Search results for: generalized estimating equations

Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

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Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: identification, Hammerstein-Wiener, optimization, quantization

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Authors: Oren Shtayermman

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The current investigation expended on research among parents caring for a child who is diagnosed with an autism spectrum disorder (ASD). An online web survey was used to collect data from 253 parents caring for a child with a diagnosis of ASD. Both parents reported on elevated levels of parental stress associated with caring for the child on the spectrum. In addition, lower levels of marital satisfaction were found in both parents. About 13% of the parents in the sample met the diagnostic criteria for Major Depressive Disorder and About 15% of the parents met the diagnostic criteria for Generalized Anxiety Disorder. Although the majority of the sample was females (94%) significant differences were found between males and females in relation to meeting the diagnostic criteria for Major Depressive Disorder and for Generalized Anxiety Disorder. Higher levels of stress were associated with higher number of Generalized Anxiety Disorder symptoms and higher number of Major Depressive Disorder symptoms. Findings from this study indicate how vulnerable parents and especially females are in relation to caring to a child diagnosed with ASD. Educational Objectives: At the conclusion of the paper, the readers should be able to: -Identify levels of stress and marital satisfaction among parents caring for a child diagnosed with autism spectrum disorder, -Recognize the impact of stress on the development of mental health issues, -Name the two most common mood and anxiety related disorders associated with caring for a child diagnosed with an autism spectrum disorder.

Keywords: autism, stress, parents, children

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Authors: Srinivasacharya Darbhasayanam, Jagadeeshwar Pashikanti

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This paper analyzes the Soret and Dufour effects on mixed convection flow, heat and mass transfer from an exponentially stretching surface in a viscous fluid with Hall Effect. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations. The nonlinear coupled ordinary differential equations are reduced to a system of linear differential equations using the successive linearization method and then solved the resulting linear system using the Chebyshev pseudo spectral method. The numerical results for the velocity components, temperature and concentration are presented graphically. The obtained results are compared with the previously published results, and are found to be in excellent agreement. It is observed from the present analysis that the primary and secondary velocities and concentration are found to be increasing, and temperature is decreasing with the increase in the values of the Soret parameter. An increase in the Dufour parameter increases both the primary and secondary velocities and temperature and decreases the concentration.

Keywords: Exponentially stretching sheet, Hall current, Heat and Mass transfer, Soret and Dufour Effects

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Authors: Arunee Wongkhao, Suparat Niwitpong, Sa-aat Niwitpong

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In this paper, we propose two new confidence intervals for the difference between the inverse of normal means with known coefficients of variation. One of these two confidence intervals for this problem is constructed based on the generalized confidence interval and the other confidence interval is constructed based on the closed form method of variance estimation. We examine the performance of these confidence intervals in terms of coverage probabilities and expected lengths via Monte Carlo simulation.

Keywords: coverage probability, expected length, inverse of normal mean, coefficient of variation, generalized confidence interval, closed form method of variance estimation

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Authors: Mohamed Ouzzane, Mahmoud Bady

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Due to energy and environment context, research is looking for the use of clean and energy efficient system in cooling industry. In this regard, the ejector represents one of the promising solutions. The thermal ejector is a passive component used for thermal compression in refrigeration and cooling systems, usually activated by heat either waste or solar. The present study introduces a theoretical analysis of the cooling system which uses a gas ejector thermal compression. A theoretical model is developed and applied for the design and simulation of the ejector, as well as the whole cooling system. Besides the conservation equations of mass, energy and momentum, the gas dynamic equations, state equations, isentropic relations as well as some appropriate assumptions are applied to simulate the flow and mixing in the ejector. This model coupled with the equations of the other components (condenser, evaporator, pump, and generator) is used to analyze profiles of pressure and velocity (Mach number), as well as evaluation of the cycle cooling capacity. A FORTRAN program is developed to carry out the investigation. Properties of refrigerant R134a are calculated using real gas equations. Among many parameters, it is thought that the generator pressure is the cornerstone in the cycle, and hence considered as the key parameter in this investigation. Results show that the generator pressure has a great effect on the ejector and on the whole cooling system. At high generator pressures, strong shock waves inside the ejector are created, which lead to significant condenser pressure at the ejector exit. Additionally, at higher generator pressures, the designed system can deliver cooling capacity for high condensing pressure (hot season).

