Search results for: Philips mathematical model

Authors: Ritesh Watharkar, Sourabh Chakraborty, Brijesh Srivastava

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Reduction of water from the fruits and vegetables using different drying techniques is widely employed to prolong the shelf life of these food commodities. Heat transfer occurs inside the sample by conduction and mass transfer takes place by diffusion in accordance with temperature and moisture concentration gradient respectively during drying. This study was undertaken to study and model the thin layer drying behavior of Bhimkol pulp. The drying was conducted in a tray drier at 500c temperature with 5, 10 and 15 % concentrations of added maltodextrin. The drying experiments were performed at 5mm thickness of the thin layer and the constant air velocity of 0.5 m/s.Drying data were fitted to different thin layer drying models found in the literature. Comparison of fitted models was based on highest R2(0.9917), lowest RMSE (0.03201), and lowest SSE (0.01537) revealed Middle equation as the best-fitted model for thin layer drying with 10% concentration of maltodextrin. The effective diffusivity was estimated based on the solution of Fick’s law of diffusion which is found in the range of 3.0396 x10-09 to 5.0661 x 10-09. There was a reduction in drying time with the addition of maltodextrin as compare to the raw pulp.

Keywords: Bhimkol, diffusivity, maltodextrine, Midilli model

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Authors: T. N. Mac, B. Shahbodaghkhan, N. Khalili

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A new elastic-viscoplastic (EVP) constitutive model is proposed for the analysis of time-dependent behavior of clay. The proposed model is based on the bounding surface plasticity and the concept of viscoplastic consistency framework to establish continuous transition from plasticity to rate dependent viscoplasticity. Unlike the overstress based models, this model will meet the consistency condition in formulating the constitutive equation for EVP model. The procedure of deriving the constitutive relationship is also presented. Simulation results and comparisons with experimental data are then presented to demonstrate the performance of the model.

Keywords: bounding surface, consistency theory, constitutive model, viscosity

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Authors: M. Capocelli, A. Caputo, M. De Falco, D. Mazzei, V. Piemonte

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This paper presents the experimental results and the related modeling of a thermal energy storage (TES) facility, ideated and realized by ENEA and realizing the thermocline with an innovative geometry. Firstly, the thermal energy exchange model of an equivalent shell & tube heat exchanger is described and tested to reproduce the performance of the spiral exchanger installed in the TES. Through the regression of the experimental data, a first-order thermocline model was also validated to provide an analytical function of the thermocline, useful for the performance evaluation and the comparison with other systems and implementation in simulations of integrated systems (e.g. power plants). The experimental data obtained from the plant start-up and the short-cut modeling of the system can be useful for the process analysis, for the scale-up of the thermal storage system and to investigate the feasibility of its implementation in actual case-studies.

Keywords: CSP plants, thermal energy storage, thermocline, mathematical modelling, experimental data

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Authors: Pawan Kumar Gupta, Sumana Ghosh

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Parkinson's Disease (PD) is a long-term neurodegenerative movement disorder of the central nervous system with vast symptoms related to the motor system. The common symptoms of PD are tremor, rigidity, bradykinesia/akinesia, and postural instability, but the clinical symptom includes other motor and non‐motor issues. The motor symptoms of the disease are consequence of death of the neurons in a region of the midbrain known as substantia nigra pars compacta, leading to decreased level of a neurotransmitter known as dopamine. The cause of this neuron death is not clearly known but involves formation of Lewy bodies, an abnormal aggregation or clumping of the protein alpha-synuclein in the neurons. Unfortunately, there is no cure for PD, and the management of this disease is challenging. Therefore, it is critical for a patient to be diagnosed at early stages. A limited choice of drugs is available to improve the symptoms, but those become less and less effective over time. Apart from that, with rapid growth in the field of science and technology, other methods such as multi-area brain stimulation are used to treat patients. In order to develop advanced techniques and to support drug development for treating PD patients, an accurate mathematical model is needed to explain the underlying relationship of dopamine secretion in the brain with the hand tremors. There has been a lot of effort in the past few decades on modeling PD tremors and treatment effects from a computational point of view. These models can effectively save time as well as the cost of drug development for the pharmaceutical industry and be helpful for selecting appropriate treatment mechanisms among all possible options. In this review paper, an effort is made to investigate studies on PD modeling and analysis and to highlight some of the key advances in the field over the past centuries with discussion on the current challenges.

