Wyniki wyszukiwania dla: SYSTEM OF EQUATIONS
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On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems
PublikacjaWe show the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems, where a C1-smooth potential satisfies a relaxed superquadratic growth condition, its gradient is bounded in the time variable, and a forcing term is sufficiently small in the space of square integrable functions. The idea of our proof is to approximate the original system by time-periodic ones, with larger and larger...
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Ellipticity of gradient poroelasticity
PublikacjaWe discuss the ellipticity properties of an enhanced model of poroelastic continua called dilatational strain gradient elasticity. Within the theory there exists a deformation energy density given as a function of strains and gradient of dilatation. We show that the equilibrium equations are elliptic in the sense of Douglis–Nirenberg. These conditions are more general than the ordinary and strong ellipticity but keep almost all...
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Reduction of Computational Complexity in Simulations of the Flow Process in Transmission Pipelines
PublikacjaThe paper addresses the problem of computational efficiency of the pipe-flow model used in leak detection and identification systems. Analysis of the model brings attention to its specific structure, where all matrices are sparse. With certain rearrangements, the model can be reduced to a set of equations with tridiagonal matrices. Such equations can be solved using the Thomas algorithm. This method provides almost the same values...
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Geometrically nonlinear FEM analysis of 6-parameter resultant shell theory based on 2-D Cosserat constitutive model
PublikacjaWe develop the elastic constitutive law for the resultant statically and kinematically exact, nonlinear, 6-parameter shell theory. The Cosserat plane stress equations are integrated through-the- thickness under assumption of the Reissner-Mindlin kinematics. The resulting constitutive equations for stress resultant and couple resultants are expressed in terms of two micropolar constants: the micropolar modulus Gc and the micropolar...
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Integrable zero-range potentials in a plane
PublikacjaWe examine general statements in the Wronskian representation of Darboux transformations for plane zero-range potentials. Such expressions naturally contain scattering problem solution. We also apply Abel theorem to Wronskians for differential equations and link it to chain equations for Darboux transforms to fix conditions for further development of the underlying distribution concept. Moutard transformations give a convenient...
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Non-linear static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum
PublikacjaIn this research, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and non-linear strains of Von-Karman was studied. The bi-layer carbon sheets were modeled as a double-layered plate, and van der Waals forces between layers were considered. The governing equations and boundary conditions were obtained using the first order shear...
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[AEiE] Selected topics of electrical engineering - models of electrical machines
Kursy Online{mlang pl} Dyscyplina: automatyka, elektronika i elektrotechnika Zajęcia fakultatywne dla doktorantów II roku Prowadzący: dr hab. inż. Andrzej Wilk, prof. PG, prof. dr hab. inż. Zbigniew Krzemiński Liczba godzin: 15 Forma zajęć: wykład {mlang} {mlang en} Discipline: control, electronic and electrical engineering Facultative course for 2nd-year PhD students Academic teachers: dr hab. inż. Andrzej Wilk, prof. PG, prof....
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Fractional Order Circuit Elements Derived from Electromagnetism
PublikacjaIn this paper, derivations of fractional-order (FO) circuit-element equations from electromagnetism are presented. Whilst many papers are devoted to FO modelling of electrical circuits, there are no strong foundations for such an approach. Therefore, we investigate relations between the FO electromagnetism and the FO circuit theory. Our derivations start from quasi-static (QS) approximations of Maxwell's equations in media with...
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Identification of transition curves in vehicular roads and railways
PublikacjaIn the paper attention is focused on the necessity to systematize the procedure for determining the shape of transition curves used in vehicular roads and railway routes. There has been presented a universal method of identifying curvature in transition curves by using differential equations. Curvature equations for such known forms of transition curves as clothoid, quartic parabola, the Bloss curve, cosinusoid and sinusoid, have...
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On Applications of Fractional Derivatives in Electromagnetic Theory
PublikacjaIn this paper, concepts of fractional-order (FO) derivatives are analysed from the point of view of applications in the electromagnetic theory. The mathematical problems related to the FO generalization of Maxwell's equations are investigated. The most popular formulations of the fractional derivatives, i.e., Riemann-Liouville, Caputo, Grünwald-Letnikov and Marchaud definitions, are considered. Properties of these derivatives are...
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Nonlinear resultant theory of shells accounting for thermodiffusion
PublikacjaThe complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells...
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Absorbing Boundary Conditions Derived Based on Pauli Matrices Algebra
PublikacjaIn this letter, we demonstrate that a set of absorbing boundary conditions (ABCs) for numerical simulations of waves, proposed originally by Engquist and Majda and later generalized by Trefethen and Halpern, can alternatively be derived with the use of Pauli matrices algebra. Hence a novel approach to the derivation of one-way wave equations in electromagnetics is proposed. That is, the classical wave equation can be factorized...
