On Deterministic Chaos: Disclosing the Missing Mathematics from the Lorenz-Haken Equations

The original 3D Lorenz-Haken equations -which describe laser dynamics- are converted into 2-second-order differential equations out of which the so far missing mathematics is extracted. Leaning on high-order trigonometry, important outcomes are pulled out: A fundamental result attributes chaos to forbidden periodic solutions, inside some precisely delimited region of the control parameter space that governs self-pulsing.

A Practical Construction Technique to Enhance the Performance of Rock Bolts in Tunnels

In Swedish tunnel construction, a critical issue that has been repeatedly acknowledged is corrosion and, consequently, failure of the rock bolts in rock support systems. The defective installation of rock bolts results in the formation of cavities in the cement mortar that is regularly used to fill the area under the dome plates. These voids allow for water-ingress to the rock bolt assembly, which results in corrosion of rock bolt components and eventually failure. In addition, the current installation technique consists of several manual steps with intense labor works that are usually done in uncomfortable and exhausting conditions, e.g., under the roof of the tunnels. Such intense tasks also lead to a considerable waste of materials and execution errors. Moreover, adequate quality control of the execution is hardly possible with the current technique. To overcome these issues, a non-shrinking/expansive cement-based mortar filled in the paper packaging has been developed in this study which properly fills the area under the dome plates without or with the least remaining cavities, ultimately that diminishes the potential of corrosion. This article summarizes the development process and the experimental evaluation of this technique for the installation of rock bolts. In the development process, the cementitious mortar was first developed using specific cement and shrinkage reducing/expansive additives. The mechanical and flow properties of the mortar were then evaluated using compressive strength, density, and slump flow measurement methods. In addition, isothermal calorimetry and shrinkage/expansion measurements were used to elucidate the hydration and durability attributes of the mortar. After obtaining the desired properties in both fresh and hardened conditions, the developed dry mortar was filled in specific permeable paper packaging and then submerged in water bath for specific intervals before the installation. The tests were enhanced progressively by optimizing different parameters such as shape and size of the packaging, characteristics of the paper used, immersion time in water and even some minor characteristics of the mortar. Finally, the developed prototype was tested in a lab-scale rock bolt assembly with various angles to analyze the efficiency of the method in real life scenario. The results showed that the new technique improves the performance of the rock bolts by reducing the material wastage, improving environmental performance, facilitating and accelerating the labor works, and finally enhancing the durability of the whole system. Accordingly, this approach provides an efficient alternative for the traditional way of tunnel bolt installation with considerable advantages for the Swedish tunneling industry.

Soil-Structure Interaction Models for the Reinforced Foundation System: A State-of-the-Art Review

Challenges of weak soil subgrade are often resolved either by stabilization or reinforcing it. However, it is also practiced to reinforce the granular fill to improve the load-settlement behavior of it over weak soil strata. The inclusion of reinforcement in the engineered granular fill provided a new impetus for the development of enhanced Soil-Structure Interaction (SSI) models, also known as mechanical foundation models or lumped parameter models. Several researchers have been working in this direction to understand the mechanism of granular fill-reinforcement interaction and the response of weak soil under the application of load. These models have been developed by extending available SSI models such as the Winkler Model, Pasternak Model, Hetenyi Model, Kerr Model etc., and are helpful to visualize the load-settlement behavior of a physical system through 1-D and 2-D analysis considering beam and plate resting on the foundation, respectively. Based on the literature survey, these models are categorized as ‘Reinforced Pasternak Model,’ ‘Double Beam Model,’ ‘Reinforced Timoshenko Beam Model,’ and ‘Reinforced Kerr Model’. The present work reviews the past 30+ years of research in the field of SSI models for reinforced foundation systems, presenting the conceptual development of these models systematically and discussing their limitations. A flow-chart showing procedure for compution of deformation and mobilized tension is also incorporated in the paper. Special efforts are taken to tabulate the parameters and their significance in the load-settlement analysis, which may be helpful in future studies for the comparison and enhancement of results and findings of physical models. 