Keywords: Parkinson's disease, deep brain stimulation, tremor, modeling

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Authors: Shashi Sharma, V. K. Katiyar, Uaday Singh

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The ability to manipulate magnetic particles in fluid flows by means of inhomogeneous magnetic fields is used in a wide range of biomedical applications including magnetic drug targeting (MDT). In MDT, magnetic carrier particles bounded with drug molecules are injected into the vascular system up-stream from the malignant tissue and attracted or retained at the specific region in the body with the help of an external magnetic field. Although the concept of MDT has been around for many years, however, wide spread acceptance of the technique is still looming despite the fact that it has shown some promise in both in vivo and clinical studies. This is because traditional MDT has some inherent limitations. Typically, the magnetic force is not very strong and it is also very short ranged. Since the magnetic force must overcome rather large hydrodynamic forces in the body, MDT applications have been limited to sites located close to the surface of the skin. Even in this most favorable situation, studies have shown that it is difficult to collect appreciable amounts of the MDCPs at the target site. To overcome these limitations of the traditional MDT approach, Ritter and co-workers reported the implant assisted magnetic drug targeting (IA-MDT). In IA-MDT, the magnetic implants are placed strategically at the target site to greatly and locally increase the magnetic force on MDCPs and help to attract and retain the MDCPs at the targeted region. In the present work, we develop a mathematical model to study the capturing of magnetic nanoparticles flowing in a fluid in an implant assisted cylindrical channel under the magnetic field. A coil of ferromagnetic SS 430 has been implanted inside the cylindrical channel to enhance the capturing of magnetic nanoparticles under the magnetic field. The dominant magnetic and drag forces, which significantly affect the capturing of nanoparticles, are incorporated in the model. It is observed through model results that capture efficiency increases from 23 to 51 % as we increase the magnetic field from 0.1 to 0.5 T, respectively. The increase in capture efficiency by increase in magnetic field is because as the magnetic field increases, the magnetization force, which is attractive in nature and responsible to attract or capture the magnetic particles, increases and results the capturing of large number of magnetic particles due to high strength of attractive magnetic force.

Keywords: capture efficiency, implant assisted-magnetic drug targeting (IA-MDT), magnetic nanoparticles, modelling

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Authors: N. Gharbi

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Constraint Satisfaction problems are mathematical problems that are often used to model many real-world problems for which we look if there exists a solution satisfying all its constraints. Table constraints are important for modeling parts of many problems since they list all combinations of allowed or forbidden values. However, they admit practical limitations because they are sometimes too large to be represented in a direct way. In this paper, we present a survey of the different categories of the proposed approaches to compress table constraints in order to reduce both space and time complexities.

Keywords: constraint programming, compression, data mining, table constraints

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Authors: S. Sabzchi Asl, N. Tahouni, M. H. Panjeshahi

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Benchmarking of a process with respect to energy consumption, without accomplishing a full retrofit study, can save both engineering time and money. In order to achieve this goal, the first step is to develop a conceptual-mathematical model that can easily be applied to a group of similar processes. In this research, we have aimed to identify a set of key parameters for the model which is supposed to be used for benchmarking of combined cycle power plants. For this purpose, three similar combined cycle power plants were studied. The results showed that ambient temperature, pressure and relative humidity, number of HRSG evaporator pressure levels and relative power in part load operation are the main key parameters. Also, the relationships between these parameters and produced power (by gas/ steam turbine), gas turbine and plant efficiency, temperature and mass flow rate of the stack flue gas were investigated.

Keywords: combined cycle power plant, energy benchmarking, modelling, retrofit

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Authors: Benjamin Castillo, Luis Pastenes, Fernando Cordova

