Search results for: mathematical shape deformation model

Authors: Ella Tyuryumina, Alexey Neznanov

Abstract:

Finding algorithms to predict the growth of tumors has piqued the interest of researchers ever since the early days of cancer research. A number of studies were carried out as an attempt to obtain reliable data on the natural history of breast cancer growth. Mathematical modeling can play a very important role in the prognosis of tumor process of breast cancer. However, mathematical models describe primary tumor growth and metastases growth separately. Consequently, we propose a mathematical growth model for primary tumor and primary metastases which may help to improve predicting accuracy of breast cancer progression using an original mathematical model referred to CoM-IV and corresponding software. We are interested in: 1) modelling the whole natural history of primary tumor and primary metastases; 2) developing adequate and precise CoM-IV which reflects relations between PT and MTS; 3) analyzing the CoM-IV scope of application; 4) implementing the model as a software tool. The CoM-IV is based on exponential tumor growth model and consists of a system of determinate nonlinear and linear equations; corresponds to TNM classification. It allows to calculate different growth periods of primary tumor and primary metastases: 1) ‘non-visible period’ for primary tumor; 2) ‘non-visible period’ for primary metastases; 3) ‘visible period’ for primary metastases. The new predictive tool: 1) is a solid foundation to develop future studies of breast cancer models; 2) does not require any expensive diagnostic tests; 3) is the first predictor which makes forecast using only current patient data, the others are based on the additional statistical data. Thus, the CoM-IV model and predictive software: a) detect different growth periods of primary tumor and primary metastases; b) make forecast of the period of primary metastases appearance; c) have higher average prediction accuracy than the other tools; d) can improve forecasts on survival of BC and facilitate optimization of diagnostic tests. The following are calculated by CoM-IV: the number of doublings for ‘nonvisible’ and ‘visible’ growth period of primary metastases; tumor volume doubling time (days) for ‘nonvisible’ and ‘visible’ growth period of primary metastases. The CoM-IV enables, for the first time, to predict the whole natural history of primary tumor and primary metastases growth on each stage (pT1, pT2, pT3, pT4) relying only on primary tumor sizes. Summarizing: a) CoM-IV describes correctly primary tumor and primary distant metastases growth of IV (T1-4N0-3M1) stage with (N1-3) or without regional metastases in lymph nodes (N0); b) facilitates the understanding of the appearance period and manifestation of primary metastases.

Keywords: breast cancer, exponential growth model, mathematical modelling, primary metastases, primary tumor, survival

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Authors: Hyo Lim Kang, Tae An Kim, Seung Ho Han

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A 3-way reversing valve has been used in automotive washing machines to remove remaining oil and dirt on machined engine and transmission blocks. It provides rapid and accurate changes of water flow direction without any precise control device. However, due to its complicated bottom-plug shape, a cavitation occurs in a wide range of the bottom-plug in a downstream. In this study, the cavitation index and POC (percent of cavitation) were used to evaluate quantitatively the cavitation phenomena occurring at the bottom-plug. An optimal shape design was carried out via parametric study for geometries of the bottom-plug, in which a simple CAE-model was used in order to avoid time-consuming CFD analysis and hard to achieve convergence. To verify the results of numerical analysis, a flow visualization test was carried out using a test specimen with a transparent acryl pipe according to ISA-RP75.23. The flow characteristics such as the cavitation occurring in the downstream were investigated by using a flow test equipment with valve and pump including a flow control system and high-speed camera.

Keywords: cavitation, flow visualization test, optimal shape design, percent of cavitation, reversing valve

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: R. Bennai, H. Ait Atmane, H. Fourne, B. Ayache

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In this work, an analytical approach using a refined theory of hyperbolic shear deformation of a beam was developed to study the buckling of graduated sandwiches beams under different boundary conditions. The effects of transverse shear strains and the transverse normal deformation are considered. The constituent materials of the beam are supposed gradually variable depending on the height direction based on a simple power distribution law in terms of the volume fractions of the constituents; the two materials with which we worked are metals and ceramics. The core layer is taken homogeneous and made of an isotropic material; while the banks layers consist of functionally graded materials with a homogeneous fraction compared to the middle layer. In the end, illustrative examples are presented to show the effects of changes in different parameters such as (material graduation, the stretching effect of the thickness, boundary conditions and thickness ratio-length) on the vibration free of an FGM sandwich beams.

