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Wyniki wyszukiwania dla: ENERGY 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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Examples of numerical simulations of two-dimensional unsaturated flow with VS2DI code using different interblock conductivity averaging schemes
PublikacjaFlow 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...
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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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Influence of heterogeneous air entry pressure on large scale unsaturated flow in porous media
PublikacjaThe paper presents numerical simulations of water infiltration in unsaturated porous media containing coarse-textured inclusions embed- ded in fine-textured background material. The calculations are performed using the two-phase model for water and air flow and a simplified model known as the Richards equation. It is shown that the Richards equation cannot correctly describe flow in the presence of heterogeneities. How- ever, its...
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Existence and uniqueness of solutions for single-population McKendrick-von Foerster models with renewal
PublikacjaWe study a McKendrick-von Foerster type equation with renewal. This model is represented by a single equation which describes one species which produces young individuals. The renewal condition is linear but takes into account some history of the population. This model addresses nonlocal interactions between individuals structured by age. The vast majority of size-structured models are also treatable. Our model generalizes a number...
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Numerical modelling and experimental verification of compressible squeeze film pressure
PublikacjaThe validity of using the Reynolds equation for compressible squeeze film pressure was tested with computational fluid dynamics (CFD). A squeeze film air bearing was instrumented with pressure sensors and non-contacting displacement probes to provide transient measurements of film thickness and pressure. The film thickness measurements also provided input parameters to the numerical prediction. However, numerical results showed...
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Analytical Buckling of FG Nanobeams on The Basis of A New One Variable First-Order Shear Deformation Beam Theory
PublikacjaIn this work, buckling analysis of functionally graded (FG) nanobeams based on a new refined beam theory has been analyzed. The beam is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new obtained beam theory has only one variable which lead to one equation similar to Euler beam theory and also is free of any shear correction factor. The...
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DL_MG: A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution
PublikacjaThe 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...
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ESTIMATING AVERSION TO RANK INEQUALITY UNDERLYING SELECTED ITALIAN INDICES OF INCOME INEQUALITY
PublikacjaIn this paper, we estimate aversion to rank inequality (ATRI) underlying selected Italian income inequality indices, I, notably the Pietra index, the Bonferroni index and the “new” Zenga index. We measure ATRI by the parameter v of the generalised Gini index G(v). ATRI is distinct from aversion to income inequality, as measured by parameter ε of Atkinson’s index A(ε). We propose eliciting v from the equation I = GE(v). As, in general,...
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Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
PublikacjaUsing the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...
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A Quasi-2D MOSFET Model — 2D-to-Quasi-2D Transformation
PublikacjaA quasi-two-dimensional (quasi-2D) representation of the MOSFET channel is proposed in this work. The representation lays the foundations for a quasi 2D MOSFET model. The quasi 2D model is a result of a 2D into quasi 2D transformation. The basis for the transformation are an analysis of a current density vector field and such phenomena as Gradual Channel Detachment Effect (GCDE), Channel Thickness Modulation Effect (CTME), and...
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublikacjaIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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Biomass estimation using a length-weight relationship in beetle larvae (Coleoptera: Aphodiidae, Histeridae, Hydrophilidae, Staphylinidae) obtained from cow dung
PublikacjaThis research enabled the relationship between length and dry body mass to be determined for 158 beetle larvaetaken from cow dung in north-eastern Poland. The larvae were divided into three morphological types, for which the power and linear function of the body length-weight relationship were determined. The linear regression equation characterizes the relationship between body weight and...
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Subcritical bifurcation of free elastic shell of biological cluster
PublikacjaIn this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...
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Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations
PublikacjaThe light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo (MC) algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present implementation...
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Calculations of labyrinth seals with and without diagnostic extraction in fluid-flow machines
PublikacjaLabyrinth seals are essential components of steam turbine unit constructions. Two types of labyrinth seals can be named, the first of which is the seal without diagnostic steam extraction, and the second – with extraction. The distribution of flow parameters along the packing is affected remarkably by the average seal clearance. The presence of diagnostic extraction leads to the equation system which is determinable and can be...
