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Search results for: analytical solution
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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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Advancement of Non-Newtonian Fluid with Hybrid Nanoparticles in a Convective Channel and Prabhakar’s Fractional Derivative—Analytical Solution
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Analytical solution of non-stationary heat conduction problem for two sliding layers with time-dependent friction conditions
PublicationIn this article we conduct an overview of various types of thermal contact conditions at the sliding interface. We formulate a problem of non-stationary heat conduction in two sliding layers with generalized thermal contact conditions allowing for dependence of the heat-generation coefficient and contact heat transfer coefficient on time. We then derive an analytical solution of the problem by constructing a special coordinate...
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Volume optimization of high-speed surface-mounted permanent magnet synchronous motor based on sequential quadratic programming technique and analytical solution
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Analytical and numerical solution of a coupled KdV-MKdV system.
PublicationTransformacje Darboux zostały użyte do rozwiązania układu równań KdV-MKdV.
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Analytical and numerical solution of a coupled KdV - MKdV system.
PublicationTransformację Darboux zastosowano do całkowania układów równań KdV - MKdV.Reprezentacja Laxa używa 2x2 macierzowe zagadnienie spektralne drugiego rzędu. Numeryczną metodę wprowadzono razem z dowodem zbieżności.
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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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Certain family of analytical solutions of nonlinear von Neumann equations
PublicationIn this paper we present a slight generalization of certain type of Darboux transformation, that may be used sub-sequently in a convenient way. This method allows to obtain families of solutions of nonlinear von Neumann equations, that are used in particular in DNA modeling.
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Chemically induced deformation of a porous layer coupled with advective–dispersive transport. Analytical solutions
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Importance of sign conventions on analytical solutions to the wave-induced cyclic response of a poro-elastic seabed
PublicationThis paper discusses the influence of different sign conventions for strains and stresses, i.e. the solid mechanics sign convention and the soil mechanics sign convention, on the form of governing partial differential equations (the static equilibrium equations and the continuity equation) used to describe the wave-induced cyclic response of a poro-elastic seabed due to propagation of a sinusoidal surface water-wave. Some selected...
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COMMENTS ON EXISTING ANALYTICAL SOLUTIONS TO THE WAVE-INDUCED CYCLIC RESPONSE OF A POROUS SEABED OF INFINITE THICKNESS
PublicationThis paper deals with the wave-induced cyclic response of a porous seabed (by means of oscillating parameters: pore-fluid pressure, soil displacement components, effective normal stress and shear stress components) due to a surface sinusoidal water-wave propagating over a seabed of infinite thickness. The main existing analytical solutions to the governing problem are critically discussed, pointing out their meaningful errors and...
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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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Influence of pH and low-molecular weight organic compounds in solution on selected spectroscopic and analytical parameters of flowing liquid anode atmospheric pressure glow discharge (FLA-APGD) for the optical emission spectrometric (OES) determination of Ag, Cd, and Pb
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Quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi^4 model
PublicationAnalytical form of quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi^4 model is obtained through zeta function regularisation with account of all rest variables of a d-dimensional theory. Qualitative dependence of quantum corrections on parameters of the classical systems is also evaluated for a much broader class of potentials u(x) = b^2 f(bx) + C with b and C as arbitrary real constants
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A standard analytical method as the common good and pollution abatement measure
PublicationA standard method can be considered as a common-good “resource,” and the solution to “the commons” problems usually lies in societal self-organization. The multi-criteria decision analysis (MCDA) was applied to model complex phenomena, such as the standard selection for imidacloprid determination. In this process, the standard was self-selected by the analytical chemistry society. The results show that analytical chemistry is a...
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Complementary green analytical procedure index (ComplexGAPI) and software
PublicationIt is not easy to find appropriate tools for the evaluation of the “green”nature of analytical methodologies which involve the use of compounds, materials, or chemicals manufactured prior to the analytical step. Here, we propose a new metric for the evaluation of analytical procedures based on the GAC attributes. The proposed solution expands on the well-known green analytical procedure index by adding additional fields pertaining...
