Search results for: logistics equation

Authors: Reza Mollapourasl, Majid Haghi

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In this study, we develop local meshfree methods known as radial basis function-generated finite difference (RBF-FD) method and Hermite finite difference (RBF-HFD) method to design stencil weights and spatial discretization for Helmholtz equation. The convergence and stability of schemes are investigated numerically in three dimensions with irregular shaped domain. These localized meshless methods incorporate the advantages of the RBF method, finite difference and Hermite finite difference methods to handle the ill-conditioning issue that often destroys the convergence rate of global RBF methods. Moreover, numerical illustrations show that the proposed localized RBF type methods are efficient and applicable for problems with complex geometries. The convergence and accuracy of both schemes are compared by solving a test problem.

Keywords: radial basis functions, Hermite finite difference, Helmholtz equation, stability

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Authors: Sylvie Michel, Sylvie Gerbaix, Marc Bidan

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The COVID-19 pandemic has been a major and global disruption that has affected all supply chains on a worldwide scale. Consequently, the question posed by this communication is to understand how - in the face of such disruptions - supply chains, including their actors, management tools, and processes, react, survive, adapt, and even improve. To do so, the concepts of resilience and antifragility applied to a supply chain have been leveraged. This article proposes to perceive resilience as a step to surpass in moving towards antifragility. The research objective is to propose an analytical framework to measure and compare resilience and antifragility, with antifragility seen as a property of a system that improves when subjected to disruptions rather than merely resisting these disruptions, as is the case with resilience. A unique case study was studied - MSF logistics (France) - using a qualitative methodology. Semi-structured interviews were conducted in person and remotely in multiple phases: during and immediately after the COVID crisis (8 interviews from March 2020 to April 2021), followed by a new round from September to November 2023. A Delphi method was employed. The interviews were analyzed using coding and a thematic framework. One of the theoretical contributions is consolidating the field of supply chain resilience research by precisely characterizing the dimensions of resilience for a humanitarian supply chain (Reorganization, Collaboration mediated by IS, Humanitarian culture). In this regard, a managerial contribution of this study is providing a guide for managers to identify the four dimensions and sub-dimensions of supply chain resilience. This enables managers to focus their decisions and actions on dimensions that will enhance resilience. Most importantly, another contribution is comparing the concepts of resilience and antifragility and proposing an analytical framework for antifragility—namely, the mechanisms on which MSF logistics relied to capitalize on uncertainties, contingencies, and shocks rather than simply enduring them. For MSF Logistics, antifragility manifested through the ability to identify opportunities hidden behind the uncertainties and shocks of COVID-19, reducing vulnerability, and fostering a culture that encourages innovation and the testing of new ideas. Logistics, particularly in the humanitarian domain, must be able to adapt to environmental disruptions. In this sense, this study identifies and characterizes the dimensions of resilience implemented by humanitarian logistics. Moreover, this research goes beyond the concept of resilience to propose an analytical framework for the concept of antifragility. The organization studied emerged stronger from the COVID-19 crisis due to the mechanisms we identified, allowing us to characterize antifragility. Finally, the results show that the information system plays a key role in antifragility.

Keywords: antifragility, humanitarian supply chain, information systems, qualitative research, resilience.

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Maryam Khazaei Pool, Lori Lewis

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This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method, Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper, we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions, including Burgers equation, spline functions, and B-spline functions, are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided, and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ equation, Septic B-spline, modified cubic B-spline differential quadrature method, exponential cubic B-spline technique, B-spline Galerkin method, quintic B-spline Galerkin method

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Authors: Aleksandar Dedic, Dusko Salemovic, Milorad Danilovic, Radomir Kuzmanovic

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This paper takes into consideration the influence of bonding energy of water on energy demand of vacuum wood drying using the specific method of obtaining sorption isotherms. The experiment was carried out on oak wood at vacuum pressures of: 0.7 bar, 0.5bar and 0.3bar. The experimental work was done to determine a mathematical equation between the moisture content and energy of water-bonding. This equation helps in finding the average amount of energy of water-bonding necessary in calculation of energy consumption by use of the equation of heat balance in real drying chambers. It is concluded that the energy of water-bonding is large enough to be included into consideration. This energy increases at lower values of moisture content, when drying process approaches to the end, and its average values are lower on lower pressure.

