Cross Learning The Art Of ?mathematical? Modelling
The mental power one gets from learning mathematics is the acquisition of the art of proper thinking and effective reasoning. An epidemic model was formulated include a memory term which gives information on the past history of the disease that helped improved our medical understanding of infectious diseases.
Have you ever asked yourself; what are the secrets of modelling wastewater treatment plants WWTPs? How to model WWTP? What is the meaning of modelling and simulation? Is it easy? How to start? What are the tools to be used? What is the information you need? What is the software applicable? What are the limitations! Here’s the solution. This thesis provides quick and advanced methods to help you model WWTPs. Try and don’t hesitate. After while, you can model any WWTP easily! You will be a unique pioneer in this field.
The contents and description in this book include the use and application of Mathematical and Statistical Modeling. The basic principles of flow (Darcy's Law and Mass Balance Equation) are used in describing basic flow of groundwater. It has been also shown that, how mathematical methods (FEM) integrated with newly advanced computer software tools (GMSH and FEniCS) are used for simulation of groundwater flow study. The mathematical methods (FEM) are used in analyzing real problems (Characteristics’ of hydraulic head in groundwater flow) with the help of computer aided programs. Simulation tool is finally developed and tested in different conditions for a specific water site system.
There are several methods to model and predict the blast overpressure of a vapour cloud explosion. Some of it has been developed and researched to its maturity to give a validated result against real incident data. However, the calculation of vapour cloud explosion overpressure using turbulence flame speed method is still in its infancy. The equations and variables have not been perfected to accommodate every possible scenario. In this exercise, the explosion of unleaded petrol vapour at the Buncefield Oil Storage Depot, Hertfordshire is modelled using the turbulence flame speed method. Some assumptions regarding the obstacles, the pitch between the obstacles, the behaviour of the flow and the geometries has been made to accommodate the model. The result varies, with most of the explosion overpressure being over predict, especially if the flame has gone through more than two obstacles with blockage ratio (BR) higher than 90%.
Berry Teaching & Applying ?mathematical? Modelling (int Conf On The Teach Of Math Model)
User modelling in Exploratory Learning Environments (ELEs) is an emerging field with several challenges to be addressed. Due to the freedom given to learners, the amount of information generated is very large, making the modelling process very challenging. Consequently, only relevant information should be used in the user modelling process. This, however, leads to other challenges such as identification of relevant information, finding an optimal knowledge representation and defining an inference mechanism by which this knowledge is used in diagnosing the learner. This research addresses the challenges of user modelling in ELEs by monitoring learners' behaviour and taking into account only relevant actions in the context of an ELE for the domain of mathematical generalisation. An iterative approach was used, in line with the iterative design of the ELE. The modelling mechanism employed a modified version of Case-based Reasoning and was evaluated using pedagogical scenarios and data from simulated and real students. This approach has the advantage of storing only relevant information and allows learner diagnosis during as well as at the end of a task.
The book offers a modern description of the mathematical methods required for solving a wide class of problems in the theory of elasticity, heat conductivity, thermo- and electroelasticity for composites of regular structure. It will be of use for professionals working in the fields of mechanics of continuous media, composites, as well as for postgraduates and students specializing in the field of materials science.
The book "Mathematical Modelling of Subsurface Seepage Flow over Sloping Beds" focuses on development of analytic techniques for estimation of surface-groundwater interactions in sloping aquifers under seepage and recharge conditions. Each chapter of the book deals with real world surface-groundwater interaction problems whose solutions are important for hydrologists, water resources managers and environmental engineers. With simple mathematical approach, the author demonstrates formulation of several archetypal stream-aquifer problems with stationary or moving boundary conditions, and illustrates the results with numerical examples. Mathematical models and analytic solutions developed in this book provide a holistic view of flow dynamics in stream-aquifer system. Closed form expressions derived in the book can serve as test cases for numerical models and guidelines for experimental studies.