CFD Simulations for Studying Flow Behaviors in Dipping Tank in Continuous Latex Gloves Production Lines

Medical latex gloves are made from the latex compound in production lines. Latex dipping is considered one of the most important processes that directly affect the final product quality. In a continuous production line, a chain conveyor carries the formers through the process and partially submerges them into an open channel flow in a latex dipping tank. In general, the conveyor speed is determined by the desired production capacity, and the latex-dipping tank can then be designed accordingly. It is important to understand the flow behavior in the dipping tank in order to achieve high quality in the process. In this work, Computational Fluid Dynamics (CFD) was used to simulate the flow past an array of formers in a simplified latex dipping process. The computational results showed both the flow structure and the vortex generation between two formers. The maximum shear stress over the surface of the formers was used as the quality metric of the latex-dipping process when adjusting operation parameters.

Three-Dimensional State with Doublet Mechanics

In this study, it is aimed to obtain general stress expressions for the examination of mechanical behaviors of planar straight axis nano rods by using doublet mechanics. The superiority of this method over other scale dependent methods is that it is directly related to the structure of nanomaterial and it models solid structure with points at finite distances between them. In other words, value of small scale effect is known exactly. To the best of authors’ knowledge, after micro modulus matrix is obtained by using Generalized Hooke’s Law and the essential transformation matrix expressing relationships between macro and micro stress and strain matrix, the stress equations that include the effect of axial extension are acquired for the three-dimensional state for the first time in the literature. In plane and out of plane static and dynamic behaviors can be studied using analytical and/or numerical approaches without any restrictions. Since the value of the small scale size parameter is precisely known in the theory used, it is thought that the results to be obtained will be more accurate than other scale size theories.

Applying the Crystal Model Approach on Light Nuclei for Calculating Radii and Density Distribution

A new model namely, the crystal model, has been modified to calculate radius and density distribution of light nuclei up to 8Be. The crystal model has been modified according to solid state physics which uses the analogy between nucleon distribution and atoms distribution in the crystal. The model has analytical analysis to calculate the radius where the density distribution of light nuclei has been obtained from the analogy of crystal lattice. The distribution of nucleons over crystal has been discussed in general form. The equation used to calculate binding energy was taken from the solid-state model of repulsive and attractive force. The numbers of the protons were taken to control repulsive force where the atomic number was responsible for the attractive force. The parameter has been calculated from the crystal model was found to be proportional to the radius of the nucleus. The density distribution of light nuclei was taken as a summation of two clusters distribution as in 6Li=alpha+deuteron configuration. A test has been done on the data obtained for radius and density distribution using double folding for d+6,7Li with M3Y nucleon-nucleon interaction. Good agreement has been obtained for both radius and density distribution of light nuclei. The model failed to calculate the radius of 9Be, so modifications should be done to overcome discrepancy.

Environmental Impact Assessment of Ceramic Tile Materials Used in Jordan on Indoor Radon Level

In this investigation, activity concentration of 226Ra, 232Th, and 40K, of some ceramic tile materials used in the local market of Jordan for interior decoration were determined by making use of High Purity Germanium (HPGe) detector. Twenty samples of different country of origin and sizes used in Jordan were analyzed. The concentration values of the last-mentioned radionuclides ranged from 30 Bq.kg-1 (Sample from Jordan) to 98 Bq.kg-1 (Sample from China) for 226Ra, 31 Bq.kg-1 (Sample from Italy) to 98 Bq.kg-1 (Sample from China) for 232Th, and 129 Bq.kg-1 (Sample from Spain) to 679 Bq.kg-1 (Sample from Italy) for 40K. Based on the calculated activity concentrations, some radiological parameters have been calculated to test the radiation hazards in the ceramic tiles. In this work, the following parameters: Total absorbed dose rate (DR), Annual effective dose rate (HR), Radium equivalent activity (Raeq), Radon emanation coefficient F (%) and Radon mass exhalation rate (Em) were calculated for all ceramic tiles and listed in the body of the work. Fortunately, the average calculated values of all parameters are less than the recommended values for each parameter. Consequently, almost all the examined ceramic materials appear to have low radon emanation coefficients. As a result of that investigation, no problems on people can appear by using those ceramic tiles in Jordan.

