Search results for: mathematical oil model development dynamics

Authors: Sabyasachi Mukhopadhyay, Joseph Ogutu, Hans-Peter Piepho

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We aim to model dynamics of wildlife or pastoral livestock population for understanding of their population change and hence for wildlife conservation and promoting human welfare. The study is motivated by an age-sex structured population counts in different regions of Serengeti-Mara during the period 1989-2003. Developing reliable and realistic models for population dynamics of large herbivore population can be a very complex and challenging exercise. However, the Bayesian statistical domain offers some flexible computational methods that enable the development and efficient implementation of complex population dynamics models. In this work, we have used a novel Bayesian state-space model to analyse the dynamics of topi and hartebeest populations in the Serengeti-Mara Ecosystem of East Africa. The state-space model involves survival probabilities of the animals which further depend on various factors like monthly rainfall, size of habitat, etc. that cause recent declines in numbers of the herbivore populations and potentially threaten their future population viability in the ecosystem. Our study shows that seasonal rainfall is the most important factors shaping the population size of animals and indicates the age-class which most severely affected by any change in weather conditions.

Keywords: bayesian state-space model, Markov Chain Monte Carlo, population dynamics, conservation

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Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

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A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic

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Authors: Imran Hashmi, Sipkaduwa Arachchige Sashika Sureni Wickramasooriya

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Gene-drive technology has emerged as a promising tool for disease control by influencing the population dynamics of disease-carrying organisms. Various gene drive mechanisms, derived from global laboratory experiments, aim to strategically manage and prevent the spread of targeted diseases. One prominent strategy involves population replacement, wherein genetically modified mosquitoes are introduced to replace the existing local wild population. To enhance our understanding and aid in the design of effective release strategies, we employ a comprehensive mathematical model. The utilized approach employs agent-based modeling, enabling the consideration of individual mosquito attributes and flexibility in parameter manipulation. Through the integration of an agent-based model and a meta-population spatial approach, the dynamics of gene drive mosquito spreading in a released site are simulated. The model's outcomes offer valuable insights into future population dynamics, providing guidance for the development of informed release strategies. This research significantly contributes to the ongoing discourse on the responsible and effective implementation of gene drive technology for disease vector control.

Keywords: gene drive, agent-based modeling, disease-carrying organisms, malaria

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Authors: Dino Carpentras, Alejandro Dinkelberg, Michael Quayle

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Opinion dynamics models use an agent-based modeling approach to model people’s opinions. Model's properties are usually explored by testing the two 'degrees of freedom': the interaction rule and the network topology. The latter defines the connection, and thus the possible interaction, among agents. The interaction rule, instead, determines how agents select each other and update their own opinion. Here we show the existence of the third degree of freedom. This can be used for turning one model into each other or to change the model’s output up to 100% of its initial value. Opinion dynamics models represent the evolution of real-world opinions parsimoniously. Thus, it is fundamental to know how real-world opinion (e.g., supporting a candidate) could be turned into a number. Specifically, we want to know if, by choosing a different opinion-to-number transformation, the model’s dynamics would be preserved. This transformation is typically not addressed in opinion dynamics literature. However, it has already been studied in psychometrics, a branch of psychology. In this field, real-world opinions are converted into numbers using abstract objects called 'scales.' These scales can be converted one into the other, in the same way as we convert meters to feet. Thus, in our work, we analyze how this scale transformation may affect opinion dynamics models. We perform our analysis both using mathematical modeling and validating it via agent-based simulations. To distinguish between scale transformation and measurement error, we first analyze the case of perfect scales (i.e., no error or noise). Here we show that a scale transformation may change the model’s dynamics up to a qualitative level. Meaning that a researcher may reach a totally different conclusion, even using the same dataset just by slightly changing the way data are pre-processed. Indeed, we quantify that this effect may alter the model’s output by 100%. By using two models from the standard literature, we show that a scale transformation can transform one model into the other. This transformation is exact, and it holds for every result. Lastly, we also test the case of using real-world data (i.e., finite precision). We perform this test using a 7-points Likert scale, showing how even a small scale change may result in different predictions or a number of opinion clusters. Because of this, we think that scale transformation should be considered as a third-degree of freedom for opinion dynamics. Indeed, its properties have a strong impact both on theoretical models and for their application to real-world data.

