Search results for: mathematical and computational methods

Authors: S. A. Sadegh Zadeh, C. Kambhampati

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Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Keywords: all-or-none, computational modelling, mathematical model, transmembrane voltage, action potential

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Authors: Deepshikha Shukla, C. H. Solanki, Mayank K. Desai

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Amongst all the natural hazards, earthquakes have the potential for causing the greatest damages. Since the earthquake forces are random in nature and unpredictable, the quantification of the hazards becomes important in order to assess the hazards. The time and place of a future earthquake are both uncertain. Since earthquakes can neither be prevented nor be predicted, engineers have to design and construct in such a way, that the damage to life and property are minimized. Seismic hazard analysis plays an important role in earthquake design structures by providing a rational value of input parameter. In this paper, both mathematical, as well as computational methods adopted by researchers globally in the past five years, will be discussed. Some mathematical approaches involving the concepts of Poisson’s ratio, Convex Set Theory, Empirical Green’s Function, Bayesian probability estimation applied for seismic hazard and FOSM (first-order second-moment) algorithm methods will be discussed. Computational approaches and numerical model SSIFiBo developed in MATLAB to study dynamic soil-structure interaction problem is discussed in this paper. The GIS-based tool will also be discussed which is predominantly used in the assessment of seismic hazards.

Keywords: computational methods, MATLAB, seismic hazard, seismic measurements

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

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A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An in-compressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping

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Authors: Agarana Michael C., Akinlabi Esther T., Pule Kholopane

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Innovation in manufacturing process technologies and associated product design affects the prospects for manufacturing today and in near future. In this study some theoretical methods, useful as tools in advanced manufacturing, are considered. In particular, some basic Mathematical, Operational Research, Heuristic, and Statistical techniques are discussed. These techniques/methods are very handy in many areas of advanced manufacturing processes, including process planning optimization, modelling and analysis. Generally the production rate requires the application of Mathematical methods. The Emerging Trends Processes in Advanced Manufacturing can be enhanced by using Mathematical Modelling and Optimization techniques.

Keywords: mathematical modelling, optimization, emerging trends, advanced manufacturing

Procedia PDF Downloads 259

Authors: Han Hyuk Cho, Hanik Jo

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In recent years, coding education has been globally emphasized, and the Free Semester System and coding education were introduced to the public schools from the beginning of 2016 and 2018 respectively in Korea. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this paper aims to design ‘Coding Environment’ and Minecraft-like Turtlecraft in which learners can design and construct mathematical objects through mathematical symbolic expressions. Students can transfer the constructed mathematical objects to the Turtlecraft environment (open-source codingmath website), and also can print them out through 3D printers. Furthermore, we design learnable mathematics and coding curriculum by representing the figurate numbers and patterns in terms of executable expression in the coding context and connecting them to algebraic symbols, which will allow students to experience mathematical patterns and symbolic coding expressions.

Keywords: coding education, computational thinking, mathematics education, TurtleMAL and Turtlecraft

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Authors: John Allard, Alex Rich, Iris Aguilar, Zachary Dodds

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With this paper we present several experiences deploying novel, low-cost resources for computing with 3D spatial models. Certainly, computing with 3D models undergirds some of our field’s most important contributions to the human experience. Most often, those are contrived artifacts. This work extends that tradition by focusing on novel resources that deliver uncontrived models of a system’s current surroundings. Atop this new capability, we present several projects investigating the student-accessibility of the computational tools for reasoning about the 3D space around us. We conclude that, with current scaffolding, real-world 3D models are now an accessible and viable foundation for creative computational work.

Keywords: 3D vision, matterport model, real-world 3D models, mathematical and computational methods

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Authors: Hanife Merve Öztürk, Sıdıka Dalgan

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In this project, a capacity analysis study is done at TAT A. Ş. Maret Plant. Production capacity of products which generate 80% of sales amount are determined. Obtained data entered the LEKIN Scheduling Program and we get production schedules by using heuristic methods. Besides heuristic methods, as mathematical model, disjunctive programming formulation is adapted to flexible job shop problems by adding a new constraint to find optimal schedule solution.