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Fundamentals of classical and analytical mechanics
PublikacjaThe book is a monographic description of the present attempt to Newtonian and Lagrangian mechanics. But also, it could be found as a supplementary educational material useful for the graduate courses in mechanics taken by students majoring in mechanical engineering, physics or physical science. In the book you can find a brief introduction to concepts and principles of algebra of vectors; Kinematics of particles, mainly focused...
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Geometrically nonlinear FEM analysis of FGM shells based on neutral physical surface approach in 6-parameter shell theory
PublikacjaThe paper presents the formulation of the elastic constitutive law for functionally graded materials (FGM) on the grounds of nonlinear 6-parameter shell theory with the 6th parameter being the drilling degree of freedom. The material law is derived by through-the-thickness integration of the Cosserat plane stress equations. The constitutive equations are formulated with respect to the neutral physical surface. The influence of...
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A Nonlinear Model of a Mesh Shell
PublikacjaFor a certain class of elastic lattice shells experiencing finite deformations, a continual model using the equations of the so-called six-parameter shell theory has been proposed. Within this model, the kinematics of the shell is described using six kinematically independent scalar degrees of freedom — the field of displacements and turns, as in the case of the Cosserat continuum, which gives reason to call the model under consideration...
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Electromagnetic-based derivation of fractional-order circuit theory
PublikacjaIn this paper, foundations of the fractional-order circuit theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order...
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Simulations of flows in the coastal zone of the Baltic Sea
Dane BadawczeThe study area is located in the Southern Baltic, within Polish Marine Areas, adjacent to the coastline in the vicinity of Lubiatowo village, where The Coastal Research Station (CRS) – a field laboratory of the Institute of Hydro-Engineering of the Polish Academy of Sciences (IBW PAN) –is situated. The numerical reconstruction of the coastal flow was...
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Analytical Steady-State Model of the Pipeline Flow Process
PublikacjaThe paper addresses the issue of modeling the flow process in transmission pipelines. A base model used for numerical simulation is introduced. Under certain assumptions concerning steady state analysis, the differential equations describing the process are solved analytically for two cases: zero and nonzero inclination angle α. These equations describe a constant flow rate and a corresponding distribution of the pressure along...
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Analytical method of determining dynamic properties of thermocouples used in measurements of quick – changing temperatures of exhaust gases in marine diesel engines
PublikacjaThe article presents selected issues of mathematical modeling of heat exchange between the thermocouple and the exhaust gas flowing them, in unsteady conditions. On the way of energy balancing consideration of thermodynamic processes developed differential equations describing the dynamic properties for three versions of the design sheathed thermocouples: with weld isolated from the sheath, with weld welded the sheath and with...
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Numerical solution of threshold problems in epidemics and population dynamics
PublikacjaA new algorithm is proposed for the numerical solution of threshold problems in epidemics and population dynamics. These problems are modeled by the delay-differential equations, where the delay function is unknown and has to be determined from the threshold conditions. The new algorithm is based on embedded pair of continuous Runge–Kutta method of order p = 4 and discrete Runge–Kutta method of order q = 3 which is used for the...
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Efficiency of acoustic heating in the Maxwell fluid
PublikacjaThe nonlinear effects of sound in a fluid describing by the Maxwell model of the viscous stress tensor is the subject of investigation. Among other, viscoelastic biological media belong to this non-newtonian type of fluids. Generation of heating of the medium caused by nonlinear transfer of acoustic energy, is discussed in details. The governing equation of acoustic heating is derived by means of the special linear combination...
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Macro-elements and Model Order Reduction for Efficient Three-Dimensional FEM Analysis
PublikacjaAn efficient model order reduction (MOR) methodology for three dimensional vector finite element method (FEM) is developed to accelerate simulations of the structures containing features that cause strong variations of mesh density. As the result of presented algorithm, FEM subsystems of equations corresponding to the selected refined region are converted into a very compact sets of linear equations, called macro-elements.Numerical...
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Efficiency of acoustic heating in the Maxwell fluid
PublikacjaThe nonlinear effects of sound in a fluid describing by the Maxwell model of the viscous stress tensor is the subject of investigation. Among other, viscoelastic biological media belong to this non-newtonian type of fluids. Generation of heating of the medium caused by nonlinear transfer of acoustic energy, is discussed in details. The governing equation of acoustic heating is derived by means of the special linear combination...
