Field Transforms for Multilayered Cylindrical and Spherical Structures of Finite Conductivity

1975 ◽  
Vol 53 (11) ◽  
pp. 1078-1087 ◽  
Author(s):  
E. Bahar
Keyword(s):  
Radius Of Curvature ◽  
Finite Conductivity ◽  
Electromagnetic Propagation ◽  
Wave Guides ◽  
Spherical Structures ◽  
Fourier Type ◽  
The Relationship ◽  
Conducting Cylinders ◽  
Dielectric Structures ◽  
Watson Transform

Problems of propagation around multilayered cylindrical or spherical structures possessing highly conducting cores have been analyzed in terms of discrete sets of modes. However, when propagation through the core of the structure is significant and of particular interest, the discrete set of modes is not suitable for the complete expansion of the electromagnetic fields.To provide a suitable basis for the expansion of the electromagnetic field in nonuniform multilayered, cylindrical or spheroidal, dielectric structures we derive expressions for the electric and magnetic field transforms consisting of both a discrete and a continuous spectrum of waves. The relationship between these transforms, the Kontorowich–Lebedev transform, and the discrete Watson transform is discussed. When the radius of curvature of the structure is infinite these transforms merge with generalized Fourier type transforms.The transforms can be used to investigate electromagnetic propagation through irregularly shaped dielectric wave guides, and through irregularly shaped spheroids. It can also be used to solve the problem of propagation in the interior (concave side) of irregularly shaped conducting cylinders or spheroids.

scholarly journals Ray Tracing Modeling of Electromagnetic Propagation for On-Chip Wireless Optical Communications

2018 ◽  
Vol 8 (4) ◽  
pp. 39 ◽  
Author(s):  
Franco Fuschini ◽  
Marina Barbiroli ◽  
Marco Zoli ◽  
Gaetano Bellanca ◽  
Giovanna Calò ◽  
...  
Keyword(s):  
Ray Tracing ◽  
Path Loss ◽  
Wireless Channel ◽  
Electromagnetic Propagation ◽  
Networks On Chip ◽  
Spatial Properties ◽  
Radiation Properties ◽  
Wireless Optical Communications ◽  
On Chip ◽  
The Relationship

Multi-core processors are likely to be a point of no return to meet the unending demand for increasing computational power. Nevertheless, the physical interconnection of many cores might currently represent the bottleneck toward kilo-core architectures. Optical wireless networks on-chip are therefore being considered as promising solutions to overcome the technological limits of wired interconnects. In this work, the spatial properties of the on-chip wireless channel are investigated through a ray tracing approach applied to a layered representation of the chip structure, highlighting the relationship between path loss, antenna positions and radiation properties.

Relationship of Semicircular Canal Size to Vestibular-Nerve Afferent Sensitivity in Mammals

2007 ◽  
Vol 98 (6) ◽  
pp. 3197-3205 ◽  
Author(s):  
Aizhen Yang ◽  
Timothy E. Hullar
Keyword(s):  
Semicircular Canal ◽  
High Frequency ◽  
High Gain ◽  
Vestibular Nerve ◽  
Radius Of Curvature ◽  
Horizontal Canal ◽  
Vestibular Nerve Afferents ◽  
The Relationship ◽  
Irregular Afferents ◽  
Anterior Canal

