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FURTHER REMARKS ON THE NEO-CLASSICAL NAVIER-STOKES EQUATIONS
PublicationThe seminal Navier-Stokes equations have been stated yet before creation of principles of thermodynamics and the first and second laws. In the literature there is the common opinion that the Navier-Stokes equations cannot be taken as a thermodynamically correct model of “working fluid” which is able to describe transformation of “ heat” into “work” and vice versa. Therefore, in the paper, a new exposition of thermodynamically...
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On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution
PublicationAmong various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In...
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Bezczujnikowe sterowanie trakcyjnym silnikiem IPMSM małej mocy
PublicationThis paper describes an algorithm for estimation of IPMSM angular rotor position. The algorithm uses derivatives of motor phase currents resulting from PWM modulation to obtain the rotor position. Control of the IPMSM electromagnetic torque requires a precise estimation of the rotor angular position throughout the wide speed range. This involves using a set of estimation methods switched with the dependence on the actual rotor...
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Modal Reduction and Analysis of Gyroscopic Systems
PublicationThe paper introduces the method of the modal reduction of systems that experience the Coriolis acceleration or gyroscopic effect component. In such cases corresponding system equations are non-self-adjoined. To solve the problem modal reduced model is built up for the system without Coriolis acceleration or gyroscopic effect terms. These phenomena are included by application of any lumping technique. Hence, the final reduced model...
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Hybrid, Approximate Models of Distributed-Parameter Systems
PublicationThe paper introduces the method of distributed-parameter systems modelling. It enables to obtain low order modal model of the system that experiences Coriolis acceleration component and gyroscopic effect. In such cases, corresponding system equations are non-self-adjoined. To solve this problem modal reduced model is built up for the system without Coriolis acceleration or gyroscopic effect terms. These phenomena are next included...
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Modal Adjustment of Rayleigh Based Structural Damping and Coordinate-Partitioning Algorithm Dedicated to Frictionless Contact Constraints between Multibody System and Structure Modelled with Finite Elements
PublicationThe paper presents a dedicated numerical algorithm. The algorithm is advantageous during investigations of the dynamics of a hybrid multibody / finite-elements system. We focus our attention on interactions resulting from mechanical contact. Pointwise contact connects a vertex of the multibody structure and a surface of the elastic reference body. Instead of a positive value of the relative penetration factor, constraint equations...
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Viscous versus electromagnetic damping – amplification in a neighbourhood of a mechanism singular position
PublicationIn the paper, damping of vibrations are considered and compared in a mechanical and in a electromechanical system. In the system, a continuous beam is considered as the main vibrating element. The compared dissipations methods are based on: viscous dampers and DC generators. To increase the possible damping effectiveness, velocity amplification is proposed, i.e., a mechanism is introduced between the beam and the damping element....
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The application of nonlinear curvature sections in the turnout diverging track
PublicationThe paper presents the analytical method of modelling the diverging track of railway turnout with nonlinear curvature sections. These sections were used for smoothing the graph of curvature in the extreme areas of turnout. The problem of the curvature distribution was identified with the use of differential equations. The resulting solutions are of universal nature for example the ability of assuming any values of curvature at...
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2D inverse method of turbomachinery stage design
Publication1. How 2D model for turbomachinery stages has developed historically. 2. Recent understanding of physical background of 2D model. 3. Curvilinear system of non-orthogonal coordinates in the application to 2D model. 4. Set of basic equations. 5. Closing conditions for the inverse problem. 6. Examples of solutions a)
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Modern control strategy of bidirectional DAB converter with consideration of control nonlinearity
PublicationThis paper focuses on the control strategy for modern universal bidirectional Dual Active Bridge (DAB) converters for microgrid systems. An analysis of the converter equations was carried out, and typical problems related to the influence of dead time on the system operation were discussed. A closed control loop was developed, then tested by simulation and on a laboratory stand.
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Forced Vibrations in a Dynamic System That Is Damped By a Mechanism Which Trans-Pass Through Its Singular Position
PublicationThe paper focuses on forced vibrations of a mechanical system. The system is composed of two structurally different parts: multibody modelled and finite elements modelled. To improve its numerical behaviour, author-proposed technique of tuning of modal properties is proposed. To combine the two sub-models, constraint equations are introduced and dynamics equations are extended with appropriate Lagrange multipliers. A slightly modified...