Keywords: scheduling, flexible job shop problem, shifting bottleneck heuristic, mathematical modelling

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Authors: Zahid Ullah, Atlas Khan

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The rapid advancements in data collection, storage, and processing capabilities have led to an explosion of data in various domains. In this era of big data, mathematical sciences play a crucial role in uncovering valuable insights and driving informed decision-making through data analytics. The purpose of this abstract is to present the latest advances in mathematical sciences and their application in harnessing the power of data analytics. This abstract highlights the interdisciplinary nature of data analytics, showcasing how mathematics intersects with statistics, computer science, and other related fields to develop cutting-edge methodologies. It explores key mathematical techniques such as optimization, mathematical modeling, network analysis, and computational algorithms that underpin effective data analysis and interpretation. The abstract emphasizes the role of mathematical sciences in addressing real-world challenges across different sectors, including finance, healthcare, engineering, social sciences, and beyond. It showcases how mathematical models and statistical methods extract meaningful insights from complex datasets, facilitating evidence-based decision-making and driving innovation. Furthermore, the abstract emphasizes the importance of collaboration and knowledge exchange among researchers, practitioners, and industry professionals. It recognizes the value of interdisciplinary collaborations and the need to bridge the gap between academia and industry to ensure the practical application of mathematical advancements in data analytics. The abstract highlights the significance of ongoing research in mathematical sciences and its impact on data analytics. It emphasizes the need for continued exploration and innovation in mathematical methodologies to tackle emerging challenges in the era of big data and digital transformation. In summary, this abstract sheds light on the advances in mathematical sciences and their pivotal role in unveiling the power of data analytics. It calls for interdisciplinary collaboration, knowledge exchange, and ongoing research to further unlock the potential of mathematical methodologies in addressing complex problems and driving data-driven decision-making in various domains.

Keywords: mathematical sciences, data analytics, advances, unveiling

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Authors: A. Mohammadi, M. Moghimi, S. Mohammadi

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Engineers need computational methods which could provide solutions less sensitive to the environmental effects, so the techniques should be used which take the uncertainty to account to control and minimize the risk associated with design and operation. In order to consider uncertainty in engineering problem, the optimization problem should be solved for a suitable range of the each uncertain input variable instead of just one estimated point. Using deterministic optimization problem, a large computational burden is required to consider every possible and probable combination of uncertain input variables. Several methods have been reported in the literature to deal with problems under uncertainty. In this paper, different methods presented and analyzed.

Keywords: uncertainty, Monte Carlo simulated, stochastic programming, scenario method

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Authors: Emhimed Saffor

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In this paper, the problem of edge detection in digital images is considered. Three methods of edge detection based on mathematical morphology algorithm were applied on two sets (Brain and Chest) CT images. 3x3 filter for first method, 5x5 filter for second method and 7x7 filter for third method under MATLAB programming environment. The results of the above-mentioned methods are subjectively evaluated. The results show these methods are more efficient and satiable for medical images, and they can be used for different other applications.

Keywords: CT images, Matlab, medical images, edge detection

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Authors: Dairo Jose Hernandez Paez

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The quantum theory of atoms in molecules (QTAIM) allows us to obtain topological information on electronic density in quantum mechanical systems. The QTAIM starts by considering the electron density as a continuous mathematical object. On the other hand, the discretization of electron density is also a mathematical object, which, from discrete mathematics, would allow a new approach to its topological study. From this point of view, it is necessary to develop a series of steps that provide the theoretical support that guarantees its application. Some of the steps that we consider most important are mentioned below: (1) obtain good representations of the electron density through computational calculations, (2) design a methodology for the discretization of electron density, and construct the simplicial complex. (3) Make an analysis of the discrete vector field associating the simplicial complex. (4) Finally, in this research, we propose to use the discrete Morse theory as a mathematical tool to carry out studies of electron density topology.