The relationship between semicircular canal radius of curvature and afferent sensitivity has not been experimentally determined. We characterized mouse semicircular canal afferent responses to sinusoidal head rotations to facilitate interspecies and intraspecies comparisons of canal size to sensitivity. The interspecies experiment compared the horizontal canal afferent responses among animals ranging in size from mouse to rhesus monkey. The intraspecies experiment compared afferent responses from the larger anterior canal to those from the smaller horizontal canal of mice. The responses of mouse vestibular-nerve afferents showed a low- and high-frequency phase lead and high-frequency gain enhancement. Regular horizontal-canal afferents showed a sensitivity to 0.5-Hz sinusoidal rotations of 0.10 ± 0.03 (SD) spike · s−1/deg · s−1 and high-gain irregular afferents showed a sensitivity of 0.25 ± 0.11 spike · s−1/deg · s−1. The interspecies comparison showed that the sensitivity of regular afferents was related to the radius of curvature R according to the formula Gr = 0.23R − 0.09 ( r2 = 0.86) and the sensitivity of irregular afferents was related to radius according to the formula Gi = 0.32R + 0.01 ( r2 = 0.67). The intraspecies comparison showed that regularly firing anterior canal afferents were significantly more sensitive than those from the relatively smaller horizontal canal, with Gr = 0.25R. This suggests that canal radius of curvature is closely related to afferent sensitivity both among and within species. If the relationship in humans is similar to that demonstrated here, the sensitivity of their regular vestibular-nerve afferents to 0.5-Hz rotations is likely to be about 0.67 spike · s−1/deg · s−1 and of their high-gain irregular afferents about 1.06 spikes · s−1/deg · s−1.

scholarly journals Morphological Aspects of Ciliary Motility

1967 ◽  
Vol 50 (6) ◽  
pp. 241-258 ◽  
Author(s):  
Peter Satir
Keyword(s):  
The Other ◽  
Radius Of Curvature ◽  
Arc Length ◽  
Apparent Displacement ◽  
Shaft Length ◽  
Ciliary Motility ◽  
Morphological Aspects ◽  
Circular Arcs ◽  
The Relationship

In Elliptio complanatus lateral cilia, two distinct patterns of filament termination can be discerned. In one case, all nine filaments are present and all are single; in the second, at least one filament is missing but doublets are still present. These probably represent different configurations within one cilium in different stroke positions; to get from one to the other, some peripheral filaments must move with respect to others. The data are consistent with the hypothesis that the filaments themselves do not change length, but rather slide past one another to accommodate increasing curvature. The bent regions of the cilium are in the form of circular arcs. In a few cases, apparent displacement of filaments at the tip (Δl) can be shown to be accounted for if we assume that all differences are generated within these arcs. The displacement per degree of bend is 35 A. Regions of bent arc are initially confined to the base of the cilium but move up the shaft as straight regions appear below them. From the relationship between arc length and radius of curvature, a shaft length that is the unit that initially bends and slides may be defined. Quantal displacements of the length of one 14S dynein may perhaps occur at sites between filaments at opposite sides of such a unit as sliding occurs.

Influence of molecular structure on the dynamic thermoelasticity of polyphasic polymer systems

1985 ◽  
Vol 63 (1) ◽  
pp. 189-195
Author(s):  
Robert H. Marchessault ◽  
Terry L. Bluhm ◽  
Hrire M. Gharapetian ◽  
Pudupadi R. Sundararajan
Keyword(s):  
Dimethyl Formamide ◽  
Polymer Systems ◽  
X Ray ◽  
X Ray Scattering ◽  
Order Of Magnitude ◽  
Spherical Structures ◽  
Thermoelastic Response ◽  
Heat Pulses ◽  
Molecular Morphology ◽  
The Relationship

The relationship between the dynamic thermoelastic behavior and molecular morphology of polyphasic polymer systems was studied. A sensitive tensometer equipped with a 50 W/I2 V heating lamp provided uniform and controlled heat pulses to one side of the film. For various extension ratios, the stress change (Δσ) as a function of the sample temperature, was recorded, both for increasing and decreasing extension ratios.The amount of increase in stress Δσ with temperature was different for Kraton GX-6500 samples cast from either toluene, cyclohexane, or heptane. The variation of Act with temperature was dependent on the extension ratio and was always greater for increasing extension. The slope of Δσ with temperature decreased at 100–150% elongation in all Kraton GX-6500 samples during increasing extension. However, this slope increased at higher elongations. Small angle X-ray scattering studies on Kraton GX-6500 showed the presence of lamellar, rod shape, and spherical structures in samples cast from toluene, cyclohexane, and heptane solvents, respectively. The extreme dependence of elastomeric behavior on polyphasic morphology caused Kraton samples to show a strong decline in thermoelastic response with cycling.X-ray studies on the films of Spandex, cast from dimethyl formamide, at different extension ratios showed the onset of crystallization at about 150% elongation. The thermoelastic studies performed on Spandex films also showed an increase in slope of Δσ vs. T at 150–170% elongations, which was attributed to the influence of increased crystalline orientation on thermoelastic response. X-ray studies on unstretched and stretched Hytrel films showed the presence of crystallinity. The magnitude of Δσ and variation with temperature for Hytrel films was greater than that of either Spandex, Kraton GX-6500, or cross-linked natural rubber.By comparison with the latter, only Hytrel was superior in the magnitude of Δσ variations with temperature. This was attributed to intrinsic crystallinity and the orientation which developed on stretching. At extension ratios λ = 2, Δσ for Hytrel was an order of magnitude greater than for cross-linked natural rubber.