Keywords: degrees of freedom, empirical validation, opinion scale, opinion dynamics

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Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

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Authors: Rui Mao, Heming Ji, Xiaoyu Wang

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Keystroke dynamics are widely used in identity recognition. It has the advantage that the individual typing rhythm is difficult to imitate. It also supports continuous authentication through the keyboard without extra devices. The existing keystroke dynamics authentication methods based on machine learning have a drawback in supporting relatively complex scenarios with massive data. There are drawbacks to both feature extraction and model optimization in these methods. To overcome the above weakness, an authentication model of keystroke dynamics based on deep learning is proposed. The model uses feature vectors formed by keystroke content and keystroke time. It ensures efficient continuous authentication by cooperating attention mechanisms with the combination of CNN and Bi-LSTM. The model has been tested with Open Data Buffalo dataset, and the result shows that the FRR is 3.09%, FAR is 3.03%, and EER is 4.23%. This proves that the model is efficient and accurate on continuous authentication.

Keywords: keystroke dynamics, identity authentication, deep learning, CNN, LSTM

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Recently, crystal growth technologies have made progress by the requirement for the high quality of crystal materials. To control the crystal growth dynamics actively by external forces is useuful for reducing composition non-uniformity. In this study, a control method based on model predictive control using thermal inputs is proposed for crystal growth dynamics of semiconductor materials. The control system of crystal growth dynamics considered here is governed by the continuity, momentum, energy, and mass transport equations. To establish the control method for such thermal fluid systems, we adopt model predictive control known as a kind of optimal feedback control in which the control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. The objective of this study is to establish a model predictive control method for crystal growth dynamics of semiconductor materials.

Keywords: model predictive control, optimal control, process control, crystal growth

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Authors: Mechlouch Ridha Fethi

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This paper presents a recent mathematical model in political sciences concerning democracy. The model is represented by a logarithmic equation linking the Relative Index of Democracy (RID) to Participation Ratio (PR). Firstly the meanings of the different parameters of the model were presented; and the variation curve of the RID according to PR with different critical areas was discussed. Secondly, the model was applied to a virtual group where we show that the model can be applied depending on the gender. Thirdly, it was observed that the model can be extended to different language models of democracy and that little use to assess the state of democracy for some International organizations like UNO.

Keywords: democracy, mathematic, modelization, quantification

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Authors: Muhammmad Riandhy Anindika Yudhy, Harry Patria, Ramadhani Santoso

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Loss of containment is the primary hazard that process safety management is concerned within the oil and gas industry. Escalation to more serious consequences all begins with the loss of containment, starting with oil and gas release from leakage or spillage from primary containment resulting in pool fire, jet fire and even explosion when reacted with various ignition sources in the operations. Therefore, the heart of process safety management is avoiding loss of containment and mitigating its impact through the implementation of safeguards. The most effective safeguard for the case is an early detection system to alert Operations to take action prior to a potential case of loss of containment. The detection system value increases when applied to a long surface pipeline that is naturally difficult to monitor at all times and is exposed to multiple causes of loss of containment, from natural corrosion to illegal tapping. Based on prior researches and studies, detecting loss of containment accurately in the surface pipeline is difficult. The trade-off between cost-effectiveness and high accuracy has been the main issue when selecting the traditional detection method. The current best-performing method, Real-Time Transient Model (RTTM), requires analysis of closely positioned pressure, flow and temperature (PVT) points in the pipeline to be accurate. Having multiple adjacent PVT sensors along the pipeline is expensive, hence generally not a viable alternative from an economic standpoint.A conceptual approach to combine mathematical modeling using computational fluid dynamics and a supervised machine learning model has shown promising results to predict leakage in the pipeline. Mathematical modeling is used to generate simulation data where this data is used to train the leak detection and localization models. Mathematical models and simulation software have also been shown to provide comparable results with experimental data with very high levels of accuracy. While the supervised machine learning model requires a large training dataset for the development of accurate models, mathematical modeling has been shown to be able to generate the required datasets to justify the application of data analytics for the development of model-based leak detection systems for petroleum pipelines. This paper presents a review of key leak detection strategies for oil and gas pipelines, with a specific focus on crude oil applications, and presents the opportunities for the use of data analytics tools and mathematical modeling for the development of robust real-time leak detection and localization system for surface pipelines. A case study is also presented.