Keywords: FGM materials, refined shear deformation theory, stretching effect, buckling

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Authors: Kayode Oshinubi, Brice Kammegne, Jacques Demongeot

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The use of mathematical tools like Partial Differential Equations and Ordinary Differential Equations have become very important to predict the evolution of a viral disease in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China causing a severe and potentially fatal respiratory syndrome, i.e., COVID-19. Since then, it has become a pandemic declared by World Health Organization (WHO) on March 11, 2020 which has spread around the globe. A reaction-diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process in which different substances are transformed, and a diffusion process that causes a distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic by the bias of reaction-diffusion equations. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined using the Lyapunov function are considered and the endemic equilibrium point exists and is stable if it satisfies Routh–Hurwitz criteria. Also, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We showed the spatial distribution of the model compartments when the basic reproduction rate $\mathcal{R}_0 < 1$ and $\mathcal{R}_0 > 1$ and sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model. We demonstrate the model's effectiveness by performing numerical simulations. We investigate the impact of vaccination and the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. To the public health policymakers, we offered a better understanding of the COVID-19 management.

Keywords: COVID-19, SEIRV epidemic model, reaction-diffusion equation, basic reproduction number, vaccination, spatial distribution

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Authors: Mahmudjon Kuchkarov, Marufjon Kuchkarov

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The origin of ‘Human Language’ is still a secret and the most interesting subject of historical linguistics. The core element is the nature of labeling or coding the things or processes with symbols and sounds. In this paper, we investigate human’s involuntary Paired Sounds and Shape Production (PSSP) and its contribution to the development of early human communication. Aimed at twenty-six volunteers who provided many physical movements with various difficulties, the research team investigated the natural, repeatable, and paired sounds and shape productions during human activities. The paper claims the involvement of Paired Sounds and Shape Production (PSSP) in the phonetic origin of some modern words and the existence of similarities between elements of PSSP with characters of the classic Latin alphabet. The results may be used not only as a supporting idea for existing theories but to create a closer look at some fundamental nature of the origin of the languages as well.

Keywords: body shape, body language, coding, Latin alphabet, merging method, movement language, movement sound, natural sound, origin of language, pairing, phonetics, sound and shape production, word origin, word semantic

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Authors: Paras Ram, Vikas Kumar

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The transmission of Malaria with seasonal were studied through the use of mathematical models. The data from the annual number of Malaria cases reported to the Division of Epidemiology, Ministry of Public Health, Thailand during the period 1997-2011 were analyzed. The transmission of Malaria with seasonal was studied by formulating a mathematical model which had been modified to describe different situations encountered in the transmission of Malaria. In our model, the population was separated into two groups: the human and vector groups, and then constructed a system of nonlinear differential equations. Each human group was divided into susceptible, infectious in hot season, infectious in rainy season, infectious in cool season and recovered classes. The vector population was separated into two classes only: susceptible and infectious vectors. The analysis of the models was given by the standard dynamical modeling.

Keywords: ferrofluid, magnetic field, porous medium, rotating disk, Neuringer-Rosensweig Model

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Authors: Ledeza Jordan Babiano

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Translating statements into mathematical notations is one of the processes in word problem-solving. However, based on the literature, students still have difficulties with this skill. The purpose of this study was to investigate the translation errors of the students when they translate algebraic word problems into mathematical structures and locate the errors via the lens of the Translation-Verification Model. Moreover, this qualitative research study employed content analysis. During the data-gathering process, the students were asked to answer a six-item algebra word problem questionnaire, and their answers were analyzed by experts through blind coding using the Translation-Verification Model to determine their translation errors. After this, a focus group discussion was conducted, and the data gathered was analyzed through thematic analysis to determine the causes of the students’ translation errors. It was found out that students’ prevalent error in translation was the interpretation error, which was situated in the Attribute construct. The emerging themes during the FGD were: (1) The procedure of translation is strategically incorrect; (2) Lack of comprehension; (3) Algebra concepts related to difficulty; (4) Lack of spatial skills; (5) Unprepared for independent learning; and (6) The content of the problem is developmentally inappropriate. These themes boiled down to the major concept of independent learning preparedness in solving mathematical problems. This concept has subcomponents, which include contextual and conceptual factors in translation. Consequently, the results provided implications for instructors and professors in Mathematics to innovate their teaching pedagogies and strategies to address translation gaps among students.

