Corrosion Activity of Carbon Steel B450C and Low Chromium Ferritic Stainless Steel 430 in Chloride-Containing Cement Extract Solution

The carbon steel B450C and low chromium SS 430 ferritic samples were exposed for 30 days to chloride-containing (5 g L−1 NaCL) cement extract solution. The initial pH ≈ 13.88 decreased to pH ≈ 9.6, associated mainly with the consumption of OH− ions and the formation of γ-FeOOH, α-FeOOH, Fe3O4 and Cr(OH)3, as suggested by XRD and XPS analysis, in the presence of CaCO3 and NaCl crystals. The deep corrosion damages on B450C were observed around particles of Cu and S as local cathodes, while the first pitting events on the SS 430 surface appeared after 30 days of exposure. The change in the activity of each type of steel was provided by the potentiodynamic polarization curves (PDP). Two equivalent electrical circuits (EC) were proposed for quantitative analysis of EIS (Nyquist and Bode diagrams). The calculated polarization resistance (Rp), as an indicator of the stability of passive films, indicated that SS 430 presented relatively constant values, being two-three orders of magnitude higher than those of the carbon steel B450C. The calculated thickness (d) of the SS 430 passive layers was ≈0.5 nm and, in contrast, that of the B450C passive layers tends to disappear after 30 days.

Riemann Zeta Based Surge Modelling of Continuous Real Functions in Electrical Circuits

Riemann zeta is defined as a function of a complex variable that analytically continues the sum of the Dirichlet series, when the real part is greater than unity. In this paper, the Riemann zeta associated with the finite energy possessed by a 2mm radius, free falling water droplet, crashing into a plane is considered. A modified zeta function is proposed which is incorporated to the spherical coordinates and real analysis has been performed. Through real analytic continuation, the single point of contact of the drop at the instant of touching the plane is analyzed. The zeta function is extracted at the point of destruction of the drop, where it defines a unique real function. A special property is assumed for some continuous functions, where the function’s first derivative and first integral combine together to a nullity at all points. Approximate reverse synthesis of such a function resulted in a special waveform named the dying-surge. Extending the proposed concept to general continuous real functions resulted in the synthesis of the corresponding function’s Dying-surge model. The Riemann zeta function associated with the water droplet can also be modeled as a dying–surge. The Dying- surge model corresponds to an electrical squeezing or compression of a waveform, which was originally defined over infinite arguments, squeezed to a finite number of values for arguments placed very close together with defined final and penultimate values. Synthesized results using simulation software are also presented, along with the analysis. The presence of surges in electrical circuits will correspond to electrical compression of some unknown continuous, real current or voltage function and the method can be used to estimate the original unknown function.

Deep Learning Neural Network Algorithm for Computation of SPICE Transient Simulation of Nonlinear Time Dependent Circuits

In this paper, a special method based on the neural network is presented, which is conveniently used to precompute the steps of numerical integration. This method approximates the behaviour of the numerical integrator with respect to the local truncation error. In other words, it allows the precomputation of the individual steps in such a way that they do not need to be estimated by an algorithm but can be directly estimated by a neural network. Experimental tests were performed on a series of electrical circuits with different component parameters. The method was tested for two integration methods implemented in the simulation program SPICE (Trapez and Gear). For each type of circuit, a custom network was trained. Experimental simulations showed that for well-defined problems with a sufficiently trained network, the method allows in most cases reducing the total number of iteration steps performed by the algorithm during the simulation computation. Applications of this method, drawbacks, and possible further optimizations are also discussed.

Study of electrical circuits using Runge Kutta method of order 4

In this paper, Runge Kutta method of order 4 is used to study the electrical circuits designs through past, intermediate and present voltages. When integrating differential equations with Runge Kutta method of order 4, a constant step size (ℎ) is used until a testing procedure confirms that the discontinuity occurs in the present integration interval. This step size function calculations would take place at the end of the functional calculations, but before the dependent variables were updated. Runge Kutta methods along with convolution are given by array interpretation (Butcher matrix) representation, this leads to identify the equilibrium state. The input parameters indicate the voltage coefficient controlled by current sources and measures it a random periodic time. The output parameters provide stable independent values and calculated from past voltage and current values. Finally solutions are compared with exact values and RK method of order 4 along with Heun, Midpoint and Taylors’s method with various ℎ values.

Comparative analyses of electrical circuits with conventional and revisited definitions of circuit elements: a fractional conformable calculus approach

Purpose The purpose of this paper is to comparatively analyze the electrical circuits defined with the conventional and revisited time domain circuit element definitions in the context of fractional conformable calculus and to promote the combined usage of conventional definitions, fractional conformable derivative and conformable Laplace transform. Design/methodology/approach The RL, RC, LC and RLC circuits described by both conventional and revisited time domain circuit element definitions has been analyzed by means of the fractional conformable derivative based differential equations and conformable Laplace transform. The comparison among the obtained results and those based on the methodologies adopted in the previous works has been made. Findings The author has found that the conventional definitions-based solution gives a physically reasonable result unlike its revisited definitions-based counterpart and the solutions based on those previous methodologies. A strong agreement to the time domain state space concept-based solution can be observed. The author has also shown that the scalar valued solution can be directly obtained by singularity free conformable Laplace transform-based methodology unlike such state space concept based one. Originality/value For the first time, the revisited time domain definitions of resistance and inductance have been proposed and applied together with the revisited definition of capacitance in electrical circuit analyses. The advantage of the combined usage of conventional time definitions, fractional conformable derivative and conformable Laplace transform has been suggested and the impropriety of applying the revisited definitions in circuit analysis has been pointed out.

Geometric Algebra Framework Applied to Circuits with Non-sinusoidal Voltages and Currents

We apply a well known technique of theoretical physics, known as Geometric Algebra or Clifford algebra, to linear electrical circuits with non-sinusoidal voltages and currents. We rederive from the first principles the Geometric Algebra approach to the apparent power decomposition. The important new point consists in a choice of a natural convenient basis in the Clifford vector space which simplifies considerably the presentation. Thus we are able to derive a number of general results which are missing in the former papers. In particular, a natural correspondence with the Current Physical Components approach is shown.