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Search results for: approximation algorithm
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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Theory of valence-band and core-level photoemission from plutonium dioxide
PublicationThe correlated-band theory implemented as a combination of the local-density approximation with the dynamical mean-field theory is applied to PuO2. An insulating electronic structure, consistent with the experimental valence-band photoemission spectra, is obtained. The calculations yield a nonmagnetic ground state that is characterized by a noninteger filling of the plutonium 5f shell. The noninteger filling as well as the satellites...
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Residue-Pole Methods for Variability Analysis of S-parameters of Microwave Devices with 3D FEM and Mesh Deformation
PublicationThis paper presents a new approach for variability analysis of microwave devices with a high dimension of uncertain parameters. The proposed technique is based on modeling an approximation of system by its poles and residues using several modeling methods, including ordinary kriging, Adaptive Polynomial Chaos (APCE), and Support Vector Machine Regression (SVM). The computational cost is compared with the traditional Monte-Carlo...
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Fast Basis Function Estimators for Identification of Nonstationary Stochastic Processes
PublicationThe problem of identification of a linear nonsta-tionary stochastic process is considered and solved using theapproach based on functional series approximation of time-varying parameter trajectories. The proposed fast basis func-tion estimators are computationally attractive and yield resultsthat are better than those provided by the local least squaresalgorithms. It is shown that two...
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FIR Filter Design Using Distributed Maximal Flatness Method
PublicationIn the paper a novel method for filter design based on the distributed maximal flatness method is presented. The proposed approach is based on the method used to design the most common FIR fractional delay filter - the maximally flat filter. The MF filter demonstrates excellent performance but only in a relatively narrow frequency range around zero frequency but its magnitude response is no greater than one. This ,,passiveness”...
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Trust Dynamics Analysis of CTR Scheme Subversion under Virtual Anonymity and Trust-Unaware Partner Selection
PublicationWe propose a framework to study Markovian trust value dynamics in a centralized Computational Trust and Reputation (CTR) scheme under trust-unaware partner selection using a mean-value approximation. Analytically founded answers are sought to questions like: Can dishonest agents subvert the CTR scheme (i.e., acquire higher trust values than honest agents)? Is indirect reciprocity incentivized? Is there a qualitative impact of a...
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On refined constitutive equations in the six-field theory of elastic shells
PublicationWithin the resultant six-field shell theory, the second approximation to the complementary energy density of an isotropic elastic shell undergoing small strains is constructed. In this case, the resultant drilling couples are expressed explicitly by the stress resultants and stress couples as well as by amplitudes of the quadratic and cubic distributions of an intrinsic deviation vector. The refined 2D strain-stress and stress-strain...
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A Method for Optimising the Blade Profile in Kaplan Turbine
PublicationThis paper introduces a method of blade profile optimisation for Kaplan-type turbines, based on modelling the interaction between rotor and stator blades. Rotor and stator blade geometry is described mathematically by means of a midline curve and thickness distribution. Genetic algorithms are then used to find a global optimum that minimises the loss coefficient. This allows for variety of possible blade shapes and configurations....
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Contextualizing a Knowledge Base by Approximation – A Case Study
PublicationModular knowledge bases give their users opportunity to store and access knowledge at different levels of generality. In this paper we present how to organize a modular knowledge bases organized into contexts in which a user can express their knowledge in much simplified way, yet without losing its precision. The work is centered around the notion of approximation - i.e. reducing the arity of predicates used. The presentation is...
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Response features for fast EM-driven design of miniaturized impedance matching transformers
PublicationA framework for low-cost EM-driven design optimization of compact impedance matching transformers is presented. Our technique is based on a bottom-up design where design requirements for the transformer circuit are translated into specifications for its building blocks. These elementary cells are optimized using response features. Subsequently, the entire circuit is fine-tuned using local response surface approximation models and...