Keywords: mathematical structure, algebra word problems, translation, errors

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Authors: Ji Chen, Chunhui Zhang, Fanming Zeng, Lei Zhang, Ying Li, Wei Zhang

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Based on the synthetic principle of force, a pre-compressed nonlinear isolator with quasi-zero-stiffness (QZS) is developed for shock isolation of ship equipment. The proposed isolator consists of a vertical spring with positive stiffness and several lateral springs with negative stiffness. An analytical expression of vertical stiffness of the nonlinear isolator is derived and numerical simulation on the effect of the geometric design parameters is carried out. Besides, a pre-compressed QZS shock isolation system model is established. The stiffness characteristic of the system is studied and the effects of excitation amplitude and friction damping on shock isolation performance are discussed respectively. The research results show that in comparison with linear shock isolation system, the pre-compressed QZS shock isolation system could realize constant-force or approximately constant-force function and perform better anti-impact performance.

Keywords: quasi-zero-stiffness, constant-force, pre-compressed, large deformation, shock isolation, friction damping

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Authors: Sara A. Pakvis, Giulia Scalet, Stefania Marconi, Ferdinando Auricchio, Matthijs Langelaar

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In recent developments in the field of multi-material additive manufacturing, differences in material properties are exploited to create printed shape-memory structures, which are referred to as 4D-printed structures. New printing techniques allow for the deliberate introduction of prestresses in the specimen during manufacturing, and, in combination with the right design, this enables new functionalities. This research focuses on bi-polymer 4D-printed structures, where the transformation process is based on a heat-induced glass transition in one material lowering its Young’s modulus, combined with an initial prestress in the other material. Upon the decrease in stiffness, the prestress is released, which results in the realization of an essentially pre-programmed deformation. As the design of such functional multi-material structures is crucial but far from trivial, a systematic methodology to find the design of 4D-printed structures is developed, where a finite element model is combined with a density-based topology optimization method to describe the material layout. This modeling approach is verified by a convergence analysis and validated by comparing its numerical results to analytical and published data. Specific aspects that are addressed include the interplay between the definition of the prestress and the material interpolation function used in the density-based topology description, the inclusion of a temperature-dependent stiffness relationship to simulate the glass transition effect, and the importance of the consideration of geometric nonlinearity in the finite element modeling. The efficacy of topology optimization to design 4D-printed structures is explored by applying the methodology to a variety of design problems, both in 2D and 3D settings. Bi-layer designs composed of thermoplastic polymers are printed by means of the fused deposition modeling (FDM) technology. Acrylonitrile butadiene styrene (ABS) polymer undergoes the glass transition transformation, while polyurethane (TPU) polymer is prestressed by means of the 3D-printing process itself. Tests inducing shape transformation in the printed samples through heating are performed to calibrate the prestress and validate the modeling approach by comparing the numerical results to the experimental findings. Using the experimentally obtained prestress values, more complex designs have been generated through topology optimization, and samples have been printed and tested to evaluate their performance. This study demonstrates that by combining topology optimization and 4D-printing concepts, stimuli-responsive structures with specific properties can be designed and realized.

Keywords: 4D-printing, glass transition, shape memory polymer, topology optimization

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Authors: Mahbub C. Mishu, Venktesh N. Dubey, Tamas Hickish, Jonathan Cole

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Pressure ulcer is a common problem for today's healthcare industry. It occurs due to external load applied to the skin. Also when the subject is immobile for a longer period of time and there is continuous load applied to a particular area of human body,blood flow gets reduced and as a result pressure ulcer develops. Body support surface has a significant role in preventing ulceration so it is important to know the characteristics of support surface under loading conditions. In this paper we have presented mathematical models of different types of viscoelastic materials and also we have shown the validation of our simulation results with experiments.

Keywords: pressure ulcer, viscoelastic material, mathematical model, experimental validation

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Authors: E. Tandis, E. Assareh

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Designing the optimal shape of MW wind turbine blades is provided in a number of cases through evolutionary algorithms associated with mathematical modeling (Blade Element Momentum Theory). Evolutionary algorithms, among the optimization methods, enjoy many advantages, particularly in stability. However, they usually need a large number of function evaluations. Since there are a large number of local extremes, the optimization method has to find the global extreme accurately. The present paper introduces a new population-based hybrid algorithm called Genetic-Based Bees Algorithm (GBBA). This algorithm is meant to design the optimal shape for MW wind turbine blades. The current method employs crossover and neighborhood searching operators taken from the respective Genetic Algorithm (GA) and Bees Algorithm (BA) to provide a method with good performance in accuracy and speed convergence. Different blade designs, twenty-one to be exact, were considered based on the chord length, twist angle and tip speed ratio using GA results. They were compared with BA and GBBA optimum design results targeting the power coefficient and solidity. The results suggest that the final shape, obtained by the proposed hybrid algorithm, performs better compared to either BA or GA. Furthermore, the accuracy and speed convergence increases when the GBBA is employed