Keywords: air cooling system, refrigeration, thermal ejector, thermal compression

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Authors: J. P. Chollom, G. M. Kumleng, S. Longwap

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The search for higher order A-stable linear multi-step methods has been the interest of many numerical analysts and has been realized through either higher derivatives of the solution or by inserting additional off step points, supper future points and the likes. These methods are suitable for the solution of stiff differential equations which exhibit characteristics that place a severe restriction on the choice of step size. It becomes necessary that only methods with large regions of absolute stability remain suitable for such equations. In this paper, high order block implicit multi-step methods of the hybrid form up to order twelve have been constructed using the multi-step collocation approach by inserting one or more off step points in the multi-step method. The accuracy and stability properties of the new methods are investigated and are shown to yield A-stable methods, a property desirable of methods suitable for the solution of stiff ODE’s. The new High Order Block Implicit Multistep methods used as block integrators are tested on stiff differential systems and the results reveal that the new methods are efficient and compete favourably with the state of the art Matlab ode23 code.

Keywords: block linear multistep methods, high order, implicit, stiff differential equations

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Authors: Mary Chriselda A

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This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: Vallence Ngabo M., Leonard Atuhaire, Peter Clever Rutayisire

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The main aim of this study was to establish the differences in both the determinants of stunting and the causal mechanism through which the identified determinants influence stunting amongst male and female under-fives in Uganda. Literature shows that male children below the age of five years are at a higher risk of being stunted than their female counterparts. Specifically, studies in Uganda indicate that being a male child is positively associated with stunting, while being a female is negatively associated with stunting. Data for 904 males and 829 females under-fives was extracted form UDHS-2016 survey dataset. Key variables for this study were identified and used in generating relevant models and paths. Structural equation modeling techniques were used in their generalized form (GSEM). The generalized nature necessitated specifying both the family and link functions for each response variable in the system of the model. The sex of the child (b4) was used as a grouping factor and the height for age (HAZ) scores were used to construct the status for stunting of under-fives. The estimated models and path clearly indicated that the set of underlying factors that influence male and female under-fives respectively was different and the path through which they influence stunting was different. However, some of the determinants that influenced stunting amongst male under-fives also influenced stunting amongst the female under-fives. To reduce the stunting problem to the desirable state, it is important to consider the multifaceted and complex nature of the risk factors that influence stunting amongst the under-fives but, more importantly, consider the different sex-specific factors and their causal mechanism or paths through which they influence stunting.

Keywords: stunting, underfives, sex of the child, GSEM, causal mechanism

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Authors: Yaowei Hu, Yongkai Wu, Lu Zhang, Xintao Wu

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Causal inference from observational data is receiving wide applications in many fields. However, unidentifiable situations, where causal effects cannot be uniquely computed from observational data, pose critical barriers to applying causal inference to complicated real applications. In this paper, we develop a bounding method for estimating the average causal effect (ACE) under unidentifiable situations due to hidden confounders. We propose to parameterize the unknown exogenous random variables and structural equations of a causal model using neural networks and implicit generative models. Then, with an adversarial learning framework, we search the parameter space to explicitly traverse causal models that agree with the given observational distribution and find those that minimize or maximize the ACE to obtain its lower and upper bounds. The proposed method does not make any assumption about the data generating process and the type of the variables. Experiments using both synthetic and real-world datasets show the effectiveness of the method.

Keywords: average causal effect, hidden confounding, bound estimation, generative adversarial learning

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Authors: Ishit Sheth, Chandrasekhar Jinendran, Chinmaya Ranjan Sahu

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A fourteen degree of freedom (DOF) ride and handling control mathematical model is developed for a car using generalized boltzmann hamel equation which will create a basis for design of ride and handling controller. Mathematical model developed yield equations of motion for non-holonomic constrained systems in quasi-coordinates. The governing differential equation developed integrates ride and handling control of car. Model-based systems engineering approach is implemented for simulation using matlab/simulink, vehicle’s response in different DOF is examined and later validated using commercial software (ADAMS). This manuscript involves detailed derivation of full car vehicle model which provides response in longitudinal, lateral and yaw motion to demonstrate the advantages of the developed model over the existing dynamic model. The dynamic behaviour of the developed ride and handling model is simulated for different road conditions.

