The paper deals with a non-linear problem of long water waves approaching a sloping beach. In order to describe the phenomenon we apply the Lagrange’s system of material variables. With these variables it is much easier to solve boundary conditions, especially conditions on a shoreline. The formulation is based on the fundamental assumption for long waves propagating in shallow water of constant depth that vertical material lines of fluid particles remain vertical during entire motion of the fluid. The analysis is confined to one – dimensional case of unsteady water motion within a ’triangular’ body of fluid. The partial differential equations of fluid motion, obtained by means of a variational procedure, are then substituted by a system of equations resulting from a perturbation scheme with the second order expansion with respect to a small parameter. In this way the original problem has been reduced to a system of linear partial differential equations with variable coefficients. The latter equations are, in turn, substituted by a system of difference equations, which are then integrated in a discrete time space by means of the Wilson-µ method. The procedure developed in this paper may be a convenient tool in analysing non-breaking waves propagating in coastal zones of seas. Moreover, the model can also deliver useful results for cases when breaking of waves near a shoreline may be expected.
A new concept (notion) of the practical stability of positive fractional discrete-time linear systems is introduced. Necessary and sufficient conditions for the practical stability of the positive fractional systems are established. It is shown that the positive fractional systems are practically unstable if corresponding standard positive fractional systems are asymptotically unstable.
New tests (criterions) for checking the reachability and the observability of positive linear-discrete-time systems are proposed. The tests do not need checking of rank conditions of the reachability and observability matrices of the systems. Simple sufficient conditions for the unreachability and unobservability of the systems are also established.
A new class of positive fractional 2D hybrid linear systems is introduced. The solution of the hybrid system is derived. The classical Cayley-Hamilton theorem is extended for fractional 2D hybrid systems. Necessary and sufficient conditions for the positivity are established.
New frequency domain methods for stability analysis of linear continuous-time fractional order systems with delays of the retarded type are given. The methods are obtained by generalisation to the class of fractional order systems with delays of the Mikhailov stability criterion and the modified Mikhailov stability criterion known from the theory of natural order systems without and with delays. The study is illustrated by numerical examples of time-delay systems of commensurate and non-commensurate fractional orders.
Air core solenoids, possibly single layer and with significant spacing between turns, are often used to ensure low stray capacitance, as they are used as part of many sensors and instruments. The problem of the correct estimation of the stray capacitance is relevant both during design and to validate measurement results; the expected value is so low to be influenced by any stray capacitance of the external measurement instrument. A simplified method is proposed that does not perturb the stray capacitance of the solenoid under test; the method is based on resonance with an external capacitor and on the use of a linear regression technique.
The positivity of fractional descriptor linear continuous-time systems is investigated. The solution to the state equation of the systems is derived. Necessary and sufficient conditions for the positivity of fractional descriptor linear continuous-time systems are established. The considerations are illustrated by numerical examples.
The concept of strong stability is extended for positive and compartmental linear systems. It is shown that: 1) the asymptotically stable positive and compartmental systems are strongly stable if the eigenvalues of the system matrix are distinct, 2) electrical circuits consisting of resistances, capacitances (inductances) and source voltages are strongly stable.
A new soft-fault diagnosis approach for analog circuits with parameter tolerance is proposed in this paper. The approach uses the fuzzy nonlinear programming (FNLP) concept to diagnose an analog circuit under test quantitatively. Node-voltage incremental equations, as constraints of FNLP equation, are built based on the sensitivity analysis. Through evaluating the parameters deviations from the solution of the FNLP equation, it enables us to state whether the actual parameters are within tolerance ranges or some components are faulty. Examples illustrate the proposed approach and show its effectiveness.
This work presents the studies on the electrochemical process of thin palladium layers formation onto electrodeposited cobalt coatings. The suggested methodology consists of the preparation of thick and smooth cobalt substrate via galvanostatic electrodeposition. Cobalt coatings were prepared under different cathodic current density conditions from acidic bath containing cobalt sulphate and addition of boric acid. Obtained cobalt layers were analyzed by x-ray diffraction to determine their phase composition. Freshly prepared cobalt coatings were modificated by the galvanic displacement method in PdCl2 solution, to obtain smooth and compact Pd layer. The comparison of electrocatalytic properties of Co coatings with Co/Pd ones enabled to determine the influence of Palladium presence in cathodic deposits on the hydrogen evolution process.
In the paper finite-dimensional time-variable dynamical control systems described by linear stochastic ordinary differential state equations with single time-variable point delay in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems necessary and sufficient conditions for different kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems are also presented.
The paper deals with the problems of designing observers and unknown input observers for discrete-time Lipschitz non-linear systems. In particular, with the use of the Lyapunov method, three different convergence criteria of the observer are developed. Based on the achieved results, three different design procedures are proposed. Then, it is shown how to extend the proposed approach to the systems with unknown inputs. The final part of the paper presents illustrative examples that confirm the effectiveness of the proposed techniques. The paper also presents a MATLAB® function that implements one of the design procedures.
In this paper, pole placement-based design and analysis of a free piston Stirling engine (FPSE) is presented and compared to the well-defined Beale number design technique. First, dynamic and thermodynamic equations governing the engine system are extracted. Then, linear dynamics of the free piston Stirling engine are studied using dynamic systems theory tools such as root locus. Accordingly, the effects of variations of design parameters such as mass of pistons, stiffness of springs, and frictional damping on the locations of dominant closed-loop poles are investigated. The design procedure is thus conducted to place the dominant poles of the dynamic system at desired locations on the s-plane so that the unstable dynamics, which is the required criterion for energy generation, is achieved. Next, the closed-loop poles are selected based on a desired frequency so that a periodical system is found. Consequently, the design parameters, including mass and spring stiffness for both power and displacer pistons, are obtained. Finally, the engine power is calculated through the proposed control-based analysis and the result is compared to those of the experimental work and the Beale number approach. The outcomes of this work clearly reveal the effectiveness of the control-based design technique of FPSEs compared to the well-known approaches such as Beale number.
