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Title: A Video Annotation and Indexing System (sequence unknown), IPRO 327 - Deliverables
Creator: Dhagam, Karthik, Donchev, Alexander, Homawoo, Sergio, Litas, Alexander, Orlichenko, Anton, Osswald, Christian, Petsod, Jason, Rawlings, Ori, Shaffer, Joshua, Smith, Antoinette, Yates, Andrew, Yu, Hee Jeoung
Date: 2009-12
Description: Much information available on the Web is in video format. The problem with this medium is users cannot comment on particular scenes within the...
Show moreMuch information available on the Web is in video format. The problem with this medium is users cannot comment on particular scenes within the videos and there is no method of searching for specific content within the videos. The team proposes to develop a system that will allow users to make fine-grained comments on scenes within the video and then to use these comments to aid in search within videos.
Deliverables for IPRO 327: A video annotation and indexing system for the fall 2009 semester
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Title: WIDESPAN: 2030-board 2
Creator: Ninan, Janice
Date: 2011-05, 2010-12
Description: Widespan design.Investigating the integration of windmills into longspan structure and investigating the axial forces of tension to span...
Show moreWidespan design.Investigating the integration of windmills into longspan structure and investigating the axial forces of tension to span grater spans using virtual depth concepts with slender lightweight design.
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Title: VIBRATIONAL CONTROL OF AN EXOTHERMIC REACTION IN A CSTR - THEORY AND EXPERIMENTS
Creator: Cinar, A., Deng, J., Meerkov, S. M., Shu, X. S.
Date: 1987-03
Publisher: AMER INST CHEMICAL ENGINEERS
Description: Vibrational control is a method for modification of dynamic properties of linear and nonlinear systems by introducing fast, zero-average...
Show moreVibrational control is a method for modification of dynamic properties of linear and nonlinear systems by introducing fast, zero-average oscillations in the system's parameters. In this paper, forced oscillations introduced in the input flow rates of an exothermic continuous stirred-tank reactor (CSTR) are shown to result in a modification of the S-shaped steady state curve. This modification leads to a possibility of operating a CSTR at an asymptotically stable period regime located in the vicinity of an unstable steady state of the reactor system with stationary input flow rates. Thus, vibrations of the input flow rates can be viewed as a stabilizing mechanism for exothermic CSTR's.
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Title: QUALITY-OF-SERVICE AWARE SCHEDULING AND DEFECT TOLERANCE IN REAL-TIME EMBEDDED SYSTEMS
Creator: Li, Zheng
Date: 2015, 2015-05
Description: For real-time embedded systems, such as control systems used in medical, automotive and avionics industry, tasks deployed on such systems...
Show moreFor real-time embedded systems, such as control systems used in medical, automotive and avionics industry, tasks deployed on such systems often have stringent real-time, reliability and energy consumption constraints. How to schedule real-time tasks under various QoS constraints is a challenging issue that has drawn attention from the research community for decades. In this thesis, we study task execution strategies that not only minimize system energy consumption but also guarantee task deadlines and reliability satisfaction. We first consider the scenario when all tasks are of the same criticality. For this case, two task execution strategies, i.e. checkpointing based and task re-execution based strategies are developed. Second, considering the scenario when tasks are of different criticalities, a heuristic search based energy minimization strategy is also proposed. When tasks are of different criticalities, a commonly used approach to guaranteeing high-criticality task deadlines is to remove low-criticality tasks whenever the system is overloaded. With such an approach, the QoS provided to low-criticality tasks is rather poor, it can cause low-criticality tasks to have high deadline miss rate and less accumulated execution time. To overcome this shortcoming, we develop a time reservation based scheduling algorithm and a two-step optimization algorithm to meet high-criticality task deadlines, while minimizing low-criticality task deadline miss rate and maximizing their accumulated execution time, respectively. As many-core techniques mature, many real-time embedded systems are built upon many-core platforms. However, many-core platforms have high wear-out failure rate. Hence, the last issue to be addressed in the thesis is how to replace defective cores on many-core platforms so that deployed applications’ real-time properties can be maintained. We develop an offline and an online application-aware system reconfiguration strategy to minimize the impact of the physical layer changes on deployed real-time applications. All the developed approaches are evaluated through extensive simulations. The results indicate that the developed approaches are more effective in addressing the identified problems compared to the existing ones in the literature.