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Time-Domain Description of Point-Source Acoustic Wavefields as a Useful Approach in Ultrasonic Techniques
PublicationIn traditional acoustics, field problems are usually treated in the frequency domain, broadband fields being reduced to superposition of harmonic spectrum components. However, this approach is inherently acausal and it is known that in case of arbitrary signals, the distribution-based, time-domain description can be more effective. The present paper is an attempt to expand the time-domain linear systems formalism onto space problems...
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Time-domain description of point-source acoustic wavefields as a useful approach in ultrasonic techniques
PublicationIn traditional acoustics, field problems are usually treated in the frequency domain, broadband fields being reduced to superposition of harmonic spectrum components. However, this approach is inherently acausal and it is known that in case of arbitrary signals, the distribution-based, time-domain description can be more effective. The present paper is an attempt to expand the time-domain linear systems formalism onto space problems...
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Stability analysis of nanobeams in hygrothermal environment based on a nonlocal strain gradient Timoshenko beam model under nonlinear thermal field
PublicationThis article is dedicated to analyzing the buckling behavior of nanobeam subjected to hygrothermal environments based on the principle of the Timoshenko beam theory. The hygroscopic environment has been considered as a linear stress field model, while the thermal environment is assumed to be a nonlinear stress field based on the Murnaghan model. The size-dependent effect of the nanobeam is captured by the nonlocal strain gradient...
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Symbolic multibody models for digital-twin applications
PublicationSymbolic generation of multibody systems equations of motion appeared in the 1980s. In addition to their computational advantage over their numerical counterparts, symbolic models can be very easily and straightforwardly interfaced with a wide range of software environments and hardware devices. These two features place this approach in a pole position to participate and intervene in the design of digital twins for systems such...
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Predicting Value of Binding Constants of Organic Ligands to Beta-Cyclodextrin: Application of MARSplines and Descriptors Encoded in SMILES String
PublicationThe quantitative structure–activity relationship (QSPR) model was formulated to quantify values of the binding constant (lnK) of a series of ligands to beta–cyclodextrin (β-CD). For this purpose, the multivariate adaptive regression splines (MARSplines) methodology was adopted with molecular descriptors derived from the simplified molecular input line entry specification (SMILES) strings. This approach allows discovery of regression...
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Proportional-Derivative and Model-based Controllers used for a Serial Type Manipulator in case of a Variable Mass Payload
PublicationIn the paper, numerical analysis of dynamics of a variable mass system is considered. Its reference example is a serial-like manipulator composed of revolute joints and rigid bodies. Payload of its gripper is considered as its variable mass element (mass and inertia irregularly between subsequent payloads). For the rest of the system, inertia parameters are considered as known (precisely identified during the assembling process)....
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Magnetoacoustic heating in a quasi-isentropic magnetic gas
PublicationThe nonlinear heating of a plasma which associates with the transfer of energy of magnetoacoustic waves into that of the entropy mode, is analytically studied. A plasma is uniform and motionless at equilibrium. Perturbations in a plasma are described by a system of ideal magnetohydrodynamic equations. The equilibrium straight magnetic strength and the wave vector form a constant angle which varies from 0 to π/2. There exist four...
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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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Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations
PublicationThe light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo (MC) algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present implementation...
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Justyna Signerska-Rynkowska dr inż.
PeopleI am currently an assistant professor (adjunct) at Gdansk University of Technology (Department of Differential Equations and Mathematics Applications). My scientific interests include dynamical systems theory, chaos theory and their applications to modeling of biological phenomena, especially to neurosciences. In June 2013 I completed PhD in Mathematics at the Institute of Mathematics of Polish Academy of Sciences (IMPAN) (thesis...
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Determination of the refractive index and wavelength‐dependent optical properties of few‐layer CrCl3 within the Fresnel formalism
PublicationBased on previous reports on the optical microscopy contrast of mechanically exfoliated few layer CrCl3 transferred on 285 nmand 270 nmSiO2 on Si(100), we focus on the experimental determination of an effective mean complex refractive index via a fitting analysis based on the Fresnel equations formalism. Accordingly, the layer and wavelength-dependent absorbance and reflectance are calculated. Layer and wavelength-dependent optical...
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Testing Stability of Digital Filters Using Multimodal Particle Swarm Optimization with Phase Analysis
PublicationIn this paper, a novel meta-heuristic method for evaluation of digital filter stability is presented. The proposed method is very general because it allows one to evaluate stability of systems whose characteristic equations are not based on polynomials. The method combines an efficient evolutionary algorithm represented by the particle swarm optimization and the phase analysis of a complex function in the characteristic equation....
