Search results for: predictive equations

Authors: Mezghiche Kamel

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We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

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Authors: Israel Ibarra Solis, Juan Carlos Rodriguez Sierra, Ma. del Carmen Salazar Hernandez, Isis Rodriguez Sanchez, David Perez Guerrero

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At the present paper we try to explain the analysis techniques use for the lubricating oil in a maintenance period of a city bus (Mercedes Benz Boxer 40), which is call ‘R-24 route’, line Coecillo Centro SA de CV in Leon Guanajuato, to estimate the optimal time for the oil change. Using devices such as the rotational viscometer and the atomic absorption spectrometer, they can detect the incipient form when the oil loses its lubricating properties and, therefore, cannot protect the mechanical components of diesel engines such these trucks. Timely detection of lost property in the oil, it allows us taking preventive plan maintenance for the fleet.

Keywords: atomic absorption spectrometry, maintenance, predictive velocity rate, lubricating oils

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Authors: Muhammad Babar Shahzad

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The purpose of our study is to investigate the relationship between perceived job autonomy and turnover intention in sales & marketing staff. Perceived job autonomy is considered one of most studied dimension of Job Characteristic Model. But still there is a confusion in scholars about predictive role of perceived job autonomy in turnover intention. In line of more complex research on this relation, we investigated the relationship between perceived job autonomy and turnover intention. Did nature of job have any impact on this relationship. On the call of different authors we take interactive effect of perceived job autonomy and procedural justice on turnover intention. Predictive role of distributive justice to employee outcomes is not deniable. But predictive role of distributive justice will be prone in different contextual influences. Interactive role of distributive justice and perceived job autonomy is also not tested before. We collected date from 279 marketing and sales managers working in financial institution, FMCG industries, Pharamesutical Industry & Bank. Strong and direct negative relation was found in perceived job autonomy, distributive justice & procedural justice on turnover intention. Distributive and procedural justice is also amplifying the negative relationship of perceived job autonomy and turnover intention. Limitation and future direction for research is also discussed.

Keywords: perceived job autonomy, turnover intention, procedural justice, distributive job

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Authors: Hamdi Beji, Toufik Kanit, Tanguy Messager

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This study aims to construct a predictive model proficient in foreseeing the linear elastic and thermal characteristics of composite materials, drawing on a multitude of influencing parameters. These parameters encompass the shape of inclusions (circular, elliptical, square, triangle), their spatial coordinates within the matrix, orientation, volume fraction (ranging from 0.05 to 0.4), and variations in contrast (spanning from 10 to 200). A variety of machine learning techniques are deployed, including decision trees, random forests, support vector machines, k-nearest neighbors, and an artificial neural network (ANN), to facilitate this predictive model. Moreover, this research goes beyond the predictive aspect by delving into an inverse analysis using genetic algorithms. The intent is to unveil the intrinsic characteristics of composite materials by evaluating their thermomechanical responses. The foundation of this research lies in the establishment of a comprehensive database that accounts for the array of input parameters mentioned earlier. This database, enriched with this diversity of input variables, serves as a bedrock for the creation of machine learning and genetic algorithm-based models. These models are meticulously trained to not only predict but also elucidate the mechanical and thermal conduct of composite materials. Remarkably, the coupling of machine learning and genetic algorithms has proven highly effective, yielding predictions with remarkable accuracy, boasting scores ranging between 0.97 and 0.99. This achievement marks a significant breakthrough, demonstrating the potential of this innovative approach in the field of materials engineering.

Keywords: machine learning, composite materials, genetic algorithms, mechanical and thermal proprieties

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Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

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The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: bonded rubber, quasi-static test, shape factor, apparent Young’s modulus

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Authors: Ayliana Dharmawan, Heng Yong Sheng, Zhang Xiaojin, Tan Thai Lian

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To facilitate discharge planning, doctors are presently required to assign an Estimated Discharge Date (EDD) for each patient admitted to the hospital. This assignment of the EDD is largely based on the doctor’s judgment. This can be difficult for cases which are complex or relatively new to the doctor. It is hypothesized that a data-driven approach would be able to facilitate the doctors to make accurate estimations of the discharge date. Making use of routinely collected data on inpatient discharges between January 2013 and May 2016, a predictive model was developed using machine learning techniques to predict the Length of Stay (and hence the EDD) of inpatients, at the point of admission. The predictive performance of the model was compared to that of the clinicians using accuracy measures. Overall, the best performing model was found to be able to predict EDD with an accuracy improvement in Average Squared Error (ASE) by -38% as compared to the first EDD determined by the present method. It was found that important predictors of the EDD include the provisional diagnosis code, patient’s age, attending doctor at admission, medical specialty at admission, accommodation type, and the mean length of stay of the patient in the past year. The predictive model can be used as a tool to accurately predict the EDD.