Ph.D. in Computer Science, May 2015
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Title: UNDERSTANDING REACTION MECHANISMS AND CONTROLLING REACTIVE SURFACE SPECIES DURING ATOMIC LAYER DEPOSITION OF METAL CHALCOGENIDES
Creator: Weimer, Matthew S.
Date: 2016, 2016-07
Description: Atomic layer deposition (ALD) is a thin film growth technique that relies on self-limiting reactions between vapor precursors and a surface....
Show moreAtomic layer deposition (ALD) is a thin film growth technique that relies on self-limiting reactions between vapor precursors and a surface. Significant progress has been made in the scope of materials grown by ALD, enabled by precursor development and investigation of surface reaction mechanisms; progress is still necessary. This dissertation has two portions. The first is the development of organometallic compounds to engender new material growth by ALD. Second is the development of X-ray absorption spectroscopy (XAS) tools and techniques for observations of the metal coordination environment during ALD. One material that can be difficult to make is doped materials. Composition of a doped material determines the film properties. One example is vanadium doped indium sulfide. This material was purposed as an intermediate bandgap solar absorbing material which can absorb multiple ranges of light. Two new precursors were developed for the growth of indium sulfide and vanadium sulfide. The indium sulfide material grown has shown superior film photocurrent qualities and doping of vanadium into indium sulfide with fine control over atomic placement was achieved. Films were grown that showed secondary absorptions which aligned with theoretical calculations. The flexibility of the V(III) precursor is shown by a short study on the control of the difficult vanadium-oxygen system in the deposition of stoichiometric oxides. To illustrate how XAS can be used in conjunction with other techniques tin dioxide growth from a stannylene precursor and hydrogen peroxide was studied. From ex situ XAS measurements nucleation, growth and termination reaction mechanism were discovered. Next, a mobile ALD reactor allowed for in situ XAS measurements to be performed on “flat” substrates for the first time. Specifically, the local coordination environment and surface reactions were followed while erbium was doped into alumina and coordination environment of manganese was investigated in the growth of manganese-doped zinc oxide, with the ability to probe in-plane versus out-of-plane bonds. These unique in situ XAS experiments allow for greater understand of metal and non-metal precursors as they interact with surfaces. This enhanced understanding enables new precursor development which leads to better control over surface chemistry and new materials.
Ph.D. in Chemistry, July 2016
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Title: DISTRIBUTED VIDEO CODING FOR RESOURCE CONSTRAINED VIDEO APPLICATIONS
Creator: Liu, Wenhui
Date: 2014, 2014-05
Description: Video coding technology has played a key role in the explosion of current multimedia society with increasing resolution and quality. Such big...
Show moreVideo coding technology has played a key role in the explosion of current multimedia society with increasing resolution and quality. Such big success is largely built on the conventional video coding paradigm where motion estimation and compensation are performed at the encoder. This asymmetry in complexity is well-suited for the applications where the video sequence is encoded once and decoded many times. However, some new emerging applications such as wireless video surveillance, wireless PC cameras and multimedia sensor networks require a low complexity encoding, while possibly a ording a high complexity decoding. Therefore, a challenging problem emerges with the new type of visual communication system is how to achieve low complexity encoding video compression while maintaining good coding e ciency. Distributed video coding (DVC) provides low complexity encoding solutions for video communication with limited computational power or energy constraints. In DVC, the source video information is independently encoded at lightweight encoders. At the decoder, all the received bitstreams are jointly exploited their statistical dependencies between them. In such a way, motion estimation and its computational complexity is shifted from the encoder to the decoder. However, DVC also has its own restrictions. The low coding e ciency remains a challenging issue for DVC compare to the conventional video coding. Although DVC is robust to channel loss due to its intrinsic feature of independent encoders and joint decoder, the error resiliency for medium to large transmission errors is weak. In this dissertation, previously proposed low-complexity DVC (LC-DVC) architecture is rstly introduced. After that, a continued work is presented to further improve quality of SI. The proposed method is called spatio-temporal joint bilateral upsampling (STJBU) based SI generation, where geometric closeness of pixels and their photometric similarity is exploited to reduce the noise while preserving the edge xiv information. Moreover, a distributed multiple description coding (DMDC) scheme is proposed by combining the multiple description (MD) coding into LC-DVC to improve its error resiliency. All the proposed schemes are well described and the ratedistortion analyses are presented in this dissertation. All these features have made the LC-DVC a great solution for resource constraints applications.