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The pathogen growth in animal source foods is a common problem in the food industry, causing monetary losses due to the spoiling of products or food intoxication outbreaks in the community. In this sense, the quality of the product is reflected by the population of deteriorating agents present in it, which are mainly bacteria. The factors which are likely associated with freshness in animal source foods are temperature and processing, storage, and transport times. However, the level of deterioration of products depends, in turn, on the characteristics of the bacterial population, causing the decomposition or spoiling, such as pH level and toxins. Knowing the growth dynamics of the agents that are involved in product contamination allows the monitoring for more efficient processing. This means better quality and reasonable costs, along with a better estimation of necessary time and temperature intervals for transport and storage in order to preserve product quality. The objective of this project is to design a secondary model that allows measuring the impact on temperature bacterial growth and the competition for pH adequacy and release of bacteriocins in order to describe such phenomenon and, thus, estimate food product half-life with the least possible risk of deterioration or spoiling. In order to achieve this objective, the authors propose an analysis of a three-dimensional ordinary differential which includes; logistic bacterial growth extended by the inhibitory action of bacteriocins including the effect of the medium pH; change in the medium pH levels through an adaptation of the Luedeking-Piret kinetic model; Bacteriocin concentration modeled similarly to pH levels. These three dimensions are being influenced by the temperature at all times. Then, this differential system is expanded, taking into consideration the variable temperature and the concentration of pulsed bacteriocins, which represent characteristics inherent of the modeling, such as transport and storage, as well as the incorporation of substances that inhibit bacterial growth. The main results lead to the fact that temperature changes in an early stage of transport increased the bacterial population significantly more than if it had increased during the final stage. On the other hand, the incorporation of bacteriocins, as in other investigations, proved to be efficient in the short and medium-term since, although the population of bacteria decreased, once the bacteriocins were depleted or degraded over time, the bacteria eventually returned to their regular growth rate. The efficacy of the bacteriocins at low temperatures decreased slightly, which equates with the fact that their natural degradation rate also decreased. In summary, the implementation of the mathematical model allowed the simulation of a set of possible bacteria present in animal based products, along with their properties, in various transport and storage situations, which led us to state that for inhibiting bacterial growth, the optimum is complementary low constant temperatures and the initial use of bacteriocins.

Keywords: bacterial growth, bacteriocins, mathematical modelling, temperature

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Authors: Nisha Singh, Neeru Adlakha

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Calcium signalling is one of the most important intracellular signalling mechanisms. A lot of approaches and investigators have been made in the study of calcium signalling in various cells to understand its mechanisms over recent decades. However, most of existing investigators have mainly focussed on the study of calcium signalling in various cells without paying attention to the dependence of calcium signalling on other chemical ions like inositol-1; 4; 5 triphosphate ions, etc. Some models for the independent study of calcium signalling and inositol-1; 4; 5 triphosphate signalling in various cells are present but very little attention has been paid by the researchers to study the interdependence of these two signalling processes in a cell. In this paper, we propose a coupled mathematical model to understand the interdependence of inositol-1; 4; 5 triphosphate dynamics and calcium dynamics in a myocyte cell. Such studies will provide the deeper understanding of various factors involved in calcium signalling in myocytes, which may be of great use to biomedical scientists for various medical applications.

Keywords: calcium signalling, coupling, finite difference method, inositol 1, 4, 5-triphosphate

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Authors: Kingsley Nnaemeka Ogbu, Constantine Mbajiorgu

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Vegetation has a marked effect on runoff and has become an important component in hydrologic model. The watershed Resources Management (WRM) model, a process-based, continuous, distributed parameter simulation model developed for hydrologic and soil erosion studies at the watershed scale lack a crop growth component. As such, this model assumes a constant parameter values for vegetation and hydraulic parameters throughout the duration of hydrologic simulation. Our approach is to develop a crop growth algorithm based on the original plant growth model used in the Environmental Policy Integrated Climate Model (EPIC) model. This paper describes the development of a single crop growth model which has the capability of simulating all crops using unique parameter values for each crop. Simulated crop growth processes will reflect the vegetative seasonality of the natural watershed system. An existing model was employed for evaluating vegetative resistance by hydraulic and vegetative parameters incorporated into the WRM model. The improved WRM model will have the ability to evaluate the seasonal variation of the vegetative roughness coefficient with depth of flow and further enhance the hydrologic model’s capability for accurate hydrologic studies

Keywords: crop yield, roughness coefficient, PAR, WRM model

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Authors: Renata Masarova, Bohuslava Juhasova, Martin Juhas, Zuzana Sutova

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In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: dynamic system, transfer matrix, inverse matrix, modeling

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Authors: Marinka K. Baghdasaryan, Siranush M. Muradyan, Avgen A. Gasparyan

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Analytical expressions of the current and angular errors, as well as the frequency characteristics of an induction converter describing the relation with its structural parameters, the core and winding characteristics are obtained. Based on estimation of the dependences obtained, a mathematical problem of parametric optimization is formulated which can successfully be used for investigation and diagnosing an induction converter.

