Variable-density jet flows induced by concentrated sources of momentum and energy

The planar and axisymmetric variable-density flows induced in a quiescent gas by a concentrated source of momentum that is simultaneously either a source or a sink of energy are investigated for application to the description of the velocity and temperature far fields in laminar gaseous jets with either large or small values of the initial jet-to-ambient temperature ratio. The source fluxes of momentum and heat are used to construct the characteristic scales of velocity and length in the region where the density differences are of the order of the ambient density, which is slender for the large values of the Reynolds number considered herein. The problem reduces to the integration of the dimensionless boundary-layer conservation equations, giving a solution that depends on the gas transport properties but is otherwise free of parameters. The boundary conditions at the jet exit for integration are obtained by analysing the self-similar flow that appears near the heat source in planar and axisymmetric configurations and also near the heat sink in the planar case. Numerical integrations of the boundary-layer equations with these conditions give solutions that describe accurately the velocity and temperature fields of very hot planar and round jets and also of very cold plane jets in the far field region where the density and temperature differences are comparable to the ambient values. Simple scaling arguments indicate that the point source description does not apply, however, to cold round jets, whose far field region is not large compared with the jet development region, as verified by numerical integrations

A Special Perturbation Method in Orbital Dynamics

Bead models are used in dynamical simulation of tethers. These models discretize a cable using beads distributed along its length. The time evolution is obtained nu- merically. Typically the number of particles ranges between 5 and 50, depending on the required accuracy. Sometimes the simulation is extended over long periods (several years). The complex interactions between the cable and its spatial environment require to optimize the propagators —both in runtime and precisión that constitute the central core of the process. The special perturbation method treated on this article conjugates simpleness of computer implementation, speediness and precision, and is capable to propagate the orbit of whichever material particle. The paper describes the evolution of some orbital elements, which are constants in a non-perturbed problem, but which evolve in the time scale imposed by the perturbation. It can be used with any kind of orbit and it is free of sin- gularities related to small inclination and/or small eccentricity. The use of Euler parameters makes it robust.

Global research alliance modelling platform (GRAMP): an open web platform for modelling greenhouse gas emissions from agro-ecosystems

Carbon (C) and nitrogen (N) process-based models are important tools for estimating and reporting greenhouse gas emissions and changes in soil C stocks. There is a need for continuous evaluation, development and adaptation of these models to improve scientific understanding, national inventories and assessment of mitigation options across the world. To date, much of the information needed to describe different processes like transpiration, photosynthesis, plant growth and maintenance, above and below ground carbon dynamics, decomposition and nitrogen mineralization. In ecosystem models remains inaccessible to the wider community, being stored within model computer source code, or held internally by modelling teams. Here we describe the Global Research Alliance Modelling Platform (GRAMP), a web-based modelling platform to link researchers with appropriate datasets, models and training material. It will provide access to model source code and an interactive platform for researchers to form a consensus on existing methods, and to synthesize new ideas, which will help to advance progress in this area. The platform will eventually support a variety of models, but to trial the platform and test the architecture and functionality, it was piloted with variants of the DNDC model. The intention is to form a worldwide collaborative network (a virtual laboratory) via an interactive website with access to models and best practice guidelines; appropriate datasets for testing, calibrating and evaluating models; on-line tutorials and links to modelling and data provider research groups, and their associated publications. A graphical user interface has been designed to view the model development tree and access all of the above functions.

Flight dynamics and stability of kites in steady and unsteady wind conditions

The flight dynamics and stability of a kite with a single main line flying in steady and unsteady wind conditions are discussed. A simple dynamic model with five degrees of freedom is derived with the aid of Lagrangian formulation, which explicitly avoids any constraint force in the equations of motion. The longitudinal and lateral–directional modes and stability of the steady flight under constant wind conditions are analyzed by using both numerical and analytical methods. Taking advantage of the appearance of small dimensionless parameters in the model, useful analytical formulas for stable-designed kites are found. Under nonsteady wind-velocity conditions, the equilibrium state disappears and periodic orbits occur. The kite stability and an interesting resonance phenomenon are explored with the aid of a numerical method based on Floquet theory.