A Risk Assessment Tool for the Contamination of Aflatoxins on Dried Figs based on Machine Learning Algorithms

Aflatoxins are highly poisonous and carcinogenic compounds produced by species of the genus Aspergillus spp. that can infect a variety of agricultural foods, including dried figs. Biological and environmental factors, such as population, pathogenicity and aflatoxinogenic capacity of the strains, topography, soil and climate parameters of the fig orchards are believed to have a strong effect on aflatoxin levels. Existing methods for aflatoxin detection and measurement, such as high-performance liquid chromatography (HPLC), and enzyme-linked immunosorbent assay (ELISA), can provide accurate results, but the procedures are usually time-consuming, sample-destructive and expensive. Predicting aflatoxin levels prior to crop harvest is useful for minimizing the health and financial impact of a contaminated crop. Consequently, there is interest in developing a tool that predicts aflatoxin levels based on topography and soil analysis data of fig orchards. This paper describes the development of a risk assessment tool for the contamination of aflatoxin on dried figs, based on the location and altitude of the fig orchards, the population of the fungus Aspergillus spp. in the soil, and soil parameters such as pH, saturation percentage (SP), electrical conductivity (EC), organic matter, particle size analysis (sand, silt, clay), concentration of the exchangeable cations (Ca, Mg, K, Na), extractable P and trace of elements (B, Fe, Mn, Zn and Cu), by employing machine learning methods. In particular, our proposed method integrates three machine learning techniques i.e., dimensionality reduction on the original dataset (Principal Component Analysis), metric learning (Mahalanobis Metric for Clustering) and K-nearest Neighbors learning algorithm (KNN), into an enhanced model, with mean performance equal to 85% by terms of the Pearson Correlation Coefficient (PCC) between observed and predicted values.

Bound State Solutions of the Schrödinger Equation for Hulthen-Yukawa Potential in D-Dimensions

In this work, we used the Hulthen-Yukawa potential to obtain the bound state energy eigenvalues of the Schrödinger equation in D-dimensions within the frame work of the Nikiforov-Uvarov (NU) method. We demonstrated the graphical behaviour of the Hulthen and the Yukawa potential and investigated how the screening parameter and the potential depth affected the structure and the nature of the bound state eigenvalues. The results we obtained showed that increasing the screening parameter lowers the energy eigenvalues. Also, the eigenvalues acted as an inverse function of the potential depth. That is, increasing the potential depth reduces the energy eigenvalues.

The Evaluation of New Generation Cardiovascular Risk Markers in Childhood Obesity

Obesity, as excessive fat accumulation in the body, is a global health problem. The prevalence of obesity and its complications increase due to easy access to high-energy food and decreased physical activity. Cardiovascular diseases (CVDs) constitute a significant part of obesity-related morbidity and mortality. Since the effects of obesity on cardiovascular system may start during childhood without clinical findings, elucidating the mechanisms of cardiovascular changes associated with childhood obesity became more important. In this study, we aimed to investigate some biochemical parameters which may be involved in obesity-related pathologic processes of CVDs. One hundred and seventy-seven children were included in the study, and they were divided into four groups based upon WHO criteria and presence of the metabolic syndrome (MetS): children with normal-BMI, obesity, morbid obesity, and MetS. High-sensitive cardiac troponin T (hs-cTnT), cardiac myosin binding protein C (cMyBP-C), trimethylamine N-oxide (TMAO), soluble tumor necrosis factor-like weak inducer (sTWEAK), chromogranin A (CgA), multimerin-2 levels, and other biochemical parameters were measured in serum samples. Anthropometric measurements and clinical findings of the children were recorded. Statistical analyses were performed. Children with normal-BMI had significantly higher CgA levels than children with obesity, morbid obesity, and MetS (p < 0.05). Cardiac MyBP-C levels of children with MetS were significantly higher than of children with normal-BMI and OB children (p < 0.05). There was no significant difference in hs-cTnT, sTWEAK, TMAO and multimerin-2 between the groups (p>0.05). These results suggested that cMyBP-C and CgA molecules may be involved in the pathogenesis of obesity-related CVDs.

Simulation with Uncertainties of Active Controlled Vibration Isolation System for Astronaut’s Exercise Platform

In a task to assist NASA in analyzing the dynamic forces caused by operational countermeasures of an astronaut’s exercise platform impacting the spacecraft, an active proportional-integral-derivative controller commanding a linear actuator is proposed in a vibration isolation system to regulate the movement of the exercise platform. Computer simulation shows promising results that most exciter forces can be reduced or even eliminated. This paper emphasizes on parameter uncertainties, variations and exciter force variations. Drift and variations of system parameters in the vibration isolation system for astronaut’s exercise platform are analyzed. An active controlled scheme is applied with the goals to reduce the platform displacement and to minimize the force being transmitted to the spacecraft structure. The controller must be robust enough to accommodate the wide variations of system parameters and exciter forces. Computer simulation for the vibration isolation system was performed via MATLAB/Simulink and Trick. The simulation results demonstrate the achievement of force reduction with small platform displacement under wide ranges of variations in system parameters. 