Keywords: bonding energy, drying, isosters, oak, vacuum

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Authors: Suprit Pradhan, Sushil Pradhan

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Photosynthesis is a physiological process where green plants prepare their food from carbon dioxide from the atmosphere and water being absorbed from the soil in presence of sun light and chlorophyll. From this definition it is clear that four reactants (Carbon Dioxide, Water, Light and Chlorophyll) are essential for the process to proceed and the product is a sugar or carbohydrate ultimately stored as starch. The entire process has “Light Reaction” (Photochemical) and “Dark Reaction” (Biochemical). Biochemical reactions are very much complicated being catalysed by various enzymes and the path of carbon is known as “Calvin Cycle” according to the name of its discover. The overall reaction which is now universally accepted can be explained like this. Six molecules of carbon dioxide react with twelve molecules of water in presence of chlorophyll and sun light to give only one molecule of sugar (Carbohydrate) six molecules of water and six molecules of oxygen is being evolved in gaseous form. This is the accepted equation and also chemically balanced. However while teaching the subject the author came across a new balanced equation from among the students who happened to be the daughter of the author. In the new balanced equation in place of twelve water molecules in the reactant side seven molecules can be expressed and accordingly in place of six molecules of water in the product side only one molecule of water is produced. The energetics of the photosynthesis as related to the environment and the newly reported balanced chemical equation has been discussed in detail in the present research paper presentation in this international conference on energy, environmental and chemical engineering.

Keywords: biochemistry, enzyme , isotope, photosynthesis

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Authors: Piyarat Parklug, Busaba Supawattanaobodee, Penpat Pinyowattanasilp

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The radioactive iodine thyroid uptake (RAIU) has been widely used to differentiate the cause of thyrotoxicosis and treatment. Twenty-four hours RAIU is routinely used to calculate the dose of radioactive iodine (RAI) therapy; however, 2 days protocol is required. This study aims to evaluate the modification of Penpat Pinyowattanasilp equation application by the exclusion of outlier data, 3 hours RAIU less than 20% and more than 80%, to improve prediction of 24-hour uptake. The equation is predicted 24 hours RAIU (P24RAIU) = 32.5+0.702 (3 hours RAIU). Then calculating separation first and second therapeutic doses in Graves’ disease patients. Methods; This study was a retrospective study at Faculty of Medicine Vajira Hospital in Bangkok, Thailand. Inclusion were Graves’ disease patients who visited RAI clinic between January 2014-March 2019. We divided subjects into 2 groups according to first and second therapeutic doses. Results; Our study had a total of 151 patients. The study was done in 115 patients with first RAI dose and 36 patients with second RAI dose. The P24RAIU are highly correlated with actual 24-hour RAIU in first and second therapeutic doses (r = 0.913, 95% CI = 0.876 to 0.939 and r = 0.806, 95% CI = 0.649 to 0.897). Bland-Altman plot shows that mean differences between predictive and actual 24 hours RAI in the first dose and second dose were 2.14% (95%CI 0.83-3.46) and 1.37% (95%CI -1.41-4.14). The mean first actual and predictive therapeutic doses are 8.33 ± 4.93 and 7.38 ± 3.43 milliCuries (mCi) respectively. The mean second actual and predictive therapeutic doses are 6.51 ± 3.96 and 6.01 ± 3.11 mCi respectively. The predictive therapeutic doses are highly correlated with the actual dose in first and second therapeutic doses (r = 0.907, 95% CI = 0.868 to 0.935 and r = 0.953, 95% CI = 0.909 to 0.976). Bland-Altman plot shows that mean difference between predictive and actual P24RAIU in the first dose and second dose were less than 1 mCi (-0.94 and -0.5 mCi). This modification equation application is simply used in clinical practice especially patient with 3 hours RAIU in range of 20-80% in a Thai population. Before use, this equation for other population should be tested for the correlation.