Permanent deformation estimates of dynamic equipment foundations: Application to a gas turbine in granular soils

Permanent displacements of a gas turbine founded on a fine, poorly graded, and medium density sand are studied. The amplitudes and modes of vibration are computed using Barkan´s formulation, and the “High-Cycle Accumulation” (HCA) model is employed to account for accumulated deformations due to the high number of cycles. The methodology is simple: it can be easily incorporated into standard mathematical software, and HCA model parameters can be estimated based on granulometry and index properties. Special attention is devoted to ‘transient’ situations at equipment´s start-up, during which a range of frequencies – including frequencies that could be similar to the natural frequencies of the ground – is traversed. Results show that such transient situations could be more restrictive than stationary situations corresponding to normal operation. Therefore, checking the stationary situation only might not be enough, and studying the influence of transient situations on computed permanent displacements is needed to produce a proper foundation design

Long-term dynamics of fast rotating tethers around planetary satellites

We derive a semi-analytic formulation that enables the study of the long-term dynamics of fast-rotating inert tethers around planetary satellites. These equations take into account the coupling between the translational and rotational motion, which has a non-negligible impact on the dynamics, as the orbital motion of the tether center of mass strongly depends on the tether plane of rotation and its spin rate, and vice-versa. We use these governing equations to explore the effects of this coupling on the dynamics, the lifetime of frozen orbits and the precession of the plane of rotation of the tether.

The Proper Generalized Decomposition With Application In Problems Of Dynamics

In this paper we address the new reduction method called Proper Generalized Decomposition (PGD) which is a discretization technique based on the use of separated representation of the unknown fields, specially well suited for solving multidimensional parametric equations. In this case, it is applied to the solution of dynamics problems. We will focus on the dynamic analysis of an one-dimensional rod with a unit harmonic load of frequency (ω) applied at a point of interest. In what follows, we will present the application of the methodology PGD to the problem in order to approximate the displacement field as the sum of the separated functions. We will consider as new variables of the problem, parameters models associated with the characteristic of the materials, in addition to the frequency. Finally, the quality of the results will be assessed based on an example.

Ammonia and methane gas emissions from pig slurry: variability induced through feeding strategies