Keywords: Blade Design, Optimization, Genetic Algorithm, Bees Algorithm, Genetic-Based Bees Algorithm, Large Wind Turbine

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Authors: Sergey Podluzhnyy

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One of the most important tasks of investment and pension fund management is building decision support system which helps to make right decision on corporate bond portfolio formation. Today there are several basic methods of bond portfolio management. They are duration management, immunization and convexity management. Identified methods have serious disadvantage: they do not take into account credit risk or insolvency risk of issuer. So, identified methods can be applied only for management and evaluation of high-quality sovereign bonds. Applying article proposes mathematical model for building an optimal in case of risk and yield corporate bond portfolio. Proposed model takes into account the default probability in formula of assessment of bonds which results to more correct evaluation of bonds prices. Moreover, applied model provides tools for visualization of the efficient frontier of corporate bonds portfolio taking into account the exposure to credit risk, which will increase the quality of the investment decisions of portfolio managers.

Keywords: corporate bond portfolio, default probability, effective boundary, portfolio optimization task

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Authors: Jamal Hussain Al-Smail

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Hydrogen fuel cells (HFCs) are environmentally friendly, energy converter devices that convert the chemical energy of the reactants (oxygen and hydrogen) to electricity through electrochemical reactions. The level of the electricity production of HFCs mainly increases depending on the oxygen distribution in the HFC’s cathode gas diffusion layer (GDL). With a constant porosity of the GDL, the electrochemical reaction can have a great variation that reduces the cell’s productivity and stability. Our findings bring a methodology in finding porosity designs of the diffusion layer to improve the oxygen distribution such that it results in a stable oxygen-hydrogen reaction. We first introduce a mathematical model involving the mass and momentum transport equations, in which a porosity function of the GDL is incorporated as a control for the fluid flow. We then derive numerical methods for solving the mathematical model. In conclusion, we present our numerical results to show how to design the GDL porosity to result in a uniform oxygen distribution.

Keywords: fuel cells, material porosity design, mathematical modeling, porous media

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Authors: Hassan Al Salman

Abstract:

We consider a nonlinear parabolic cross diffusion model arising in applied mathematics. A fully practical piecewise linear finite element approximation of the model is studied. By using entropy-type inequalities and compactness arguments, existence of a global weak solution is proved. Providing further regularity of the solution of the model, some uniqueness results and error estimates are established. Finally, some numerical experiments are performed.

Keywords: cross diffusion model, entropy-type inequality, finite element approximation, numerical analysis

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Authors: Geetika Barman, B. S. Daya Sagar

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In this article, we proposed a pixel-wise classification of hyperspectral images using a mathematical morphology operator-based distance metric called “dilation distance” and “erosion distance”. This method involves measuring the spatial distance between the spectral features of a hyperspectral image across the bands. The key concept of the proposed approach is that the “dilation distance” is the maximum distance a pixel can be moved without changing its classification, whereas the “erosion distance” is the maximum distance that a pixel can be moved before changing its classification. The spectral signature of the hyperspectral image carries unique class information and shape for each class. This article demonstrates how easily the dilation and erosion distance can measure spatial distance compared to other approaches. This property is used to calculate the spatial distance between hyperspectral image feature vectors across the bands. The dissimilarity matrix is then constructed using both measures extracted from the feature spaces. The measured distance metric is used to distinguish between the spectral features of various classes and precisely distinguish between each class. This is illustrated using both toy data and real datasets. Furthermore, we investigated the role of flat vs. non-flat structuring elements in capturing the spatial features of each class in the hyperspectral image. In order to validate, we compared the proposed approach to other existing methods and demonstrated empirically that mathematical operator-based distance metric classification provided competitive results and outperformed some of them.

