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Wyniki wyszukiwania dla: STATE-SPACE EQUATIONS
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Krylov Space Iterative Solvers on Graphics Processing Units
PublikacjaCUDA architecture was introduced by Nvidia three years ago and since then there have been many promising publications demonstrating a huge potential of Graphics Processing Units (GPUs) in scientific computations. In this paper, we investigate the performance of iterative methods such as cg, minres, gmres, bicg that may be used to solve large sparse real and complex systems of equations arising in computational electromagnetics.
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Numerical analysis of open channel steady gradually varied flow using the simplified saint-venant equations
PublikacjaFor one-dimensional open-channel flow modeling, the energy equation is usually used. There exist numerous approaches using the energy equation for open-channel flow computations, which resulted in the development of several very efficient methods for solving this problem applied to channel networks. However, the dynamic equation can be used for this purpose as well. This paper introduces a method for solving a system of non-linear...
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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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Numerical tests of time-stepping schemes in the context of FEM for 6-field shell dynamics
PublikacjaThe paper deals with integration of dynamic equations of irregular shells performed with relatively long time steps. Numerical instability appearing often in this kind of analysis motivated the authors to present some studies based on numerical tests referring to convergence problems of finite element analysis as well the applied stability conditions. The analysis is carried out on simulations of shell dynamics with the where the...
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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
PublikacjaThe 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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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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Physics-guided neural networks (PGNNs) to solve differential equations for spatial analysis
PublikacjaNumerous examples of physically unjustified neural networks, despite satisfactory performance, generate contradictions with logic and lead to many inaccuracies in the final applications. One of the methods to justify the typical black-box model already at the training stage and lead to many inaccuracies in the final applications. One of the methods to justify the typical black-box model already at the training stage involves extending...
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Solid State Phenomena
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Asynchronous Method of Simultaneous Object Position and Orientation Estimation with Two Transmitters
PublikacjaThis paper proposes an object location method for all types of applications, including the Internet of Things. The proposed method enables estimations of the position and orientation of an object on a plane or in space, especially during motion, by means of location signals transmitted simultaneously from two transmitters placed on the object at a known distance from each other. A mathematical analysis of the proposed method and...
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Surface finite viscoelasticity and surface anti-plane waves
PublikacjaWe introduce the surface viscoelasticity under finite deformations. The theory is straightforward generalization of the Gurtin–Murdoch model to materials with fading memory. Surface viscoelasticity may reflect some surface related creep/stress relaxation phenomena observed at small scales. Discussed model could also describe thin inelastic coatings or thin interfacial layers. The constitutive equations for surface stresses are...
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Variational principles for bound states of Schrödinger and Dirac equations allowing the use of discontinuous trial functions
PublikacjaWe present systematic constructions of variational principles for energies of bound states of the Schroedinger and Dirac equations. The principles allow the use of discontinuous trial functions. The method employed is based on a generalized Lagrange procedure. Relationships between our variational principles and those available in the literature are established.
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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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2-D constitutive equations for orthotropic Cosserat type laminated shells in finite element analysis
PublikacjaWe propose 2-D Cosserat type orthotropic constitutive equations for laminated shells for the purpose of initial failure estimation in a laminate layer. We use nonlinear 6-parameter shell theory with asymmetric membrane strain measures and Cosserat kinematics as the framework. This theory is specially dedicated to the analysis of irregular shells, inter alia, with orthogonal intersections, since it takes into account the drilling...
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Fracture mechanics model of cutting power versus widespread regression equations while wood sawing with circular saw blades
PublikacjaA comparison of the theoretical cutting power consumption results forecasted with the model (FM_CM model) which include work of separation (fracture toughness) in addition to plasticity and friction, and two widespread regression equations while wood sawing with circular saw blades has been described. in and cutting power consumption forecasted. In computations of the cutting power consumption during rip sawing of Scots pine wood...
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Successive Iterative Method for Higher-Order Fractional Differential Equations Involving Stieltjes Integral Boundary Conditions
PublikacjaIn this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.