Keywords: pipeline, leakage, detection, AI

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Authors: Sadia Arshad, Ayesha Sohail, Sana Javed, Khadija Maqbool, Salma Kanwal

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The dynamical study of the carriers play an essential role in the evolution and global transmission of infectious diseases and will be discussed in this study. To make this approach novel, we will consider the fractional order model which is generalization of integer order derivative to an arbitrary number. Since the integration involved is non local therefore this property of fractional operator is very useful to study epidemic model for infectious diseases. An extended numerical method (ODE solver) is implemented on the model equations and we will present the simulations of the model for different values of fractional order to study the effect of carriers on transmission dynamics. Global dynamics of fractional model are established by using the reproduction number.

Keywords: Fractional differential equation, Numerical simulations, epidemic model, transmission dynamics

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Authors: Adekunle Taiwo Adenike, I. K. Ogundoyin

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Lassa fever is a neglected tropical virus that has become a significant public health issue in Nigeria, with the country having the greatest burden in Africa. This paper presents a Geo-Computational Model for Analysis and Prediction of Lassa Fever Dynamics and Outbreaks in Nigeria. The model investigates the dynamics of the virus with respect to environmental factors and human populations. It confirms the role of the rodent host in virus transmission and identifies how climate and human population are affected. The proposed methodology is carried out on a Linux operating system using the OSGeoLive virtual machine for geographical computing, which serves as a base for spatial ecology computing. The model design uses Unified Modeling Language (UML), and the performance evaluation uses machine learning algorithms such as random forest, fuzzy logic, and neural networks. The study aims to contribute to the control of Lassa fever, which is achievable through the combined efforts of public health professionals and geocomputational and machine learning tools. The research findings will potentially be more readily accepted and utilized by decision-makers for the attainment of Lassa fever elimination.

Keywords: geo-computational model, lassa fever dynamics, lassa fever, outbreak prediction, nigeria

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Authors: Endrik Mifta Shaiful, Firman Riyudha

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Acquired Immunodeficiency Syndrome (AIDS) is one of the world's deadliest diseases caused by the Human Immunodeficiency Virus (HIV) that infects white blood cells and cause a decline in the immune system. AIDS quickly became a world epidemic disease that affects almost all countries. Therefore, mathematical modeling approach to the spread of HIV and AIDS is needed to anticipate the spread of HIV and AIDS which are widespread. The purpose of this study is to determine the parameter estimation on mathematical models of HIV transmission and AIDS using cumulative data of people with HIV and AIDS each year in Indonesia. In this model, there are parameters of r ∈ [0,1) which is the effectiveness of the treatment in patients with HIV. If the value of r is close to 1, the number of people with HIV and AIDS will decline toward zero. The estimation results indicate when the value of r is close to unity, there will be a significant decline in HIV patients, whereas in AIDS patients constantly decreases towards zero.

Keywords: HIV, AIDS, parameter estimation, mathematical models

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Authors: Sadia Arshad

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The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks.

Keywords: fractional calculus, modeling, stability, numerical solution

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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: Javier Navarro Garcia, Narciso Vazquez Carretero

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

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

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Authors: Tareq Oshan

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Facility location and size decisions are important to any company because they affect profitability and success. However, warehouses are exposed to various risks of failure that affect their activity. This paper presents a mixed-integer non-linear mathematical model that can be used to determine optimal warehouse locations and sizes, which warehouses to fortify, and which branches should be assigned to specific warehouses when there is a risk of warehouse failure. Every branch is assigned to a fortified primary warehouse or a nonfortified primary warehouse and a fortified backup warehouse. The standard method and an introduced method, based on the average probabilities, for linearizing this mathematical model were used. A Canadian case study was used to demonstrate the developed mathematical model, followed by some sensitivity analysis.

Keywords: supply chain network design, fortified warehouse, mixed-integer mathematical model, warehouse failure risk

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Authors: Fahad Alsharari, Mohd Salmi Md. Noorani

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A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron-Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift AZ, x is in M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, we find a new method of calculating the topological entropy of the Motzkin shift M(M,N) without any measure theoretical discussion.