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Symmetry-Breaking Bifurcation for Free Elastic Shell of Biological Cluster, Part 2
PublikacjaWe will be concerned with a two-dimensional mathematical model for a free elastic shell of biological cluster. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of the shell of biological cluster may be found as solutions of a certain nonlinear functional-differential equation with several physical parameters. For each multiparameter this...
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NUMERICAL SIMULATION OF CRATER CREATING PROCESS IN DYNAMIC REPLACEMENT METHOD BY SMOOTH PARTICLE HYDRODYNAMICS
PublikacjaA theoretical base of SPH method, including the governing equations, discussion of importance of the smoothing function length, contact formulation, boundary treatment and finally utilization in hydrocode simulations are presented. An application of SPH to a real case of large penetrations (crater creating) into the soil caused by falling mass in Dynamic Replacement Method is discussed. An influence of particles spacing on method...
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Investigations On Water Circulation in Animal Sea-Water Basins – On the Example of Seals′ Breeding Pools
PublikacjaThis paper presents general comments concerning investigations on water circulation in animal breeding pools containing sea water. As an example are given results of computer simulation of water circulation in seals’ breeding pools situated in Marine Station at Hel, belonging to Oceanographic Institute, Gdansk University. A mathematical model of three main pools was prepared with taking into account their inflow and outflow water...
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Water uptake in protective organic coatings and its reflection in measured coating impedance
PublikacjaWater uptake in commercially available epoxy coating on mild steel using impedance spectroscopy and gravimetry was studied. The water content in the coating was determined using the Brasher-Kingsbury equation and various methods of coating capacitance calculation used in the literature. The obtained results were compared with reference gravimetric data. An overestimation of values obtained from impedance data in relation to gravimetric...
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Experimental and Numerical Analysis of Air Trapping in a Porous Medium with Coarse Textured Inclusions
PublikacjaThe paper presents a 2D upward infiltration experiment performed on a model porous medium consisting of fine sand background with two inclusions made of coarser sands. The purpose of the experiment was to investigate the effects of structural air trapping, which occurs during infiltration as a result of heterogeneous material structure. The experiment shows that a significant amount of air becomes trapped in each of the inclusions. Numerical...
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Directed pulse dynamics
PublikacjaIntroducing a projection method into a one-dimensional model of a pulse propagation in isotropic media, we derive and investigate a system of equation describing dynamics ultrashort pulses of opposite directions ofpropagation and ones with interaction of directed pulses with different polarization.
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Numerical Method for Stability Testing of Fractional Exponential Delay Systems
PublikacjaA numerical method for stability testing of fractional exponential systems including delays is presented in this contribution. We propose the numerical test of stability for a very general class of systems with a transfer function, which includes polynomials and exponentials of fractional powers of the Laplace variable s combined with delay terms. Such a system is unstable if any root of its characteristic equation, which usually...
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Experimental investigation of two-phase thermosyphon heat exchanger charged with acetone
PublikacjaThis paper presents thermal characteristics of prototype of a two-phase thermosyphon heat exchanger (TPTHEx) charged with acetone as a working fluid. The TPTHEx consists of two horizontal cylindrical vessels connected by two risers and a downcomer. Tube bundles placed in the lower and upper cylinders work as an evaporator and a condenser, respectively. The tested TPTHEx operates in a vacuum. Therefore, the working liquid is boiled...
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Parametric method applicable in assessing breakout force and time for lifting slender bodies from seabed
PublikacjaThe article presents a parametric method applicable in assessing the suction force of a slender body to the seabed, and prognosing the body extrication time. Along with the body weight in water, the information on the suction force is essential for assessing the force needed to lift the object from the seabed. Based on the Foda theory and the resulting integral equation, which relates the maximum suction force with basic parameters...
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Projecting procedure for meta-material fiber
PublikacjaWe would like to show new way of derivation evolution equation for short pulses in dielectric waveguide including one model of metamaterial waveguide. This derivation model rely on projecting to the orthogonal basis. In our case to orthogonal basis for cylindrical waveguide.
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Determination of t8/5 cooling times for underwater local dry welding of steel
PublikacjaKnowledge 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...
