Spatial linear global instability analysis of the HIFiRE-5 elliptic cone model flow

The linear instability of the three-dimensional boundary-layer over the HIFiRE-5 flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, at Mach 7, has been analyzed through spatial BiGlobal analysis, in a effort to understand transition and accurately predict local heat loads on next-generation ight vehicles. The results at an intermediate axial section of the cone, Re x = 8x10 5, show three different families of spatially amplied linear global modes, the attachment-line and cross- ow modes known from earlier analyses, and a new global mode, peaking in the vicinity of the minor axis of the cone, termed \center-line mode". We discover that a sequence of symmetric and anti-symmetric centerline modes exist and, for the basic ow at hand, are maximally amplied around F* = 130kHz. The wavenumbers and spatial distribution of amplitude functions of the centerline modes are documented

Accurate Parabolic Navier-Stokes solutions of the supersonic flow around and elliptic cone

Flows of relevance to new generation aerospace vehicles exist, which are weakly dependent on the streamwise direction and strongly dependent on the other two spatial directions, such as the flow around the (flattened) nose of the vehicle and the associated elliptic cone model. Exploiting these characteristics, a parabolic integration of the Navier-Stokes equations is more appropriate than solution of the full equations, resulting in the so-called Parabolic Navier-Stokes (PNS). This approach not only is the best candidate, in terms of computational efficiency and accuracy, for the computation of steady base flows with the appointed properties, but also permits performing instability analysis and laminar-turbulent transition studies a-posteriori to the base flow computation. This is to be contrasted with the alternative approach of using order-of-magnitude more expensive spatial Direct Numerical Simulations (DNS) for the description of the transition process. The PNS equations used here have been formulated for an arbitrary coordinate transformation and the spatial discretization is performed using a novel stable high-order finite-difference-based numerical scheme, ensuring the recovery of highly accurate solutions using modest computing resources. For verification purposes, the boundary layer solution around a circular cone at zero angle of attack is compared in the incompressible limit with theoretical profiles. Also, the recovered shock wave angle at supersonic conditions is compared with theoretical predictions in the same circular-base cone geometry. Finally, the entire flow field, including shock position and compressible boundary layer around a 2:1 elliptic cone is recovered at Mach numbers 3 and 4

A Schwarz lemma for Kahler affine metrics and the canonical potential of a proper convex cone

This is an account of some aspects of the geometry of Kahler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for Kahler affine metrics of Yau s Schwarz lemma for volume forms. By a theorem of Cheng and Yau, there is a canonical Kahler affine Einstein metric on a proper convex domain, and the Schwarz lemma gives a direct proof of its uniqueness up to homothety. The potential for this metric is a function canonically associated to the cone, characterized by the property that its level sets are hyperbolic affine spheres foliating the cone. It is shown that for an n -dimensional cone, a rescaling of the canonical potential is an n -normal barrier function in the sense of interior point methods for conic programming. It is explained also how to construct from the canonical potential Monge-Ampère metrics of both Riemannian and Lorentzian signatures, and a mean curvature zero conical Lagrangian submanifold of the flat para-Kahler space.

Definición e implementación de métricas objetivas para la evaluación funcional del miembro superior: aplicación a población con lesión medular cervical