The main purpose of this study was to develop the general mass and stiffness matrices for standard beam equation and eventually obtain the finite element equations for mbira reed. So far few studies have been done on mathematical modelling of a beam using finite elements, with applications to an mbira reed. However none of these studies had considered the aspect of a tapering mbira reed. Thus, the study also intends to examine the relationships that exist between the natural frequencies and the varying dimensions and properties of the mbira reed. The finite element method was used as a numerical method to solve the mathematical model of the mbira reed. A MATLAB code was prepared for the same. The usefulness of this study is that -mbira manufacturers may use the results to select the type and dimensions of metal suitable for mbira reeds. -the outcomes add more knowledge to the existing literature on mbira. -modellers may develop interest to conduct more studies on mbira. - it is useful to engineers who mostly use finite element method in designing and development of different products.
This work is considered a successful attempt to solve the problem of solar drying of mango and the related quality attributes resulted from the drying process and storage conditions.Three experiments were conducted through the cooperation among the Department of Agricultural Engineering, Faculty of Agriculture, University of Khartoum, Sudan and the Food Research Centre, Ministry of Science and Technology, Sudan and the Institute of Agricultural Engineering, University of Goettingen, Germany to study thin layer solar drying of mango and the related quality attributes resulted from the drying process and sorption isotherms of solar dried mango slices. The first experiment was conducted at the Food Research Centre under controlled conditions using an air oven. Only the influence of drying temperatures at 50°C, 60°C, 70°C, 80°C and 90°C on many drying behaviour and quality were studied.In the second experiment, a natural convection solar dryer was designed and constructed to dry mango slices. The constructed dryer consisted of a drying chamber and a solar collector combined in one unit. Inside the drying chamber there were two movable mesh wire trays for easy loading and unloading.
Monitoring learners’ activities and evaluating their interaction with a Learning Management System (LMS) is one of the major issues in the teaching and learning environment. Conventional Learning Management System (LMS) lacks automation in the coordination and management of student activities and courses management. In this book we survey a few state-of-the–art LMSs with an intention to identify their standard features and weaknesses. The work presents a conceptual model that applies software agent technology to overcome some of the weaknesses of existing LMSs. This book also discusses how the software agent technology is used to assist lecturers in monitoring learners’ activities and managing their profiles. The agent will analyze the profiles and make recommendation to the instructors of each learner’s level of interaction to the LMS. These interaction levels serve as good indicators for the lecturers to know the commitment of their students in studying and submitting their assignments via the LMS.
The growth of population, indiscriminate establishment of industries, auto-mobiles etc., are some of the major causes for the atmospheric pollution, besides power shortage. There is a growing concern that pollution together with accelerated growth and development of nations may alter the climate due to the release of large amount of soot, carbon emission and other pollutants into the atmosphere in the form of ultra-fine dust particles which are suspended in the atmosphere called aerosols. They play an important role in the atmospheric processes favouring cloud formation due to large size aerosols and having adverse effects on health, depending on their size due to coagulation process. This book focuses on mathematical modelling of dispersion of aerosols in the presence/absence of electric field and first order chemical reaction using different dispersion models. The problems addressed here are representative of aerosol removal mechanisms. In order to keep the environmental problems mathematically tractable few simplifying assumptions have been made to the extent that they do not obscure the actual phenomena which was purportedly modelled in a restrictive yet representative sense.
This is basically a review of the Mathematical modeling which is a common practice now a days in industry. A Literature is also given here which comprise of linearity, non linearity and overview of techniques given by various authors along with their solution techniques.An efficient technique is also given which reduce computational time.The technique can be used for various models linear as well as non linear. The technique is simulated with industrial parameters too.