Esta Tesis doctoral fue desarrollada para estudiar las emisiones de amoniaco (NH3) y metano (CH4) en purines de cerdos, y los efectos ocasionados por cambios en la formulación de la dieta. Con este propósito, fueron llevados a cabo tres estudios. El experimento 1 fue realizado con el objetivo de analizar los factores de variación de la composición de purines y establecer ecuaciones de predicción para emisiones potenciales de NH3 y CH4. Fueron recogidas setenta y nueve muestras de piensos y purines durante dos estaciones del año (verano y invierno) de granjas comerciales situadas en dos regiones de España (Centro y Mediterráneo). Se muestrearon granjas de gestación, maternidad, lactación y cebo. Se determinó la composición de piensos y purines, y la emisión potencial de NH3 y CH4. El contenido de nutrientes de los piensos fue usado como covariable en el análisis. La espectroscopia de reflectancia del infrarrojo cercano (NIRS) se evaluó como herramienta de predicción de la composición y potencial emisión de gases del purín. Se encontró una amplia variabilidad en la composición de piensos y purines. Las granjas del Mediterráneo tenían mayor pH (P<0,001) y concentración de cenizas (P =0,02) en el purín que las del Centro. El tipo de granja también afectó al contenido de extracto etéreo (EE) del purín (P =0,02), observando los valores más elevados en las instalaciones de animales jóvenes. Los resultados sugieren un efecto tampón de la fibra de la dieta en el pH del purín y una relación directa (P<0,05) con el contenido de fibra fecal. El contenido de proteína del pienso no afectó al contenido de nitrógeno del purín, pero disminuyó (P=0,003) la concentración de sólidos totales (ST) y de sólidos volátiles (SV). Se obtuvieron modelos de predicción de la emisión potencial de NH3 (R2=0,89) y CH4 (R2=0,61) partir de la composición del purín. Los espectros NIRS mostraron una buena precisión para la estimación de la mayor parte de los constituyentes, con coeficientes de determinación de validación cruzada (R2cv) superiores a 0,90, así como para la predicción del potencial de emisiones de NH3 y CH4 (R2cv=0,84 y 0,68, respectivamente). El experimento 2 fue realizado para investigar los efectos del nivel de inclusión de dos fuentes de sub-productos fibrosos: pulpa de naranja (PN) y pulpa de algarroba (PA), en dietas iso-fibrosas de cerdos de cebo, sobre la composición del purín y las emisiones potenciales de NH3 y CH4. Treinta cerdos (85,4±12,3 kg) fueron alimentados con cinco dietas iso-nutritivas: control comercial trigo/cebada (C) y cuatro dietas experimentales incluyendo las dos fuentes de sub-productos a dos niveles (75 y 150 g/kg) en una estructura 2 × 2 factorial. Después de 14 días de periodo de adaptación, heces y orina fueron recogidas separadamente durante 7 días para medir la digestibilidad de los nutrientes y el nitrógeno (N) excretado (6 réplicas por dieta) en cerdos alojados individualmente en jaulas metabólicas. Las emisiones de NH3 y CH4 fueron medidas después de la recogida de los purínes durante 11 y 100 días respectivamente. La fuente y el nivel de subproductos fibrosos afectó a la eficiencia digestiva de diferentes formas, ya que los coeficientes de digestibilidad total aparente (CDTA) para la materia seca (MS), materia orgánica (MO), fracciones fibrosas y energía bruta (EB) aumentaron con la PN pero disminuyeron con la inclusión de PA (P<0,05). El CDTA de proteína bruta (PB) disminuyó con la inclusión de las dos fuentes de fibra, siendo más bajo al mayor nivel de inclusión. La concentración fecal de fracciones fibrosas aumentó (P<0,05) con el nivel de inclusión de PA pero disminuyó con el de PN (P<0,01). El nivel más alto de las dos fuentes de fibra en el pienso aumentó (P<0,02) el contenido de PB fecal pero disminuyó el contenido de N de la orina (de 205 para 168 g/kg MS, P<0,05) en todas las dietas suplementadas comparadas con la dieta C. Adicionalmente, las proporciones de nitrógeno indigerido, nitrógeno soluble en agua, nitrógeno bacteriano y endógeno excretado en heces no fueron afectados por los tratamientos. Las características iniciales del purín no difirieron entre las diferentes fuentes y niveles de fibra, excepto para el pH que disminuyó con la inclusión de altos niveles de sub-productos. La emisión de NH3 por kg de purín fue más baja en todas las dietas suplementadas con fibras que en la dieta C (2,44 vs.1,81g de promedio, P<0,05). Además, purines de dietas suplementadas con alto nivel de sub-productos tendieron (P<0,06) a emitir menos NH3 por kg de nitrógeno total y mostraron un potencial más bajo para emitir CH4, independientemente de la fuente de fibra. El experimento 3 investigó los efectos de la fuente de proteína en dietas prácticas. Tres piensos experimentales fueron diseñados para sustituir una mescla de harina y cascarilla de soja (SOJ) por harina de girasol (GIR) o por DDGS del trigo (DDGST). La proporción de otros ingredientes fue modificada para mantener los contenidos de nutrientes similares a través de las dietas. El cambio