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Numerical and Analytical Investigation of Aluminium Bracket Strengthening
PublicationThis paper focuses on an analytical and numerical investigation of aluminium brackets used to fasten light-weight curtain walls to building facilities. The authors propose a solution to increase the load capacity of aluminium brackets by means of additional cover plates (straps). This paper also includes a short survey of literature and material properties concerning the EN AW-6060 T6 aluminium alloy. This paper suggests an initiation...
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Multicriteria Decision Analysis and Grouping of Analytical Procedures for Phthalates Determination in Disposable Baby Diapers
PublicationThis study presents the application of one of the tools from the multicriteria decision analysis set (MCDA), the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Selected green analytical chemistry metrics were used to rank analytical procedures for the phthalate determination in disposable baby diapers. Nine analytical procedures were assessed in order to find one that has the lowest environmental impact...
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Secondary emission influenced fluorescence decay of a homogeneous fluorophore solution
PublicationAn analytical expression is found allowing the calculation of the secondary emission influenced fluorescence decay of a homogeneous fluorophore solution. Before starting the calculation one has to know the shape of the primary fluorescence decay of the fluorophore and the value of the parameter kappa denoting the ratio of the secondary to primary steady-state fluorescence intensities. The method elaborated by Budo and Ketskemety...
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Application of TOPSIS for Selection and Assessment of Analytical Procedures for Ibuprofen Determination in Wastewater
PublicationThis paper describes the possible implementation of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) as green analytical chemistry metrics tools. TOPSIS is one of the multi-criteria decision analysis (MCDA) tools that is applied in the selection of the best alternative from many possible. In this case we have applied it to assess the nineteen analytical procedures for ibuprofen determination in wastewater...
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Solution of the dike-break problem using finite volume method and splitting technique
PublicationIn the paper the finite volume method (FVM) is presented for the solution of two-dimensional shallow water equations. These equations are frequently used to simulate the dam-break and dike-break induced flows. The applied numerical algorithm of FVM is based on the wave-propagation algorithm which ensures a stable solution and simultaneously minimizes the numerical errors. The dimensional decomposition according to the coordinate...
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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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Application of multicriteria decision analysis in solvent type optimization for chlorophenols determination with a dispersive liquid–liquid microextraction
PublicationThis study presents a novel support tool for the optimization and development of analytical methods. The tool is based on multi-criteria decision analysis (MCDA), namely the Technique for Order of Preference by Similarity to the Ideal Solution (TOPSIS), that allows users to rank possible solutions according to their requirements. In this study, we performed rankings of pairs of eight extraction and three dispersive solvents used...
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The analytical design method of railway route’s main directions intersection area
PublicationThe paper presents a design method related to railway track sections situated in a bend. In the method advantage is taken of an analytical form of description by using appropriate mathematical formulae. This may becomeparticularly usefulwhen the investigations are based on the data obtained from mobile satellite measurements. In the paper attention is concentrated on an universal approach creating an opportunity to diversify the...
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Development of novel smartphone-based methods of wine quality assessment
PublicationThe doctoral dissertation concerns the development of novel smartphone-based analytical methods of wine quality evaluation, which would be in line with the stipulations of green and equitable analytical chemistry. This solution is based on the analysis of biogenic amines and selected bioactive compounds. The dissertation is based on four articles containing the results of research which led to the development of smartphone-based...
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Flexural buckling and post-buckling of columns made of aluminium alloy
PublicationThe paper concerns flexural buckling and initial post-buckling of axially compressed columns made of aluminium alloy described by the Ramberg-Osgood relationship. The non-linear differential equation of the problem is derived using the stationary total energy principle and the assumptions of classical beam theory within a finite range. The approximate analytical solution of the equation leading to the buckling loads and initial...
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Variational Method of Finding Streamlines in Ring Cascades for Creeping Flows
PublicationThis paper presents a new, analytical method of finding streamlinesfor creeping flows inside a ring cascade which is composed of an infinite number of infinitely thin blades. An analytical solution has been obtained through minimisation of a dissipation functional by means of variational calculus method. The necessary condition for optimum of a functional gives the Stokes equation if some additional assumptions are introduced....
