The Dikin-Karmarkar Principle for Steepest Descent

This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/16565Steepest feasible descent methods for inequality constrained optimization problems have commonly been plagued by short steps. The consequence of taking short steps is slow convergence to non-stationary points (zigzagging). In linear programming, both the projective algorithm of Karmarkar (1984) and its affined-variant, originally proposed by Dikin (1967), can be viewed as steepest feasible descent methods. However, both of these algorithms have been demonstrated to be effective and seem to have overcome the problem of short steps. These algorithms share a common norm. It is this choice of norm, in the context of steepest feasible descent, that we refer to as the Dikin-Karmarkar Principle. This research develops mathematical theory to quantify the short step behavior of Euclidean norm steepest feasible descent methods and the avoidance of short steps for steepest feasible descent with respect to the Dikin-Karmarkar norm. While the theory is developed for linear programming problems with only nonnegativity constraints on the variables. Our numerical experimentation demonstrates that this behavior occurs for the more general linear program with equality constraints added. Our numerical results also suggest that taking longer steps is not sufficient to ensure the efficiency of a steepest feasible descent algorithm. The uniform way in which the Dikin-Karmarkar norm treats every boundary is important in obtaining a satisfactory convergence

Theoretical analysis of a novel integrated energy system formed by a microturbine and a exhaust fired single-double effect absorption chiller

Integrated Energy Systems (IES) combine a distributed power generation system (DG) such as a microturbine generator (MTG) or a fuel cell with thermally activated technologies (TAT) such as absorption cooling. This integration maximizes the efficiency of energy use by utilizing on-site most of the waste heat generated by DG, and reduces harmful emissions to the environment. This study investigates the energy and exergy performance of an IES. This system is comprised of an MTG with internal recuperator and a novel absorption cooling cycle. The absorption cycle is a single-double effect exhaust fired cycle, which recuperates the heat exchanged from the MTG exhaust gases using two generators at two different levels of temperature. The selection of the DG element, the TAT element and their internal configurations is based upon a real IES commercial unit that has been tested in the APEP-UCI DG testing facilities in Irvine, California. This unit has an electrical power capacity of 28 kW and a cooling capacity of 14 refrigeration tons (49.2 kW). Inputs for the thermodynamic models developed for the MTG and for the absorption cycle are derived from experimental variables that will be controlled in the testing phase. The MTG model is using empirical correlations for key model parameters (pressure ratio, turbine inlet temperature, etc.) from previous studies in order to predict the observed change in performance with part load operation. The calculated mass flow rate and temperature of the exhaust gases are inputs for the absorption cycle model, together with cooling and chilled water inlet temperatures and flow rates. Heat and mass transferefficiencies along with heat transfer coefficients for the suite of heat exchangers comprising the single-double effect absorption cycle are determined from proprietary testing data provided by the manufacturers

Fuel injector: Air swirl characterization aerothermal modeling, phase 2, volume 1

A well integrated experimental/analytical investigation was conducted to provide benchmark quality relevant to a prefilming type airblast fuel nozzle and its interaction with the combustor dome air swirler. The experimental investigation included a systematic study of both single-phase flows that involved single and twin co-axial jets with and without swirl. A two-component Phase Doppler Particle Analyzer (PDPA) was used to document the interaction of single and co-axial air jets with glass beads that simulate nonevaporating spray and simultaneously avoid the complexities associated with fuel atomization processes and attendant issues about the specification of relevant boundary conditions. The interaction of jets with methanol spray produced by practical airblast nozzle was also documented in the spatial domain of practical interest. Model assessment activities included the use of three turbulence models (k-epsilon, algebraic second moment (ASM), and differential second moment (DSM)) for the carrier phase, deterministic or stochastic Lagrangian treatment of the dispersed phase, and advanced numerical schemes. Although qualitatively good comparison with data was obtained for most of the cases investigated, the model deficiencies in regard to modeled dissipation rate transport equation, single length scale, pressure-strain correlation, and other critical closure issues need to be resolved before one can achieve the degree of accuracy required to analytically design combustion systems

Trends. Warranted Dogmatism against the Closed Mind: Preliminary Look at the Intelligence Agency\u27s (CIA) Groat Case

In this article, the author analyzes the arrest of former CIA employee, Douglas F. Groat

Early home-based recognition of anaemia via general danger signs, in young children, in a malaria endemic community in north-east Tanzania

BACKGROUND: Ethnographic studies from East Africa suggest that cerebral malaria and anaemia are not classified in local knowledge as malaria complications, but as illnesses in their own right. Cerebral malaria 'degedege' has been most researched, in spite of anaemia being a much more frequent complication in infants, and not much is known on how this is interpreted by caretakers. Anaemia is difficult to recognize clinically, even by health workers. METHODS: Ethnographic longitudinal cohort field study for 14 months, with monthly home-visits in families of 63 newborn babies, identified by community census, followed throughout April – November 2003 and during follow-up in April-May 2004. Interviews with care-takers (mostly mothers) and observational studies of infants and social environment were combined with three haemoglobin (Hb) screenings, supplemented with reports from mothers after health facility use. RESULTS: General danger signs, reported by mothers, e.g. infant unable to breast-feed or sit, too weak to be carried on back – besides of more alarming signs such as sleeping all time, loosing consciousness or convulsing – were well associated with actual or evolving moderate to severe anaemia (Hb ≤ 5–8 g/dl). By integrating the local descriptions of danger symptoms and signs, and comparing with actual or evolving low Hb, an algorithm to detect anaemia was developed, with significant sensitivity and specificity. For most danger signs, mothers twice as often took young children to traditional healers for herbal treatment, rather than having their children admitted to hospital. As expected, pallor was more rarely recognized by mothers, or primary reason for treatment seeking. CONCLUSION: Mothers do recognize and respond to symptoms and danger signs related to development of anaemia, the most frequent complication of malaria in young children in malaria endemic areas. Mothers' observations and actions should be reconsidered and integrated in management of childhood illness programmes