Keywords: discrete mathematics, Discrete Morse theory, electronic density, computational calculations

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Authors: Wei Sun, Yan Dong

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There is an increasing interest in introducing computational thinking at an early age. Computational thinking, like mathematical thinking, engineering thinking, and scientific thinking, is a kind of analytical thinking. Learning computational thinking skills is not only to improve technological literacy, but also allows learners to equip with practicable skills such as problem-solving skills. As people realize the importance of computational thinking, the field of educational technology faces a problem: how to choose appropriate tools and activities to help students develop computational thinking skills. Robots are gradually becoming a popular teaching tool, as robots provide a tangible way for young children to access to technology, and controlling a robot through programming offers them opportunities to engage in developing computational thinking. This study explores whether the introduction of flowcharts into the robotics programming courses can help children convert natural language into a programming language more easily, and then to better cultivate their computational thinking skills. An experimental study was adopted with a sample of children ages six to seven (N = 16) participated, and a one-meter-tall humanoid robot was used as the teaching tool. Results show that children can master basic programming concepts through robotic courses. Children's computational thinking has been significantly improved. Besides, results suggest that flowcharts do have an impact on young children’s computational thinking skills development, but it only has a significant effect on the "sequencing" and "correspondence" skills. Overall, the study demonstrates that the humanoid robot and flowcharts have qualities that foster young children to learn programming and develop computational thinking skills.

Keywords: robotics, computational thinking, programming, young children, flow chart

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Authors: Janneth González, George Barreto, Ludis Morales, Angélica Sabogal

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Sea anemone neurotoxins are peptides that interact with Na+ and K+ channels, resulting in specific alterations on their functions. Some of these neurotoxins (1ROO, 1BGK, 2K9E, 1BEI) are important for the treatment of nearly eighty autoimmune disorders due to their specificity for Kv1.3 channel. The aim of this study was to identify the common residues among these neurotoxins by computational methods, and establish whether there is a pattern useful for the future generation of a treatment for autoimmune diseases. Our results showed eight new key common residues between the studied neurotoxins interacting with a histidine ring and the selectivity filter of the receptor, thus showing a possible pattern of interaction. This knowledge may serve as an input for the design of more promising drugs for autoimmune treatments.

Keywords: neurotoxins, potassium channel, Kv1.3, computational methods, autoimmune diseases

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Authors: Javier Navarro Garcia, Narciso Vazquez Carretero

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Eurocode 1, part 1-4, wind actions, includes in its article 1.5 the possibility of using numerical calculation methods to obtain information on the loads acting on a building. On the other hand, the analysis using computational fluids dynamics (CFD) in aerospace, aeronautical, and industrial applications is already in widespread use. The application of techniques based on CFD analysis on the building to study its aerodynamic behavior now opens a whole alternative field of possibilities for civil engineering and architecture; optimization of the results with respect to those obtained by applying the regulations, the possibility of obtaining information on pressures, speeds at any point of the model for each moment, the analysis of turbulence and the possibility of modeling any geometry or configuration. The present work compares the results obtained on a building, with respect to its aerodynamic behavior, from a mathematical model based on the analysis by CFD with the results obtained by applying Eurocode1, part1-4, wind actions. It is verified that the results obtained by CFD techniques suppose an optimization of the wind action that acts on the building with respect to the wind action obtained by applying the Eurocode1, part 1-4, wind actions. In order to carry out this verification, a 45m high square base truncated pyramid building has been taken. The mathematical model on CFD, based on finite volumes, has been calculated using the FLUENT commercial computer application using a scale-resolving simulation (SRS) type large eddy simulation (LES) turbulence model for an atmospheric boundary layer wind with turbulent component in the direction of the flow.

Keywords: aerodynamic, CFD, computacional fluids dynamics, computational mechanics

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Authors: Aymen Laadhari

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The cardiovascular system is centered on the heart and is characterized by a very complex structure with different physical scales in space (e.g. micrometers for erythrocytes and centimeters for organs) and time (e.g. milliseconds for human brain activity and several years for development of some pathologies). The development and numerical implementation of mathematical models of the cardiovascular system is a tremendously challenging topic at the theoretical and computational levels, inducing consequently a growing interest over the past decade. The accurate computational investigations in both healthy and pathological cases of processes related to the functioning of the human cardiovascular system can be of great potential in tackling several problems of clinical relevance and in improving the diagnosis of specific diseases. In this talk, we focus on the specific task of simulating three particular phenomena related to the cardiovascular system on the macroscopic, mesoscopic and microscopic scales, respectively. Namely, we develop numerical methodologies tailored for the simulation of (i) the haemodynamics (i.e., fluid mechanics of blood) in the aorta and sinus of Valsalva interacting with highly deformable thin leaflets, (ii) the hyperelastic anisotropic behaviour of cardiomyocytes and the influence of calcium concentrations on the contraction of single cells, and (iii) the dynamics of red blood cells in microvasculature. For each problem, we present an appropriate fully Eulerian finite element methodology. We report several numerical examples to address in detail the relevance of the mathematical models in terms of physiological meaning and to illustrate the accuracy and efficiency of the numerical methods.

