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The Arrhenius plot (logarithmic plot vs. inverse temperature) is represented by a straight line if the Arrhenius equation holds. A curved Arrhenius plot (mostly concave) is usually described phenomenologically, often using polynomials of T or 1/T. Many modifications of the Arrhenius equation based on different models have also been published, which fit the experimental data better or worse. This paper proposes two solutions for the concave-curved Arrhenius plot. The first is based on consecutive A→B→C reaction with rate constants k1 ≪ k2 at higher temperatures and k1 ≫ k2 (or at least k1 > k2) at lower temperatures. The second is based on the substitution of the temperature T the by temperature difference T − T0 in the Arrhenius equation, where T0 is the maximum temperature at which the Arrheniusprocess under study does not yet occur.

A simply curved Weibull plot means that the studied data set has a three-parameter Weibull distribution with a non-zero location parameter representing the lower or the upper limit of the data set. This paper introduces a four-parameter Weibull distribution with both of these limits that can be applied in both reliability and materials engineering. A very reliable indicator of this distribution is the double-curved Weibull plot. The great advantage of this distribution is the fact that the corresponding hazard rate curve can be bathtub-shaped with a great ability to fit the measured data.

This comprehensive review examines the phenomena of stress corrosion cracking (SCC) and chloride-induced stress corrosion cracking (Cl-SCC) in materials commonly used in the oil and gas industry, with a focus on austenitic stainless steels. The study reveals that SCC initiation can occur at temperatures as low as 20 °C, while Cl-SCC propagation rates significantly increase above 60 °C, reaching up to 0.1 mm/day in environments with high chloride concentrations. Experimental methods such as Slow Strain Rate Tests (SSRTs), Small Punch Tests (SPTs), and Constant-Load Tests (CLTs) were employed to quantify the impacts of temperature, chloride concentration, and pH on SCC susceptibility. The results highlight the critical role of these factors in determining the susceptibility of materials to SCC. The review emphasizes the importance of implementing various mitigation strategies to prevent SCC, including the use of corrosion-resistant alloys, protective coatings, cathodic protection, and corrosion inhibitors. Additionally, regular monitoring using advanced sensor technologies capable of detecting early signs of SCC is crucial for preventing the onset of SCC. The study concludes with practical recommendations for enhancing infrastructure resilience through meticulous material selection, comprehensive environmental monitoring, and proactive maintenance strategies, aimed at safeguarding operational integrity and ensuring environmental compliance. The review underscores the significance of considering the interplay between mechanical stresses and corrosive environments in the selection and application of materials in the oil and gas industry. Low pH levels and high temperatures facilitate the rapid progression of SCC, with experimental results indicating that stainless steel forms passive films with more defects under these conditions, reducing corrosion resistance. This interplay highlights the need for a comprehensive understanding of the complex interactions between materials, environments, and mechanical stresses to ensure the long-term integrity of critical infrastructure.

The kinetics of phase transformations is usually described by the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation. The article shows that this equation cannot give a sufficiently general description of austenitization kinetics of ferritic nodular cast iron. Therefore, another kinetics equation is proposed which catches the main circumstances and substance of austenitization more accurately than the JMAK equation does. It shows that the crucial phenomena in the transformation are not only the processes of the creation and growth of new austenite grains but also the change in specific volume and the chemical liquation of alloying additives, which retard the subsequent conversion. The proposed equation together with the Arrhenius equation allows describing simultaneously the temporal and temperature dependence of austenitization conversion including the partial transformation at insufficiently high overheating of transformed iron. It is verified by successful regression of experimental data, whose results allow drawing predictive curves for temperatures from the experimental temperature region or from its near vicinity, for which the conversion was not determined.

Gait and motion stability analysis in gait dysfunction problems is a very interesting research area. Usually, patients who undergo vestibular deafferentation are affected by changes in their dynamic balance. Therefore, it is important both patients and physicians are able to monitor the progress of the so-called vestibular compensation to observe the rehabilitation process objectively. Currently, the quantification of their progress is highly dependent on the physician’s opinion. In this article, we designed a novel methodology to classify the gait disorders associated with unilateral vestibular deafferentation in patients undergoing vestibular schwannoma surgery (model of complete vestibular loss associated with imbalance due to vestibular nerve section and eventual labyrinthectomy). We present a dual-head attentional transformer-LSTM (DHAT-LSTM) to evaluate the problem of rehabilitation from gait dysfunction, which is observed by a Kinect. A system consisting of a key-point-RCNN detector is used to compute body landmark measures and evaluate gait dysfunction based on a DHAT-LSTM network. This structure is used to quantitatively assess gait classification by tracking skeletal features based on the temporal variation of feature sequences. The proposed deep network analyses the features of the patient’s movement. These extracted high-level representations are then fed to the final evaluation of gait dysfunction. The result analytically demonstrates its effectiveness in classification evaluation when used in conjunction with state-of-the-art pose estimation and feature extraction techniques. An accuracy greater than 81% was achieved for given sets of individuals using velocity-based, angle-based, and position features for both the whole body and the symmetric features of the body.

