Search results for: predictive equations

Authors: Duncan Oteki, Andebut Yeneneh, Daba Gedafa, Nabil Suleiman

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Most agencies lack the equipment required to measure the dynamic modulus (|E*|) of asphalt mixtures, necessitating the need to use predictive models. This study compared measured |E*| values for nine North Dakota asphalt mixes using the original Witczak, modified Witczak, and Hirsch models. The influence of temperature on the |E*| models was investigated, and Pavement ME simulations were conducted using measured |E*| and predictions from the most accurate |E*| model. The results revealed that the original Witczak model yielded the lowest Se/Sy and highest R² values, indicating the lowest bias and highest accuracy, while the poorest overall performance was exhibited by the Hirsch model. Using predicted |E*| as inputs in the Pavement ME generated conservative distress predictions compared to using measured |E*|. The original Witczak model was recommended for predicting |E*| for low-reliability pavements in North Dakota.

Keywords: asphalt mixture, binder, dynamic modulus, MEPDG, pavement ME, performance, prediction

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Authors: Vandana N. Purav

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The Dynamical systems concept is a mathematical formalization for any fixed rule that describes the time dependence of a points position in its ambient space. e.g. pendulum of a clock, the number of fish each spring in a lake, the number of rabbits spring in an enclosure, etc. The Dynamical system theory used to describe the complex nature that is dynamical systems with differential equations called continuous dynamical system or dynamical system with difference equations called discrete dynamical system. The concept of dynamical system has its origin in Newtonian mechanics.

Keywords: dynamical systems, Fibonacci numbers, Newtonian mechanics, discrete dynamical system

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Authors: Thanooja Naushad, Meena Natarajan, Tushar Vasant Kulkarni

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Background: The Lacey Assessment of Preterm Infants (LAPI) is used in clinical practice to identify premature babies at risk of neuromotor impairments, especially cerebral palsy. This study attempted to find the validity of the Lacey assessment of preterm infants to predict neuromotor outcomes of premature babies at 12 months corrected age and to compare its predictive ability with the brain ultrasound. Methods: This prospective cohort study included 89 preterm infants (45 females and 44 males) born below 35 weeks gestation who were admitted to the neonatal intensive care unit of a government hospital in Dubai. Initial assessment was done using the Lacey assessment after the babies reached 33 weeks postmenstrual age. Follow up assessment on neuromotor outcomes was done at 12 months (± 1 week) corrected age using two standardized outcome measures, i.e., infant neurological international battery and Alberta infant motor scale. Brain ultrasound data were collected retrospectively. Data were statistically analyzed, and the diagnostic accuracy of the Lacey assessment of preterm infants (LAPI) was calculated -when used alone and in combination with the brain ultrasound. Results: On comparison with brain ultrasound, the Lacey assessment showed superior specificity (96% vs. 77%), higher positive predictive value (57% vs. 22%), and higher positive likelihood ratio (18 vs. 3) to predict neuromotor outcomes at one year of age. The sensitivity of Lacey assessment was lower than brain ultrasound (66% vs. 83%), whereas specificity was similar (97% vs. 98%). A combination of Lacey assessment and brain ultrasound results showed higher sensitivity (80%), positive (66%), and negative (98%) predictive values, positive likelihood ratio (24), and test accuracy (95%) than Lacey assessment alone in predicting neurological outcomes. The negative predictive value of the Lacey assessment was similar to that of its combination with brain ultrasound (96%). Conclusion: Results of this study suggest that the Lacey assessment of preterm infants can be used as a supplementary assessment tool for premature babies in the neonatal intensive care unit. Due to its high specificity, Lacey assessment can be used to identify those babies at low risk of abnormal neuromotor outcomes at a later age. When used along with the findings of the brain ultrasound, Lacey assessment has better sensitivity to identify preterm babies at particular risk. These findings have applications in identifying premature babies who may benefit from early intervention services.

