Mathematical toolbox and its application in the development of laboratory scale vertical axis wind turbine

Wind turbine works with the principle of extracting energy from the wind to generate electricity. The power generated is directly proportional to the wind speed available. There are two major types of wind turbine design, namely the horizontal and vertical axis wind turbine depending on the orientation of the turbine rotor and its generator. This paper deals with the design of vertical turbine due to its advantage of operating at a low wind speed over that of horizontal turbine. The analysis of change in the parameters of a vertical axis wind turbine is investigated to get the optimized way in which the rotor of the turbine is to be designed. This is done through modelling and simulation of the turbine using various parameters in the MATLAB/SIMULINK environment. A graphical user interface is created for a generic model of vertical axis wind turbine that is used to determine its parameters

Spatial Anisotropies and Temporal Fluctuations in Extracellular Matrix Network Texture during Early Embryogenesis

Early stages of vertebrate embryogenesis are characterized by a remarkable series of shape changes. The resulting morphological complexity is driven by molecular, cellular, and tissue-scale biophysical alterations. Operating at the cellular level, extracellular matrix (ECM) networks facilitate cell motility. At the tissue level, ECM networks provide material properties required to accommodate the large-scale deformations and forces that shape amniote embryos. In other words, the primordial biomaterial from which reptilian, avian, and mammalian embryos are molded is a dynamic composite comprised of cells and ECM. Despite its central importance during early morphogenesis we know little about the intrinsic micrometer-scale surface properties of primordial ECM networks. Here we computed, using avian embryos, five textural properties of fluorescently tagged ECM networks — (a) inertia, (b) correlation, (c) uniformity, (d) homogeneity, and (e) entropy. We analyzed fibronectin and fibrillin-2 as examples of fibrous ECM constituents. Our quantitative data demonstrated differences in the surface texture between the fibronectin and fibrillin-2 network in Day 1 (gastrulating) embryos, with the fibronectin network being relatively coarse compared to the fibrillin-2 network. Stage-specific regional anisotropy in fibronectin texture was also discovered. Relatively smooth fibronectin texture was exhibited in medial regions adjoining the primitive streak (PS) compared with the fibronectin network investing the lateral plate mesoderm (LPM), at embryonic stage 5. However, the texture differences had changed by embryonic stage 6, with the LPM fibronectin network exhibiting a relatively smooth texture compared with the medial PS-oriented network. Our data identify, and partially characterize, stage-specific regional anisotropy of fibronectin texture within tissues of a warm-blooded embryo. The data suggest that changes in ECM textural properties reflect orderly time-dependent rearrangements of a primordial biomaterial. We conclude that the ECM microenvironment changes markedly in time and space during the most important period of amniote morphogenesis—as determined by fluctuating textural properties

Texture measures at each embryonic stage (HH5 through HH7), averaged over orientation and spatial scale.

<p>The overall trend (spatial anisotropy and temporal fluctuations) in the textural measures during stages 5 through 7 was evident upon averaging the Haralick feature values (from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0038266#pone-0038266-g002" target="_blank">figures 2</a> through <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0038266#pone-0038266-g003" target="_blank"></a><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0038266#pone-0038266-g004" target="_blank"></a><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0038266#pone-0038266-g005" target="_blank">5</a>) over orientation (0°, 45°, 90° and135°) and scale (offsets 1 through 4 corresponding to each orientation). Values are mean ± S.D. Fibrillin-2 lateral network at stage 5 is shown in green, while lateral and medial fibronectin networks are shown in red and blue, respectively. Statistically significant differences (P<0.05) between ROIs were represented by “ * ”.</p

The relative textural differences between lateral and medial fibronectin networks during HH stage 6 of embryonic development.

<p>During HH stage 6 of embryonic development, the medial fibronectin network (b) demonstrated increased values of inertia across all offsets (c) compared with the lateral fibronectin network (a). The correlation values (d) in both medial and lateral networks demonstrated similar fall-off trends as a function of offset whereas a relative decrease in uniformity (e) and homogeneity (f) values marked the medial fibronectin distribution along the PS. The local entropy values of the medial network (h) were higher than the lateral network (g) as well. PS: Primitive Streak, Scale bar: 100 µm.</p

Texture timing-diagram summarizing the relative textural quality of medio-lateral fibronectin networks during avian developmental stages 5 through 7.