Smartphone-Based Human Activity Recognition by Machine Learning Methods

As smartphones are continually upgrading, their software and hardware are getting smarter, so the smartphone-based human activity recognition will be described more refined, complex and detailed. In this context, we analyzed a set of experimental data, obtained by observing and measuring 30 volunteers with six activities of daily living (ADL). Due to the large sample size, especially a 561-feature vector with time and frequency domain variables, cleaning these intractable features and training a proper model become extremely challenging. After a series of feature selection and parameters adjustments, a well-performed SVM classifier has been trained. 

Adaptive Kalman Filter for Noise Estimation and Identification with Bayesian Approach

Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, adaptive Kalman filter with Bayesian approach for identification of variances in measurement parameter noise is developed. Next, it is applied for estimation of the dynamical state and measurement data in discrete linear dynamical system. This algorithm at each step time estimates noise variance in measurement noise and state of system with Kalman filter. Next, approximation is designed at each step separately and consequently sufficient statistics of the state and noise variances are computed with a fixed-point iteration of an adaptive Kalman filter. Different simulations are applied for showing the influence of noise variance in measurement data on algorithm. Firstly, the effect of noise variance and its distribution on detection and identification performance is simulated in Kalman filter without Bayesian formulation. Then, simulation is applied to adaptive Kalman filter with the ability of noise variance tracking in measurement data. In these simulations, the influence of noise distribution of measurement data in each step is estimated, and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained. 

Gas Injection Transport Mechanism for Shale Oil Recovery

The United States is now energy self-sufficient due to the production of shale oil reserves. With more than half of it being tapped daily in the United States, these unconventional reserves are massive and provide immense potential for future energy demands. Drilling horizontal wells and fracking are the primary methods for developing these reserves. Regrettably, recovery efficiency is rarely greater than 10%. Gas injection enhanced oil recovery offers a significant benefit in optimizing recovery of shale oil. This could be either through huff and puff, gas flooding, and cyclic gas injection. Methane, nitrogen, and carbon (IV) oxide, among other high-pressure gases, can be injected. Operators use Darcy's law to assess a reservoir's productive capacity, but they are unaware that the law may not apply to shale oil reserves. This is due to the fact that, unlike pressure differences alone, diffusion, concentration, and gas selection all play a role in the flow of gas injected into the wellbore. The reservoir drainage and oil sweep efficiency rates are determined by the transport method. This research evaluates the parameters that influence gas injection transport mechanism. Understanding the process could accelerate recovery by two to three times.

Separation of Composites for Recycling: Measurement of Electrostatic Charge of Carbon and Glass Fiber Particles

Composite waste from manufacturing can consist of different fiber materials, including blends of different fiber. Commercially, the recycling of composite waste is currently limited to carbon fiber waste and recycling glass fiber waste is currently not economically viable due to the low cost of virgin glass fiber and the reduced mechanical properties of the recovered fibers. For this reason, the recycling of hybrid fiber materials, where carbon fiber is blended with glass fibers, cannot be processed economically. Therefore, a separation method is required to remove the glass fiber materials during the recycling process. An electrostatic separation method is chosen for this work because of the significant difference between carbon and glass fiber electrical properties. In this study, an experimental rig has been developed to measure the electrostatic charge achievable as the materials are passed through a tube. A range of particle lengths (80-100 µm, 6 mm and 12 mm), surface state conditions (0%SA, 2%SA and 6%SA), and several tube wall materials have been studied. A polytetrafluoroethylene (PTFE) tube and recycled fiber without sizing agent were identified as the most suitable parameters for the electrical separation method. It was also found that shorter fiber lengths helped to encourage particle flow and attain higher charge values. These findings can be used to develop a separation process to enable the cost-effective recycling of hybrid fiber composite waste. 

Energy Management System with Temperature Rise Prevention on Hybrid Ships

Marine shipping has now become one of the major worldwide contributors to pollution and greenhouse gas emissions. Hybrid ships technology based on multiple energy sources has taken a great scope of research to get rid of ship emissions and cut down fuel expenses. Insufficiency between power generated and the demand load to withstand the transient behavior on ships during severe climate conditions will lead to a blackout. Thus, an efficient energy management system (EMS) is a mandatory scope for achieving higher system efficiency while enhancing the lifetime of the onboard storage systems is another salient EMS scope. Considering energy storage system conditions, both the battery state of charge (SOC) and temperature represent important parameters to prevent any malfunction of the storage system that eventually degrades the whole system. In this paper, a two battery packs ratio fuzzy logic control model is proposed. The overall aim is to control the charging/discharging current while including both the battery SOC and temperature in the energy management system. The full designs of the proposed controllers are described and simulated using Matlab. The results prove the successfulness of the proposed controller in stabilizing the system voltage during both loading and unloading while keeping the energy storage system in a healthy condition.

