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Search results for: COMPLEX LINEAR SYSTEM OF EQUATIONS
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The nonlinear effects of sound in a liquid with relaxation losses
PublicationThe nonlinear effects of sound in electrolyte with a chemical reaction are examined. The dynamic equations that govern non-wave modes in the field of intense sound are derived, and acoustic forces of vortex, entropy, and relaxation modes are determined in the cases of low-frequency sound and high-frequency sound. The difference in the nonlinear effects of sound in electrolyte and in a gas with excited vibrational degrees of molecules,...
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Monotone iterative method for first-order differential equations at resonance
PublicationThis 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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MAGNETOACOUSTIC HEATING AND STREAMING IN A PLASMA WITH FINITE ELECTRICAL CONDUCTIVITY
PublicationNonlinear effects of planar and quasi-planar magnetosound perturbations are discussed. Plasma is assumed to be an ideal gas with a finite electrical conductivity permeated by a magnetic filed orthogonal to the trajectories of gas particles. the excitation of non-wave modes in the filed of intense magnetoacoustic perturbations, i.e., magnetoaciustic heating and streaming, is discussed. The analysis includes a derivation if instantaneous...
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Functional delay fractional equations
PublicationIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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Reduced order models in computational electromagnetics (in memory of Ruediger Vahldieck)
PublicationThis paper reviews research of Ruediger Vahldieck's group and the group at the Gdansk University of Technology in the area of model order reduction techniques for accelerating full-wave simulations. The applications of reduced order models to filter design as well as of local and nested(multilevel) macromodels for solving 3D wave equations and wave-guiding problems using finite difference and finite element methods are discussed.
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Positive solutions to Sturm–Liouville problems with non-local boundary conditions
PublicationIn this paper, the existence of at least three non-negative solutions to non-local boundary-value problems for second-order differential equations with deviating arguments α and ζ is investigated. Sufficient conditions, which guarantee the existence of positive solutions, are obtained using the Avery–Peterson theorem. We discuss our problem for both advanced and delayed arguments. An example is added to illustrate the results.
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Control of mass concentration of reagents by sound in a gas with nonequilibrium chemical reactions
PublicationThe weakly nonlinear dynamics of a chemically reacting gas is studied. Nonlinear interaction of acoustic and nonacoustic types of motion are considered. We decompose the base equations using the relationships of the gas-dynamic perturbations specific for every type of motion. The governing equation for the mass fraction of a reagent influenced by dominating sound is derived and discussed. The conclusions concern the equilibrium...
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Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory
PublicationIn this paper, the damped forced vibration of single-walled carbon nanotubes (SWCNTs) is analyzed using a new shear deformation beam theory. The SWCNTs are modeled as a flexible beam on the viscoelastic foundation embedded in the thermal environment and subjected to a transverse dynamic load. The equilibrium equations are formulated by the new shear deformation beam theory which is accompanied with higher-order nonlocal strain...
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A Novel Approach to Fully Nonlinear Mathematical Modeling of Tectonic Plates
PublicationThe motion of the Earth's layers due to internal pressures is simulated in this research with an efficient mathematical model. The Earth, which revolves around its axis of rotation and is under internal pressure, will change the shape and displacement of the internal layers and tectonic plates. Applied mathematical models are based on a new approach to shell theory involving both two and three-dimensional approaches. It is the...
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On a flexomagnetic behavior of composite structures
PublicationThe popularity of the studies is getting further on the flexomagnetic (FM) response of nano-electro-magneto machines. In spite of this, there are a few incompatibilities with the available FM model. This study indicates that the accessible FM model is inappropriate when considering the converse magnetization effect that demonstrates the necessity and importance of deriving a new FM relation. Additionally, the literature has neglected...
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Monotone iterative method to second order differential equations with deviating arguments involving Stieltjes integral boundary conditions
PublicationWe 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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Some fundamental aspects of self-levitating sliding contact bearings and their practical implementations
PublicationIn this study, fundamental aspects and mechanisms of acoustic levitation together with governing equations are presented first. Then, the acoustic levitation phenomenon is considered as a new way to design air suspension systems capable of self-levitation. A particular emphasis is laid on journal bearings and their specific geometrical configuration. A practical feasibility of using acoustic levitation to separate contacting surfaces...
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Elastoplastic material law in 6-parameter nonlinear shell theory
PublicationWe develop the elastoplastic constitutive relations for nonlinear exact 6-parameter shell theory. A J2-type theory with strain hardening is formulated that takes into account asymmetric membrane strain measures. The incremental equations are solved using implicit Euler scheme with closest point projection algorithm. The presented test example shows the correctness of the proposed approach. Influence of micropolar material parameters...
