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Search results for: NUMERICAL STABILITY
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Mathematical analysis of a generalised p53-Mdm2 protein gene expression model
PublicationWe propose the generalisation of the p53-Mdm2 protein gene expression model introduced by Monk (2003). We investigate the stability of a unique positive steady state and formulate conditions which guarantee the occurrence of the Hopf bifurcation. We show that oscillatory behaviour can be caused not only by time lag in protein transcription process, but also can be present in the model without time delay. Moreover, we investigate...
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Method of lines for physiologically structured models with diffusion
PublicationWe deal with a size-structured model with diffusion. Partial differential equations are approximated by a large system of ordinary differential equations. Due to a maximum principle for this approximation method its solutions preserve positivity and boundedness. We formulate theorems on stability of the method of lines and provide suitable numerical experiments.
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ANALYSIS OF THE p53 PROTEIN GENE EXPRESSION MODEL
PublicationWe study the asymptotic behaviour of the solutions of the p53-Mdm2 model proposed by Monk (2003). The p53 gene is crucial for cellular inhibition of the angiogenesis process, while Mdm2 is a negative regulator of the p53 tumor-suppressor. We investigate the stability of the positive steady state and perform some numerical experiments.
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Difference functional inequalities and applications.
PublicationThe paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.
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Long-term hindcast simulation of currents in the Baltic Sea
Open Research DataThe dataset contains the results of numerical modelling of currents over a period of 50 years (1958-2007) in the Baltic Sea . A long-term hindcast simulation was performed using a three-dimensional hydrodynamic model PM3D (Kowalewski and Kowalewska-Kalkowska, 2017), a new version of the M3D model (Kowalewski, 1997). The hydrodynamic model was coupled...
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Uproszczone metody obliczania wyboczenia silosów z blachy falistej wzmocnionych słupami na podstawie analizy MES i wyników doświadczalnych
PublicationRozprawa doktorska dotyczy zagadnienia stateczności i nośności granicznej stalowych silosów z płaszczem z blachy falistej wzmocnionych pionowymi słupami. Przeprowadzono zaawansowane analizy numeryczne MES oraz badania doświadczalne dotyczące wyboczenia/stateczności analizowanych silosów. Analizy numeryczne zostały przeprowadzone w zakresie liniowej oraz nieliniowej analizy stateczności, z uwzględnieniem wstępnych imperfekcji geometrycznych...
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Solving the Problem of Dynamic Adaptability of Artificial Intelligence Systems that Control Dynamic Technical Objects
PublicationThis paper investigates the increase in the response speed and stability of artificial intelligence systems that control dynamic technical objects. The problem of calculating the optimal time of switching an artificial intelligence system between software classes by the criterion of the rigidity degree of the model of a control object is considered. The solution of this problem is proposed for the general case of the control object...
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Geo-engineering computer simulation seems attractive but is it the real world?
PublicationCorrect formulation of the differential equation system for equilibriom conditions of subsoil, especially in terms of controlled numerical calculation, is discussed. The problem of solution stability is also considered. The solution of problems, which are ill-posed, have no practical value in the majority of cases and is this way the engineering prognosis can lead to real disaster. The object of this paper is quite relevant if...
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Running characteristics of aerodynamic bearing with self-lifting capability at low rotational speed
PublicationAn aerodynamic journal bearing that is capable of self-generating squeeze-film pressure is presented and its dynamic characteristics investigated numerically and experimentally. A numerical method based on a time marching static model was applied to assess the orbit trajectory path of the rotor upon a perturbation. Experimental results were obtained to validate the effect of the self- generated squeeze-film pressure on the stability...
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Analysis of EN 1993-1-6 guidelines about determining amplitudes of equivalent imperfections of steel cylindrical shells subjected to uniform external pressure
PublicationCivil engineering structures should be designed with reference to relevant standards. One of them is a Eurocode 3 standard EN 1993-1-6:2007: Design of steel structures Part 1-6: Strength and Stability of Shell Structures. According to this standard, the value of buckling load can be determined using different approaches: classical hand calculations (stress design) and geometrical and material non-linear analysis of an imperfect...
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Buckling of thin-walled columns accounting for initial geometrical imperfections
PublicationThe paper is devoted to the effect of some geometrical imperfections on the critical buckling load of axially compressed thin-walled I-columns. The analytical formulas for the critical torsional and flexural buckling loads accounting for the initial curvature of the column axis or the twist angle respectively are derived. The classical assumptions of theory of thin-walled beams with non-deformable cross-sections are adopted. The...
