Search Results for « Mathematical models »

The major methods of mathematical modelling of solidification and melting problems are reviewed in this paper. Different analytical methods, nowadays still used as standard references to validate numerical models, are presented. Various mathematical formulations to numerically solve solidification and melting problems are categorized. Relative merits and disadvantages of each formulation are analysed. Recent advances in modelling solidification and melting problems associated with convective motion of liquid phase are discussed. Based on this comprehensive survey, basic guidelines are outlined to choose a correct mathematical formulation for solving solidification and melting problems.

The research described in this proposal is currently being supported by the US Department of Energy under the contract Mathematical Models of Hysteresis''. Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of our work under the above contract. Our ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories''. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. Our research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. Our study has by and large been centered around the following topics: various generalizations and extensions of the classical Preisach model, finding of necessary and sufficient conditions for the representation of actual hysteretic nonlinearities by various Preisach type models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models has constituted the main direction of the research, some effort has also been made to establish some interesting connections between these models and such topics as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks.

Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor's resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.

A mathematical model is presented for a complete lithium–sulfur cell. The model includes various electrochemical and chemical (precipitation) reactions, multicomponent transport phenomena in the electrolyte, and the charge transfer within and between solid and liquid phases. A change in the porosity of the porous cathode and separator due to precipitation reactions is also included in the model. The model is used to explain the physical reasons for the two-stage discharge profiles that are typically obtained for lithium–sulfur cells.

Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host-pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works.

Fluid flow is very important to quality in the continuous casting of steel. With the high cost of empirical investigation and the increasing power of computer hardware and software, mathematical modeling is becoming an important tool to understand fluid flow phenomena. This paper reviews recent developments in modeling phenomena related to fluid flow in the continuous casting mold region, and the resulting implications for improving the process. These phenomena include turbulent flow in the nozzle and mold, the transport of bubbles and inclusion particles, multi-phase flow phenomena, the effect of electromagnetic forces, heat transfer, interfacial phenomena and interactions between the steel surface and the slag layers, the transport of solute elements and segregation. The work summarized in this paper can help to provide direction for further modeling investigation of the continuous casting mold, and to improve understanding of this important process.

Math-education reformers encourage the incorporation of mathematical modeling activities into K-12 curricula. Many of the purported educational benefits derive from the authenticity of the activities-how well they reflect the everyday and occupational mathematical practices of adults. But a paucity in the literature of observational descriptions of adult modeling behavior has made it difficult to judge the authenticity of classroom activities and their potential to prepare students for out-of-school problem solving. The ethnographic study reported here investigated the everyday problem-solving activity of structural engineers in practice. Modeling was found to be central to and ubiquitous in the engineers' work, giving rise to some of their greatest intellectual challenges. These engineers use, adapt, and create models of various representation forms and degrees of abstraction. Two major challenges of modeling emerged: understanding inaccessible phenomena and keeping track of models. These challenges, and the nature of engineering models themselves, are not well reflected in the modeling tasks typically prescribed for the K-12 classroom, which will likely limit their educational benefits.