Parabolic Curvature Research Articles

Oscillating water column wave energy converter arrays coupled with a parabolic-wall energy concentrator in regular and irregular wave conditions

Based upon previous research on a single, high-efficiency Oscillating Water Column (OWC) wave energy capture system (Mayon et al., 2021), this work further extends the numerical investigation to the layout design and performance of the wave energy convertor (WEC) array coupled with a parabolic, energy concentrating wall in both regular and irregular incident wave conditions. A heuristic method to identify the optimal siting of the component, cylindrical OWC WECs in the array, installed in the concave opening of the wall is presented. The most advantageous location of the chambers is found to lie on a parabolic curvature line which is inset from the wall. Two separate arrays composed of three and five component OWCs are investigated in a range of regular wave conditions. The hydrodynamic power and efficiency of each chamber in each of the arrays is determined, and subsequently the aggregated array performance is established. It is found that the primary OWC chamber in the array configuration can attain approximately the same hydrodynamic power output as a single, isolated OWC chamber located the parabolic wall focus, albeit with a narrower energy capture bandwidth. The secondary and tertiary component chambers in the arrays contribute a lesser, yet still considerable quantity of hydrodynamic power to the consolidated system. The cumulative hydrodynamic efficiency of the collective arrays is less than the hydrodynamic efficiency of a single OWC chamber at the wall focus, but more efficient than an isolated OWC chamber positioned in open-sea conditions. Moreover, the hydrodynamic efficiency of the arrays exhibits better stability across the range of incident wave periods investigated, denoting that the individual component chambers in the array are efficacious at different incident wave conditions. The five chamber array is comprehensively analysed in irregular incident wave conditions. The array system is demonstrated to maintain a high power output and efficient behaviour in irregular incident wave conditions-an effect attributable to the reflecting wall influence. In summary, the five-chamber array configuration yields a higher power output and improved stability in terms of efficiency performance when compared with the three-chamber array configuration in regular waves. The array maintains this exceptional performance in irregular incident wave conditions.

Uniform gradient estimates of generalized parabolic mean curvature type equations with oblique boundary value problems

Uniform gradient estimates of generalized parabolic mean curvature type equations with oblique boundary value problems

Selective Area Epitaxy of Highly Strained InGaAs Quantum Wells (980-990 nm) in Ultrawide Windows Using Metalorganic Chemical Vapor Deposition.

We employed the selective-area-epitaxy technique using metalorganic chemical vapor deposition to fabricate and study samples of semiconductor heterostructures that incorporate highly strained InGaAs quantum wells (980-990 nm emission wavelength). Selective area epitaxy of InGaAs quantum wells was performed on templates that had a patterned periodic structure consisting of a window (where epitaxial growth occurred) and a passive mask (where epitaxial growth was suppressed), each with a width of 100 µm for every element. Additionally, a selectively grown potential barrier layer was included, which was characterized by an almost parabolic curvature profile of the surface. We conducted a study on the influence of the curvature profile of the growth surface on the optical properties of InGaAs quantum wells and the spatial distribution of composition in an ultrawide window. Our results showed that, under fixed selective-area-epitaxy conditions, the composition of the InxGa1-xAs and the wavelength of the quantum-well emission changed across the width of the window. Our study demonstrates that increasing the curvature profile of the growth surface of highly strained quantum wells leads to a transition in the photoluminescence wavelength distribution profile across the window, from quasi-parabolic to inverted parabolic.