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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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MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION
PublicationThe purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic...
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Development of a Response Assessment Tool for a Floating Dock System
PublicationDocking operations of ships require a response assessment to ensure structural and personnel safety. Environmental loads and improper ballast adjustments are the main threats to the docking operations. They can cause severe structural damages and stability loss to a floating dock system which includes a floating dock and a docked vessel, even if the velocities of the dock and the vessel are very low during the docking process....
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Weighted difference schemes for systems of quasilinear first order partial functional differential equations
PublicationThe 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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Running performance of an aerodynamic journal bearing with squeeze film effect
PublicationResults of theoretical and experimental studies concerning the performance of an aerodynamic journal bearing of which running is assisted by squeeze film ultrasonic levitation (SFUL) are presented in this paper. The SFUL mechanism not only can separate journal from the bearing at the start and stop phases of operation but also can significantly contribute to the dynamic stability of the bearing when it runs at speed. Computer calculations...
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Wstępny plan badań węzła z mimośrodem dodatnim w kratownicy z kształtowników o przekrojach poprzecznych otwartych. -(Autorka otrzymała wyróżnienie za tą publikację)
PublicationW celu określenia wpływu mimośrodowego przecinania się prętów w kratownicy z kształtowników giętych na zimno, o przekrojach poprzecznych otwartych na nośność i stateczność węzłów dźwigarów kratowych, opracowano model badawczy oraz przeprowadzono wstępną analizę numeryczną przedmiotowego węzła, w programie Marc Mentat. Uzyskane wyniki wskazują na potrzebę uzupełnienia obciążenia o parę sił poziomych w modelu badawczym.
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Analysis of the influence of geometrical imperfections on the equivalent load stabilizing roof truss with lateral bracing system
PublicationThe paper is focused on the numerical analysis of the stability and load bearing capacity of a flat steel truss. The structure was supported by elastic lateral braces. The translational and rotational brace stiffness was taken into account. The linear buckling analysis were performed for the beam and shell model of the truss. The nonlinear static analysis were conducted for the structure initial geometric imperfections. As a result...
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Flow Process Models for Pipeline Diagnosis
PublicationThis chapter examines the problem of modeling and parameterization of the transmission pipeline flow process. First, the base model for discrete time is presented, which is a reference for other developed models. Then, the diagonal approximation (AMDA) method is proposed, in which the tridiagonal sub-matrices of the recombination matrix are approximated by their diagonal counterparts, which allows for a simple determination of...
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Accuracy of the Discrete Green's Function Formulation of the FDTD Method
PublicationThis paper reports an evaluation of the accuracy of the discrete Greens function (DGF) formulation of the finite-difference time-domain (FDTD) method. Recently, the closed-form expression for the DGF and its efficient numerical implementation were presented, which facilitates applications of the DGF in FDTD simulations of radiation and scattering problems. So far, the accuracy of the DGF formulation of the FDTD method has been...
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A comprehensive approach to double inverted pendulum modelling
PublicationThe problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used....
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FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
PublicationIn this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced....
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A Fortran-95 algorithm to solve the three-dimensional Higgs boson equation in the de Sitter space-time
Open Research DataA numerically efficient finite-difference technique for the solution of a fractional extension of the Higgs boson equation in the de Sitter space-time is designed. The model under investigation is a multidimensional equation with Riesz fractional derivatives of orders in (0,1)U(1,2], which considers a generalized potential and a time-dependent diffusion...
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DETERMINATION OF THE AERODYNAMIC DRAG OF PNEUMATIC LIFE RAFTS AS A FACTOR FOR INCREASING THE RELIABILITY OF RESCUE OPERATIONS
PublicationEnsuring the safety of ship crews at sea is of the utmost importance. Life rafts are one of the basic components of any seagoing vessel and ensuring their stability is an important component of maritime research. This study concerns the determination of the aerodynamic drag coefficients of pneumatic life rafts in a full range of wind speed and directions. The drag coefficients are based on full-scale experimental studies and numerical...
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Dual-Polarized Wideband Bandpass Metasurface-Based Filter
PublicationThis paper presents a novel metasurface-based bandpass filter. The structure is realized by simply patterning a double-sided AD250 substrate, and does not require any vias or insertion of lumped elements. The top layer is an annular- aperture-array with multiple inner conductors, whereas the bottom layer is a first-order Hilbert-curve array. FEM-based simulation results of the filter are obtained using HFSS. The experimental validation...