PH.D in Electrical Engineering, May 2014
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Title: Nonlinear time series models for multivariable dynamic processes
Creator: Cinar, A.
Date: 1995-11
Publisher: ELSEVIER SCIENCE BV
Description: Several paradigms are available for developing nonlinear dynamic input-output models of processes. Polynomial models, threshold models, models...
Show moreSeveral paradigms are available for developing nonlinear dynamic input-output models of processes. Polynomial models, threshold models, models based on spline functions, and polynomial models with exponential and trigonometric functions can describe various types of nonlinearities and pathological behavior observed in many physical processes. A unified nonlinear model development framework is not available, and the search of the appropriate nonlinear structure is part of the model development effort. Various artificial neural network structures and nonlinear time series model structures are presented and illustrated by developing a model from data sets generated by a series of example systems. The use of a nonlinear model development paradigm which is not compatible with the types of nonlinearities that exist in the data can have a significant effect on model development effort and model accuracy.
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Title: MATHEMATICAL-MODELS OF COCURRENT SPRAY-DRYING
Creator: Negiz, A., Lagergren, E. S., Cinar, A.
Date: 1995-10
Publisher: AMER CHEMICAL SOC
Description: A steady state mathematical model for a cocurrent spray dryer-is developed. The model includes the mass, momentum, and energy balances for a...
Show moreA steady state mathematical model for a cocurrent spray dryer-is developed. The model includes the mass, momentum, and energy balances for a single drying droplet as well as the total energy and mass balances of the drying medium. A log normal droplet size distribution is assumed to hold at the exit of the twin-fluid atomizer located at the top of the drying chamber. The discretization of this log normal distribution with a certain number of bins yields a system of nonlinear coupled first-order differential equations as a function of the axial distance of the drying chamber. This system of equations is used to compute the axial changes in droplet diameter, density, velocity, moisture, and temperature for the droplets at each representative bin. Furthermore, the distributions of important process parameters such as droplet moisture content, diameter, density, and temperature are also obtainable along the length of the chamber. On the basis of the developed model, a constrained nonlinear optimization problem is solved, where the exit particle moisture content is minimized with respect to the process inputs subjected to a fixed mean particle diameter at the chamber exit. Response surface studies based on empirical models are also performed to illustrate the effectiveness of these techniques in achieving the optimal solution when an a priori model is not available. The structure of empirical models obtained from the model is shown to be in agreement with the structure of the empirical models obtained from the experimental studies.
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Title: Planning for Human Implantation of a Cortical Visual Prosthesis (sequence unknown), IPRO 334 - Deliverables: IPRO 334 Final Report F09
Creator: Bern, David, Chen, Shanyl, Deroo, Mary, Gorski, David, Kelly, Thomas, Leasenby, Alex, Li, Zhi, Pyrkh, Hanna, Subhani, Maham, Taneja, Aanchal
Date: 2009-12
Description: The Intracortical Visual Prosthesis is based upon that concept that by implanting a large number of subminiature electrodes within the human...
Show moreThe Intracortical Visual Prosthesis is based upon that concept that by implanting a large number of subminiature electrodes within the human visual cortex, coordinated temporal-spatial image information can be artificially communicated to the human visual cortex in the form of electrical currents, acting as a sensory substitute for normal vision.
Sponsorship: IIT Laboratory of Neural Prosthetic Research
Deliverables for IPRO 334: Planning for Human Implantation of a Cortical Visual Prosthesis for the fall 2009 semester
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Title: ECONOMIC BASED CONTROL SYSTEM DESIGN
Creator: Omell, Benjamin Peter
Date: 2013, 2013-12
Description: EMPC differs from traditional MPC by directly utilizing a profit based function as the objective as opposed to a quadratic function that...
