Low-Dimensional Modelling for optimal streaks in the blasius boundary layer

This paper is concerned with the low dimensional structure of optimal streaks in the Blasius boundary layer. Optimal streaks are well known to exhibit an approximate self-similarity, namely the streamwise velocity re-scaled with their maximum remains almost independent of both the spanwise wavenumber and the streamwise coordinate. However, the reason of this self-similar behavior is still unexplained as well as unexploited. After revisiting the structure of the streaks near the leading edge singularity, two additional approximately self-similar relations involving the velocity components and their wall normal derivatives are identified. Based on these properties, we derive a low dimensional model with two degrees of freedom. The comparison with the results obtained from the linearized boundary layer equations shows that this model is consistent and provide good approximations.

Lacunarity of the Spatial Distributions of Soil Types in Europe.

Lacunarity as a means of quantifying textural properties of spatial distributions suggests a classification into three main classes of the most abundant soils that cover 92% of Europe. Soils with a well-defined self-similar structure of the linear class are related to widespread spatial patterns that are nondominant but ubiquitous at continental scale. Fractal techniques have been increasingly and successfully applied to identify and describe spatial patterns in natural sciences. However, objects with the same fractal dimension can show very different optical properties because of their spatial arrangement. This work focuses primary attention on the geometrical structure of the geographical patterns of soils in Europe. We made use of the European Soil Database to estimate lacunarity indexes of the most abundant soils that cover 92% of the surface of Europe and investigated textural properties of their spatial distribution. We observed three main classes corresponding to three different patterns that displayed the graphs of lacunarity functions, that is, linear, convex, and mixed. They correspond respectively to homogeneous or self-similar, heterogeneous or clustered and those in which behavior can change at different ranges of scales. Finally, we discuss the pedological implications of that classification.

Nanoinformatics approaches for information extraction and text mining in nanomedical research texts