The determination of the form of a probability density function (PDF3) of diameters for nodular particles by using a probability density function (PDF2), which form is empirically estimated from cross-sections of these nodules in a metallographic specimen, can be regarded as a special case of Wicksell's corpuscle problem (WCP). The estimation of the PDF3 for the nodular particles provides information about the kinetics of these particles nucleation, and so about the kinetics of their growth. This information is essential for building more accurate mathematical models of the alloy crystallization. In the paper there are presented two derivations of the methods used for the estimation of the PDF3 form. The first method bases on diameters received from a planar cross-section. The second one uses also data from the planar cross-section but not the diameters only chords. Both methods provide practical rules for the analysis of the empirical diameters’ and chord’s size distribution and allow to estimate the mean value of the external surface area of the particles.
Landfill leachate makes a potential source of ground water pollution. Municipal waste landfill substratum can be used for removal of pollutants from leachate. Model research was performed with use of a sand bed and artificially prepared leachates. Effectiveness of filtration in a bed of specific thickness was assessed based on the total solids content. Result of the model research indicated that the mass of pollutants contained in leachate filtered by a layer of porous soil (mf) depends on the mass of pollutants supplied (md). Determined regression functions indicate agreement with empirical values of variable m′f. The determined regression functions allow for qualitative and quantitative assessment of influence of the analysed independent variables (m′d, l, ω) on values of mass of pollutants flowing from the medium sand layer. Results of this research can be used to forecast the level of pollution of soil and underground waters lying in the zone of potential impact of municipal waste landfill.
In this paper, we propose a concept of a continuous-time filter of constant component that exhibits a very short response in the time domain if compared to the traditional time-invariant filter. The improvement of the filter dynamics was achieved as a result of the time-varying parameters which were introduced to the filter structure. Such a designed filter is then applied in a system which switches many distorted signals which should be filtered as fast as possible. The paper is of review nature and presents both a theoretical background of the proposed filter and the results of simulations.
The minimum energy control problem for the positive descriptor discrete-time linear systems with bounded inputs by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the positivity and reachability of descriptor discrete-time linear systems are given. Conditions for the existence of solution and procedure for computation of optimal input and the minimal value of the performance index is proposed and illustrated by a numerical example.
The work deals with the heat analysis of generalized Burgers nanofluid over a stretching sheet. The Rosseland approximation is used to model the non-linear thermal radiation and incorporated non-uniform heat source/sink effect. The governing equations reduced to a set of nonlinear ordinary differential equations under considering the suitable similarity transformations. The obtained ordinary differential equations equations are solved numerically by Runge-Kutta-Fehlberg order method. The effect of important parameters on velocity, temperature and concentration distributions are analyzed and discussed through the graphs. It reveals that temperature increases with the increase of radiation and heat source/sink parameter.
Following the results presented in , we present an efficient approach to the Schur parametrization/modeling of a subclass of second-order time-series which we term p-stationary time-series, yielding a uniform hierarchy of algorithms suitable for efficient implementations and being a good starting point for nonlinear generalizations to higher-order non-Gaussian nearstationary time-series.
We studied the thermophilous grass Bromus erectus in Central Europe to determine its pattern of population genetic structure and genetic diversity, using ISSR-PCR fingerprinting to analyze 200 individuals from 37 populations. We found three genetic groups with a clear geographic structure, based on a Bayesian approach. The first group occurred west and south of the Alps, the second east and north of the Alps, and the third was formed by four genetically depauperated populations in Germany. The populations from Germany formed a subset of the Bohemian-Moravian populations, with one private allele. Two differentiation centers, one in the Atlantic- Mediterranean and the second in the Pannonian-Balkan area, were recognized by species distribution modeling. The geographic distribution of the genetic groups coincides with the syntaxonomic split of the Festuco-Brometea class into the Festucetalia valesiaceae and Brometalia erecti orders. We found a statistically significant decrease in mean ISSR bands per individual from south to north, and to a lesser extent from the east to west. The former was explained by Holocene long-distance migrations from southern refugia, the latter by the difference in the gradient of anthropopression. We hypothesize a cryptic northern shelter of the species in Central Europe in the putative Moravian-Bohemian refugium.
A novel design of a circuit used for NTC thermistor linearization is proposed. The novelty of the proposed design consists in a specific combination of two linearization circuits, a serial-parallel resistive voltage divider and a two-stage piecewise linear analog-to-digital converter. At the output of the first linearization circuit the quasi-linear voltage is obtained. To remove the residual voltage nonlinearity, the second linearization circuit, i.e., a two-stage piecewise linear analog-to-digital converter is employed. This circuit is composed of two flash analog-to-digital converters. The first analog-to-digital converter is piecewise linear and it is actually performing the linearization, while the second analog-to-digital converter is linear and it is performing the reduction of the quantization error introduced by the first converter. After the linearization is performed, the maximal absolute value of a difference between the measured and real temperatures is 0.014°C for the temperature range between −25 and 75°C, and 0.001°C for the temperature range between 10 and 40°C.
A complete parametric approach is proposed for the design of the Luenberger type function Kx observers for descriptor linear systems. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, parametric expressions for all the coefficient matrices of the observer are derived. The approach provides all the degrees of design freedom, which can be utilized to achieve some additional design requirements. An illustrative example shows the effect of the proposed approach.