Show moreEMPC differs from traditional MPC by directly utilizing a profit based function as the objective as opposed to a quadratic function that minimizes the distance from a set point that is predetermined. However, implementation of EMPC can result in unexpected and at times pathological closed-loop behavior, including inventory creep, bang-bang actuation and instability. To address these issues, an infinite-horizon version of EMPC is developed and shown to avoid many of the performance issues observed in the finite-horizon version. First, modifications to the EMPC problem will be used for the conceptual development of the Economic Linear Optimal Controller (ELOC), which is a statistically constrained linear feedback controller. Then, pointwise- in-time constraints can be reintroduced using one of two methods; Constrained ELOC or Infinite-Horizon EMPC (IH-EMPC). We also investigate the impact of problem formulation modifications on the ELOC. The first issue is that of disturbance modeling and the second is the impact of controller sample-time. The third topic concerns incorporation of computational delay in the feedback-loop, using both full and partial state information structures. Finally an illustration of the impact of plant-model mismatch is presented. The Constrained ELOC formulation is further modified to allow for market responsive smart grid applications. In particular an Integrated Gasification Combined Cycle (IGCC) process with hydrogen storage will be used to demonstrate the Constrained ELOC for such applications. The ELOC will be used as a vehicle to exploit dispatch capabilities by pursuing directly the objective of maximizing revenue. The idea being that process modifications to enable dispatch capabilities will allow for a time-shift of power production away from periods of low energy value to periods of high value. An in depth discussion is provided on how energy value forecasts are incorporated into the design of the constrained ELOC. Finally, an extension of the ix ELOC to the controller embedded equipment design is provided. The work concludes with a discussion of the computational aspects of solving the ELOC problem. In particular, the impact of reverse-convex constraints inherent to the ELOC problem are discussed along with existing solution methods. The main contribution of this final chapter is a novel application of the Generalized Bender’s Decomposition (GBD) algorithm to the ELOC problem. This new approach is shown to retain global optimality, reduce computational effort (by orders of magnitude) and expand the class of problems one can solve.
PH.D in Chemical Engineering, December 2013
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Title: POWER OPTIMIZATION IN DEEP SUBMICRON VLSI CIRCUITS: FROM SYSTEM LEVEL TO CIRCUIT LEVEL
Creator: Tong, Qiang
Date: 2017, 2017-07
Description: As VLSI technology advances to deep sub-micron regime, power consumption has become a critical concern in VLSI circuits. Therefore, power...
Show moreAs VLSI technology advances to deep sub-micron regime, power consumption has become a critical concern in VLSI circuits. Therefore, power optimization becomes mandatory in VLSI design nowadays. To reduce the power consumption, many techniques have been proposed at various levels of VLSI circuits design: system level, register-transfer level(RTL), and circuit/transistor level. This dissertation starts with a review of system level power optimization techniques. Experiments on a computer architecture simulation system have been conducted to compare the impact of different programming styles at system level on power consumption. The results could be used as an intuitive guidance for programmers with intention for implementing power-aware system. The second topic in this dissertation is a clustering based clock gating technique, targeting power reduction at RT-Level. Clock gating is an effective and popular method to reduce dynamic power in VLSI circuits, it can be applied at both RT-level and gate level. The basic idea of clock gating is to disable the clock of one or more sequential logics (majorly flip-flops) when the input data of the logic cells do not change. In this dissertation, a clustering based clock gating technique is proposed, the technique exploits activity information of each flip-flop, and clusters them into groups according to their activity correlations. As the leakage power has become a major concern in VLSI design, the proposed As the leakage power has become a major concern in VLSI design, the proposed clustering method is extended down to gate level and a clustering based hybrid clock gating and power gating technique is proposed. The technique can reduce both the dynamic power and leakage power in VLSI circuits. As process technology scaling down to deep submicron regime, bulk CMOS technology has encountered many challenges due to short channel effect (SCE), which degrades the reliability and feasibility of MOSFET devices. New technologies such as FinFET and carbon nanotube FET (CNFET) are two promising substitute solutions in the following decade to address SCE issue. Part of this dissertation presents circuit design using these new process technologies for low power VLSI circuits. More specifically, two SRAM cell designs using FinFET and CNFET devices are proposed. The new designs can improve performance while reduce power consumption.
Ph.D. in Electrical Engineering, July 2017
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Title: Devices that Assist Blind & Visually-Impaired Individuals in Swimming and Other Exercise Activities (sequence unknown), IPRO 310 - Deliverables
Creator: Dykeman, Kimberly, Healton, Michaela, Lipman, Timothy, Ludwig, Ross, Park, Jay, Reilly, Jeffrey, Sarkar, Smita, Sirk, Phillip, Toro, Branden
Date: 2009-12
Description: The objective is to develop, test, and implement assistive technology with the community that promotes safety and improves independence of...