Keywords: induction converters, magnetic circuit material, current and angular errors, frequency response, mathematical formulation, structural parameters

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Authors: Bayan Bevrani, Robert L. Burdett, Prasad K. D. V. Yarlagadda

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This article focuses upon multi-modal transportation systems (MMTS) and the issues surrounding the determination of system capacity. For that purpose a multi-objective framework is advocated that integrates all the different modes and many different competing capacity objectives. This framework is analytical in nature and facilitates a variety of capacity querying and capacity expansion planning.

Keywords: analytical model, capacity analysis, capacity query, multi-modal transportation system (MMTS)

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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: Jui-Ching Chou

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Numerical simulation is a popular method used to evaluate the effects of soil liquefaction on a structure or the effectiveness of a mitigation plan. Many constitutive models (UBCSAND model, PM4 model, SANISAND model, etc.) were presented to model the liquefaction phenomenon. In general, inputs of a constitutive model need to be calibrated against the soil cyclic resistance before being applied to the numerical simulation model. Then, simulation results can be compared with results from simplified liquefaction potential assessing methods. In this article, inputs of the UBCSAND model, a simple elastic-plastic stress-strain model, are calibrated against several popular generic liquefaction triggering curves of simplified liquefaction potential assessing methods via FLAC program. Calibrated inputs can provide engineers to perform a preliminary evaluation of an existing structure or a new design project.

Keywords: calibration, liquefaction, numerical simulation, UBCSAND Model

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Authors: Sadia Arshad, Yifa Tang, Dumitru Baleanu

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A fractional order mathematical model is proposed that incorporate CD8+ cells, natural killer cells, cytokines and tumor cells. The tumor cells growth in the absence of an immune response is modeled by logistic law as it was the simplest form for which predictions also agreed with the experimental data. Natural Killer Cells are our first line of defense. NK cells directly kill tumor cells through several mechanisms, including the release of cytoplasmic granules containing perforin and granzyme, expression of tumor necrosis factor (TNF) family members. The effect of the NK cells on the tumor cell population is expressed with the product term. Rational form is used to describe interaction between CD8+ cells and tumor cells. A number of cytokines are produced by NKs, including tumor necrosis factor TNF, IFN, and interleukin (IL-10). Source term for cytokines is modeled by Michaelis-Menten form to indicate the saturated effects of the immune response. Stability of the equilibrium points is discussed for biologically significant values of bifurcation parameters. We studied the treatment of fractional order system by investigating analytical conditions of tumor eradication. Numerical simulations are presented to illustrate the analytical results.

Keywords: cancer model, fractional calculus, numerical simulations, stability analysis

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Authors: El Andari Chifaa, Bouaziz Rached

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The central focus of this paper was to check whether the Okun’s law in Tunisia is valid or not. For this purpose, we have used quarterly time series data during the period 1990Q1-2014Q1. Firstly, we applied the error correction model instead of the difference version of Okun's Law, the Engle-Granger and Johansen test are employed to find out long run association between unemployment, production, and how error correction mechanism (ECM) is used for short run dynamic. Secondly, we used the gap version of Okun’s law where the estimation is done from three band pass filters which are mathematical tools used in macro-economic and especially in business cycles theory. The finding of the study indicates that the inverse relationship between unemployment and output is verified in the short and long term, and the Okun's law holds for the Tunisian economy, but with an Okun’s coefficient lower than required. Therefore, our empirical results have important implications for structural and cyclical policymakers in Tunisia to promote economic growth in a context of lower unemployment growth.

Keywords: Okun’s law, validity, unit root, cointegration, error correction model, bandpass filters

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Authors: Andreas Stollwitzer, Lara Bettinelli, Josef Fink