Keywords: finite element method, cardiovascular system, Eulerian framework, haemodynamics, heart valve, cardiomyocyte, red blood cell

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Authors: Mohammadali Abedini Sanigy, Jiangang Fei

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In this paper, a mathematical optimization model was developed to maximize the profit in a vegetable production planning problem. It serves as a decision support system that assists farmers in land allocation to crops and harvest scheduling decisions. The developed model can handle different rotation rules in two consecutive cycles of production, which is a common practice in organic production system. Moreover, different production methods of the same crop were considered in the model formulation. The main strength of the model is that it is not restricted to predetermined production periods, which makes the planning more flexible. The model is classified as a mixed integer programming (MIP) model and formulated in PYOMO -a Python package to formulate optimization models- and solved via Gurobi and CPLEX optimizer packages. The model was tested with secondary data from 'Australian vegetable growing farms', and the results were obtained and discussed with the computational test runs. The results show that the model can successfully provide reliable solutions for real size problems.

Keywords: crop rotation, harvesting, mathematical model formulation, vegetable production

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Authors: Susmita Panda, Arnab Banerjee, Ajinkya Baxy, Bappaditya Manna

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The design of short to medium-span high-speed bridges in critical locations is an essential aspect of vehicle-bridge interaction. Due to dynamic interaction between moving load and bridge, mathematical models or finite element modeling computations become time-consuming. Thus, to reduce the computational effort, a universal approximator using an artificial neural network (ANN) has been used to evaluate the dynamic response of the bridge. The data set generation and training of surrogate models have been conducted over the results obtained from mathematical modeling. Further, the robustness of the surrogate model has been investigated, which showed an error percentage of less than 10% with conventional methods. Additionally, the dependency of the dynamic response of the bridge on various load and bridge parameters has been highlighted through a parametric study.

Keywords: artificial neural network, mode superposition method, moving load analysis, surrogate models

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Authors: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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Authors: Mohsen Ziaee

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In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.

Keywords: scheduling, flexible job shop, makespan, mixed integer linear programming

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Authors: Aidan J. Bowes, Reaz Hasan

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The automotive industry is continually aiming to develop the aerodynamics of car body design. This may be for a variety of beneficial reasons such as to increase speed or fuel efficiency by reducing drag. However recently there has been a greater amount of focus on wind noise produced while driving. Designers in this industry seek a combination of both simplicity of approach and overall effectiveness. This combined with the growing availability of commercial CFD (Computational Fluid Dynamics) packages is likely to lead to an increase in the use of RANS (Reynolds Averaged Navier-Stokes) based CFD methods. This is due to these methods often being simpler than other CFD methods, having a lower demand on time and computing power. In this investigation the effectiveness of turbulent flow and acoustic noise prediction using RANS based methods has been assessed for different wing mirror geometries. Three different RANS based models were used, standard k-ε, realizable k-ε and k-ω SST. The merits and limitations of these methods are then discussed, by comparing with both experimental and numerical results found in literature. In general, flow prediction is fairly comparable to more complex LES (Large Eddy Simulation) based methods; in particular for the k-ω SST model. However acoustic noise prediction still leaves opportunities for more improvement using RANS based methods.