Keywords: inpatient, estimated discharge date, EDD, prediction, data-driven

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: Amandeep Sharma, Digvaijay Verma, Ruplal Choudhary

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Food processing is an activity across the globe that help in better handling of agricultural produce, including dairy, meat, and fish. The operations carried out in the food industry includes raw material quality authenticity; sorting and grading; processing into various products using thermal treatments – heating, freezing, and chilling; packaging; and storage at the appropriate temperature to maximize the shelf life of the products. All this is done to safeguard the food products and to ensure the distribution up to the consumer. The approaches to develop predictive models based on mathematical or statistical tools or empirical models’ development has been reported for various milk processing activities, including plant maintenance and wastage. Recently AI is the key factor for the fourth industrial revolution. AI plays a vital role in the food industry, not only in quality and food security but also in different areas such as manufacturing, packaging, and cleaning. A new conceptual model was developed, which shows that smaller sample size as only spectra would be required to predict the other values hence leads to saving on raw materials and chemicals otherwise used for experimentation during the research and new product development activity. It would be a futuristic approach if these tools can be further clubbed with the mobile phones through some software development for their real time application in the field for quality check and traceability of the product.

Keywords: predictive modlleing, ann, ai, food

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Authors: Yan Zhang

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Predictive maintenance is a technique to predict when an in-service machine will fail so that maintenance can be planned in advance. Analytics-driven predictive maintenance is gaining increasing attention in many industries such as manufacturing, utilities, aerospace, etc., along with the emerging demand of Internet of Things (IoT) applications and the maturity of technologies that support Big Data storage and processing. This study aims to build an end-to-end analytics solution that includes both real-time machine condition monitoring and machine learning based predictive analytics capabilities. The goal is to showcase a general predictive maintenance solution architecture, which suggests how the data generated from field machines can be collected, transmitted, stored, and analyzed. We use a publicly available aircraft engine run-to-failure dataset to illustrate the streaming analytics component and the batch failure prediction component. We outline the contributions of this study from four aspects. First, we compare the predictive maintenance problems from the view of the traditional reliability centered maintenance field, and from the view of the IoT applications. When evolving to the IoT era, predictive maintenance has shifted its focus from ensuring reliable machine operations to improve production/maintenance efficiency via any maintenance related tasks. It covers a variety of topics, including but not limited to: failure prediction, fault forecasting, failure detection and diagnosis, and recommendation of maintenance actions after failure. Second, we review the state-of-art technologies that enable a machine/device to transmit data all the way through the Cloud for storage and advanced analytics. These technologies vary drastically mainly based on the power source and functionality of the devices. For example, a consumer machine such as an elevator uses completely different data transmission protocols comparing to the sensor units in an environmental sensor network. The former may transfer data into the Cloud via WiFi directly. The latter usually uses radio communication inherent the network, and the data is stored in a staging data node before it can be transmitted into the Cloud when necessary. Third, we illustrate show to formulate a machine learning problem to predict machine fault/failures. By showing a step-by-step process of data labeling, feature engineering, model construction and evaluation, we share following experiences: (1) what are the specific data quality issues that have crucial impact on predictive maintenance use cases; (2) how to train and evaluate a model when training data contains inter-dependent records. Four, we review the tools available to build such a data pipeline that digests the data and produce insights. We show the tools we use including data injection, streaming data processing, machine learning model training, and the tool that coordinates/schedules different jobs. In addition, we show the visualization tool that creates rich data visualizations for both real-time insights and prediction results. To conclude, there are two key takeaways from this study. (1) It summarizes the landscape and challenges of predictive maintenance applications. (2) It takes an example in aerospace with publicly available data to illustrate each component in the proposed data pipeline and showcases how the solution can be deployed as a live demo.

