We introduce a mathematical model for the evolution of a cancer disease at the organism scale, taking into account for the metastases and their sizes as well as action of several therapies such as primary tumor surgery, chemotherapy and anti-angiogenic therapy. The mathematical problem is a renewal equation with bi-dimensional structuring variable. Mathematical analysis and functional analysis of an underlying Sobolev space are performed. Existence, uniqueness, regularity and asymptotic behavior of the solutions are proven in the autonomous case. A lagrangian numerical scheme is introduced and analyzed. Convergence of this scheme proves existence in the non-autonomous case. The effect of concentration of the boundary data into a Dirac mass is also investigated. Possible applications of the model are numerically illustrated for clinical issues such as the failure of anti-angiogenic monotherapies, scheduling of combined cytotoxic and anti-angiogenic therapies and metronomic chemotherapies. In order to give mathematical answers to these clinical problems an optimal control problem is formulated, analyzed and simulated.
Woven fabric composites are widely used in structural applications due to ease in their fabrication. Damping is an important parameter in structures for controlling the resonant vibrations. However, models that predict the loss factors in damping for bi-directional composites are not found in literature. This book provides mathematical prediction of damping loss factors in woven fabric composites. This book is intended to serve as a reference to research scholars and practicing engineers working in the area.
This work is a Ph.D research work that looks into the control of the blood glucose/insulin levels in an insulin-dependent diabetic patient. The study was made mathematically using mathematical models for the blood glucose and insulin levels for a diabetic patient. The models were solved and analysis carried out which helps to elucidate the problems of diabetes in a person. Control procedure was also demonstrated.
The paper discusses the peculiarities of mathematical modeling of high-temperature processes in tubular rotary kilns on the examples of firing the cement mixture and mixture for the production of alumina. Also discussed methods of studies of the kinetics of solid-phase processes using calorimetry heat flow, as well as the solution of inverse problems of parametrical identification of kinetic models. Refer formulation and solution of tasks obtaining optimal temperature profile using the method of nonlinear programming.
The experimentation on pedal powered process machine has been studied. An experimental data based models for the pedal powered chaff cutting machine system has been established for responses of the system such as Instantaneous Resistive Torque.These empirical models predict the performance of the pedal Powered Chaff Cutting Machine . The Optimum values of various independent parameters were arrived at on the basis of optimization of the models. An Artificial Neural Network simulation has been developed for the phenomenon which truly represents the degree of interaction of various independent variables.
A monitoring mission to study the shape and estimate initial dilution of the S. Jacinto outfall plume using an Autonomous Underwater Vehicle was performed on July 30, 2002. In order to reduce the uncertainty about plume location and concentrate the vehicle mission only in the hydrodynamic mixing zone, outputs of a near-field prediction model, based on effective real-time in situ measurements of current speed and direction and density stratification, were opportunistically used to specify in real time the mission transects. The surface characteristics of the outfall plume were found to be influenced strongly by the relatively weak stratification and low current velocities. Dilution was estimated using a TS-diagram with initial mixing lines between wastewater and ambient waters. In order to efficiently map the plume dispersion least-squares collocation method technique was applied. This book is an important reference in the field and tells how AUVs can provide high-quality measurements of physical properties of effluent plumes in a quite effective manner.
Model is a miniature representation of something; a pattern of something to be made; an example for imitation or emulation; a description or analogy used to help visualize something (e.g., an atom) that cannot be directly observed; a system of postulates, data and inferences presented as a mathematical description of an entity or state of affairs. This definition suggests that modeling is an activity, a cognitive activity in which we think about and make models to describe how devices or objects of interest behave. We can use words, drawings or sketches, physical models, computer programs, or mathematical formulas. In other words, the modeling activity can be done in several languages, often simultaneously. Since we are particularly interested in using the language of mathematics to make models. Mathematical model is a representation in mathematical terms of the behavior of real devices and objects. We want to know how to make or generate mathematical representations or models, how to validate them, how to use them, and how and when their use is limited. However, before delving into these important issues, it is worth talking about why we do mathematical modeling.