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A Simulative Comparison of Ship Domains and Their Polygonal Approximations
PublicationThe paper investigates the impact of a precise ship domain shape on the size of collision avoidance manoeuvres. The considered collision avoidance manoeuvres include both course and speed alterations. Various ship domains are compared with their polygonal approximations, which vary in the number of points of a domain contour and placement of these points. The best of all considered approximations is determined in the course of...
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Errors of a Linear Current Approximation in High-Speed PMSM Drives
PublicationCurrent sampling techniques and predictive algorithms used in the digital control of electric drives rely on a simple mathematical model that assumes linear current changes upon constant supplying voltages. This paper identifies rotor movement as a factor that makes this assumption invalid when the rotor covers an angular distance of a few tens of degrees during the control interval duration. The errors of the linear current approximation...
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Elastic scattering of electrons from chloroform
PublicationWe present experimental and theoretical cross sections for elastic electron scattering from CHCl3. This is an important target because of its relevance to environmental chemistry and the plasma etching industry as a source of chlorine radicals. The experimental results were obtained at incident electron energies ranging from 0.5 to 800 eV in the 10deg-130deg scattering angle range. Theoretically, the scattering cross sections in...
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Cavity-expansion approximation for projectile impact and penetration into sand
PublicationA one-dimensional problem of a spherical cavity expanding at a constant velocity from zero initial radius in an infinite granular medium, which has the first-kind self-similar solution, is considered. We are solving this dynamic spherical cavity-expansion problem to model rigid spheres penetrating into a granular media. Elastic–plastic deformation of the granular media is described in a barotropic approximation, using the high-pressure...
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On FEM analysis of Cosserat-type stiffened shells. Static and stability linear analysis
PublicationThe present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam...
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Variable-fidelity shape optimization of dual-rotor wind turbines
PublicationPurpose Dual-rotor wind turbines (DRWTs) are a novel type of wind turbines that can capture more power than their single-rotor counterparts. Because their surrounding flow fields are complex, evaluating a DRWT design requires accurate predictive simulations, which incur high computational costs. Currently, there does not exist a design optimization framework for DRWTs. Since the design optimization of DRWTs requires numerous model...
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Strategies for computationally feasible multi-objective simulation-driven design of compact RF/microwave components
PublicationMulti-objective optimization is indispensable when possible trade-offs between various (and usually conflicting) design objectives are to be found. Identification of such design alternatives becomes very challenging when performance evaluation of the structure/system at hand is computationally expensive. Compact RF and microwave components are representative examples of such a situation: due to highly compressed layouts and considerable...
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Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
PublicationWe consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is...
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Active Dynamic Thermography imaging of wound healing processes in cardio surgery
PublicationThe surgery is a branch of medicine, that is integrally connected to wounds. Despite using sterile tools and compliance with aseptic rolls, some of the surgery wounds become infected. In clinical practice there is a lack of cheap, objective methods and tools for quantitative definition and estimation of the surgery wound healing progress. This paper presents preliminary results of Active Dynamic Thermography (ADT) parametric imaging...
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Depth Determination Accuracy of the Modified Prony Method in a Swath Mapping Application
PublicationThis article presents the performance of the modified Prony method in a swath mapping application. Depth determination accuracy is assessed by processing raw signal acquired by an EdgeTech 6205 swath bathymetry system over flat seafloor. An updated version of the method, proposed previously by the authors, is used to determine the number of signal echoes. The number of signal echoes is essential for performing the low-rank approximation...
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Using Wearable Electronics to Estimate Usefulness of Heart Rate Variability for Bathing Person Identif Cation
PublicationIn this paper the possibility of person identification based on biosignal is investigated. The work focus on the analysis of the changes in intervals between successive R-waves of electrocardiogram (ECG) recorded by wearable electronics in form of a necklaces. The main idea behind this project is to find efficient tool which may prevent sudden consciousness loss episodes or even sudden death episodes related to rapid temperature...
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Local basis function estimators for identification of nonstationary systems
PublicationThe problem of identification of a nonstationary stochastic system is considered and solved using local basis function approximation of system parameter trajectories. Unlike the classical basis function approach, which yields parameter estimates in the entire analysis interval, the proposed new identification procedure is operated in a sliding window mode and provides a sequence of point (rather than interval) estimates. It is...