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Compatibility of Crude Oil Blends─Processing Issues Related to Asphaltene Precipitation, Methods of Instability Prediction─A Review
PublicationProcessing crude oil of variable composition, especially due to the need to process crude oil blends obtained from various sources, presents a tremendous process challenge. This is mainly due to the destabilization of the colloidal system manifested mostly by the precipitation of the asphaltene fraction. The precipitation of asphaltenes from crude oil is a serious problem during extraction, transport, and processing. In the latter...
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Straightened characteristics of McKendrick-von Foerster equation
PublicationWe study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...
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Buckling analyses of metal cylindrical silos containing bulk solids during filling
PublicationThe paper presents 3D results on stability of thin-walled cylindrical metal silos made of isotropic rolled and corrugated plates containing bulk solids. The behavior of bulk solids was described using a hypoplastic constitutive model. Nonlinear finite element (FE) analyses with both geometric and material nonlinearity were performed with a perfect and an imperfect silo shell wherein initial geometric imperfections were taken into...
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Influence of the air phase on water flow in dikes
PublicationNumerical models are often used to describe flow and deformation processes occurring in dikes during flood events. Modeling of such phenomena is a challenging task, due to the complexity of the system, consisting of three material phases: soil skeleton, pore water and pore air. Additional difficulties are transient loading caused by variable in time water levels, heterogeneity of the soil or air...
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On Wrinkling in Sandwich Panels with an Orthotropic Core
PublicationThis paper deals with the local loss of stability (wrinkling) problem of a thin facing of a sandwich panel. Classical solutions to the problem of facing instability resting on a homogeneous and isotropic substructure (a core) are compared. The relations between strain energy components associated with different forms of core deformations are discussed. Next, a new solution for the orthotropic core is presented in detail, which...
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An interval estimator for chlorine monitoring in drinking water distribution systems under uncertain system dynamics, inputs and chlorine concentration measurement errors
PublicationThe design of an interval observer for estimation of unmeasured state variables with application to drinking water distribution systems is described. In particular, the design process of such an observer is considered for estimation of the water quality described by the concentration of free chlorine. The interval observer is derived to produce the robust interval bounds on the estimated water quality state variables. The stability...
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Computational Bar Size Optimization of Single Layer Dome Structures Considering Axial Stress and Shape Disturbance
PublicationA computational method is proposed in this paper to minimize the material usage in the construction of modern spatial frame structures by prestressing a minimal number of members. The computational optimization is conducted in two steps. Firstly, a numerical model of a single-layer dome structure is used to minimize the cross-sectional area through several iterations. Different assumed ratios (r) ranging from 0.95 to 0.75 are multiplied...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Experimental investigation of joint with positive eccentricity in CFS truss
PublicationDue to technological restrictions, in the case of trusses made of CFS open cross-sections, positive eccentricities in the truss joints have become very frequent. Therefore studies concerning the load-bearing capacity of truss joints with positive eccentricity were undertaken. It was assumed that the resistance of cold-formed steel (CFS) open cross-section truss joints located on compression chords and with positive eccentricity...
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Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublicationWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...
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Selected local stability problems of channel section flanges made of aluminium alloys
PublicationThe paper addresses the issue of local buckling of compressed flanges of cold-formed thin-walled channel columns and beams with nonstandard flanges composed of aluminium alloys. The material behaviour follows the Ramberg–Osgood law. It should be noted that the proposed solution may be also applied for other materials, for example: stainless steel, carbon steel. The paper is motivated by an increasing interest in nonstandard cold-formed...
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Electrical properties of organic and perovskite systems used in solar cells
PublicationNowadays, a great progress in the areas of molecular and hybrid photovoltaics is observed. The devices based on organic and perovskite materials are getting attention mostly due to their low cost production process. However, their efficiency and stability are still lower than for inorganic materials which make them less popular. Therefore, a detailed understanding of the device physics is fundamental for organic and perovskite...
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NUMERICAL SIMULATION OF CRATER CREATING PROCESS IN DYNAMIC REPLACEMENT METHOD BY SMOOTH PARTICLE HYDRODYNAMICS
PublicationA theoretical base of SPH method, including the governing equations, discussion of importance of the smoothing function length, contact formulation, boundary treatment and finally utilization in hydrocode simulations are presented. An application of SPH to a real case of large penetrations (crater creating) into the soil caused by falling mass in Dynamic Replacement Method is discussed. An influence of particles spacing on method...
