Search
displaying 1000 best results Help
Search results for: NONLINEAR MUSKINGUM EQUATION
-
Examples of numerical simulations of two-dimensional unsaturated flow with VS2DI code using different interblock conductivity averaging schemes
PublicationFlow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions), water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighboring nodes or cells of the numerical...
-
The α-µ model of the multipath fading channel
Open Research DataThe dataset contains the results of simulations that are part of the research on modelling the multipath fading in the communication channel. The envelope of the α-µ fading process is generated using the Monte-Carlo simulation (MCS) in the LabVIEW programming environment.
-
Local buckling and initial post-buckling behaviour of channel member flange - analytical approach
PublicationThe local buckling and initial post-buckling behaviour of the cold-formed channel member flange is investigated. The governing nonlinear differential equation for axially compressed columns and beams undergoing pure bending is derived using the stationary total potential energy principle. The critical stress and initial post-buckling equilibrium path is determined by means of a perturbation approach. The results obtained allow...
-
RADIATION OF HIGH INTENSITY SOUND BY CIRCULAR DISC BY MEANS OF THE NUMERICAL METHOD
PublicationThe main goal of this paper is to find sound pressure distribution radiated by the circular piezoelectric disc that vibrates with the finite amplitude. There has been presented the pressure distribution close to the radiating surface. Also it is shown the sound pressure distribution in the 3D form. The mathematic modeling was carried out on the base of the nonlinear acoustic equation with the proper boundary condition. The axial...
-
About definition of modes and magnetosonic heating in a plasma’s flow: Especial cases of perpendicular and nearly perpendicular wave vector and magnetic field
PublicationDynamics of hydrodynamic perturbations in a plasma depend strongly on an angle between the wave vector and equilibrium straight magnetic field. The case of perpendicular propagation is especial. There are only two (fast) magnetosonic modes since two (slow) ones degenerate into the stationary one with zero speed of propagation. This demands individual definition of wave modes by the links of hydrodynamic relations. These links are...
-
DL_MG: A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution
PublicationThe solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential -- a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the...
-
Determination of t8/5 cooling times for underwater local dry welding of steel
PublicationKnowledge of thermal history is the basic condition for studying the structure - properties of welded joints. The determinant of thermal history is the thermal cycle, whose in-situ measurements are still a big challenge. Water as the welding environment complicates this issue even more. The article presents a method to determine an equation for calculating t8/5 cooling times for underwater gas metal arc welding of unalloyed steels...
-
The Dynamic Model of Magnetic Hysteresis
PublicationThis paper presents the scalar dynamic magnetic hysteresis model based on the Preisach theory. The important role in this theory played hysteresis operator states. The changes of these operators` states are not immediate in the dynamic model but they are a function of time and parameter k representing the magnetic properties of the material. In this paper the transient state of the hysteresis operator is defined by the nonlinear...
-
Verification of Formulas for Periods of Adjacent Buildings Used to Assess Minimum Separation Gap Preventing Structural Pounding during Earthquakes
PublicationInsufficient separation distance between adjacent buildings may lead to serious damages during earthquakes due to structural pounding. The best way to prevent collisions is to provide sufficiently large separation distance between the structures. In this paper, the periods of two closely-spaced linear and nonlinear buildings have been investigated so as to accurately assess the minimum in-between separation gap. A new equation...
-
HYGRO-MAGNETIC VIBRATION OF THE SINGLE-WALLED CARBON NANOTUBE WITH NONLINEAR TEMPERATURE DISTRIBUTION BASED ON A MODIFIED BEAM THEORY AND NONLOCAL STRAIN GRADIENT MODEL
PublicationIn this study, vibration analysis of single-walled carbon nanotube (SWCNT) has been carried out by using a refined beam theory, namely one variable shear deformation beam theory. This approach has one variable lesser than a contractual shear deformation theory such as first-order shear deformation theory (FSDT) and acts like classical beam approach but with considering shear deformations. The SWCNT has been placed in an axial or...
-
Solving Boundary Value Problems for Second Order Singularly Perturbed Delay Differential Equations by ε-Approximate Fixed-Point Method
PublicationIn this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by cubic spline vh defined by its values vi = vh(ti) at grid points ti, i = 0, 1, ... ,N. The necessary for construction the cubic spline and missing the first derivatives at the boundary...