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Ways of Harmonising Polish Competition Law with the Competition Law of the EU
PublicationThis article discusses the harmonisation of laws within the EU focusing on the specific ways of achieving an approximation of the Polish legal system with European competition law. It identifies and gives an overview of three specific ways of harmonising national laws with EU antitrust provisions: (1) spontaneous (or bottom-up) harmonisation; (2) judicial harmonisation and; (3) legislative harmonisation by means of EU Directives....
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The Implementation of the Taxonomic Spatial Measure of Development in the Analysis of Convergence in the Standard of Living
PublicationThe main goal of this paper is to analyse the existence of the social convergence in the European Union between 19952012. The social convergence refers to a reduction in the dispersion of the standard of living across countries. A taxonomic spatial measure of development was used as the standard of living approximation. The use of the new approach proposed by E. Antczak allowed for an explanation of the disparities in the analysed...
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A Compact Basis for Reliable Fast Frequency Sweep via the Reduced-Basis Method
PublicationA reliable reduced-order model (ROM) for fast frequency sweep in time-harmonic Maxwell’s equations by means of the reduced-basis method is detailed. Taking frequency as a parameter, the electromagnetic field in microwave circuits does not arbitrarily vary as frequency changes, but evolves on a very low-dimensional manifold. Approximating this low-dimensional manifold by a low dimension subspace, namely, reduced-basis space, gives...
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A spline-based FE approach to modelling of high frequency dynamics of 1-D structures
PublicationIn this paper a computational methodology leading to the development of a new class of FEs, based on the application of continuous and smooth approximation polynomials, being splines, has been presented. Application of the splines as appropriately defined piecewise elemental shape functions led the authors to the formulation of a new approach for FEM, named as spFEM, where contrary to the well-known NURBS approach, the boundaries...
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Enhancing capabilities of Atomic Force Microscopy by tip motion harmonics analysis
PublicationMotion of a tip used in an atomic force microscope can be described by the Lennard-Jones potential, approximated by the van der Waals force in a long-range interaction. Here we present a general framework of approximation of the tip motion by adding three terms of Taylor series what results in non-zero harmonics in an output signal. We have worked out a measurement system which allows recording of an excitation tip signal and its...
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Convergence of rational multistep methods of of Adams-Padé type
PublicationRational generalizations of multistep schemes, where the linear stiff part of a given problem is treated by an A-stable rational approximation, have been proposed by several authors, but a reasonable convergence analysis for stiff problems has not been provided so far. In this paper we directly relate this approach to exponential multistep methods, a subclass of the increasingly popular class of exponential integrators. This natural,...
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Approximate models and parameter analysis of the flow process in transmission pipelines
Publicationthe paper deals with the problem of early leak detection in transmission pipelines. First we present the derivation of state-space equations of the flow process in the pipelines. This description is then aggregated in order to obtain a principal model. Next, the problem of process model parameterization is addressed, taking into account the maximization of a model stability margin. The location of the maximum is determined using...
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Energy conversion in systems-contained laser irradiated metallic nanoparticles - comparison of results from analytical solutions and numerical methods
PublicationThis work introduces the theoretical method of metallic nanoparticles’ (NPs’) heat and mass transfer where the particles are coated on a surface (base), together with considering the case wherein nanoparticles move freely in a pipe. In order to simulate the heat transfer, energy and radiative transfer equations are adjusted to the considered issue. NPs’ properties are determined following the nanofluidic theories, whereas absorption...
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Optimization of a Fabry-Perot Sensing Interferometer design for an optical fiber sensor of hematocrit level
PublicationContinuous measurement of the hemato crit level in blo o d can p otentially b e p erformed using optical bre sensors. The FabryPerot interferometric sensors are a promising candidate in this application. The most imp ortant step in the design of the sensor is design of the sensing interferometer. Adequate cavity length and high interference contrast are two most imp ortant requirements in this application. The design metho d of...