Keywords: equation, Graves’disease, prediction, 24-hour uptake

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Authors: Samuel Ahamefula Mba

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Fluid turbulence is a complex and nonlinear phenomenon that occurs in various natural and industrial processes. Understanding turbulence remains a challenging task due to its intricate nature. One approach to gain insights into turbulence is through the study of entropy, which quantifies the disorder or randomness of a system. This research presents a numerical investigation of entropy signatures in fluid turbulence. The work is to develop a numerical framework to describe and analyse fluid turbulence in terms of entropy. This decomposes the turbulent flow field into different scales, ranging from large energy-containing eddies to small dissipative structures, thus establishing a correlation between entropy and other turbulence statistics. This entropy-based framework provides a powerful tool for understanding the underlying mechanisms driving turbulence and its impact on various phenomena. This work necessitates the derivation of the Poisson equation for pressure transformation of Navier-Stokes equation and using Chebyshev-Finite Difference techniques to effectively resolve it. To carry out the mathematical analysis, consider bounded domains with smooth solutions and non-periodic boundary conditions. To address this, a hybrid computational approach combining direct numerical simulation (DNS) and Large Eddy Simulation with Wall Models (LES-WM) is utilized to perform extensive simulations of turbulent flows. The potential impact ranges from industrial process optimization and improved prediction of weather patterns.

Keywords: turbulence, Navier-Stokes equation, Poisson pressure equation, numerical investigation, Chebyshev-finite difference, hybrid computational approach, large Eddy simulation with wall models, direct numerical simulation

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Authors: Ismail Seçer

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The purpose of this study is to analyze the relationship between school burnout and academic motivation in high school students. The working group of the study consists of 455 students from the high schools in Erzurum city center, selected with appropriate sampling method. School Burnout Scale and Academic Motivation Scale were used in the study to collect data. Correlation analysis and structural equation modeling were used in the analysis of the data collected through the study. As a result of the study, it was determined that there are significant and negative relations between school burnout and academic motivation, and the school burnout has direct and indirect significant effects on the getting over himself, using knowledge and exploration dimension through the latent variable of academic motivation. Lastly, it was determined that school burnout is a significant predictor of academic motivation.

Keywords: school burnout, motivation, structural equation modeling, university

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Authors: Merouane Salhi, Toufik Zebbiche, Omar Abada

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When the stagnation pressure of perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas does not remain perfect. Its state equation change and it becomes a real gas. In this case, the effects of molecular size and inter molecular attraction forces intervene to correct the state equation. The aim of this work is to show and discuss the effect of stagnation pressure on supersonic thermo dynamical, physical and geometrical flow parameters, to find a general case for real gas. With the assumptions that Berthelot’s state equation accounts for molecular size and inter molecular force effects, expressions are developed for analyzing supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The designs parameters for supersonic nozzle like thrust coefficient depend directly on stagnation parameters of the combustion chamber. The application is for air. A computation of error is made in this case to give a limit of perfect gas model compared to real gas model.

Keywords: supersonic flow, real gas model, Berthelot’s state equation, Simpson’s method, condensation function, stagnation pressure

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Authors: Abbas Ebrahimi, Mohammad Zandsalimy

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The main purpose of this study is to investigate the feasibility of using FPGA (Field Programmable Gate Arrays) chips as alternatives for the conventional CPUs to accelerate the numerical solution of the Laplace equation. FPGA is an integrated circuit that contains an array of logic blocks, and its architecture can be reprogrammed and reconfigured after manufacturing. Complex circuits for various applications can be designed and implemented using FPGA hardware. The reconfigurable hardware used in this paper is an SoC (System on a Chip) FPGA type that integrates both microprocessor and FPGA architectures into a single device. In the present study the Laplace equation is implemented and solved numerically on both reconfigurable hardware and CPU. The precision of results and speedups of the calculations are compared together. The computational process on FPGA, is up to 20 times faster than a conventional CPU, with the same data precision. An analytical solution is used to validate the results.

Keywords: accelerating numerical solutions, CFD, FPGA, hardware definition language, numerical solutions, reconfigurable hardware

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Authors: Mohammad Reza Shahnazari, Reza Kazemi, Ali Saberi

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Most of the engineering problems are in nonlinear forms. Nonlinear boundary layer problems defined in infinite intervals contain specific complexities, especially in boundary layer condition conformance. As an example of these nonlinear complex problems, the well-known Blasius equation can be mentioned, which itself is one of the classic boundary layer problems. No analytical solution has been proposed yet for the Blasius equation due to its complexity. In this paper, an analytical method, namely the Kourosh method, based on the singularity perturbation method and the Liao homotopy analysis is utilized to solve the Blasius problem. In this method, an inner solution is developed in the [0,1] interval to expedite the solution convergence. The magnitude of the f ˝(0), as an essential quantity for determining the physical parameters, is directly calculated from the solution of the boundary condition problem. The advantages of this solution are that it does not need any numerical solution, it has a closed form and that its validation is shown in the entire [0,∞] interval. Furthermore, all of the desirable parameters could be extracted through a series of simple analytical operations from the final solution. This solution also satisfies the continuity conditions, which is one of the main contributions of this paper in comparison with most of the other proposed analytical solutions available in the literature. Comparison with numerical solutions reveals that the proposed method is highly accurate and convenient for application.