Keywords: acoustics, aerodynamics, RANS models, turbulent flow

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Authors: Musaab Riyadh, Norwati Mustapha, Dina Riyadh

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Trajectory similarity can be defined as the cost of transforming one trajectory into another based on certain similarity method. It is the core of numerous mining tasks such as clustering, classification, and indexing. Various approaches have been suggested to measure similarity based on the geometric and dynamic properties of trajectory, the overlapping between trajectory segments, and the confined area between entire trajectories. In this article, an evaluation of these approaches has been done based on computational cost, usage memory, accuracy, and the amount of data which is needed in advance to determine its suitability to stream mining applications. The evaluation results show that the stream mining applications support similarity methods which have low computational cost and memory, single scan on data, and free of mathematical complexity due to the high-speed generation of data.

Keywords: global distance measure, local distance measure, semantic trajectory, spatial dimension, stream data mining

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Authors: Waziri Victor Onomza, John K. Alhassan, Idris Ismaila, Noel Dogonyaro Moses

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This paper describes the problem of building secure computational services for encrypted information in the Cloud Computing without decrypting the encrypted data; therefore, it meets the yearning of computational encryption algorithmic aspiration model that could enhance the security of big data for privacy, confidentiality, availability of the users. The cryptographic model applied for the computational process of the encrypted data is the Fully Homomorphic Encryption Scheme. We contribute theoretical presentations in high-level computational processes that are based on number theory and algebra that can easily be integrated and leveraged in the Cloud computing with detail theoretic mathematical concepts to the fully homomorphic encryption models. This contribution enhances the full implementation of big data analytics based cryptographic security algorithm.

Keywords: big data analytics, security, privacy, bootstrapping, homomorphic, homomorphic encryption scheme

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Authors: Bin Liu

Abstract:

Prokaryotic promoter, consisted of two short DNA sequences located at in -35 and -10 positions, is responsible for controlling the initiation and expression of gene expression. Different types of promoters have different functions, and their consensus sequences are similar. In addition, their consensus sequences may be different for the same type of promoter, which poses difficulties for promoter identification. Unfortunately, all existing computational methods treat promoter identification as a binary classification task and can only identify whether a query sequence belongs to a specific promoter type. It is desired to develop computational methods for effectively identifying promoters and their types. Here, a two-layer predictor is proposed to try to deal with the problem. The first layer is designed to predict whether a given sequence is a promoter and the second layer predicts the type of promoter that is judged as a promoter. Meanwhile, we also analyze the importance of feature and sequence conversation in two aspects: promoter identification and promoter type identification. To the best knowledge of ours, it is the first computational predictor to detect promoters and their types.

Keywords: promoter, promoter type, random forest, sequence information

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Authors: Victor Onomza Waziri, John K. Alhassan, Idris Ismaila, Noel Dogonyara

Abstract:

This paper describes the problem of building secure computational services for encrypted information in the Cloud. Computing without decrypting the encrypted data; therefore, it meets the yearning of computational encryption algorithmic aspiration model that could enhance the security of big data for privacy or confidentiality, availability and integrity of the data and user’s security. The cryptographic model applied for the computational process of the encrypted data is the Fully Homomorphic Encryption Scheme. We contribute a theoretical presentations in a high-level computational processes that are based on number theory that is derivable from abstract algebra which can easily be integrated and leveraged in the Cloud computing interface with detail theoretic mathematical concepts to the fully homomorphic encryption models. This contribution enhances the full implementation of big data analytics based on cryptographic security algorithm.

Keywords: big data analytics, security, privacy, bootstrapping, Fully Homomorphic Encryption Scheme

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Authors: Divya Vats, Sanjay Mahajani

Abstract:

The clarification of sugarcane juice plays a pivotal role in the production of non-centrifugal sugar (NCS), profoundly influencing the quality of the final NCS product. In this study, we have investigated the kinetics and mathematical modeling of the batch clarification process. The turbidity of the clarified cane juice (NTU) emerges as the determinant of the end product’s color. Moreover, this parameter underscores the significance of considering other variables as performance indicators for accessing the efficacy of the clarification process. Temperature-controlled experiments were meticulously conducted in a laboratory-scale batch mode. The primary objective was to discern the essential and optimized parameters crucial for augmenting the clarity of cane juice. Additionally, we explored the impact of pH and flocculant loading on the kinetics. Particle Image Velocimetry (PIV) is employed to comprehend the particle-particle and fluid-particle interaction. This technique facilitated a comprehensive understanding, paving the way for the subsequent multiphase computational fluid dynamics (CFD) simulations using the Eulerian-Lagrangian approach in the Ansys fluent. Impressively, these simulations accurately replicated comparable velocity profiles. The final mechanism of this study helps to make a mathematical model and presents a valuable framework for transitioning from the traditional batch process to a continuous process. The ultimate aim is to attain heightened productivity and unwavering consistency in product quality.