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On a 3D material modelling of smart nanocomposite structures
PublikacjaSmart composites (SCs) are utilized in electro-mechanical systems such as actuators and energy harvesters. Typically, thin-walled components such as beams, plates, and shells are employed as structural elements to achieve the mechanical behavior desired in these composites. SCs exhibit various advanced properties, ranging from lower order phenomena like piezoelectricity and piezomagneticity, to higher order effects including flexoelectricity...
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Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method
PublikacjaIn this paper, bending analysis of rectangular functionally graded (FG) nanoplates under a uniform transverse load has been considered based on the modified couple stress theory. Using Hamilton’s principle, governing equations are derived based on a higher-order shear deformation theory (HSDT). The set of coupled equations are solved using the dynamic relaxation (DR) method combined with finite difference (FD) discretization technique...
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generation of the vorticity mode by sound in a bingham plastic
PublikacjaThis study investigates interaction between acoustic and non-acoustic modes, such as vorticity mode,in some class of a non-newtonian fluid called Bingham plastic. The instantaneous equations describinginteraction between different modes are derived. The attention is paid to the nonlinear effects in the fieldof intense sound. The resulting equations which describe dynamics of both sound and the vorticity modeapply to both periodic...
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Transition curve with smoothed curvature at its ends for railway roads
PublikacjaIn the paper, in view of a railway ballasted track, a new concept of transition curve of linear form of curvature along its length and smoothed extreme regions is presented. For this purpose use has been made of an original, universal method for identifying transition curves by means of differential equations. Some general curvature equations for three regions investigated have been determined to be followed by appropriate parametric...
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Ellipticity in couple-stress elasticity
PublikacjaWe discuss ellipticity property within the linear couple-stress elasticity. In this theory, there exists a deformation energy density introduced as a function of strains and gradient of macrorotations, where the latter are expressed through displacements. So the couple-stress theory could be treated as a particular class of strain gradient elasticity. Within the micropolar elasticity, the model is called Cosserat pseudocontinuum...
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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
PublikacjaIn this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their...
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Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory
PublikacjaThis article is intended to analyze forced vibrations of a piezoelectric-piezomagnetic ceramic nanoplate by a new refined shear deformation plate theory in conjunction with higher-order nonlocal strain gradient theory. As both stress nonlocality and strain gradient size-dependent effects are taken into account using the higher-order nonlocal strain gradient theory, the governing equations of the composite nanoplate are formulated....
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Vibro-Electrical Behavior of a Viscoelastic Piezo-Nanowire in an Elastic Substrate Considering Stress Nonlocality and Microstructural Size-Dependent Effects
PublikacjaThis research deals with dynamics response of a Pol/BaTiO3 nanowire including viscosity influences. The wire is also impressed by a longitudinal electric field. Hamilton's principle and Lagrangian strains are employed in conjunction with a refined higher-order beam theory in order to derive equations of motion. By combining nonlocality and small size...
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On analytical solution of stationary two dimensional boundary problem of natural convection
PublikacjaApproximate 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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Instantaneous Heating and Cooling Caused by Periodic or Aperiodic Sound of Any Characteristic Duration in a Gas with Vibrational Relaxation
PublikacjaThermodynamic relaxation of internal degrees of a molecule's freedom in a gas occurs with some characteristic time. This makes wave processes in a gas behave differently depending on the ratio of characteristic duration of perturbations and the relaxation time. In particular, generation of the secondary non-wave modes by intense sound in a nonlinear flow dependens on frequency. These kinds of interaction are considered in this...
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On forced vibrations of piezo-flexomagnetic nano-actuator beams
PublikacjaThe effect of excitation frequency on the piezomagnetic Euler-Bernoulli nanobeam taking the flexomagnetic material phenomenon into consideration is investigated in this chapter. The magnetization with strain gradients creates flexomagneticity. We couple simultaneously the piezomagnetic and flexomagnetic properties in an inverse magnetization. Resemble the flexoelectricity, the flexomagneticity is also size-dependent. So, it has...
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A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions
PublikacjaIn this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding...
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On the plastic buckling of curved carbon nanotubes
PublikacjaThis research, for the first time, predicts theoretically static stability response of a curved carbon nanotube (CCNT) under an elastoplastic behavior with several boundary conditions. The CCNT is exposed to axial compressive loads. The equilibrium equations are extracted regarding the Euler–Bernoulli displacement field by means of the principle of minimizing total potential energy. The elastoplastic stress-strain is concerned...