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Structural properties of hypothetical CeBa2Cu3O7 compound from LSDA+DMFT calculations
PublicationThe hypothetical stoichiometric CeBa2Cu3O7 (Ce123) compound, which has not been synthesized as a single phase yet, was studied by the density functional theory (DFT). We utilized a method which merges the local spin density approximation (LSDA) with the dynamical mean-field theory (DMFT) to account for the electronic correlations. The LSDA+DMFT calculations were performed in the high-temperature range. The particular emphasis was...
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Shape Optimisation of Kaplan Turbine Blades Using Genetic Algorithms
PublicationThis monograph is a comprehensive guide to a method of blade profile optimisation for Kaplan-type turbines. This method is based on modelling the interaction between rotor and stator blades. Additionally, the shape of the draft tube is investigated. The influence of the periodic boundary condition vs. full geometry is also discussed. Evolutionary algorithms (EA) are used as an optimisation method together with artificial neural...
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Chemometrics for Selection, Prediction, and Classification of Sustainable Solutions for Green Chemistry—A Review
PublicationIn this review, we present the applications of chemometric techniques for green and sustainable chemistry. The techniques, such as cluster analysis, principal component analysis, artificial neural networks, and multivariate ranking techniques, are applied for dealing with missing data, grouping or classification purposes, selection of green material, or processes. The areas of application are mainly finding sustainable solutions...
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Global Optimization for Recovery of Clipped Signals Corrupted With Poisson-Gaussian Noise
PublicationWe study a variational formulation for reconstructing nonlinearly distorted signals corrupted with a Poisson-Gaussian noise. In this situation, the data fidelity term consists of a sum of a weighted least squares term and a logarithmic one. Both of them are precomposed by a nonlinearity, modelling a clipping effect, which is assumed to be rational. A regularization term, being a piecewise rational approximation of the ℓ0 function...
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The use of Markov chains in the social convergence analysis
PublicationThe main goal of this article is to analyze the social convergence process using Markov chains. In this research, term social convergence refers to the reduction of dispersion in the standard of living among countries. The use of Markov chains in the social convergence analysis allowed describing movements of observational units within the distribution and providing more details about the mechanism of the convergence process. A...
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Novel Analytic-Numerical Model of Free Convection: with Leading Edge Considered
PublicationA novel solution of the free convection boundary problem is represented in analytical form for velocity and temperature for an isothermal vertical plate, as an example. These fields are built as a Taylor Series in the x coordinate with coefficients as functions of the vertical coordinate (y). We restrict ourselves by cubic approximation for both functions. The basic Navier-Stokes and Fourier-Kirchhoff equations and boundary conditions...
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Stability by linear approximation for time scale dynamical systems
PublicationWe study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...
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The Method of a Two-Level Text-Meaning Similarity Approximation of the Customers’ Opinions
PublicationThe method of two-level text-meaning similarity approximation, consisting in the implementation of the classification of the stages of text opinions of customers and identifying their rank quality level was developed. Proposed and proved the significance of major hypotheses, put as the basis of the developed methodology, notably about the significance of suggestions about the existence of analogies between mathematical bases of...
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Distribution of the displacement sequence of an orientation preserving circle homeomorphism
PublicationIn some applications not only the knowledge of the behaviour of trajectories of a map is important, but also their displacements. We describe in detail the distribution of elements of the displacement sequence along a trajectory of an orientation preserving circle homeomorphism ϕ with irrational rotation number ϱ(ϕ). The values of displacement are dense in a set which depends on the map γ (semi-)conjugating ϕ with the rotation...
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Size Reduction of Microwave Couplers by EM-Driven Optimization
PublicationThis work addresses simulation-driven design optimization of compact microwave couplers that explicitly aims at circuit footprint area reduction. The penalty function approach allows us to minimize the area of the circuit while ensuring a proper power division between the output ports and providing a sufficient bandwidth with respect to return loss and isolation around the operating frequency. Computational cost of the optimization...
