Inverted Cone Research Articles

Focusing of inertial waves by a vertically annular forcing

A theory of inertial wave focusing generated by a vertically oscillating slender torus immersed in a uniformly rotating fluid is presented. The analytical solution of the velocity field shows that, under an axisymmetric annular forcing in inviscid rotating fluid, the wave rays form a double cone symmetric about the plane on which the torus is located. At the two vertices of the double cone, the waves are in a shock-like manner focus causing localized surges of energy. After focusing, the waves continue their propagation and form a new inverted cone with the same cone angle, such that both cones are symmetric about the focal point. These results are in good agreement with the experimental and numerical study by Duran-Matute et al. [Phys. Rev. E 87, 041001(R) (2013)]. When friction effects occur, the wave pattern changes substantially and the wave away from the focal point is significantly attenuated so that the symmetry about the focal point is broken. As a consequence, the wave beam widens and the focusing effect becomes weaker with increasing Ekman number (Ek), which indicates the ratio of the viscous force to the Coriolis force. Furthermore, for the same Ek, the focusing effect tends to disappear when the forcing frequency is close to zero or twice the angular velocity of rotating flow. For forcing frequency close to the angular velocity of a rotating fluid, the amplitude of the vertical velocity at the focal point reaches its maximum, which corresponds to a wave propagation angle of 60 degrees.

Seismic Reflection Data Reveal the 3D Subsurface Structure of Pit Craters

AbstractPit craters are quasi‐circular depressions observed on rocky and icy planetary bodies, as well as numerous asteroids. Pit craters are thought to form by overburden collapse into a subsurface cavity or volumetrically depleted zone. Importantly, the surface size and distribution of pit craters may provide an important record of otherwise inaccessible subsurface processes. However, because we cannot access the subsurface of many planetary bodies, we rely on physical and numerical models to infer processes linked to pit crater formation. Here, we use 3D seismic reflection data to quantify the palaeosurface and subsurface geometry of 59 Late Jurassic pit craters buried to depths of ∼3 km within a sedimentary basin, offshore NW Australia. The pit craters are typically funnel‐like, with an inverted conical upper section underlain by a pipe. Pit crater depths, that is, the height of inverted cone sections, correlate with their plan‐view length, consistent with observations of pit craters elsewhere; this trend is rendered less apparent by later sediment‐infilling. For the first time, we show some pit crater pipes connect to underlying igneous dikes or steeply dipping, likely dilatational portions of normal faults. Although some pit craters seemed to have formed due to faulting and others to dyking, they cannot be differentiated based on their surface expression. Our data also suggest pit crater size may not relate to the mechanical properties of the host material. Overall, we conclude that the surface expression of pit craters on Earth and other planetary bodies may not be diagnostic of subsurface processes or properties.

Multifunctional Inverse Opal Microneedle Arrays for Drug Delivery and Monitoring.

Microneedle arrays (MNs) have a demonstrated value in transdermal drug delivery systems. Attempts to this technology focus on the generation of functional MNs to achieve intelligent drug delivery. Here, multifunctional inverse opal microneedle (IOMN) arrays with the abilities are reported to load various drugs and monitor drug release. The IOMNs are generated by using poly(ethylene glycol) diacrylate (PEGDA) to replicate hierarchical structure templates that are composed of self-assembled silica colloidal nanoparticles in the inverted cone structure wells. Because of their interconnected porous structures, different actives, or drugs can be loaded into the IOMNs without organic solvents and chemical polymerization. It is demonstrated that when these drugs loaded IOMNs pierce the skin at position of interest and for slow release, the average refractive index of the IOMNs decreases with the release process, resulting in a corresponding blueshift of their characteristic spectrum. Thus, by measuring the wavelength shift value of the IOMNs, the amount of releaseddrugs can be monitored, providing essential guidance for efficient clinical treatment. These features indicate that the IOMNs are valuable smart drug delivery systems in personalized therapy.

Evaluating the impact of tree morphologies and planting densities on outdoor thermal comfort in tropical residential precincts in Singapore

Trees play an essential role in improving outdoor thermal comfort amidst rapid urbanization and impending climate change. Physiological Equivalent Temperature (PET) is used as the thermal comfort metric, derived based on a combination of in-situ measured meteorological parameters and numerically simulated pedestrian-level radiant exchange. The numerical model is developed based on surface energy balance coupled with the Monte Carlo ray-tracing technique and is validated with in-situ measurements. We study the thermal comfort enhancement potential of four typical tree morphologies at varied planting densities in the residential precincts in tropical Singapore. Firstly, we examine the temporal evolution and spatial distribution of PET in a matured residential precinct (MRP) on a typical hot day. Trees with large canopies either in diameter or height, i.e., umbrella and oblong trees, are most effective in improving outdoor thermal comfort. In particular, the umbrella trees improve the precinct mean PET by 1 class from “Warm” to “Slightly warm” at 14:00. Amongst different land features, the mean reduced PET is highest on land features near trees, i.e., grass, by up to 4.35 °C. Secondly, we evaluate the effects of varied planting densities in a new residential precinct (NRP), where open grass patches exist between buildings. At 14:00, tree planting densities of 2.20, 12.20, 29.33, and 36.76 trees per 10,000 m2 are needed per 1 °C of mean reduced PET for umbrella, oblong, round to inverted cone trees, respectively. Our findings provide insights on the choice of tree morphology and planting density to mitigate the thermal stress of high-density living.