Using Hydraulic Theory to Monitor Dense Overflows in a Parabolic Channel

Abstract Deep ocean passages are advantageous sites for long-term monitoring of deep transport and other physical properties relevant to climate. Rotating hydraulic theory provides potential for simplifying monitoring strategy by reducing the number of quantities that need to be measured. However, the applicability of these theories has been limited by idealizations such as restriction to zero or uniform potential vorticity (pv) and to channels with rectangular cross sections. Here the relationship between the flow characteristics in a canonical sea strait and its upstream condition is studied using uniform pv rotating hydraulic theory and a reduced-gravity shallow-water numerical model that allows for variation in pv. The paper is focused mainly on the sensitivity of the hydraulic solution to the strait geometry. We study the dynamics of channels with continuously varying (parabolic) cross sections to account for the rounded nature of sea-strait topographies and potentially improve monitoring strategies for realistic channel geometries. The results show that far enough from the channel entrance, the hydraulically controlled flow in the strait is insensitive to the basin circulation regardless of parabolic curvature. The controlled transport relation is derived for the case of uniform pv theory. Comparing the model to theory, we find that the measurement of the wetted edges of the interface height at the critical section can be used to estimate the volume flux. Based on this finding, we suggest three monitoring strategies for transport estimation and compare the estimates with the observed values at the Faroe Bank Channel. The results showed that the estimated transports are within the range of observed values. Significance Statement The paper investigates the relationship between the flow characteristics in an idealized sea strait and its upstream condition using rotating hydraulic theory and numerical modeling. We study the dynamics of channels with continuously varying (parabolic) cross sections to account for the rounded nature of sea-strait topographies and potentially improve monitoring strategies for realistic channel geometries. We suggest three monitoring strategies for transport estimation and apply the methods to the Faroe Bank Channel. Our estimates of dense water transport are within the range of observed values. This is significant, because the suggested monitoring strategies only require 1–3 measurements to estimate the transport at a given passage and can be used to guide observing systems.

Phenology forcing model to estimate phenology shifting ability of extreme environmental events.

The current study considered the climate extreme index (CEI) values originated from extreme environmental events (EEEs) by following the National Oceanic and Atmospheric Administration (NOAA) guidelines. The EEEs were fractionated into six sub-categories (i.e., high temperature, low temperature, high precipitation, low precipitation, drought, and wind), and the combined impact of CEIs was utilized to develop an algorithm for the estimation of the phenology sensitivity index (PSi). Finally, the CEIs, and the PSi were undergone the development of the phenology forcing (PF) model. The developed model showed a high sensitivity at the CEI value of as low as ≥1.0. Furthermore, the uncertainty index varied between 0.03 and 0.07, making a parabolic curvature at increasing CEIs (1.0–15.0). The current study precisely estimates the tendency of EEEs for phenology change. It will assist in policy-making and planning crop cultivation plans for achieving sustainable development goal 2 (SDG2) of the Food and Agriculture Organization (FAO).

Ternary association reactions of H3O+, NO+ and O2+• with N2, O2, CO2 and H2O; implications for selected ion flow tube mass spectrometry analyses of air and breath

The reactions of the reagent ions used for trace gas analysis in selected ion flow tube mass spectrometry (SIFT-MS), R+ , viz. H3 O+ , NO+ and O2 + , with the major gases in air and breath samples, M, viz. N2 , O2 , CO2 and H2 O, are investigated. These reactions are seen to form weakly-bound adduct ions, R+ M, by ternary association reactions that must not be mistaken for genuine volatile organic compound (VOC) analyte ions. The ternary association rate coefficients mediated by helium (He) carrier gas atoms, k3a , have been determined for all combinations of R+ and M, which form R+ M adduct ions ranging in m/z from 47 (H3 O+ N2 ) to 76 (O2 +• CO2 ). This was achieved by adding variable amounts of M (up to 0.5mbar pressure) into the He carrier gas (pressure of 1.33 mbar) in a SIFT-MS flow tube at 300 K. Parabolic curvature was observed on some of the semi-logarithmic decay curves that allowed the rate coefficients mediated by M molecules, k3b , to be estimated. Values of k3a were found to range from 1 × 10-31 cm6 s-1 to 5 × 10-29 cm6 s-1 , which form mass spectral R+ M "ghost peaks" of significant strength when analysing VOCs at parts-per-billion concentrations. It was seen that the R+ M adduct ions (except when M is H2 O) react with H2 O molecules by ligand switching forming the readily recognised monohydrates of the initial reagent cations R+ H2 O. Whilst this ligand switching diminishes the R+ M adduct ghost peaks, it does not eliminate them entirely. The significance of these adduct ions for trace gas analysis by SIFT-MS in the low m/z region is alluded to, and some examples are given of m/z spectral overlaps of the R+ M and R+ H2 O adduct cations with analyte cations of VOCs formed by analysis of complex media like exhaled breath, warning that ghost peaks will be enhanced using nitrogen carrier gas in SIFT-MS.

