Epileptic seizures as condensed sleep: an analysis of network dynamics from electroencephalogram signals

Both deepening sleep and evolving epileptic seizures are associated with increasing slow-wave activity. Larger-scale functional networks derived from electroencephalogram indicate that in both transitions dramatic changes of communication between brain areas occur. During seizures these changes seem to be 'condensed', because they evolve more rapidly than during deepening sleep. Here we set out to assess quantitatively functional network dynamics derived from electroencephalogram signals during seizures and normal sleep. Functional networks were derived from electroencephalogram signals from wakefulness, light and deep sleep of 12 volunteers, and from pre-seizure, seizure and post-seizure time periods of 10 patients suffering from focal onset pharmaco-resistant epilepsy. Nodes of the functional network represented electrical signals recorded by single electrodes and were linked if there was non-random cross-correlation between the two corresponding electroencephalogram signals. Network dynamics were then characterized by the evolution of global efficiency, which measures ease of information transmission. Global efficiency was compared with relative delta power. Global efficiency significantly decreased both between light and deep sleep, and between pre-seizure, seizure and post-seizure time periods. The decrease of global efficiency was due to a loss of functional links. While global efficiency decreased significantly, relative delta power increased except between the time periods wakefulness and light sleep, and pre-seizure and seizure. Our results demonstrate that both epileptic seizures and deepening sleep are characterized by dramatic fragmentation of larger-scale functional networks, and further support the similarities between sleep and seizures.

Laser-induced transient grating analysis of dynamics of interaction between sensory rhodopsin II D75N and the HtrII transducer.

The interaction between sensory rhodopsin II (SRII) and its transducer HtrII was studied by the time-resolved laser-induced transient grating method using the D75N mutant of SRII, which exhibits minimal visible light absorption changes during its photocycle, but mediates normal phototaxis responses. Flash-induced transient absorption spectra of transducer-free D75N and D75N joined to 120 amino-acid residues of the N-terminal part of the SRII transducer protein HtrII (DeltaHtrII) showed only one spectrally distinct K-like intermediate in their photocycles, but the transient grating method resolved four intermediates (K(1)-K(4)) distinct in their volumes. D75N bound to HtrII exhibited one additional slower kinetic species, which persists after complete recovery of the initial state as assessed by absorption changes in the UV-visible region. The kinetics indicate a conformationally changed form of the transducer portion (designated Tr*), which persists after the photoreceptor returns to the unphotolyzed state. The largest conformational change in the DeltaHtrII portion was found to cause a DeltaHtrII-dependent increase in volume rising in 8 micros in the K(4) state and a drastic decrease in the diffusion coefficient (D) of K(4) relatively to those of the unphotolyzed state and Tr*. The magnitude of the decrease in D indicates a large structural change, presumably in the solvent-exposed HAMP domain of DeltaHtrII, where rearrangement of interacting molecules in the solvent would substantially change friction between the protein and the solvent.

Revealing regional deforestation dynamics in north-eastern Madagascar - Insights from multi-temporal land cover change analysis

The north-eastern escarpment of Madagascar harbours the island’s last remaining large-scale humid forest massifs surrounded by a small-scale agricultural mosaic. There is high deforestation, commonly thought to be caused by shifting cultivation practiced by local land users to produce upland rice. However, little is known about the dynamics between forest and shifting cultivation systems at a regional level. Our study presents a first attempt to quantify changes in the extent of forest and different agricultural land cover classes, and to identify the main dynamics of land cover change for two intervals, 1995–2005 and 2005–2011. Over the 16-year study period, the speed of forest loss increased, the total area of upland rice production remained almost stable, and the area of irrigated rice fields slightly increased. While our findings seem to confirm a general trend of land use intensification, deforestation through shifting cultivation is still on the rise. Deforestation mostly affects the small forest fragments interspersed in the agricultural mosaic and is slowly leading to a homogenization of the landscape. These findings have important implications for future interventions to slow forest loss in the region, as the processes of agricultural expansion through shifting cultivation versus intensified land use cannot per se be considered mutually exclusive.