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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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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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Closed Form Constraint Equations Used to Express Frictionless Slip of Multibody Systems Attached to Finite Elements—Application to a Contact between a Double Pendulum and a Beam
PublikacjaThis paper focuses on the numerical modeling of the dynamics of mechanical systems. Robots that can inspect high-voltage lines inspired this research. Their control systems must anticipate potential grab positions appropriately. We intend to formulate equations dedicated to the numerical description of the robot/cable contact. The investigated problem is not straightforward, since parts of the modeled systems are numerically inhomogeneous....
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Linear Time-Varying Dynamic-Algebraic Equations of Index One on Time Scales
PublikacjaIn this paper, we introduce a class of linear time-varying dynamic-algebraic equations (LTVDAE) of tractability index one on ar- bitrary time scales. We propose a procedure for the decoupling of the considered class LTVDAE. Explicit formulae are written down both for transfer operator and the obtained decoupled system. A projector ap- proach is used to prove the main statement of the paper and sufficient conditions of decoupling...
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Effective Equations for the Optimum Seismic Gap Preventing Earthquake-Induced Pounding between Adjacent Buildings Founded on Different Soil Types
PublikacjaThe best approach to avoid collisions between adjacent structures during earthquakes is to provide sufficient spacing between them. However, the existing formulas for calculating the optimum seismic gap preventing pounding were found to provide inaccurate results upon the consideration of different soil types. The aim of this paper is to propose new equations for the evaluation of the sufficient in-between separation gap for buildings...
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General solution of quantum mechanical equations of motion with time-dependent Hamiltonians: A Lie algebraic approach
PublikacjaThe unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic techniques in this context and elaborate the theory for SU(2) and SU(1,1). In these cases we give explicit formulae for obtaining general solutions from special ones. We show that the constructions...
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Nonlinear phenomena of small-scale sound in a gas with exponential stratification
PublikacjaThe nonlinear dynamics of perturbations, quickly varying in space, with comparatively large characteristic wavenumbers k: k>1/H, is considered. H is the scale of density and pressure reduction in unperturbed gas, as the coordinate (H is the so-called height of the uniform equilibrium gas). Coupling nonlinear equations which govern the sound and the entropy mode in a weakly nonlinear flow are derived. They describe the dynamics...
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A Universal Gains Selection Method for Speed Observers of Induction Machine
PublikacjaProperties of state observers depend on proper gains selection. Each method of state estimation may require the implementation of specific techniques of finding those gains. The aim of this study is to propose a universal method of automatic gains selection and perform its verification on an induction machine speed observer. The method utilizes a genetic algorithm with fitness function which is directly based on the impulse response...
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Analytical ‘Steady-State’-Based Derivation and Clarification of the Courant-Friedrichs-Lewy Condition for Pipe Flow
PublikacjaThis 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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Multiple Solutions to Third-Order Differential Equations with Derivative Dependence and Deviating Arguments
PublikacjaIn this paper, we give some new results for multiplicity of positive (nonnegative) solutions for third-order differential equations with derivative dependence, deviating arguments and Stieltjes integral boundary conditions. We discuss our problem with advanced argument α and arbitrary β ∈ C([0,1],[0,1]), see problem (2). It means that argument β can change the character on [0,1], so β can be delayed in some set J ⊂ [0,1] and advanced...
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Discussion of “Development of an Accurate Time integration Technique for the Assessment of Q-Based versus h-Based Formulations of the Diffusion Wave Equation for Flow Routing” by K. Hasanvand, M.R. Hashemi and M.J. Abedini
PublikacjaThe discusser read the original with great interest. It seems, however, that some aspects of the original paper need additional comments. The authors of the original paper discuss the accuracy of a numerical solution of the diffusion wave equation formulated with respect to different state variables. The analysis focuses on nonlinear equations in the form of a single transport equation with the discharge Q (volumetric flow rate)...