Keywords: brain ultrasound, lacey assessment of preterm infants, neuromotor outcomes, preterm

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Authors: Melissa C. Monney

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Psychological testing has been of interest to researchers for many years as useful tools in assessing and diagnosing various disorders as well as to assist in understanding human behavior. However, for over 20 years now, researchers and laypersons alike have been interested in using them for other purposes, such as determining factors in employee selection, promotion, and even termination. In recent years, psychological assessments have been useful in facilitating workplace decision processing, regarding employee circulation within organizations. This literature review explores four of the most commonly used psychological tests in workplace environments, namely cognitive ability, emotional intelligence, integrity, and personality tests, as organizations have used these tests to assess different factors of human behavior as predictive measures of future employee behaviors. The findings suggest that while there is much controversy and debate regarding the validity and reliability of these tests in workplace settings as they were not originally designed for these purposes, the use of such assessments in the workplace has been useful in decreasing costs and employee turnover as well as increase job satisfaction by ensuring the right employees are selected for their roles.

Keywords: cognitive ability, personality testing, predictive validity, workplace behavior

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Authors: Yiming Jin, Yuanhao Gao

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In this paper, using the method of multiple scales, the second sub-harmonic resonance in vortex-induced vibrations (VIV) of a marine pipeline close to the seabed is investigated based on a developed wake oscillator model. The amplitude-frequency equations are also derived. It is found that the oscillation will increase all the time when both discriminants of the amplitude-frequency equations are positive while the oscillation will decay when the discriminants are negative.

Keywords: vortex-induced vibrations, marine pipeline, seabed, sub-harmonic resonance

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Najib K. Dankadai, Ahmad 'Athif Mohd Faudzi, Khairuddin Osman, Muhammad Rusydi Muhammad Razif, IIi Najaa Aimi Mohd Nordin

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Researches in soft actuators are now growing rapidly because of their adequacy to be applied in sectors like medical, agriculture, biological and welfare. This paper presents system identification (SI) and control of the force generated by a two chambers pneumatic soft actuator (PSA). A force mathematical model for the actuator was identified experimentally using data acquisition card and MATLAB SI toolbox. Two control techniques; a predictive functional control (PFC) and conventional proportional integral and derivative (PID) schemes are proposed and compared based on the identified model for the soft actuator flexible mechanism. Results of this study showed that both of the proposed controllers ensure accurate tracking when the closed loop system was tested with the step, sinusoidal and multi step reference input through MATLAB simulation although the PFC provides a better response than the PID.

Keywords: predictive functional control (PFC), proportional integral and derivative (PID), soft actuator, system identification

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Authors: Jacky Liu

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This paper develops a team sports outcome prediction system with potential for wide-ranging applications across various disciplines. Despite significant advancements in predictive analytics, existing studies in sports outcome predictions possess considerable limitations, including insufficient feature engineering and underutilization of advanced machine learning techniques, among others. To address these issues, we extend the Sports Cross Industry Standard Process for Data Mining (SRP-CRISP-DM) framework and propose a unique, comprehensive predictive system, using National Basketball Association (NBA) data as an example to test this extended framework. Our approach follows a holistic methodology in feature engineering, employing both Time Series and Non-Time Series Data, as well as conducting Explanatory Data Analysis and Feature Selection. Furthermore, we contribute to the discourse on target variable choice in team sports outcome prediction, asserting that point spread prediction yields higher profits as opposed to game-winner predictions. Using machine learning algorithms, particularly XGBoost, results in a significant improvement in predictive accuracy of team sports outcomes. Applied to point spread betting strategies, it offers an astounding annual return of approximately 900% on an initial investment of $100. Our findings not only contribute to academic literature, but have critical practical implications for sports betting. Our study advances the understanding of team sports outcome prediction a burgeoning are in complex system predictions and pave the way for potential profitability and more informed decision making in sports betting markets.

Keywords: machine learning, team sports, game outcome prediction, sports betting, profits simulation

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Authors: Vishwesh Kulkarni, Nikhil Bellarykar

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Cellular complexity stems from the interactions among thousands of different molecular species. Thanks to the emerging fields of systems and synthetic biology, scientists are beginning to unravel these regulatory, signaling, and metabolic interactions and to understand their coordinated action. Reverse engineering of biological networks has has several benefits but a poor quality of data combined with the difficulty in reproducing it limits the applicability of these methods. A few years back, many of the commonly used predictive algorithms were tested on a network constructed in the yeast Saccharomyces cerevisiae (S. cerevisiae) to resolve this issue. The network was a synthetic network of five genes regulating each other for the so-called in vivo reverse-engineering and modeling assessment (IRMA). The network was constructed in S. cereviase since it is a simple and well characterized organism. The synthetic network included a variety of regulatory interactions, thus capturing the behaviour of larger eukaryotic gene networks on a smaller scale. We derive a new set of algorithms by solving a nonlinear optimization problem and show how these algorithms outperform other algorithms on these datasets.