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The expansion of the high-speed rail network over the past decades has resulted in new challenges for engineers, including traffic-induced resonance vibrations of railway bridges. Excessive resonance-induced speed-dependent accelerations of railway bridges during high-speed traffic can lead to negative consequences such as fatigue symptoms, distortion of the track, destabilisation of the ballast bed, and potentially even derailment. A realistic prognosis of bridge vibrations during high-speed traffic must not only rely on the right choice of an adequate calculation model for both bridge and train but first and foremost on the use of dynamic model parameters which reflect reality appropriately. However, comparisons between measured and calculated bridge vibrations are often characterised by considerable discrepancies, whereas dynamic calculations overestimate the actual responses and therefore lead to uneconomical results. This gap between measurement and calculation constitutes a complex research issue and can be traced to several causes. One major cause is found in the dynamic properties of the ballasted track, more specifically in the persisting, substantial uncertainties regarding the consideration of the ballasted track (mechanical model and input parameters) in dynamic calculations. Furthermore, the discrepancy is particularly pronounced concerning the damping values of the bridge, as conservative values have to be used in the calculations due to normative specifications and lack of knowledge. By using a large-scale test facility, the analysis of the dynamic behaviour of ballasted track has been a major research topic at the Institute of Structural Engineering/Steel Construction at TU Wien in recent years. This highly specialised test facility is designed for isolated research of the ballasted track's dynamic stiffness and damping properties – independent of the bearing structure. Several mechanical models for the ballasted track consisting of one or more continuous spring-damper elements were developed based on the knowledge gained. These mechanical models can subsequently be integrated into bridge models for dynamic calculations. Furthermore, based on measurements at the test facility, model-dependent stiffness and damping parameters were determined for these mechanical models. As a result, realistic mechanical models of the railway bridge with different levels of detail and sufficiently precise characteristic values are available for bridge engineers. Besides that, this contribution also presents another practical application of such a bridge model: Based on the bridge model, determination equations for the damping factor (as Lehr's damping factor) can be derived. This approach constitutes a first-time method that makes the damping factor of a railway bridge calculable. A comparison of this mathematical approach with measured dynamic parameters of existing railway bridges illustrates, on the one hand, the apparent deviation between normatively prescribed and in-situ measured damping factors. On the other hand, it is also shown that a new approach, which makes it possible to calculate the damping factor, provides results that are close to reality and thus raises potentials for minimising the discrepancy between measurement and calculation.

Keywords: ballasted track, bridge dynamics, damping, model design, railway bridges

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Authors: Rui Li, Min Wen, Kim Bang Salling

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For the modern railways, maintenance is critical for ensuring safety, train punctuality and overall capacity utilization. The cost of railway maintenance in Europe is high, on average between 30,000 – 100,000 Euros per kilometer per year. In order to reduce such maintenance expenditures, this paper presents a mixed 0-1 linear mathematical model designed to optimize the predictive railway tamping activities for ballast track in the planning horizon of three to four years. The objective function is to minimize the tamping machine actual costs. The approach of the research is using the simple dynamic model for modelling condition-based tamping process and the solution method for finding optimal condition-based tamping schedule. Seven technical and practical aspects are taken into account to schedule tamping: (1) track degradation of the standard deviation of the longitudinal level over time; (2) track geometrical alignment; (3) track quality thresholds based on the train speed limits; (4) the dependency of the track quality recovery on the track quality after tamping operation; (5) Tamping machine operation practices (6) tamping budgets and (7) differentiating the open track from the station sections. A Danish railway track between Odense and Fredericia with 42.6 km of length is applied for a time period of three and four years in the proposed maintenance model. The generated tamping schedule is reasonable and robust. Based on the result from the Danish railway corridor, the total costs can be reduced significantly (50%) than the previous model which is based on optimizing the number of tamping. The different maintenance strategies have been discussed in the paper. The analysis from the results obtained from the model also shows a longer period of predictive tamping planning has more optimal scheduling of maintenance actions than continuous short term preventive maintenance, namely yearly condition-based planning.

Keywords: integer programming, railway tamping, predictive maintenance model, preventive condition-based maintenance

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Authors: Dairo Jose Hernandez Paez

Abstract:

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

Procedia PDF Downloads 95

Authors: Kingsley Nnaemeka Ogbu, Constantine Mbajiorgu

Abstract:

Vegetation has a marked effect on runoff and has become an important component in hydrologic model. The watershed Resources Management (WRM) model, a process-based, continuous, distributed parameter simulation model developed for hydrologic and soil erosion studies at the watershed scale lack a crop growth component. As such, this model assumes a constant parameter values for vegetation and hydraulic parameters throughout the duration of hydrologic simulation. Our approach is to develop a crop growth algorithm based on the original plant growth model used in the Environmental Policy Integrated Climate Model (EPIC) model. This paper describes the development of a single crop growth model which has the capability of simulating all crops using unique parameter values for each crop. Simulated crop growth processes will reflect the vegetative seasonality of the natural watershed system. An existing model was employed for evaluating vegetative resistance by hydraulic and vegetative parameters incorporated into the WRM model. The improved WRM model will have the ability to evaluate the seasonal variation of the vegetative roughness coefficient with depth of flow and further enhance the hydrologic model’s capability for accurate hydrologic studies.

