Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

Quantum hydrodynamic models for semiconductors with and without collisions

In dieser Arbeit werden Quantum-Hydrodynamische (QHD) Modelle betrachtet, die ihren Einsatz besonders in der Modellierung von Halbleiterbauteilen finden. Das QHD Modell besteht aus den Erhaltungsgleichungen für die Teilchendichte, das Momentum und die Energiedichte, inklusive der Quanten-Korrekturen durch das Bohmsche Potential. Zu Beginn wird eine Übersicht über die bekannten Ergebnisse der QHD Modelle unter Vernachlässigung von Kollisionseffekten gegeben, die aus ein­em Schrödinger-System für den gemischten-Zustand oder aus der Wigner-Glei­chung hergeleitet werden können. Nach der Reformulierung der eindimensionalen QHD Gleichungen mit linearem Potential als stationäre Schrö­din­ger-Gleichung werden die semianalytischen Fassungen der QHD Gleichungen für die Gleichspannungs-Kurve betrachtet. Weiterhin werden die viskosen Stabilisierungen des QHD Modells be­rück­sich­tigt, sowie die von Gardner vorgeschlagene numerische Viskosität für das {sf upwind} Finite-Differenzen Schema berechnet. Im Weiteren wird das viskose QHD Modell aus der Wigner-Glei­chung mit Fokker-Planck Kollisions-Ope­ra­tor hergeleitet. Dieses Modell enthält die physikalische Viskosität, die durch den Kollision-Operator eingeführt wird. Die Existenz der Lösungen (mit strikt positiver Teilchendichte) für das isotherme, stationäre, eindimensionale, viskose Modell für allgemeine Daten und nichthomogene Randbedingungen wird gezeigt. Die dafür notwendigen Abschätzungen hängen von der Viskosität ab und erlauben daher den Grenzübergang zum nicht-viskosen Fall nicht. Numerische Simulationen der Resonanz-Tunneldiode modelliert mit dem nichtisothermen, stationären, eindimensionalen, viskosen QHD Modell zeigen den Einfluss der Viskosität auf die Lösung. Unter Verwendung des von Degond und Ringhofer entwickelten Quanten-Entropie-Minimierungs-Verfahren werden die allgemeinen QHD-Gleichungen aus der Wigner-Boltzmann-Gleichung mit dem BGK-Kollisions-Operator hergeleitet. Die Herleitung basiert auf der vorsichtige Entwicklung des Quanten-Max­well­ians in Potenzen der skalierten Plankschen Konstante. Das so erhaltene Modell enthält auch vertex-Terme und dispersive Terme für die Ge­schwin­dig­keit. Dadurch bleibt die Gleichspannungs-Kurve für die Re­so­nanz-Tunnel­diode unter Verwendung des allgemeinen QHD Modells in einer Dimension numerisch erhalten. Die Ergebnisse zeigen, dass der dispersive Ge­schwin­dig­keits-Term die Lösung des Systems stabilisiert.

Numerical coupling of thermal-electric network models and energy-transport equations including optoelectronic semiconductor devices

In this work the numerical coupling of thermal and electric network models with model equations for optoelectronic semiconductor devices is presented. Modified nodal analysis (MNA) is applied to model electric networks. Thermal effects are modeled by an accompanying thermal network. Semiconductor devices are modeled by the energy-transport model, that allows for thermal effects. The energy-transport model is expandend to a model for optoelectronic semiconductor devices. The temperature of the crystal lattice of the semiconductor devices is modeled by the heat flow eqaution. The corresponding heat source term is derived under thermodynamical and phenomenological considerations of energy fluxes. The energy-transport model is coupled directly into the network equations and the heat flow equation for the lattice temperature is coupled directly into the accompanying thermal network. The coupled thermal-electric network-device model results in a system of partial differential-algebraic equations (PDAE). Numerical examples are presented for the coupling of network- and one-dimensional semiconductor equations. Hybridized mixed finite elements are applied for the space discretization of the semiconductor equations. Backward difference formluas are applied for time discretization. Thus, positivity of charge carrier densities and continuity of the current density is guaranteed even for the coupled model.