Keywords: non-centrifugal sugar, particle image velocimetry, computational fluid dynamics, mathematical modeling, turbidity

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Authors: Amin Jamili

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Nowadays, the majority of international trade in goods is carried by sea, and especially by ships deployed in the industrial and tramp segments. This paper addresses routing the tramp ships and determining the schedules including the arrival times to the ports, berthing times at the ports, and the departure times in an operational planning level. In the operational planning level, the weather can be almost exactly forecasted, however in some routes some uncertainties may remain. In this paper, the voyaging times between some of the ports are considered to be uncertain. To that end, a two-stage stochastic mathematical model is proposed. Moreover, a case study is tested with the presented model. The computational results show that this mathematical model is promising and can represent acceptable solutions.

Keywords: routing, scheduling, tram ships, two stage stochastic model, uncertainty

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Authors: M. K. Balyan

Abstract:

The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: dynamical diffraction, hologram, object image, X-ray holography

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Authors: Sandeep Singh

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In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: El Hassene Osmani, Mounir Haddou, Naceurdine Bensalem

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In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely, the obstacle problem. We present a relaxed formulation for the problem using smoothing functions. Since we adopt a numerical point of view, we first relax the feasible domain of the problem, then using both mathematical programming methods and penalization methods, we get optimality conditions with smooth Lagrange multipliers. Some numerical experiments using IPOPT algorithm (Interior Point Optimizer) are presented to verify the efficiency of our approach.

Keywords: complementarity problem, IPOPT, Lagrange multipliers, mathematical programming, optimal control, smoothing methods, variationally inequalities

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Authors: Shreyas S. Hegde, Anindya Deb, Suresh Nagesh

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Computational bio-mechanics is developing rapidly as a non-invasive tool to assist the medical fraternity to help in both diagnosis and prognosis of human body related issues such as injuries, cardio-vascular dysfunction, atherosclerotic plaque etc. Any system that would help either properly diagnose such problems or assist prognosis would be a boon to the doctors and medical society in general. Recently a lot of work is being focused in this direction which includes but not limited to various finite element analysis related to dental implants, skull injuries, orthopedic problems involving bones and joints etc. Such numerical solutions are helping medical practitioners to come up with alternate solutions for such problems and in most cases have also reduced the trauma on the patients. Some work also has been done in the area related to the use of computational fluid mechanics to understand the flow of blood through the human body, an area of hemodynamics. Since cardio-vascular diseases are one of the main causes of loss of human life, understanding of the blood flow with and without constraints (such as blockages), providing alternate methods of prognosis and further solutions to take care of issues related to blood flow would help save valuable life of such patients. This project is an attempt to use computational fluid dynamics (CFD) to solve specific problems related to hemodynamics. The hemodynamics simulation is used to gain a better understanding of functional, diagnostic and theoretical aspects of the blood flow. Due to the fact that many fundamental issues of the blood flow, like phenomena associated with pressure and viscous forces fields, are still not fully understood or entirely described through mathematical formulations the characterization of blood flow is still a challenging task. The computational modeling of the blood flow and mechanical interactions that strongly affect the blood flow patterns, based on medical data and imaging represent the most accurate analysis of the blood flow complex behavior. In this project the mathematical modeling of the blood flow in the arteries in the presence of successive blockages has been analyzed using CFD technique. Different cases of blockages in terms of percentages have been modeled using commercial software CATIA V5R20 and simulated using commercial software ANSYS 15.0 to study the effect of varying wall shear stress (WSS) values and also other parameters like the effect of increase in Reynolds number. The concept of fluid structure interaction (FSI) has been used to solve such problems. The model simulation results were validated using in vivo measurement data from existing literature

Keywords: computational fluid dynamics, hemodynamics, blood flow, results validation, arteries

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