Keywords: synthetic gene network, network identification, optimization, nonlinear modeling

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Phakamani Xaba, Robert Huberts, Bilainu Oboirien

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The present study was aimed at developing & comparing two neural-network-based predictive models to predict shelf-life/product age of South African margarine using free fatty acid (FFA), water droplet size (D3.3), water droplet distribution (e-sigma), moisture content, peroxide value (PV), anisidine valve (AnV) and total oxidation (totox) value as input variables to the model. Brick margarine products which had varying ages ranging from fresh i.e. week 0 to week 47 were sourced. The brick margarine products which had been stored at 10 & 25 °C and were characterized. JMP and MATLAB models to predict shelf-life/ margarine age were developed and their performances were compared. The key performance indicators to evaluate the model performances were correlation coefficient (CC), root mean square error (RMSE), and mean absolute percentage error (MAPE) relative to the actual data. The MATLAB-developed model showed a better performance in all three performance indicators. The correlation coefficient of the MATLAB model was 99.86% versus 99.74% for the JMP model, the RMSE was 0.720 compared to 1.005 and the MAPE was 7.4% compared to 8.571%. The MATLAB model was selected to be the most accurate, and then, the number of hidden neurons/ nodes was optimized to develop a single predictive model. The optimized MATLAB with 10 neurons showed a better performance compared to the models with 1 & 5 hidden neurons. The developed models can be used by margarine manufacturers, food research institutions, researchers etc, to predict shelf-life/ margarine product age, optimize addition of antioxidants, extend shelf-life of products and proactively troubleshoot for problems related to changes which have an impact on shelf-life of margarine without conducting expensive trials.

Keywords: margarine shelf-life, predictive modelling, neural networks, oil oxidation

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Authors: Haonan Hu, Shuge Lei, Dasheng Sun, Huabin Zhang, Kehong Yuan, Jian Dai, Jijun Tang

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This paper focuses on the classification task of breast ultrasound images and conducts research on the reliability measurement of classification results. A dual-channel evaluation framework was developed based on the proposed inference reliability and predictive reliability scores. For the inference reliability evaluation, human-aligned and doctor-agreed inference rationals based on the improved feature attribution algorithm SP-RISA are gracefully applied. Uncertainty quantification is used to evaluate the predictive reliability via the test time enhancement. The effectiveness of this reliability evaluation framework has been verified on the breast ultrasound clinical dataset YBUS, and its robustness is verified on the public dataset BUSI. The expected calibration errors on both datasets are significantly lower than traditional evaluation methods, which proves the effectiveness of the proposed reliability measurement.

Keywords: medical imaging, ultrasound imaging, XAI, uncertainty measurement, trustworthy AI

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Authors: Raphael de Oliveira Garcia, Samuel Rocha de Oliveira

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We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional Finite Volume, namely Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods dependent on Riemann problems, applied to equations Euler in order to verify their main features and make comparisons among those methods. It was then implemented the method of Finite Volume Centered of Nessyahu-Tadmor, a numerical schemes that has a formulation free and without dimensional separation of Riemann problem solvers, even in two or more spatial dimensions, at this point, already applied in equations GRMHD. Finally, the Nessyahu-Tadmor method was possible to obtain stable numerical solutions - without spurious oscillations or excessive dissipation - from the magnetized accretion disk process in rotation with respect to a central black hole (BH) Schwarzschild and immersed in a magnetosphere, for the ejection of matter in the form of jet over a distance of fourteen times the radius of the BH, a record in terms of astrophysical simulation of this kind. Also in our simulations, we managed to get substructures jets. A great advantage obtained was that, with the our code, we got simulate GRMHD equations in a simple personal computer.