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Air trapping problem during infiltration on the large areas
PublikacjaThe process of flow modeling in unsaturated porous medium is often found in many fields of sciences: geology, fluid mechanics, thermodynamics, microbiology or chemistry. Problem is relatively complicated due to complexity of the system which contains three phases: water, air and soil skeleton. The flow of water in such a medium can be described using two-phase (2PH) flow formulation, which accounts the inflow of air and water phases,...
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Alternative convolution approach to friction in unsteady pipe flow
PublikacjaIn the paper some aspects of the unsteady friction in pipe flow expressed by the convolution are analyzed. This additional term introduced into the motion equation involves the accelerations of fluid occurring in the past and a weighting function. The essence of such approach is to assume the appropriate form of weighting function. However, until now no fully reliable formula for this function has been found. To avoid some inconveniences...
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A quasi-2D small-signal MOSFET model - main results
PublikacjaDynamic properties of the MOS transistor under small-signal excitation are determined by kinetic parameters of the carriers injected into the channel, i.e., the low-field mobility, velocity saturation, mobility at the quiescent-point (Q-point), longitudinal electric field in the channel, by dynamic properties of the channel, as well as by an electrical coupling between the perturbed carrier concentration in the channel and the...
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Verification of algorithms determining wave loads on support structure of wind turbine
PublikacjaThe offshore wind turbines require determination of wave loads on their support structure. This structure is fixed and, therefore, this problem is reduced to solving only the diffraction problem, which is determined by Laplace equation and conditions on the following boundaries: on the support structure, on the sea free surface and on its bottom, and at infinity on free surface. The linear problem was applied to determine the wave...
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Interaction between acoustic and non-acoustic mode in bubbly liquid
PublikacjaThe nonlinear interaction of acoustic and entropy modes in a bubbly liquid is the subject of investigation. Thedynamic equation governing an excess density of the entropy mode is derived. Nonlinearity and dispersion are the reasons forexcitation of the entropy mode. The nonlinear interaction of modes as a reason for bubble to grow due to sound, is discovered.Some numerical examples of the modes interactions are made.
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublikacjaIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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Nonlinear planar modeling of massive taut strings travelled by a force-driven point-mass
PublikacjaThe 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...
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MODELLING OF TOXIC COMPOUNDS EMISSION IN MARINE DIESEL ENGINE DURING TRANSIENT STATES AT VARIABLE PRESSURE OF FUEL INJECTION
PublikacjaTransient states are an important part of the spectrum of engine loads, especially the traction engines. In the case of marine diesel engines, transient states are of particular importance in reducing the analysis of motion units for special areas and maneuvering in port, the participation of transient states in the load spectrum significantly increases, also, the emission of toxic compounds from this period increases proportionally....
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TIME-AND-SPACE STRUCTURE OF FORCE-DRIVEN RIGID SPHEREWAVEFIELD
PublikacjaThis paper introduces a time-domain, causality-inspired description of a vector-source acoustic wavefield of arbitrary time evolution, where a sphere is a practical realisation of quasi-point contact surface without which a point force would not be able to exert an impact onto non-viscous fluid. At every space location, the resulting acoustic field is described by a pair of physical variables characterising the time evolution of...
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Verification of baffle factor for straight pipe flow
PublikacjaDuring the water disinfection devices designing, it is often assumed that the baffle factor for a straight pipe reactors is equal to one. It would be possible only for the plug flow, which is a simplified model of the flow and does not appear in real situations. The paper contains an equation which enables calculation of the real value of the baffle factor for the pipe flow.
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Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space
PublikacjaUsing the Mountain Pass Theorem, we establish the existence of periodic solution for Euler–Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.
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Numerical Test for Stability Evaluation of Analog Circuits
PublikacjaIn this contribution, a new numerical test for the stability evaluation of analog circuits is presented. Usually, if an analog circuit is unstable then the roots of its characteristic equation are localized on the right half-plane of the Laplace s- plane. Because this region is unbounded, we employ the bilinear transformation to map it into the unit disc on the complex plane. Hence, the existence of any root inside the unit disc...