Show moreThe objective is to develop, test, and implement assistive technology with the community that promotes safety and improves independence of blind and visually impaired (BVI) swimmers.
Sponsorship: Chicago Lighthouse for the Blind & Visually-Impaired. Notre Dame University
Deliverables for IPRO 310:Devices that Assist Blind & Visually-Impaired Individuals in Swimming and Other Exercise Activities for the fall 2009 semester.
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Title: WIDESPAN
Creator: Ninan, Janice
Date: 2011-05, 2010-12
Description: Widespan design.Investigating the integration of windmills into longspan structure and investigating the axial forces of tension to span...
Show moreWidespan design.Investigating the integration of windmills into longspan structure and investigating the axial forces of tension to span grater spans using virtual depth concepts with slender lightweight design.
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Title: Using Assessment Data to Improve Library Services : presented at ILA 2007 conference
Creator: Stewart, Christopher, Uth, Charles
Date: 2007-10
Description: IIT Libraries conducted LibQUAL+ service quality assessment in 2004 and 2006. This presentation will outline strategies we undertook to...
Show moreIIT Libraries conducted LibQUAL+ service quality assessment in 2004 and 2006. This presentation will outline strategies we undertook to address issues identified in the 2004 assessment, and evaluate their success based on assessment results in 2006. We will also discuss the importance of measuring academic library effectiveness in higher education’s emerging outcomes-based culture.
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Title: High Performance Green Homes (sequence unknown), IPRO 317 - Deliverables: IPRO 317 Midterm Presentation F09
Creator: Bhat, Adnan, Campbell, Brittanie, Cink, Jefferey, Gutstein, Yehuda, Hadi, Shuaib, Hafdi, Kamal, Hasan, Hasan, Kenig, Elezar, Lipski, Brian, Lollino, Luca, Margolis, Jordan, Nigamatzyanov, Tagir, Patel, Hiren, Patel, Neal, Shehada, Hazem, Toops, Melissa, Trauner, Crystal, Zgourdah, Mourad
Date: 2009-12
Description: The purpose of this project is to show how a team committed to helping people help save the world can leapfrog today's best designs. As...
Show moreThe purpose of this project is to show how a team committed to helping people help save the world can leapfrog today's best designs. As opposed to the tradition of minimum design standards that just meeting the building code, highest practical design standards are the focus. True sustainability is the goal of this project, including; Zero Carbon Emissions, Net Zero Energy, 100% Solar Power, 10 times the traditional design life, 1/10th the maintenance, rot proof, termite proof, fire proof, hurricane and earthquake resistant. The project team, using cutting edge technology, will develop all aspects of a start-up design and build company to promote High Performance Green Homes. This project will provide a great opportunity for IIT students to experience a challenging and interesting project and to significantly contribute to a better world.
Sponsorship: Jimmy Eng
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Title: STAR Results from the RHIC Beam Energy Scan, Proceedings of the XLIII International Symposium on Multiparticle Dynamics
Creator: Wang, Hui
Date: 2013-09-15, 2013-09-15
Publisher: IIT Press
Description: The Beam Energy Scan Program is launched by RHIC to study the QCD phase diagram. The goal is to explore the possible QCD phase boundary and...
Show moreThe Beam Energy Scan Program is launched by RHIC to study the QCD phase diagram. The goal is to explore the possible QCD phase boundary and search for possible QCD critical point. In 2010 and 2011, experiments collected data at √sNN=7.7, 11.5, 19.6, 27, 39 and 62.4 GeV, covering a wide range of baryon chemical potential from μB 420 to 70 MeV. In this presentation, we will report some latest results of the Beam Energy Scan Program from the STAR collaboration.
Sponsorship: IIT College of Science, High Energy Physics Division of Argonne National Laboratory
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Title: BIOPHYSICAL AND BIOCHEMICAL STUDY OF NATIVE AND EDITED DYSTROPHIN ROD REGION
Creator: Mangat, Khushdeep
Date: 2014, 2014-12
Description: Duchenne Muscular Dystrophy (DMD) is a severe X-linked recessive disease affecting 1 in 3500 boys that is characterized by the degeneration of...
