Wyniki wyszukiwania dla: NONLINEAR SYSTEMS
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Magnetosonic Excitation of the Entropy Perturbations in a Plasma with Thermal Conduction Depending on Temperature
PublikacjaNonlinear excitation of the entropy perturbations by magnetosonic waves in a uniform and infinite plasma model is considered. The wave vector of slow or fast mode forms an arbitrary angle (0 B B ) with the equilibrium straight magnetic field, and all perturbations are functions of the time and longitudinal coordinate. Thermal conduction is the only factor which destroys isentropicity of wave perturbations and causes the nonlinear...
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Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance
PublikacjaThe impetus of writing this paper is to propose an efficient detection mechanism to scan the surface profile of a micro-sample using cantilever-based atomic force microscopy (AFM), operating in non-contact mode. In order to implement this scheme, the principal parametric resonance characteristics of the resonator are employed, benefiting from the bifurcation-based sensing mechanism. It is assumed that the microcantilever is made...
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Acoustic heating produced in resonators filled by a newtonian fluid
PublikacjaAcoustic heating in resonators is studied. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in the linear part of the final equation, but preserving terms belonging to the thermal mode responsible for heating. This equation is instantaneous and includes nonlinear acoustic terms that form a...
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Modelling of joining route segments of differential curvature
PublikacjaThe paper presents a new general method of modelling route segments curvature using differential equations. The method enables joining of route segments of different curvature. Transitional curves of linear and nonlinear curvatures have been identified in the case of joining two circular arcs by S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph...
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Validation of lumbar spine finite element model
Dane BadawczeThe functional biomechanics of the lumbar spine have been better understood by finite element method (FEM) simulations. However, there are still areas where the behavior of soft tissues can be better modeled or described in a different way. The purpose of this research is to develop and validate a lumbar spine section intended for biomechanical research....
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Feedback Control of Multiphase Induction Machines with Backstepping Technique
PublikacjaThe paper presents the control possibility of five phase induction machines. In the proposed solution the machine model vector form is not transformed to the (dq)-coordinate system, that is connected to rotor flux vector, but utilizes the stationary system ( αβ ). Moreover, the nonlinear model linearization is based on demonstrated nonlinear variables transformation for i-orthogonal ( αβ )(n) planes. By introducing the backstepping...
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Efficiency of acoustic heating in the Maxwell fluid
PublikacjaThe nonlinear effects of sound in a fluid describing by the Maxwell model of the viscous stress tensor is the subject of investigation. Among other, viscoelastic biological media belong to this non-newtonian type of fluids. Generation of heating of the medium caused by nonlinear transfer of acoustic energy, is discussed in details. The governing equation of acoustic heating is derived by means of the special linear combination...
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Efficiency of acoustic heating in the Maxwell fluid
PublikacjaThe nonlinear effects of sound in a fluid describing by the Maxwell model of the viscous stress tensor is the subject of investigation. Among other, viscoelastic biological media belong to this non-newtonian type of fluids. Generation of heating of the medium caused by nonlinear transfer of acoustic energy, is discussed in details. The governing equation of acoustic heating is derived by means of the special linear combination...
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Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.
PublikacjaDeparting from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity,...
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Isogeometric Shell FE Analysis of the Human Abdominal Wall
PublikacjaIn this paper a nonlinear isogeometric Kirchhoff-Love shell model of the human abdominal wall is proposed. Its geometry is based on in vivo measurements obtained from a polygon mesh that is transformed into a NURBS surface, and then used directly for the finite element analysis. The passive response of the abdominal wall model under uniform pressure is considered. A hyperelastic membrane model based on the Gasser-Ogden-Holzapfel...
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Accurate Computation of IGBT Junction Temperature in PLECS
PublikacjaIn the article, a new method to improve the accuracy of the insulated-gate bipolar transistor (IGBT) junction temperature computations in the piecewise linear electrical circuit simulation (PLECS) software is proposed and described in detail. This method allows computing the IGBT junction temperature using a nonlinear compact thermal model of this device in PLECS. In the method, a nonlinear compact thermal model of the IGBT is...
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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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Excitation of Non-Wave Modes by Sound of Arbitrary Frequency in a Chemically Reacting Gas
PublikacjaThe nonlinear phenomena in the field of high intensity sound propagating in a gas with a chemical reaction, are considered. A chemical reaction of A → B type is followed by dispersion and attenuation of sound which may be atypical during irreversible thermodynamic processes under some conditions. The first and second order derivatives of heat produced in the chemical reaction evaluated at the equilibrium temperature, density and...
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Random field modelling of mechanical behaviour of corroded thin steel plate specimens
PublikacjaThe objective of this work is to explore the possibility of corrosion degradation modelling of thin steel plate specimens with the use of random field approach. The mechanical properties are obtained via the nonlinear Finite Element Analysis with the use of an explicit dynamic solver. The fully nonlinear material model is adopted to obtain the proper stress-strain response. Sensitivity analysis considering the main statistical...