Exact Solutions of the Two-Dimensional Discrete Nonlinear Schr\"odinger Equation with Saturable Nonlinearity

We show that the two-dimensional, nonlinear Schr\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero

Examining Differential Item Functioning From A Latent Class Perspective

Current approaches for studying differential item functioning (DIF) using manifest groups are problematic since these groups are treated as homogeneous in nature. Additionally, manifest variables such as sex and ethnicity are proxies for more fundamental differences - educational advantage/disadvantage attributes. A simulation study was conducted to highlight issues arising from the use of standard DIF detection procedures. Results of this study showed that as the amount of overlap between manifest groups and latent classes decreased, so did the power to correctly identify items with DIF. Furthermore, the true magnitude of the DIF was obscured making it increasingly more difficult to eliminate items on that basis. After some problems with manifest group approaches for DIF had been identified, a recovery study was conducted using the WINBUGS software in the analysis of the mixed Rasch model for detecting DIF. In this study the mixed Rasch model also showed a lack of power to detect items with DIF when the sample size was small. However, this approach was able to identify the proportion of and ability distribution for each manifest group within latent classes, thereby providing a mechanism for judging the appropriateness of using manifest variables as proxies for latent ones. Finally, a series of protocols was developed for examining DIF using a latent class approach, and these were used to examine differential item functioning on a test of language proficiency for English language learners. Results showed that 74% of Hispanic and 83% of Asian examinees were in one latent class, meaning any DIF found by comparing manifest groups would be an artifact of a relatively small number of examinees. Examination of the output from the latent class analysis provided potentially important insights into the causes of DIF, however covariates were not predictive of latent class membership

Optimization of Jet Mixing Into a Rich, Reacting Crossflow

Radial jet mixing of pure air into a fuel-rich, reacting crossflow confined to a cylindrical geometry is addressed with a focus on establishing an optimal jet orifice geometry. The purpose of this investigation was to determine the number of round holes that most effectively mixes the jets with the mainstream flow, and thereby minimizes the residence time of near-stoichiometric and unreacted packets. Such a condition might reduce pollutant formation in axially staged, gas turbine combustor systems. Five different configurations consisting of 8, 10, 12, 14, and 18 round holes are reported here. An optimum number of jet orifices is found for a jet-to-mainstream momentum-flux ratio (J) of 57 and a mass-flow ratio (MR) of 2.5. For this condition, the 14-orifice case produces the lowest spatial unmixedness and the most uniformly-distributed species concentrations and temperature profiles at a plane located one duct diameter length from the jet orifice inlet

Jet Mixing in a Reacting Cylindrical Crossflow

This paper addresses the mixing of air jets into the hot, fuel-rich products of a gas turbine primary zone. The mixing, as a result, occurs in a reacting environment with chemical conversion and substantial heat release. The geometry is a crossflow confined in a cylindrical duct with side-wall injection of jets issuing from round orifices. A specially designed reactor, operating on propane, presents a uniform mixture without swirl to mixing modules consisting of 8, 9, 10, and 12 holes at a momentum-flux ratio of 57 and a jet-to-mainstream mass-flow ratio of 2.5. Concentrations of O2, CO2, CO, and HC are obtained upstream, downstream, and within the orifice plane. O2 profiles indicate jet penetration while CO2, CO, and HC profiles depict the extent of reaction. Jet penetration is observed to be a function of the number of orifices and is found to affect the mixing in the reacting system. The results demonstrate that one module (the 12-hole) produces near-optimal penetration defined here as a jet penetration closest to the module half-radius, and hence the best uniform mixture at a plane one duct radius from the orifice leading edge

Influence of Geometry and Flow Variation on Jet Mixing and NO Formation in a Model Staged Combustor Mixer with Eight Orifices

A series of non-reacting parametric experiments was conducted to investigate the effect of geometric and flow variations on mixing of cold jets in an axis-symmetric, heated cross flow. The confined, cylindrical geometries tested represent the quick mix region of a Rich-Burn/Quick-Mix/Lean-Burn (RQL) combustor. The experiments show that orifice geometry and jet to mainstream momentum-flux ratio significantly impact the mixing characteristic of jets in a cylindrical cross stream. A computational code was used to extrapolate the results of the non-reacting experiments to reacting conditions in order to examine the nitric oxide (NO) formation potential of the configurations examined. The results show that the rate of NO formation is highest immediately downstream of the injection plane. For a given momentum-flux ratio, the orifice geometry that mixes effectively in both the immediate vicinity of the injection plane, and in the wall regions at downstream locations, has the potential to produce the lowest NO emissions. The results suggest that further study may not necessarily lead to a universal guideline for designing a low NO mixer. Instead, an assessment of each application may be required to determine the optimum combination of momentum-flux ratio and orifice geometry to minimize NO formation. Experiments at reacting conditions are needed to verify the present results