Keywords: dilation distance, erosion distance, hyperspectral image classification, mathematical morphology

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Authors: Sharifullah Ahmed

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Shallow foundation on soft soils without ground improvement can represent a high level of settlement. In such a case, an alternative to pile foundations may be shallow strip footings placed on a soil system in which the upper layer is untreated or cement-treated compacted sand to limit the settlement within a permissible level. This research work deals with a rigid plane-strain strip footing of 2.5m width placed on a soil consisting of untreated or cement treated sand layer underlain by homogeneous soft clay. Both the thin and thick compared the footing width was considered. The soft inorganic cohesive NC clay layer is considered undrained for plastic loading stages and drained in consolidation stages, and the sand layer is drained in all loading stages. FEM analysis was done using PLAXIS 2D Version 8.0 with a model consisting of clay deposits of 15m thickness and 18m width. The soft clay layer was modeled using the Hardening Soil Model, Soft Soil Model, Soft Soil Creep model, and the upper improvement layer was modeled using only the Hardening Soil Model. The system is considered fully saturated. The value of natural void ratio 1.2 is used. Total displacement fields of strip footing and subsoil layers in the case of Untreated and Cement treated Sand as Upper layer are presented. For Hi/B =0.6 or above, the distribution of major deformation within an upper layer and the influence zone of footing is limited in an upper layer which indicates the complete effectiveness of the upper layer in bearing the foundation effectively in case of the untreated upper layer. For Hi/B =0.3 or above, the distribution of major deformation occurred within an upper layer, and the function of footing is limited in the upper layer. This indicates the complete effectiveness of the cement-treated upper layer. Brittle behavior of cemented sand and fracture or cracks is not considered in this analysis.

Keywords: displacement, ground improvement, influence depth, PLAXIS 2D, primary and secondary settlement, sand mat, soft clay

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Authors: Oday Al-Mamoori, J. Enrique Martinez-Rueda

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'C' shape yielding devices (C-devices) are effective tools for introducing supplemental sources of energy dissipation by hysteresis. Studies have shown that C-devices made of mild steel can be successfully applied as integral parts of seismic retrofitting schemes. However, explicit modelling of these devices can become cumbersome, expensive and time consuming. The device under study in this article has been previously used in non-invasive dissipative bracing for seismic retrofitting. The device is cut from a mild steel plate and has an overall shape that resembles that of a rectangular portal frame with circular interior corner transitions to avoid stress concentration and to control the extension of the dissipative region of the device. A number of inelastic finite element (FE) analyses using either inelastic 2D plane stress elements or inelastic fibre frame elements are reported and used to calibrate a 1D equivalent inelastic spring model that effectively reproduces the cyclic response of the device. The more elaborate FE model accounts for the frictional forces developed between the steel plate and the bolts used to connect the C-device to structural members. FE results also allow the visualization of the inelastic regions of the device where energy dissipation is expected to occur. FE analysis results are in a good agreement with experimental observations.

Keywords: C-device, equivalent nonlinear spring, FE analyses, reversed cyclic tests

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Authors: Ella Tyuryumina, Alexey Neznanov

Abstract:

This paper is devoted to mathematical modelling of the progression and stages of breast cancer. We propose Consolidated mathematical growth model of primary tumor and secondary distant metastases growth in patients with lymph nodes metastases (CoM-III) as a new research tool. We are interested in: 1) modelling the whole natural history of primary tumor and secondary distant metastases growth in patients with lymph nodes metastases; 2) developing adequate and precise CoM-III which reflects relations between primary tumor and secondary distant metastases; 3) analyzing the CoM-III scope of application; 4) implementing the model as a software tool. Firstly, the CoM-III includes exponential tumor growth model as a system of determinate nonlinear and linear equations. Secondly, mathematical model corresponds to TNM classification. It allows to calculate different growth periods of primary tumor and secondary distant metastases growth in patients with lymph nodes metastases: 1) ‘non-visible period’ for primary tumor; 2) ‘non-visible period’ for secondary distant metastases growth in patients with lymph nodes metastases; 3) ‘visible period’ for secondary distant metastases growth in patients with lymph nodes metastases. The new predictive tool: 1) is a solid foundation to develop future studies of breast cancer models; 2) does not require any expensive diagnostic tests; 3) is the first predictor which makes forecast using only current patient data, the others are based on the additional statistical data. Thus, the CoM-III model and predictive software: a) detect different growth periods of primary tumor and secondary distant metastases growth in patients with lymph nodes metastases; b) make forecast of the period of the distant metastases appearance in patients with lymph nodes metastases; c) have higher average prediction accuracy than the other tools; d) can improve forecasts on survival of breast cancer and facilitate optimization of diagnostic tests. The following are calculated by CoM-III: the number of doublings for ‘non-visible’ and ‘visible’ growth period of secondary distant metastases; tumor volume doubling time (days) for ‘non-visible’ and ‘visible’ growth period of secondary distant metastases. The CoM-III enables, for the first time, to predict the whole natural history of primary tumor and secondary distant metastases growth on each stage (pT1, pT2, pT3, pT4) relying only on primary tumor sizes. Summarizing: a) CoM-III describes correctly primary tumor and secondary distant metastases growth of IA, IIA, IIB, IIIB (T1-4N1-3M0) stages in patients with lymph nodes metastases (N1-3); b) facilitates the understanding of the appearance period and inception of secondary distant metastases.

