Application Of Difference Equations Research Articles

Comparative study on the equation of state of detonation products

The equation of state (EOS) for detonation products can predict explosive performance with basic information about density, enthalpy of formation, and elemental composition. However, to achieve higher prediction accuracy, it is necessary to select an appropriate EOS for the specific detonation parameters being calculated. To study the applicability of different equations of states for explosive products, five EOSs, Becker–Kistiakowsky–Wilson, Kihara–Hikita–Tanaka, Virial-Wu (VLW), Lennard-Jones–Devonshire (LJD), and Jacobs–Cowperthwaite–Zwisler (JCZ), were used to calculate the Hugoniot curve of nitrogen and the detonation performance of typical explosives. The calculation results show that all five EOSs can provide reasonably accurate predictions of the Hugoniot curve of nitrogen on the relative volume-pressure plane. Moreover, the EOSs can accurately predict the detonation velocity and pressure of explosives within a wide range of initial densities. When it comes to temperature calculations, LJD and JCZ demonstrate higher prediction accuracy. Additionally, the results indicate that VLW may not be suitable for calculating the overdriven detonation of explosives, particularly at higher pressures.

Research on actual or industrial applications of difference equations: a chimerical task?

Relationships between difference and differential equations are examined, to understand why the applications of the first to problems of real life, are not as well developed as the applications of the second. In this goal, a review of journals devoted to both types of equations is done, strengthened by the analysis of the MSC2020-Mathematics Subject Classification System. The screening of 296 Issues of the Journal of Difference Equations and Applications published since 1995 highlights that only a low ratio of the published papers are concerned with applications, even if this ratio is slightly increasing for 27 years. An analysis of first, what are possible relationships between actual problems and difference equations, and second, what could be an application of difference equations are discussed. Finally, some avenues of work to increase the number of applications are explored.

Dynamical properties of some rational systems of difference equations

We explore the equilibrium points, local and global dynamics, rate of convergence, instability and boundedness of positive solution of some rational systems of difference equations. As an application of difference equations in mathematical biology, we also explore the local dynamics about equilibrium points of the discrete‐time Levin's model. Finally, obtained results are verified numerically.

Investigating equations for measuring dissolved inorganic nutrient uptake in oligotrophic conditions

AbstractMultiple different equations have been used to quantify nutrient uptake rates from stable isotope tracer label incorporation experiments. Each of these equations implicitly assumes an underlying model for phytoplankton nutrient uptake behavior within the incubation bottle and/or pelagic environment. However, the applicability of different equations remains in question and uncertainty arising from subjective choices of which equation to use is never reported. In this study, I use two approaches to investigate the conditions under which different nutrient uptake equations should be used. First, I utilized a moderate‐complexity pelagic ecosystem model that explicitly models the δ15N values of all model compartments (NEMURO + 15N) to conduct simulated nitrate uptake and ammonium uptake incubations and quantify the accuracy of different nutrient uptake equations. Second, I used results of deckboard diel nutrient uptake experiments to quantify the biases of 24‐h incubations relative to six consecutive 4‐h incubations. Using both approaches, I found that equations that account for nutrient regeneration (i.e., isotope dilution) are more accurate than equations that do not, particularly when nutrient concentrations are low but uptake is relatively high. Furthermore, I find that if the goal is to estimate in situ uptake rates it is appropriate to use an in situ correction to standard equations. I also present complete equations for quantifying uncertainty in nutrient uptake experiments using each nutrient uptake equation and make all of these calculations available as Excel spreadsheets and Matlab scripts.

Оценка применимости различных уравнений состояния реального газа для этилена

Оценка применимости различных уравнений состояния реального газа для этилена

МЕТОД КОНТРОЛЯ СОСТОЯНИЯ КАТУШЕК ИНДУКТИВНОСТИ В ИЗМЕРИТЕЛЯХ ПАРАМЕТРОВ ВЯЗКИХ СРЕД

Method for monitoring of inductance coils (actuating and measuring) state in gauges is proposed. Discrete representation of processes running in inductance coils is offered. Discrete inductance model is built. Difference equations describing operation principle of this model have been received and solution of these equations for this model is found. The application of difference equations and recurrence mathematical procedures for inductive structures analysis at breakdown of was justified. It was taken the features of breakdown of the basic homogeneous topology and topology inductor model

Applicability of different equations in modeling the thermodynamic and transport properties of aqueous and non-aqueous ionic liquid solutions

Applicability of different electrolyte based models has been tested in correlating the osmotic coefficient values of aqueous and nonaqueous binary ionic liquid solutions considering both the complete and partial dissociation of the ionic liquids. In local composition models the sum of a long-range and a short-range term is used. When the partial dissociation of ionic liquid is considered, the Pitzer–Debye–Hückel and Fowler–Guggenheim equations were used to calculate the long-range electrostatic interaction. In the Fowler–Guggenheim equation, for calculating Debye inverse length the necessary degree of association has been determined from osmotic coefficient data by Chemical Model (CM1). The correlation equations for excess molar volume of the NRTL–NRF, mNRTL, NRF–Wilson and NRF–mNRTL models for ionic liquid or electrolyte solutions were also derived. The performance of these equations was compared with the other available models for correlating the excess molar volume of ionic liquid solutions. Taking into account of complete or partial dissociation of ionic liquids, fitting quality of solution viscosities of various ionic liquids were examined using the Eyring’s absolute rate theory and different electrolyte local composition models and Clegg–Pitzer equations.

Application of Difference Equations in Predictive Control Systems for DC-DC Converters

Application of Difference Equations in Predictive Control Systems for DC-DC Converters

Application of difference equations in divisibility

We present an easy applicable method which, for a large class of integer sequences A(n), shows when all their terms are divisible by a natural number m≠1.