In mathematical bio-sciences we study the applications of mathematical modeling and mathematical techniques to get an insight into the problems of bio-sciences. The mathematical model is a comprehensive process of representing real Phenomena in terms of Mathematical Equations, and extracting from them useful information for understanding and predicting the process of idealization. The study of blood flow characteristics in human circulatory system in the presence of stenosis, has been the subject of researchers in recent years. A serious study of this problem has been done by Young 1968 who presented a mathematical model to analyses theoretically the effects of stenosis on flow characteristics of blood and concluded that the resistance to the flow and the wall shear stress increase with the increase in stenosis size. The blood flow through large arteries considered as Newtonian flow by Lee JS 1974. while the blood flow through small arteries is considered as non-Newtonian by Chan et all 2007.
The aim of the present is to acquaint the readers with the mathematical models extensively used not only in natural and engineering sciences, but also in a variety of disciplines of social sciences. Since the modeling of devices and phenomena is essential to both engineering and science, engineers and scientists have very practical reasons for doing mathematical modeling. In addition, engineers, scientists, and mathematicians want to experience the sheer joy of formulating mathematical models. These models are helpful to study the effects of different components, and to make predictions about their behavior and find tremendous applications through their use in facilitating economic evaluation and in a number of decision-making contexts including risk assessment, service planning and capacity modeling. The use of mathematical models avoids intuition and, in certain cases, the risk involved, time consumed and the cost associated with the study of primary research. I sincerely hope that this book will be a source of inspiration to the budding researchers and scientists for the discovery of new principles, ideas and concepts underlying a variety of disciplines of Mathematical Sciences.
This research shows the application of multi-attribute decision making tools as applied to identifying key nodes in social and dark networks. From the social network side we used the Kite and the Knoke Information Networks as examples and for the dark network we used the Noordin 79 node network. Our results are useful in that they show a methodology to rank order key nodes. Even more important is the use of sensitivity analysis in the modeling process as the subjective decision maker’s weights change.
Mathematical modeling of bubbles dynamics is presented in turbulent flow to study the behaviour of vapour growth bubble between two phases (vapour-superheated liquids) flow. Theoretical study of the growth problem is solved analytically in terms of initial void fraction and initial bubble velocity. The growth problem in a viscous superheated liquid is investigated under the proposed pressure of Plesset and Zwick. The growth of bubble radius in a constant and variable dynamical viscosity is studied. The effect of constant and variable dynamical viscosity for two different cases of pressure is studied. The initial time of growth of vapour bubbles between two phase laminar-turbulent flow is introduced in thermal stage. This book is suitable and will be interesting for all researchers in related fields.
Although viscoelastic flows are characterized by a very low Mach number regime, it involves a weakly compressible liquid phase, which requires a special treatment. This work is devoted to the mathematical modeling and numerical simulation for viscoelastic fluids. It follows directly a previous publication, PhD dissertation of the author. A Unified purely hyperbolic mathematical model for compressible and incompressible viscoelastic fluids is presented. To complete the mathematical model, a complete chapter is devoted to describe a new procedure to determine the correct type and number of boundary conditions for hyperbolic systems. Then a new model describing the non-isothermal viscoelastic flows is introduced while keeping the hyperbolic nature of the system. The main advantage of the proposed model over the existing ones is its hyperbolic nature, which overcomes some of the drawbacks of the available models. The proposed model is then solved numerically using a hybrid finite element/finite difference scheme.
The book examines the problems of mathematical modeling of complex, including information systems. Fundamental problems of information theory, coding theory, complexity theory, algorithms, theory, probability theory, theoretical cryptography are considered. The basic mathematical problems of information security are discussed. Special attention is given to the availability of presentation. Relationships of fundamental mathematical tasks and problems of information security are obtained.