Keywords: Full Vehicle Model, MBSE, Non Holonomic Constraints, Boltzmann Hamel Equation

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Authors: Ramzi B. Albadarneh

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In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

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Authors: Rajkumar Ghosh

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The study presents an overview of the many uses and approaches for estimating out-of-sequence thrust movement in earthquake mitigation. The study investigates how knowing and forecasting thrust movement during seismic occurrences might assist to effective earthquake mitigation measures. The review begins by discussing out-of-sequence thrust movement and its importance in earthquake mitigation strategies. It explores how typical techniques of estimating thrust movement may not capture the full complexity of seismic occurrences and emphasizes the benefits of include out-of-sequence data in the analysis. A thorough review of existing research and studies on out-of-sequence thrust movement estimates for earthquake mitigation. The study demonstrates how to estimate out-of-sequence thrust movement using multiple data sources such as GPS measurements, satellite imagery, and seismic recordings. The study also examines the use of out-of-sequence thrust movement estimates in earthquake mitigation measures. It investigates how precise calculation of thrust movement may help improve structural design, analyse infrastructure risk, and develop early warning systems. The potential advantages of using out-of-sequence data in these applications to improve the efficiency of earthquake mitigation techniques. The difficulties and limits of estimating out-of-sequence thrust movement for earthquake mitigation. It addresses data quality difficulties, modelling uncertainties, and computational complications. To address these obstacles and increase the accuracy and reliability of out-of-sequence thrust movement estimates, the authors recommend topics for additional study and improvement. The study is a helpful resource for seismic monitoring and earthquake risk assessment researchers, engineers, and policymakers, supporting innovations in earthquake mitigation measures based on a better knowledge of thrust movement dynamics.

Keywords: earthquake mitigation, out-of-sequence thrust, satellite imagery, seismic recordings, GPS measurements

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Authors: M. Zamurad Shah, M. Kemal Ozgoren, Raza Samar

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This paper presents a 3D guidance scheme for Unmanned Aerial Vehicles (UAVs). The proposed guidance scheme is based on the sliding mode approach using nonlinear sliding manifolds. Generalized 3D kinematic equations are considered here during the design process to cater for the coupling between longitudinal and lateral motions. Sliding mode based guidance scheme is then derived for the multiple-input multiple-output (MIMO) system using the proposed nonlinear manifolds. Instead of traditional sliding surfaces, nonlinear sliding surfaces are proposed here for performance and stability in all flight conditions. In the reaching phase control inputs, the bang-bang terms with signum functions are accompanied with proportional terms in order to reduce the chattering amplitudes. The Proposed 3D guidance scheme is implemented on a 6-degrees-of-freedom (6-dof) simulation of a UAV and simulation results are presented here for different 3D trajectories with and without disturbances.

Keywords: unmanned aerial vehicles, sliding mode control, 3D guidance, nonlinear sliding manifolds

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Authors: Ch. Surawut, D. Sukawat

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In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: dynamic equation, downscaling, inverse distance, weight interpolation

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Authors: Alireza Lohrasbi, Alireza Lavaei, Mohammadali M. Shahlaei

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The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Arbitrary Lagrangian Eulerian (ALE) finite element modeling technique.

Keywords: dam break, Naiver-Stokes equations, free-surface flows, Arbitrary Lagrangian-Eulerian

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Authors: S. Ahmed, P. Dlask, B. Hasan

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There are several ways to estimate the cost of the construction project: simple and detailed. The process of estimating cost is usually done during the design stage, which should take long-time and the designer must give attention to all details. This paper explain the causes of the deviations occurring in the cost of the construction project, and determines the reasons of these differences between contractual cost and final cost of the construction project, through the study of literature review related to this field, and benefiting from the experience of workers in the field of building (owners, contractors) through designing a questionnaire, and finding the most ten important reasons and explain the relation between the contractual cost and the final cost according to these reasons. The difference between those values will be showed through diagrams drawn using the statistical program. In addition to studying the effects of overrun costs on the advancing of the project, and identify the most five important effects. According to the results, we can propose the right direction for the final cost evaluation and propose some measures that would help to control and adjust the deviation in the costs.

Keywords: construction projects, building, cost, estimating costs, delay, overrun

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Authors: Geeta Partap, Nitika Chugh

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The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: microstretch, deflection, exponential load, Laplace transforms, residue theorem, simply supported

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Authors: Orkide Donma, Mustafa M. Donma