Modeling and Numerical Studies of Three‐Dimensional Conically Shaped Microwells Using Non‐Uniform Photolithography

AbstractConical microwells have found a wide range of applications such as in cancer diagnostics, cell spheroid formation, and three‐dimensional oncology models. Numerous microengineered fabrication techniques have been developed for the formation of such conically shaped microwells. Among many, non‐uniform photolithography (NUPL) in a PDMS microfluidic channel with a glass substrate, can be used to create polymeric microwells with tapered‐bottom and parabolic curvatures. Here, the parabolic well formation of microwells is numerically investigated using NUPL to better understand its key mechanisms. Temporal and spatial free‐radical diffusion are incorporated into the modeling of photopolymerization. In addition, the 3D‐shape tuning ability of NUPL is modeled for the synthesis of microwells through a variation of UV light intensity induced by the presence of opaque materials. The model and simulation results predict the time‐evolution of microwell formation with parabolic well features. The effects of the conical shape‐tuning parameters are numerically determined, i.e., the aspect ratio of the well diameter to channel height and the non‐uniformity of UV light intensity on the microwell depth and parabolic curvature. Numerical work provides meaningful insights into NUPL to optimize and design polymeric microwells with shape features tuned to their application.

Self-expanders to inverse curvature flows by homogeneous functions

In this paper, we study self-expanding solutions to a large class of parabolic inverse curvature flows by homogeneous symmetric functions of principal curvatures in Euclidean spaces. These flows include the inverse mean curvature flow and many nonlinear flows in the literature. We first show that the only compact self-expanders to any of these flows are round spheres. Secondly, we show that complete non-compact self-expanders to any of these flows with asymptotically cylindrical ends must be rotationally symmetric. Thirdly, we show that when such a flow is uniformly parabolic, there exist complete rotationally symmetric self-expanders which are asymptotic to two round cylinders with different radii. These extend some earlier results of inverse mean curvature flow to a wider class of flows.

Investigation on design methods for cable mesh configuration of deployable space antenna reflector

Mesh reflectors are always a preferable option for large size deployable antenna reflector over solid surface reflectors due to their flexibility of adjustment in minimum possible space and ability to get deployed to full configuration in space. Maintaining surface properties and accuracy are two important requirements in the design of the mesh reflector for the performance of cable network antenna reflectors. The present work considers the various design approaches for cable mesh configuration of space deployable antenna reflectors. The equal force density shape forming criteria such is applied for obtaining the desired parabolic curvature of the mesh configuration. The ring structure for the deployable mechanism is considered as rigid linkages for designing mesh configuration. A generalized numbering scheme for nodes and cable mesh link is formulated for carrying forward various shapes forming criteria which help in making an algorithm. The algorithm for a better understanding of these methods is developed using MATLAB with nodal coordinates and its connection. Mesh configuration is developed with a different number of divisions. A study is also carried out for finding the required number of divisions for a highly accurate parabolic profile for a particular band frequency. A demonstration model is developed and a comparison of the coordinates of the prototype is made with those arrived at using the model.