Keywords: entropy, Motzkin shift, mathematical model, theory

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Authors: Jožef Ritonja

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The biochemical industry is one of the most important modern industries. Biochemical reactors are crucial devices of the biochemical industry. The essential bioprocess carried out in bioreactors is the fermentation process. A thorough insight into the fermentation process and the knowledge how to control it are essential for effective use of bioreactors to produce high quality and quantitatively enough products. The development of the control system starts with the determination of a mathematical model that describes the steady state and dynamic properties of the controlled plant satisfactorily, and is suitable for the development of the control system. The paper analyses the fermentation process in bioreactors thoroughly, using existing mathematical models. Most existing mathematical models do not allow the design of a control system for controlling the fermentation process in batch bioreactors. Due to this, a mathematical model was developed and presented that allows the development of a control system for batch bioreactors. Based on the developed mathematical model, a control system was designed to ensure optimal response of the biochemical quantities in the fermentation process. Due to the time-varying and non-linear nature of the controlled plant, the conventional control system with a proportional-integral-differential controller with constant parameters does not provide the desired transient response. The improved adaptive control system was proposed to improve the dynamics of the fermentation. The use of the adaptive control is suggested because the parameters’ variations of the fermentation process are very slow. The developed control system was tested to produce dairy products in the laboratory bioreactor. A carbon dioxide concentration was chosen as the controlled variable. The carbon dioxide concentration correlates well with the other, for the quality of the fermentation process in significant quantities. The level of the carbon dioxide concentration gives important information about the fermentation process. The obtained results showed that the designed control system provides minimum error between reference and actual values of carbon dioxide concentration during a transient response and in a steady state. The recommended control system makes reference signal tracking much more efficient than the currently used conventional control systems which are based on linear control theory. The proposed control system represents a very effective solution for the improvement of the milk fermentation process.

Keywords: biochemical reactor, fermentation process, modelling, adaptive control

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Authors: S. Shamohammadi, L. Razavi

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This paper based on the principle concepts of SCS-CN model, a new mathematical model for computation of retention potential (S) presented. In the mathematical model, not only precipitation-runoff concepts in SCS-CN model are precisely represented in a mathematical form, but also new concepts, called “maximum retention” and “total retention” is introduced, and concepts of potential retention capacity, maximum retention, and total retention have been separated from each other. In the proposed model, actual retention (F), maximum actual retention (Fmax), total retention (S), maximum retention (Smax), and potential retention (Sp), for the first time clearly defined, so that Sp is not variable, but a function of morphological characteristics of the watershed. Indeed, based on the mathematical relation of the conceptual curve of SCS-CN model, the proposed model provides a new method for the computation of actual retention in watershed and it simply determined runoff based on. In the corresponding relations, in addition to Precipitation (P), Initial retention (Ia), cumulative values of actual retention capacity (F), total retention (S), runoff (Q), antecedent moisture (M), potential retention (Sp), total retention (S), we introduced Fmax and Fmin referring to maximum and minimum actual retention, respectively. As well as, ksh is a coefficient which depends on morphological characteristics of the watershed. Advantages of the modified version versus the original model include a better precision, higher performance, easier calibration and speed computing.

Keywords: model, mathematical, retention, watershed, SCS

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Authors: Oleg Oborin

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This paper is dedicated to the development of the model, which can be used to evaluate the effectiveness of long-term corporate strategies and identify the best strategies. The theoretical model of the relatively homogenous product market (such as iron and steel industry, mobile services or road transport) has been developed. In the model, the market consists of a large number of companies with different internal characteristics and objectives. The companies can perform mergers and acquisitions in order to increase their market share. The model allows the simulation of long-time dynamics of the market (for a period longer than 20 years). Therefore, a large number of simulations on random input data was conducted in the framework of the model. After that, the results of the model were compared with the dynamics of real markets, such as the US steel industry from the beginning of the XX century to the present day, and the market of mobile services in Germany for the period between 1990 and 2015.

Keywords: Economic Modelling, Long-Time Strategy, Mergers and Acquisitions, Simulation

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Authors: Jia-Shiun Chen, Quoc-Viet Huynh

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This work develops a flexible-body dynamic model of an all-terrain vehicle (ATV), capable of recovering dynamic stresses while the ATV travels on random bumpy roads. The fatigue life of components is forecasted as well. While considering the interaction between dynamic forces and structure deformation, the proposed model achieves a highly accurate structure stress prediction and fatigue life prediction. During the simulation, stress time history of the ATV structure is retrieved for life prediction. Finally, the hot sports of the ATV frame are located, and the frame life for combined road conditions is forecasted, i.e. 25833.6 hr. If the usage of vehicle is eight hours daily, the total vehicle frame life is 8.847 years. Moreover, the reaction force and deformation due to the dynamic motion can be described more accurately by using flexible body dynamics than by using rigid-body dynamics. Based on recommendations made in the product design stage before mass production, the proposed model can significantly lower development and testing costs.