Analysis of hand kinematics reveals inter-individual differences in intertemporal decision dynamics

During intertemporal decisions, the preference for smaller, sooner reward over larger-delayed rewards (temporal discounting, TD) exhibits substantial inter-subject variability; however, it is currently unclear what are the mechanisms underlying this apparently idiosyncratic behavior. To answer this question, here we recorded and analyzed mouse movement kinematics during intertemporal choices in a large sample of participants (N = 86). Results revealed a specific pattern of decision dynamics associated with the selection of “immediate” versus “delayed” response alternatives, which well discriminated between a “discounter” versus a “farsighted” behavior—thus representing a reliable behavioral marker of TD preferences. By fitting the Drift Diffusion Model to the data, we showed that differences between discounter and farsighted subjects could be explained in terms of different model parameterizations, corresponding to the use of different choice mechanisms in the two groups. While farsighted subjects were biased toward the “delayed” option, discounter subjects were not correspondingly biased toward the “immediate” option. Rather, as shown by the dynamics of evidence accumulation over time, their behavior was characterized by high choice uncertainty.

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

IDENTIFICATION AND ANALYSIS OF A NOVEL ROLE FOR THE TOUSLED-LIKE KINASE IN REGULATING MITOTIC SPINDLE DYNAMICS

Deregulation of kinase activity is one example of how cells become cancerous by evading evolutionary constraints. The Tousled kinase (Tsl) was initially identified in Arabidopsis thaliana as a developmentally important kinase. There are two mammalian orthologues of Tsl and one orthologue in C. elegans, TLK-1, which is essential for embryonic viability and germ cell development. Depletion of TLK-1 leads to embryonic arrest large, distended nuclei, and ultimately embryonic lethality. Prior to terminal arrest, TLK-1-depleted embryos undergo aberrant mitoses characterized by poor metaphase chromosome alignment, delayed mitotic progression, lagging chromosomes, and supernumerary centrosomes. I discovered an unanticipated requirement for TLK-1 in mitotic spindle assembly and positioning. Normally, in the newly-fertilized zygote (P0) the maternal pronucleus migrates toward the paternal pronucleus at the posterior end of the embryo. After pronuclear meeting, the pronuclear-centrosome complex rotates 90° during centration to align on the anteroposterior axis followed by nuclear envelope breakdown (NEBD). However, in TLK-1-depleted P0 embryos, the centrosome-pronuclear complex rotation is significantly delayed with respect to NEBD and chromosome congression, Additionally, centrosome positions over time in tlk-1(RNAi) early embryos revealed a defect in posterior centrosome positioning during spindle-pronuclear centration, and 4D analysis of centrosome positions and movement in newly fertilized embryos showed aberrant centrosome dynamics in TLK-1-depleted embryos. Several mechanisms contribute to spindle rotation, one of which is the anchoring of astral microtubules to the cell cortex. Attachment of these microtubules to the cortices is thought to confer the necessary stability and forces in order to rotate the centrosome-pronuclear complex in a timely fashion. Analysis of a microtubule end-binding protein revealed that TLK-1-depleted embryos exhibit a more stochastic distribution of microtubule growth toward the cell cortices, and the types of microtubule attachments appear to differ from wild-type embryos. Additionally, fewer astral microtubules are in the vicinity of the cell cortex, thus suggesting that the delayed spindle rotation could be in part due to a lack of appropriate microtubule attachments to the cell cortex. Together with recently published biochemical data revealing the Tousled-like kinases associate with components of the dynein microtubule motor complex in humans, these data suggest that Tousled-like kinases play an important role in mitotic spindle assembly and positioning.