La nanotecnología es un área de investigación de reciente creación que trata con la manipulación y el control de la materia con dimensiones comprendidas entre 1 y 100 nanómetros. A escala nanométrica, los materiales exhiben fenómenos físicos, químicos y biológicos singulares, muy distintos a los que manifiestan a escala convencional. En medicina, los compuestos miniaturizados a nanoescala y los materiales nanoestructurados ofrecen una mayor eficacia con respecto a las formulaciones químicas tradicionales, así como una mejora en la focalización del medicamento hacia la diana terapéutica, revelando así nuevas propiedades diagnósticas y terapéuticas. A su vez, la complejidad de la información a nivel nano es mucho mayor que en los niveles biológicos convencionales (desde el nivel de población hasta el nivel de célula) y, por tanto, cualquier flujo de trabajo en nanomedicina requiere, de forma inherente, estrategias de gestión de información avanzadas. Desafortunadamente, la informática biomédica todavía no ha proporcionado el marco de trabajo que permita lidiar con estos retos de la información a nivel nano, ni ha adaptado sus métodos y herramientas a este nuevo campo de investigación. En este contexto, la nueva área de la nanoinformática pretende detectar y establecer los vínculos existentes entre la medicina, la nanotecnología y la informática, fomentando así la aplicación de métodos computacionales para resolver las cuestiones y problemas que surgen con la información en la amplia intersección entre la biomedicina y la nanotecnología. Las observaciones expuestas previamente determinan el contexto de esta tesis doctoral, la cual se centra en analizar el dominio de la nanomedicina en profundidad, así como en el desarrollo de estrategias y herramientas para establecer correspondencias entre las distintas disciplinas, fuentes de datos, recursos computacionales y técnicas orientadas a la extracción de información y la minería de textos, con el objetivo final de hacer uso de los datos nanomédicos disponibles. El autor analiza, a través de casos reales, alguna de las tareas de investigación en nanomedicina que requieren o que pueden beneficiarse del uso de métodos y herramientas nanoinformáticas, ilustrando de esta forma los inconvenientes y limitaciones actuales de los enfoques de informática biomédica a la hora de tratar con datos pertenecientes al dominio nanomédico. Se discuten tres escenarios diferentes como ejemplos de actividades que los investigadores realizan mientras llevan a cabo su investigación, comparando los contextos biomédico y nanomédico: i) búsqueda en la Web de fuentes de datos y recursos computacionales que den soporte a su investigación; ii) búsqueda en la literatura científica de resultados experimentales y publicaciones relacionadas con su investigación; iii) búsqueda en registros de ensayos clínicos de resultados clínicos relacionados con su investigación. El desarrollo de estas actividades requiere el uso de herramientas y servicios informáticos, como exploradores Web, bases de datos de referencias bibliográficas indexando la literatura biomédica y registros online de ensayos clínicos, respectivamente. Para cada escenario, este documento proporciona un análisis detallado de los posibles obstáculos que pueden dificultar el desarrollo y el resultado de las diferentes tareas de investigación en cada uno de los dos campos citados (biomedicina y nanomedicina), poniendo especial énfasis en los retos existentes en la investigación nanomédica, campo en el que se han detectado las mayores dificultades. El autor ilustra cómo la aplicación de metodologías provenientes de la informática biomédica a estos escenarios resulta efectiva en el dominio biomédico, mientras que dichas metodologías presentan serias limitaciones cuando son aplicadas al contexto nanomédico. Para abordar dichas limitaciones, el autor propone un enfoque nanoinformático, original, diseñado específicamente para tratar con las características especiales que la información presenta a nivel nano. El enfoque consiste en un análisis en profundidad de la literatura científica y de los registros de ensayos clínicos disponibles para extraer información relevante sobre experimentos y resultados en nanomedicina —patrones textuales, vocabulario en común, descriptores de experimentos, parámetros de caracterización, etc.—, seguido del desarrollo de mecanismos para estructurar y analizar dicha información automáticamente. Este análisis concluye con la generación de un modelo de datos de referencia (gold standard) —un conjunto de datos de entrenamiento y de test anotados manualmente—, el cual ha sido aplicado a la clasificación de registros de ensayos clínicos, permitiendo distinguir automáticamente los estudios centrados en nanodrogas y nanodispositivos de aquellos enfocados a testear productos farmacéuticos tradicionales. El presente trabajo pretende proporcionar los métodos necesarios para organizar, depurar, filtrar y validar parte de los datos nanomédicos existentes en la actualidad a una escala adecuada para la toma de decisiones. Análisis similares para otras tareas de investigación en nanomedicina ayudarían a detectar qué recursos nanoinformáticos se requieren para cumplir los objetivos actuales en el área, así como a generar conjunto de datos de referencia, estructurados y densos en información, a partir de literatura y otros fuentes no estructuradas para poder aplicar nuevos algoritmos e inferir nueva información de valor para la investigación en nanomedicina. ABSTRACT Nanotechnology is a research area of recent development that deals with the manipulation and control of matter with dimensions ranging from 1 to 100 nanometers. At the nanoscale, materials exhibit singular physical, chemical and biological phenomena, very different from those manifested at the conventional scale. In medicine, nanosized compounds and nanostructured materials offer improved drug targeting and efficacy with respect to traditional formulations, and reveal novel diagnostic and therapeutic properties. Nevertheless, the complexity of information at the nano level is much higher than the complexity at the conventional biological levels (from populations to the cell). Thus, any nanomedical research workflow inherently demands advanced information management. Unfortunately, Biomedical Informatics (BMI) has not yet provided the necessary framework to deal with such information challenges, nor adapted its methods and tools to the new research field. In this context, the novel area of nanoinformatics aims to build new bridges between medicine, nanotechnology and informatics, allowing the application of computational methods to solve informational issues at the wide intersection between biomedicine and nanotechnology. The above observations determine the context of this doctoral dissertation, which is focused on analyzing the nanomedical domain in-depth, and developing nanoinformatics strategies and tools to map across disciplines, data sources, computational resources, and information extraction and text mining techniques, for leveraging available nanomedical data. The author analyzes, through real-life case studies, some research tasks in nanomedicine that would require or could benefit from the use of nanoinformatics methods and tools, illustrating present drawbacks and limitations of BMI approaches to deal with data belonging to the nanomedical domain. Three different scenarios, comparing both the biomedical and nanomedical contexts, are discussed as examples of activities that researchers would perform while conducting their research: i) searching over the Web for data sources and computational resources supporting their research; ii) searching the literature for experimental results and publications related to their research, and iii) searching clinical trial registries for clinical results related to their research. The development of these activities will depend on the use of informatics tools and services, such as web browsers, databases of citations and abstracts indexing the biomedical literature, and web-based clinical trial registries, respectively. For each scenario, this document provides a detailed analysis of the potential information barriers that could hamper the successful development of the different research tasks in both fields (biomedicine and nanomedicine), emphasizing the existing challenges for nanomedical research —where the major barriers have been found. The author illustrates how the application of BMI methodologies to these scenarios can be proven successful in the biomedical domain, whilst these methodologies present severe limitations when applied to the nanomedical context. To address such limitations, the author proposes an original nanoinformatics approach specifically designed to deal with the special characteristics of information at the nano level. This approach consists of an in-depth analysis of the scientific literature and available clinical trial registries to extract relevant information about experiments and results in nanomedicine —textual patterns, common vocabulary, experiment descriptors, characterization parameters, etc.—, followed by the development of mechanisms to automatically structure and analyze this information. This analysis resulted in the generation of a gold standard —a manually annotated training or reference set—, which was applied to the automatic classification of clinical trial summaries, distinguishing studies focused on nanodrugs and nanodevices from those aimed at testing traditional pharmaceuticals. The present work aims to provide the necessary methods for organizing, curating and validating existing nanomedical data on a scale suitable for decision-making. Similar analysis for different nanomedical research tasks would help to detect which nanoinformatics resources are required to meet current goals in the field, as well as to generate densely populated and machine-interpretable reference datasets from the literature and other unstructured sources for further testing novel algorithms and inferring new valuable information for nanomedicine.