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Coupled nonlinear Schrödinger equations in optic fibers theory
PublicationIn 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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Multi-layered mineral glass units used as viewport elements of underwater ship structures
PublicationIn the paper, Authors deals with viewport elements of underwater marine constructions. If a single-plate viewport constructions are considered, big thicknesses of the glass plate are required to resist the pressure. To build the viewports from the commercially accessible glass panes, multi-layered glass units are proposed in the paper. Numerical calculations are presented, summarized and compared with experimental tests. Focusing...
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Modeling of medium flow processes in transportation pipelines - the synthesis of their state-space models and the analysis of the mathematical properties of the models for leak detection purposes
PublicationThe dissertation concerns the issue of modeling the pipeline flow process under incompressible and isothermal conditions, with a target application to the leak detection and isolation systems. First, an introduction to the model-based process diagnostics is provided, where its basic terminology, tools, and methods are described. In the following chapter, a review of the state of the art in the field of leak detection and isolation...
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Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein
PublicationWe analyse a model of Hes1 gene transcription and protein synthesis with a negative feedback loop. The effect of multiple binding sites in the Hes1 promoter as well as the dimer formation process are taken into account. We consider three, possibly different, time scales connected with: (i) the process of binding to/dissolving from a binding site, (ii) formation and dissociation of dimers, (iii) production and degradation of Hes1...
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Analytical ‘Steady-State’-Based Derivation and Clarification of the Courant-Friedrichs-Lewy Condition for Pipe Flow
PublicationThis article addresses the problem of choosing the optimal discretization grid for emulating fluid flow through a pipeline. The aggregated basic flow model is linearized near the operating point obtained from the steady state analytic solution of the differential equations under consideration. Based on this model, the relationship between the Courant number (μ) and the stability margin is examined. The numerically set coefficient...
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Medially positioned plate in first metatarsophalangeal joint arthrodesis
PublicationObjective The purpose of this study was to biomechanically compare the stability of first metatarsophalangeal (MTP1) joint arthrodesis with dorsally and medially positioned plates. Methods A physical model of the MTP1 joint consists of printed synthetic bones, a titanium locking plate and screws. In the experiments, samples with dorsally and medially positioned plates were subjected to loading of ground load character in a universal...
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Effect of Different Bromine Sources on the Dual Cation Mixed Halide Perovskite Solar Cells
PublicationRecent research has shown that perovskite solar cells with a mixed dual A-cation have much better structural stability without loss of efficiency than single cation devices. Mixed cation perovskites create a lot of questions about the salts being used for the formation of the best-quality layer. Here, we have investigated three sources of bromide in the perovskite absorption layer, using lead bromide (PbBr2), formamidinium bromide...
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Optimization of Stabilizing Systems in Protection of Cultural Heritage: The Case of the Historical Retaining Wall in the Wisłoujście Fortress
PublicationThe aim of the paper is to propose new quantitative criteria for selecting the optimal method of securing and repairing a historical object, which take into account Structural, Conservation and Architectural aspects (the S–C–A method). Construction works on cultural heritage sites tend to be challenging and require an interdisciplinary approach. Therefore, they are strictly related to the philosophy of sustainable development which...
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Local buckling of composite channel columns
PublicationThe investigation concerns local buckling of compressed flanges of axially compressed composite channel columns. Cooperation of the member flange and web is taken into account here. The buckling mode of the member flange is defined by rotation angle a flange about the line of its connection with the web. The channel column under investigation is made of unidirectional fibre-reinforced laminate. Two approaches to member orthotropic...
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Simulations of air and water flow in a model dike during overflow experiments
PublicationFlow in flood dikes, earth dams, and embankments occurs in variably saturated conditions, with pores of the earth material filled partly with water and partly with air. In routine engineering analysis, the influence of pore air is neglected and the air pressure is assumed equal to atmospheric. In some circumstances, for example, during overtopping of the dike by water, the effect of pore air on water flow and stability of the structure...
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Buckling resistance of a metal column in a corrugated sheet silo - experiments and non-linear stability calculations
PublicationThe results of experimental and numerical tests of a single corrugated sheet silo column’s buckling resistance are presented in this study. The experiments were performed in a real silo with and without bulk solid (wheat). A very positive impact of the bulk solid on the column buckling resistance occurred. The experimental results were first compared to the buckling resistance calculated by Eurocode 3 formulae. The comparison revealed that...
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On local buckling of cold-formed channel members
PublicationThe paper deals with local buckling of the compressed flanges of cold-formed thin-walled channel beams subjected to pure bending or axially compressed columns. Arbitrarily shaped flanges of open cross-sections and the web-flange interactions are taken into account. Buckling deformation of a beam flange is described by displacement related to torsion of the flange about the line of its connection with the web. Total potential energy...