Workshop on Mathematics in Industry 2012
Title: Mathematical Modeling of Combustion in Rotary Kilns
Summary:
The presentation will describe the Rotary Kiln and the modeling of the processes inside this equipment. The rotary kiln is a heavy equipment which is used at the mineral processing industry, especially cement fabrication, to the calcination of materials at very high temperatures. The heat input to the process is based on the combustion of several types of fuels. Therefore, inside the rotary kiln we can identify many physical and chemical processes which can be mathematically modeled and enable the simulation of the equipment operation under different conditions. The use of high-end CFD (Computational Fluid Dynamics) represents the ultimate application of that mathematical modeling.
Dynamis intends to present a practical case: the modeling of the world’s largest Nickel Ore Calcining Kiln.
Presentation by:
Guilherme Martins Ferreira – Partner at Dynamis Mecânica Aplicada – Graduated as Mechanical Engineer at Escola Politécnica (São Paulo State University) in 1983, post-graduated in Thermal Engineering and Fluid Mechanics. Highly experienced at Chemical Industry, Petrochemicals, Agro-industry, Power Generation, Cement & Lime, Mineral Processing, Metallurgy, Iron-making & Steelmaking, Pulp & Paper, Ceramics, Glass , Oil & Gas and Nuclear Industries.
Title: Mathematical Modeling and Operational Research: Some Case Studies and Lessons of Mountaineering
Júlio Michael Stern – Department of Applied Mathematics – University of São Paulo
Abstract
The title of this conference is an upbeat version of Lições de Abismo, a novel by Gustavo Corção, where the author wishes to have had some lessons preparing him for the difficult challenges he has to overcome.
Consulting for industry and commercial or financial enterprises was for me a real challenge, for my first encounter with applied mathematics was the book of Prof. Chaim Hoenig - Application of Topology to Analysis.
I wish I had some Lessons in Mountaineering, teaching me some basic tricks and other not so trivial survival skills for consulting in applied mathematics. Unfortunately, I never had such preparatory lessons.
Nevertheless, I ended up doing quite a few interesting projects on "real" applied mathematics, including several PITE and PIPE projects at FAPESP. Some of my recollections about these projects can be found in section 4 of
http://www.ime.usp.br/~jstern/vitae/jmst2.pdf and accompanying slides http://www.ime.usp.br/~jstern/vitae/jmsts2.pdf
I will try to extract from these recollections some lessons in mountaineering.
Title of Talk: Calculating the SAR to Power up an Implantable Neural Interface for Wireless Communications with Human Motor Cortex
Mario Alexandre Gazziro - Department of Computer Science - University of São Paulo
Abstract: This presentation will introduce the major project named "Implantable Neural Interface" developed by ICMC, IFSC and EESC from USP, UFABC, USF (University of South Florida-USA) and by Brazil Research Lab (BRL) from IBM, with the objective to provide a wireless brain-computer interface, allowing mankind a security access to the human motor cortex, with focus on SAR (Specific Absorption Rate) modeling. A SAR limit of 2W/kg averaged over any contiguous 10g head tissue was recommended by the Council of European Union for the general public. The results will show how many electrodes can be powered within an security level for the brain.
Title: A Perspective of University-Industry Collaboration – A Pedagogical Approach
SPEAKER: Weldon A. Lodwick
AFFILIATION: University of Colorado Denver, Department of Statistical and Mathematical Sciences – Applied Mathematics Graduate Program
ABSTRACT: This presentation will focus on how to bring actual applied mathematical problems from industries and institutions into the classroom to be researched with a solution, hopefully, returned. This pedagogical instrument of training graduate and undergraduate students in applied mathematics, not only prepares students for jobs in applied mathematics, it is an exercise in applied mathematical research beneficial to the sponsoring industry/institution and also serving for masters and PhD topics as well as research articles. This is a regularly scheduled three hours per week, fifteen week class, called the mathematics clinic given each semester (sometimes we have 2 clinics in a semester), which is required by all undergraduate mathematics students and PhD students. The mathematics clinic is a distinguishing feature of our department. I will present the 30 year experience of the mathematics department at the University of Colorado Denver of which I have been a part from the first one in 1982, 15 years as the director of the program, with examples of various clinics. The outline of the presentation is as follows:
1. Introduction – what is a mathematics clinic, how do we obtain problems?
2. The structure of the clinic – how a mathematics clinic is run?
3. Our experience
a. Our first clinic (1982) – Three Mile Island Nuclear Power Plant Disaster, parallel computer implementation of simulations, Delcor Computers and US Department of Energy
b. Various clinics
i. Plant Variety Protection - USDA
ii. Lockheed-Martin Vehicle Launch Unit – optimal Uranus probe design
iii. Lockheed-Martin – the use of neural networks to control rocket launches
iv. A Sewer System Geographic Information System – South Suburban Sanitation District No. 1, Centennial, Littleton, and Englewood, Colorado
v. Trash collection and snow mashing routing problem – City of Denver
vi. Radiation Therapy of Cancer Tumors – Computerized Medical Systems (St. Louis, Missouri) and University Hospital Radiation Oncology unit
vii. Intelligent Mathematical Programming Systems – Shell Oil, Amoco (now BP)
