Versions are found for Linux, Windows, and Mac. The versions can be run under Matlab version 2012 and newer. Versions are also found for Octave and a stand-alone C library. The last can be used for making stand-alone programs to run on e.g. clusters without the overhead of Matlab or Octave. The different versions are compiled specifically for the individual customers.
Since the third edition of Differential Equations with MATLAB first appeared in 2012, there have been many changes and enhancements to MATLAB and Simulink. These include addition of live scripts, new plotting commands, and major changes to the Symbolic Math Toolbox. This revised version brings the text completely up to date with the 2019a release of MATLAB.
matlab 2012 torrent 18
Download: https://tinurli.com/2vKOuL
Tree frogs climb smooth surfaces utilising capillary forces arising from an air-fluid interface around their toe pads, whereas torrent frogs are able to climb in wet environments near waterfalls where the integrity of the meniscus is at risk. This study compares the adhesive capabilities of a torrent frog to a tree frog, investigating possible adaptations for adhesion under wet conditions. We challenged both frog species to cling to a platform which could be tilted from the horizontal to an upside-down orientation, testing the frogs on different levels of roughness and water flow. On dry, smooth surfaces, both frog species stayed attached to overhanging slopes equally well. In contrast, under both low and high flow rate conditions, the torrent frogs performed significantly better, even adhering under conditions where their toe pads were submerged in water, abolishing the meniscus that underlies capillarity. Using a transparent platform where areas of contact are illuminated, we measured the contact area of frogs during platform rotation under dry conditions. Both frog species not only used the contact area of their pads to adhere, but also large parts of their belly and thigh skin. In the tree frogs, the belly and thighs often detached on steeper slopes, whereas the torrent frogs increased the use of these areas as the slope angle increased. Probing small areas of the different skin parts with a force transducer revealed that forces declined significantly in wet conditions, with only minor differences between the frog species. The superior abilities of the torrent frogs were thus due to the large contact area they used on steep, overhanging surfaces. SEM images revealed slightly elongated cells in the periphery of the toe pads in the torrent frogs, with straightened channels in between them which could facilitate drainage of excess fluid underneath the pad.
Much less is known about adhesion and toe pad morphology in rock or torrent frogs. Ohler [9] carried out a preliminary study on the toe pad morphology of torrent-living ranid frogs, demonstrating that the toe pads of Amolops had distinct anatomical differences from the typical pattern seen in tree frogs. The only relevant biomechanical work is a preliminary study of adhesion in the Trinidadian stream frog, Mannophryne trinitatis [10]. This species is good at adhering to rough wet surfaces, but very poor at sticking to dry rough ones. It also slips on smooth wet surfaces. This suggests that torrent frogs can cope with running water so long as the surfaces are rough.
Brunei, with several species of torrent frog capable of adhering to vertical rocks in waterfalls, and rock frogs capable of fast movement over wet rocks [11], presented a very good opportunity to study these frogs that are clearly specialists in adhesion under wet and flooded conditions. The present study compares the attachment capabilities of a torrent frog species to those of a tree frog species to see first whether there are differences in performance between the two species under different conditions (substrates varying in wetness and roughness), and second what these differences are based upon. For instance, is adhesive performance dominated by the area of contact used by the frogs, or do the two species show a difference in force per unit area that they can generate; i. e. are the toe pads of the torrent frogs more effective under wet conditions?
Our study focused on the comparison of a tree frog and a torrent frog species (Figure 1). Tree frogs are known to be good climbers [2], [12] but, unlike torrent frogs, are not found on rocks where there is fast flowing water. We chose male individuals of the Harlequin Tree frog (Rhacophorus pardalis) and male individuals of the Black-spotted Rock frog (Staurois guttatus). For an easier distinction between the two, we will refer to R. pardalis as the tree frog and to S. guttatus as the torrent frog. Both species were abundant around the Kuala Belalong Field Studies Centre, Ulu Temburong National Park (Brunei Darussalam, northern Borneo), where the experiments were carried out during two six-week visits (May/ June 2010 and 2012). The torrent frogs were found near waterfalls on fast flowing streams, where they could be captured on rocks (day) or surrounding vegetation (night). The tree frogs were caught at night on vegetation near small ponds in the forest. Although not identical in either body mass or snout-vent length (SVL), they were the best species match that was obtainable in sufficient numbers in the local area. Body mass was measured using an electronic balance (Mettler), while SVL was measured using callipers. Values are given in Table 1. The frogs were housed in plastic tanks, containing structural elements (rocks, branches and leaves) and ca. 1 depth of water. After the experiments, the frogs were released at the sites where they were captured.
All statistical tests were carried out using the statistical toolbox in Matlab (v2012a, Mathworks Corp., USA). Data for contact area was extracted at angles of 45 intervals from 0 to 180, which allowed us to draw statistical comparisons between these categories.
We will begin by examining the performance of the tree frog (Figure 3, white boxes), which forms the reference for judging the performance of the torrent frog. Slip angles are a measure of the frog's friction force, though are limited to the mass of the frog, since maximum values are given by an absence of slipping at 90. On the dry and wetted surfaces (low flow rates), very few of the tree frogs (R. pardalis) slipped at angles below 90, regardless of surface roughness. Only on the flooded surfaces (high flow rates) did performance decrease dramatically (, Test No. 3 in Table S1 in Supplementary Materials S1). Lowest slip angles occurred on the smooth surface, but recovered slightly with increased surface roughness (Figure 3A).