Keywords: breast cancer, exponential growth model, mathematical model, primary tumor, secondary metastases, survival

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Authors: Gholamhassan Kakha, Mohsen Jami, Daniel Alex Merino Natorce

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Sustainable development refers to the creation of a balance between the development and the environment too; it consists of three key principles namely environment, society and economy. These three parameters are related to each other and the imbalance occurs in each will lead to the disparity of the other parts. Mining is one of the most important tools of the economic growth and social welfare in many countries. Meanwhile, assessment of the environmental impacts has directed to the attention of planners toward the natural environment of the areas surrounded by mines and allowing for monitoring and controlling of the current situation by the designers. In this look upon, a semi-quantitative model using a matrix method is presented for assessing the environmental impacts in the BOOG Granite Mine located in Sistan and Balouchestan, one of the provinces of Iran for determining the effective factors and environmental components. For accomplishing this purpose, the initial data are collected by the experts at the next stage; the effect of the factors affects each environmental component is determined by specifying the qualitative viewpoints. Based on the results, factors including air quality, ecology, human health and safety along with the environmental damages resulted from mining activities in that area. Finally, the results gained from the assessment of the environmental impact are used to evaluate the sustainability by using Philips mathematical model. The results show that the sustainability of this area is weak, so environmental preventive measures are recommended to reduce the environmental damages to its components.

Keywords: sustainable development, environmental impacts' assessment, BOOG granite, Philips mathematical model

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Authors: Khaled R. Khater

Abstract:

This paper fits in soil-structure interaction division. Its theme is soil retaining structures. Hence, the cantilever secant-pile wall imposed itself, focusing on the capping beam. Four research questions are prompted and beg an answer. How to calculate the forces that control capping beam design? What is the statical system of ‘capping beam-secant pile’ as one unit? Is it possible to design it to satisfy pre-specific lateral deformation? Is it possible to suggest permissible lateral deformation limits? Briefly, pile head displacements induced by Plaxis-2D are converted to forces needed for STAAD-Pro 3D models. Those models are constructed based on the proposed structural system. This is the paper’s idea and methodology. Parametric study performed considered three sand densities, one pile rigidity, and two excavation depths, i.e., 3.0 m and 5.0 m. The research questions are satisfactorily answered. This paper could be a first step towards standardizing analysis, design, and lateral deformations checks.

Keywords: capping beam, secant pile, numerical, design aids, sandy soil

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Authors: Martin Kendra, Jaroslav Mašek, Juraj Čamaj, Martin Búda

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The paper deals with possibilities of increase train capacity by using a new type of railway wagon. In the first part is created a mathematical model to calculate the capacity of the train. The model is based on the main limiting parameters of the train - maximum number of axles per train, the maximum gross weight of the train, the maximum length of train and number of TEUs per one wagon. In the second part is the model applied to four different model trains with different composition of the train set and three different average weights of TEU and a train consisting of a new type of wagons. The result is to identify where the carrying capacity of the original trains is higher, respectively less than a capacity of the train consisting of a new type of wagons.