Analysis and visualization of the dynamics of research groups in terms of projects and co-authored publications : A case study of library and information science in Argentina

Objective: The present study offers a novel methodological contribution to the study of the configuration and dynamics of research groups, through a comparative perspective of the projects funded (inputs) and publication co-authorships (output). Method: A combination of bibliometric techniques and social network analysis was applied to a case study: the Departmento de Bibliotecología (DHUBI), Universidad Nacional de La Plata, Argentina, for the period 2000-2009. The results were interpreted statistically and staff members of the department, were interviewed. Results: The method makes it possible to distinguish groups, identify their members and reflect group make-up through an analytical strategy that involves the categorization of actors and the interdisciplinary and national or international projection of the networks that they configure. The integration of these two aspects (input and output) at different points in time over the analyzed period leads to inferences about group profiles and the roles of actors. Conclusions: The methodology presented is conducive to micro-level interpretations in a given area of study, regarding individual researchers or research groups. Because the comparative input-output analysis broadens the base of information and makes it possible to follow up, over time, individual and group trends, it may prove very useful for the management, promotion and evaluation of science

Analysis and visualization of the dynamics of research groups in terms of projects and co-authored publications : A case study of library and information science in Argentina

Objective: The present study offers a novel methodological contribution to the study of the configuration and dynamics of research groups, through a comparative perspective of the projects funded (inputs) and publication co-authorships (output). Method: A combination of bibliometric techniques and social network analysis was applied to a case study: the Departmento de Bibliotecología (DHUBI), Universidad Nacional de La Plata, Argentina, for the period 2000-2009. The results were interpreted statistically and staff members of the department, were interviewed. Results: The method makes it possible to distinguish groups, identify their members and reflect group make-up through an analytical strategy that involves the categorization of actors and the interdisciplinary and national or international projection of the networks that they configure. The integration of these two aspects (input and output) at different points in time over the analyzed period leads to inferences about group profiles and the roles of actors. Conclusions: The methodology presented is conducive to micro-level interpretations in a given area of study, regarding individual researchers or research groups. Because the comparative input-output analysis broadens the base of information and makes it possible to follow up, over time, individual and group trends, it may prove very useful for the management, promotion and evaluation of science

Analysis and visualization of the dynamics of research groups in terms of projects and co-authored publications : A case study of library and information science in Argentina

Objective: The present study offers a novel methodological contribution to the study of the configuration and dynamics of research groups, through a comparative perspective of the projects funded (inputs) and publication co-authorships (output). Method: A combination of bibliometric techniques and social network analysis was applied to a case study: the Departmento de Bibliotecología (DHUBI), Universidad Nacional de La Plata, Argentina, for the period 2000-2009. The results were interpreted statistically and staff members of the department, were interviewed. Results: The method makes it possible to distinguish groups, identify their members and reflect group make-up through an analytical strategy that involves the categorization of actors and the interdisciplinary and national or international projection of the networks that they configure. The integration of these two aspects (input and output) at different points in time over the analyzed period leads to inferences about group profiles and the roles of actors. Conclusions: The methodology presented is conducive to micro-level interpretations in a given area of study, regarding individual researchers or research groups. Because the comparative input-output analysis broadens the base of information and makes it possible to follow up, over time, individual and group trends, it may prove very useful for the management, promotion and evaluation of science

The dynamics of spending and absorption of aid : panel data analysis

In September 1999, the International Monetary Fund (IMF) established the Poverty Reduction and Growth Facility (PRGF) to make the reduction of poverty and the enhancement of economic growth the fundamental objectives of lending operations in its poorest member countries. This paper studies the spending and absorption of aid in PRGF-supported programs, verifies whether the use of aid is programmed to be smoothed over time, and analyzes how considerations about macroeconomic stability influence the programmed use of aid. The paper shows that PRGF-supported programs permit countries to utilize all increases in aid within a few years, showing smoothed use of aid inflows over time. Our results reveal that spending is higher than absorption in both the long-run and short-run use of aid, which is a robust finding of the study. Furthermore, the paper demonstrates that the long-run spending exceeds the injected increase of aid inflows in the economy. In addition, the paper finds that the presence of a PRGF-supported program does not influence the actual absorption or spending of aid.