Keywords: runoff, roughness coefficient, PAR, WRM model

Procedia PDF Downloads 367

Authors: Merouane Salhi, Mohamed Roudane, Abdelkader Kirad

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In this work, we present a new form of characteristics method, which is a technique for solving partial differential equations. Typically, it applies to first-order equations; the aim of this method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data. This latter developed under the real gas theory, because when the thermal and the caloric imperfections of a gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with the gas parameters. The gas doesn’t stay perfect. Its state equation change and it becomes for a real gas. The presented equations of the characteristics remain valid whatever area or field of study. Here we need have inserted the developed Prandtl Meyer function in the mathematical system to find a new model when the effect of stagnation pressure is taken into account. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation, the thermodynamic parameters and the value of Prandtl Meyer function. However, with the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analyzing the supersonic flow for thermally and calorically imperfect gas. The supersonic parameters depend directly on the stagnation parameters of the combustion chamber. The resolution has been made by the finite differences method using the corrector predictor algorithm. As results, the developed mathematical model used to design 2D minimum length nozzles under effect of the stagnation parameters of fluid flow. A comparison for air with the perfect gas PG and high temperature models on the one hand and our results by the real gas theory on the other of nozzles shapes and characteristics are made.

Keywords: numerical methods, nozzles design, real gas, stagnation parameters, supersonic expansion, the characteristics method

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Authors: Hossein Bazmara, Kaamran Raahemifar, Mostafa Sefidgar, Madjid Soltani

Abstract:

Angiogenesis is formation of new blood vessels from existing vessels. Due to flow of blood in vessels, during angiogenesis, blood flow plays an important role in regulating the angiogenesis process. Multiple mathematical models of angiogenesis have been proposed to simulate the formation of the complicated network of capillaries around a tumor. In this work, a multi-scale model of angiogenesis is developed to show the effect of blood flow on capillaries and network formation. This model spans multiple temporal and spatial scales, i.e. intracellular (molecular), cellular, and extracellular (tissue) scales. In intracellular or molecular scale, the signaling cascade of endothelial cells is obtained. Two main stages in development of a vessel are considered. In the first stage, single sprouts are extended toward the tumor. In this stage, the main regulator of endothelial cells behavior is the signals from extracellular matrix. After anastomosis and formation of closed loops, blood flow starts in the capillaries. In this stage, blood flow induced signals regulate endothelial cells behaviors. In cellular scale, growth and migration of endothelial cells is modeled with a discrete lattice Monte Carlo method called cellular Pott's model (CPM). In extracellular (tissue) scale, diffusion of tumor angiogenic factors in the extracellular matrix, formation of closed loops (anastomosis), and shear stress induced by blood flow is considered. The model is able to simulate the formation of a closed loop and its extension. The results are validated against experimental data. The results show that, without blood flow, the capillaries are not able to maintain their integrity.

Keywords: angiogenesis, endothelial cells, multi-scale model, cellular Pott's model, signaling cascade

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Authors: Kayijuka Idrissa

Abstract:

This work investigates a mathematical study for traffic flow and traffic density in Kigali city roads and the data collected from the national police of Rwanda in 2012. While working on this topic, some mathematical models were used in order to analyze and compare traffic variables. This work has been carried out on Kigali roads specifically at roundabouts from Kigali Business Center (KBC) to Prince House as our study sites. In this project, we used some mathematical tools to analyze the data collected and to understand the relationship between traffic variables. We applied the Poisson distribution method to analyze and to know the number of accidents occurred in this section of the road which is from KBC to Prince House. The results show that the accidents that occurred in 2012 were at very high rates due to the fact that this section has a very narrow single lane on each side which leads to high congestion of vehicles, and consequently, accidents occur very frequently. Using the data of speeds and densities collected from this section of road, we found that the increment of the density results in a decrement of the speed of the vehicle. At the point where the density is equal to the jam density the speed becomes zero. The approach is promising in capturing sudden changes on flow patterns and is open to be utilized in a series of intelligent management strategies and especially in noncurrent congestion effect detection and control.