Uniqueness theorems of self-conformal solutions to inverse curvature flows

It is known from the literature that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and parabolic curvature flows by degree − 1 -1 homogeneous functions of principal curvatures in the Euclidean space. In this article, we prove that the round sphere is rigid in a stronger sense: under some natural conditions such as star-shapedness, round spheres are the only closed solutions to the above-mentioned flows which evolve by diffeomorphisms generated by conformal Killing fields.

Introducing a New Curve with Symmetrical Parabolic Curvature for Horizontal Alignment

AbstractSimple circular curves have been proposed by the road specifications to be implemented in horizontal alignment. In these curves, the centrifugal force is applied suddenly to the vehicles at...

The Competition of Roughness and Curvature in Area-Constrained Polymer Models

The competition between local Brownian roughness and global parabolic curvature experienced in many random interface models reflects an important aspect of the KPZ universality class. It may be summarised by an exponent triple $(1/2,1/3,2/3)$ representing local interface fluctuation, local roughness (or inward deviation) and convex hull facet length. The three effects arise, for example, in droplets in planar Ising models (Alexander, '01, Hammond, '11,'12). In this article, we offer a new perspective on this phenomenon. We consider directed last passage percolation model in the plane, a paradigmatic example in the KPZ universality class, and constrain the maximizing path under the additional requirement of enclosing an atypically large area. The interface suffers a constraint of parabolic curvature as before, but now its local structure is the KPZ fixed point polymer's rather than Brownian. The local interface fluctuation exponent is thus two-thirds rather than one-half. We prove that the facet lengths of the constrained path's convex hull are governed by an exponent of $3/4$, and inward deviation by an exponent of $1/2$. That is, the exponent triple is now $(2/3,1/2,3/4)$ in place of $(1/2,1/3,2/3)$. This phenomenon appears to be shared among various isoperimetrically extremal circuits in local randomness. Indeed, we formulate a conjecture to this effect concerning such circuits in supercritical percolation, whose Wulff-like first-order behaviour was recently established (Biskup, Louidor, Procaccia and Rosenthal, '12).

Molecular structure controls on micropore evolution in coal vitrinite during coalification

Micropores (<2 nm) play an important role in coalbed methane adsorption, desorption, and diffusion. However, the mechanisms of micropore formation and evolution still need further study. This study primarily focuses on molecular structure controls on micropore evolution during coalification. CO2 adsorption experiments were employed to characterize micropore structure in coals, and 13C nuclear magnetic resonance (13C NMR) and X-ray diffraction (XRD) were employed to characterize the molecular structures of those coal samples. The results demonstrated that micropore evolution during laboratory simulated coalification was similar to that in geo-time-scale natural maturation. This suggests that laboratory simulated coalification can be an effective method for studying micropore evolution during coalification. Micropore evolution in laboratory simulated coalification and natural maturation both exhibited a parabolic curvature with coal rank, with a minimum at ~1.4%. When vitrinite reflectance (Ro) was <1.4%, micropores were mainly controlled by the aliphatic part of the coal samples, and micropore volume decreased with decreasing aliphatic functional groups. When Ro varied from 1.4% to 4.0%, micropore structure was mainly controlled by aromatic parts and coal crystallite structure. In this coalification stage, micropore volume showed linear correlation with the fraction of aromatic bridgehead carbon, the fraction of protonated aromatic carbon, and the ratio of aromatic bridge carbon to aromatic peripheral carbon (XBP). Moreover, the increase in lateral sizes (La) and the decrease in interlayer spacing (d002) both resulted in the increase in micropore volume. In conclusion, the coal microporosity and its evolution were primarily determined by coal molecular structure. In different coalification stages, microporosity and its evolution were controlled by different sub-portions of the whole molecular structure. These findings can provide mechanistic insights of gas sorption and diffusion, as gas sorption and diffusion behaviors are simultaneously controlled by both pore structure and molecular structure.