Analysis of lateral dynamics of railway vehicles on viaducts with coupled models

The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require 3D coupled vehicle-bridge models, and consideration of wheel to rail contact, a phenomenon which is complex and costly to model in detail. We describe here a fully nonlinear coupled model, described in absolute coordinates and incorporated into a commercial finite element framework. Two applications are presented, firstly to a vehicle subject to a strong wind gust traversing a br idge, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle. The second application is to a real viaduct in a high-speed line, with a long continuous deck and tall piers with high lateral compliance. The results show the safety of the traffic as well as the relevance of considering the wind action and the nonlinear response.

An experimental analysis od the stability and the dynamics of asixymmetric liquid bridges between unequal disks

In this paper experimental results related to both stability an the dynamic of a asiximmetric liquid bridge between unequal disk are presented. Experiments have been performed by using a drop tower facility and the response of the liquid bridge to a sudden change of the acceleration level acting on it has bee obtained.

Methods for the analysis of multi-scale cell dynamics from fluorescence microscopy images

La embriogénesis es el proceso mediante el cual una célula se convierte en un ser un vivo. A lo largo de diferentes etapas de desarrollo, la población de células va proliferando a la vez que el embrión va tomando forma y se configura. Esto es posible gracias a la acción de varios procesos genéticos, bioquímicos y mecánicos que interaccionan y se regulan entre ellos formando un sistema complejo que se organiza a diferentes escalas espaciales y temporales. Este proceso ocurre de manera robusta y reproducible, pero también con cierta variabilidad que permite la diversidad de individuos de una misma especie. La aparición de la microscopía de fluorescencia, posible gracias a proteínas fluorescentes que pueden ser adheridas a las cadenas de expresión de las células, y los avances en la física óptica de los microscopios han permitido observar este proceso de embriogénesis in-vivo y generar secuencias de imágenes tridimensionales de alta resolución espacio-temporal. Estas imágenes permiten el estudio de los procesos de desarrollo embrionario con técnicas de análisis de imagen y de datos, reconstruyendo dichos procesos para crear la representación de un embrión digital. Una de las más actuales problemáticas en este campo es entender los procesos mecánicos, de manera aislada y en interacción con otros factores como la expresión genética, para que el embrión se desarrolle. Debido a la complejidad de estos procesos, estos problemas se afrontan mediante diferentes técnicas y escalas específicas donde, a través de experimentos, pueden hacerse y confrontarse hipótesis, obteniendo conclusiones sobre el funcionamiento de los mecanismos estudiados. Esta tesis doctoral se ha enfocado sobre esta problemática intentando mejorar las metodologías del estado del arte y con un objetivo específico: estudiar patrones de deformación que emergen del movimiento organizado de las células durante diferentes estados del desarrollo del embrión, de manera global o en tejidos concretos. Estudios se han centrado en la mecánica en relación con procesos de señalización o interacciones a nivel celular o de tejido. En este trabajo, se propone un esquema para generalizar el estudio del movimiento y las interacciones mecánicas que se desprenden del mismo a diferentes escalas espaciales y temporales. Esto permitiría no sólo estudios locales, si no estudios sistemáticos de las escalas de interacción mecánica dentro de un embrión. Por tanto, el esquema propuesto obvia las causas de generación de movimiento (fuerzas) y se centra en la cuantificación de la cinemática (deformación y esfuerzos) a partir de imágenes de forma no invasiva. Hoy en día las dificultades experimentales y metodológicas y la complejidad de los sistemas biológicos impiden una descripción mecánica completa de manera sistemática. Sin embargo, patrones de deformación muestran el resultado de diferentes factores mecánicos en interacción con otros elementos dando lugar a una organización mecánica, necesaria para el desarrollo, que puede ser cuantificado a partir de la metodología propuesta en esta tesis. La metodología asume un medio continuo descrito de forma Lagrangiana (en función de las trayectorias de puntos materiales que se mueven en el sistema en lugar de puntos espaciales) de la dinámica del movimiento, estimado a partir de las imágenes mediante métodos de seguimiento de células o de técnicas de registro de imagen. Gracias a este esquema es posible describir la deformación instantánea y acumulada respecto a un estado inicial para cualquier dominio del embrión. La aplicación de esta metodología a imágenes 3D + t del pez zebra sirvió para desvelar estructuras mecánicas que tienden a estabilizarse a lo largo del tiempo en dicho embrión, y que se organizan a una escala semejante