Keywords: Blasius equation, boundary layer, Kourosh method, analytical solution

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Authors: Süleyman Günes

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The crucial effects of the COVID-19 pandemic have on social and economic systems in Turkey as well as all over the world. It has impacted logistic providers and worldwide supply chains. Unexpected risks played a central role in creating vulnerabilities for logistics service operations during the pandemic terms. This study aims to research and design qualitative and quantitive contributions to logistic services. The COVID-19 pandemic brought unavoidable risks to the logistics industry in Turkey. The Logistic Service Providers (LSPs) have learned how to ensure uncertainties and risks triggered by main and adverse effects. The risks that LSPs encounter during the COVID-19 pandemic have been investigated and unveiled, and identified uncertainties and risks. The cause-effect structures were displayed by the qualitative and quantitive studies. The results suggest that supply chains and demand changes triggered by the COVID-19 pandemic while it influenced financial failure and forecast horizon with operational performances.

Keywords: logistic service providers, COVID-19, development, financial failure

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Authors: Vandenbroucke Karel, Georges Annabel, Schuurman Dimitri

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In the past years, bundling of transport flows, whether or not implemented in an intermodal process, has popped up as a promising concept in the logistics sector. Bundling of transport flows is a process where two or more shippers decide to synergize their shipped goods over a common transport lane. Promoted by the European Commission, several programs have been set up and have shown their benefits. Bundling promises both shippers and logistics service providers economic, societal and ecological benefits. By bundling transport flows and thus reducing truck (or other carrier) capacity, the problems of driver shortage, increased fuel prices, mileage charges and restricted hours of service on the road are solved. In theory, the advantages of bundled transport exceed the drawbacks, however, in practice adoption among shippers remains low. In fact, bundling is mentioned as a disruptive process in the rather traditional logistics sector. In this context, a Belgian company asked iMinds Living Labs to set up a Living Lab research project with the goal to investigate how the uptake of bundling transport flows can be accelerated and to check whether an online data sharing platform can overcome the adoption barriers. The Living Lab research was conducted in 2016 and combined quantitative and qualitative end-user and market research. Concretely, extensive desk research was conducted and combined with insights from expert interviews with four consultants active in the Belgian logistics sector and in-depth interviews with logistics professionals working for shippers (N=10) and LSP’s (N=3). In the article, we present findings which show that there are several factors slowing down the uptake of bundling transport flows. Shippers are hesitant to change how they currently work and they are hesitant to work together with other shippers. Moreover, several practical challenges impede shippers to work together. We also present some opportunities that can accelerate the adoption of bundling of transport flows. First, it seems that there is not enough support coming from governmental and commercial organizations. Secondly, there is the chicken and the egg problem: too few interested parties will lead to no or very few matching lanes. Shippers are therefore reluctant to partake in these projects because the benefits have not yet been proven. Thirdly, the incentive is not big enough for shippers. Road transport organized by the shipper individually is still seen as the easiest and cheapest solution. A solution for the abovementioned challenges might be found in the online data sharing platform of the Belgian company. The added value of this platform is showing shippers possible matching lanes, without the shippers having to invest time in negotiating and networking with other shippers and running the risk of not finding a match. The interviewed shippers and experts indicated that the online data sharing platform is a very promising concept which could accelerate the uptake of bundling of transport flows.

Keywords: adoption barriers, bundling of transport, shippers, transport optimization

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Authors: Nattida Wannaruk, Wasawat Nakkiew

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This research aims to study the factors that affect the performance of green supply chain management in the Lampang ceramics industry. The data investigation of this research was questionnaires which were gathered from 20 factories in the Lampang ceramics industry. The research factors are divided into five major groups which are green design, green purchasing, green manufacturing, green logistics and reverse logistics. The questionnaire has consisted of four parts that related to factors green supply chain management and general information of the Lampang ceramics industry. Then, the data were analyzed using descriptive statistic and priority of each factor by using the analytic hierarchy process (AHP). The understanding of factors affecting the green supply chain management of Lampang ceramics industry was indicated in the summary result along with each factor weight. The result of this research could be contributed to the development of indicators or performance evaluation in the future.