In this paper, we designed a methodology to classify facial nerve function after head and neck surgery. It is important to be able to observe the rehabilitation process objectively after a specific brain surgery, when patients are often affected by face palsy. The dataset that is used for classification problems in this study only contains 236 measurements of 127 patients of complex observations using the most commonly used House–Brackmann (HB) scale, which is based on the subjective opinion of the physician. Although there are several traditional evaluation methods for measuring facial paralysis, they still suffer from ignoring facial movement information. This plays an important role in the analysis of facial paralysis and limits the selection of useful facial features for the evaluation of facial paralysis. In this paper, we present a triple-path convolutional neural network (TPCNN) to evaluate the problem of mimetic muscle rehabilitation, which is observed by a Kinect stereovision camera. A system consisting of three modules for facial landmark measure computation and facial paralysis classification based on a parallel convolutional neural network structure is used to quantitatively assess the classification of facial nerve paralysis by considering facial features based on the region and the temporal variation of facial landmark sequences. The proposed deep network analyzes both the global and local facial movement features of a patient’s face. These extracted high-level representations are then fused for the final evaluation of facial paralysis. The experimental results have verified the better performance of TPCNN compared to state-of-the-art deep learning networks.

An advanced statistical analysis of patients’ faces after specific surgical procedures that temporarily negatively affect the patient’s mimetic muscles is presented. For effective planning of rehabilitation, which typically lasts several months, it is crucial to correctly evaluate the improvement of the mimetic muscle function. The current way of describing the development of rehabilitation depends on the subjective opinion and expertise of the clinician and is not very precise concerning when the most common classification (House–Brackmann scale) is used. Our system is based on a stereovision Kinect camera and an advanced mathematical approach that objectively quantifies the mimetic muscle function independently of the clinician’s opinion. To effectively deal with the complexity of the 3D camera input data and uncertainty of the evaluation process, we designed a three-stage data-analytic procedure combining the calculation of indicators determined by clinicians with advanced statistical methods including functional data analysis and ordinal (multiple) logistic regression. We worked with a dataset of 93 distinct patients and 122 sets of measurements. In comparison to the classification with the House–Brackmann scale the developed system is able to automatically monitor reinnervation of mimetic muscles giving us opportunity to discriminate even small improvements during the course of rehabilitation.

The kinetics of diffusion-dependent phase transformations (including austenitisation of ferrite in dual steels or ferritic nodular cast irons) is very often described by the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation. This description is not complete when the conversion is only partial due to insufficient overheating, as the equilibrium fraction of ferrite transformed into austenite cannot be determined directly from the JMAK equation. Experimental kinetic curves of partial austenitisation at various temperatures can be fitted using the JMAK equation, but the equilibrium fraction of the newly formed phase for each temperature has to be calculated as a regression parameter. In addition, the temperature dependence of the kinetic exponent in the JMAK equation is quite complicated and cannot be expressed by a simple general function. On the contrary, the equation of autoinhibition used for the description of austenitisation kinetics in present work directly gives the equilibrium fraction at partial conversion. It describes transformation kinetics at various temperatures independently of whether the conversion is complete or partial. Rate constants of the equation of autoinhibition depend on temperature according to the Arrhenius equation. In addition, the equation of autoinhibition has no weakness as the JMAK equation has, which consists in questionable temperature dependence of kinetic exponent.

In the oil and gas industry, the corrosion attributed to hydrogen sulfide (H2S) is one of the most significant challenges. This review paper systematically investigates the diverse facets of H2S corrosion, including its sources, corrosion locations, mechanisms, and resultant corrosion products. Understanding different forms of H2S corrosion, such as stress-oriented hydrogen-induced cracking (SO-HIC), sulfide stress cracking (SSC), and hydrogen-induced cracking (HIC), provides a thorough comprehension of these phenomena. The paper discusses critical factors influencing H2S corrosion, such as temperature, flow rate, pH, and H2S concentration, highlighting their implications for sustainable practices in the oil and gas sector. The review emphasizes the significance of monitoring and mitigation strategies, covering continuous monitoring, applying corrosion inhibitors, selecting materials, and conducting thorough data analysis and reporting. Furthermore, the role of training in fostering a sustainable approach to H2S corrosion management is highlighted. This exploration advances the overarching goal of sustainable development in the oil and gas industries by providing insights into understanding, monitoring, and mitigating H2S corrosion. The findings presented here offer a foundation for developing environmentally conscious strategies and practices to guarantee the long-term viability and flexibility of refinery operations.

This paper focuses on the statistical analysis of mimetic muscle rehabilitation after head and neck surgery causing facial paresis in patients after head and neck surgery. Our work deals with an evaluation problem of mimetic muscle rehabilitation that is observed by a Kinect stereo-vision camera. After a specific brain surgery, patients are often affected by face palsy, and rehabilitation to renew mimetic muscle innervation takes several months. It is important to be able to observe the rehabilitation process in an objective way. The most commonly used House–Brackmann (HB) scale is based on the clinician’s subjective opinion. This paper compares different methods of supervised learning classification that should be independent of the clinician’s opinion. We compare a parametric model (based on logistic regression), non-parametric model (based on random forests), and neural networks. The classification problem that we have studied combines a limited dataset (it contains only 122 measurements of 93 patients) of complex observations (each measurement consists of a collection of time curves) with an ordinal response variable. To balance the frequencies of the considered classes in our data set, we reclassified the samples from HB4 to HB3 and HB5 to HB6—it means that only four HB grades are used for classification algorithm. The parametric statistical model was found to be the most suitable thanks to its stability, tractability, and reasonable performance in terms of both accuracy and precision.