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

An introduction to flow and transport in fractal models of porous media: Part I

This special issue gathers together a number of recent papers on fractal geometry and its applications to the modeling of flow and transport in porous media. The aim is to provide a systematic approach for analyzing the statics and dynamics of fluids in fractal porous media by means of theory, modeling and experimentation. The topics covered include lacunarity analyses of multifractal and natural grayscale patterns, random packing's of self-similar pore/particle size distributions, Darcian and non-Darcian hydraulic flows, diffusion within fractals, models for the permeability and thermal conductivity of fractal porous media and hydrophobicity and surface erosion properties of fractal structures.

Dynamic stability of long axisymmetric liquid bridges

This paper deals with the non-linear forced oscillations of axisymmetric long liquid bridges between equal disks. The dynamics of the liquid bridge has been analyzed by using a self-similar, one-dimensional model already used in similar problems. The influence of the dynamics on the static stability limits, as well as the main characteristics of the non-linear behaviour of long liquid bridges, have been studied with in the range of validity of the mathematical model used here.

On the stability limits of long nonaxisymmetric cylindrical liquid bridges

There is a self-similar solution for the stability limits of long, almost cylindrical liquid bridges between equal disks subjected to both axial and lateral accelerations. The stability limits depend on only two variables; the so-called reduced axial, and lateral Bond numbers. A novel experimental setup that involved rotating a horizontal cylindrical liquid bridge about a vertical axis of rotation was designed to test the stability limits predicted by the self-similar solution. Analytical predictions compared well with both numerical and experimental results.