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Kinetics of nitrogen removal processes in constructed wetlands
PublikacjaThe aim of this paper is to present a state-of-the-art review of the kinetics of nitrogen removal in constructed wetlands. Biological processes of nitrogen removal from wastewater can be described using equations and kinetic models. Hence, these kinetic models which have been developed and evaluated allow for predicting the removal of nitrogen in treatment wetlands. One of the most important, first order removal model, which is...
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The behavioural model of graphene field-effect transistor
PublikacjaThe behavioural model of a graphene field-effect transistor (GFET) is proposed. In this approach the GFET element is treated as a “black box” with only external terminals available and without considering the physical phenomena directly. The presented circuit model was constructed to reflect steady-states characteristics taking also into account GFET capacitances. The authors’ model is defined by a relatively small number of equations...
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Different types of solvability conditions for differential operators
PublikacjaSolvability conditions for linear differential equations are usually formulated in terms of orthogonality of the right-hand side to solutions of the homogeneous adjoint equation. However, if the corresponding operator does not satisfy the Fredholm property such solvability conditions may be not applicable. For this case, we obtain another type of solvability conditions, for ordinary differential equations on the real axis, and...
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Relativity of arithmetic as a fundamental symmetry of physics
PublikacjaArithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters ‘plus’ or ‘times’ one has certain freedom of interpreting this operation. This leads to some freedom in definitions of derivatives, integrals and, thus, practically all equations occurring in...
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Na granicy wody i lądu – pojęcie niebieskiej przestrzeni urbanistycznej
PublikacjaObecnie obserwuje się wzrost zainteresowania projektowaniem urbanistycznym i architektonicznym z wykorzystaniem wody lub wręcz projektowania nowych terenów miejskich na obszarach wodnych. Sposób postrzegania strefy graniczenia wody i lądu w mieście ulega transformacji, a związek między tymi dwoma tkankami – znacznemu zacieśnieniu, w skutek czego w ostatnim dziesięcioleciu zaczęło kształtować się pojęcie niebieskich przestrzeni miejskich....
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublikacjaIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Adam Dąbrowski dr inż.
OsobyAdam Dąbrowski uzyskał stopień doktora nauk inżynieryjno-technicznych w dyscyplinie inżynieria mechaniczna na Politechnice Gdańskiej oraz ukończył studia II stopnia na kierunku mechatronika na Technische Universität Hamburg a także double degree Engineering and Management of Space Systems na Hochschule Bremen. Posiada doświadczenie przemysłowe (Instytut Lotnictwa w Warszawie, SICK AG w Hamburgu, Blue Dot Solutions w Gdańsku, Niemieckie...
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Monotone iterative method to second order differential equations with deviating arguments involving Stieltjes integral boundary conditions
PublikacjaWe use a monotone iterative method for second order differential equations with deviating arguments and boundary conditions involving Stieltjes integrals. We establish sufficient conditions which guarantee that such problems have extremal solutions in the corresponding region bounded by lower and upper solutions. We also discuss the situation when problems have coupled quasi-solutions. We illustrate our results by three examples.
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Explicit and implicit difefrence methods for quasilinear first order partial functional differential equations.
PublikacjaInitial boundary value problems of the Dirichlet type for quasilinear functional differential equations are considered. Explicit difference schemes of the Euler type and implicit difference methods are investigated. Suffcient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that assumptions on the regularity of given functions are the same for both classes...
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The modelling method of discrete-continuous systems
PublikacjaThe paper introduces a method of discrete-continuous systems modelling. In the proposed method a three-dimensional system is divided into finite elements in only two directions, with the third direction remaining continuous. The thus obtained discrete-continuous model is described by a set of partial differential equations. General difference equations of discrete system are obtained using the rigid finite element method. The limit...
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Effective highly accurate time integrators for linear Klein-Gordon equations across the scales
PublikacjaWe propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant...
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Effective highly accurate time integrators for linear Klein-Gordon equations across the scales
PublikacjaWe propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant...
