Potential in microroughness domain of metal surface employed in cathodic protection mode

This effort presents the results of investigation of cathodic protection process of a section of the main pipeline, which has been operating in cathodic protection mode for a long time and which insulation has completely exfoliated from metal surface, and a cavity between is filled with water and salt impurities. In this case, a decisive factor is a fact that a metal surface is covered with microroughnesses in the form of protrusions with almost conical shape. The surface is immersed in electrolyte. At the electrolyte-metal interface, a potential difference is formed - a corrosion potential, which creates an unstable equilibrium among the potentials of metal and electrolyte. A mathematical model is designed and implemented into a numerical algorithm and computer program. A computational experiment has been carried out to calculate the potential around microroughness. The model describes a change in potential in this area at incomplete and complete cathodic protection of metal surface. The basis of computational model is a selection of one of metal protrusions of material microheterogeneity and placing it in a cylinder, which diameter coincides with that one of the lower base of this protrusion, and its upper part passes through the apex of the protrusion. Mathematical model equations with corresponding boundary conditions and their discrete implementation are presented. The solution of problems is obtained by iterative procedures based on reference values of protective potential taken from practice. The results of computational experiment are presented in the form of graphs: 1) potential distribution in the field of electrolytes; 2) changes in electrolyte potential at the border with protrusion at different values of polarization potential; 3) changes in polarization resistance in the area (calculated). The geometry of computational domain was also varied, and the values of protective potential were determined to ensure the absence of corrosion. Keywords: corrosion, microroughness, protective potential, plastic current density, electrolyte

Distinct Contributions of the Cerebellum and Basal Ganglia to Arithmetic Procedures

Humans exhibit complex mathematical skills, often attributed to the exceptionally large neocortex. Using a neuropsychological approach, we report that degeneration within two subcortical structures, the basal ganglia and cerebellum, impairs performance in symbolic arithmetic. Moreover, we identify distinct computational impairments in individuals with Parkinson’s disease (PD) or cerebellar degeneration (CD). The CD group exhibited a disproportionate cost when arithmetic sum increased, suggesting that the cerebellum is critical for iterative procedures required for calculations. The PD group exhibited a disproportionate cost for equations with an increasing number of addends, suggesting that the basal ganglia are critical for the coordination of multiple cognitive operations. In Experiment 2, the two patient groups exhibited intact practice gains for repeated equations at odds with an alternative hypothesis that these impairments were related to memory retrieval. Overall, the results provide a novel demonstration of the contribution of subcortical structures to the computations required for complex cognition.

Numerical modelling of the bearing capacity of a beam cross-section

The paper presents a procedure for numerical modelling of the rod cross-section bearing capacity. Equilibrium between cross sectional forces and cross-sectional stresses is determined by iterative procedures. According to the described procedure, the load-bearing capacity of the cross-section is determined according to the isotropic linear and nonlinear behavior of the material, for homogeneous and inhomogeneous cross-sections. The nonlinear behavior of the material reduces the stiffness of the cross section of the rod EA and EI, with a significant increase in the deformation values ε and κ. The applicability of the calculation and analysis of obtained results is presented using numerical examples.

Empirical Bayes Method for Boltzmann Machines

The framework of the empirical Bayes method allows the estimation of the values of the hyperparameters in the Boltzmann machine by maximizing a specific likelihood function referred to as the empirical Bayes likelihood function. However, the maximization is computationally difficult because the empirical Bayes likelihood function involves intractable integrations of the partition function. The method presented in this chapter avoids this computational problem by using the replica method and the Plefka expansion, which is quite simple and fast because it does not require any iterative procedures and gives reasonable estimates under certain conditions.

Different Distributional Errors-in-Circular-Variables Models

The modeling of functional relationship between circular variables is gaining an increasing interest. Existing models assume the errors have same distributions, but the case of different distributional errors is yet as investigated. This paper considers the modeling of functional relationship for circular variables with different distributional errors. Two functional relationship models are proposed by assuming a combination of von Mises and wrapped Cauchy errors, with a distinction between known and unknown ratio of error concentrations. Parameters of the proposed models are estimated using the maximum likelihood method based on numerical iterative procedures. The properties of parameters' estimators are investigated via an extensive simulation study. Results show a direct relationship between the performance of parameters estimates and the sample size, and the concentration parameters. For illustration, the proposed models are applied on wind directions data in two main cities in the Gaza Strip, Palestine.

Experimental design for verification and validation of harmonic vibration control systems

Verification and validation represent an important procedure for model-based systems engineering design processes. One of the crucial tasks for verification and validation is to test whether the control system has reached performance limit. This is challenging since complicated theories and complex steps are often involved to achieve such an objective; meanwhile, the state of the art for testing performance limit requires iterative procedures. A simple and one-off experimental design for telling whether a control system reaches its performance limit is thus necessitated. This article introduces a remarkable test criterion for fulfilling the requirement. Both theoretical foundation and experiment design procedures are presented. Numerical examples are illustrated for the proposed method, where it is also shown that the simple method can be generalized to determining performance limit maps over both frequencies and physical parameters.

On the JK Iterative Process in Banach Spaces

In the recent progress, different iterative procedures have been constructed in order to find the fixed point for a given self-map in an effective way. Among the other things, an effective iterative procedure called the JK iterative scheme was recently constructed and its strong and weak convergence was established for the class of Suzuki mappings in the setting of Banach spaces. The first purpose of this research is to obtain the strong and weak convergence of this scheme in the wider setting of generalized α -nonexpansive mappings. Secondly, by constructing an example of generalized α -nonexpansive maps which is not a Suzuki map, we show that the JK iterative scheme converges faster as compared the other iterative schemes. The presented results of this paper properly extend and improve the corresponding results of the literature.

Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces

We consider the class of mappings endowed with the condition E in a nonlinear domain called 2-uniformly convex hyperbolic space. We provide some strong and Δ -convergence theorems for this class of mappings under the Agarwal iterative process. In order to support the main outcome, we procure an example of mappings endowed with the condition E and prove that its Agarwal iterative process is more effective than Mann and Ishikawa iterative processes. Simultaneously, our results hold in uniformly convex Banach, CAT(0), and some CAT( κ ) spaces. This approach essentially provides a new setting for researchers who are working on the iterative procedures in fixed point theory and applications.

Some High-Order Convergent Iterative Procedures for Nonlinear Systems with Local Convergence

In this study, we suggested the local convergence of three iterative schemes that works for systems of nonlinear equations. In earlier results, such as from Amiri et al. (see also the works by Behl et al., Argryos et al., Chicharro et al., Cordero et al., Geum et al., Guitiérrez, Sharma, Weerakoon and Fernando, Awadeh), authors have used hypotheses on high order derivatives not appearing on these iterative procedures. Therefore, these methods have a restricted area of applicability. The main difference of our study to earlier studies is that we adopt only the first order derivative in the convergence order (which only appears on the proposed iterative procedure). No work has been proposed on computable error distances and uniqueness in the aforementioned studies given on Rk. We also address these problems too. Moreover, by using Banach space, the applicability of iterative procedures is extended even further. We have examined the convergence criteria on several real life problems along with a counter problem that completes this study.