Modeling Microwave Backscattering From Parabolic Rice Leaves

Scattering from rice leaves contributes substantially to total vegetation canopy backscattering and detailed knowledge about it is necessary for developing a microwave scattering model. A parabolic curve is generally adopted to simulate the leaf shape but this is rarely incorporated into the calculation of the scattering. In this paper, two specific models, one based on physical optics (PO) approximation and the other on the discrete dipole approximation (DDA), are presented to involve the parabolic leaf curvature effects. Three typical leaves were chosen from 1433 parabolic leaves obtained during ground measurements. The PO and DDA models were used to calculate the leaf scattering. The generalized Rayleigh–Gans (GRG) approximation was also included in the simulation. The method of moments, a computational electromagnetic method, was utilized to evaluate the accuracy of each model. Validation of the models was conducted at incidence angles ranging from 10° to 60°, incidence azimuthal angles ranging from 0° to 360°, and incidence frequencies of 1.2 GHz (L-band), 5.4 GHz (C-band), and 9.65 GHz (X-band). Among the GRG approximation, the DDA model and the PO model, the latter gave the best accuracy −>65% in the cases tested, while the GRG model was the least accurate. The high accuracy of the PO model was maintained at both the low and high frequency bands. The PO model, therefore, has great potential for use to interpret radar measurements from rice fields and other types of vegetation canopy.

Transforming the economic value of hillside housing—A case study of Seoul, South Korea

This study examines transforming real estate value of urban hillside for residential developments, drawing on two-fold panel analyses: a random-effect panel modeling and a growth-curve panel modeling, in Seoul, South Korea from 1990 to 2015. The results reveal the reduced gap between the land values in hillside and low-lying residential sites as moving toward 2015, evidenced by the rapidly growing rate of increase of land value in the former, whereby the parabolic curvature of the land value trajectory increased from 0.00152 to 0.00156, compared to that of the latter, whereby the equivalent to that decreased from 0.00224 to 0.00214. The results also suggest that the negative effect of higher elevation has decreased to approximately zero (−0.625% per 10-m increment) and projected to turn positive, in hillside residential sites, while the equivalent to that in the low-lying residential sites has been exacerbated (−3.786% per 10-m increment). By helping the understanding of the past, current and future hillside housing development—how the hillside sites have been and will be reevaluated by passage of time, this study will provide practical lessons in planning urban housing and natural amenity resources.

Crack-tip shape in the crack-growth rate transition of filled elastomers

The velocity transition in crack-growth dynamics and the accompanying changes in crack tip shapes are investigated for the elastomers composed of styrene-butadiene rubber and silica filler (SBR/SI). The concentrations of filler and cross-link (ϕf and cx, respectively), and temperature (T) are extensively varied in order to change the degree of nonlinearity in elasticity of the elastomers. The shapes of the crack tip are characterized by three parameters, i.e., the deviation δ from the parabolic one expected by the linear elastic fracture mechanics (LEFM), the parabolic curvature a, and the non-dimensional quantity aδ. The dependence of these parameters on the input tearing energy Γ is successfully explained by the weakly nonlinear theory of dynamic fracture (WNLT), which considers the contribution of the second-order shear modulus μ(2) to the strain field in addition to that of the first-order shear modulus μ(1), independently of ϕf, cx and T, unless δ exceeds a limit value (δC). SBR/SI shows an appreciably larger value of δC than the carbon-black filled acrylonitrile butadiene (NBR/CB) elastomers. The smaller value of δC for NBR/CB is attributed to that the contribution of the third-order nonlinear modulus μ(3)/μ(1), which is not considered in WNLT, is appreciably higher than that in SBR/SI. The magnitude of the threshold tearing energy Γc for the onset of the velocity transition shows a good correlation with the fracture toughness Wc normalized by the nonlinear elastic constant μ(1)3/μ(2)2 in WNLT. This result indicates that the magnitude is governed by the combined effect of the degree of nonlinearity in elasticity and the fracture toughness.

Effects of Leaflet Design on Transvalvular Gradients of Bioprosthetic Heart Valves.