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Postquarter-Point Case of Ship’s Side-Berthing and Its Influence on Marine Fender Pitch
PublicationThis paper presents a critical analysis of some selected codes and practical recommendations used as basic rules in the design procedures of modern marine fender systems. The first part of the discussion pertains to the existing equations used in calculating the eccentricity coefficient in the ship’s kinetic energy equation and the maximum allowable fender pitch (spacing) in a set of fenders installed along a quay wall. A new approach...
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Service time distribution influence on end-to-end call setup delay calculation in networks with Session Initiation Protocol
PublicationThe most important GoS parameter for networks with SIP protocol is end-to-end call setup delay. So far there were no coherent models allowing calculation of these parameters for networks with SIP protocol. Few models were developed but they are insufficient. In the paper we propose model which allows end-to-end call setup delay calculation for networks with SIP protocol. The model is using chain of M/G/1/K models and is applicable...
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Study of Slip Effects in Reverse Roll Coating Process Using Non-Isothermal Couple Stress Fluid
PublicationThe non-isothermal couple stress fluid inside a reverse roll coating geometry is considered. The slip condition is considered at the surfaces of the rolls. To develop the flow equations, the mathematical modelling is performed using conservation of momentum, mass, and energy. The LAT (lubrication approximation theory) is employed to simplify the equations. The closed form solution for velocity, temperature, and pressure gradient...
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Design and simulation of a new prototype of piezoelectric cantilever sensor/actuator for analysis of the soft tissues properties
PublicationThis paper is devoted to a new prototype of piezoelectric cantilever transducer dedicated for the characterization of the mechanical properties of soft tissues. General description of the actuator’s structure is presented including the basic principles of the measurement. The chosen geometry of the prototype is discussed and compared with the existing one. Constitutive equations are presented for the active and passive layer of...
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A new prototype of piezoelectric bending resonant transducer for analysis of soft tissues properties
PublicationThis paper is devoted to a new piezoelectric bending resonant transducer prototype dedicated to the characterization of the mechanical properties of soft tissue. A general description of the actuator’s structure is presented including the basic principles of the measurement. The chosen geometry of the prototype is discussed and compared with the existing version. Constitutive equations are presented for the active and passive layer...
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On Von Karman Equations and the Buckling of a Thin Circular Elastic Plate
PublicationWe 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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Enhanced trap-assisted recombination in organic semiconductors
PublicationAn analytical model to describe the interaction of excitons and charge transfer states with deep traps is formulated for the case of molecular materials. Here, we have considered the influence of a trap-assisted recombination on this phenomenon. The final expression for the effective recombination rate has been derived from the Shockley–Read–Hall theory and kinetic equations which characterize different photophysical processes....
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State Observer for Doubly-fed Induction Generator
PublicationIn the paper a new state observer for doubly-fed generator has been proposed. In the new approach an extended mathematical model of the doubly fed generator is used to form equations of the introduced z type observer. Stability of the observer has been verified through poles placement analyses. The active and reactive powers of the generator are controlled by a nonlinear multiscalar control method. Simulation and experimental results...
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Simulation of influence of the air gap asymmetryon voltage waveforms of a synchronous machine
PublicationResults of simulation of a synchronous generator with the air gap asymmetry characterised by eccentricity are presented in the paper. The Lagrange's energy method has been used in derivation of the model equations. Analysis of influence of the air gap asymmetry on characteristics of self and mutual inductances of windings, as well as analysis of induced voltage waveforms as a function of the air gap asymmetry have been performed....
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Design of Microstrip UWB Balun Using Quasi-TEM Approach Aided by the Artificial Neural Network
PublicationThe design procedure for UWB balun realized in the microstrip technology is proposed in the paper. The procedure applies Artificial Neural Network which corrects the dimensions of the approximate design found by appropriate scaling of the dimensions of the prototype. The scale coefficients for longitudinal and transverse dimensions of microstrip lines are determined from electromagnetic modeling based on transmission line equations....
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<title>Cavity digital control testing system by Simulink step operation method for TESLA linear accelerator and free electron laser</title>
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Dynamic Modeling of COVID-19 Disease with Impact of Lockdown in Pakistan and Malaysia
PublicationBeing researchers, it is an utmost responsibility to provide insight on social issues thus, this work addresses the dynamic modeling of first and most contagious disease named as COVID-19 caused by coronavirus. The first case of COVID-19 appeared in Pakistan was on 26th February 2020 and in Malaysia on 27th February 2020; both patients had foreign travel history. In the paper, the number of total affected cases and total deaths...
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Assessment of codes recommendations for the evaluation of the seismic gap of buildings founded on different soil types
PublicationSeveral equations have been proposed in the literature to evaluate the seismic gap preventing earthquake-induced structural pounding, such as the ones based on the absolute sum of the peak displacements (ABS), the square root of the sum of the squares (SRSS), the double difference method (DDC), Australian code and the approach proposed by Naderpour et al. The aim of this paper is to investigate the accuracy of these equations taking...