Coherent structures in statistically-stationary homogeneous shear turbulence

La región cerca de la pared de flujos turbulentos de pared ya está bien conocido debido a su bajo número de Reynolds local y la separación escala estrecha. La región lejos de la pared (capa externa) no es tan interesante tampoco, ya que las estadísticas allí se escalan bien por las unidades exteriores. La región intermedia (capa logarítmica), sin embargo, ha estado recibiendo cada vez más atención debido a su propiedad auto-similares. Además, de acuerdo a Flores et al. (2007) y Flores & Jiménez (2010), la capa logarítmica es más o menos independiente de otras capas, lo que implica que podría ser inspeccionado mediante el aislamiento de otras dos capas, lo que reduciría significativamente los costes computacionales para la simulación de flujos turbulentos de pared. Algunos intentos se trataron después por Mizuno & Jiménez (2013), quien simulan la capa logarítmica sin la región cerca de la pared con estadísticas obtenidas de acuerdo razonablemente bien con los de las simulaciones completas. Lo que más, la capa logarítmica podría ser imitado por otra turbulencia sencillo de cizallamiento de motor. Por ejemplo, Pumir (1996) encontró que la turbulencia de cizallamiento homogéneo estadísticamente estacionario (SS-HST) también irrumpe, de una manera muy similar al proceso de auto-sostenible en flujos turbulentos de pared. Según los consideraciones arriba, esta tesis trata de desvelar en qué medida es la capa logarítmica de canales similares a la turbulencia de cizalla más sencillo, SS-HST, mediante la comparación de ambos cinemática y la dinámica de las estructuras coherentes en los dos flujos. Resultados sobre el canal se muestran mediante Lozano-Durán et al. (2012) y Lozano-Durán & Jiménez (2014b). La hoja de ruta de esta tarea se divide en tres etapas. En primer lugar, SS-HST es investigada por medio de un código nuevo de simulación numérica directa, espectral en las dos direcciones horizontales y compacto-diferencias finitas en la dirección de la cizalla. Sin utiliza remallado para imponer la condición de borde cortante periódica. La influencia de la geometría de la caja computacional se explora. Ya que el HST no tiene ninguna longitud característica externa y tiende a llenar el dominio computacional, las simulaciopnes a largo plazo del HST son ’mínimos’ en el sentido de que contiene sólo unas pocas estructuras media a gran escala. Se ha encontrado que el límite principal es el ancho de la caja de la envergadura, Lz, que establece las escalas de longitud y velocidad de la turbulencia, y que las otras dos dimensiones de la caja debe ser suficientemente grande (Lx > 2LZ, Ly > Lz) para evitar que otras direcciones estando limitado también. También se encontró que las cajas de gran longitud, Lx > 2Ly, par con el paso del tiempo la condición de borde cortante periódica, y desarrollar fuertes ráfagas linealizadas no físicos. Dentro de estos límites, el flujo muestra similitudes y diferencias interesantes con otros flujos de cizalla, y, en particular, con la capa logarítmica de flujos turbulentos de pared. Ellos son exploradas con cierto detalle. Incluyen un proceso autosostenido de rayas a gran escala y con una explosión cuasi-periódica. La escala de tiempo de ruptura es de aproximadamente universales, ~20S~l(S es la velocidad de cizallamiento media), y la disponibilidad de dos sistemas de ruptura diferentes permite el crecimiento de las ráfagas a estar relacionado con algo de confianza a la cizalladura de turbulencia inicialmente isotrópico. Se concluye que la SS-HST, llevado a cabo dentro de los parámetros de cílculo apropiados, es un sistema muy prometedor para estudiar la turbulencia de cizallamiento en general. En segundo lugar, las mismas estructuras coherentes como en los canales estudiados por Lozano-Durán et al. (2012), es decir, grupos de vórticidad (fuerte disipación) y Qs (fuerte tensión de Reynolds tangencial, -uv) tridimensionales, se estudia mediante simulación numérica directa de SS-HST con relaciones de aspecto de cuadro aceptables y número de Reynolds hasta Rex ~ 250 (basado en Taylor-microescala). Se discute la influencia de la intermitencia de umbral independiente del tiempo. Estas estructuras tienen alargamientos similares en la dirección sentido de la corriente a las familias separadas en los canales hasta que son de tamaño comparable a la caja. Sus dimensiones fractales, longitudes interior y exterior como una función del volumen concuerdan bien con sus homólogos de canales. El estudio sobre sus organizaciones espaciales encontró que Qs del mismo tipo están alineados aproximadamente en la dirección del vector de velocidad en el cuadrante al que pertenecen, mientras Qs de diferentes tipos están restringidos por el hecho de que no debe haber ningún choque de velocidad, lo que hace Q2s (eyecciones, u < 0,v > 0) y Q4s (sweeps, u > 0,v < 0) emparejado en la dirección de la envergadura. Esto se verifica mediante