Keywords: Lampang ceramics industry, green supply chain management, analysis hierarchy process (AHP), factors affecting

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

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

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

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Authors: Egemen Sert, Leila Hedayatifar, Rachel A. Rigg, Amir Akhavan, Olha Buchel, Dominic Elias Saadi, Aabir Abubaker Kar, Alfredo J. Morales, Yaneer Bar-Yam

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The complexity of providing timely and cost-effective distribution of finished goods from industrial facilities to customers makes effective operational coordination difficult, yet effectiveness is crucial for maintaining customer service levels and sustaining a business. Logistics planning becomes increasingly complex with growing numbers of customers, varied geographical locations, the uncertainty of future orders, and sometimes extreme competitive pressure to reduce inventory costs. Linear optimization methods become cumbersome or intractable due to a large number of variables and nonlinear dependencies involved. Here we develop a complex systems approach to optimizing logistics networks based upon dimensional reduction methods and apply our approach to a case study of a manufacturing company. In order to characterize the complexity in customer behavior, we define a “customer space” in which individual customer behavior is described by only the two most relevant dimensions: the distance to production facilities over current transportation routes and the customer's demand frequency. These dimensions provide essential insight into the domain of effective strategies for customers; direct and indirect strategies. In the direct strategy, goods are sent to the customer directly from a production facility using box or bulk trucks. In the indirect strategy, in advance of an order by the customer, goods are shipped to an external warehouse near a customer using trains and then "last-mile" shipped by trucks when orders are placed. Each strategy applies to an area of the customer space with an indeterminate boundary between them. Specific company policies determine the location of the boundary generally. We then identify the optimal delivery strategy for each customer by constructing a detailed model of costs of transportation and temporary storage in a set of specified external warehouses. Customer spaces help give an aggregate view of customer behaviors and characteristics. They allow policymakers to compare customers and develop strategies based on the aggregate behavior of the system as a whole. In addition to optimization over existing facilities, using customer logistics and the k-means algorithm, we propose additional warehouse locations. We apply these methods to a medium-sized American manufacturing company with a particular logistics network, consisting of multiple production facilities, external warehouses, and customers along with three types of shipment methods (box truck, bulk truck and train). For the case study, our method forecasts 10.5% savings on yearly transportation costs and an additional 4.6% savings with three new warehouses.

Keywords: logistics network optimization, direct and indirect strategies, K-means algorithm, dimensional reduction

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Authors: E. Behmanesh, J. Pannek

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The distribution-allocation problem is known as one of the most comprehensive strategic decision. In real-world cases, it is impossible to solve a distribution-allocation problem in traditional ways with acceptable time. Hence researchers develop efficient non-traditional techniques for the large-term operation of the whole supply chain. These techniques provide near-optimal solutions particularly for large scales test problems. This paper, presents an integrated supply chain model which is flexible in the delivery path. As the solution methodology, we apply a memetic algorithm with a novelty in population presentation. To illustrate the performance of the proposed memetic algorithm, LINGO optimization software serves as a comparison basis for small size problems. In large size cases that we are dealing with in the real world, the Genetic algorithm as the second metaheuristic algorithm is considered to compare the results and show the efficiency of the memetic algorithm.

Keywords: integrated logistics network, flexible path, memetic algorithm, genetic algorithm

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Authors: Phuoc Si Nguyen

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Infinite impulse response (IIR) filters can be designed from an analogue low pass prototype by using frequency transformation in the s-domain and bilinear z-transformation with pre-warping frequency; this method is known as frequency transformation from the s-domain to the z-domain. This paper will introduce a new method to transform an IIR digital filter to another type of IIR digital filter (low pass, high pass, band pass, band stop or narrow band) using a technique based on inverse bilinear z-transformation and inverse matrices. First, a matrix equation is derived from inverse bilinear z-transformation and Pascal’s triangle. This Low Pass Digital to Digital Filter Pascal Matrix Equation is used to transform a low pass digital filter to other digital filter types. From this equation and the inverse matrix, a Digital to Digital Filter Pascal Matrix Equation can be derived that is able to transform any IIR digital filter. This paper will also introduce some specific matrices to replace the inverse matrix, which is difficult to determine due to the larger size of the matrix in the current method. This will make computing and hand calculation easier when transforming from one IIR digital filter to another in the digital domain.