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A chemo-mechano-thermodynamical contact theory for adhesion, friction, and (de)bonding reactions
PublicationThis work presents a self-contained continuum formulation for coupled chemical, mechanical, and thermal contact interactions. The formulation is very general and, hence, admits arbitrary geometry, deformation, and material behavior. All model equations are derived rigorously from the balance laws of mass, momentum, energy, and entropy in the framework of irreversible thermodynamics, thus exposing all the coupling present in the...
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Mechanical simulation of artificial gravity in torus-shaped and cylindrical spacecraft
PublicationLarge deformations and stress analyses in two types of space structures that are intended for people to live in space have been studied in this research. The structure under analysis is assumed to rotate around the central axis to create artificial gravitational acceleration equal to the gravity on the Earth's surface. The analysis is fully dynamic, which is formulated based on the energy method by using the first-order shear deformation...
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On Dynamic Boundary Conditions Within the Linear Steigmann-Ogden Model of Surface Elasticity and Strain Gradient Elasticity
PublicationWithin the strain gradient elasticity we discuss the dynamic boundary conditions taking into account surface stresses described by the Steigmann–Ogden model. The variational approach is applied with the use of the least action functional. The functional is represented as a sum of surface and volume integrals. The surface strain and kinetic energy densities are introduced. The Toupin–Mindlin formulation of the strain gradient elasticity...
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On the correspondence between two- and three-dimensional Eshelby tensors
PublicationWe consider both three-dimensional (3D) and two-dimensional (2D) Eshelby tensors known also as energy–momentum tensors or chemical potential tensors, which are introduced within the nonlinear elasticity and the resultant nonlinear shell theory, respectively. We demonstrate that 2D Eshelby tensor is introduced earlier directly using 2D constitutive equations of nonlinear shells and can be derived also using the throughthe-thickness...
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New Approach to Arc Fitting for Railway Track Realignment
PublicationThis article presents a new method of arc fitting for railway track realignment. The theoretical foundations are presented, along with a detailed algorithm of the iterative computational process. This method is based on solving a set of linearized pseudo-observation equations. The formulas of the functional model of the fitting problem were derived, and a special form of objective function is proposed. An iterative method for optimization...
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On dynamics of origami-inspired rod
PublicationWe discuss the dynamics of a relatively simple origami-inspired structure considering discrete and continuum models. The latter was derived as a certain limit of the discrete model. Here we analyze small in-plane deformations and related equations of infinitesimal motions. For both models, dispersion relations were derived and compared. The comparison of the dispersion relations showed that the continuum model can capture the behavior...
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Designing acoustic scattering elements using machine learning methods
PublicationIn the process of the design and correction of room acoustic properties, it is often necessary to select the appropriate type of acoustic treatment devices and make decisions regarding their size, geometry, and location of the devices inside the room under the treatment process. The goal of this doctoral dissertation is to develop and validate a mathematical model that allows predicting the effects of the application of the scattering...
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Multi-headed chimera states in coupled pendula
PublicationWe discuss the occurrence of the chimera states in the network of coupled, excited by the clock’s mechanisms pendula. We find the patterns of multi-headed chimera states in which pendula clustered in different heads behave differently (oscillate with different frequencies) and create different types of synchronous states (complete or phase synchronization). The mathematical model of the network shows that the observed chimera states...
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Non-Wave Variations in Temperature Caused by Sound in a Chemically Reacting Gas
PublicationA weakly nonlinear generation of non-acoustic modes in the field of sound in a gas is considered. An exotericchemical reaction of A->B type, which takes place in a gas, may be reversible or not. Two types of sound areconsidered, low-frequency and high-frequency as compared with the characteristic time of a chemical reaction.For both these cases, the governing equations of non-acoustic modes are derived and conclusions of the efficiencyof...
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Research on the wear evenness of the tool in flat lapping
PublicationIn this paper, the dimensionless distribution of the material removal stock and the trajectories of abrasive grains cutting in single-sided lapping process are presented. They were numerically simulated based on the tribological model and kinematics equations. It can be observed that the trajectories geometry of single abrasive as well the velocities have a great influence on the final geometrical deviation. During machining, the...
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Strong ellipticity conditions and infinitesimal stability within nonlinear strain gradient elasticity
PublicationWe discuss connections between the strong ellipticity condition and the infinitesimal instability within the nonlinear strain gradient elasticity. The strong ellipticity (SE) condition describes the property of equations of statics whereas the infinitesimal stability is introduced as the positive definiteness of the second variation of an energy functional. Here we establish few implications which simplify the further analysis...