Keywords: loading units, theoretical capacity model, train capacity, wagon for intermodal transport

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Authors: Meitham Amereh, Mohsen Akbari, Ben Nadler

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Cancer has been recognized as one of the most challenging problems in biology and medicine. Aggressive tumors are a lethal type of cancers characterized by high genomic instability, rapid progression, invasiveness, and therapeutic resistance. Their behavior involves complicated molecular biology and consequential dynamics. Although tremendous effort has been devoted to developing therapeutic approaches, there is still a huge need for new insights into the dark aspects of tumors. As one of the key requirements in better understanding the complex behavior of tumors, mathematical modeling and continuum physics, in particular, play a pivotal role. Mathematical modeling can provide a quantitative prediction on biological processes and help interpret complicated physiological interactions in tumors microenvironment. The pathophysiology of aggressive tumors is strongly affected by the extracellular cues such as stresses produced by mechanical forces between the tumor and the host tissue. During the tumor progression, the growing mass displaces the surrounding extracellular matrix (ECM), and due to the level of tissue stiffness, stress accumulates inside the tumor. The produced stress can influence the tumor by breaking adherent junctions. During this process, the tumor stops the rapid proliferation and begins to remodel its shape to preserve the homeostatic equilibrium state. To reach this, the tumor, in turn, upregulates epithelial to mesenchymal transit-inducing transcription factors (EMT-TFs). These EMT-TFs are involved in various signaling cascades, which are often associated with tumor invasiveness and malignancy. In this work, we modeled the tumor as a growing hyperplastic mass and investigated the effects of mechanical stress from surrounding ECM on tumor invasion. The invasion is modeled as volume-preserving inelastic evolution. In this framework, principal balance laws are considered for tumor mass, linear momentum, and diffusion of nutrients. Also, mechanical interactions between the tumor and ECM is modeled using Ciarlet constitutive strain energy function, and dissipation inequality is utilized to model the volumetric growth rate. System parameters, such as rate of nutrient uptake and cell proliferation, are obtained experimentally. To validate the model, human Glioblastoma multiforme (hGBM) tumor spheroids were incorporated inside Matrigel/Alginate composite hydrogel and was injected into a microfluidic chip to mimic the tumor’s natural microenvironment. The invasion structure was analyzed by imaging the spheroid over time. Also, the expression of transcriptional factors involved in invasion was measured by immune-staining the tumor. The volumetric growth, stress distribution, and inelastic evolution of tumors were predicted by the model. Results showed that the level of invasion is in direct correlation with the level of predicted stress within the tumor. Moreover, the invasion length measured by fluorescent imaging was shown to be related to the inelastic evolution of tumors obtained by the model.

Keywords: cancer, invasion, mathematical modeling, microfluidic chip, tumor spheroids

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Authors: Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa

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A generalized log-logistic distribution with variable shapes of the hazard rate was introduced and studied, extending the log-logistic distribution by adding an extra parameter to the classical distribution, leading to greater flexibility in analysing and modeling various data types. The proposed distribution has a large number of well-known lifetime special sub-models such as; Weibull, log-logistic, exponential, and Burr XII distributions. Its basic mathematical and statistical properties were derived. The method of maximum likelihood was adopted for estimating the unknown parameters of the proposed distribution, and a Monte Carlo simulation study is carried out to assess the behavior of the estimators. The importance of this distribution is that its tendency to model both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub shape) or reversed “bathtub” shape hazard rate functions which are quite common in survival and reliability data analysis. Furthermore, the flexibility and usefulness of the proposed distribution are illustrated in a real-life data set and compared to its sub-models; Weibull, log-logistic, and BurrXII distributions and other parametric survival distributions with 3-parmaeters; like the exponentiated Weibull distribution, the 3-parameter lognormal distribution, the 3- parameter gamma distribution, the 3-parameter Weibull distribution, and the 3-parameter log-logistic (also known as shifted log-logistic) distribution. The proposed distribution provided a better fit than all of the competitive distributions based on the goodness-of-fit tests, the log-likelihood, and information criterion values. Finally, Bayesian analysis and performance of Gibbs sampling for the data set are also carried out.

Keywords: hazard rate function, log-logistic distribution, maximum likelihood estimation, generalized log-logistic distribution, survival data, Monte Carlo simulation

Procedia PDF Downloads 173

Authors: N. Tadrisi Parsa, A. R. Vali, R. Ghasemi

Abstract:

Diabetes is a growing health problem in worldwide. Especially, the patients with Type 1 diabetes need strict glycemic control because they have deficiency of insulin production. This paper attempts to control blood glucose based on body mathematical body model. The Bergman minimal mathematical model is used to develop the nonlinear controller. A novel back-stepping based sliding mode control (B-SMC) strategy is proposed as a solution that guarantees practical tracking of a desired glucose concentration. In order to show the performance of the proposed design, it is compared with conventional linear and fuzzy controllers which have been done in previous researches. The numerical simulation result shows the advantages of sliding mode back stepping controller design to linear and fuzzy controllers.