la inspección de estructuras de velocidad, otros cuadrantes como la uw y vw en SS-HST y las familias separadas en el canal. La alineación sentido de la corriente de Qs ligada a la pared con el mismo tipo en los canales se debe a la modulación de la pared. El campo de flujo medio condicionado a pares Q2-Q4 encontró que los grupos de vórticidad están en el medio de los dos, pero prefieren los dos cizalla capas alojamiento en la parte superior e inferior de Q2s y Q4s respectivamente, lo que hace que la vorticidad envergadura dentro de las grupos de vórticidad hace no cancele. La pared amplifica la diferencia entre los tamaños de baja- y alta-velocidad rayas asociados con parejas de Q2-Q4 se adjuntan como los pares alcanzan cerca de la pared, el cual es verificado por la correlación de la velocidad del sentido de la corriente condicionado a Q2s adjuntos y Q4s con diferentes alturas. Grupos de vórticidad en SS-HST asociados con Q2s o Q4s también están flanqueadas por un contador de rotación de los vórtices sentido de la corriente en la dirección de la envergadura como en el canal. La larga ’despertar’ cónica se origina a partir de los altos grupos de vórticidad ligada a la pared han encontrado los del Álamo et al. (2006) y Flores et al. (2007), que desaparece en SS-HST, sólo es cierto para altos grupos de vórticidad ligada a la pared asociados con Q2s pero no para aquellos asociados con Q4s, cuyo campo de flujo promedio es en realidad muy similar a la de SS-HST. En tercer lugar, las evoluciones temporales de Qs y grupos de vórticidad se estudian mediante el uso de la método inventado por Lozano-Durán & Jiménez (2014b). Las estructuras se clasifican en las ramas, que se organizan más en los gráficos. Ambas resoluciones espaciales y temporales se eligen para ser capaz de capturar el longitud y el tiempo de Kolmogorov puntual más probable en el momento más extrema. Debido al efecto caja mínima, sólo hay un gráfico principal consiste en casi todas las ramas, con su volumen y el número de estructuras instantáneo seguien la energía cinética y enstrofía intermitente. La vida de las ramas, lo que tiene más sentido para las ramas primarias, pierde su significado en el SS-HST debido a las aportaciones de ramas primarias al total de Reynolds estrés o enstrofía son casi insignificantes. Esto también es cierto en la capa exterior de los canales. En cambio, la vida de los gráficos en los canales se compara con el tiempo de ruptura en SS-HST. Grupos de vórticidad están asociados con casi el mismo cuadrante en términos de sus velocidades medias durante su tiempo de vida, especialmente para los relacionados con las eyecciones y sweeps. Al igual que en los canales, las eyecciones de SS-HST se mueven hacia arriba con una velocidad promedio vertical uT (velocidad de fricción) mientras que lo contrario es cierto para los barridos. Grupos de vórticidad, por otra parte, son casi inmóvil en la dirección vertical. En la dirección de sentido de la corriente, que están advección por la velocidad media local y por lo tanto deforman por la diferencia de velocidad media. Sweeps y eyecciones se mueven más rápido y más lento que la velocidad media, respectivamente, tanto por 1.5uT. Grupos de vórticidad se mueven con la misma velocidad que la velocidad media. Se verifica que las estructuras incoherentes cerca de la pared se debe a la pared en vez de pequeño tamaño. Los resultados sugieren fuertemente que las estructuras coherentes en canales no son especialmente asociado con la pared, o incluso con un perfil de cizalladura dado. ABSTRACT Since the wall-bounded turbulence was first recognized more than one century ago, its near wall region (buffer layer) has been studied extensively and becomes relatively well understood due to the low local Reynolds number and narrow scale separation. The region just above the buffer layer, i.e., the logarithmic layer, is receiving increasingly more attention nowadays due to its self-similar property. Flores et al. (20076) and Flores & Jim´enez (2010) show that the statistics of logarithmic layer is kind of independent of other layers, implying that it might be possible to study it separately, which would reduce significantly the computational costs for simulations of the logarithmic layer. Some attempts were tried later by Mizuno & Jimenez (2013), who simulated the logarithmic layer without the buffer layer with obtained statistics agree reasonably well with those of full simulations. Besides, the logarithmic layer might be mimicked by other simpler sheardriven turbulence. For example, Pumir (1996) found that the statistically-stationary homogeneous shear turbulence (SS-HST) also bursts, in a manner strikingly similar to the self-sustaining process in wall-bounded turbulence. Based on these considerations, this thesis tries to reveal to what extent is the logarithmic layer of channels similar to the simplest shear-driven turbulence, SS-HST, by comparing both kinematics and dynamics of coherent