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

The dynamics of early-type galaxies as a tool to understand their hot coronae and their IMF

Dynamical models of galaxies are a powerful tool to study and understand several astrophysical problems related to galaxy formation and evolution. This thesis is focussed on a particular type of dynamical models, that are widely used in literature, and are based on the solution of the Jeans equations. By means of a numerical Jeans solver code, developed on purpose and able to build state-of-the-art advanced axisymmetric galaxy models, two of the main currently investigated issues in the field of research of early-type galaxies (ETGs) are addressed. The first topic concerns the hot and X-ray emitting gaseous coronae that surround ETGs. The main goal is to explain why flat and rotating galaxies generally exhibit haloes with lower gas temperatures and luminosities with respect to rounder and velocity dispersion supported systems. The second astrophysical problem addressed concerns instead the stellar initial mass function (IMF) of ETGs. Nowadays, this is a very controversial issue due to a growing number of works on ETGs, based on different and independent techniques, that show evidences of a systematic variation of the IMF normalization as a function of galaxy velocity dispersion or mass. These studies are changing the previous opinion that the IMF of ETGs was the same as that of spiral galaxies, and hence universal throughout the whole large family of galaxies.

Direct and inverse transient eddy current problems

Die vorliegende Arbeit behandelt Vorwärts- sowie Rückwärtstheorie transienter Wirbelstromprobleme. Transiente Anregungsströme induzieren elektromagnetische Felder, welche sogenannte Wirbelströme in leitfähigen Objekten erzeugen. Im Falle von sich langsam ändernden Feldern kann diese Wechselwirkung durch die Wirbelstromgleichung, einer Approximation an die Maxwell-Gleichungen, beschrieben werden. Diese ist eine lineare partielle Differentialgleichung mit nicht-glatten Koeffizientenfunktionen von gemischt parabolisch-elliptischem Typ. Das Vorwärtsproblem besteht darin, zu gegebener Anregung sowie den umgebungsbeschreibenden Koeffizientenfunktionen das elektrische Feld als distributionelle Lösung der Gleichung zu bestimmen. Umgekehrt können die Felder mit Messspulen gemessen werden. Das Ziel des Rückwärtsproblems ist es, aus diesen Messungen Informationen über leitfähige Objekte, also über die Koeffizientenfunktion, die diese beschreibt, zu gewinnen. In dieser Arbeit wird eine variationelle Lösungstheorie vorgestellt und die Wohlgestelltheit der Gleichung diskutiert. Darauf aufbauend wird das Verhalten der Lösung für verschwindende Leitfähigkeit studiert und die Linearisierbarkeit der Gleichung ohne leitfähiges Objekt in Richtung des Auftauchens eines leitfähigen Objektes gezeigt. Zur Regularisierung der Gleichung werden Modifikationen vorgeschlagen, welche ein voll parabolisches bzw. elliptisches Problem liefern. Diese werden verifiziert, indem die Konvergenz der Lösungen gezeigt wird. Zuletzt wird gezeigt, dass unter der Annahme von sonst homogenen Umgebungsparametern leitfähige Objekte eindeutig durch die Messungen lokalisiert werden können. Hierzu werden die Linear Sampling Methode sowie die Faktorisierungsmethode angewendet.

Bianchi type II cosmology in Hořava–Lifshitz gravity

In this work a Bianchi type II space-time within the framework of projectable Horava Lifshitz gravity was investigated; the resulting field equations in the infrared limit λ = 1 were analyzed qualitatively. We have found the analytical solutions for a toy model in which only the higher curvature terms cubic in the spatial Ricci tensor are considered. The resulting behavior is still described by a transition among two Kasner epochs, but we have found a different transformation law of the Kasner exponents with respect to the one of Einstein's general relativity.