en la fuente de proteína dio lugar a diferencias en el contenido de fibra neutro detergente ligada a proteína bruta (FNDPB), fibra soluble (FS) y lignina ácido detergente (LAD) en la dieta. Veinticuatro cerdos (ocho por dieta), con 52,3 o 60,8 kg en la primera y segunda tanda respectivamente, fueron alojados individualmente en jaulas metabólicas. Durante un periodo de 7 días fue determinado el balance de MS, el CDTA de los nutrientes y la composición de heces y orina. Se realizó el mismo procedimiento del experimento 2 para medir las emisiones de NH3 y CH4 de los purines de cada animal. Ni la ingestión de MS ni el CDTA de la MS o de la energía fueron diferentes entre las dietas experimentales, pero el tipo de pienso afectó (P<0.001) la digestibilidad de la PB, que fue mayor para GIR (0,846) que para SOJ (0,775), mientras que la dieta DDGST mostró un valor intermedio (0,794). La concentración fecal de PB fue por tanto influenciada (P<0,001) por el tratamiento, observándose la menor concentración de PB en la dieta GIR y la mayor en la dieta SOJ. La proporción de N excretado en orina o heces disminuyó de 1,63 en la dieta GIR hasta 0,650 en la dieta SOJ, como consecuencia de perdidas más bajas en orina y más altas en heces, con todas las fracciones de nitrógeno fecales creciendo en paralelo a la excreción total. Este resultado fue paralelo a una disminución de la emisión potencial de NH3 (g/kg purín) en la dieta SOJ con respecto a la dieta GIR (desde 1,82 a 1,12, P<0,05), dando valores intermedios (1,58) para los purines de la dieta DDGST. Por otro lado, el CDTA de la FS y de la fibra neutro detergente (FND) fueron afectados (P<0,001 y 0,002, respectivamente) por el tipo de dieta, siendo más bajas en la dieta GIR que en la dieta SOJ; además, se observó un contenido más alto de FND (491 vs. 361g/kg) en la MS fecal para la dieta GIR que en la dieta SOJ, presentando la dieta DDGST valores intermedios. El grado de lignificación de la FND (FAD/FND x 100) de las heces disminuyó en el orden GIR>DDGST>SOJ (desde 0,171 hasta 0,109 y 0,086, respectivamente) en paralelo a la disminución del potencial de emisión de CH4 por g de SV del purín (desde 301 a 269 y 256 mL, respectivamente). Todos los purines obtenidos en estos tres experimentos y Antezana et al. (2015) fueron usados para desarrollar nuevas calibraciones con la tecnología NIRS, para predecir la composición del purín y el potencial de las emisiones de gases. Se observó una buena precisión (R2cv superior a 0,92) de las calibraciones cuando muestras de los ensayos controlados (2, 3 y Antezana et al., 2015) fueron añadidas, aumentando el rango de variación. Una menor exactitud fue observada para TAN y emisiones de NH3 y CH4, lo que podría explicarse por una menor homogeneidad en la distribución de las muestras cuando se amplía el rango de variación del estudio. ABSTRACT This PhD thesis was developed to study the emissions of ammonia (NH3) and methane (CH4) from pig slurry and the effects caused by changes on diet formulation. For these proposes three studies were conducted. Experiment 1 aimed to analyse several factors of variation of slurry composition and to establish prediction equations for potential CH4 and NH3 emissions. Seventy-nine feed and slurry samples were collected at two seasons (summer and winter) from commercial pig farms sited at two Spanish regions (Centre and Mediterranean). Nursery, growing-fattening, gestating and lactating facilities were sampled. Feed and slurry composition were determined, and potential CH4 and NH3 emissions measured. Feed nutrient contents were used as covariates in the analysis. Near infrared reflectance spectroscopy (NIRS) was evaluated as a predicting tool for slurry composition and potential gaseous emissions. A wide variability was found both in feed and slurry composition. Mediterranean farms had a higher pH (P<0.001) and ash (P=0.02) concentration than those located at the centre of Spain. Also, type of farm affected ether extract (EE) content of the slurry (P=0.02), with highest values obtained for the youngest animal facilities. Results suggested a buffer effect of dietary fibre on slurry pH and a direct relationship (P<0.05) with fibre constituents of manure. Dietary protein content did not affect slurry nitrogen content (N) but decreased (P=0.003) in total solid (TS) and volatile solids (VS) concentration. Prediction models of potential NH3 emissions (R2=0.89) and biochemical CH4 potential (B0) (R2=0.61) were obtained from slurry composition. Predictions from NIRS showed a high accuracy for most slurry constituents with coefficient of determination of cross validation (R2cv) above 0.90 and a similar accuracy of prediction of potential NH3 and CH4 emissions (R2cv=0.84 and 0.68, respectively) thus models based on slurry composition from commercial farms. Experiment 2 was conducted to investigate the effects of increasing the level of two sources of fibrous by-products, orange pulp (OP) and carob meal (CM), in iso-fibrous diets for growing-finishing pig, slurry