Mathematical ecology deals with the development of mathematical model for studying the patron of relationship between organism and their environment. Mathematical modeling is a useful tool to understand the behavior of natural systems. We hope this reference book will meet the needs of theoretical biologist for modeling and analysis of few real world problems. It is well known fact that environment is getting polluted by different types of chemicals, emitted due to various human activities. The biological populations are regularly exposed to several natural and artificial chemicals which are toxic to them and their environment as well. Many of researchers, while developing population models, studied the interacting species systems with nutrient cycling. Further, with the advancement of mathematical ecology, the researchers also developed and studied the effects of pollutant on interacting species system using mathematical models. It may be noted here that a title or no attention has been given towards the study of the effect of pollutant on interacting species systems with nutrient cycling using mathematical models.
Wetting Phenomenon of Fibrous Structures: Test Methods and Mathematical Modelling of the System. Experiments are inevitable in order to collect required information about the investigated target. Unfortunately in most of the cases it is time consuming and usually additional auxiliary appliances are needed. For the investigation of the processes that are being performed in a macroscopic or in a microscopic levels, nowadays used test methods may not be a sufficient tool. Analysis for this type of processes can be simplified by implementation of mathematical modeling. It can also save time, visualize the process and deliver reliable results.
In ecology, we are faced with modelling complex systems involving many variables corresponding to interacting populations structured in different compartmental classes, ages and spatial patches. Models that incorporate such a variety of aspects would lead to systems of equations with many variables and parameters. Mathematical analysis of these models would, in general, be impossible. In many real cases, the dynamics of the system corresponds to two or more time scales. For example, individual decisions can be rapid in comparison to growth of the populations. In that case, it is possible to perform aggregation methods that allow one to build a reduced model that governs the dynamics of a lower dimensional system, at a slow time scale. In this book, we present a review of aggregation methods for time continuous models. We also present applications in population dynamics.
Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. Mathematical Thinking and Writing teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point. Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure. After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas.* Covers the full range of techniques used in proofs, including contrapositive, induction, and proof by contradiction* Explains identification of techniques and how they are applied in the specific problem* Illustrates how to read written proofs with many step by step examples* Includes 20% more exercises than the first edition that are integrated into the material instead of end of chapter* The Instructors Guide and Solutions Manual points out which exercises simply must be either assigned or at least discussed because they undergird later results
Open University, e-learning, web-education, and other related terms are common these days, but the objective behind them can not be achieved fully without ICT tools availability in both rural and urban areas. Generic model for determining the level of ICT tools’ dispersion and its applicability, adaptability and availability for e-learning, open university system and distance learning was developed. Under-developed and developing nations problems include inflation rate, literacy, bandwidth, telecommunication and electricity. These were found having effect on ICT tools diffusion and were used for simulation and development of the models. Software was developed for the implementation of the models while data were gathered and analyzed to show trend of its availability and verification of the models. This book shows that, the higher the ICT tools dispersion, the better the access to e-learning and its related areas. Government and other stakeholders in under-developed, developing and developed nations should study this book and find a way of giving opportunity to make ICT tools available everywhere for better access to education anywhere you may be.
A mathematical framework on relaxation losses of heating of magnetite nanoparticles synthesized with Polydimethylsiloxane (PDMS) gel encasement is presented. Numerical solution of the mathematical model showed explicit dependence of the temperature rise of the device on frequency and amplitude of the external applied field, relaxation time and volume fraction of the nanoparticles. Hyperthermia therapeutic temperature of 41 – 46oC can be achieved with an external field of frequency and amplitude in the ranges 2.16 – 2.19 kHz and 9.77 – 9.89 kA/m respectively. Also, viscosity and volume fraction of the nanoparticles lies in the ranges 1.1 – 1.2 mPa.s and 0.12 – 0.14 respectively. Simulation of the heat diffusion profile of the implant and its surrounding tumor was done using Abaqus/CAE 6.9, a finite element simulation package. In 2D, the results showed that for maximum generated temperatures of 52oC and 55oC, the tumor temperature was maintained within the therapeutic range for more than thirty minutes in conformity with predicted theory. However, the tumor temperature falls below the therapeutic range for generated temperature of 45oC.