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Basal metabolic rate (BMR) is widely used and an accepted measure of energy expenditure. Its principal determinant is body mass. However, this parameter is also correlated with a variety of other factors. The objective of this study is to measure BMR and compare it with the values obtained from predictive equations in adults classified according to their body mass index (BMI) values. 276 adults were included into the scope of this study. Their age, height and weight values were recorded. Five groups were designed based on their BMI values. First group (n = 85) was composed of individuals with BMI values varying between 18.5 and 24.9 kg/m². Those with BMI values varying from 25.0 to 29.9 kg/m² constituted Group 2 (n = 90). Individuals with 30.0-34.9 kg/m², 35.0-39.9 kg/m², > 40.0 kg/m² were included in Group 3 (n = 53), 4 (n = 28) and 5 (n = 20), respectively. The most commonly used equations to be compared with the measured BMR values were selected. For this purpose, the values were calculated by the use of four equations to predict BMR values, by name, introduced by Food and Agriculture Organization (FAO)/World Health Organization (WHO)/United Nations University (UNU), Harris and Benedict, Owen and Mifflin. Descriptive statistics, ANOVA, post-Hoc Tukey and Pearson’s correlation tests were performed by a statistical program designed for Windows (SPSS, version 16.0). p values smaller than 0.05 were accepted as statistically significant. Mean ± SD of groups 1, 2, 3, 4 and 5 for measured BMR in kcal were 1440.3 ± 210.0, 1618.8 ± 268.6, 1741.1 ± 345.2, 1853.1 ± 351.2 and 2028.0 ± 412.1, respectively. Upon evaluation of the comparison of means among groups, differences were highly significant between Group 1 and each of the remaining four groups. The values were increasing from Group 2 to Group 5. However, differences between Group 2 and Group 3, Group 3 and Group 4, Group 4 and Group 5 were not statistically significant. These insignificances were lost in predictive equations proposed by Harris and Benedict, FAO/WHO/UNU and Owen. For Mifflin, the insignificance was limited only to Group 4 and Group 5. Upon evaluation of the correlations of measured BMR and the estimated values computed from prediction equations, the lowest correlations between measured BMR and estimated BMR values were observed among the individuals within normal BMI range. The highest correlations were detected in individuals with BMI values varying between 30.0 and 34.9 kg/m². Correlations between measured BMR values and BMR values calculated by FAO/WHO/UNU as well as Owen were the same and the highest. In all groups, the highest correlations were observed between BMR values calculated from Mifflin and Harris and Benedict equations using age as an additional parameter. In conclusion, the unique resemblance of the FAO/WHO/UNU and Owen equations were pointed out. However, mean values obtained from FAO/WHO/UNU were much closer to the measured BMR values. Besides, the highest correlations were found between BMR calculated from FAO/WHO/UNU and measured BMR. These findings suggested that FAO/WHO/UNU was the most reliable equation, which may be used in conditions when the measured BMR values are not available.

Keywords: adult, basal metabolic rate, fao/who/unu, obesity, prediction equations

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Authors: Jonathan D. Moore, Mark G. Reith, David S. Long

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Serious games (SGs) have been shown to be an effective teaching tool in many contexts. Because of the success of SGs, several design frameworks have been created to expedite the process of making original serious games to teach specific learning objectives (LOs). Even with these frameworks, the time required to create a custom SG from conception to implementation can range from months to years. Furthermore, it is even more difficult to design a game framework that allows an instructor to create customized game variants supporting multiple LOs within the same field. This paper proposes a refactoring methodology to apply the theoretical principles from well-established design frameworks to a pre-existing serious game. The expected result is a generalized game that can be quickly customized to teach LOs not originally targeted by the game. This methodology begins by describing the general components in a game, then uses a combination of two SG design frameworks to extract the teaching elements present in the game. The identified teaching elements are then used as the theoretical basis to determine the range of LOs that can be taught by the game. This paper evaluates the proposed methodology by presenting a case study of refactoring the serious game Battlespace Next (BSN) to teach joint military capabilities. The range of LOs that can be taught by the generalized BSN are identified, and examples of creating custom LOs are given. Survey results from users of the generalized game are also provided. Lastly, the expected impact of this work is discussed and a road map for future work and evaluation is presented.

Keywords: serious games, learning objectives, game design, learning theory, game framework

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Authors: Godwin Chigozie Okpara

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This paper using standard GARCH, EGARCH, and TARCH models on day of the week return series (of 246 days) from the Nigerian Stock market estimated the model variants’ VaR. An asymmetric return distribution and fat-tail phenomenon in financial time series were considered by estimating the models with normal, student t and generalized error distributions. The analysis based on Akaike Information Criterion suggests that the EGARCH model with student t innovation distribution can furnish more accurate estimate of VaR. In the light of this, we apply the likelihood ratio tests of proportional failure rates to VaR derived from EGARCH model in order to determine the short and long positions VaR performances. The result shows that as alpha ranges from 0.05 to 0.005 for short positions, the failure rate significantly exceeds the prescribed quintiles while it however shows no significant difference between the failure rate and the prescribed quantiles for long positions. This suggests that investors and portfolio managers in the Nigeria stock market have long trading position or can buy assets with concern on when the asset prices will fall. Precisely, the VaR estimates for the long position range from -4.7% for 95 percent confidence level to -10.3% for 99.5 percent confidence level.

