Browsing by Subject "Mathematical model"
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Item Excel model for electric markets : ERCOT(2016-05) Cuevas, Pedro Pablo; Dyer, James S.; Butler, John C.(Clinical associate professor); Hahn, JoeThe effects of changing regulatory and fuel-cost environments have far reaching implications on the ability of electric markets to plan and provide cheap, clean, and reliable electric grids. The current state of the art tools for modeling the regulations and fuel prices requires days to process and access to these tools is also held by a small number licensed users that must also have the training and technical ability to run the model, which limits the study of planning and electricity market design.. This thesis presents an Excel model that simulates the operations of ERCOT over the next fifteen years. Tradeoffs between accuracy, run time, cost, and model complexity will be discussed. The advantages of this model are speed and accessibility, which will allow more users to understand the major implications of policy discussions and scenarios without needing a commercial tool. The model predicts the fuel mix and average market price for 2014 with less than a 1% and 2% error respectively. For 2015, the model predicts the fuel mix with less than a 5% error. Using the current trends assumptions, the model predicts that by 2030 the energy mix will undergo significant changes. Coal generation will drop from 28% to 21%, while gas generation will decline from 48% to 46%. Renewable generation will increase with wind going from 12% to 17% and solar from 0% to 7%. The model also predicts that a carbon tax between $20 and $60 per short ton of CO2, could rise the operational and capital costs of ERCOT in present value terms until 2030 from $75 billion to $218 billion. Finally the model forecasts that the reserve margin in ERCOT will not reach the target of 13.75% in 2020 and that renewable energy addition does not affect this indicator. Even more, the reserve margin is increased when solar energy enters the market.Item Integration of microvascular, interstitial, and lymphatic function to determine the effect of their interaction on interstitial fluid volume(2009-05-15) Dongaonkar, Ranjeet ManoharAlthough the physics of interstitial fluid balance is relatively well understood, clinical options for the treatment of edema, the accumulation of fluid in the interstitium, are limited. Two related reasons for this failure can be identified. First, the processes involved in the transfer of fluid and proteins into the interstitium from the microvasculature, and their transfer out of the interstitium via the lymphatic system, are governed by complex equations that are not amenable to manipulation by physiologists. Second, the fundamental processes involved include complex anatomical structures that are not amenable to characterization by engineers. The dual tools of the batwing model and simplified mathematical modeling can be used to address the main objective: to integrate microvascular, interstitial, and lymphatic function to determine the effect of their interaction on interstitial fluid volume. In order to address this objective and the limitations of the current state of knowledge of the field, three specific aims were achieved. 1) Develop a simple, transparent, and general algebraic approach that predicts interstitial fluid pressure, volume and protein concentration resulting from the interaction of microvascular, interstitial and lymphatic function. These algebraic solutions provide a novel characterization of interstitial fluid pressure as a balance point between the two processes that determine interstitial inflow and outflow. 2) Develop a simple, algebraic formulation of Edemagenic Gain (the change in interstitial fluid volume resulting from changes in effective microvascular driving pressure) in terms of microvascular, interstitial and lymphatic structural parameters. By separating the structural parameters from functional variables, this novel approach indicates how these critical parameters interact to determine the tendency to form edema. 3) To expand the list of known interactions of microvascular, interstitial, and lymphatic functions to include the direct interaction of venular and lymphatic function. Venomotion was found not only to extrinsically pump lymph but also to mechanically trigger intrinsic lymphatic contractions. These three advances together represent a new direction in the field of interstitial fluid balance, and could only be possible by taking an interdisciplinary approach integrating physiology and engineering.Item Mathematical model of the central battery for a major oil producing field(Texas Tech University, 1976-05) Skinner, David RandellNot available.Item Probabilistic modeling of microelectromechanical systems (MEMS)(Texas Tech University, 2002-12) Khandaker, Morshed P. H.Micro-Electro-Mechanical Systems (MEMS) are a fast-developing technology that have a potential to permeate most engineering and medical applications. For this technology to continue expanding, issues regarding the cost of manufacturing and reliability of the devices have to be addressed. To improve the reliability, probabilistic design methodologies are potent in both the modeling and testing of high-performance MEMS. The benefit of probabilistic design approaches is a more rational basis for making design decisions that balance component or system efficiency with reliability or safety. Probabilistic methods are used to assess uncertainties involved in the manufacturing of MEMS devices. Probabilistic methods guide the design of these devices to achieve reliable design in a most efficient way. The objectives of the research work were to formulate and analyze probabilistic failure criteria on a simplified capacitive accelerometer mode. In this respect, comprehensive probabilistic and deterministic analysis was carried out for the selected model. The scope of work is threefold. First, two probabilistic failure criteria will be investigated on the capacitive structure, namely probabilistic clearance failure criterion and probabilistic fracture toughness failure criterion. Second, four kinds of probabilistic analyses for characterization of MEMS will be used: probability of failure, sensitivity analysis, safety index, and probability-based design. Third, three kinds of finite element analyses, namely static, modal and spectral analysis, will be used to see the deterministic response and will be compared with probabilistic resultItem Thermal lensing in ocular media(2009-05) Vincelette, Rebecca Lee; Welch, Ashley J., 1933-; Rockwell, Benjamin A.This research was a collaborative effort between the Air Force Research Laboratory (AFRL) and the University of Texas to examine the laser-tissue interaction of thermal lensing induced by continuous-wave, CW, near-infrared, NIR, laser radiation in the eye and its influence on the formation of a retinal lesion from said radiation. CW NIR laser radiation can lead to a thermal lesion induced on the retina given sufficient power and exposure duration as related to three basic parameters; the percent of transmitted energy to, the optical absorption of, and the size of the laser-beam created at the retina. Thermal lensing is a well-known phenomenon arising from the optical absorption, and subsequent temperature rise, along the path of the propagating beam through a medium. Thermal lensing causes the laser-beam profile delivered to the retina to be time dependent. Analysis of a dual-beam, multidimensional, high-frame rate, confocal imaging system in an artificial eye determined the rate of thermal lensing in aqueous media exposed to 1110, 1130, 1150 and 1318-nm wavelengths was related to the power density created along the optical axis and linear absorption coefficient of the medium. An adaptive optics imaging system was used to record the aberrations induced by the thermal lens at the retina in an artificial eye during steady-state. Though the laser-beam profiles changed over the exposure time, the CW NIR retinal damage thresholds between 1110-1319-nm were determined to follow conventional fitting algorithms which neglected thermal lensing. A first-order mathematical model of thermal lensing was developed by conjoining an ABCD beam propagation method, Beer's law of attenuation, and a solution to the heat-equation with respect to radial diffusion. The model predicted that thermal lensing would be strongest for small (< 4-mm) 1/e² laser-beam diameters input at the corneal plane and weakly transmitted wavelengths where less than 5% of the energy is delivered to the retina. The model predicted thermal lensing would cause the retinal damage threshold for wavelengths above 1300-nm to increase with decreasing beam-diameters delivered to the corneal plane, a behavior which was opposite of equivalent conditions simulated without thermal lensing.