scholarly journals Experimental Study on Ultrasonic Shot Peening Forming and Surface Properties of AALY12

2015 ◽  
Vol 1094 ◽  
pp. 339-342
Author(s):  
Chao Xun Liu ◽  
Shi Hong Lu ◽  
Wei Miao ◽  
Pan Feng Song ◽  
Tian Rui Wu
Keyword(s):  
Experimental Study ◽  
Surface Roughness ◽  
Electric Current ◽  
Shot Peening ◽  
Processing Time ◽  
Radius Of Curvature ◽  
Micro Hardness ◽  
Current Time ◽  
Ultrasonic Shot Peening ◽  
The Relationship

Ultrasonic shot peening (USP) on AALY12 sheet was studied. Several parameters (arc heights, surface roughness, surface topography and micro hardness) with different USP process parameters were measured. The research proposes that radius of curvature of shot peened sheet increases with time and electric current decreasing, while increases with pin diameter increasing, and radius of curvature reaches a saturation level after a specific processing time and electric current. An empirical model of the relationship between radius of curvature and pin diameter, electric current, time was also obtained. The research shows that the increment of surface and vertical micro hardness of material is more obvious with longer time and higher value of electric current, which can be up to 20% and 28% respectively.

Modelling of circular wave guides

1992 ◽  
Vol 70 (10-11) ◽  
pp. 1092-1098 ◽  
Author(s):  
A. Delage ◽  
K. A. McGreer ◽  
E. Rainville
Keyword(s):  
Integrated Circuit ◽  
Beam Propagation Method ◽  
Two Dimensions ◽  
Effective Index ◽  
Radius Of Curvature ◽  
Index Method ◽  
Photonic Integrated Circuit ◽  
Circular Arcs ◽  
Straight Line ◽  
Wave Guides

In many circumstances the design of interconnects in a photonic integrated circuit can be simplified by using low loss curved wave guides in the shapes of circular arcs. Radiative losses associated with the curvature have been computed as a function of the radius of curvature. The technique takes advantage of the effective index method to reduce the problem from two dimensions to one dimension (1D) and uses a change of coordinate that transforms an arc of circle into a straight line. This transformation results in a monotonous increase of the refractive index as function of r (the distance from the centre of the circle) for original constant index regions. The new system is solved by discretizing this varying effective index onto many small layers of constant index over a window large enough to contain the region where the field is not negligible. A multilayer algorithm in 1D is then used to find complex propagation constants in which the imaginary part is related to the fundamental energy loss owing to the curvature. The solution also gives the shape of the field necessary to match the mode profiles at the junction between the straight and curved part of the wave guide. The basic change of variable has been extended to the finite difference solution of the scalar wave equation and to the beam propagation method.