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Instantaneous Heating and Cooling Caused by Periodic or Aperiodic Sound of Any Characteristic Duration in a Gas with Vibrational Relaxation
PublikacjaThermodynamic relaxation of internal degrees of a molecule's freedom in a gas occurs with some characteristic time. This makes wave processes in a gas behave differently depending on the ratio of characteristic duration of perturbations and the relaxation time. In particular, generation of the secondary non-wave modes by intense sound in a nonlinear flow dependens on frequency. These kinds of interaction are considered in this...
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Local buckling of thin-walled channel member flange made of aluminum alloy
PublikacjaThe 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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Asynchronous Wide Area Multilateration System
PublikacjaA new method for a location service in the wide area multilateration (WAM) system is outlined. This method, which is called asynchronous WAM (AWAM), enables calculation of the geographical position of an aircraft without knowledge of relative time differences (RTDs) between measuring ground stations (sensors). The AWAM method is based on the measurement of round trip times (RTTs) between the aircraft and the serving ground station,...
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Fluid–solid interaction on a thin platelet with high-velocity flow: vibration modelling and experiment
PublikacjaThe paper concerns the nonlinear behaviour of a thin platelet that is streamlined in an aerodynamic tunnel. The air velocity in the aerodynamic tunnel was at 858.9 km/h or 0.7 Ma (Ma—Mach number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound). This experiment was numerically simulated using FSI (fluid–solid interaction) tools, namely the coupling...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublikacjaIn this article, specific methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublikacjaIn this study, dedicated methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Rapid Design Tuning of Miniaturized Rat-Race Couplers Using Regression-Based Equivalent Network Surrogates
PublikacjaA simple technique for fast design tuning of compact rat-race couplers is presented. Our approach involves equivalent circuit representation, corrected by nonlinear functions of frequency with coefficients extracted through nonlinear regression. At the same time, the tuning process connects two levels of coupler representation: EM simulation of the entire circuit and re-optimization of the coupler building blocks (slow-wave cells...
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Synthesis of coupled lossy resonator filters.
PublikacjaA technique for fast synthesis of coupling matrix low-pass prototypes of generalized. Chebyshev bandpass filters with lossy resonators is presented in this letter. The coupling matrix is found by solving a nonlinear least squares problem based on zeros and poles of filter's transfer functions.
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Flexural behavior of composite structural insulated panels with magnesium oxide board facings
PublikacjaThe current report is devoted to the flexural analysis of a composite structural insulated panel (CSIP) with magnesium oxide board facings and expanded polystyrene (EPS) core, that was recently introduced to the building industry. An advanced nonlinear FE model was created in the ABAQUS environment, able to simulate the CSIP’s flexural behavior in great detail. An original custom code procedure was developed, which allowed to include...
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Mathematical Modelling of a Seismic Isolation System to Protect Structures During Damaging Earthquakes
PublikacjaThe present study aims to determine the effectiveness of a nonlinear mathematical model in simulating complex mechanical behaviour of a seismic isolation system to protect structures during strong and damaging earthquakes. In order to construct the Polymeric Bearings considered in this research, a specially prepared flexible polyurethane elastomer with increased damping properties has been used. The usefulness of the proposed mathematical...
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Determination of the optimal curvature of the turnout diverging track for HSR using dynamic analysis
PublikacjaThe paper presents an analytical method of identifying the curvature of the turnout diverging track consisting of sections of varying curvature. Such turnout is mainly applied on High Speed Railway. Both linear and nonlinear (polynomial) curvatures of the turnout diverging track are considered in the paper. Obtained solutions enable to assume curvature values at the beginning and end point of the geometrical layout of the turnout.The...
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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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On the theorem of Tverberg
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Borsuk-Ulam type theorems on product spaces II
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Fixed point index for $G$-equivariant multivalued maps
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Minimal number of periodic points for smooth self-maps of two-holed 3-dimensional closed ball
PublikacjaDla ciągłego odwzorowania f przestrzeni określonej w tytule w siebie, które posiada rzeczywiste wartości własne na drugiej grupie homologii, wyznaczona została minimalna liczba punktów r-periodycznych w klasie wszystkich gładkich odwzorowań homotopijnych z f.
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The Conley index and spectral sequences
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On the space of equivariant local maps
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Spectral sequences and detailed connection matrices
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
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Computer assisted method for proving existence of periodic orbits
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Regularity of weak solutions for aclass of elliptic PDEs in Orlicz-Sobolev spaces
PublikacjaWe consider the elliptic partial differential equation in the divergence form $$-\div(\nabla G(\nabla u(x))) t + F_u (x, u(x)) = 0,$$ where $G$ is a convex, anisotropic function satisfying certain growth and ellipticity conditions We prove that weak solutions in $W^{1,G}$ are in fact of class $W^{2,2}_{loc}\cap W^{1,\infty}_{loc}$.
