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Asynchronous time difference of arrival (ATDOA) method
PublikacjaA new method for a location service in the asynchronous wireless sensor networks is outlined. This method, which is called asynchronous time difference of arrival (ATDOA), enables calculation of the position of a mobile node without knowledge of relative time differences (RTDs) between measuring sensors. The ATDOA method is based on the measurement of time difference of arrival between the node and the same sensor at the discrete...
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Significant Production of Thermal Energy in Partially Ionized Hyperbolic Tangent Material Based on Ternary Hybrid Nanomaterials
PublikacjaNanoparticles are frequently used to enhance the thermal performance of numerous materials. This study has many practical applications for activities that have to minimize losses of energy due to several impacts. This study investigates the inclusion of ternary hybrid nanoparticles in a partially ionized hyperbolic tangent liquid passed over a stretched melting surface. The fluid motion equation is presented by considering the...
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Magnetoacoustic heating in a quasi-isentropic magnetic gas
PublikacjaThe 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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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 the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublikacjaIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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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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Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.
PublikacjaDeparting from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity,...
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Shub’s conjecture for smooth longitudinal maps of S^m
PublikacjaLet f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f , reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m = 2 and in a weak form for m = 3.
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Local fixed point indices of iterations of planar maps
PublikacjaW artykule podana zostaje postać indeksów iteracji dla pewnej klasy odwzorowań planarnych. Podstawowymi narzędziami stosowanym w pracy są liczba Nielsena i indeks Conleya.
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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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High-precision bearing estimation for active sonar with cylindrical array performed by interpolated array transformation
PublikacjaThe article presents a method for improving the accuracy of bearing in multibeam sonar with a cylindrical array. The antenna’s non-linear shape and the resulting non-uniform sampling of the signal in space, mean that known methods of high-resolution spectral analysis cannot be used. In order to apply an algorithm from this group, a linear virtual antenna must be produced. The paper presents a technique of mapping a cylindrical...
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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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Hopf bifurcation in time‐delayed gene expression model with dimers
PublikacjaWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the formation of dimers (i.e., complex formed by two protein monomers), the way in which dimers bind to DNA and time delay in translation process. For the model consisting of three ordinary differential equations with time delay, we derive conditions for stability of the positive...
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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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Buckling analysis of a non-concentric double-walled carbon nanotube
PublikacjaOn the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient and the van der Waals interaction...
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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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Correlation between natural frequencies and buckling load in a stiffened shell
PublikacjaThe paper deals with correlation between natural frequencies and buckling load of a stiffened shell composed of corrugated sheets and vertical stiffeners (columns). The simplified shell segment represents the buckling behaviour of a whole silo with sparsely distributed columns. The paper covers variants of linear buckling anal-yses, dynamic eigenvalue analyses and geometrically non-linear analyses of a segment modelled with shell...
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Simulation of hybridized nanofluids flowing and heat transfer enhancement via 3-D vertical heated plate using finite element technique
PublikacjaThe present study probed the creation of heat energy and concentrating into Newtonian liquids across vertical 3D-heated plates. The role of the Soret and Dufour theories in concentrating and energy formulas is discussed. The role of hybrid nanoparticles is introduced to illustrate particle efciency in terms of solute and thermal energy. It is removed a viscous dissipation process and a changing magnetic feld. The proposed approach...
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High Dynamic Range Microwave Displacement and Rotation Sensors Based on the Phase of Transmission in Groove Gap Waveguide Technology
PublikacjaThis research is focused on the design and realization of displacement sensors in gap waveguide technology. It is shown that with a small but fundamental change in the structure of a conventional gap waveguide, a linear displacement can be sensed. To this end, a unique feature of gap waveguides, i.e. the fact that no electrical connection between the top and bottom parts of the gap waveguide is required, is used. It is further shown...
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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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Generation and Propagation of Nonlinear Waves in a Towing Tank
PublikacjaThe paper presents the results of the research focused on linear and nonlinear wave generation and propagation in a deepwater towing tank equipped with a single flap-type wavemaker of variable draft. The problem of wave generation and propagation has been theoretically formulated and solved by applying an analytical method; linear and nonlinear solutions were obtained. The linear solution has been verified experimentally. The...
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A new hyperbolic-polynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition
PublikacjaA 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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Investigation of stability and limit load of a truss overhead opened bridge
PublikacjaThe paper presents selected methods of determining stability and limit load of a truss top chord in opened bridges. These methods include linear buckling and non-linear static analysis based on the finite element method and algorithms based on design code procedures. The described methods were tested on an example of a steel footbridge situated in Straszyn. The results of stability analysis are compared. The results of geometrical...
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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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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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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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Torsional buckling and post-buckling of columns made of aluminium alloy
PublikacjaThe paper concerns torsional buckling and the initial post-buckling of axially compressed thin-walled aluminium alloy columns with bisymmetrical cross-section. It is assumed that the column material behaviour is described by the Ramberg–Osgood constitutive equation in non-linear elastic range. The stationary total energy principle is used to derive the governing non-linear differential equation. An approximate solution of the equation...