structures in the two flows. Results about the channel are shown by Lozano-Dur´an et al. (2012) and Lozano-Dur´an & Jim´enez (20146). The roadmap of this task is divided into three stages. First, SS-HST is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, longterm simulations of HST are ‘minimal’ in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, Lz, which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large (Lx > 2LZ, Ly > Lz) to prevent other directions to be constrained as well. It is also found that very long boxes, Lx > 2Ly, couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wallbounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, ~ 20S~l (S is the mean shear rate), and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general. Second, the same coherent structures as in channels studied by Lozano-Dur´an et al. (2012), namely three-dimensional vortex clusters (strong dissipation) and Qs (strong tangential Reynolds stress, -uv), are studied by direct numerical simulation of SS-HST with acceptable box aspect ratios and Reynolds number up to Rex ~ 250 (based on Taylor-microscale). The influence of the intermittency to time-independent threshold is discussed. These structures have similar elongations in the streamwise direction to detached families in channels until they are of comparable size to the box. Their fractal dimensions, inner and outer lengths as a function of volume agree well with their counterparts in channels. The study about their spatial organizations found that Qs of the same type are aligned roughly in the direction of the velocity vector in the quadrant they belong to, while Qs of different types are restricted by the fact that there should be no velocity clash, which makes Q2s (ejections, u < 0, v > 0) and Q4s (sweeps, u > 0, v < 0) paired in the spanwise direction. This is verified by inspecting velocity structures, other quadrants such as u-w and v-w in SS-HST and also detached families in the channel. The streamwise alignment of attached Qs with the same type in channels is due to the modulation of the wall. The average flow field conditioned to Q2-Q4 pairs found that vortex clusters are in the middle of the pair, but prefer to the two shear layers lodging at the top and bottom of Q2s and Q4s respectively, which makes the spanwise vorticity inside vortex clusters does not cancel. The wall amplifies the difference between the sizes of low- and high-speed streaks associated with attached Q2-Q4 pairs as the pairs reach closer to the wall, which is verified by the correlation of streamwise velocity conditioned to attached Q2s and Q4s with different heights. Vortex clusters in SS-HST associated with Q2s or Q4s are also flanked by a counter rotating streamwise vortices in the spanwise direction as in the channel. The long conical ‘wake’ originates from tall attached vortex clusters found by del A´ lamo et al. (2006) and Flores et al. (2007b), which disappears in SS-HST, is only true for tall attached vortices associated with Q2s but not for those associated with Q4s, whose averaged flow field is actually quite similar to that in SS-HST. Third, the temporal evolutions of Qs and vortex clusters are studied by using the method invented by Lozano-Dur´an & Jim´enez (2014b). Structures are sorted into branches, which are further organized into graphs. Both spatial and temporal resolutions are chosen to be able to capture the most probable pointwise Kolmogorov length and time at the most extreme moment. Due to the minimal box effect, there is only one main graph consist by almost all the branches, with its instantaneous volume and number of structures follow the intermittent kinetic energy and enstrophy. The lifetime of branches, which makes more sense for primary branches, loses its meaning in SS-HST because the contributions of primary branches to total Reynolds stress or enstrophy are almost negligible. This is also true in the outer layer of channels. Instead, the lifetime of graphs in channels are compared with the bursting time in SS-HST. Vortex clusters are associated with almost the same quadrant in terms of their mean velocities during their life time, especially for those related with ejections and sweeps. As in channels, ejections in SS-HST move upwards with an average vertical velocity uτ (friction velocity) while the opposite is true for sweeps. Vortex clusters, on the other hand, are almost still in the vertical direction. In the streamwise direction, they are advected by the local mean velocity and thus deformed by the mean velocity difference. Sweeps and ejections move faster and slower than the mean velocity respectively, both by 1.5uτ . Vortex clusters move with the same speed as the mean velocity. It is verified that the incoherent structures near the wall is due to the wall instead of small size. The results suggest that coherent structures in channels are not particularly associated with the wall, or even with a given shear profile.