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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublikacjaLet $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points...
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Selections and approximations of convex-valued equivariant mappings
PublikacjaUdowodniono szereg twierdzeń o współzmienniczych selekcjach i aproksymacjach ciągłych, mierzalnych i typu Caratheodory'ego dla odwzorowań G-współzmienniczych o wartościach wypukłych, gdzie G jest grupą zwartą Liego. Tw. typu Michaela, Celliny, Browdera, Kuratowskiego-Ryll-Nardzewskiego, Castaing itd.
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On homotopy Conley index for multivalued flows in Hilbert spaces
PublikacjaPodano aproksymacyjną definicję indeksu homotopijnego, otrzymując naturalne związki z podobnymi niezmiennikami. Zbadano własności tego niezmiennika i zastosowano do badania gradientowych potoków wykazując pewne geometryczne własności zbiorów niezmienniczych
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Conley index in Hilbert spaces and the Leray-Schauder degree
PublikacjaZdefiniowane są liczby Bettiego i charakterystyka Eulera LS-indeksu dla potoków generowanych przez pole zwarte w przestrzeni Hilberta. Główna teza pracy to wzór typu Poincare-Hopfa łączący wspomnianą chatrakterystykę Eulera ze stopniem Leray-Schaudera.
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
PublikacjaFor a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m 4, we provide an algorithm for estimating the values of the topological invariant D^m_r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing D^m_r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013),...
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Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator
PublikacjaWe consider a generalization of the Allen-Cahn type equation in divergence form $-\rm{div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$. This is more general than the usual Laplace operator. We prove the existence and regularity of heteroclinic solutions under standard ellipticity and $m$-growth conditions.
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Fixed point indices of iterations of planar homeomorphisms.
PublikacjaW pracy bada się postać indeksów iteracji lokalnych homeomorfizmów płaszczyzny.
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Moment resistance of I-section end-plate roof girder splices; a case study
PublikacjaThis article deals with the problem of determining the resistance of end-plate connections. A nonlinear FEM model of the joint was constructed in order to predict its carrying capacity. A standard code procedure was done as well. The analyses have been done to assess atypical end-plate joints designed and constructed as a part of roof structures.
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About definition of modes and magnetosonic heating in a plasma’s flow: Especial cases of perpendicular and nearly perpendicular wave vector and magnetic field
PublikacjaDynamics of hydrodynamic perturbations in a plasma depend strongly on an angle between the wave vector and equilibrium straight magnetic field. The case of perpendicular propagation is especial. There are only two (fast) magnetosonic modes since two (slow) ones degenerate into the stationary one with zero speed of propagation. This demands individual definition of wave modes by the links of hydrodynamic relations. These links are...
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Globalisation and world economic poverty: The significance of hidden dimensions
PublikacjaThe aim of our research is to examine how individual dimensions of globalization affect economic poverty in the World. for this, regression models are estimated with FGT0 or FGT1 poverty measures as dependent variables and KOF indices of globalization as despendent variables. The poverty indices are estimated for 119 countries' income didtributions assuming log-normality and using Gini estimates from the WID2 database and GDP/capita...
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A Model-Based Improved Control of Dissolved Oxygen Concentration in Sequencing Wastewater Batch Reactor
PublikacjaBiochemical processes at wastewater treatment plant are complex, nonlinear, time varying and multivariable. Moreover, relationships between processes are very strong. One of the most important issues is exerting proper control over dissolved oxygen levels during nitrification phase. This parameter has a very large impact on activity of microorganisms in activated sludge and on quality of pollution removal processes. Oxygen is supplied...
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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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Determination of the Theoretical and Actual Working Volume of a Hydraulic Motor—Part II (The Method Based on the Characteristics of Effective Absorbency of the Motor)
Publikacja: In this article, the second method of determination of the theoretical and actual working volume of a hydraulic motor is described. The proposed new method is based on the characteristics of effective absorbency of the motor. The effective absorbency has been defined as the ratio of flow rate in a motor to the rotational speed of the motor’s shaft. It has been shown that the effective absorbency is a nonlinear function of the...
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Methods of solving the Atkins equation determine shear angle with taking into consideration a modern fracture mechanics
PublikacjaIn the paper are presented methods of solving nonlinear Atkins equation . The Atkins equation describe shear angle with taking into account properties of material cutting. To solve Atkins equation has been used iterative methods: Newton method and simplified method of simple iteration. Method of simple iteration is presented in the form of Java application.