Keywords: statistical methods, traffic flow, Poisson distribution, car moving technics

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Authors: Raj K. Gupta, X. Gary Tan, Andrzej Przekwas

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Bomb blasts from Improvised Explosive Devices (IEDs) account for vast majority of terrorist attacks worldwide. Injuries caused by IEDs result from a combination of the primary blast wave, penetrating fragments, and human body accelerations and impacts. This paper presents a multiscale computational model of coupled blast physics, whole human body biodynamics and injury biomechanics of sensitive organs. The disparity of the involved space- and time-scales is used to conduct sequential modeling of an IED explosion event, CFD simulation of blast loads on the human body and FEM modeling of body biodynamics and injury biomechanics. The paper presents simulation results for blast-induced brain injury coupling macro-scale brain biomechanics and micro-scale response of sensitive neuro-axonal structures. Validation results on animal models and physical surrogates are discussed. Results of our model can be used to 'replicate' filed blast loadings in laboratory controlled experiments using animal models and in vitro neuro-cultures.

Keywords: blast waves, improvised explosive devices, injury biomechanics, mathematical models, traumatic brain injury

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Authors: Sharad Singh, Ajay Kumar Sinha

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Coupled dampers like viscoelastic-frictional dampers for supplemental damping are a newer technique. In this paper, innovative Visco-frictional damping models have been presented and investigated. This paper attempts to couple frictional and fluid viscous dampers into a single unit of supplemental dampers. Visco-frictional damping model is developed by series and parallel coupling of frictional and fluid viscous dampers using Maxwell and Kelvin-Voigat models. The time analysis has been performed using numerical simulation on an SDOF system with varying fundamental periods, subject to a set of 12 ground motions. The simulation was performed using the direct time integration method. MATLAB programming tool was used to carry out the numerical simulation. The response behavior has been analyzed for the varying time period and added damping. This paper compares the response reduction behavior of the two modes of coupling. This paper highlights the performance efficiency of the suggested damping models. It also presents a mathematical modeling approach to visco-frictional dampers and simultaneously suggests the suitable mode of coupling between the two sub-units.

Keywords: hysteretic damping, Kelvin model, Maxwell model, parallel coupling, series coupling, viscous damping

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Authors: Masahiro Ohmura, Koh Kakusho, Takeshi Okadome

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This paper presents a regression model with autocorrelated errors in which the inputs are social moods obtained by analyzing the adjectives in Twitter posts using a document topic model. The regression model predicts Dow Jones Industrial Average (DJIA) more precisely than autoregressive moving-average models.

Keywords: stock market prediction, social moods, regression model, DJIA

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Authors: Adji Achmad Rinaldo Fernandes

Abstract:

SEM analysis is a complex multivariate analysis because it involves a number of exogenous and endogenous variables that are interconnected to form a model. The measurement model is divided into two, namely, the reflective model (reflecting) and the formative model (forming). Before carrying out further tests on SEM, there are assumptions that must be met, namely the linearity assumption, to determine the form of the relationship. There are three modeling approaches to path analysis, including parametric, nonparametric and semiparametric approaches. The aim of this research is to develop semiparametric SEM and obtain the best model. The data used in the research is secondary data as the basis for the process of obtaining simulation data. Simulation data was generated with various sample sizes of 100, 300, and 500. In the semiparametric SEM analysis, the form of the relationship studied was determined, namely linear and quadratic and determined one and two knot points with various levels of error variance (EV=0.5; 1; 5). There are three levels of closeness of relationship for the analysis process in the measurement model consisting of low (0.1-0.3), medium (0.4-0.6) and high (0.7-0.9) levels of closeness. The best model lies in the form of the relationship X1Y1 linear, and. In the measurement model, a characteristic of the reflective model is obtained, namely that the higher the closeness of the relationship, the better the model obtained. The originality of this research is the development of semiparametric SEM, which has not been widely studied by researchers.