al del mapa de diferenciación celular y con indicios de correlación con patrones de expresión genética. También se aplicó la metodología al estudio del tejido amnioserosa de la Drosophila (mosca de la fruta) durante el cierre dorsal, obteniendo indicios de un acoplamiento entre escalas subcelulares, celulares y supracelulares, que genera patrones complejos en respuesta a la fuerza generada por los esqueletos de acto-myosina. En definitiva, esta tesis doctoral propone una estrategia novedosa de análisis de la dinámica celular multi-escala que permite cuantificar patrones de manera inmediata y que además ofrece una representación que reconstruye la evolución de los procesos como los ven las células, en lugar de como son observados desde el microscopio. Esta metodología por tanto permite nuevas formas de análisis y comparación de embriones y tejidos durante la embriogénesis a partir de imágenes in-vivo. ABSTRACT The embryogenesis is the process from which a single cell turns into a living organism. Through several stages of development, the cell population proliferates at the same time the embryo shapes and the organs develop gaining their functionality. This is possible through genetic, biochemical and mechanical factors that are involved in a complex interaction of processes organized in different levels and in different spatio-temporal scales. The embryogenesis, through this complexity, develops in a robust and reproducible way, but allowing variability that makes possible the diversity of living specimens. The advances in physics of microscopes and the appearance of fluorescent proteins that can be attached to expression chains, reporting about structural and functional elements of the cell, have enabled for the in-vivo observation of embryogenesis. The imaging process results in sequences of high spatio-temporal resolution 3D+time data of the embryogenesis as a digital representation of the embryos that can be further analyzed, provided new image processing and data analysis techniques are developed. One of the most relevant and challenging lines of research in the field is the quantification of the mechanical factors and processes involved in the shaping process of the embryo and their interactions with other embryogenesis factors such as genetics. Due to the complexity of the processes, studies have focused on specific problems and scales controlled in the experiments, posing and testing hypothesis to gain new biological insight. However, methodologies are often difficult to be exported to study other biological phenomena or specimens. This PhD Thesis is framed within this paradigm of research and tries to propose a systematic methodology to quantify the emergent deformation patterns from the motion estimated in in-vivo images of embryogenesis. Thanks to this strategy it would be possible to quantify not only local mechanisms, but to discover and characterize the scales of mechanical organization within the embryo. The framework focuses on the quantification of the motion kinematics (deformation and strains), neglecting the causes of the motion (forces), from images in a non-invasive way. Experimental and methodological challenges hamper the quantification of exerted forces and the mechanical properties of tissues. However, a descriptive framework of deformation patterns provides valuable insight about the organization and scales of the mechanical interactions, along the embryo development. Such a characterization would help to improve mechanical models and progressively understand the complexity of embryogenesis. This framework relies on a Lagrangian representation of the cell dynamics system based on the trajectories of points moving along the deformation. This approach of analysis enables the reconstruction of the mechanical patterning as experienced by the cells and tissues. Thus, we can build temporal profiles of deformation along stages of development, comprising both the instantaneous events and the cumulative deformation history. The application of this framework to 3D + time data of zebrafish embryogenesis allowed us to discover mechanical profiles that stabilized through time forming structures that organize in a scale comparable to the map of cell differentiation (fate map), and also suggesting correlation with genetic patterns. The framework was also applied to the analysis of the amnioserosa tissue in the drosophila’s dorsal closure, revealing that the oscillatory contraction triggered by the acto-myosin network organized complexly coupling different scales: local force generation foci, cellular morphology control mechanisms and tissue geometrical constraints. In summary, this PhD Thesis proposes a theoretical framework for the analysis of multi-scale cell dynamics that enables to quantify automatically mechanical patterns and also offers a new representation of the embryo dynamics as experienced by cells instead of how the microscope captures instantaneously the processes. Therefore, this framework enables for new strategies of quantitative analysis and comparison between embryos and tissues during embryogenesis from in-vivo images.