composition and potential NH3 and CH4 emissions. Thirty pigs (85.4±12.3 kg) were fed five iso-nutritive diets: a commercial control wheat/barley (C) and four experimental diets including two sources of fibrous by-products OP and CM and two dietary levels (75 and 150 g/kg) in a 2 × 2 factorial arrangement. After a 14-day adaptation period, faeces and urine were collected separately for 7 days to measure nutrient digestibility and the excretory patterns of N from pigs (6 replicates per diet) housed individually in metabolic pens. For each animal, the derived NH3 and CH4 emissions were measured in samples of slurry over an 11 and 100-day storage periods, respectively. Source and level of the fibrous by-products affected digestion efficiency in a different way as the coefficients of total tract apparent digestibility (CTTAD) for dry matter (DM), organic matter (OM), fibre fractions and gross energy (GE) increased with OP but decreased with CM (P<0.05). Crude protein CTTAD decreased with the inclusion of both sources of fibre, being lower at the highest dietary level. Faecal concentration of fibre fractions increased (P<0.05) with the level of inclusion of CM but decreased with that of OP (P<0.01). High dietary level for both sources of fibre increased (P<0.02) CP faecal content but urine N content decreased (from 205 to 168 g/kg DM, P<0.05) in all the fibre-supplemented compared to C diet. Additionally, the proportions of undigested dietary, water soluble, and bacterial and endogenous debris of faecal N excretion were not affected by treatments. The initial slurry characteristics did not differ among different fibre sources and dietary levels, except pH, which decreased at the highest by-product inclusion levels. Ammonia emission per kg of slurry was lower in all the fibre-supplemented diets than in C diet (2.44 vs. 1.81g as average, P<0.05). Additionally, slurries from the highest dietary level of by-products tended (P<0.06) to emit less NH3 per kg of initial total Kjeldahl nitrogen (TKN) and showed a lower biochemical CH4 potential , independently of the fibre source. Experiment 3 investigated the effects of protein source in practical diets. Three experimental feeds were designed to substitute a mixture of soybean meal and soybean hulls (SB diet) with sunflower meal (SFM) or wheat DDGS (WDDGS). The proportion of other ingredients was also modified in order to maintain similar nutrient contents across diets. Changes in protein source led to differences in dietary content of neutral detergent insoluble crude protein (NDICP), soluble fibre (SF) and acid detergent lignin (ADL). Twenty-four pigs (eight per diet), weighing 52.3 or 60.8 kg at the first and second batch respectively, were housed individually in metabolic pens to determine during a 7-day period DM balance, CTTAD of nutrients, and faecal and urine composition. Representative slurry samples from each animal were used to measure NH3 and CH4 emissions over an 11 and or 100-day storage period, respectively. Neither DM intake, nor DM or energy CTTAD differed among experimental diets, but type of feed affected (P<0.001) CP digestibility, which was highest for SFM (0.846) than for SB (0.775) diet, with WDDGS-based diet giving an intermediate value (0.794). Faecal DM composition was influenced (P<0.001) accordingly, with the lowest CP concentration found for diet SFM and the highest for SB. The ratio of N excreted in urine or faeces decreased from SFM (1.63) to SB diet (0.650), as a consequence of both lower urine and higher faecal losses, with all the faecal N fractions increasing in parallel to total excretion. This result was parallel to a decrease of potential NH3 emission (g/kg slurry) in diet SB with respect to diet SFM (from 1.82 to 1.12, P<0.05), giving slurry from WDDGS-based diet an intermediate value (1.58). Otherwise, SF and insoluble neutral detergent fibre (NDF) CTTAD were affected (P<0.001 and P=0.002, respectively) by type of diet, being lower for SFM than in SB-diet; besides, a higher content of NDF (491 vs. 361 g/kg) in faecal DM was observed for SFM with respect to SB based diet, with WDDGS diet being intermediate. Degree of lignification of NDF (ADL/NDF x 100) of faeces decreased in the order SFM>WDDGS>SB (from 0.171 to 0.109 and 0.086, respectively) in parallel to a decrease of biochemical CH4 potential per g of VS of slurry (from 301 to 269 and 256 ml, respectively). All slurry samples obtained from these three experiments and Antezana et al. (2015) were used to develop new calibrations with NIRS technology, to predict the slurry composition and potential gaseous emissions of samples with greater variability in comparison to experiment 1. Better accuracy (R2cv above 0.92) was observed for calibrations when samples from controlled trials experiments (2, 3 and Antezana et al., 2015) were included, increasing the range of variation. A lower accuracy was observed for TAN, NH3 and CH4 gaseous emissions, which might be explained by the less homogeneous distribution with a wider range of data.