Keywords: finite volume methods, central schemes, fortran 90, relativistic astrophysics, jet

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Authors: Kwan-u Kim, Jin-Sim, Ryong-Jin Jang, Sung-Duk Kim

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106 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not solve correctly one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition to it, they did not treat the astronomical and physical phenomena in a physical way based on the exact physical laws obtained from the solution of the geodesic equations in Schwarzschild metric, so some former scholars mentioned that Einstein’s theoretical basis of general theory of relativity was obscure and incorrect, but they have not given a correct physical solution to the problems. Furthermore, because general theory of relativity has not given a quantitative solution to the obscure and incorrect problems, generalization of gravitational theory although the former scholars thought of it and tried to do it. In order to solve the problems it is necessary to explore theobscure and incorrect problems in general theory of relativity based on the physical laws and to find out the methodology of solving the problems. Therefore, first of all, as the first sarytep for achieving the purpose, the correct solution of the geodesic equation in Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results has been presented, the obscure and incorrect problems have been showed and an analysis of them has been made on the basis of the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild

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Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop

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In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.

Keywords: heat transfer, nanofluid, shrinking surface, stability analysis, three-dimensional flow

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Authors: Arash Ghahraman, Gyula Bene

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The object of this study is to investigate the effect of viscosity on the propagation of free-surface waves in an incompressible viscous fluid layer of arbitrary depth. While we provide a more detailed study of properties of linear surface waves, the description of fully nonlinear waves in terms of KdV-like (Korteweg-de Vries) equations is discussed. In the linear case, we find that in shallow enough fluids, no surface waves can propagate. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for any given horizontal wave number. The numerical results show that there can be two types of non-propagating modes. One type is always present, and there exist still infinitely many of such modes at the same parameters. In contrast, there can be zero, one or two modes belonging to the other type. Another significant feature is that KdV-like equations. They describe propagating nonlinear viscous surface waves. Since viscosity gives rise to a new wavenumber that cannot be small at the same time as the original one, these equations may not exist. Nonetheless, we propose a reasonable nonlinear description in terms of 1+1 variate functions that make possible successive approximations.

Keywords: free surface wave, water waves, KdV equation, viscosity

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Authors: Nasim Nosoudi, Amir Zadeh, Hunter White, Joshua Conrad, Joon W. Shim

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De novo Malignancy has become one of the major causes of death after transplantation, so early cancer diagnosis and detection can drastically improve survival rates post-transplantation. Most previous work focuses on using artificial intelligence (AI) to predict transplant success or failure outcomes. In this work, we focused on predicting de novo malignancy after liver transplantation using AI. We chose the patients that had malignancy after liver transplantation with no history of malignancy pre-transplant. Their donors were cancer-free as well. We analyzed 254,200 patient profiles with post-transplant malignancy from the US Organ Procurement and Transplantation Network (OPTN). Several popular data mining methods were applied to the resultant dataset to build predictive models to characterize de novo malignancy after liver transplantation. Recipient's bilirubin, creatinine, weight, gender, number of days recipient was on the transplant waiting list, Epstein Barr Virus (EBV), International normalized ratio (INR), and ascites are among the most important factors affecting de novo malignancy after liver transplantation

Keywords: De novo malignancy, bilirubin, data mining, transplantation

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Authors: Syukri Himran, Erwin Eka Putra, Nanang Roni

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This study explains the natural convection of viscous fluid flowing on semi-infinite vertical plate. A set of the governing equations describing the continuity, momentum and energy, have been reduced to dimensionless forms by introducing the references variables. To solve the problems, the equations are formulated by explicit finite-difference in time dependent form and computations are performed by Fortran program. The results describe velocity, temperature profiles both in transient and steady state conditions. An approximate value of heat transfer coefficient and the effects of Pr on convection flow are also presented.

Keywords: natural convection, vertical plate, velocity and temperature profiles, steady and unsteady

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Authors: Gizem Akcan, Erdinc Ozturk

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The purpose of the study was to determine some psychosocial variables that predict dissociation in university students. These psychosocial variables were perceived childhood trauma, alexithymia, and gender. 150 (75 males, 75 females) university students (bachelor, master and postgraduate) were enrolled in this study. They were chosen from universities in Istanbul at the education year of 2016-2017. Dissociative Experiences Scale (DES), Childhood Trauma Questionnaire (CTQ) and Toronto Alexithymia Scale were used to assess related variables. Demographic Information Form was given to students in order to have their demographic information. Frequency Distribution, Linear Regression Analysis, and t-test analysis were used for statistical analysis. Childhood trauma and alexithymia were found to have predictive value on dissociation among university students. However, physical abuse, physical neglect and emotional neglect sub dimensions of childhood trauma and externally-oriented thinking sub dimension of alexithymia did not have predictive value on dissociation. Moreover, there was no significant difference between males and females in terms of dissociation scores of participants.