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NUMERICAL SIMULATION OF CRATER CREATING PROCESS IN DYNAMIC REPLACEMENT METHOD BY SMOOTH PARTICLE HYDRODYNAMICS
PublikacjaA 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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A quasi-2D small-signal MOSFET model - main results
PublikacjaDynamic properties of the MOS transistor under small-signal excitation are determined by kinetic parameters of the carriers injected into the channel, i.e., the low-field mobility, velocity saturation, mobility at the quiescent-point (Q-point), longitudinal electric field in the channel, by dynamic properties of the channel, as well as by an electrical coupling between the perturbed carrier concentration in the channel and the...
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The equations for interactions of polarization modes in optical fibres including the kerr effect
PublikacjaWe have derived coupled nonlinear Schro¨ dinger equations (CNLSE) for arbitrary polarized light propagation in a single-mode fibre employing electromagnetic field complete description. We used a basis of transverse eigenmodes with appropriate projecting; hence, the nonlinear constants depend on the waveguide geometry. Accounting for a weak nonlinearity, which is connected to the Kerr effect, we have given explicit expressions for...
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Monitoring of Chlorine Concentration in Drinking Water Distribution Systems Using an Interval Estimator
PublikacjaThis paper describes the design of an interval observer for the estimation of unmeasured quality state variables in drinking water distribution systems. The estimator utilizes a set bounded model of uncertainty to produce robust interval bounds on the estimated state variables of the water quality. The bounds are generated by solving two differential equations. Hence the numerical efficiency is sufficient for on-line monitoring...
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SOLID STATE IONICS
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Numerical Methods for Partial Differential Equations
Kursy OnlineCourse description: This course focuses on modern numerical techniques for linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations (PDEs), and integral equations fundamental to a large variety of applications in science and engineering. Topics include: formulations of problems in terms of initial and boundary value problems; finite difference and finite element discretizations; boundary element approach;...
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An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors
PublikacjaAn isogeometric finite element formulation for geometrically and materially nonlinear Timoshenko beams is presented, which incorporates in-plane deformation of the cross-section described by two extensible director vectors. Since those directors belong to the space R3, a configuration can be additively updated. The developed formulation allows direct application of nonlinear three-dimensional constitutive equations without zero...
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Surface and interfacial anti-plane waves in micropolar solids with surface energy
PublikacjaIn this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for surface and interfacial elasticity....
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A DISCRETE-CONTINUOUS METHOD OF MECHANICAL SYSTEM MODELLING
PublikacjaThe paper describes a discrete-continuous method of dynamic system modelling. The presented approach is hybrid in its nature, as it combines the advantages of spatial discretization methods with those of continuous system modelling methods. In the proposed method, a three-dimensional system is discretised in two directions only, with the third direction remaining continuous. The thus obtained discrete-continuous model is described...
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Sensorless low speed PMSM motor control with cogging torque compensation
PublikacjaThe paper presents sensorless control of a low speed permanent magnet synchronous machine with use of modified state observer. An overview of the PMSM motor used in the research setup was presented. The problem of drive torque ripple, resulting mainly from the occurrence of a significant cogging torque, was discussed. A solution compensating the torque ripple of the PMSM motor was proposed. A start-up procedure of the speed control...
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Positive solutions to second-order differential equations with dependence on the first-order derivative and nonlocal boundary conditions
PublikacjaIn this paper, we consider the existence of positive solutions for second-order differential equations with deviating arguments and nonlocal boundary conditions. By the fixed point theorem due to Avery and Peterson, we provide sufficient conditions under which such boundary value problems have at least three positive solutions. We discuss our problem both for delayed and advanced arguments α and also in the case when α(t)=t, t∈[0,1]....
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Fractional-order Systems and Synchronous Generator Voltage Regulator
PublikacjaModern regulators of synchronous generators, including voltage regulators, are digital systems, in their vast majority with standard structures contained in the IEEE standard. These are systems described with stationary differential equations of integral order. Differential equations of fractional order are not employed in regulators for synchronous generator control. This paper presents an analysis of the possibilities of using...