High-Frequency Features in the Distribution of Relaxation Times Related to Frequency Dispersion Effects in SOFCs

Electrochemical impedance spectroscopy (EIS) is commonly used for the characterization of electrochemical systems, such as solid oxide fuel cells (SOFCs). In recent years, the distribution of relaxation times (DRT) analysis has attracted increasing interest as a tool for investigating electrochemical loss mechanisms in fuel cells due to its ability to resolve electrochemical features that overlap in complex planes. Among the methods used for the deconvolution of the distribution function of relaxation times, DRTtools is commonly used due to its user-friendly graphical user interface. In this study, we investigate the root cause of the expression of additional DRT features in the high-frequency range and link them to characteristic properties of the processes that contribute to the polarization loss of SOFCs. Identification of the root cause leading to the expression of the features is performed by conducting a simulation study with synthetic EIS spectra that are then analyzed using DRTtools. It has been shown that the constant phase element behavior of high-frequency processes in SOFCs is the root cause of the expression of additional peaks in the high-frequency range of the DRT.

Complex Entropy and Its Application in Decision-Making for Medical Diagnosis

In decision-making systems, how to measure uncertain information remains an open issue, especially for information processing modeled on complex planes. In this paper, a new complex entropy is proposed to measure the uncertainty of a complex-valued distribution (CvD). The proposed complex entropy is a generalization of Gini entropy that has a powerful capability to measure uncertainty. In particular, when a CvD reduces to a probability distribution, the complex entropy will degrade into Gini entropy. In addition, the properties of complex entropy, including the nonnegativity, maximum and minimum entropies, and boundedness, are analyzed and discussed. Several numerical examples illuminate the superiority of the newly defined complex entropy. Based on the newly defined complex entropy, a multisource information fusion algorithm for decision-making is developed. Finally, we apply the decision-making algorithm in a medical diagnosis problem to validate its practicability.

Exceptional nexus with a hybrid topological invariant

Branch-point singularities known as exceptional points (EPs), which carry a nonzero topological charge, can emerge in non-Hermitian systems. We demonstrate with both theory and acoustic experiments an “exceptional nexus” (EX), which is not only a higher-order EP but also the cusp singularity of multiple exceptional arcs (EAs). Because the parameter space is segmented by the EAs, the EX possesses a hybrid topological invariant (HTI), which consists of distinct winding numbers associated with Berry phases accumulated by cyclic paths on different complex planes. The HTI is experimentally characterized by measuring the critical behaviors of the wave functions. Our findings constitute a major advance in the fundamental understanding of non-Hermitian systems and their topology, possibly opening new avenues for applications.

TOPOLOGICAL PROPERTIES OF FRACTAL JULIA SETS RELATED TO THE SIGNS OF REAL AND REACTIVE ELECTRIC POWERS

This paper focuses on applying fractal Julia sets to observe the topological properties related to the signs of the real and reactive electric powers. To perform this, different power combinations were used to represent the fractal diagrams with an algorithm that considers the mathematical model of Julia sets. The study considers three cases: the first study considers the change of real power when the reactive power is fixed; the second study deals with the change of the reactive power when the real power is fixed; and finally, the third study contemplates that both real and reactive powers change. Furthermore, the fractal diagrams of the power in the four quadrants of the complex plane are studied to identify the topological properties for each sign. A qualitative analysis of the diagrams helps identify that complex power loads present some fractal graphic patterns with respect to the signs considered in the different quadrants of the complex planes. The diagrams represented in the complex planes save a relation in the forms and structure with other points studied, concluding that the power is related to other figures in other quadrants. Thus, this result allows a new study of the behavior of power in an electrical circuit by showing a clear relation of the different fractal diagrams obtained by the Julia sets.

Formulation of dynamical theory of X-ray diffraction for perfect crystals in the Laue case using the Riemann surface

The dynamical theory for perfect crystals in the Laue case was reformulated using the Riemann surface, as used in complex analysis. In the two-beam approximation, each branch of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg condition and the reflection strength. By representing these parameters on complex planes, these characteristics can be graphically depicted on the Riemann surface. In the conventional case, the absorption is small and the real part of the reflection strength is large, so the formulation is the same as the traditional analysis. However, when the real part of the reflection strength is small or zero, the two branches of the dispersion surface cross, and the dispersion relationship becomes similar to that of the Bragg case. This is because the geometrical relationships among the parameters are similar in both cases. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters. Furthermore, the present method analytically revealed many characteristic features of the dispersion surface and will be quite instructive for further numerical calculations of rocking curves.

Vibration Testing

This chapter deals with vibration testing, which aims to identify inclusions, cracks, or shape changes in a structure by measuring its modal characteristics. The measured eigenparameters are related to the defect or damage location, orientation, and size. The chapter derives asymptotic formulas for eigenvalue perturbations due to small inclusions, cracks, and shape deformations. The main ingredients in deriving the results are the integral equations and the theory of meromorphic operator-valued functions. Using integral representations of solutions to the harmonic oscillatory linear elastic equation, this problem is reduced to the study of characteristic values of integral operators in the complex planes. The chapter focuses on three kinds of elastic inclusions: holes, hard inclusions, and soft inclusions.