A generalized mathematical theory and experimental verification of proportional notches

A theory and generalized synthesis procedure is advocated for the design of weir notches and orifice-notches having a base in any given shape, to a depth a, such that the discharge through it is proportional to any singular monotonically-increasing function of the depth of flow measured above a certain datum. The problem is reduced to finding an exact solution of a Volterra integral equation in Abel form. The maximization of the depth of the datum below the crest of the notch is investigated. Proof is given that for a weir notch made out of one continuous curve, and for a flow proportional to the mth power of the head, it is impossible to bring the datum lower than (2m − 1)a below the crest of the notch. A new concept of an orifice-notch, having discontinuity in the curve and a division of flow into two distinct portions, is presented. The division of flow is shown to have a beneficial effect in reducing the datum below (2m − 1)a from the crest of the weir and still maintaining the proportionality of the flow. Experimental proof with one such orifice-notch is found to have a constant coefficient of discharge of 0.625. The importance of this analysis in the design of grit chambers is emphasized.

Size effect in self consolidating concrete beams with and without notches

The aim of this study is to obtain the fracture characteristics of low and medium compressive strength self consolidating concrete (SCC) for notched and un-notched plain concrete beams by using work of fracture G(F) and size effect model G(f) methods and comparing them with those of normal concrete and high performance concrete. The results show that; (i) with an increase in compressive strength, G(F) increases and G(f) decreases; (ii) with an increase in depth of beam, the decrease in nominal stress of notched beam is more when compared with that of a notchless beam.

The influence of Notches on Domain Dynamics in Ferroelectric Nanowires

The extent to which notches inhibit axial switching of polarization in ferroelectric nanowires was investigated by monitoring the switching behavior of single crystal BaTiO(3) wires before and after patterning triangular notches along their lengths. Static zero-field domain patterns suggested a strong domain-notch interaction, implying that notches should act as pinning sites for domain wall propagation. Surprisingly though, notches appeared to assist, rather than inhibit, polar switching. The origin of this effect was rationalized using finite element modeling of the electric field distribution along the notched wire; it was found that the air gap associated with the notch acted to enhance the local field, both in the air, and in the adjacent region of the ferroelectric. It seems that this local field enhancement outweighs any pinning interactions.

A comprehensive analysis of tidal notches in the Mediterranean Sea

Recent works (Evelpidou et al., 2012) suggest that the modern tidal notch is disappearing worldwide due sea level rise over the last century. In order to assess this hypothesis, we measured modern tidal notches in several of sites along the Mediterranean coasts. We report observations on tidal notches cut along carbonate coasts from 73 sites from Italy, France, Croatia, Montenegro, Greece, Malta and Spain, plus additional observations carried outside the Mediterranean. At each site, we measured notch width and depth, and we described the characteristics of the biological rim at the base of the notch. We correlated these parameters with wave energy, tide gauge datasets and rock lithology. Our results suggest that, considering 'the development of tidal notches the consequence of midlittoral bioerosion' (as done in Evelpidou et al., 2012) is a simplification that can lead to misleading results, such as stating that notches are disappearing. Important roles in notch formation can be also played by wave action, rate of karst dissolution, salt weathering and wetting and drying cycles. Of course notch formation can be augmented and favoured also by bioerosion which can, in particular cases, be the main process of notch formation and development. Our dataset shows that notches are carved by an ensemble rather than by a single process, both today and in the past, and that it is difficult, if not impossible, to disentangle them and establish which one is prevailing. We therefore show that tidal notches are still forming, challenging the hypothesis that sea level rise has drowned them.

On the affinity of Chuaria–Tawuia complex : a multidisciplinary study

In this study, biometric and structural engineering tool have been used to examine a possible relationship within Chuaria–Tawuia complex and micro-FTIR (Fourier Transform Infrared Spectroscopy) analyses to understand the biological affinity of Chuaria circularis Walcott, collected from the Mesoproterozoic Suket Shales of the Vindhyan Supergroup and the Neoproterozoic Halkal Shales of the Bhima Group of peninsular India. Biometric analyses of well preserved carbonized specimens show wide variation in morphology and uni-modal distribution. We believe and demonstrate to a reasonable extent that C. circularis most likely was a part of Tawuia-like cylindrical body of algal origin. Specimens with notch/cleft and overlapping preservation, mostly recorded in the size range of 3–5 mm, are of special interest. Five different models proposed earlier on the life cycle of C. circularis are discussed. A new model, termed as ‘Hybrid model’ based on present multidisciplinary study assessing cylindrical and spherical shapes suggesting variable cell wall strength and algal affinity is proposed. This model discusses and demonstrates varied geometrical morphologies assumed by Chuaria and Tawuia, and also shows the inter-relationship of Chuaria–Tawuia complex. Structural engineering tool (thin walled pressure vessel theory) was applied to investigate the implications of possible geometrical shapes (sphere and cylinder), membrane (cell wall) stresses and ambient pressure environment on morphologically similar C. circularis and Tawuia. The results suggest that membrane stresses developed on the structures similar to Chuaria–Tawuia complex were directly proportional to radius and inversely proportional to the thickness in both cases. In case of hollow cylindrical structure, the membrane stresses in circumferential direction (hoop stress) are twice of the longitudinal direction indicating that rupture or fragmentation in the body of Tawuia would have occurred due to hoop stress. It appears that notches and discontinuities seen in some of the specimens of Chuaria may be related to rupture suggesting their possible location in 3D Chuaria. The micro-FTIR spectra of C. circularis are characterized by both aliphatic and aromatic absorption bands. The aliphaticity is indicated by prominent alkyl group bands between 2800–3000 and 1300–1500 cm−1. The prominent absorption signals at 700–900 cm−1 (peaking at 875 and 860 cm−1) are due to aromatic CH out of plane deformation. A narrow, strong band is centred at 1540 cm−1 which could be COOH band. The presence of strong aliphatic bands in FTIR spectra suggests that the biogeopolymer of C. circularis is of aliphatic nature. The wall chemistry indicates the presence of ‘algaenan’—a biopolymer of algae.