Keywords: childhood trauma, dissociation, alexithymia, gender

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Authors: Ahmed Alghurabi, Mysara Mohyaldinn, Shiferaw Jufar, Obai Younis, Abdullah Abduljabbar

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Erosion modeling equations were typically acquired from regulated experimental trials for solid particles entrained in single-phase or multi-phase flows. Evidently, those equations were later employed to predict the erosion damage caused by the continuous impacts of solid particles entrained in streamflow. It is also well-known that the particle impact angle and velocity do not change drastically in gas-sand flow erosion prediction; hence an accurate prediction of erosion can be projected. On the contrary, high-density fluid flows, such as water flow, through complex geometries, such as sand screens, greatly affect the sand particles’ trajectories/tracks and consequently impact the erosion rate predictions. Particle tracking models and erosion equations are frequently applied simultaneously as a method to improve erosion visualization and estimation. In the present work, computational fluid dynamic (CFD)-based erosion modeling was performed using a commercially available software; ANSYS Fluent. The continuous phase (water flow) behavior was simulated using the realizable K-epsilon model, and the secondary phase (solid particles), having a 5% flow concentration, was tracked with the help of the discrete phase model (DPM). To accomplish a successful erosion modeling, three erosion equations from the literature were utilized and introduced to the ANSYS Fluent software to predict the screen wire-slot velocity surge and estimate the maximum erosion rates on the screen surface. Results of turbulent kinetic energy, turbulence intensity, dissipation rate, the total pressure on the screen, screen wall shear stress, and flow velocity vectors were presented and discussed. Moreover, the particle tracks and path-lines were also demonstrated based on their residence time, velocity magnitude, and flow turbulence. On one hand, results from the utilized erosion equations have shown similarities in screen erosion patterns, locations, and DPM concentrations. On the other hand, the model equations estimated slightly different values of maximum erosion rates of the wire-wrapped screen. This is solely based on the fact that the utilized erosion equations were developed with some assumptions that are controlled by the experimental lab conditions.

Keywords: CFD simulation, erosion rate prediction, material loss due to erosion, water-sand flow

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Authors: X. Wang, J. S. Kuang

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The Fixed-angle Softened Truss Model with Tension-stiffening (FASTMT) has a superior performance in predicting the shear behaviour of reinforced concrete (RC) membrane elements, especially for the post-cracking behaviour. Nevertheless, massive computational work is inevitable due to the multiple transcendental equations involved in the stress-strain relationship. In this paper, an iterative root-finding technique is introduced to FASTMT for solving quickly the transcendental equations of the tension-stiffening effect of RC membrane elements. This fast FASTMT, which performs in MATLAB, uses the bisection method to calculate the tensile stress of the membranes. By adopting the simplification, the elapsed time of each loop is reduced significantly and the transcendental equations can be solved accurately. Owing to the high efficiency and good accuracy as compared with FASTMT, the fast FASTMT can be further applied in quick prediction of shear behaviour of complex large-scale RC structures.

Keywords: bisection method, FASTMT, iterative root-finding technique, reinforced concrete membrane

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Authors: T. Watanabe

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Combustion analysis of suspended sodium droplet is performed by solving numerically the Navier-Stokes equations and the energy conservation equations. The combustion model consists of the pre-ignition and post-ignition models. The reaction rate for the pre-ignition model is based on the chemical kinetics, while that for the post-ignition model is based on the mass transfer rate of oxygen. The calculated droplet temperature is shown to be in good agreement with the existing experimental data. The temperature field in and around the droplet is obtained as well as the droplet shape variation, and the present numerical model is confirmed to be effective for the combustion analysis.

Keywords: analysis, combustion, droplet, sodium

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Authors: Xuezhang Hou

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In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined.