On the application of meshfree methods to the nonlinear dynamics of multibody systems

Esta tesis propone una completa formulación termo-mecánica para la simulación no-lineal de mecanismos flexibles basada en métodos libres de malla. El enfoque se basa en tres pilares principales: la formulación de Lagrangiano total para medios continuos, la discretización de Bubnov-Galerkin, y las funciones de forma libres de malla. Los métodos sin malla se caracterizan por la definición de un conjunto de funciones de forma en dominios solapados, junto con una malla de integración de las ecuaciones discretas de balance. Dos tipos de funciones de forma se han seleccionado como representación de las familias interpolantes (Funciones de Base Radial) y aproximantes (Mínimos Cuadrados Móviles). Su formulación se ha adaptado haciendo sus parámetros compatibles, y su ausencia de conectividad predefinida se ha aprovechado para interconectar múltiples dominios de manera automática, permitiendo el uso de mallas de fondo no conformes. Se propone una formulación generalizada de restricciones, juntas y contactos, válida para sólidos rígidos y flexibles, siendo estos últimos discretizados mediante elementos finitos (MEF) o libres de malla. La mayor ventaja de este enfoque reside en que independiza completamente el dominio con respecto de las uniones y acciones externas a cada sólido, permitiendo su definición incluso fuera del contorno. Al mismo tiempo, también se minimiza el número de ecuaciones de restricción necesarias para la definición de uniones realistas. Las diversas validaciones, ejemplos y comparaciones detalladas muestran como el enfoque propuesto es genérico y extensible a un gran número de sistemas. En concreto, las comparaciones con el MEF indican una importante reducción del error para igual número de nodos, tanto en simulaciones mecánicas, como térmicas y termo-mecánicas acopladas. A igualdad de error, la eficiencia numérica de los métodos libres de malla es mayor que la del MEF cuanto más grosera es la discretización. Finalmente, la formulación se aplica a un problema de diseño real sobre el mantenimiento de estructuras masivas en el interior de un reactor de fusión, demostrando su viabilidad en análisis de problemas reales, y a su vez mostrando su potencial para su uso en simulación en tiempo real de sistemas no-lineales. A new complete formulation is proposed for the simulation of nonlinear dynamic of multibody systems with thermo-mechanical behaviour. The approach is founded in three main pillars: total Lagrangian formulation, Bubnov-Galerkin discretization, and meshfree shape functions. Meshfree methods are characterized by the definition of a set of shape functions in overlapping domains, and a background grid for integration of the Galerkin discrete equations. Two different types of shape functions have been chosen as representatives of interpolation (Radial Basis Functions), and approximation (Moving Least Squares) families. Their formulation has been adapted to use compatible parameters, and their lack of predefined connectivity is used to interconnect different domains seamlessly, allowing the use of non-conforming meshes. A generalized formulation for constraints, joints, and contacts is proposed, which is valid for rigid and flexible solids, being the later discretized using either finite elements (FEM) or meshfree methods. The greatest advantage of this approach is that makes the domain completely independent of the external links and actions, allowing to even define them outside of the boundary. At the same time, the number of constraint equations needed for defining realistic joints is minimized. Validation, examples, and benchmarks are provided for the proposed formulation, demonstrating that the approach is generic and extensible to further problems. Comparisons with FEM show a much lower error for the same number of nodes, both for mechanical and thermal analyses. The numerical efficiency is also better when coarse discretizations are used. A final demonstration to a real problem for handling massive structures inside of a fusion reactor is presented. It demonstrates that the application of meshfree methods is feasible and can provide an advantage towards the definition of nonlinear real-time simulation models.