Audiological results with Baha in conductive and mixed hearing loss

The level of improvement in the audiological results of Baha(®) users mainly depends on the patient's preoperative hearing thresholds and the type of Baha sound processor used. This investigation shows correlations between the preoperative hearing threshold and postoperative aided thresholds and audiological results in speech understanding in quiet of 84 Baha users with unilateral conductive hearing loss, bilateral conductive hearing loss and bilateral mixed hearing loss. Secondly, speech understanding in noise of 26 Baha users with different Baha sound processors (Compact, Divino, and BP100) is investigated. Linear regression between aided sound field thresholds and bone conduction (BC) thresholds of the better ear shows highest correlation coefficients and the steepest slope. Differences between better BC thresholds and aided sound field thresholds are smallest for mid-frequencies (1 and 2 kHz) and become larger at 0.5 and 4 kHz. For Baha users, the gain in speech recognition in quiet can be expected to lie in the order of magnitude of the gain in their hearing threshold. Compared to its predecessor sound processors Baha(®) Compact and Baha(®) Divino, Baha(®) BP100 improves speech understanding in noise significantly by +0.9 to +4.6 dB signal-to-noise ratio, depending on the setting and the use of directional microphone. For Baha users with unilateral and bilateral conductive hearing loss and bilateral mixed hearing loss, audiological results in aided sound field thresholds can be estimated with the better BC hearing threshold. The benefit in speech understanding in quiet can be expected to be similar to the gain in their sound field hearing threshold. The most recent technology of Baha sound processor improves speech understanding in noise by an order of magnitude that is well perceived by users and which can be very useful in everyday life.

[Sarcomas and mixed mesodermal tumors of the uterus]

Malignant mesodermal tumors of the uterus are an inhomogenous group of uterine malignancies with different pathogenesis, clinical presentation and prognosis. These rare tumors represent approximately 1 % of all uterine malignancies. The aggressive carcinosarcomas or mixed muellerian tumors are defined by mixed malignant epithelial and malignant mesodermal histopathology and are of the same precursor cell origin like endometrial cancer. Thus, carcinosarcomas were reclassified by the FIGO as an aggressive type of endometrial cancer and treated like type II endometrial cancer. Adenosarcomas are also mixed tumors with benign epithelial proliferation and malignant mesodermal cell growth, have a good prognosis and represent less than 5 % of all mesodermal uterine malignancies. Besides carcinosarcomas, the pure mesodermal leiomyosarcomas are the most common mesodermal malignancies. Patients with leiomyosarcamos are usually perimenopausal, and although more than half of the patients present with symptoms, diagnosis occurs incidentally in most cases in final histopathologic workup of an excised putative myoma or uterus. Adequate anamnesis, gynecologic examination and careful imaging by transvaginal ultrasound in the preoperative setting might hint to correct differential diagnosis in many cases. Overall the prognosis of uterine leiomyomas is poor. Malignancies of the endometrial stroma are very rare and divided in two subgroups, the mostly estrogen receptor positive endometrial stromal sarcoma, which occur preferably in premenopausal women and show a favorable prognosis, and the very aggressive undifferentiated endometrial sarcomas. The more rare undifferentiated endometrial sarcomas occur in postmenopausal women and most patients die in the first two years after diagnosis. Risk stratification of preoperative differential diagnosis requires improvements and the correct histopathologic workup of mesodermal uterine malignancies is still a challenge for pathologists.

Deletion of P399_E401 in NADPH cytochrome P450 oxidoreductase results in partial mixed oxidase deficiency

P450 oxidoreductase (POR) is the electron donor for all microsomal P450s including steroidogenic enzymes CYP17A1, CYP19A1 and CYP21A2. We found a novel POR mutation P399_E401del in two unrelated Turkish patients with 46,XX disorder of sexual development. Recombinant POR proteins were produced in yeast and tested for their ability to support steroid metabolizing P450 activities. In comparison to wild-type POR, the P399_E401del protein was found to decrease catalytic efficiency of 21-hydroxylation of progesterone by 68%, 17α-hydroxylation of progesterone by 76%, 17,20-lyase action on 17OH-pregnenolone by 69%, aromatization of androstenedione by 85% and cytochrome c reduction activity by 80%. Protein structure analysis of the three amino acid deletion P399_E401 revealed reduced stability and flexibility of the mutant. In conclusion, P399_E401del is a novel mutation in POR that provides valuable genotype-phenotype and structure-function correlation for mutations in a different region of POR compared to previous studies. Characterization of P399_E401del provides further insight into specificity of different P450s for interaction with POR as well as nature of metabolic disruptions caused by more pronounced effect on specific P450s like CYP17A1 and aromatase.