The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Spectral bifurcations in dispersive wave turbulence

Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed—the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)—depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date—over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.

A family of membrane-embedded metalloproteases involved in regulated proteolysis of membrane-associated transcription factors

We present evidence that the sporulation protein SpoIVFB of Bacillus subtilis is a member of a newly recognized family of metalloproteases that have catalytic centers adjacent to or within the membrane. SpoIVFB is required for converting the membrane-associated precursor protein, pro-σK, to the mature and active transcription factor σK by proteolytic removal of an N-terminal extension of 20 amino acids. SpoIVFB and other family members share the conserved sequence HEXXH, a hallmark of metalloproteases, as well as a second conserved motif NPDG, which is unique to the family. Both motifs, which are expected to form the catalytic center of the protease, overlap hydrophobic segments that are predicted to be separate transmembrane domains. The only other characterized member of this family of membrane-embedded metalloproteases is the mammalian Site-2 protease (S2P), which is required for the intramembrane cleavage of the eukaryotic transcription factor sterol regulatory element binding protein (SREBP). We report that amino acid substitutions in the two conserved motifs of SpoIVFB impair pro-σK processing and σK-directed gene expression during sporulation. These results and those from a similar analysis of S2P support the interpretation that both proteins are founding members of a family of metalloproteases involved in the activation of membrane-associated transcription factors. Thus, the pathways that govern the activation of the prokaryotic transcription factor pro-σK and the mammalian transcription factor SREBP not only are analogous but also use processing enzymes with strikingly homologous features.

Predicting species diversity in tropical forests

A fundamental question in ecology is how many species occur within a given area. Despite the complexity and diversity of different ecosystems, there exists a surprisingly simple, approximate answer: the number of species is proportional to the size of the area raised to some exponent. The exponent often turns out to be roughly 1/4. This power law can be derived from assumptions about the relative abundances of species or from notions of self-similarity. Here we analyze the largest existing data set of location-mapped species: over one million, individually identified trees from five tropical forests on three continents. Although the power law is a reasonable, zeroth-order approximation of our data, we find consistent deviations from it on all spatial scales. Furthermore, tropical forests are not self-similar at areas ≤50 hectares. We develop an extended model of the species-area relationship, which enables us to predict large-scale species diversity from small-scale data samples more accurately than any other available method.

Symmetries in geology and geophysics

Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth’s topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters.

Sequence-specific recognition of cytosine C5 and adenine N6 DNA methyltransferases requires different deformations of DNA.

DNA methyltransferases modify specific cytosines and adenines within 2-6 bp recognition sequences. We used scanning force microscopy and gel shift analysis to show that M.HhaI, a cytosine C-5 DNA methyltransferase, causes only a 2 degree bend upon binding its recognition site. Our results are consistent with prior crystallographic analysis showing that the enzyme stabilizes an extrahelical base while leaving the DNA duplex otherwise unperturbed. In contrast, similar analysis of M.EcoRI, an adenine N6 DNA methyltransferase, shows an average bend angle of approximately 52 degrees. This distortion of DNA conformation by M.EcoRI is shown to be important for sequence-specific binding.

Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.