Keywords: Internet of Things, machine learning, predictive maintenance, streaming data

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Authors: Tohru Kawabe

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In this paper, a new SMC (Sliding Mode Control) method with MP (Model Predictive Control) integral action for the slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method introduce the integral term with standard SMC gain , where the integral gain is optimized for each control period by the MPC algorithms. The aim of this method is to improve the safety and the stability of EVs under braking by controlling the wheel slip ratio. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: sliding mode control, model predictive control, integral action, electric vehicle, slip suppression

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Authors: Miral Selim, May Haggag, Ibrahim Abotaleb

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The aging of transportation infrastructure presents significant challenges, particularly concerning the monitoring and maintenance of bridges. This study investigates the application of Random Forest algorithms for predictive modeling of bridge conditions, utilizing data from the US National Bridge Inventory (NBI). The research is significant as it aims to improve bridge management through data-driven insights that can enhance maintenance strategies and contribute to overall safety. Random Forest is chosen for its robustness, ability to handle complex, non-linear relationships among variables, and its effectiveness in feature importance evaluation. The study begins with comprehensive data collection and cleaning, followed by the identification of key variables influencing bridge condition ratings, including age, construction materials, environmental factors, and maintenance history. Random Forest is utilized to examine the relationships between these variables and the predicted bridge conditions. The dataset is divided into training and testing subsets to evaluate the model's performance. The findings demonstrate that the Random Forest model effectively enhances the understanding of factors affecting bridge conditions. By identifying bridges at greater risk of deterioration, the model facilitates proactive maintenance strategies, which can help avoid costly repairs and minimize service disruptions. Additionally, this research underscores the value of data-driven decision-making, enabling better resource allocation to prioritize maintenance efforts where they are most necessary. In summary, this study highlights the efficiency and applicability of Random Forest in predictive modeling for bridge management. Ultimately, these findings pave the way for more resilient and proactive management of bridge systems, ensuring their longevity and reliability for future use.

Keywords: data analysis, random forest, predictive modeling, bridge management

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Authors: Jaan Lellep, Shahid Mubasshar

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A numerical solution is developed for simply supported nanoarches based on the non-local theory of elasticity. The nanoarch under consideration has a step-wise variable cross-section and is weakened by crack-like defects. It is assumed that the cracks are stationary and the mechanical behaviour of the nanoarch can be modeled by Eringen’s non-local theory of elasticity. The physical and thermal properties are sensitive with respect to changes of dimensions in the nano level. The classical theory of elasticity is unable to describe such changes in material properties. This is because, during the development of the classical theory of elasticity, the speculation of molecular objects was avoided. Therefore, the non-local theory of elasticity is applied to study the vibration of nanostructures and it has been accepted by many researchers. In the non-local theory of elasticity, it is assumed that the stress state of the body at a given point depends on the stress state of each point of the structure. However, within the classical theory of elasticity, the stress state of the body depends only on the given point. The system of main equations consists of equilibrium equations, geometrical relations and constitutive equations with boundary and intermediate conditions. The system of equations is solved by using the method of separation of variables. Consequently, the governing differential equations are converted into a system of algebraic equations whose solution exists if the determinant of the coefficients of the matrix vanishes. The influence of cracks and steps on the natural vibration of the nanoarches is prescribed with the aid of additional local compliance at the weakened cross-section. An algorithm to determine the eigenfrequencies of the nanoarches is developed with the help of computer software. The effects of various physical and geometrical parameters are recorded and drawn graphically.

Keywords: crack, nanoarches, natural frequency, step

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations

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Authors: Michelle R. Sullivan