Keywords: hyperbolic dynamic system, sliding model control, semigroup of linear operators, partial differential equations

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Authors: M. A. C. S. Sampath Fernando, James M. Curran, Renate Meyer

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Model assessment, in the Bayesian context, involves evaluation of the goodness-of-fit and the comparison of several alternative candidate models for predictive accuracy and improvements. In posterior predictive checks, the data simulated under the fitted model is compared with the actual data. Predictive model accuracy is estimated using information criteria such as the Akaike information criterion (AIC), the Bayesian information criterion (BIC), the Deviance information criterion (DIC), and the Watanabe-Akaike information criterion (WAIC). The goal of an information criterion is to obtain an unbiased measure of out-of-sample prediction error. Since posterior checks use the data twice; once for model estimation and once for testing, a bias correction which penalises the model complexity is incorporated in these criteria. Cross-validation (CV) is another method used for examining out-of-sample prediction accuracy. Leave-one-out cross-validation (LOO-CV) is the most computationally expensive variant among the other CV methods, as it fits as many models as the number of observations. Importance sampling (IS), truncated importance sampling (TIS) and Pareto-smoothed importance sampling (PSIS) are generally used as approximations to the exact LOO-CV and utilise the existing MCMC results avoiding expensive computational issues. The reciprocals of the predictive densities calculated over posterior draws for each observation are treated as the raw importance weights. These are in turn used to calculate the approximate LOO-CV of the observation as a weighted average of posterior densities. In IS-LOO, the raw weights are directly used. In contrast, the larger weights are replaced by their modified truncated weights in calculating TIS-LOO and PSIS-LOO. Although, information criteria and LOO-CV are unable to reflect the goodness-of-fit in absolute sense, the differences can be used to measure the relative performance of the models of interest. However, the use of these measures is only valid under specific circumstances. This study has developed 11 models using normal, log-normal, gamma, and student’s t distributions to improve the PCR stutter prediction with forensic data. These models are comprised of four with profile-wide variances, four with locus specific variances, and three which are two-component mixture models. The mean stutter ratio in each model is modeled as a locus specific simple linear regression against a feature of the alleles under study known as the longest uninterrupted sequence (LUS). The use of AIC, BIC, DIC, and WAIC in model comparison has some practical limitations. Even though, IS-LOO, TIS-LOO, and PSIS-LOO are considered to be approximations of the exact LOO-CV, the study observed some drastic deviations in the results. However, there are some interesting relationships among the logarithms of pointwise predictive densities (lppd) calculated under WAIC and the LOO approximation methods. The estimated overall lppd is a relative measure that reflects the overall goodness-of-fit of the model. Parallel log-likelihood profiles for the models conditional on equal posterior variances in lppds were observed. This study illustrates the limitations of the information criteria in practical model comparison problems. In addition, the relationships among LOO-CV approximation methods and WAIC with their limitations are discussed. Finally, useful recommendations that may help in practical model comparisons with these methods are provided.

Keywords: cross-validation, importance sampling, information criteria, predictive accuracy

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Authors: Md. S. Ansari, S. S. Motsa

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In this paper, an analysis has been made on the flow of non-Newtonian viscoelastic nanofluid over a linearly stretching sheet under the influence of uniform magnetic field. Heat transfer characteristics is analyzed taking into the effect of nonlinear radiation and non-uniform heat source/sink. Transport equations contain the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The relevant partial differential equations are non-dimensionalized and transformed into ordinary differential equations by using appropriate similarity transformations. The transformed, highly nonlinear, ordinary differential equations are solved by spectral local linearisation method. The numerical convergence, error and stability analysis of iteration schemes are presented. The effects of different controlling parameters, namely, radiation, space and temperature-dependent heat source/sink, Brownian motion, thermophoresis, viscoelastic, Lewis number and the magnetic force parameter on the flow field, heat transfer characteristics and nanoparticles concentration are examined. The present investigation has many industrial and engineering applications in the fields of coatings and suspensions, cooling of metallic plates, oils and grease, paper production, coal water or coal–oil slurries, heat exchangers’ technology, and materials’ processing and exploiting.

Keywords: magnetic field, nonlinear radiation, non-uniform heat source/sink, similar solution, spectral local linearisation method, Rosseland diffusion approximation

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Authors: Peña A. Roland R., Lozano P. Jean P.

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The waterflooding process is an enhanced oil recovery (EOR) method that appears tremendously successful. This paper shows the importance of the role of the numerical modelling of waterflooding and how to provide a better description of the fluid flow during this process. The mathematical model is based on the mass conservation equations for the oil and water phases. Rock compressibility and capillary pressure equations are coupled to the mathematical model. For discretizing and linearizing the partial differential equations, we used the Finite Volume technique and the Newton-Raphson method, respectively. The results of three scenarios for waterflooding in porous media are shown. The first scenario was estimating the water saturation in the media without rock compressibility and without capillary pressure. The second scenario was estimating the front of the water considering the rock compressibility and capillary pressure. The third case is to compare different fronts of water saturation for three fluids viscosity ratios without and with rock compressibility and without and with capillary pressure. Results of the simulation indicate that the rock compressibility and the capillary pressure produce changes in the pressure profile and saturation profile during the displacement of the oil for the water.