Geometric Analysis of a Foldable Barrel Vault With Origami

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Jianguo Cai ◽  
Yixiang Xu ◽  
Jian Feng
Keyword(s):  
Geometric Analysis ◽  
Radius Of Curvature ◽  
Spherical Trigonometry ◽  
Longitudinal Length ◽  
Relationship Of ◽  
The Relationship

This paper investigates the geometry of a foldable barrel vault with modified Miura-ori patterns, which displays a curvature during the motion. The principal of spherical trigonometry was used to obtain the relationship of the inclined angles between adjacent folded papers of Miura-ori. Then, the radius, span, rise, and longitudinal length of the foldable barrel vault in all configurations throughout the motion are determined. The results show that the radius of curvature grows exponentially and the span increases during deployment. Furthermore, the rise increases first, followed by a decrease with increasing deployment angle.

scholarly journals Evaluation of the Relationships between Corneal Parameters, Ocular Biometry, and Myopia Magnitude

2021 ◽  
Vol 50 (10) ◽  
pp. 3077-3084
Author(s):  
Mohd Izzuddin Hairol ◽  
Norlaili Arif ◽  
Pui Theng Yong ◽  
Mariah Asem Shehadeh Saleh Ali ◽  
Nik Nor Adlina Nik Idris ◽  
...  
Keyword(s):  
Axial Length ◽  
Corneal Thickness ◽  
Anterior Chamber Depth ◽  
Radius Of Curvature ◽  
Corneal Curvature ◽  
Ocular Biometry ◽  
Corneal Asphericity ◽  
Corneal Radius ◽  
The Difference ◽  
The Relationship

Axial length of the eye correlates with the magnitude of myopia. However, there are conflicting reports on the relationship between certain corneal parameters with myopia magnitude. The objective of this study was to compare ocular biometry and corneal parameters between emmetropic and myopic groups. Participants (n=127) were categorized as emmetropia (spherical equivalent, SE, ±0.50D), low myopia (-0.75D≤SE<-6.00D) and high myopia (SE≥-6.00D). The difference in axial length, anterior chamber depth, and vitreous chamber depth between emmetrope, low myope, and high myope were highly significant (one-way ANOVA, all p<0.001) with significant correlations between SE and all these parameters (simple regressions, all p<0.001). However, central corneal thickness, corneal radius of curvature, and corneal asphericity between these groups, and the correlations between the ocular parameters with SE were not significantly different (all p>0.05). Corneal curvature correlated significantly with axial length (p=0.001) but not with myopia magnitude (p=0.91). Rather than myopia magnitude, axial length appears to be more sensitive to detect changes in corneal curvature in myopes. In conclusion, myopic patients’ axial length should be carefully considered for interventions that involve the cornea, such as orthokeratology and refractive surgery.

scholarly journals The effects of relative food item size on optimal tooth cusp sharpness during brittle food item processing

2014 ◽  
Vol 11 (101) ◽  
pp. 20140965 ◽  
Author(s):  
Michael A. Berthaume ◽  
Elizabeth R. Dumont ◽  
Laurie R. Godfrey ◽  
Ian R. Grosse
Keyword(s):  
Food Item ◽  
Radius Of Curvature ◽  
Fe Model ◽  
Tooth Shape ◽  
Coefficients Of Variation ◽  
Selective Forces ◽  
Item Size ◽  
The Relationship ◽  
Negative Relationships ◽  
Shape Analyses

Teeth are often assumed to be optimal for their function, which allows researchers to derive dietary signatures from tooth shape. Most tooth shape analyses normalize for tooth size, potentially masking the relationship between relative food item size and tooth shape. Here, we model how relative food item size may affect optimal tooth cusp radius of curvature (RoC) during the fracture of brittle food items using a parametric finite-element (FE) model of a four-cusped molar. Morphospaces were created for four different food item sizes by altering cusp RoCs to determine whether optimal tooth shape changed as food item size changed. The morphospaces were also used to investigate whether variation in efficiency metrics (i.e. stresses, energy and optimality) changed as food item size changed. We found that optimal tooth shape changed as food item size changed, but that all optimal morphologies were similar, with one dull cusp that promoted high stresses in the food item and three cusps that acted to stabilize the food item. There were also positive relationships between food item size and the coefficients of variation for stresses in food item and optimality, and negative relationships between food item size and the coefficients of variation for stresses in the enamel and strain energy absorbed by the food item. These results suggest that relative food item size may play a role in selecting for optimal tooth shape, and the magnitude of these selective forces may change depending on food item size and which efficiency metric is being selected.

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