Additive Friction Stir Manufacturing Process: Interest in Understanding Thermal Phenomena and Numerical Modeling of the Temperature Rise Phase

Additive Friction Stir Manufacturing, or AFSM, is a new industrial process that follows the emergence of friction-based processes. The AFSM process is a solid-state additive process using the energy produced by the friction at the interface between a rotating non-consumable tool and a substrate. Friction depends on various parameters like axial force, rotation speed or friction coefficient. The feeder material is a metallic rod that flows through a hole in the tool. There is still a lack in understanding of the physical phenomena taking place during the process. This research aims at a better AFSM process understanding and implementation, thanks to numerical simulation and experimental validation performed on a prototype effector. Such an approach is considered a promising way for studying the influence of the process parameters and to finally identify a process window that seems relevant. The deposition of material through the AFSM process takes place in several phases. In chronological order these phases are the docking phase, the dwell time phase, the deposition phase, and the removal phase. The present work focuses on the dwell time phase that enables the temperature rise of the system due to pure friction. An analytic modeling of heat generation based on friction considers as main parameters the rotational speed and the contact pressure. Another parameter considered influential is the friction coefficient assumed to be variable, due to the self-lubrication of the system with the rise in temperature or the materials in contact roughness smoothing over time. This study proposes through a numerical modeling followed by an experimental validation to question the influence of the various input parameters on the dwell time phase. Rotation speed, temperature, spindle torque and axial force are the main monitored parameters during experimentations and serve as reference data for the calibration of the numerical model. This research shows that the geometry of the tool as well as fluctuations of the input parameters like axial force and rotational speed are very influential on the temperature reached and/or the time required to reach the targeted temperature. The main outcome is the prediction of a process window which is a key result for a more efficient process implementation.

A 3D Numerical Environmental Modeling Approach for Assessing Transport of Spilled Oil in Porous Beach Conditions under a Meso-Scale Tank Design

Shorelines are vulnerable to significant environmental impacts from oil spills. Stranded oil can cause potential short- to long-term detrimental effects along beaches that include injuries to ecosystem, socio-economic and cultural resources. In this study, a three-dimensional (3D) numerical modeling approach is developed to evaluate the fate and transport of spilled oil for hypothetical oiled shoreline cases under various combinations of beach geomorphology and environmental conditions. The developed model estimates the spatial and temporal distribution of spilled oil for the various test conditions, using the finite volume method and considering the physical transport (dispersion and advection), sinks, and sorption processes. The model includes a user-friendly interface for data input on variables such as beach properties, environmental conditions, and physical-chemical properties of spilled oil. An experimental meso-scale tank design was used to test the developed model for dissolved petroleum hydrocarbon within shorelines. The simulated results for effects of different sediment substrates, oil types, and shoreline features for the transport of spilled oil are comparable to that obtained with a commercially available model. Results show that the properties of substrates and the oil removal by shoreline effects have significant impacts on oil transport in the beach area. Sensitivity analysis, through the application of the one-step-at-a-time method (OAT), for the 3D model identified hydraulic conductivity as the most sensitive parameter. The 3D numerical model allows users to examine the behavior of oil on and within beaches, assess potential environmental impacts, and provide technical support for decisions related to shoreline clean-up operations.

Associations among Fetuin A, Cortisol and Thyroid Hormones in Children with Morbid Obesity and Metabolic Syndrome