Performance characterization of VGCF/epoxy nanocomposite sensors under static load cycles and in static structural health monitoring

Compared to conventional metal-foil strain gauges, nanocomposite piezoresistive strain sensors have demonstrated high strain sensitivity and have been attracting increasing attention in recent years. To fulfil their ultimate success, the performance of vapor growth carbon fiber (VGCF)/epoxy nanocomposite strain sensors subjected to static cyclic loads was evaluated in this work. A strain-equivalent quantity (resistance change ratio) in cantilever beams with intentionally induced notches in bending was evaluated using the conventional metal-foil strain gauges and the VGCF/epoxy nanocomposite sensors. Compared to the metal-foil strain gauges, the nanocomposite sensors are much more sensitive to even slight structural damage. Therefore, it was confirmed that the signal stability, reproducibility, and durability of these nanocomposite sensors are very promising, leading to the present endeavor to apply them for static structural health monitoring.

Vision in water

The purpose of this study is to determine visual performance in water, including the influence of pupil size. The water en-vironment was simulated by placing a goggle filled with saline in front of eyes, with apertures placed at the front of the goggle. Correction factors were determined for the different magnification under this condition in order to to estimate vision in water. Experiments were conducted on letter visual acuity (7 participants), grating resolution (8 participants), and grating contrast sensitivity (1 participant). For letter acuity, mean loss in vision in water, compared to corrected vision in air, varied between 1.1 log minutes of arc resolution (logMAR) for a 1mm aperture to 2.2 logMAR for a 7mm aperture. The vision in minutes of arc was described well by a linear relationship with pupil size. For grating acuity, mean loss varied between 1.1 logMAR for a 2mm aperture to 1.2 logMAR for a 6mm aperture. Contrast sensitivity for a 2mm aperture dete-riorated as spatial frequency increased, with 2 log unit loss by 3 cycles/degree. Superimposed on this deterioration were depressions (notches) in sensitivity, with the first three notches occurring at 0.45, 0.8 and 1.3 cycles/degree with esti-mates for water of 0.39, 0.70 and 1.13 cycles/degree. In conclusion, vision in water is poor. It becomes worse as pupil size increases, but the effects are much more marked for letter targets than for grating targets.

Vision in water

Purpose: To determine visual performance in water, including the influence of pupil size. Method: The water environment was simulated by placing a goggle filled with saline in front of eyes, with apertures placed at the front of the goggle. Correction factors were determined for the different magnification under this condition to estimate vision in water. Experiments were conducted on letter visual acuity (7 participants), grating resolution (8 participants), and grating contrast sensitivity (1 participant). Results: For letter acuity, mean loss in vision in water, compared to corrected vision in air, varied between 1.1 log minutes of arc resolution (logMAR) for a 1mm aperture to 2.2 logMAR for a 7mm aperture. The vision in minutes of arc was described well by a linear relationship with pupil size. For grating acuity, mean loss varied between 1.1 logMAR for a 2mm aperture to 1.2 logMAR for a 6mm aperture. Contrast sensitivity for a 2mm aperture deteriorated as spatial frequency increased, with 2 log unit loss by 3 cycles/degree. Superimposed on this deterioration were depressions (notches) in sensitivity, with the first three notches occurring at 0.45, 0.8 and 1.3 cycles/degree and with estimates for water of 0.39, 0.70 and 1.13 cycles/degree. Conclusion: Vision in water is poor. It becomes worse as pupil size increases, but the effects are much more marked for letter targets than for grating targets.

Influence of Elastic-Constants on Mode-I Stress-Intensity Factors in 3-Dimensional Crack Problems

Plates with V-through edge notches subjected to pure bending and specimens with rectangular edge-through-notches subjected to combined bending and axial pull were investigated (under live-load and stress-frozen conditions) in a completely nondestructive manner using scattered-light photoelasticity. Stress-intensity factors (SIFs) were evaluated by analysing the singular stress distributions near crack-tips. Improved methods are suggested for the evaluation of SIFs. The thickness-wise variation of SIFs is also obtained in the investigation. The results obtained are compared with the available theoretical solutions.