Pararotor dynamics: center of mass displacement from the blade plane—analytical approach

The pararotor is a biology-inspired decelerator device based on the autorotation of a rotary wing whose main purpose is to guide a load descent into a certain atmosphere. This paper focuses on a practical approach to the general dynamic stability of a pararotor whose center of mass is displaced from the blade plane. The analytical study departs from the motion equations of pararotor flight, considering the center of mass displacement from the blade plane, studied over a number of simplifying hypotheses that allows determining the most important influences to flight behavior near equilibrium. Two practical indexes are developed to characterize the stability of a pararotor in terms of geometry, inertia, and the aerodynamic characteristics of the device. Based on these two parameters, a stability diagram can be defined upon which stability regions can be identified. It was concluded that the ability to reach stability conditions depends mainly on a limited number of parameters associated with the pararotor configuration: the relationship between moments of inertia, the position of the blades, the planform shape (associated with the blade aerodynamic coefficients and blade area), and the vertical distance between the center of mass and the blade plane. These parameters can be evaluated by computing practical indexes to determine stability behavior.

Behavior of several two-dimensional fluid equations in singular scenarios

We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts.

Constraints on nebular dynamics and chemistry based on observations of annealed magnesium silicate grains in comets and in disks surrounding Herbig Ae/Be stars

Understanding dynamic conditions in the Solar Nebula is the key to prediction of the material to be found in comets. We suggest that a dynamic, large-scale circulation pattern brings processed dust and gas from the inner nebula back out into the region of cometesimal formation—extending possibly hundreds of astronomical units (AU) from the sun—and that the composition of comets is determined by a chemical reaction network closely coupled to the dynamic transport of dust and gas in the system. This scenario is supported by laboratory studies of Mg silicates and the astronomical data for comets and for protoplanetary disks associated with young stars, which demonstrate that annealing of nebular silicates must occur in conjunction with a large-scale circulation. Mass recycling of dust should have a significant effect on the chemical kinetics of the outer nebula by introducing reduced, gas-phase species produced in the higher temperature and pressure environment of the inner nebula, along with freshly processed grains with “clean” catalytic surfaces to the region of cometesimal formation. Because comets probably form throughout the lifetime of the Solar Nebula and processed (crystalline) grains are not immediately available for incorporation into the first generation of comets, an increasing fraction of dust incorporated into a growing comet should be crystalline olivine and this fraction can serve as a crude chronometer of the relative ages of comets. The formation and evolution of key organic and biogenic molecules in comets are potentially of great consequence to astrobiology.

Dynamics of maize endosperm development and DNA endoreduplication.

Endosperm development in Zea mays is characterized by a period of intense mitotic activity followed by a period in which mitosis is essentially eliminated and the cell cycle becomes one of alternating S and G phases, leading to endoreduplication of the nuclear DNA. The endosperm represents a significant contribution to the grain yield of maize; thus, methods that facilitate the study of cellular kinetics may be useful in discerning cellular and molecular components of grain yield. Two mathematical models have been developed to describe the kinetics of endosperm growth. The first describes the kinetics of mitosis during endosperm development; the second describes the kinetics of DNA endoreduplication during endosperm development. The mitotic model is a modification of standard growth curves. The endoreduplication model is composed of six differential equations that represent the progression of nuclei from one DNA content to another during the endoreduplication process. Total nuclei number per endosperm and the number of 3C, 6C, 12C, 24C, 48C, and 96C nuclei per endosperm (C is the haploid DNA content per nucleus) for inbred W64A from 8 to 18 days after pollination were determined by flow cytometry. The results indicate that the change in number of nuclei expressed as a function of the number of days after pollination is the same from one yearly crop to another. These data were used in the model to determine the endosperm growth rate, the maximum nuclei number per endosperm, and transition rates from one C value to the next higher C value. The kinetics of endosperm development are reasonably well represented by the models. Thus, the models provide a means to quantify the complex pattern of endosperm development.

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.

Spin dynamics of current-driven single magnetic adatoms and molecules

A scanning tunneling microscope can probe the inelastic spin excitations of a single magnetic atom in a surface via spin-flip assisted tunneling in which transport electrons exchange spin and energy with the atomic spin. If the inelastic transport time, defined as the average time elapsed between two inelastic spin flip events, is shorter than the atom spin-relaxation time, the scanning tunnel microscope (STM) current can drive the spin out of equilibrium. Here we model this process using rate equations and a model Hamiltonian that describes successfully spin-flip-assisted tunneling experiments, including a single Mn atom, a Mn dimer, and Fe Phthalocyanine molecules. When the STM current is not spin polarized, the nonequilibrium spin dynamics of the magnetic atom results in nonmonotonic dI/dV curves. In the case of spin-polarized STM current, the spin orientation of the magnetic atom can be controlled parallel or antiparallel to the magnetic moment of the tip. Thus, spin-polarized STM tips can be used both to probe and to control the magnetic moment of a single atom.