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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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Features of Nonlinear Sound Propagation in Vibrationally Excited Gases
PublicationWeakly nonlinear sound propagation in a gas where molecular vibrational relaxation takes place is studied. New equations which govern the sound in media where the irreversible relaxation may take place are derived and discussed. Their form depends on the regime of excitation of oscillatory degrees of freedom, equilibrium (reversible) or non-equilibrium (irreversible), and on the comparative frequency of the sound in relation to...
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Nonlinear phenomena of small-scale sound in a gas with exponential stratification
PublicationThe 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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Complex Variables and Elliptic Equations
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Neoclassical Navier–Stokes Equations Considering the Gyftopoulos–Beretta Exposition of Thermodynamics
PublicationThe seminal Navier-Stokes equations were stated even before the creation of the foundations of thermodynamics and its first and second laws. There is a widespread opinion in the literature on thermodynamic cycles that the Navier-Stokes equations cannot be taken as a thermodynamically correct model of a local "working fluid", which would be able to describe the conversion of "heating" into "working" (Carnot's type cycles) and vice...
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THE PROBLEM OF AIRFLOW AROUND BUILDINGS CLUSTERS IN DIFFERENT CONFIGURATIONS
PublicationIn the paper, the authors discuss the construction of a model of an exemplary urban layout. Numerical simulation has been performed by means of a commercial software Fluent using two different turbulence models: the popular k-ε realizable one, and the Reynolds Stress Model (RSM), which is still being developed. The former is a 2-equations model, while the latter – is a RSM model – that consists of 7 equations. The studies have...
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Design of compound curves adapted to the satellite measurements
PublicationThe paper deals with a novelty related to the design of a region for an alternative railway track direction adequate for mobile satellite measurements. The new approach may become particularly useful in the design of the existing track axis control when the determination of both the main track directions becomes impossible. The only solution in that case is to apply to the geometrical system two circular arcs of a different radius,...
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Usefulness of the voltamperometric method for assessment of the purity of soil
PublicationThis paper presents a voltammetric analysis of soil. It shows that the voltammetry is a useful method for the assessment of soil contaminated with heavy metal ions. There are two major problems with voltammetry analysis: the diffusion coefficient and the measurement system. The paper contains a short literature study of mathematical equations and a study of differences between soil and water measurements. Suggestions of the solution...
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Modal modification of structural damping applied to increase the stability and convergence of numerical integration
PublicationThe presented paper refers to numerical tests done on systems fused of multibody and finite-element parts. The appearance of its multibody part gives rise to significant nonlinear components, i.e., second-order nonlinear differential equations express the dynamics. We usually solve these equations by “step-by-step” integration methods. When using the currently available integration algorithms, we approximate these initial systems...
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Ultrashort Opposite Directed Pulses Dynamics with Kerr Effect and Polarization Account
PublicationWe present the application of projection operator methods to solving the problem of the propagation and interaction of short optical pulses of different polarizations and directions in a nonlinear dispersive medium. We restrict ourselves by the caseof one-dimensional theory, taking into account material dispersion and Kerr nonlinearity. The construction of operators is delivered in two variants: for the Cauchy problem and for the...
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Exact resultant equilibrium conditions in the non-linear theory of branching and self-intersecting shells
PublicationWe formulate the exact, resultant equilibrium conditions for the non-linear theory of branching and self-intersecting shells. The conditions are derived by performing direct through-the-thickness integration in the global equilibrium conditions of continuum mechanics. At each regular internal and boundary point of the base surface our exact, local equilibrium equations and dynamic boundary conditions are equivalent, as expected,...
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Novel Interpolation Method of Multi-DFT-Bins for Frequency Estimation of Signal with Parameter Step Change
PublicationThe IpDFT(Interpolation Discrete Fourier Trans-form) method is one of the most commonly used non-parametric methods. However, when a parameter (frequency, amplitude or phase) step changes in the DFT period, the DFT coefficients will be distorted seriously, resulting in the large estimation error of the IpDFT method. Hence, it is a key challenge to find an IpDFT method, which not only can eliminate the effect of the step-changed...