Asymptotic and computational analysis of mistuning effects on the dynamics of bladed disks

Es bien conocido que las pequeñas imperfecciones existentes en los álabes de un rótor de turbomaquinaria (conocidas como “mistuning”) pueden causar un aumento considerable de la amplitud de vibración de la respuesta forzada y, por el contrario, tienen típicamente un efecto beneficioso en el flameo del rótor. Para entender estos efectos se pueden llevar a cabo estudios numéricos del problema aeroelástico completo. Sin embargo, el cálculo de “mistuning” usando modelos de alta resolución es una tarea difícil de realizar, ya que los modelos necesarios para describir de manera precisa el componente de turbomáquina (por ejemplo rotor) tienen, necesariamente, un número muy elevado de grados de libertad, y, además, es necesario hacer un estudio estadístico para poder explorar apropiadamente las distribuciones posibles de “mistuning”, que tienen una naturaleza aleatoria. Diferentes modelos de orden reducido han sido desarrollados en los últimos años para superar este inconveniente. Uno de estos modelos, llamado “Asymptotic Mistuning Model (AMM)”, se deriva de la formulación completa usando técnicas de perturbaciones que se basan en que el “mistuning” es pequeño. El AMM retiene sólo los modos relevantes para describir el efecto del mistuning, y permite identificar los mecanismos clave involucrados en la amplificación de la respuesta forzada y en la estabilización del flameo. En este trabajo, el AMM se usa para estudiar el efecto del “mistuning” de la estructura y de la amortiguación sobre la amplitud de la respuesta forzada. Los resultados obtenidos son validados usando modelos simplificados del rotor y también otros de alta definición. Además, en el marco del proyecto europeo FP7 "Flutter-Free Turbomachinery Blades (FUTURE)", el AMM se aplica para diseñar distribuciones de “mistuning” intencional: (i) una que anula y (ii) otra que reduce a la mitad la amplitud del flameo de un rotor inestable; y las distribuciones obtenidas se validan experimentalmente. Por último, la capacidad de AMM para predecir el comportamiento de flameo de rotores con “mistuning” se comprueba usando resultados de CFD detallados. Abstract It is well known that the small imperfections of the individual blades in a turbomachinery rotor (known as “mistuning”) can cause a substantial increase of the forced response vibration amplitude, and it also typically results in an improvement of the flutter vibration characteristics of the rotor. The understanding of these phenomena can be attempted just by performing numerical simulations of the complete aeroelastic problem. However, the computation of mistuning cases using high fidelity models is a formidable task, because a detailed model of the whole rotor has to be considered, and a statistical study has to be carried out in order to properly explore the effect of the random mistuning distributions. Many reduced order models have been developed in recent years to overcome this barrier. One of these models, called the Asymptotic Mistuning Model (AMM), is systematically derived from the complete bladed disk formulation using a consistent perturbative procedure that exploits the smallness of mistuning to simplify the problem. The AMM retains only the essential system modes that are involved in the mistuning effect, and it allows to identify the key mechanisms of the amplification of the forced response amplitude and the flutter stabilization. In this work, AMM methodolgy is used to study the effect of structural and damping mistuning on the forced response vibration amplitude. The obtained results are verified using a one degree of freedom model of a rotor, and also high fidelity models of the complete rotor. The AMM is also applied, in the frame of the European FP7 project “Flutter-Free Turbomachinery Blades (FUTURE)”, to design two intentional mistuning patterns: (i) one to complete stabilize an unstable rotor, and (ii) other to approximately reduce by half its flutter amplitude. The designed patterns are validated experimentally. Finally, the ability of AMM to predict the flutter behavior of mistuned rotors is checked against numerical, high fidelity CFD results.