Keywords: flexible-body dynamics, veicle, dynamics, fatigue, durability

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Authors: Giulio Mangano, Alberto De Marco, Giovanni Zenezini

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The concept of City Logistics (CL) has emerged to improve the impacts of last mile freight distribution in urban areas. In this paper, a System Dynamics (SD) model exploring the dynamics of the diffusion of a ICT platform for CL management across different populations is proposed. For the development of the model two sources have been used. On the one hand, the major diffusion variables and feedback loops are derived from a literature review of existing diffusion models. On the other hand, the parameters are represented by the value propositions delivered by the platform as a response to some of the users’ needs. To extract the most important value propositions the Business Model Canvas approach has been used. Such approach in fact focuses on understanding how a company can create value for her target customers. These variables and parameters are thus translated into a SD diffusion model with three different populations namely municipalities, logistics service providers, and own account carriers. Results show that, the three populations under analysis fully adopt the platform within the simulation time frame, highlighting a strong demand by different stakeholders for CL projects aiming at carrying out more efficient urban logistics operations.

Keywords: city logistics, simulation, system dynamics, business model

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Authors: C. E. Madubueze, S. C. Madubueze, S. Ajama

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Cholera is a disease that is predominately common in developing countries due to poor sanitation and overcrowding population. In this paper, a deterministic model for the dynamics of cholera is developed and control measures such as health educational message, therapeutic treatment, and vaccination are incorporated in the model. The effective reproduction number is computed in terms of the model parameters. The existence and stability of the equilibrium states, disease free and endemic equilibrium states are established and showed to be locally and globally asymptotically stable when R0 < 1 and R0 > 1 respectively. The existence of backward bifurcation of the model is investigated. Furthermore, numerical simulation of the model developed is carried out to show the impact of the control measures and the result indicates that combined control measures will help to reduce the spread of cholera in the population

Keywords: backward bifurcation, cholera, equilibrium, dynamics, stability

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Authors: Andra Blumberga, Armands Gravelsins, Haralds Vigants, Dagnija Blumberga

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The paper discovers biotechonomy development analysis by use of system dynamics modelling. The research is connected with investigations of biomass application for production of bioproducts with higher added value. The most popular bioresource is wood, and therefore, the main question today is about future development and eco-design of products. The paper emphasizes and evaluates energy sector which is open for use of wood logs, wood chips, wood pellets and so on. The main aim for this research study was to build a framework to analyse development perspectives for wood pellet production. To reach the goal, a system dynamics model of energy wood supplies, processing, and consumption is built. Production capacity, energy consumption, changes in energy and technology efficiency, required labour source, prices of wood, energy and labour are taken into account. Validation and verification tests with available data and information have been carried out and indicate that the model constitutes the dynamic hypothesis. It is found that the more is invested into pellets production, the higher the specific profit per production unit compared to wood logs and wood chips. As a result, wood chips production is decreasing dramatically and is replaced by wood pellets. The limiting factor for pellet industry growth is availability of wood sources. This is governed by felling limit set by the government based on sustainable forestry principles.

Keywords: bioenergy, biotechonomy, system dynamics modelling, wood pellets

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Authors: Michel Wakim, Rodrigo Rivera Tinoco

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Supersonic ejector is an economical device that use high pressure vapor to compress a low pressure vapor without any rotating parts or external power sources. Entrainment ratio is a major characteristic of the ejector performance, so the ejector performance is highly dependent on its geometry. The aim of this paper is to design ejector geometry, based on pre-specified operating conditions, and to study the flow behavior inside the ejector by using computational fluid dynamics ‘CFD’ by using ‘ANSYS FLUENT 15.0’ software. In the first section; 1-D mathematical model is carried out to predict the ejector geometry. The second part describes the flow behavior inside the designed model. CFD is the most reliable tool to reveal the mixing process at different parts of the supersonic turbulent flow and to study the effect of the geometry on the effective ejector area. Finally, the results show the effect of the geometry on the entrainment ratio.