Keywords: bilinear z-transformation, frequency transformation, inverse bilinear z-transformation, IIR digital filters

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: functionally graded beam, free vibration, elastic foundation, Engesser-Timoshenko beam theory

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary condition to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful to study various optical phenomena.

Keywords: deep learning, optical Soliton, neural network, partial differential equation

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

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Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation

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Authors: Avinash Nayak, Debopam Das

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The current work implements the variational principle to find the optimum initial perturbation that provides maximum growth in an impulsively blocked channel flow. The conventional method for studying temporal stability has always been through modal analysis. In most of the transient flows, this modal analysis is still followed with the quasi-steady assumption, i.e. change in base flow is much slower compared to perturbation growth rate. There are other studies where transient analysis on time dependent flows is done by formulating the growth of perturbation as an initial value problem. But the perturbation growth is sensitive to the initial condition. This study intends to find the initial perturbation that provides the maximum growth at a later time. Here, the expression of base flow for blocked channel is derived and the formulation is based on the two dimensional perturbation with stream function representing the perturbation quantity. Hence, the governing equation becomes the Orr-Sommerfeld equation. In the current context, the cost functional is defined as the ratio of disturbance energy at a terminal time 'T' to the initial energy, i.e. G(T) = ||q(T)||2/||q(0)||2 where q is the perturbation and ||.|| defines the norm chosen. The above cost functional needs to be maximized against the initial perturbation distribution. It is achieved with the constraint that perturbation follows the basic governing equation, i.e. Orr-Sommerfeld equation. The corresponding adjoint equation is derived and is solved along with the basic governing equation in an iterative manner to provide the initial spatial shape of the perturbation that provides the maximum growth G (T). The growth rate is plotted against time showing the development of perturbation which achieves an asymptotic shape. The effects of various parameters, e.g. Reynolds number, are studied in the process. Thus, the study emphasizes on the usage of optimal perturbation and its growth to understand the stability characteristics of time dependent flows. The assumption of quasi-steady analysis can be verified against these results for the transient flows like impulsive blocked channel flow.

Keywords: blocked channel flow, calculus of variation, hydrodynamic stability, optimal perturbation

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Authors: Mokhtar Labiod, Nabil Ikhlef, Keltoum Bouherine, Olivier Leroy

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A numerical model for the radio-frequency (RF) Argon discharge chamber is developed to simulate the low pressure low temperature inductively coupled plasma. This model will be of fundamental importance in the design of the plasma magnetic control system. Electric and magnetic fields inside the discharge chamber are evaluated by solving a magnetic vector potential equation. To start with, the equations of the ideal magnetohydrodynamics theory will be presented describing the basic behaviour of magnetically confined plasma and equations are discretized with finite element method in cylindrical coordinates. The discharge chamber is assumed to be axially symmetric and the plasma is treated as a compressible gas. Plasma generation due to ionization is added to the continuity equation. Magnetic vector potential equation is solved for the electromagnetic fields. A strong dependence of the plasma properties on the discharge conditions and the gas temperature is obtained.

Keywords: direct-coupled model, magnetohydrodynamic, modelling, plasma torch simulation

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Authors: S. S. Abas, Y. M. Yatim

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In this paper the unsteady, slender, symmetric dry patch in an infinitely wide and thin liquid film of Newtonian fluid draining under gravity down an inclined plane in the presence of strong surface-tension effect is considered. A similarity transformation, named a travelling-wave similarity solution is used to reduce the governing partial differential equation into the ordinary differential equation which is then solved numerically using a shooting method. The introduction of surface-tension effect on the flow leads to a fourth-order ordinary differential equation. The solution obtained predicts that the dry patch has a quartic shape and the free surface has a capillary ridge near the contact line which decays in an oscillatory manner far from it.