Keywords: capillary pressure, numerical simulation, rock compressibility, two-phase flow

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Authors: Partha P. Gopmandal, S. Bhattacharyya

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We investigate the thermal end effect on the pseudo-steady state behavior of the isotachophoretic transport of ionic species in a 2-D microchannel. Both ends of the channel are kept at a constant temperature which may lead to significant changes in electrophoretic migration speed. A mathematical model based on Nernst-Planck equations for transport of ions coupled with the equation for temperature field is considered. In addition, the charge conservation equations govern the potential field due to the external electric field. We have computed the equations for ion transport, potential and temperature in a coupled manner through the finite volume method. The diffusive terms are discretized via central difference scheme, while QUICK (Quadratic Upwind Interpolation Convection Kinematics) scheme is used to discretize the convective terms. We find that the thermal end effect has significant effect on the isotachophoretic (ITP) migration speed of the analyte. Our result shows that the ITP velocity for temperature dependent case no longer varies linearly with the applied electric field. A detailed analysis has been made to provide a range of the key parameters to minimize the Joule heating effect on ITP transport of analytes.

Keywords: finite volume method, isotachophoresis, QUICK scheme, thermal effect

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Authors: Julia Zimmerman, Gaurav Savant

Abstract:

This study aims to evaluate the efficacy of the U.S. Army Corp of Engineers’ River Analysis System (HEC-RAS) application to modeling the hydraulics of estuaries. HEC-RAS has been broadly used for a variety of riverine applications. However, it has not been widely applied to the study of circulation in estuaries. This report details the model development and validation of a combined 1D/2D unsteady flow hydraulic model using HEC-RAS for estuaries and they are associated with tidally influenced rivers. Two estuaries, Galveston Bay and Delaware Bay, were used as case studies. Galveston Bay, a bar-built, vertically mixed estuary, was modeled for the 2005 calendar year. Delaware Bay, a drowned river valley estuary, was modeled from October 22, 2019, to November 5, 2019. Water surface elevation was used to validate both models by comparing simulation results to NOAA’s Center for Operational Oceanographic Products and Services (CO-OPS) gauge data. Simulations were run using the Diffusion Wave Equations (DW), the Shallow Water Equations, Eulerian-Lagrangian Method (SWE-ELM), and the Shallow Water Equations Eulerian Method (SWE-EM) and compared for both accuracy and computational resources required. In general, the Diffusion Wave Equations results were found to be comparable to the two Shallow Water equations sets while requiring less computational power. The 1D/2D combined approach was valid for study areas within the 2D flow area, with the 1D flow serving mainly as an inflow boundary condition. Within the Delaware Bay estuary, the HEC-RAS DW model ran in 22 minutes and had an average R² value of 0.94 within the 2-D mesh. The Galveston Bay HEC-RAS DW ran in 6 hours and 47 minutes and had an average R² value of 0.83 within the 2-D mesh. The longer run time and lower R² for Galveston Bay can be attributed to the increased length of the time frame modeled and the greater complexity of the estuarine system. The models did not accurately capture tidal effects within the 1D flow area.

Keywords: Delaware bay, estuarine hydraulics, Galveston bay, HEC-RAS, one-dimensional modeling, two-dimensional modeling

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Authors: Alexandra Andrade Brandão Soares, Paulo Batista Gonçalves

Abstract:

Using a modal expansion that satisfies the boundary and continuity conditions and expresses the modal couplings characteristic of cylindrical shells in the nonlinear regime, the equations of motion are discretized using the Galerkin method. The resulting algebraic equations are solved by the Newton-Raphson method, thus obtaining the nonlinear frequency-amplitude relation. Finally, a parametric analysis is conducted to study the influence of the geometry of the shell, the gradient of the functional material and vibration modes on the degree and type of nonlinearity of the cylindrical shell, which is the main contribution of this research work.

Keywords: cylindrical shells, dynamics, functionally graded material, nonlinear vibrations

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