Obesity is a disease with an ever-increasing prevalence throughout the world. The metabolic network associated with obesity is very complicated. In metabolic syndrome (MetS), it becomes even more difficult to understand. Within this context, hormones, cytokines, and many others participate in this complex matrix. The collaboration among all of these parameters is a matter of great wonder. Cortisol, as a stress hormone, is closely associated with obesity. Thyroid hormones are involved in the regulation of energy as well as glucose metabolism with all of its associates. Fetuin A has been known for years; however, the involvement of this parameter in obesity discussions is rather new. Recently, it has been defined as one of the new generation markers of obesity. In this study, the aim was to introduce complex interactions among all to be able to make clear comparisons, at least for a part of this complicated matter. Morbid obese (MO) children participated in the study. Two groups with 46 MO children and 43 with MetS were constituted. All children included in the study were above 99th age- and sex-adjusted body mass index (BMI) percentiles according to World Health Organization criteria. Forty-three morbid obese children in the second group also had MetS components. Informed consent forms were filled by the parents of the participants. The institutional ethics committee has given approval for the study protocol. Data as well as the findings of the study were evaluated from a statistical point of view. Two groups were matched for their age and gender compositions. Significantly higher body mass index (BMI), waist circumference, thyrotropin, and insulin values were observed in the MetS group. Triiodothyronine concentrations did not differ between the groups. Elevated levels for thyroxin, cortisol, and fetuin-A were detected in the MetS group compared to the first group (p > 0.05). In MO MetS- group, cortisol was correlated with thyroxin and fetuin-A (p < 0.05). In the MO MetS+ group, none of these correlations were present. Instead, a correlation between cortisol and thyrotropin was found (p < 0.05). In conclusion, findings have shown that cortisol was the key player in severely obese children. The association of this hormone with the participants of thyroid hormone metabolism was quite important. The lack of association with fetuin A in the morbid obese MetS+ group has suggested the possible interference of MetS components in the behavior of this new generation obesity marker. The most remarkable finding of the study was the unique correlation between cortisol and thyrotropin in the morbid obese MetS+ group, suggesting that thyrotropin may serve as a target along with cortisol in the morbid obese MetS+ group. This association may deserve specific attention during the development of remedies against MetS in the pediatric population.

Relationship between Hepatokines and Insulin Resistance in Childhood Obesity

Childhood obesity is an important clinical problem, because it may lead to chronic diseases during the adulthood period of the individual. Obesity is a metabolic disease associated with low-grade inflammation. The liver occurs at the center of metabolic pathways. Adropin, fibroblast growth factor-21 (FGF-21) and fetuin A are hepatokines. Due to the immense participation of the liver in glucose metabolism, these liver derived factors may be associated with insulin resistance (IR), which is a phenomenon discussed within the scope of obesity problems. The aim of this study is to determine the concentrations of adropin, FGF-21 and fetuin A in childhood obesity, to point out possible differences between the obesity groups and to investigate possible associations among these three hepatokines in obese and morbid obese children. A total of 132 children were included in the study. Two obese groups were constituted. The groups were matched in terms of mean±SD values of ages. Body mass index values of the obese and morbid obese groups were 25.0±3.5 kg/m2 and 29.8±5.7 kg/m2, respectively. Anthropometric measurements including waist circumference, hip circumference, head circumference, and neck circumference were recorded. Informed consent forms were taken from the parents of the participants and the Ethics Committee of the institution approved the study protocol. Blood samples were obtained after an overnight fasting. Routine biochemical tests including glucose- and lipid-related parameters were performed. Concentrations of the hepatokines (adropin, FGF-21, fetuin A) were determined by enzyme-linked immunosorbent assay. Insulin resistance indices such as homeostasis model assessment for IR (HOMA-IR), alanine transaminase-to aspartate transaminase ratio (ALT/AST), diagnostic obesity notation model assessment laboratory index, diagnostic obesity notation model assessment metabolic syndrome index as well as obesity indices such as diagnostic obesity notation model assessment-II index, and fat mass index were calculated using the previously derived formulas. Statistical evaluation of the study data as well as findings of the study were performed by SPSS for Windows. Statistical difference was accepted significant when p < 0.05. Statistically significant differences were found for insulin, triglyceride, high density lipoprotein cholesterol levels of the groups. A significant increase was observed for FGF-21 concentrations in the morbid obese group. Higher adropin and fetuin A concentrations were observed in the same group in comparison with the values detected in the obese group (p > 0.05). There was no statistically significant difference between the ALT/AST values of the groups. In all of the remaining IR and obesity indices, significantly increased values were calculated for morbid obese children. Significant correlations were detected between HOMA-IR and each of the hepatokines. The highest one was the association with fetuin A (r = 0.373, p = 0.001). In conclusion, increased levels observed in adropin, FGF-21 and fetuin A have shown that these hepatokines possess increasing potential going from the obese to morbid obese state. Out of the correlations found with IR index, the most affected hepatokine was fetuin A, the parameter possibly used as the indicator of the advanced obesity stage.