Coping personality type and environmental enrichment affect aggression at weaning in pigs

This study investigated the effects of different environmental treatments and personality types on aggression at mixing of newly weaned domestic piglets. From birth to weaning, 16 litters were housed with their dams in either barren (B) or larger, substrate-enriched (E) environments. At 15 days old, piglets were classified as 'high' (HR) or low resistant' (LR) in a manual restraint test (backtest), which is thought to identify proactive (HR) and reactive (LR) stress coping strategies that may reflect different personality types. At 30 days old, 128 piglets were weaned, relocated and mixed into 32 pens comprising two HR and two LR unfamiliar pigs, balanced for sex and weaning weight. Eight B and eight E groups changed environmental condition whereas the others remained in the same type of environment. Number and duration of fights. fight outcomes and unilateral fighting were scored for 5 h post-mixing and skin lesions were counted before and 5 h, 1 day and 2 days after mixing. On the day following weaning, fighting and also exploratory and oral manipulative behaviours were measured for 6 h. Generalized Linear Mixed Model analyses suggested interactions between pre-weaning environment, post-weaning environment and personality type. Overall, pre-weaning E pigs had longer fights at weaning and mixing (P=0.01) and fought for longer on the next day (P=0.02) than pre-weaning B pigs, and inflicted more skin lesions (P=0.02). Post-weaning enrichment did not affect fighting at mixing but reduced the time spent fighting the next day (P=0.03). Personality had subtle and environment-dependent effects on fighting, and influenced the "structure" rather than the amount of aggressive behaviour. HR pigs, for instance, bullied (i.e. chased surrendering pigs) more often (P=0.009) and their fighting behaviour was less affected by their relative body weight than that of LR pigs. Post-weaning E pigs showed relatively higher levels of exploratory behaviour (P=0.02) and less oral manipulative behaviour (P=0.04) than post-weaning B pigs. In particular, switching from a good quality environment (E) to a worse quality one (B) at weaning decreased exploratory behaviour on the next day, especially for LR pigs, who also tended to fight with and orally manipulate their pen mates more in that condition, and seemed to be more affected by a deterioration of the environment. Overall, pre-weaning enrichment increased aggression after weaning whereas post-weaning enrichment reduced it, and personality type related to some aspects of fighting behaviour. (C) 2011 Elsevier B.V. All rights reserved.

Vaccination with the recombinant chimeric antigen recNcMIC3-1-R induces a non-protective Th2-type immune response in the pregnant mouse model for N. caninum infection

The major route of transmission of Neospora caninum in cattle is transplacentally from an infected cow to its progeny. Therefore, a vaccine should be able to prevent both the horizontal transmission from contaminated food or water and the vertical transmission. We have previously shown that a chimeric vaccine composed of predicted immunogenic epitopes of NcMIC3, NcMIC1 and NcROP2 (recNcMIC3-1-R) significantly reduced the cerebral infection in BALB/c mice. In this study, mice were first vaccinated, then mated and pregnant mice were challenged with 2×10(6)N. caninum tachyzoites at day 7-9 of pregnancy. Partial protection was only observed in the mice vaccinated with a tachyzoite crude protein extract but no protection against vertical transmission or cerebral infection in the dams was observed in the group vaccinated with recNcMIC3-1-R. Serological and cytokine analysis showed an overall lower cytokine level in sera associated with a dominant IL-4 expression and high IgG1 titers. Thus, the Th2-type immune response observed in the pregnant mice was not protective against experimental neosporosis, in contrary to the mixed Th1-/Th2-type immune response observed in the non-pregnant mouse model. These results demonstrate that the immunomodulation that occurs during pregnancy was not favorable for the protection against N. caninum infection conferred by vaccination with recNcMIC3-1-R.