Keywords: computational fluids dynamics, ejector, entrainment ratio, geometry optimization, performance

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Authors: Ujwal Kishor Zore, Shankar Balajirao Kausley, Aniruddha Bhalchandra Pandit

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There are some important design parameters of activated sludge process (ASP) for wastewater treatment and they must be optimally defined to have the optimized plant working. To know them, developing a mathematical model is a way out as it is nearly commensurate the real world works. In this study, a mathematical model was developed for ASP, solved under activated sludge model no 1 (ASM 1) conditions and MATLAB tool was used to solve the mathematical equations. For its real-life validation, the developed model was tested for the inputs from the municipal wastewater treatment plant and the results were quite promising. Additionally, the most cardinal assumptions required to design the treatment plant are discussed in this paper. With the need for computerization and digitalization surging in every aspect of engineering, this mathematical model developed might prove to be a boon to many biological wastewater treatment plants as now they can in no time know the design parameters which are required for a particular type of wastewater treatment.

Keywords: waste water treatment, activated sludge process, mathematical modeling, optimization

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Authors: Jian Yang, Atsushi Yagi

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Tree-grass coexistence system is of great importance for forest ecology. Mathematical models are being proposed to study the dynamics of tree-grass coexistence and the stability of the systems. However, few of the models concentrates on spatial dynamics of the tree-grass coexistence. In this study, we modified an age-structured continuous-space population model for forests, obtaining an age-structured continuous-space population model for the tree-grass competition model. In the model, for thermal competitions, adult trees can out-compete grass, and grass can out-compete seedlings. We mathematically studied the model to make sure tree-grass coexistence solutions exist. Numerical experiments demonstrated that a fraction of area that trees or grass occupies can affect whether the coexistence is stable or not. We also tried regulating the mortality of adult trees with other parameters and the fraction of area trees and grass occupies were fixed; results show that the mortality of adult trees is also a factor affecting the stability of the tree-grass coexistence in this model.

Keywords: population-structured models, stabilities of ecosystems, thermal competitions, tree-grass coexistence systems

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Authors: Gilbert Makanda

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The problem of the teaching of mathematics is studied using differential equations. A mathematical model for knowledge acquisition in mathematics is developed. In this study we adopt the mathematical model that is normally used for disease modelling in the teaching of mathematics. It is assumed that teaching is 'infecting' students with knowledge thereby spreading this knowledge to the students. It is also assumed that students who gain this knowledge spread it to other students making disease model appropriate to adopt for this problem. The results of this study show that increasing recruitment rates, learning contact with teachers and learning materials improves the number of knowledgeable students. High dropout rates and forgetting taught concepts also negatively affect the number of knowledgeable students. The developed model is then solved using Matlab ODE45 and \verb"lsqnonlin" to estimate parameters for the actual data.

Keywords: differential equations, knowledge acquisition, least squares, dynamical systems

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Authors: M. C. A. Leite, B. Chen-Charpentier, F. Agusto

Abstract:

A long-term goal of sustainable forest management is a relatively stable source of wood and a stable forest age-class structure has become the goal of many forest management practices. In the absence of disturbances, this forest management goal could easily be achieved. However, in the face of recurring insect outbreaks and other disruptive processes forest planning becomes more difficult, requiring knowledge of the effects on the forest of a wide variety of environmental factors (e.g., habitat heterogeneity, fire size and frequency, harvesting, insect outbreaks, and age distributions). The association between distinct forest disturbances and the potential effect on forest dynamics is a complex matter, particularly when evaluated over time and at large scale, and is not well understood. However, gaining knowledge in this area is crucial for a sustainable forest management. Mathematical modeling is a tool that can be used to broader the understanding in this area. In this talk we will introduce mathematical models formulation incorporating the effect of insect outbreaks either as a single disturbance in the forest population dynamics or coupled with other disturbances: either wildfire or harvesting. The results and ecological insights will be discussed.

Keywords: age-structured forest population, disturbances interaction, harvesting insects outbreak dynamics, mathematical modeling

Procedia PDF Downloads 494

Authors: N. V. Kuznetsov, O. A. Kuznetsova, G. A. Leonov, M. V. Yuldashev, R. V. Yuldashev

Abstract:

Nonlinear analysis of the phase locked loop (PLL)-based circuits is a challenging task. Thus, the simulation is widely used for their study. In this work, we consider a mathematical model of the optical Costas loop and demonstrate the limitations of simulation approach related to the existence of so-called hidden oscillations in the phase space of the model.

Keywords: optical Costas loop, mathematical model, simulation, hidden oscillation

Procedia PDF Downloads 400