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Positive romantic relationships and marriages offer a buffer against a host of physical and emotional difficulties. Conversely, poor relationship quality and marital discord can have deleterious consequences for individuals and families. Research has described non-monogamy, infidelity, and consensual non-monogamy, as both consequential and causal of relationship difficulty, or as a unique way a couple strives to make a relationship work. Much research on consensual non-monogamy has built on feminist theory and critique. To the author’s best knowledge, to date, no studies have examined the predictive relationship between individual and relationship characteristics and expectations of non-monogamy. The current longitudinal study: 1) estimated the prevalence of expectations of partner non-monogamy and 2) evaluated whether gender, sexual identity, age, education, how a couple met, and relationship quality were predictive expectations of partner non-monogamy. This study utilized the publically available longitudinal dataset, How Couples Meet and Stay Together. Adults aged 18- to 98-years old (n=4002) were surveyed by phone over 5 waves from 2009-2014. Demographics and how a couple met were gathered through self-report in Wave 1, and relationship quality and expectations of partner non-monogamy were gathered through self-report in Waves 4 and 5 (n=1047). The prevalence of expectations of partner non-monogamy (encompassing both infidelity and consensual non-monogamy) was 4.8%. Logistic regression models indicated that sexual identity, gender, education, and relationship quality were significantly predictive of expectations of partner non-monogamy. Specifically, male gender, lower education, identifying as lesbian, gay, or bisexual, and a lower relationship quality scores were predictive of expectations of partner non-monogamy. Male gender was not predictive of expectations of partner non-monogamy in the follow up logistic regression model. Age and whether a couple met online were not associated with expectations of partner non-monogamy. Clinical implications include awareness of the increased likelihood of lesbian, gay, and bisexual individuals to have an expectation of non-monogamy and the sequelae of relationship dissatisfaction that may be related. Future research directions could differentiate between non-monogamy subtypes and the person and relationship variables that lead to the likelihood of consensual non-monogamy and infidelity as separate constructs, as well as explore the relationship between predicting partner behavior and actual partner behavioral outcomes.

Keywords: open relationship, polyamory, infidelity, relationship satisfaction

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Authors: Jorge Gonzalez-Camus

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In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Arcady Ponosov

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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Wisam Ismail, Sarah Hosgood, Michael Nicholson

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The research hypothesis is that early post-transplant allograft fibrosis will be linked to donor factors and that acute rejection and/or delayed graft function in the recipient will be independent risk factors for the development of fibrosis. This research hypothesis is to explore whether acute rejection/delay graft function has an effect on the renal transplant fibrosis within the first year post live donor kidney transplant between 1998 and 2009. Methods: The study has been designed to identify five time points of the renal transplant biopsies [0 (pre-transplant), 1 month, 3 months, 6 months and 12 months] for 300 live donor renal transplant patients over 12 years period between March 1997 – August 2009. Paraffin fixed slides were collected from Leicester General Hospital and Leicester Royal Infirmary. These were routinely sectioned at a thickness of 4 Micro millimetres for standardization. Conclusions: Fibrosis at 1 month after the transplant was found significantly associated with baseline fibrosis (p<0.001) and HTN in the transplant recipient (p<0.001). Dialysis after the transplant showed a weak association with fibrosis at 1 month (p=0.07). The negative coefficient for HTN (-0.05) suggests a reduction in fibrosis in the absence of HTN. Fibrosis at 1 month was significantly associated with fibrosis at baseline (p 0.01 and 95%CI 0.11 to 0.67). Fibrosis at 3, 6 or 12 months was not found to be associated with fibrosis at baseline (p=0.70. 0.65 and 0.50 respectively). The amount of fibrosis at 1 month is significantly associated with graft survival (p=0.01 and 95%CI 0.02 to 0.14). Rejection and severity of rejection were not found to be associated with fibrosis at 1 month. The amount of fibrosis at 1 month was significantly associated with graft survival (p=0.02) after adjusting for baseline fibrosis (p=0.01). Both baseline fibrosis and graft survival were significant predictive factors. The amount of fibrosis at 1 month was not found to be significantly associated with rejection (p=0.64) after adjusting for baseline fibrosis (p=0.01). The amount of fibrosis at 1 month was not found to be significantly associated with rejection severity (p=0.29) after adjusting for baseline fibrosis (p=0.04). Fibrosis at baseline and HTN in the recipient were found to be predictive factors of fibrosis at 1 month. (p 0.02, p <0.001 respectively). Age of the donor, their relation to the patient, the pre-op Creatinine, artery, kidney weight and warm time were not found to be significantly associated with fibrosis at 1 month. In this complex model baseline fibrosis, HTN in the recipient and cold time were found to be predictive factors of fibrosis at 1 month (p=0.01,<0.001 and 0.03 respectively). Donor age was found to be a predictive factor of fibrosis at 6 months. The above analysis was repeated for 3, 6 and 12 months. No associations were detected between fibrosis and any of the explanatory variables with the exception of the donor age which was found to be a predictive factor of fibrosis at 6 months.