-
On the generalized model of shell structures with functional cross-sections
PublicationIn the present study, a single general formulation has been presented for the analysis of various shell-shaped structures. The proposed model is comprehensive and a variety of theories can be used based on it. The cross-section of the shell structure can be arbitrarily analyzed with the presented equations. In other words, various types of shell structures, including cylindrical, conical, spherical, elliptical, hyperbolic, parabolic,...
-
Acoustic streaming caused by some types of aperiodic sound. Buildup of acoustic streaming
PublicationThe analysis of streaming caused by aperiodic sound of different types (switched on at transducer sound or sound determined by initial conditions) is undertaken. The analysis bases on analytical governing equation for streaming Eulerian velocity, which is a result of decomposition of the hydrodynamic equations into acoustic and non-acoustic parts. Its driving force (of acoustic nature) represents a sum of two terms; one is the...
-
Coupled Urban Areas Inundation Model with Interaction Between Storm Water System and Surface Flow - Case Study of Sea Level Impact on Seaside Areas Flooding
PublicationInundations are becoming more frequent than ever. What is connected with increasing area of impervious surface in cities. This makes predicting urban flooding and its scale especially important. At the seaside we observe additional conditions such as sea level that makes accurate numerical modelling of issue even harder. With complex approach to the matter which is simultaneous calculation of storm water conduit flow and overland...
-
The lognormal model of the multipath fading channel
Open Research DataThe dataset contains the results of simulations that are part of the research on modelling the multipath fading in the communication channel. The lognormal fading envelope is generated using the Monte-Carlo simulation (MCS) in the LabVIEW programming environment.
-
Infiltration in a double-porosity medium: Experiments and comparison with a theoretical model
PublicationThis paper presents experimental verification of the mathematical model of unsaturated flow in double‐porosity soils developed by the asymptotic homogenization method. A series of one‐dimensional infiltration experiments was carried out in a column filled with a double‐porosity medium composed of a mixture of sand and sintered clayey spheres arranged in a periodic manner. The unsaturated hydraulic properties of each porous material...
-
Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
-
Equivariant Morse equation
PublicationThe paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
-
High performance super-twisting sliding mode control for a maritime autonomous surface ship (MASS) using ADP-Based adaptive gains and time delay estimation
PublicationThis research addresses two kinds of problems related to optimal trajectory tracking of a Maritime Autonomous Surface Ship (MASS): those caused by the time-varying external disturbances including winds, waves and ocean currents as well as those resulting from inherent dynamical uncertainties. As the paper shows, an accurate and robust optimal controller can successfully deal with both issues. An improved Optimal Adaptive Super-Twisting...
-
Solubility Characteristics of Acetaminophen and Phenacetin in Binary Mixtures of Aqueous Organic Solvents: Experimental and Deep Machine Learning Screening of Green Dissolution Media
PublicationThe solubility of active pharmaceutical ingredients is a mandatory physicochemical characteristic in pharmaceutical practice. However, the number of potential solvents and their mixtures prevents direct measurements of all possible combinations for finding environmentally friendly, operational and cost-effective solubilizers. That is why support from theoretical screening seems to be valuable. Here, a collection of acetaminophen...
-
High performance super-twisting sliding mode control for a maritime autonomous surface ship (MASS) using ADP-Based adaptive gains and time delay estimation
PublicationThis research addresses two kinds of problems related to optimal trajectory tracking of a Maritime Autonomous Surface Ship (MASS): those caused by the time-varying external disturbances including winds, waves and ocean currents as well as those resulting from inherent dynamical uncertainties. As the paper shows, an accurate and robust optimal controller can successfully deal with both issues. An improved Optimal Adaptive Super-Twisting...
-
Novel analysis methods of dynamic properties for vehicle pantographs
PublicationTransmission of electrical energy from a catenary system to traction units must be safe and reliable especially for high speed trains. Modern pantographs have to meet these requirements. Pantographs are subjected to several forces acting on their structural elements. These forces come from pantograph drive, inertia forces, aerodynamic effects, vibration of traction units etc. Modern approach to static and dynamic analysis should...