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Analytical calculations of scattering lengths for a class of long-range potentials of interest for atomic physics
PublicationWe derive two equivalent analytical expressions for an $l$th partial-wave scattering length $a_{l}$ for central potentials with long-range tails of the form % \begin{math} \displaystyle V(r)=-\frac{\hbar^{2}}{2m}\frac{Br^{n-4}}{(r^{n-2}+R^{n-2})^{2}} -\frac{\hbar^{2}}{2m}\frac{C}{r^{2}(r^{n-2}+R^{n-2})}, \end{math} % ($r\geqslant r_{s}$, $R>0$). % For $C=0$, this family of potentials reduces to the Lenz potentials discussed in...
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Theoretical consideration of free convective heat transfer from a round isothermal plate slightly inclined from the vertical
PublicationA semi-analytical solution of simplified Navier-Stokes and Fourier-Kirchhoff equations describing free convective heat transfer from a round isothermal surface slightly inclined from the vertical is presented. The solution is based on the assumption, typical for natural convection, that the velocity component normal to the surface is negligibly small in comparison to the tangential one. Next we neglect the nonlinear inertia force...
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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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Structural properties of foil bearings: a closed-form solution validated with finite element analysis
PublicationFluid film thickness in a compliant foil bearing is greatly influenced by the deflection of the bearing structure. Therefore, in order to properly model performance of a foil bearing, it is mandatory that the deflection of the compliant bearing structure due to the generated hydrodynamic pressure is determined accurately. This article proposes an easy-to-use two-dimensional model, which takes into account detailed geometry of the...
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Analytical Estimation of Power Losses in a Dual Active Bridge Converter Controlled with a Single-Phase Shift Switching Scheme
PublicationMicro-grid solutions around the world rely on the operation of DC/DC power conver- sion systems. The most commonly used solution for these topologies is the use of a dual active bridge (DAB) converter. Increasing the efficiency and reliability of this system contributes to the improvement in the stability of the entire microgrid. This paper discussed an analytical method of energy efficiency and power loss estimation in a single...
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Local buckling of composite channel columns
PublicationThe investigation concerns local buckling of compressed flanges of axially compressed composite channel columns. Cooperation of the member flange and web is taken into account here. The buckling mode of the member flange is defined by rotation angle a flange about the line of its connection with the web. The channel column under investigation is made of unidirectional fibre-reinforced laminate. Two approaches to member orthotropic...
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Synthesis, structural characterization and reactivity of new trisubstituted N1-acylamidrazones: solid state and solution studies
PublicationA series of new linear trisubstituted N1-acylamidrazones have been investigated using a variety of analytical techniques and theoretical calculations to check the influence of the type of N1-acyl substituent on the resonance forms and conformational behavior in the solid state and in solution. The 1D- and 2D-NMR experiments, supported by computational studies, revealed that in solution all amidrazones exhibit conformational syn/anti...
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Selected local stability problems of channel section flanges made of aluminium alloys
PublicationThe paper addresses the issue of local buckling of compressed flanges of cold-formed thin-walled channel columns and beams with nonstandard flanges composed of aluminium alloys. The material behaviour follows the Ramberg–Osgood law. It should be noted that the proposed solution may be also applied for other materials, for example: stainless steel, carbon steel. The paper is motivated by an increasing interest in nonstandard cold-formed...
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Two-Dimensional Gas Chromatography Coupled With Mass Spectrometry in Food Analysis
PublicationThe development of instrumental analytical techniques provided the opportunity for in-depth characterization of many food matrices. In particular, the use of gas chromatography coupled with mass spectrometry gives impressive results in terms of quality and authenticity testing, conducting food freshness evaluations and contamination assessments. A new variant of gas chromatography, namely two-dimensional gas chromatography (GC...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublicationIn this study a tin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equatio is derived with aid of the principle of stationary potential energy. The critical load for simply supported bar is found in an analytical form and it is copared with the FEM solution. Sufficient accuracy of the...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublicationIn this study a thin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical load for the simply supported bar is found in analytical form and it is compared with the FEM solution. Sufficient accuracy...