Application of different equations to adsorption isotherms of phenolic compounds on activated carbons prepared from cork

Activated carbons were prepared from solid cork wastes by physical activation with carbon dioxide or steam, and chemical activation by impregnation with phosphoric acid. In this work we show the possibility of using these activated carbons for the adsorption of phenolic compounds from the aqueous phase. The materials present a different response to the adsorptives used ( p-nitrophenol, p-chlorophenol, p-cresol and phenol), depending on the type of activation and the parameters (burn-off, absolute concentration) used in each case. All the samples were capable of retaining the contaminants, with the best result being reached by the sample with higher burn-off and the worst with the carbonised, while intermediate values were reached with the remaining samples. The experimental isotherms were analysed with two and three parameters equations (Freundlich, Langmuir, Dubinin–Radushkevich–Kaganer and Redlich–Peterson). The results obtained from the application of the equations are similar in some aspects, but the degree of confidence is quite different. The best fit was achieved with the Redlich–Peterson equation, which can be explained by the fact that this has three adjustable parameters. However, overall the Freundlich and DRK equations appear to be more useful and provide parameters which can be correlated with the structural characteristics of the solids obtained from N 2 adsorption measurements.

Two-dimensional gas and vacancy solution approaches in the thermodynamic description of adsorption equilibrium

We present two approaches to description of the adsorption equilibrium in adsorbate–adsorbent systems, the treatment where the adsorbate is considered as a two-dimensional gas, and the treatment where the adsorbate and adsorbent form a solution where the adsorbate is the solute and vacancies play the role of the solvent. In the first case the application of different equations describing the state of a two-dimensional gas leads to some fundamental adsorption isotherm equations, for example, Henry, Volmer, Hill–deBoer, Fowler–Guggenheim, and Langmuir. In contrast, the application of different equations (existing in the theory of solutions) describing the activity of the solvent (e.g., the Wilson model or the model of Flory and Huggins) leads to some new adsorption equations and the assumption of the ideality of the solvent leads to the Langmuir adsorption isotherm. We present some new adsorption equations basing on the second method described above and on the Redlich–Kister and Wohl expansions. Assuming that the activity coefficients are given by the one-constant Margules equation, the two-constant Margules equation, the van Laar equation, the Wilson equation, and, finally, the Flory–Huggins equation, we derive the respective adsorption isotherm formulas. We also present the assumptions leading to the best-known adsorption equations derived applying the first method. The equation developed by Cochran et al. is also corrected, taking into account the fundamental assumptions of the Flory–Huggins theory.

Chemically and thermally resistant lanthanoid bititanate ferroelectrics

Studies of the sequence of phases and kinetics of solid state reactions have been made in the systems of some lanthanoid oxides (CeO2, PrO2, Nd2O3, Sm2O3, La2O3) and titanium oxide. Kinetics have been studied both under isothermal and non-isothermal conditions. Application of different equations to the systems is analyzed. All the bititanates examined are being formed above 1200-1500 K. Synthesis of the intermediate product of Ln2Ti2O5 at 1120 K is described by Kroeger-Ziegler equation. The bonding of Ln2O3 with TiO2 at 1470 K proceeds as cylindric phase boundary. Ln2Ti2O7 is formed at 1500-1600 K by bulk diffusion described by Ginstling-Braunstein equation.Production technology of lanthanoid bititanate ferroelectric material resistant to chemically aggressive media and high temperature (TKC470-810 = (1500-2000). 10-6 K-1) is presented.

Limitations of evaluation methods for inhibited oxidation based on chemiluminescence

The applicability of different equations based on chemiluminescence data by which the rate coefficient of the reaction between peroxy radicals and inhibitor molecules can be calculated has been investigated.

The Determination of Loop Invariants for Programs with Arrays

This paper describes a method for the generation of loop predicates (or invariant assertions) for programs operating on arrays. The technique described is an application of difference equations.

Electromagnetic Processes in AC/DC Power Converters: Part I -- General Equations of AC-DC AND/OR DC-AC Power Converters for Steady-State and Transient Processes

In this series of articles, an attempt is made to find and to discover a mathematical method for analysis of the electromagnetic processes in ac-dc and/or dc-ac converters. This method based on the application of difference equations, makes it possible to describe the behaviour of converters in steady-state and transient processes. Analysis is applied to full-wave and half-wave power converters regardless of their specific schemes. The project will include 3 articles in this series: 1) General equations of ac-dc power converters for steady-state and transient processes, 2) Transient processes of ac-dc power converters, 3) Steady-state processes of ac-dc power converters. This series is a result of the author's investigations, begun at the Academy of Sciences of the USSR in 1969 and finished at the Ben-Gurion University of the Negev in 1975. The first stage of investigation was based on [1, 2]. Some first results were published [3, 4].

Applicability of Unit Stream Power Equation

The usefulness of a sediment transport equation to engineering depends on its applicability to natural rivers. Data collected from six river stations are used to compare the applicability of different equations. These comparisons indicate that the dimensionless unit stream power equation is the one which can provide accurate predictions of total sediment discharge in natural rivers under diversified flow and sediment conditions. The limitations to which this dimensionless unit stream power equation can be applied are explained.

Spatial Differentiation and Integration by Coherent Optical-Correlation Method

Optical differentiation and integration are not only interesting from the standpoint of optical computation, but are also important in picture processing. Based on optical correlation, or convolution, and the applications of difference equations, a technique for synthesizing the differentiation and integration filters is presented. This technique compares favorably with other methods which now exist.

Some Applications of Difference Equations in Electrotechnics

Some Applications of Difference Equations in Electrotechnics

Erratum to : Some Applications of Difference Equations in Electrotechnics

Erratum to : Some Applications of Difference Equations in Electrotechnics