Show moreDuchenne Muscular Dystrophy (DMD) is a severe X-linked recessive disease affecting 1 in 3500 boys that is characterized by the degeneration of muscle function and strength. The cause of this disease lies in gene defects that eliminate expression of the protein dystrophin. Becker Muscular Dystrophy, BMD is a milder form of disease that has a later onset and much longer survival (up to the 7th decade of life, compared to median survival of 25 years for DMD patients) because of the presence of low levels of modified dystrophin protein. BMD is very heterogeneous, however, and many cases are nearly as severe as DMD. A major therapy for DMD involves exon skipping, which produces modified forms of dystrophin that are very similar to BMD. However, how these edits impact the function of dystrophin, and how they are linked to the severity of BMD or the BMD-like state produced in DMD exon skip therapy is unknown. We investigated this in two specific cases involving a specific panel of BMD defects linked to a major cause of death, dilated cardiomyopathy (DCM). We also investigated the contribution of various exons to interaction with a signaling partner of dystrophin, neuronal nitric oxide synthetase (nNOS).
Ph.D. in Biological and Chemical Sciences, December 2014
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Title: PHYSICS-PRESERVING FINITE DIFFERENCE SCHEMES FOR THE POISSON-NERNST-PLANCK EQUATIONS
Creator: Flavell, Allen
Date: 2014, 2014-07
Description: The Poisson-Nernst-Planck equations are a system of nonlinear di erential equations that describe ow of charged particles in solution. This...
Show moreThe Poisson-Nernst-Planck equations are a system of nonlinear di erential equations that describe ow of charged particles in solution. This dissertation is about the design of numerical schemes to solve this system which preserves global properties exhibited by the system. There are two major advances presented. The rst is the design of schemes that conserve mass globally when the system is coupled with no- ux boundary conditions. Most notably, a scheme using central di erencing and TR-BDF2 achieves second order accuracy in both space and time, while also conserving global mass is presented. The second is the design of a more general scheme that preserves the time-varying properties of the free energy of the system. One such a scheme uses central di erencing in space and trapezoidal integration in time to achieve second order accuracy in both space and time, while also preserving the energy dynamics, but at the cost of requiring positivity of the solution. There is also a discussion of solution methods: the classic Newton iteration scheme is compared with a modi ed Gummel iteration scheme for the purpose of solving the transient equations. The intended application of this work is the modeling of ion channels, and many of the simulations presented use parameters consistent with models of ion channels.
Ph.D. in Applied Mathematics, July 2014
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Title: Planning the 21st Century Urban Farm: From High Rise to Neighborhood (sequence unknown), IPRO 336 - Deliverables
Creator: Bhatti, Talha, Binet, Adrien, Bredau, Jason, Chen, Emily, Davis, Jacob, Gaonkar, Gaurav, Garcia, Raul, Guerrero, Fernando, Gulling, Richard, Kagehiro, Michael, Moshfeghian, Elnaz, Nunez-gimeno, Jose, Phillips, Zachary, Plumb, Isaac, Ryan, Emily, Skaggs, Jake, Sobon, Konrad, Valmores, Travis
Date: 2009-12
Description: The purpose of this IPRO is to establish a strong foundation for the future of urban agriculture. The growing problems regarding the...
Show moreThe purpose of this IPRO is to establish a strong foundation for the future of urban agriculture. The growing problems regarding the traditional methods of agriculture, and the rate of growth of the world population, the team plans to design a method to grow food more efficiently and economically in urban areas. The team is looking at large, industrial warehouse-type buildings that have outlived their primary use, and creating a plan that utilizes these buildings to grow enough food for the surrounding communities.
Sponsorship: John Edel of Bubbly Dynamics, LLC
Deliverables for IPRO 336: Planning the 21st Century Urban Farm: From High Rise to Neighborhood for the fall 2009 semester
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Title: NUMERICAL SINGULARITY ANALYSIS
Creator: Adomaitis, R. A., Cinar, A.
Date: 1991
Publisher: PERGAMON-ELSEVIER SCIENCE LTD
Description: A numerical scheme is presented for classifying the different static bifurcation behaviors exhibited by a nonlinear system in its remaining...
Show moreA numerical scheme is presented for classifying the different static bifurcation behaviors exhibited by a nonlinear system in its remaining parameter space. This numerical technique differs from previously published schemes in that the application of singularity theory is done numerically and requires no explicit differentiations of the system in question. It also does not require the reduction of the mathematical model to a scalar equation. The utility of this multivariable scheme will be demonstrated through an application to a seven PDE tubular packed-bed reactor model.
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