-
Wear of electroplated diamond tools in lap-grinding of Al2O3 ceramic materials
PublicationCurrent development of modern products, together with ever-increasing demands for their operation and usage, necessitate the search for new processing methods. Abrasive machining is widely used in many industrial areas, especially for processing difficult-to-machine materials such as advanced ceramics. Grinding with lapping kinematics, also called lap-grinding, is still one of the innovative methods of abrasive processing being...
-
Topological Methods in Nonlinear Analysis
Journals -
Newton’s Method for the McKendrick-von Foerster Equation
PublicationIn the paper we study an age-structured model which describes the dynamics of one population with growth, reproduction and mortality rates. We apply Newton’smethod to the McKendrick-von Foerster equation in the semigroup setting. We prove its first- and second-order convergence.
-
Thermal ablation modeling via bioheat equation
PublicationWe consider Pennes’ bioheat equation and discuss an implicit numerical scheme which has better stability properties than other approaches. Our discussion concerns Carthesian geometry problems, however it carries over to spherical geometry models and more complicated shapes.
-
Straightened characteristics of McKendrick-von Foerster equation
PublicationWe study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...
-
Nonlinear planar modeling of massive taut strings travelled by a force-driven point-mass
PublicationThe planar response of horizontal massive taut strings, travelled by a heavy point-mass, either driven by an assigned force, or moving with an assigned law, is studied. A kinematically exact model is derived for the free boundary problem via a variational approach, accounting for the singularity in the slope of the deflected string. Reactive forces exchanged between the point-mass and the string are taken into account via Lagrange...
-
Nonlinear Properties of Seawater as a Factor Determining Nonlinear Wave Propagation
PublicationTaking practical advantage of nonlinear acoustical interactions occurring in seawater [1, 2] requires knowledge of the parameter of nonlinearity B=A of this medium. The literature does not offer much reports on B=A parameter value for seawater. In the few papers concerning that address the issue, results concerning ocean waters with high salinity and at large depths are given [3], while studies concerning seawater with low salinity...
-
Nonlinear Viscoelastic Properties of Polyurethane Nanocomposites
PublicationIn recent years, the nonlinear viscoelastic behaviors of elastomeric nanocomposites have been examined, especially for a wide range of rubbery composite (including natural rubber) materials. This chapter describes the influence of fillers and nanofillers on the nonlinear viscoelastic properties of elastomeric polyurethane systems. These filled elastomers (similar to the classic natural rubber reinforced elastomers), also exhibit...
-
KOLMOGOROV EQUATION SOLUTION: MULTIPLE SCATTERING EXPANSION AND PHOTON STATISTICS EVOLUTION MODELING
PublicationWe consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon...
-
Thermal ablation modeling via the bioheat equation and its numerical treatment
PublicationThe phenomenon of thermal ablation is described by Pennes’ bioheat equation. This model is based on Newton’s law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.
-
Nonlinear properties of the Gotland Deep – Baltic Sea
PublicationThe properties of the nonlinear phenomenon in water, including sea water, have been well known for many decades. The feature of the non homogeneous distribution of the speed of sound along the depth of the sea is very interesting from the physical and technical point of view. It is important especially in the observation of underwater area by means of acoustical method ( Grelowska et al ., 2013; 2014). The observation of the underwater...
-
Considerations about the applicability of the Reynolds equation for analyzing high-speed near field levitation phenomena
Publicationequation for analyzing near field levitation (NFL) phenomena. Two separate approaches were developed, experimentally verified, and applied to meet the research objective. One was based on the Reynolds equation and the other was based on general conservation equations for fluid flow solved using computational fluid dynamic (CFD). Comparing the calculation results revealed that, for certain operating conditions, differences in the...
-
The nonlinear effects of sound in a liquid with relaxation losses
PublicationThe nonlinear effects of sound in electrolyte with a chemical reaction are examined. The dynamic equations that govern non-wave modes in the field of intense sound are derived, and acoustic forces of vortex, entropy, and relaxation modes are determined in the cases of low-frequency sound and high-frequency sound. The difference in the nonlinear effects of sound in electrolyte and in a gas with excited vibrational degrees of molecules,...