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Nexus between stock markets, economic strength, R&D and environmental deterioration: new evidence from EU-27 using PNARDL approach
PublikacjaThis research investigates the impact of stock market indices, economic strength, and research and development expenditures on environmental deterioration in the EU-27 countries for the period 2000–2020. This study utilized linear and non-linear panel ARDL to estimate the short- and long-run effect. According to the results, the stock market indices have negative effect on environmental deterioration in the symmetric form. However,...
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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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The Doppler effect in a bistatic system for determining the position of moving targets
PublikacjaThe article presents the theoretical analysis and the results of numerical calculations of the Doppler effect it occurs in a system designed to determine the position and speed of a moving target. The transmitter is the source of the signal and it emits a sinusoidal, acoustic and continuous wave. Signal reflected off a moving target is received by four hydrophones. Based on the signals, four Doppler shifts are determined and inserted...
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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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Estimation of a Stochastic Burgers' Equation Using an Ensemble Kalman Filter
PublikacjaIn this work, we consider a difficult problem of state estimation of nonlinear stochastic partial differential equations (SPDE) based on uncertain measurements. The presented solution uses the method of lines (MoL), which allows us to discretize a stochastic partial differential equation in a spatial dimension and represent it as a system of coupled continuous-time ordinary stochastic differential equations (SDE). For such a system...
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Analiza numeryczna i badania doświadczalne wpływu usytuowania stężeń na nośność wyboczeniową modelu kratownicy
PublikacjaIn the present research the results of experimental test and numerical analyses of a model of a typical truss are presented. The truss linear buckling analysis and non linear static analyses with respect to material and geometrical nonlinearity are conducted. For different stiffnesses and location of braces, the critical load and limit load for the truss are calculated and the threshold bracing stiffness is found. The results of...
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On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution
PublikacjaAmong 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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A high-accuracy method of computation of x-ray waves propagation through an optical system consisting of many lenses
PublikacjaThe propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. Two differential equations are contemplated for solving the problem for electromagnetic wave propagation: first – an equation for the electric field, second – an equation derived for a complex phase of an electric field. Both equations are solved by the use of a finite-difference method. The simulation error is estimated...
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Eigenfaces, Fisherfaces, Laplacianfaces, Marginfaces – How to Face the Face Verification Task
PublikacjaThis paper describes the exhaustive tests of four known methods of linear transformations (Eigenfaces, Fisherfaces, Laplacianfaces and Marginfaces) in the context of face verification task. Additionally, we introduce a new variant of the transformation (Laplacianface + LDA), and the specific interval-based decision rule. Both of them improve the performance of face verification, in general, however, our experiments show that the...
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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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3D buckling analysis of a truss with horizontal braces
PublikacjaThe present research is devoted to the study of out-of-plane buckling of a truss with horizontal braces. The truss is a model of real roof truss scaled by factor ¼. A linear buckling and a non-linear analysis with geometric and material nonlinearity were carried out. The truss buckling and limit load for different stiffnesses and number of braces are found. Numerical analysis are verified by experiment. Threshold bracing stiffness...
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Wpływ błędów parametrów modelu maszyny indukcyjnej na działanie rozszerzonego obserwatora prędkości
PublikacjaW artykule opisano metodę odtwarzania prędkości wirnika maszyny indukcyjnej przy wykorzystaniu rozszerzonego obserwatora prędkości. Zbadano wpływ błędów parametrów modelu maszyny indukcyjnej na właściwości dynamiczne obserwatora poprzez porównanie macierzy stanu obserwatora obarczonego oraz nieobarczonego błędami parametrów. Zbadany został także wpływ błędów parametrów na jakość odtwarzania zmiennych maszyny w stanie ustalonym.
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Importance of sign conventions on analytical solutions to the wave-induced cyclic response of a poro-elastic seabed
PublikacjaThis 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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The consideration to the dynamic systems parameter identification
PublikacjaIn this paper, a concept for continuous-time dynamic systems parameter identification using modulating function approach is presented. It refers to linear as well as selected non-linear systems. It shows the possibility of direct application without converting differential equation. In particular cases direct application can decrease the amount of computation in non-linear system identification, which generally requires Fourier...
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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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Ultrashort Opposite Directed Pulses Dynamics with Kerr Effect and Polarization Account
PublikacjaWe 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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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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Asynchronous Wide Area Multilateration System
PublikacjaA new method for a location service in the wide area multilateration (WAM) system is outlined. This method, which is called asynchronous WAM (AWAM), enables calculation of the geographical position of an aircraft without knowledge of relative time differences (RTDs) between measuring ground stations (sensors). The AWAM method is based on the measurement of round trip times (RTTs) between the aircraft and the serving ground station,...
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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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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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Simulating propagation of coherent light in random media using the Fredholm type integral equation
PublikacjaStudying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g....