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Thermal Buckling Analysis of Circular Bilayer Graphene sheets Resting on an Elastic Matrix Based on Nonlocal Continuum Mechanics
PublikacjaIn this article, the thermal buckling behavior of orthotropic circular bilayer graphene sheets embedded in the Winkler–Pasternak elastic medium is scrutinized. Using the nonlocal elasticity theory, the bilayer graphene sheets are modeled as a nonlocal double–layered plate that contains small scale effects and van der Waals (vdW) interaction forces. The vdW interaction forces between the layers are simulated as a set of linear springs...
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Acoustic heating produced in the boundary layer
Publikacja: Instantaneous acoustic heating of a viscous fluid flow in a boundary layer is the subject of investigation. The governing equation of acoustic heating is derived by means of a special linear combination of conservation equations in the differential form, which reduces all acoustic terms in the linear part of the final equation but preserves terms belonging to the thermal mode. The procedure of decomposition is valid in a weakly...
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A finite element analysis of thermal energy inclination based on ternary hybrid nanoparticles influenced by induced magnetic field
PublikacjaThe use of hybrid nanoparticles to improve thermal processes is a key method that has implications for a variety of interventions utilized in many sectors. This paper aimed to look into the impacts of ternary nanoparticles on hyperbolic tangent materials to establish their thermal characteristics. Flow describing equations have been explored in the presence of heat production, non-Fourier heat flux, and an induced magnetic field....
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A non-linear direct peridynamics plate theory
PublikacjaIn this paper a direct non-local peridynamics theory for thin plates is developed. Peridynamic points are assumed to behave like rigid bodies with independent translation and finite rotation degrees of freedom. The non-local mechanical interaction between points is characterized by force and moment vectors. The balance equations including the linear momentum, the angular momentum and the energy are presented. Peridynamic deformation...
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On the existence of homoclinic type solutions of inhomogenous Lagrangian systems
PublikacjaWe study the existence of homoclinic type solutions for a class of inhomogenous Lagrangian systems with a potential satisfying the Ambrosetti-Rabinowitz superquadratic growth condition and a square integrable forcing term. A homoclinic type solution is obtained as a limit of periodic solutions of an approximative sequence of second order differential equations.
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Example of tension fabric structure analysis
PublikacjaThe aim of the work is to examine two variants of non-linear strain-stress relations accepted to description of architectural fabric. Discussion on the fundamental equations of the dense net model, used in description of coated woven fabric behaviour is presented. An analysis of tensile fabric structures subjected to the dead load and initial pretension is described.
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Singular Surface Curves in the Resultant Thermodynamics of Shells
PublikacjaWithin six-parameter shells theory we discuss the governing equations of shells with material or non-material singular curves. By singular curve we mean a surface curve where are discontinuities in some surface fields. As an example we consider shells with junctions and shells undergoing stress-induced phase transitions.
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Local material symmetry group for first- and second-order strain gradient fluids
PublikacjaUsing an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients....
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Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals
PublikacjaIn this paper, the buckling of rectangular functionally graded (FG) porous nanoplates based on threedimensional elasticity is investigated. Since, similar researches have been done in two-dimensional analyses in which only large deflections with constant thickness were studied by using various plate theories; therefore, discussion of large deformations and change in thickness of plates after deflection in this study is examined....
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Nonlinear generation of non-acoustic modes by low-frequency sound in a vibrationally relaxing gas
PublikacjaTwo dynamic equations referring to a weakly nonlinear and weakly dispersive flow of a gas in which molecular vibrational relaxation takes place. are derived. The first one governs an excess temperature associated with the thermal mode, and the second one describes variations in vibrational energy. Both quantities refer to non-wave types of gas motion. These variations are caused by the nonlinear transfer of acoustic energy into...
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Acoustic heating produced in the thermoviscous flow of a bingham plastic
PublikacjaThis study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic's viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation...
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Efficiency of acoustic heating produced in the thermoviscous flow of a fluid with relaxation
PublikacjaInstantaneous acoustic heating of a fluid with thermodynamic relaxation is the subject of investigation. Among others, viscoelastic biological media described by the Maxwell model of the viscous stress tensor, belong to this type of fluid. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in...
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Acoustic heating produced in the thermoviscous flow of a Bingham plastic
PublikacjaThis study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic's viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation...
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Fractional Spectral and Fractional Finite Element Methods: A Comprehensive Review and Future Prospects
PublikacjaIn this article, we will discuss the applications of the Spectral element method (SEM) and Finite element Method (FEM) for fractional calculusThe so-called fractional Spectral element method (f-SEM) and fractional Finite element method (f-FEM) are crucial in various branches of science and play a significant role. In this review, we discuss the advantages and adaptability of FEM and SEM, which provide the simulations of fractional...