Keywords: dry patch, Newtonian fluid, similarity solution, surface-tension effect, travelling-wave, unsteady thin-film flow

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

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In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation

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Authors: Saidu Ibrahim, Winston M. W. Shakantu

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The problem of construction material waste remains unresolved, as a significant percentage of the materials delivered to some project sites end up as waste which might result in additional project cost. Cost overrun is a problem which affects 90% of the completed projects in the world. The argument on how to eliminate it has been on-going for the past 70 years, but there is neither substantial improvement nor significant solution for mitigating its detrimental effects. Research evidence has proposed various construction cost overruns and material-waste management approaches; nonetheless, these studies failed to give a clear indication on the framework and the equation for managing construction material waste and cost overruns. Hence, this research aims to develop a conceptual framework and a mathematical equation for managing material waste and cost overrun in the construction industry. The paper adopts the desktop methodological approach. This involves comparing the causes of material waste and those of cost overruns from the literature to determine the possible relationship. The review revealed a relationship between material waste and cost overrun that; increase in material waste would result to a corresponding increase in the amount of cost overrun at both the pre-contract and the post contract stages of a project. It was found from the equation that achieving an effective construction material waste management must ensure a “Good Quality-of-Planning, Estimating, and Design Management” and a “Good Quality- of-Construction, Procurement and Site Management”; a decrease in “Design Complexity” which would reduce “Material Waste” and subsequently reduce the amount of cost overrun by 86.74%. The conceptual framework and the mathematical equation developed in this study are recommended to the professionals of the construction industry.

Keywords: conceptual framework, cost overrun, material waste, project stags

Procedia PDF Downloads 262

Authors: Marco F. Benaglia, Mei H. Chen, Kune M. Tsai, Chia H. Hung

Abstract:

As societal and family structures, consumer dietary habits, and awareness about food safety and quality continue to evolve in most developed countries, the demand for refrigerated and frozen foods has been growing, and the issues related to their preservation have gained increasing attention. A well-established cold chain logistics system is essential to avoid any temperature abuse; therefore, assessing potential disruptions in the operational processes of cold chain logistics centers becomes pivotal. This study preliminarily employs HACCP to find disruption factors in cold chain logistics centers that may cause temperature abuse. Then, concept mapping is applied: selected experts engage in brainstorming sessions to identify any further factors. The panel consists of ten experts, including four from logistics and home delivery, two from retail distribution, one from the food industry, two from low-temperature logistics centers, and one from the freight industry. Disruptions include equipment-related aspects, human factors, management aspects, and process-related considerations. The areas of observation encompass freezer rooms, refrigerated storage areas, loading docks, sorting areas, and vehicle parking zones. The experts also categorize the disruption factors based on perceived similarities and build a similarity matrix. Each factor is evaluated for its impact, frequency, and investment importance. Next, multiple scale analysis, cluster analysis, and other methods are used to analyze these factors. Simultaneously, key disruption factors are identified based on their impact and frequency, and, subsequently, the factors that companies prioritize and are willing to invest in are determined by assessing investors’ risk aversion behavior. Finally, Cumulative Prospect Theory (CPT) is applied to verify the risk patterns. 66 disruption factors are found and categorized into six clusters: (1) "Inappropriate Use and Maintenance of Hardware and Software Facilities", (2) "Inadequate Management and Operational Negligence", (3) "Product Characteristics Affecting Quality and Inappropriate Packaging", (4) "Poor Control of Operation Timing and Missing Distribution Processing", (5) "Inadequate Planning for Peak Periods and Poor Process Planning", and (6) "Insufficient Cold Chain Awareness and Inadequate Training of Personnel". This study also identifies five critical factors in the operational processes of cold chain logistics centers: "Lack of Personnel’s Awareness Regarding Cold Chain Quality", "Personnel Not Following Standard Operating Procedures", "Personnel’s Operational Negligence", "Management’s Inadequacy", and "Lack of Personnel’s Knowledge About Cold Chain". The findings show that cold chain operators prioritize prevention and improvement efforts in the "Inappropriate Use and Maintenance of Hardware and Software Facilities" cluster, particularly focusing on the factors of "Temperature Setting Errors" and "Management’s Inadequacy". However, through the application of CPT theory, this study reveals that companies are not usually willing to invest in the improvement of factors related to the "Inappropriate Use and Maintenance of Hardware and Software Facilities" cluster due to its low occurrence likelihood, but they acknowledge the severity of the consequences if it does occur. Hence, the main implication is that the key disruption factors in cold chain logistics centers’ processes are associated with personnel issues; therefore, comprehensive training, periodic audits, and the establishment of reasonable incentives and penalties for both new employees and managers may significantly reduce disruption issues.

Keywords: concept mapping, cold chain, HACCP, cumulative prospect theory

Procedia PDF Downloads 29

Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

Abstract:

We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

Procedia PDF Downloads 153

Authors: Shangerganesh Lingeshwaran

Abstract:

In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

Procedia PDF Downloads 201