En personas que padecen una Lesión Medular cervical, la función de los miembros superiores se ve afectada en mayor o menor medida, dependiendo fundamentalmente del nivel de la lesión y de la severidad de la misma. El déficit en la función del miembro superior hace que la autonomía e independencia de las personas se vea reducida en la ejecución de Actividades de la Vida Diaria. En el entorno clínico, la valoración de la función del miembro superior se realiza principalmente con escalas clínicas. Algunas de ellas valoran el nivel de dependencia o independencia en la ejecución de Actividades de la Vida Diaria, como, por ejemplo, el índice de Barthel y la escala FIM (Medida de la Independencia Funcional). Otras escalas, como Jebsen-Taylor Hand Function, miden la función del miembro superior valorando la destreza y la habilidad en la ejecución de determinadas tareas funcionales. Estas escalas son generales, es decir, se pueden aplicar a distintas poblaciones de sujetos y a la presencia de distintas patologías. Sin embargo, existen otras escalas desarrolladas específicamente para valorar una patología concreta, con el objetivo de hacer las evaluaciones funcionales más sensibles a cambios. Un ejemplo es la escala Spinal Cord Independence Measure (SCIM), desarrollada para valorar Lesión Medular. Las escalas clínicas son instrumentos de medida estandarizados, válidos para su uso en el entorno clínico porque se han validado en muestras grandes de pacientes. No obstante, suelen poseer una elevada componente de subjetividad que depende principalmente de la persona que puntúa el test. Otro aspecto a tener en cuenta, es que la sensibilidad de las escalas es alta, fundamentalmente, a cambios groseros en el estado de salud o en la función del miembro superior, de forma que cambios sutiles en el sujeto pueden no ser detectados. Además, en ocasiones, poseen saturaciones en el sistema de puntuación, de forma que mejorías que se puedan producir por encima de un determinado umbral no son detectadas. En definitiva, estas limitaciones hacen que las escalas clínicas no sean suficientes, por sí mismas, para evaluar estrategias motoras del miembro superior durante la ejecución de movimientos funcionales, siendo necesaria la búsqueda de instrumentos de medida que aporten objetividad, complementen las valoraciones y, al mismo tiempo, intenten solventar las limitaciones que poseen las escalas. Los estudios biomecánicos son ejemplos de métodos objetivos, en los que diversas tecnologías se pueden utilizar para recoger información de los sujetos. Una concreción de estos estudios son los estudios cinemáticos. Mediante tecnología optoelectrónica, inercial o electromagnética, estos estudios proporcionan información objetiva acerca del movimiento realizado por los sujetos, durante la ejecución de tareas concretas. Estos sistemas de medida proporcionan grandes cantidades de datos que carecen de una interpretación inmediata. Estos datos necesariamente deben ser tratados y reducidos a un conjunto de variables que, a priori, posean una interpretación más sencilla para ser utilizados en la práctica clínica. Estas han sido las principales motivaciones de esta investigación. El objetivo principal fue proponer un conjunto de índices cinemáticos que, de forma objetiva, valoren la función del miembro superior; y validar los índices propuestos en poblaciones con Lesión Medular, para su uso como instrumentos de valoración en el entorno clínico. Esta tesis se enmarca dentro de un proyecto de investigación: HYPER (Hybrid Neuroprosthetic and Neurorobotic Devices for Functional Compensation and Rehabilitation of Motor Disorders, referencia CSD2009-00067 CONSOLIDER INGENIO 2010). Dentro de este proyecto se lleva a cabo investigación en el desarrollo de modelos, para determinar los requisitos biomecánicos y los patrones de movimiento de los miembros superiores en sujetos sanos y personas con lesión medular. Además, se realiza investigación en la propuesta de nuevos instrumentos de evaluación funcional en el campo de la rehabilitación de los miembros superiores. ABSTRACT In people who have suffered a cervical Spinal Cord Injury, upper limbs function is affected to a greater or lesser extent, depending primarily on the level of the injury and the severity of it. The deficit in the upper limb function reduces the autonomy and independence of persons in the execution of Activities of Daily Living. In the clinical setting, assessment of upper limb function is mainly performed based on clinical scales. Some value the level of dependence or independence in performing activities of daily living, such as the Barthel Index and the FIM scale (Functional Independence Measure). Other scales, such as the Jebsen-Taylor Hand Function, measure upper limb function in terms of the skill and ability to perform specific functional tasks. These scales are general, so can be applied to different populations of subjects and the presence of different pathologies. However, there are other scales developed for a specific injury, in order to make the functional assessments more sensitive to changes. An example is the Spinal Cord Independence Measure (SCIM), developed for people with Spinal Cord Injury. The clinical scales are standardized instruments measure, valid for use in the clinical setting because they have been validated in large patient samples. However, they usually have a high level of subjectivity which mainly depends on the person who scores the test. Another aspect to take into account is the high sensitivity of the scales mainly to gross changes in the health status or upper limb function, so that subtle changes in the subject may not be detected. Moreover, sometimes, have saturations in the scoring system, so that improvements which may occur above a certain threshold are not detected. For these reasons, clinical scales are not enough, by themselves, to assess motor strategies used during movements. So, it’s necessary to find measure instruments that provide objectivity, supplement the assessments and, at the same time, solving the limitations that scales have. Biomechanical studies are examples of objective methods, in which several technologies can be used to collect information from the subjects. One kind of these studies is the kinematic movement analysis. By means of optoelectronics, inertial and electromagnetic technology, these studies provide objective information about the movement performed by the subjects during the execution of specific tasks. These systems provide large quantities of data without easy and intuitive interpretation. These data must necessarily be treated and reduced to a set of variables that, a priori, having a simpler interpretation for their use in the clinical practice. These were the main motivations of this research. The main objective was to propose a set of kinematic indices, or metrics that, objectively, assess the upper limb function and validate the proposed rates in populations with Spinal Cord Injury, for use as assessment tools in the clinical setting. This dissertation is framed within a research project: HYPER (Neurorobotic Devices for Functional Compensation and Rehabilitation of Motor Disorders, grant CSD2009- 00067 CONSOLIDER INGENIO 2010). Within this research project, research is conducted in relation to the biomechanical models development for determining the biomechanical requirements and movement patterns of the upper limb in healthy and people with Spinal Cord Injury. Moreover, research is conducted with respect to the proposed of new functional assessment instruments in the field of upper limb rehabilitation.