To summarise, there was no significant difference in performance between the species on all the dry surfaces. However, differences appeared on some of the wet surfaces (low flow rate) and were most dramatic under the high flow rates on the two rougher surfaces. The results clearly indicate that the torrent frog (S. guttatus), in contrast to the tree frog (R. pardalis), is extremely well adapted to adhering to rough surfaces under flooded conditions.
Using a special illumination technique (see Materials and Methods), the contact area of ventral body parts (toe pads, belly, thighs and uncategorised areas) of (A) the tree frog (R. pardalis) and (B) the torrent frog (S. guttatus) was measured at 0, 45, 90, 135 and 180. The photos at the top are images of the frogs at horizontal (0) and inverted (180) tilting positions. The plots represent medians of 42 trials from 6 frogs (tree frogs) and 33 trials from 6 frogs (torrent frogs), the percentages at the top representing the proportion of frogs still attached at each tilt angle.).
The torrent frogs (S. guttatus) used a similar amount of total ventral body area when they were resting against a horizontal surface (0 rotation of the platform). Pad contact area was, however, much smaller (approximately 25% of that in the larger tree frogs). As in the tree frogs, there was little change in behaviour until the platform rotation passed 70, at which point total contact area began to increase, mainly through use of belly skin. At angles between 90 and 135, the limbs were spread out sideways as in the tree frogs (though to a lesser degree) and frogs initially facing downhill would reorientate to face head-up (Video S3 or Figure S1). We tested whether this turning behaviour influenced the amount of contact area before and after the frog's re-orientation. In contrast to tree frogs, nearly all individual torrent frogs managed to reattach their belly skin after they turned around and increased their contact area even further (Mann-Whitney U-test: ). This ability might be crucial when climbing areas of fast flowing water, where quick re-attachment is a vital necessity.
To summarise, S. guttatus increased contact area with the substrate as they were rotated from 0 to 180, mainly by the use of the belly skin, while the tree frogs exhibited a decline in contact area, so that the majority were hanging on by their toe pads alone (Figure 4A, B). Note, however, that this increasing use of the body did not give torrent frogs any advantage on this smooth dry surface, as only 33% (11/33) maintained their attachment until 180, compared to 52% of the tree frogs. Total pad area was also clearly smaller in the torrent frogs, even when the difference in body size is taken into account, but they did show a greater ability to recover body contact area after a behavioural manoeuvre. Finally, limb spreading was a common behavioural feature exhibited by both frog species when rotated. Thus, it illustrates an important strategy for enhancing attachment on overhanging surfaces [17].
In the present study, we found that unrestrained torrent frogs adhered better than tree frogs to rough surfaces under wet conditions. Are there any morphological adaptations which could help to explain their better performance? Most tree frogs have hexagonal cells that are uniformly shaped (width-to-length ratio of the hexagons close to 1). However, previous work on torrent frogs [9] showed that the toe pad epithelium of ranid torrent frogs from a number of genera consisted of elongated cells (i. e. cells that deviate from a regular hexagonal shape), resulting in the channels between them providing shorter and straighter pathways from the centre of the toe pad to its edge. This has been presumed to be an adaptation for better drainage of water from under the toe pads in their flooded environment. Here we show images of the toe pads of the tree frog and torrent frog under study (Figure 6A, B), together with an image of another torrent frog species, Odorrana hosii, also found in the Brunei rainforest in the region of fast flowing rivers (Figure 6C). All three images are at the same magnification and are oriented so that the nearest edge of the pad is approximately at the top of the page. O. hosii shows the elongated shape typical of torrent frogs (width-to-length ratio smaller than 1 in the radial direction). Although usually surrounded by six other cells, the cells are not hexagons, as they mainly have curved rather than straight edges. Their ends are often pointed, especially the ends nearest the edges of the pad (see arrows in Figure 6C). As you can see from the line drawn on the image, the channels directing water towards the edge of the pad are almost straight. In our tree frog species, the pattern of epithelial cells is a lot more variable than the patterns of regular hexagons illustrated in [13] for hylid tree frogs. Most of the cells do, however, have six neighbours and straight edges, and so are irregular hexagons. Channel lengths in the direction of the edge of the pad are thus not shorter than across the pad (compare lengths of white solid and dashed lines). In our torrent frog species (S. guttatus), cell shape seems to vary with the region of the pad. In central regions, there is a tendency towards a pattern of roughly regular hexagons, but peripherally they are more elongated, the overall pattern being intermediate between those of the tree frog and O. hosii (Figure 6B). In such regions, channel lengths in the direction of the pad edge are relatively short, certainly shorter than across the pad (see lines on Figure 6B). We have also examined the structures of thigh and belly skin in both our species (Figure 7). Like the toe pad epithelium, the epithelium of the ventral surface of the tree frog (belly and ventral thigh skin) was subdivided by deep channels at intervals of about 200 μm, giving a quilted appearance, the cells being irregularly hexagonal, ca. 20 μm in diameter. In contrast, the belly and thigh skin of the torrent frog was relatively smooth, again consisting of approximately hexagonal cells of ca. 20 μm diameter. It is however unclear how these structures aid adhesion or friction. 2ff7e9595c
Comments