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Fast Multi-Objective Antenna Optimization Using Sequential Patching and Variable-Fidelity EM Models
PublicationIn this work, a technique for fast multi-objective design optimization of antenna structures is presented. In our approach, the initial approximation of the Pareto set representing the best possible trade-offs between conflicting design objectives is obtained by means of sequential patching of the design space. The latter is a stencil-based search that aims at creating a path that connects the extreme Pareto-optimal designs (obtained...
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Spurious Modes in Model Order Reduction in Variational Problems in Electromagnetics
PublicationIn this work, we address an everlasting issue in 2 model order reduction (MOR) in electromagnetics that has 3 remained unnoticed until now. Contrary to what has been 4 previously done, we identify for the very first time spurious 5 modes in MOR for time-harmonic Maxwell’s equations and 6 propose a methodology to remove their negative influence on the 7 reduced order model (ROM) response. These spurious modes 8 have nonzero resonance...
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Fast Multi-Objective Optimization of Narrow-Band Antennas Using RSA Models and Design Space Reduction
PublicationComputationally efficient technique for multi-objective design optimization of narrow-band antennas is presented. In our approach, the corrected low-fidelity antenna model (obtained through coarse-discretization EM simulations) is enhanced using frequency scaling and response correction, sampled, and utilized to obtain a fast response surface approximation (RSA) antenna surrogate. The RSA model is constructed in the reduced design space....
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Cost-efficient simulation-driven design of compact impedance matching transformers
PublicationIn this paper, an algorithmic framework for cost-efficient design optimization of miniaturized impedance matching transformers has been presented. Our approach exploits a bottom-up design that involves translating the overall design specifications for the circuit at hand to its elementary building blocks (here, compact microstrip resonant cells, CMRCs), as well as fast surrogate-assisted optimization of the cells followed by simulation-based...
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Multi-objective antenna design by means of sequential domain patching
PublicationA simple yet robust methodology for rapid multiobjective design optimization of antenna structures has been presented. The key component of our approach is sequential domain patching of the design space which is a stencil-based search that aims at creating a path that connects the extreme Pareto-optimal designs, obtained by means of single-objective optimization runs. The patching process yields the initial approximation of the...
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On analytical solution of stationary two dimensional boundary problem of natural convection
PublicationApproximate analytical solution of two dimensional problem for sta- tionary Navier-Stokes, continuity and Fourier-Kirchho equations describ- ing free convective heat transfer from isothermal surface of half innite vertical plate is presented. The problem formulation is based on the typ- ical for natural convection assumptions: the uid noncompressibility and Boussinesq approximation. We also assume that orthogonal to the plate component...
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Parameters’ Identification of Perzyna and Chaboche Viscoplastic Models for Aluminum Alloy at Temperature of 120◦C
PublicationThe main purpose of this paper is the parameters identification of the Perzyna and the Chaboche models for the aluminum alloy at elevated temperature. The additional purpose is comparison of the results for these viscoplastic models. The results have been verified by the numerical simulation of the laboratory tests. The material parameters have been calculated on the basis of the uniaxial tension test. The determination of the...
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Low-energy positron collisions with water: elastic and rotationally inelastic scattering
PublicationDifferential, integral and momentum transfer cross sections for the vibrationally elastic and rotationally inelastic scattering of positrons from water at low collision energy (E ≤ 10 eV) are reported. Several models within the R-matrix method are used to compute the body-fixed T-matrices, while the scattering calculations are performed within the fixed-nuclei approximation corrected with the standard Born-closure formula. These...
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2-Coloring number revisited
Publication2-Coloring number is a parameter, which is often used in the literature to bound the game chromatic number and other related parameters. However, this parameter has not been precisely studied before. In this paper we aim to fill this gap. In particular we show that the approximation of the game chromatic number by the 2-coloring number can be very poor for many graphs. Additionally we prove that the 2-coloring number may grow...