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Simulations of air and water flow in a model dike during overflow experiments
PublikacjaFlow in flood dikes, earth dams, and embankments occurs in variably saturated conditions, with pores of the earth material filled partly with water and partly with air. In routine engineering analysis, the influence of pore air is neglected and the air pressure is assumed equal to atmospheric. In some circumstances, for example, during overtopping of the dike by water, the effect of pore air on water flow and stability of the structure...
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A facile method for Tauc exponent and corresponding electronic transitions determination in semiconductors directly from UV–Vis spectroscopy data
PublikacjaIn this work, a facile method allowing for estimation of the exponent in the Tauc equation directly from the UV–vis spectra is presented. It is based on the Taylor expansion of the logarithmic version of the Tauc equation. The Tauc exponent is calculated from the tangent slope of the absorption data. Knowledge of this coefficient provides information about the optical transition types and is used as an input for the calculations...
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Rhamnolipid CMC Prediction
PublikacjaRelationships between the purity, pH, hydrophobicity (log Kow) of the carbon substrate, and the critical micelle concentration (CMC) of rhamnolipid type biosurfactants (RL) were investigated using a quantitative structure–property relationship (QSPR) approach and are presented here for the first time. Measured and literature CMC values of 97 RLs, representing biosurfactants at different stages of purification, were considered....
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Numerical Simulations of Seepage in Dikes Using unsaturated and Two-Phase Flow Models
PublikacjaModeling of water flow in variably saturated porous media, including flood dikes, is often based on the Richards equation, which neglects the flow of pore air, assuming that it remains at constant atmospheric pressure. However, there is also evidence that the air flow can be important, especially when the connectivity between the pore air and atmospheric air is lost. In such cases a full two-phase air-water flow model should be...
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Oxidation kinetics of Zircaloy-4 alloy at 673 K determined by GDOES technique
PublikacjaOxidation of zirconium alloys is a process that takes place during the operation of nuclear reactors and is essential for assessing the durability of fuel claddings. The present study was aimed to determine the oxidation kinetics of the Zircaloy-4 alloy using GDOES (glow discharge optical emission spectroscopy) at temperature 673 K corresponding to the conditions of use of fuel pellets. The tests were performed on non-oxidized...
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Different types of solvability conditions for differential operators
PublikacjaSolvability conditions for linear differential equations are usually formulated in terms of orthogonality of the right-hand side to solutions of the homogeneous adjoint equation. However, if the corresponding operator does not satisfy the Fredholm property such solvability conditions may be not applicable. For this case, we obtain another type of solvability conditions, for ordinary differential equations on the real axis, and...
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Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator
PublikacjaWe consider a generalization of the Allen-Cahn type equation in divergence form $-\rm{div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$. This is more general than the usual Laplace operator. We prove the existence and regularity of heteroclinic solutions under standard ellipticity and $m$-growth conditions.
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Control of mass concentration of reagents by sound in a gas with nonequilibrium chemical reactions
PublikacjaThe weakly nonlinear dynamics of a chemically reacting gas is studied. Nonlinear interaction of acoustic and nonacoustic types of motion are considered. We decompose the base equations using the relationships of the gas-dynamic perturbations specific for every type of motion. The governing equation for the mass fraction of a reagent influenced by dominating sound is derived and discussed. The conclusions concern the equilibrium...
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Green function diagonal for a class of heat equations
PublikacjaA construction of the heat kernel diagonal is considered as element of generalized zeta function theory, which gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expressions of the Green function in the case of finite-gap potential coefficient of the heat equation are constructed. An algorithm and program for Mathematica are presented...
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Novel binary mixtures of alkanolamine based deep eutectic solvents with water - thermodynamic calculation and correlation of crucial physicochemical properties
PublikacjaThis paper demonstrates the assessment of physicochemical and thermodynamic properties of aqueous solutions of novel deep eutectic solvent (DES) built of tetrabutylammonium chloride and 3-amino-1-propanol or tetrabutylammonium bromide and 3-amino-1-propanol or 2-(methylamino)ethanol or 2-(butylamino)ethanol. Densities, speeds of sound, refractive indices, and viscosities for both pure and aqueous mixtures of DES were investigated...