rCBF in hemorrhagic, non-hemorrhagic and mixed contusions after severe head injury and its effect on perilesional cerebral blood flow

Intracerebral contusions can lead to regional ischemia caused by extensive release of excitotoxic aminoacids leading to increased cytotoxic brain edema and raised intracranial pressure. rCBF measurements might provide further information about the risk of ischemia within and around contusions. Therefore, the aim of the presented study was to compare the intra- and perilesional rCBF of hemorrhagic, non-hemorrhagic and mixed intracerebral contusions. In 44 patients, 60 stable Xenon-enhanced CT CBF-studies were performed (EtCO2 30 +/- 4 mmHg SD), initially 29 hours (39 studies) and subsequent 95 hours after injury (21 studies). All lesions were classified according to localization and lesion type using CT/MRI scans. The rCBF was calculated within and 1-cm adjacent to each lesion in CT-isodens brain. The rCBF within all contusions (n = 100) of 29 +/- 11 ml/100 g/min was significantly lower (p < 0.0001, Mann-Whitney U) compared to perilesional rCBF of 44 +/- 12 ml/100 g/min and intra/perilesional correlation was 0.4 (p < 0.0005). Hemorrhagic contusions showed an intra/perilesional rCBF of 31 +/- 11/44 +/- 13 ml/100 g/min (p < 0.005), non-hemorrhagic contusions 35 +/- 13/46 +/- 10 ml/100 g/min (p < 0.01). rCBF in mixed contusions (25 +/- 9/44 +/- 12 ml/100 g/min, p < 0.0001) was significantly lower compared to hemorrhagic and non-hemorrhagic contusions (p < 0.02). Intracontusional rCBF is significantly reduced to 29 +/- 11 ml/100 g/min but reduced below ischemic levels of 18 ml/100 g/min in only 16% of all contusions. Perilesional CBF in CT normal appearing brain closed to contusions is not critically reduced. Further differentiation of contusions demonstrates significantly lower rCBF in mixed contusions (defined by both hyper- and hypodense areas in the CT-scan) compared to hemorrhagic and non-hemorrhagic contusions. Mixed contusions may evolve from hemorrhagic contusions with secondary increased perilesional cytotoxic brain edema leading to reduced cerebral blood flow and altered brain metabolism. Therefore, the treatment of ICP might be individually modified by the measurement of intra- and pericontusional cerebral blood.

Inhibition of L-type amino acid transport with non-physiological amino acids in the Pahenu2 mouse model of phenylketonuria

Phenylketonuria, an autosomal recessive Mendelian disorder, is one of the most common inborn errors of metabolism. Although currently treated by diet, many suboptimal outcomes occur for patients. Neuropathological outcomes include cognitive loss, white matter abnormalities, and hypo- or demyelination, resulting from high concentrations and/or fluctuating levels of phenylalanine. High phenylalanine can also result in competitive exclusion of other large neutral amino acids from the brain, including tyrosine and tryptophan (essential precursors of dopamine and serotonin). This competition occurs at the blood brain barrier, where the L-type amino acid transporter, LAT1, selectively facilitates entry of large neutral amino acids. The hypothesis of these studies is that certain non-physiological amino acids (NPAA; DL-norleucine (NL), 2-aminonorbornane (NB; 2-aminobicyclo-(2,1,1)-heptane-2-carboxylic acid), α-aminoisobutyrate (AIB), and α-methyl-aminoisobutyrate (MAIB)) would competitively inhibit LAT1 transport of phenylalanine (Phe) at the blood-brain barrier interface. To test this hypothesis, Pah-/- mice (n=5, mixed gender; Pah+/-(n=5) as controls) were fed either 5% NL, 0.5% NB, 5% AIB or 3% MAIB (w/w 18% protein mouse chow) for 3 weeks. Outcome measurements included food intake, body weight, brain LNAAs, and brain monoamines measured via LCMS/MS or HPLC. Brain Phe values at sacrifice were significantly reduced for NL, NB, and MAIB, verifying the hypothesis that these NPAAs could inhibit Phe trafficking into the brain. However, concomitant reductions in tyrosine and methionine occurred at the concentrations employed. Blood Phe levels were not altered indicating no effect of NPAA competitors in the gut. Brain NL and NB levels, measured with HPLC, verified both uptake and transport of NPAAs. Although believed predominantly unmetabolized, NL feeding significantly increased blood urea nitrogen. Pah-/-disturbances of monoamine metabolism were exacerbated by NPAA intervention, primarily with NB (the prototypical LAT inhibitor). To achieve the overarching goal of using NPAAs to stabilize Phe transport levels into the brain, a specific Phe-reducing combination and concentration of NPAAs must be found. Our studies represent the first in vivo use of NL, NB and MAIB in Pah-/- mice, and provide proof-of-principle for further characterization of these LAT inhibitors. Our data is the first to document an effect of MAIB, a specific system A transport inhibitor, on large neutral amino acid transport.