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Distortional buckling of thin-walled columns of closed quadratic cross-section
PublicationThe elastic stability of axially compressed column related to the cross-section distortion is investigated. Two kinds of closed quadratic cross-sections are taken into consideration with internal walls and without it. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical loads for the simply supported columns are found in an analytical form and compared with...
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Novel fast analytical method for indirect determination of MCPD fatty acid esters in edible oils and fats based on simultaneous extraction and derivatization
PublicationA novel method for indirect determination of MCPD esters levels in lipid samples has been developed. The method is based on combination of extraction and derivatisation in the same sample preparation step. It is achieved by the application of diethyl ether as extraction solvent for isolation of released from esterified forms analytes from water phase and dilution solvent for solid PBA – derivatisation agent. It is a noteworthy...
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Buckling and initial post-local buckling behaviour of cold-formed channel member flange
PublicationThe initial post-buckling behaviour of a cold-formed channel member flange after its local buckling is investigated. An axially compressed column or beam subjected to pure bending is considered. The member material is assumed to follow a linear stress-strain relationship. The governing non-linear differential equation of the problem is derived using the minimum total potential energy principle. An approximate solution for the equation...
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Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow
PublicationTo find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and...
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Discussion on “Coupled effective stress analysis of insertion problems in geotechnics with the Particle Finite Element Method” by L. Monforte, M. Arroyo, J.M. Carbonell, and A. Gens
PublicationAddressed here is the Particle Finite Element Method (PFEM) modelling of undrained CPTu penetration with regard to a reference analytical solution based on the Spherical Cavity Expansion Method (SCEM). Also discussed is the choice of the soil model and its parameters. The effect of cone interface friction on CPTu simulation is analyzed in a series of penetration tests using Arbitrary Lagrangian-Eulerian (ALE) and Updated Lagrangian...
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On Wrinkling in Sandwich Panels with an Orthotropic Core
PublicationThis paper deals with the local loss of stability (wrinkling) problem of a thin facing of a sandwich panel. Classical solutions to the problem of facing instability resting on a homogeneous and isotropic substructure (a core) are compared. The relations between strain energy components associated with different forms of core deformations are discussed. Next, a new solution for the orthotropic core is presented in detail, which...
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Local buckling of thin-walled channel member flange made of aluminum alloy
PublicationThe 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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Analytical ‘Steady-State’-Based Derivation and Clarification of the Courant-Friedrichs-Lewy Condition for Pipe Flow
PublicationThis article addresses the problem of choosing the optimal discretization grid for emulating fluid flow through a pipeline. The aggregated basic flow model is linearized near the operating point obtained from the steady state analytic solution of the differential equations under consideration. Based on this model, the relationship between the Courant number (μ) and the stability margin is examined. The numerically set coefficient...
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Size Exclusion Coupled to Reversed Phase Liquid Chromatography for the Characterization of Cranberry Products
PublicationA combination of solvent extraction, size exclusion purification, and reversed-phase liquid chromatography with UV absorption and fluorescence detection was here used for the determination of flavan-3-ols and related oligomeric compounds in cranberry products. The method relied on robust, simple, and inexpensive instrumental equipment present in most of routine analytical laboratories. Sample extracts in methanol/water/hydrochloric...
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A method for preliminary estimation of the length of midship body block to be inserted during ship’s conversion
PublicationThe paper presents a method for preliminary estimation of the length of the midship body block, which inserted in the original hull, increases the deadweight of the ship in line with a required quantity. The method may be useful for establishing the scope of conversion to better adjust the ship for transportation tasks. The problem is formulated by using a mathematical model so selected that its solution, under set of assumptions,...
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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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Application of chromogenic dye in biogenic amines determination using spectrophotometry
PublicationBiogenic amines content can be the source of information in the field of freshness and suitability of certain foods for consumption. However, most analytical methods for their determination require complicated sample preparation and expert knowledge. Because of that, a novel approach based on chromogenic dye application was proposed. After the SN1 reaction of an amine with S 0378 dye, the absorbance of the solution was measured...