Keywords: downside risk, value-at-risk, failure rate, kupiec LR tests, GARCH models

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Authors: Bouthiba Amina

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The estimation of the statistics bound to the precipitation represents a vast domain, which puts numerous challenges to meteorologists and hydrologists. Sometimes, it is necessary, to approach in value the extreme events for sites where there is little, or no datum, as well as their periods of return. The search for a model of the frequency of the heights of daily rains dresses a big importance in operational hydrology: It establishes a basis for predicting the frequency and intensity of floods by estimating the amount of precipitation in past years. The most known and the most common approach is the statistical approach, It consists in looking for a law of probability that fits best the values observed by the random variable " daily maximal rain " after a comparison of various laws of probability and methods of estimation by means of tests of adequacy. Therefore, a frequent analysis of the annual series of daily maximal rains was realized on the data of 54 pluviometric stations of the pond of high and average. This choice was concerned with five laws usually applied to the study and the analysis of frequent maximal daily rains. The chosen period is from 1970 to 2013. It was of use to the forecast of quantiles. The used laws are the law generalized by extremes to three components, those of the extreme values to two components (Gumbel and log-normal) in two parameters, the law Pearson typifies III and Log-Pearson III in three parameters. In Algeria, Gumbel's law has been used for a long time to estimate the quantiles of maximum flows. However, and we will check and choose the most reliable law.

Keywords: return period, extreme flow, statistics laws, Gumbel, estimation

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Authors: Prashant G. Metri

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A numerical model is developed to study nano liquid film flow over an unsteady stretching sheet in the presence of hydromagnetic have been investigated. Similarity transformations are used to convert unsteady boundary layer equations to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved numerically using Runge-Kutta-Fehlberg and Newton-Raphson schemes. A relationship between film thickness β and the unsteadiness parameter S is found, the effect of unsteadiness parameter S, and the hydromagnetic parameter S, on the velocity and temperature distributions are presented. The present analysis shows that the combined effect of magnetic field and viscous dissipation has a significant influence in controlling the dynamics of the considered problem. Comparison with known results for certain particular cases is in excellent agreement.

Keywords: boundary layer flow, nanoliquid, thin film, unsteady stretching sheet

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Authors: Helmi Temimi

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In this paper, we study the super-convergence properties of the discontinuous Galerkin (DG) method applied to one-dimensional mth-order ordinary differential equations without introducing auxiliary variables. We found that nth−derivative of the DG solution exhibits an optimal O (hp+1−n) convergence rates in the L2-norm when p-degree piecewise polynomials with p≥1 are used. We further found that the odd-derivatives and the even derivatives are super convergent, respectively, at the upwind and downwind endpoints.

Keywords: discontinuous, galerkin, superconvergence, higherorder, error, estimates

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Authors: H. Mahdavinezhad, M. Labbaf, H. R. Tavakoli

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In recent decades, the study and control of the destructive effects of explosive vibration in construction projects has received more attention, and several experimental equations in the field of vibration prediction as well as allowable vibration limit for various structures are presented. Researchers have developed a number of experimental equations to estimate the peak particle velocity (PPV), in which the experimental constants must be obtained at the site of the explosion by fitting the data from experimental explosions. In this study, the most important of these equations was evaluated for strong massive conglomerates around Dez Dam by collecting data on explosions, including 30 particle velocities, 27 displacements, 27 vibration frequencies and 27 acceleration of earth vibration at different distances; they were recorded in the form of two types of detonation systems, NUNEL and electric. Analysis showed that the data from the explosion had the best correlation with the cube root of the explosive, R2=0.8636, but overall the correlation coefficients are not much different. To estimate the vibration in this project, data regression was performed in the other formats, which resulted in the presentation of new equation with R2=0.904 correlation coefficient. Finally according to the importance of the studied structures in order to ensure maximum non damage to adjacent structures for each diagram, a range of application was defined so that for distances 0 to 70 meters from blast site, exponent n=0.33 and for distances more than 70 m, n =0.66 was suggested.