Characterization of a Coal Fly Ash-Cement Slurry by the Absolute Foam Index

This dissertation established a standard foam index: the absolute foam index test. This test characterized a wide range of coal fly ash by the absolute volume of air-entraining admixture (AEA) necessary to produce a 15-second metastable foam in a coal fly ash-cement slurry in a specified time. The absolute foam index test was used to characterize fly ash samples having loss on ignition (LOI) values that ranged from 0.17 to 23.3 %wt. The absolute foam index characterized the fly ash samples by absolute volume of AEA, defined as the amount of undiluted AEA solution added to obtain a 15-minute endpoint signified by 15-second metastable foam. Results were compared from several foam index test time trials that used different initial test concentrations to reach termination at selected times. Based on the coefficient of variation (CV), a 15-minute endpoint, with limits of 12 to 18 minutes was chosen. Various initial test concentrations were used to accomplish consistent contact times and concentration gradients for the 15-minute test endpoint for the fly ash samples. A set of four standard concentrations for the absolute foam index test were defined by regression analyses and a procedure simplifying the test process. The set of standard concentrations for the absolute foam index test was determined by analyzing experimental results of 80 tests on coal fly ashes with loss on ignition (LOI) values ranging from 0.39 to 23.3 wt.%. A regression analysis informed selection of four concentrations (2, 6, 10, and 15 vol.% AEA) that are expected to accommodate fly ashes with 0.39 to 23.3 wt.% LOI, depending on the AEA type. Higher concentrations should be used for high-LOI fly ash when necessary. A procedure developed using these standard concentrations is expected to require only 1-3 trials to meet specified endpoint criteria for most fly ashes. The AEA solution concentration that achieved the metastable foam in the foam index test was compared to the AEA equilibrium concentration obtained from the direct adsorption isotherm test with the same fly ash. The results showed that the AEA concentration that satisfied the absolute foam index test was much less than the equilibrium concentration. This indicated that the absolute foam index test was not at or near equilibrium. Rather, it was a dynamic test where the time of the test played an important role in the results. Even though the absolute foam index was not an equilibrium condition, a correlation was made between the absolute foam index and adsorption isotherms. Equilibrium isotherm equations obtained from direct isotherm tests were used to calculate the equilibrium concentrations and capacities of fly ash from 0.17 to 10.5% LOI. The results showed that the calculated fly ash capacity was much less than capacities obtained from isotherm tests that were conducted with higher initial concentrations. This indicated that the absolute foam index was not equilibrium. Rather, the test is dynamic where the time of the test played an important role in the results. Even though the absolute foam index was not an equilibrium condition, a correlation was made between the absolute foam index and adsorption isotherms for fly ash of 0.17 to 10.5% LOI. Several batches of mortars were mixed for the same fly ash type increasing only the AEA concentration (dosage) in each subsequent batch. Mortar air test results for each batch showed for each increase in AEA concentration, air contents increased until a point where the next increase in AEA concentration resulted in no increase in air content. This was maximum air content that could be achieved by the particular mortar system; the system reached its air capacity at the saturation limit. This concentration of AEA was compared to the critical micelle concentration (CMC) for the AEA and the absolute foam index.