Keywords: semiparametric SEM, measurement model, structural model, reflective model, formative model

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Authors: Martins Onyekwelu Onuorah, Jnr Dahiru Usman

Abstract:

Introduction: In the realm of public health, the threat posed by Monkeypox continues to elicit concern, prompting rigorous studies to understand its dynamics and devise effective containment strategies. Particularly significant is its recurrence in variable populations, such as the observed outbreak in Nigeria in 2022. In light of this, our study undertakes a meticulous analysis, employing a data-driven approach to explore, validate, and propose optimized intervention strategies tailored to the distinct dynamics of Monkeypox within varying demographic structures. Utilizing a deterministic mathematical model, we delved into the intricate dynamics of Monkeypox, with a particular focus on a variable population context. Our qualitative analysis provided insights into the disease-free equilibrium, revealing its stability when R0 is less than one and discounting the possibility of backward bifurcation, as substantiated by the presence of a single stable endemic equilibrium. The model was rigorously validated using real-time data from the Nigerian 2022 recorded cases for Epi weeks 1 – 52. Transitioning from qualitative to quantitative, we augmented our deterministic model with optimal control, introducing three time-dependent interventions to scrutinize their efficacy and influence on the epidemic's trajectory. Numerical simulations unveiled a pronounced impact of the interventions, offering a data-supported blueprint for informed decision-making in containing the disease. A comprehensive cost-effectiveness analysis employing the Infection Averted Ratio (IAR), Average Cost-Effectiveness Ratio (ACER), and Incremental Cost-Effectiveness Ratio (ICER) facilitated a balanced evaluation of the interventions’ economic and health impacts. In essence, our study epitomizes a holistic approach to understanding and mitigating Monkeypox, intertwining rigorous mathematical modeling, empirical validation, and economic evaluation. The insights derived not only bolster our comprehension of Monkeypox's intricate dynamics but also unveil optimized, cost-effective interventions. This integration of methodologies and findings underscores a pivotal stride towards aligning public health imperatives with economic sustainability, marking a significant contribution to global efforts in combating infectious diseases.

Keywords: monkeypox, equilibrium states, stability, bifurcation, optimal control, cost-effectiveness

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Authors: M. Duk, L. Grabowski, P. Magryta

Abstract:

Today's very important element relating to air transport is the environment impact issues. Nowadays there are no emissions standards for turbine and piston engines used in air transport. However, it should be noticed that the environmental effect in the form of exhaust gases from aircraft engines should be as small as possible. For this purpose, R&D centers often use special software to simulate and to estimate the negative effect of engine working process. For cooperation between the Lublin University of Technology and the Polish aviation company WSK "PZL-KALISZ" S.A., to achieve more effective operation of the ASz62IR engine, one of such tools have been used. The AVL Boost software allows to perform 1D simulations of combustion process of piston engines. ASz62IR is a nine-cylinder aircraft engine in a radial configuration. In order to analyze the impact of its working process on the environment, the mathematical model in the AVL Boost software have been made. This model contains, among others, model of the operation cycle of the cylinders. This model was based on a volume change in combustion chamber according to the reciprocating movement of a piston. The simplifications that all of the pistons move identically was assumed. The changes in cylinder volume during an operating cycle were specified. Those changes were important to determine the energy balance of a cylinder in an internal combustion engine which is fundamental for a model of the operating cycle. The calculations for cylinder thermodynamic state were based on the first law of thermodynamics. The change in the mass in the cylinder was calculated from the sum of inflowing and outflowing masses including: cylinder internal energy, heat from the fuel, heat losses, mass in cylinder, cylinder pressure and volume, blowdown enthalpy, evaporation heat etc. The model assumed that the amount of heat released in combustion process was calculated from the pace of combustion, using Vibe model. For gas exchange, it was also important to consider heat transfer in inlet and outlet channels because of much higher values there than for flow in a straight pipe. This results from high values of heat exchange coefficients and temperature coefficients near valves and valve seats. A Zapf modified model of heat exchange was used. To use the model with the flight scenarios, the impact of flight altitude on engine performance has been analyze. It was assumed that the pressure and temperature at the inlet and outlet correspond to the values resulting from the model for International Standard Atmosphere (ISA). Comparing this model of operation cycle with the others submodels of the ASz62IR engine, it could be noticed, that a full analysis of the performance of the engine, according to the ISA conditions, can be made. This work has been financed by the Polish National Centre for Research and Development, INNOLOT, under

Keywords: aviation propulsion, AVL Boost, engine model, operation cycle, aircraft engine

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