Bioprosthetic aortic valves (BAVs) are becoming the prostheses of choice in heart valve replacement. The objective of this paper is to assess the effects of leaflet geometry on the mechanics and hemodynamics of BAVs in a fluid structure interaction model. The curvature and angle of leaflets were varied in 10 case studies whereby the following design parameters were altered: a circular arch, a line, and a parabola for the radial curvature, and a circular arch, a spline, and a parabola for the circumferential curvature. Six different leaflet angles (representative of the inclination of the leaflets toward the surrounding aortic wall) were analyzed. The 3-dimensional geometry of the models were created using SolidWorks, Pointwise was used for meshing, and Comsol Multiphysics was used for implicit finite element calculations. Realistic loading was enforced by considering the time-dependent strongly-coupled interaction between blood flow and leaflets. Higher mean pressure gradients as well as von Mises stresses were obtained with a parabolic or circular curvature for radial curvature or a parabolic or spline curvature for the circumferential curvature. A smaller leaflet angle was associated with a lower pressure gradient, and, a lower von Mises stress. The leaflet curvature and angle noticeably affected the speed of valve opening, and closing. When a parabola was used for circumferential or radial curvature, leaflets displacements were asymmetric, and they opened and closed more slowly. A circular circumferential leaflet curvature, a linear leaflet radial curvature, and leaflet inclination toward the surrounding aortic wall were associated with superior BAVs mechanics.

Effect of background parabolic current on characteristics and energetics of internal solitary waves by numerical simulation

Based on modifications of the observed background parabolic current in upper layer of the northeastern South China Sea (SCS), the effects of eight kinds of background currents on the characteristics and energy conversion of internal solitary waves (ISWs) are investigated by an Internal Gravity Wave (IGW) model. It is found that, although the background current has little effect on the number of the generated ISWs, it reduces the resulted phase speed of ISW. When the background parabolic current appears with its lower boundary near or above the main thermocline, the ISW amplitude and the depth of the isopycnal undergoing maximum displacement increase; when the background parabolic current curvature is reduced, the ISW amplitude and the ratio of baroclinic to barotropic energy reduce, whilst the phase speed of ISW, the baroclinic energy, and the ratio of baroclinic kinetic energy (KE) to available potential energy (APE) increase; when the lower boundary of background parabolic current extends down to the seabed and the background current curvature is reduced, the ISW amplitude and phase speed decrease, whilst the barotropic kinetic energy, the baroclinic energy and the ratio of KE to APE increase. At a whole depth, when the lower background current curvature is reduced and the upper current curvature is increased, the ISW amplitude, and phase speed, the ratio of baroclinic to barotropic energy, the baroclinic energy, and the ratio of KE to APE all increase.

Double grow-up and global convergence of solutions for a parabolic prescribed mean curvature problem

The paper is concerned with a parabolic mean curvature type problem with a varying parameter λ. We study large time behavior of global solutions for different ranges of λ and initial data and present some new asymptotic results about global convergence and infinite time blow-up. In particular, it is shown that for suitable ranges of parameter λ and initial data, there exists a double grow-up phenomenon: the solution itself blows up at every interior point and its gradient blows up at the boundary of the domain as t→+∞. We also establish an interesting connection between global convergence and the non-classical solution of the associated stationary problem: if initial data are smaller than the non-classical solution, then the solutions must decay to zero in C1 norm as t→∞.

Convexity estimates for surfaces moving by curvature functions

We consider the evolution of compact surfaces by fully nonlinear, parabolic curvature flows for which the normal speed is given by a smooth, degree one homogeneous function of the principal curvatures of the evolving surface. Under no further restrictions on the speed function, we prove that initial surfaces on which the speed is positive become weakly convex at a singularity of the flow. This generalises the corresponding result of Huisken and Sinestrari for the mean curvature flow to the largest possible class of degree one homogeneous surface flows.