Keywords: blasting, blast-induced vibration, empirical equations, PPV, tunnel

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Authors: Khaled Benyounes

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Determination of the rock mechanical properties such as unconfined compressive strength UCS, Young’s modulus E, and tensile strength by the Brazilian test Rtb is considered to be the most important component in drilling and mining engineering project. Research related to establishing correlation between strength and physical parameters of rocks has always been of interest to mining and reservoir engineering. For this, many rock blocks of limestone were collected from the quarry located in Meftah(Algeria), the cores were crafted in the laboratory using a core drill. This work examines the relationships between mechanical properties and some physical properties of limestone. Many empirical equations are established between UCS and physical properties of limestone (such as dry bulk density, velocity of P-waves, dynamic Young’s modulus, alteration index, and total porosity). Others correlations UCS-tensile strength, dynamic Young’s modulus-static Young’s modulus have been find. Based on the Mohr-Coulomb failure criterion, we were able to establish mathematical relationships that will allow estimating the cohesion and internal friction angle from UCS and indirect tensile strength. Results from this study can be useful for mining industry for resolve range of geomechanical problems such as slope stability.

Keywords: limestone, mechanical strength, Young’s modulus, porosity

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Authors: Elisa Boatti, Ulisse Stefanelli, Alessandro Reali, Ferdinando Auricchio

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Thanks to their unusual properties, shape memory alloys (SMAs) are good candidates for advanced applications in a wide range of engineering fields, such as automotive, robotics, civil, biomedical, aerospace. In the last decades, the ever-growing interest for such materials has boosted several research studies aimed at modeling their complex nonlinear behavior in an effective and robust way. Since the constitutive response of SMAs is strongly thermomechanically coupled, the investigation of the non-isothermal evolution of the material must be taken into consideration. The present study considers an existing three-dimensional phenomenological model for SMAs, able to reproduce the main SMA properties while maintaining a simple user-friendly structure, and proposes a variational reformulation of the full non-isothermal version of the model. While the considered model has been thoroughly assessed in an isothermal setting, the proposed formulation allows to take into account the full nonisothermal problem. In particular, the reformulation is inspired to the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) formalism, and is based on a generalized gradient flow of the total entropy, related to thermal and mechanical variables. Such phrasing of the model is new and allows for a discussion of the model from both a theoretical and a numerical point of view. Moreover, it directly implies the dissipativity of the flow. A semi-implicit time-discrete scheme is also presented for the fully coupled thermomechanical system, and is proven unconditionally stable and convergent. The correspondent algorithm is then implemented, under a space-homogeneous temperature field assumption, and tested under different conditions. The core of the algorithm is composed of a mechanical subproblem and a thermal subproblem. The iterative scheme is solved by a generalized Newton method. Numerous uniaxial and biaxial tests are reported to assess the performance of the model and algorithm, including variable imposed strain, strain rate, heat exchange properties, and external temperature. In particular, the heat exchange with the environment is the only source of rate-dependency in the model. The reported curves clearly display the interdependence between phase transformation strain and material temperature. The full thermomechanical coupling allows to reproduce the exothermic and endothermic effects during respectively forward and backward phase transformation. The numerical tests have thus demonstrated that the model can appropriately reproduce the coupled SMA behavior in different loading conditions and rates. Moreover, the algorithm has proved effective and robust. Further developments are being considered, such as the extension of the formulation to the finite-strain setting and the study of the boundary value problem.

Keywords: generalized gradient flow, GENERIC formalism, shape memory alloys, thermomechanical coupling

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Authors: M. A. Ansari, A. Hussain, A. Uddin

Abstract:

A side weir is a flow diversion structure provided in the side wall of a channel to divert water from the main channel to a branch channel. The trapezoidal labyrinth weir is a special type of weir in which crest length of the weir is increased to pass higher discharge. Experimental and numerical studies related to the coefficient of discharge of trapezoidal labyrinth weir in an open channel have been presented in the present study. Group Method of Data Handling (GMDH) with the transfer function of quadratic polynomial has been used to predict the coefficient of discharge for the side trapezoidal labyrinth weir. A new model is developed for coefficient of discharge of labyrinth weir by regression method. Generalized models for predicting the coefficient of discharge for labyrinth weir using Group Method of Data Handling (GMDH) network have also been developed. The prediction based on GMDH model is more satisfactory than those given by traditional regression equations.

Keywords: discharge coefficient, group method of data handling, open channel, side labyrinth weir

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Authors: Tarul Garg, P. N. Agrawal

Abstract:

We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Flavia Smarrazzo

Abstract:

Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

Procedia PDF Downloads 281