nanoplate based on a refined plate theory in conjunction with higher-order nonlocal strain gradient theory in the thermal environment has been investigated. Regarding the higher-order nonlocal strain gradient theory, both stress nonlocality and size-dependent effects are taken into account, so the equilibrium equations which are governing on the graphene sheet have been formulated by the theory....
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublicationIn 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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Geometrically nonlinear FEM analysis of 6-parameter resultant shell theory based on 2-D Cosserat constitutive model
PublicationWe develop the elastic constitutive law for the resultant statically and kinematically exact, nonlinear, 6-parameter shell theory. The Cosserat plane stress equations are integrated through-the- thickness under assumption of the Reissner-Mindlin kinematics. The resulting constitutive equations for stress resultant and couple resultants are expressed in terms of two micropolar constants: the micropolar modulus Gc and the micropolar...
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Integrable zero-range potentials in a plane
PublicationWe examine general statements in the Wronskian representation of Darboux transformations for plane zero-range potentials. Such expressions naturally contain scattering problem solution. We also apply Abel theorem to Wronskians for differential equations and link it to chain equations for Darboux transforms to fix conditions for further development of the underlying distribution concept. Moutard transformations give a convenient...
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Application of the distributed transfer function method and the rigid finite element method for modelling of 2-D and 3-D systems
PublicationIn the paper application of the Distributed Transfer Function Method and the Rigid Finite Element Method for modelling of 2-D and 3-D systems is presented. In this method an elastic body is divided into 1-D distributed parameter elements (strips or prisms). The whole body (divided into strips or prism) is described by a set of coupled partial differential equations. Solving this equations in the state space form it is possible...
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Ellipticity of gradient poroelasticity
PublicationWe discuss the ellipticity properties of an enhanced model of poroelastic continua called dilatational strain gradient elasticity. Within the theory there exists a deformation energy density given as a function of strains and gradient of dilatation. We show that the equilibrium equations are elliptic in the sense of Douglis–Nirenberg. These conditions are more general than the ordinary and strong ellipticity but keep almost all...
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Reduction of Computational Complexity in Simulations of the Flow Process in Transmission Pipelines
PublicationThe paper addresses the problem of computational efficiency of the pipe-flow model used in leak detection and identification systems. Analysis of the model brings attention to its specific structure, where all matrices are sparse. With certain rearrangements, the model can be reduced to a set of equations with tridiagonal matrices. Such equations can be solved using the Thomas algorithm. This method provides almost the same values...
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Analysis of a gene expression model
PublicationWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the number of active binding sites, the way in which dimers bind to DNA and time delay in translation process. For a simplified model that consist of three ordinary differential equations with time delay we derive conditions for stability of the positive steady state and for the...
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Diagnostyka łożysk silnika indukcyjnego na podstawie prądu zasilającego przy użyciu sztucznych sieci neuronowych
PublicationW artykule zawarto wyniki badań dotyczące diagnostyki łożysk silnika indukcyjnego na podstawie pomiarów prądu zasilającego z wykorzystaniem sztucznych sieci neuronowych. Zaprezentowano wyniki uczenia sieci oraz rezultaty testów przeprowadzonych na danych spoza zbioru uczącego. Badania wykonane zostały na obiektach z celowo wprowadzonymi uszkodzeniami łożysk. Przedstawiona nowa koncepcja zakłada użycie zestawu sieci neuronowych...
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Dyskretno-ciągła metoda modelowania układów dynamicznych
PublicationW artykule przedstawiono oryginalną metodę modelowania układów dyskretno-ciągłych. Metoda polega na dyskretyzowaniu układu trójwymiarowego jedynie w dwóch wybranych kierunkach. W trzecim z kierunków układ pozostaje ciągły. Otrzymany w ten sposób model jest modelem dyskretno-ciągłym. Opisany jest za pomocą równań różniczkowych cząstkowych. Ogólne równania różnicowe układu dyskretnego otrzymano, wykorzystując metodę sztywnych elementów...
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Non-linear static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum
PublicationIn this research, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and non-linear strains of Von-Karman was studied. The bi-layer carbon sheets were modeled as a double-layered plate, and van der Waals forces between layers were considered. The governing equations and boundary conditions were obtained using the first order shear...
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Modal Adjustment of Rayleigh Based Structural Damping and Coordinate-Partitioning Algorithm Dedicated to Frictionless Contact Constraints between Multibody System and Structure Modelled with Finite Elements
PublicationThe paper presents a dedicated numerical algorithm. The algorithm is advantageous during investigations of the dynamics of a hybrid multibody / finite-elements system. We focus our attention on interactions resulting from mechanical contact. Pointwise contact connects a vertex of the multibody structure and a surface of the elastic reference body. Instead of a positive value of the relative penetration factor, constraint equations...
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Fractional Order Circuit Elements Derived from Electromagnetism
PublicationIn this paper, derivations of fractional-order (FO) circuit-element equations from electromagnetism are presented. Whilst many papers are devoted to FO modelling of electrical circuits, there are no strong foundations for such an approach. Therefore, we investigate relations between the FO electromagnetism and the FO circuit theory. Our derivations start from quasi-static (QS) approximations of Maxwell's equations in media with...