Keywords: bergman model, nonlinear control, back stepping, sliding mode control

Procedia PDF Downloads 361

Authors: Abdurrahim Bolukbasi, Hassan Athari, Dogan Ciloglu

Abstract:

The modeling lung respiratory system which has complex anatomy and biophysics presents several challenges including tissue-driven flow patterns and wall motion. Also, the lung pulmonary system because of that they stretch and recoil with each breath, has not static walls and structures. The direct relationship between air flow and tissue motion in the lung structures naturally prefers an FSI simulation technique. Therefore, in order to toward the realistic simulation of pulmonary breathing mechanics the development of a coupled FSI computational model is an important step. A simple but physiologically-relevant three dimensional deep long geometry is designed and fluid-structure interaction (FSI) coupling technique is utilized for simulating the deformation of the lung parenchyma tissue which produces airflow fields. The real understanding of respiratory tissue system as a complex phenomenon have been investigated with respect to respiratory patterns, fluid dynamics and tissue visco-elasticity and tidal breathing period.

Keywords: lung deformation and mechanics; Tissue mechanics; Viscoelasticity; Fluid-structure interactions; ANSYS

Procedia PDF Downloads 294

Authors: Wajid Ali Khan

Abstract:

Extensive experimentation and numerical investigation are performed to predict the machining-induced residual stresses in the end milling of AISI 1045 steel, and an optimization code has been developed using the particle swarm optimization technique. Experiments were conducted using a single factor at a time and design of experiments approach. Regression analysis was done, and a mathematical model of the cutting process was developed, thus predicting the machining-induced residual stress with reasonable accuracy. The mathematical model served as the objective function to be optimized using particle swarm optimization. The relationship between the different cutting parameters and the output variables, force, and residual stresses has been studied. The combined effect of the process parameters, speed, feed, and depth of cut was examined, and it is understood that 85% of the variation of these variables can be attributed to these machining parameters under research. A 3D finite element model is developed to predict the cutting forces and the machining-induced residual stresses in end milling operation. The results were validated experimentally and against the Johnson-cook model available in the literature.

Keywords: residual stresses, end milling, 1045 steel, optimization

Procedia PDF Downloads 87

Authors: Vineetha Bettaiah, Heggere S. Ranganath

Abstract:

This paper presents a Hierarchical Piecewise Linear Approximation (HPLA) for the representation of time series data in which the time series is treated as a curve in the time-amplitude image space. The curve is partitioned into segments by choosing perceptually important points as break points. Each segment between adjacent break points is recursively partitioned into two segments at the best point or midpoint until the error between the approximating line and the original curve becomes less than a pre-specified threshold. The HPLA representation achieves dimensionality reduction while preserving prominent local features and general shape of time series. The representation permits course-fine processing at different levels of details, allows flexible definition of similarity based on mathematical measures or general time series shape, and supports time series data mining operations including query by content, clustering and classification based on whole or subsequence similarity.

Keywords: data mining, dimensionality reduction, piecewise linear representation, time series representation

Procedia PDF Downloads 251

Authors: A. El-S. Makled, M. K. Al-Tamimi

Abstract:

A mathematical model to predict the performance parameters (thrusts, chamber pressures, fuel mass flow rates, mixture ratios, and regression rates during firing time) of hybrid rocket motor (HRM) is evaluated. The internal ballistic (IB) hybrid combustion model assumes that the solid fuel surface regression rate is controlled only by heat transfer (convective and radiative) from flame zone to solid fuel burning surface. A laboratory HRM is designed, manufactured, and tested for low thrust profile space missions (10-15 N) and for validating the mathematical model (computer program). The polymer material and gaseous oxidizer which are selected for this experimental work are polymethyle-methacrylate (PMMA) and polyethylene (PE) as solid fuel grain and gaseous oxygen (GO₂) as oxidizer. The variation of various operational parameters with time is determined systematically and experimentally in firing of up to 20 seconds, and an average combustion efficiency of 95% of theory is achieved, which was the goal of these experiments. The comparison between recording fire data and predicting analytical parameters shows good agreement with the error that does not exceed 4.5% during all firing time. The current mathematical (computer) code can be used as a powerful tool for HRM analytical design parameters.

Keywords: hybrid combustion, internal ballistics, hybrid rocket motor, performance parameters

Procedia PDF Downloads 284