Keywords: fibrosis, transplant, renal, rejection

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Authors: Sufyan Muhammad

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Recently, in achieving highly efficient but at the same time highly accurate solutions has become the major target of numerical analyst community. The concept is termed as compact schemes and has gained great popularity and consequently, we construct compact schemes for fourth order parabolic differential equations used to study vibrations in structures. For the superiority of newly constructed schemes, we consider range of examples. We have achieved followings i.e. (a) numerical scheme utilizes minimum number of stencil points (which means new scheme is compact); (b) numerical scheme is highly accurate (which means new scheme is reliable) and (c) numerical scheme is highly efficient (which means new scheme is fast).

Keywords: central finite differences, compact schemes, Bernoulli's equations, finite differences

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Authors: R. A. Petre, S. E. Nichifor, A. Craifaleanu, I. Stroe

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The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.

Keywords: Lagrange equations, relative motion, inertial reference frame, non-inertial reference frame

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Authors: Syed M. Jawwad Riaz

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There has been a lot of interest in exploring the thermodynamic properties at the horizon of a black hole geometry. Earlier, it has been shown, for different spacetimes, that the Einstein field equations at the horizon can be expressed as a first law of black hole thermodynamics. In this paper, considering r = constant slices, for the Kerr-Newman black hole, shown that the Einstein field equations for the induced 3-metric of the hypersurface is expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces. As expected, it is found that the field equations of the induced metric corresponding to the horizon can only be written as a first law of black hole thermodynamics. It is to be mentioned here that the procedure adopted is much easier, to obtain such results, as here one has to essentially deal with (n - 1)-dimensional induced metric for an n-dimensional spacetime.

Keywords: black hole space-times, Einstein's field equation, foliation, hyper-surfaces

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Alia Alghosoun, Michael Herty, Mohammed Seaid

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We present a new class of numerical techniques to solve shallow water flows over dry areas including run-up. Many recent investigations on wave run-up in coastal areas are based on the well-known shallow water equations. Numerical simulations have also performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of coastal areas. In all these simulations the shallow water equations are solved in entire domain including dry areas and special treatments are used for numerical solution of singularities at these dry regions. In the present study we propose a new method to deal with these difficulties by reformulating the shallow water equations into a new system to be solved only in the wetted domain. The system is obtained by a change in the coordinates leading to a set of equations in a moving domain for which the wet/dry interface is the reconstructed using the wave speed. To solve the new system we present a finite volume method of Lax-Friedrich type along with a modified method of characteristics. The method is well-balanced and accurately resolves dam-break problems over dry areas.

Keywords: dam-break problems, finite volume method, run-up waves, shallow water flows, wet/dry interfaces

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Authors: Edamana Krishnan, Khalil Al-Ghafri

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In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed.

Keywords: travelling wave solutions, solitary wave solutions, compactons, Jacobi elliptic functions, mapping methods

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation.

Keywords: new method AGM, sets of coupled nonlinear equations at engineering field, waves equations, integro-differential, fluid and thermal

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Authors: Yuzhi Cai

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In this paper, we discuss a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. Together with a combining forecasts technique, we then predict USD to GBP currency exchange rates. Combined forecasts contain all the information captured by the fitted QAR models at different quantile levels and are therefore better than those obtained from individual models. Our results show that an unequally weighted combining method performs better than other forecasting methodology. We found that a median AR model can perform well in point forecasting when the predictive density functions are symmetric. However, in practice, using the median AR model alone may involve the loss of information about the data captured by other QAR models. We recommend that combined forecasts should be used whenever possible.

Keywords: combining forecasts, MCMC, predictive density functions, quantile forecasting, quantile modelling

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Authors: Farhad Imanshoar

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The regime or equilibrium geometry of alluvial rivers remains a topic of fundamental scientific and engineering interest. There are several approaches to analyze the problem, namely: empirical formulas, semi-theoretical methods and rational (extreme) procedures. However, none of them is widely accepted at present, due to lack of knowledge of some physical processes associated with channel formation and the simplification hypotheses imposed in order to reduce the high quantity of involved variables. The study presented in this paper shows a new approach to estimate stable width and depth of sand-bed rivers by using developed stream power equation (DSPE). At first, a new procedure based on theoretical analysis and by considering DSPE and ultimate sediment concentration were developed. Then, experimental data for regime condition in sand-bed rivers (flow depth, flow width, sediment feed rate for several cases) were gathered. Finally, the results of this research (regime equations) are compared with the field data and other regime equations. A good agreement was observed between the field data and the values resulted from developed regime equation.