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Urban flash flood hazard identification and assessment applying geospatial techniques and hydrodynamic modeling; Erbil city case study, Kurdistan Region of Iraq
PublicationThis dissertation aims to investigate the factors behind flash flooding in Erbil's central district, located in the Kurdistan Region of Iraq, and develop a methodology for assessing flood hazards in the city, despite limited data accessibility. In this thesis, each factor was investigated, including analyzing extreme precipitation events in the last two decades, including their spatial and temporal distribution of rainfall, intensity,...
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Natural convective heat transfer from isothermalconic
PublicationTheoretical considerations on convective heat transfer from isothermal upward conicalsurfaces have been presented. The physical model of this phenomenon consists of an isothermalcone of inclination angle (φ) between the cone generating line (X) and the radius (R) of the cone base. The angle is a parameter of conical surface which varied from (φ = 0−circular horizontal plate) to (φ = π/2—vertical cylinder) . Onthe basis of Navier–Stokes...
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On analysis of nanocomposite conical structures
PublicationThis research examines the analysis of rotating truncated conical baskets reinforced by carbon nanotubes around the two independent axes. A time-dependent analysis is considered, and the nonlinear dynamic governing equations are extracted using the energy method. Carbon nanotubes (CNTs) reinforced the conical basket, and the structure's mechanical properties are determined based on the several distributions of carbon nanotubes....
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Explicit and implicit difefrence methods for quasilinear first order partial functional differential equations.
PublicationInitial 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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Multiple Solutions to Third-Order Differential Equations with Derivative Dependence and Deviating Arguments
PublicationIn 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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Wideband Macromodels in Finite Element Method
PublicationThis letter proposes a novel projection technique for accelerating Finite Element Method simulations. The algorithm is based on the Second-order Arnoldi Method for Passive Order Reduction (SAPOR). It involves generation of two projection bases and thanks to this it is applicable to the systems of equations, which contain the quadratic frequency-dependence in the input term, that arise when projection is applied locally in the selected...
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Homoclinic and Heteroclinic Orbits for a Class of Singular Planar Newtonian Systems
PublicationThe study of existence and multiplicity of solutions of differential equations possessing a variational nature is a problem of great meaning since most of them derives from mechanics and physics. In particular, this relates to Hamiltonian systems including Newtonian ones. During the past thirty years there has been a great deal of progress in the use of variational methods to find periodic, homoclinic and heteroclinic solutions...
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On Applications of Fractional Derivatives in Circuit Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling are formulated. Potential problems related to the generalization of transmission line equations with the use of FO derivatives are presented. It is demonstrated that some of formulations of the FO derivatives have limited...
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Influence of temperature and anion type on thermophysical properties of aqueous solutions of morpholine based amino acid ionic liquids
PublicationDensities and sound velocities of aqueous solutions of N-butyl-N-methylmorpholine based amino acid ionic liquids (AAILs), including N-acetyl-L-alanine, N-acetyl-Lvalinate, N-acetyl-L-leucinate, and N-acetyl-L-izoleucinate anions were measured at a temperature from 293.15 to 313.15 K at 5 K intervals and atmospheric pressure. These data were used to calculate the apparent molar volumes and the apparent molar compressibilities in...
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A quasi-2D small-signal MOSFET model - main results
PublicationDynamic 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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TIME- AND FREQUENCY-DOMAIN QUASI-2D SMALL-SIGNAL MOSFET MODELS
PublicationA novel approach to small-signal MOSFET modeling is presented in this book. As a result, time- and frequency-domain physics-based quasi-2D NQS four-terminal small-signal MOSFET models are proposed. The time-domain model provides the background to a novel DIBL-included quasi‑2D NQS four-terminal frequency-domain small-signal MOSFET model. Parameters and electrical quantities of the frequency-domain model are described by explicit...
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Design criterion for hydrodynamic vortex separators
PublicationTechnical objects designing involves determination of geometrical parameters that characterize a given object. When the device is described by the differential equations, an inverse problem brings difficulties, as geometrical values sought condition the solution to the problem. Vortex separators can be designed by the "criterion method'. Firstly, a critical particle is distinguished such that bigger particles are removed from...
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On the Nonlinea Distortions of Sound and its Coupling with Other Modes in a Gasesous Plasma with Finite Electric Conductivity in a Magnetic Field
PublicationNonlinear phenomena of the planar and quasi-planar magnetoacoustic waves are considered. We focus on deriving of equations which govern nonlinear excitation of the non-wave motions by the intense sound in initially static gaseous plasma. The plasma is treated as an ideal gas with finite electrical conductivity permeated by a magnetic field orthogonal to the trajectories of gas particles. This introduces dispersion of a flow. Magnetoacoustic...