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Nonlinear free and forced vibrations of a dielectric elastomer-based microcantilever for atomic force microscopy
PublicationThe majority of atomic force microcode (AFM) probes work based on piezoelectric actuation. However, some undesirable phenomena such as creep and hysteresis may appear in the piezoelectric actuators that limit their applications. This paper proposes a novel AFM probe based on dielectric elastomer actuators (DEAs). The DE is modeled via the use of a hyperelastic Cosserat model. Size effects and geometric nonlinearity are included...
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Deformation of an elastic second gradient spherical body under equatorial line density of dead forces
PublicationWe consider deformations of an elastic body having initially a spherical shape. Assumed deformation energy depends on the first and second gradient of displacements. We apply an equatorial line density of dead loads, that are forces per unit line length directed in radial direction and applied along the equator of the sphere. We restrict ourselves our analysis to the case of linearized second strain gradient isotropic elasticity...
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A new hyperbolic-polynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition
PublicationA drawback to the material composition of thick functionally graded materials (FGM) beams is checked out in this research in conjunction with a novel hyperbolic‐polynomial higher‐order elasticity beam theory (HPET). The proposed beam model consists of a novel shape function for the distribution of shear stress deformation in the transverse coordinate. The beam theory also incorporates the stretching effect to present an indirect...
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An Efficient PEEC-Based Method for Full-Wave Analysis of Microstrip Structures
PublicationThis article introduces an efficient method for the equivalent circuit characterization and full-wave analysis of microstrip structures, leveraging the full-wave partial element equivalent circuit (PEEC). In particular, the multilayered Green's function is evaluated using the discrete complex-image method (DCIM) and employed to establish the mixed potential integral equations. The proposed strategy considers time delays for the...
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Proportional-Derivative and Model-Based Controllers for Control of a Variable Mass Manipulator
PublicationIn the paper, numerical analysis of dynamics of a variable mass manipulator is presented. A revolute joints composed manipulator is considered. Payload of the gripper is considered as the only element characterized by unknown value of its mass (variable between subsequent operations). As in other cases of the revolute joints composed manipulators, its behaviour dependents significantly on the pose of the manipulator. When the manipulator...
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A graphical approach to yield and boundary surfaces of selected hypoplastic constitutive equations
PublicationThe 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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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublicationThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublicationThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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Computationally Effcient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems
PublicationThis paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed...
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Analytical design method of reverse curves
PublicationThe paper deals with a new approach relating to the design of the region of railway track direction alteration adapted to Mobile Satellite Measurements technique. The method may be particularly useful in situations when both the straights of the route directions cannot be connected in an elementary way using a circular arc with transition curves; this also refers to the application of a compound curve. Thus the only solution becomes...
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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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Optimization of Data Assignment for Parallel Processing in a Hybrid Heterogeneous Environment Using Integer Linear Programming
PublicationIn the paper we investigate a practical approach to application of integer linear programming for optimization of data assignment to compute units in a multi-level heterogeneous environment with various compute devices, including CPUs, GPUs and Intel Xeon Phis. The model considers an application that processes a large number of data chunks in parallel on various compute units and takes into account computations, communication including...
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Nonreciprocal cavities and the time-bandwidth limit: comment
PublicationIn their paper in Optica 6, 104 (2019), Mann et al. claim that linear, time-invariant nonreciprocal structures cannot overcome the time-bandwidth limit and do not exhibit an advantage over their reciprocal counterparts, specifically with regard to their time-bandwidth performance. In this Comment, we argue that these conclusions are unfounded. On the basis of both rigorous full-wave simulations and insightful physical justifications,...
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Precise Point Positioning Method Based on Wide-lane and Narrow-lane Phase Observations and Between Satellites Single Differencing
PublicationThe issue of using PPP method in position determination was formed in 1997. In most developed methods, ionospheric-free linear combination is used in order to eliminate the impact of the ionospheric delay. However, this approach does not provide the directly determination of the total value of the ambiguities, and the ambiguities for the individual signals. Therefore, in many publications methods of avoiding these deficiencies...
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Asynchronous WAM with Irregular Pulse Repetition
PublicationRadiolocation systems for aviation based on Multi-Lateration (MLAT) typically use a set of synchronised ground sensors to receive radio signals broadcast by onboard transmitters. In most cases, the sensor synchronisation in Wide Area Multi-Lateration Systems (WAM) is provided by Global Navigation Satellite System (GNSS) receivers. However, in the case of synchronisation failure, there is still a possibility to estimate the coordinates...