Keywords: regime equations, developed stream power equation, sand-bed rivers, semi-theoretical methods

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Authors: Mohd Tariq, Shyamal K. Nandi, Indra D. Bhatt

Abstract:

Paris polyphylla Smith (Family- Liliaceae; English name-Love apple: Local name- Satuwa) is an important folk medicinal herb of the Indian subcontinent, being a source of number of bioactive compounds for drug formulation. The rhizomes are widely used as antihelmintic, antispasmodic, digestive stomachic, expectorant and vermifuge, antimicrobial, anti-inflammatory, heart and vascular malady, anti-fertility and sedative. Keeping in view of this, the species is being constantly removed from nature for trade and various pharmaceuticals purpose, as a result, the availability of the species in its natural habitat is decreasing. In this context, it would be pertinent to conserve this species and reintroduce them in its natural habitat. Predictive distribution modelling of this species was performed in Western Himalayan Region. One such recent method is Ecological Niche Modelling, also popularly known as Species distribution modelling, which uses computer algorithms to generate predictive maps of species distributions in a geographic space by correlating the point distributional data with a set of environmental raster data. In case of P. polyphylla, and to understand its potential distribution zones and setting up of artificial introductions, or selecting conservation sites, and conservation and management of their native habitat. Among the different districts of Uttarakhand (28°05ˈ-31°25ˈ N and 77°45ˈ-81°45ˈ E) Uttarkashi, Rudraprayag, Chamoli, Pauri Garhwal and some parts of Bageshwar, 'Maximum Entropy' (Maxent) has predicted wider potential distribution of P. polyphylla Smith. Distribution of P. polyphylla is mainly governed by Precipitation of Driest Quarter and Mean Diurnal Range i.e., 27.08% and 18.99% respectively which indicates that humidity (27%) and average temperature (19°C) might be suitable for better growth of Paris polyphylla.

Keywords: biodiversity conservation, Indian Himalayan region, Paris polyphylla, predictive distribution modelling

Procedia PDF Downloads 330

Authors: Usamah Al-Ali

Abstract:

We explore the effect of expanding space on the exoticity of the matter supporting a traversable Lorentzian wormhole of zero radial tide whose line element is given by ds2 = dt^2 − a^2(t)[ dr^2/(1 − kr2 −b(r)/r)+ r2dΩ^2 in the context of General Relativity. This task is achieved by deriving the Einstein field equations for anisotropic matter field corresponding to the considered cosmological wormhole metric and performing a classification of their solutions on the basis of a variable equations of state (EoS) of the form p = ω(r)ρ. Explicit forms of the shape function b(r) and the scale factor a(t) arising in the classification are utilized to construct the corresponding energy-momentum tensor where the energy conditions for each case is investigated. While the violation of energy conditions is inevitable in case of static wormholes, the classification we performed leads to interesting solutions in which this violation is either reduced or eliminated.

Keywords: general relativity, Einstein field equations, energy conditions, cosmological wormhole

Procedia PDF Downloads 63

Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

Abstract:

Differential equations are of fundamental importance in engineering and applied mathematics, since many physical laws and relations appear mathematically in the form of such equations. The equilibrium state of structures consisting of one-dimensional elements can be described by an ordinary differential equation. The response of these kinds of structures under the loading, namely relationship between the displacement field and loading field, can be predicted by the solution of these differential equations and on satisfying the given boundary conditions. When the effect of change of geometry under loading is taken into account in modeling of equilibrium state, then these differential equations are partially integrable in quartered. They also exhibit instability characteristics when the structures are loaded compressively. The purpose of this paper is to represent the ability of the Modified Newmark Method in analyzing flexural-torsional instability of struts for both bifurcation and non-bifurcation structural systems. The results are shown to be very accurate with only a small number of iterations. The method is easily programmed, and has the advantages of simplicity and speeds of convergence and easily is extended to treat material and geometric nonlinearity including no prismatic members and linear and nonlinear spring restraints that would be encountered in frames. In this paper, these abilities of the method will be extended to the system of linear differential equations that govern strut flexural torsional stability.

Keywords: instability, torsion, flexural, buckling, modified newmark method stability

Procedia PDF Downloads 360