<p>A. Texture timing-diagram that captures the relative qualitative descriptors of texture in the ROI, weighted solely upon the scalar entropy values obtained during the stages of development (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0038266#pone-0038266-g006" target="_blank">Figure 6</a>), maps the texture as relatively “coarse/rough” and “smooth/fine.” From this qualitative perspective, the lateral fibronectin network is relatively coarse compared with the medial fibronectin network during HH stage 5 of development. However, the lateral network evolves into a relatively smooth texture during HH stage 6 of development. An absence of qualitative medio-lateral textural anisotropy in fibronectin networks during HH stage 7 is represented as overlapping diamonds that don't belong to a precise textual category. B. Embryonic ECM exhibits regional inhomogeneity of texture. The schematic demonstrates the hypothesized textural “gradient” of fibronectin (a difference in color represents a difference in the relative quality of texture) that might be relevant to mesendodermal cell motility during gastrulation. At scales coincident with the relative density of integrin (a cellular receptor for fibronectin) distribution on a mesendodermal cell, the textural anisotropy of the fibronectin network could potentially manifest as a qualitative textural “gradient” in the embryonic space, thus, influencing regional cell motility.</p

Schematic representation of extracellular matrix textural analysis.

<p>A. The embryonic extracellular matrix (ECM) was categorized into three spatial distributions (networks). The ECM associated with the antero-posterior (AP) axis was referred to as the medial network (blue). The ECM adjacent to the medial network, but not associated directly with the AP axis structures, was referred as the lateral network (red). The ECM distributions anterior and anterolateral to the Hensen's node (HN), the cranial networks (purple), were not included in the analysis. Textural analysis was performed on the immunofluorescence images of medial and lateral ECM networks. Gray-level co-occurrence matrices (GLCMs) were obtained and Haralick features were computed from the GLCMs defining the regions of interest (ROI), for four orientations (0°, 45°, 90° and 135°). Under each orientation, GLCM was computed for four offsets (1, 2, 3 and 4 pixels) thus totaling 16 offsets (4×4) for each texture parameter (inertia, correlation, uniformity and homogeneity). The entropy of the ROIs, another Haralick statistic, was used to assign a relative qualitative texture to the ROIs (ECM networks) during HH stages 5 through 7. B. A pictorial demonstration of the qualitative textural changes of the fibronectin network, assigned on the basis of scalar entropy. The approximate length of an embryo along the AP axis is 3 mm (HH stage 5), 5 mm (HH stage 6) and 7 mm (HH stage 7) respectively. The medial (blue) and lateral (red) fibronectin networks demonstrate distinct qualitative textures (coarse or smooth) at HH5 and HH6 stages. However, during HH7 there is an absence of distinct regional qualitative texture which is represented by a single oval enclosing both the medial and lateral fibronectin networks.</p

The relative textural differences between fibronectin and fibrillin-2 networks during HH stage 5 of embryonic development.

<p>A comparison of textural features between the lateral fibronectin (a) and fibrillin-2 (b) networks during HH stage 5 revealed the relatively higher values of inertia (c) and correlation (d) for the fibronectin network. The values for uniformity (e) and homogeneity (f) were relatively lower for the fibronectin network compared with the fibrillin-2 network. Meanwhile, the local entropy array of values was higher for fibronectin network (g) compared with the fibrillin-2 network (h). Scale bar: 100 µm.</p

The relative textural differences between lateral and medial fibronectin networks during HH stage 7 of embryonic development.

<p>The lateral fibronectin network (a) showed a relative increase in the rate of change of inertia values with respect to offset (c) compared with the medial fibronectin network (b) during HH stage 7. The rate of fall of correlation as a function of offset was also increased in the lateral network (d). Both uniformity (e) and homogeneity (f) of the lateral network decreased compared with the medial network. Meanwhile, the local regional entropy values of the lateral network (g) were higher compared with the medial network (h). PS: Primitive Streak, Scale bar: 100 µm.</p