-
Impact of the Finite Element Mesh Structure on the Solution Accuracy of a Two-Dimensional Kinematic Wave Equation
PublicationThe paper presents the influence of the finite element mesh structure on the accuracy of the numerical solution of a two-dimensional linear kinematic wave equation. This equation was solved using a two-level scheme for time integration and a modified finite element method with triangular elements for space discretization. The accuracy analysis of the applied scheme was performed using a modified equation method for three different...
-
A Nonlinear Model of a Mesh Shell
PublicationFor 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...
-
Generation and Propagation of Nonlinear Waves in a Towing Tank
PublicationThe 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...
-
Systems of Nonlinear Fractional Differential Equations
PublicationUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.
-
On the geometrically nonlinear vibration of a piezo-flexomagnetic nanotube
PublicationIn order to describe the behavior of thin elements used in MEMS and NEMS, it is essential to study a nonlinear free vibration of nanotubes under complicated external fields such as magnetic environment. In this regard, the magnetic force applied to the conductive nanotube with piezo-flexomagnetic elastic wall is considered. By the inclusion of Euler-Bernoulli beam and using Hamilton’s principle, the equations governing the system...
-
Equation of state for Eu-doped SrSi2O2N2
Publication -
Approximated boundary conditions of the equation of difussion
PublicationProblem podejmowany w pracy dotyczy warunku brzegowego w równaniach fizyki matematycznej, opisujących procesy migracji zanieczyszczeń. W szczególności skoncentrowano się na badaniu wpływu na rozwiązanie przyjmowanych w rozwiązaniach numerycznych aproksymacji ''odpływowego'' warunku brzegowego w jednowymiarowym równaniu adwekcji - dyspersji. Rozważania teoretyczne przeprowadzono w oparciu o rozwiązania analityczne oraz numeryczne...
-
The application of Monod equation to denitrification kinetics description in the moving bed biofilm reactor (MBBR)
PublicationIn this paper, the kinetic constants Vmax and KCOD occurring in the Monod equation, which describe the denitrification process in the moving bed, are determined. For this purpose, a laboratory moving bed biofilm reactor (MBBR) was used. The filling of the reactor consisted of EvU Perl carriers. The experiment was carried out with an excess of nitrate, and denitrification rate was dependent on the concentration of external organic...
-
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Journals -
Numerical Solution of the Two-Dimensional Richards Equation Using Alternate Splitting Methods for Dimensional Decomposition
PublicationResearch on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated conditions is an essential part of water resource management and planning. In order to determine such subsurface flow, the two-dimensional (2D) Richards equation can be used. However,...
-
The application of nonlinear curvature sections in the turnout diverging track
PublicationThe paper presents the analytical method of modelling the diverging track of railway turnout with nonlinear curvature sections. These sections were used for smoothing the graph of curvature in the extreme areas of turnout. The problem of the curvature distribution was identified with the use of differential equations. The resulting solutions are of universal nature for example the ability of assuming any values of curvature at...
-
On nonlinear dilatational strain gradient elasticity
PublicationWe call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the...
-
Acceleration waves in the nonlinear micromorphic continuum
PublicationWithin the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortion tensor may undergo jump discontinuities. Here we obtain the acoustic tensor for...
-
Application of the Monte Carlo algorithm for solving volume integral equation in light scattering simulations
PublicationVarious numerical methods were proposed for analysis of the light scattering phenomenon. Important group of these methods is based on solving the volume integral equation describing the light scattering process. The popular method from this group is the discrete dipole approximation (DDA). DDA uses various numerical algorithms to solve the discretized integral equation. In the recent years, the application of the Monte Carlo (MC)...
-
Features of Nonlinear Sound Propagation in Vibrationally Excited Gases
PublicationWeakly nonlinear sound propagation in a gas where molecular vibrational relaxation takes place is studied. New equations which govern the sound in media where the irreversible relaxation may take place are derived and discussed. Their form depends on the regime of excitation of oscillatory degrees of freedom, equilibrium (reversible) or non-equilibrium (irreversible), and on the comparative frequency of the sound in relation to...