viii. Medical Image Processing – National Jewish Lung Hospital, Denver
ix. Democratic National Convention 2008, security monitoring – Democratic Party
x. Others
4. What does an industry or institution gain?
5. What does the university, department, student gain?
6. My point of view of the possibilities of university/industrial collaboration in Brasil after a year at UNESP-SJRP
a. Non-pedagogical Approach – A talk with Professor Marcus Rocha, Univ. Federal do Para
b. Pedagogical Approach – Experience with UNESP-SJRP and Hopstital de Câncer de Barretos, “Escala de médicos” (unidade de radioterapia)
7. Concluding remarks
Title: Developing optimization software: overview, challenges and perspectives
Ernesto Birgin – Department of Computer Sciences – University of São Paulo
Abstract: Our experiences developing optimization software will be overviewed in this talk. The objective of the talk is to highlight the challenges involved in the development and long-term maintenance of open source software for nonlinear programming and discrete optimization. The dichotomy between focusing on attaining a large number of users having at hand academic problems or a few users with real applications will be tackled. Perspectives will be analyzed.
Title: Neutralization of Acid Mine Drainage
Presenter: Mario Primicerio – University of Florence
Abstract: We present a mathematical model for the flow of an acid solution through a reacting porous medium. The solid matrix is supposed to be formed by families of spheres with different radii and the fluid is supposed to saturate the pores. The system is described by the evolution of the overall ion concentration and the radii of the spheres. The structure of the mathematical problem is multi-scale in time and for each time-scale different simplified problems can be obtained. We give some analytical results and display some numerical simulations to show the behavior of the solutions. The main motivation of this research is the design and use of remediating filters in which solid particles of CaCO3 are used to neutralize a given flow of an acid mine drainage.
Singular Shocks in a Chromatography Model:
Singular Perturbation Theory and Geometric Insight
Barbara Lee Keyfitz
Department of Mathematics, The Ohio State University
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A standard model for two-component chromatographic separation provides a well-known example of a system of two hyperbolic conservation laws (quasilinear hyperbolic partial dierential equations) in a single space dimension and time. Systems of this type do not generally have smooth solutions, even for smooth data, so it is customary to seek weak solutions; and, in the standard theory, these solutions are functions of bounded variation. For particularly simple data, solutions are piecewise smooth, with simple jump discontinuities.
Recent analysis by Marco Mazzotti [7], however, has demonstrated that some chromatography models may have solutions of considerably less regularity, even for very simple data. Furthermore, Mazzotti's predictions have been veried in experiments.
Mazzotti's solutions lie in a class of functions, singular shocks , originally discovered by Keytz and Kranzer, [3,4], and subsequently studied in greater depth by Sever, [9]. Members of this class may contain measures (for example Dirac δ-functions), and elements weaker than measures. Overall, it is unclear in what sense singular shocks satisfy the conservation law.
In this talk, I expand on work by Stephen Schecter [8] which uses Geomet-ric Singular Perturbation Theory (GSPT) [2] to prove that approximations to singular shocks satisfy a well-known approximation, the self-similar Dafermos-DiPerna regularization [1], of one model system [6]. In addition to demonstrat-ing a mechanism for the approximation, GSPT also demonstrates the detailed structure of singular shock pro les. Besides the chromatography model, some examples include a classic model, which gave rise to the discovery of singu-lar shocks, of gas dynamics with the wrong variables conserved; an additional application of these ideas has led to some insights into a simplied model for incompressible two-phase flow [5].
This work is joint with Ting-Hao Hsu, Michael Sever, Charis Tsikkou, and Fu Zhang.
References
[1] C. M. Dafermos and R. J. DiPerna, The Riemann problem for certain classes of hyperbolic systems of conservation laws. J. Differential Equations 20 (1976), 90-114.
[2] C. K. R. T. Jones, Geometric singular perturbation theory. Dynamical systems (Montecatini Terme, 1994), Lecture Notes in Mathematics, Vol. 1609, Springer, Berlin, 1995, pp. 44-118.
[3] B. L. Keyfitz and H. C. Kranzer, A viscosity approximation to a system of conservation laws with no classical Riemann solution. In Nonlinear Hyperbolic Problems (Bordeaux, 1998), (eds. C. Carasso et al.), Lecture Notes in Mathematics, Vol. 1402; Springer, Berlin, 1989, pp. 185-197.
[4] B. L. Keyfitz and H. C. Kranzer, Spaces of weighted measures for conservation laws with singular shock solutions, J. Differential Equations, 118 (1995), 420-451.
[5] B. L. Keyfitz, M. Sever and F. Zhang, Viscous Singular Shock Structure for a Nonhyperbolic Two-Fluid Model, Nonlinearity , 17 (2004), 1731-1747.
[6] B. L. Keyfitz and C. Tsikkou, Conserving the Wrong Variables in Gas Dynamics: A Riemann Solution with Singular Shocks, Q. Applied Mathematics, LXX (2012), 407-436.
[7] M. Mazzotti, Non-classical composition fronts in nonlinear chromatography - Delta-shock, Indust. & Eng. Chem. Res., 48 (2009), 7733-7752.
[8] S. Schecter, Existence of Dafermos proles for singular shocks, J. Differential Equations 205 (2004), 185-210.
[9] M. Sever, Distribution solutions of nonlinear systems of conservation laws, Memoirs of the AMS, 889 (2007), 1-163.