Mathematical modeling of pulmonary acinus structure: Verification of acinar shape effects on pathway structure using rat lungs

The pulmonary acinus is the gas exchange unit in the lung and has a very complex microstructure. The structure model is essential to understand the relationship between structural heterogeneity and mechanical phenomena at the acinus level with computational approaches. We propose an acinus structure model represented by a cluster of truncated octahedra in conical, double-conical, inverted conical, or chestnut-like conical confinement to accommodate recent experimental information of rodent acinar shapes. The basis of the model is the combined use of Voronoi and Delaunay tessellations and the optimization of the ductal tree assuming the number of alveoli and the mean path length as quantities related to gas exchange. Before applying the Voronoi tessellation, controlling the seed coordinates enables us to model acinus with arbitrary shapes. Depending on the acinar shape, the distribution of path length varies. The lengths are more widely spread for the cone acinus, with a bias toward higher values, while most of the lengths for the inverted cone acinus primarily take a similar value. Longer pathways have smaller tortuosity and more generations, and duct length per generation is almost constant irrespective of generation, which agrees well with available experimental data. The pathway structure of cone and chestnut-like cone acini is similar to the surface acini's features reported in experiments. According to space-filling requirements in the lung, other conical acini may also be acceptable. The mathematical acinus structure model with various conical shapes can be a platform for computational studies on regional differences in lung functions along the lung surface, underlying respiratory physiology and pathophysiology.

A 3D DEM Model for Air Sparging Technology in the Saturated Granular Soils

This work provides a three-dimensional discrete element simulation (DEM) model to study the air sparging technology. The simulations have taken into account the multi-phases of bubble (gas) - fluid (water) - soil (solid) particles. Bubbles are treated as discrete individual particles, with buoyancy and drag forces applied to bubbles and soil particles. The trajectory of each discrete bubble particle can be tracked using the discrete element model. It is found that the diffusion of the whole bubble is inverted conical though the motion behavior of a single bubble particle is random. Furthermore, the distribution of the radius of influence (ROI) is not uniform. The bubbles become more concentrated as in the center of the inverted cone. The number of bubbles dissipated from the water surface is normally distributed. The DEM simulation is a novel approach to studying air sparging technology that can provide us a deeper insight into bubble migration at the microscopic level.

Categories of Space and Time in the Christian Supertext of the Explanatory Dictionary

This article examines religious terminology (religious vocabulary recorded in explanatory dictionaries of the Russian literary language) from the standpoint of the categorial-textual approach. The methodological basis of the research proceeds from the fact that religionyms as a system-structural integrity form a special kind of supertext in the explanatory dictionary, which is organised by universal text categories based on their thematic unity. The article analyses the textual categories of space and time which structure the supertext. The study aims to identify the specificity of categories, which are peculiar to the Christian worldview and are reflected in the explanatory dictionary. The study mostly employs the categorial-textual analysis method and techniques of the component and contextual analysis methods. The most important conclusions drawn are that the spatial category of the supertext of religionyms includes objective and conceptual spaces. Objective space is based on the hierarchical dichotomy of “the earthly” and “the heavenly”. Earthly space is structured as a field where the core is the temple, the prototypical place, the nearest periphery is the place in the temple and near the temple, while the far periphery is the territory united by Christianity. Heavenly space is a linear vertical structure with the poles in the form of heaven and hell. Conceptual space can be represented as an “inverted cone” where the concrete turns into the abstract and opens into general cultural space. The Chronos of religious discourse represents the dichotomy “the temporal” vs “the eternal”. The category of temporality in the supertext of religious names is represented by objective time existing both in profane and sacred manifestations. The general conclusion is that the types of space and time in the Christian explanatory dictionary supertext do not contradict the chronotope of religious texts. The study refers to examples from the following explanatory dictionaries: The Dictionary of the Russian Language by S. I. Ozhegov (1953); The Explanatory Dictionary of the Russian Language by S. I. Ozhegov and N. Yu. Shvedova (1994); and The Dictionary of the Russian Language edited by A. P. Evgenyeva (1985–1988).

Solution of the boundary value problem of heat conduction in a cone

In the paper we consider the boundary value problem of heat conduction in a non-cylindrical domain, which is an inverted cone, i.e. in the domain degenerating into a point at the initial moment of time. In this case, the boundary conditions contain a derivative with respect to the time variable; in practice, problems of this kind arise in the presence of the condition of the concentrated heat capacity. We prove a theorem on the solvability of a boundary value problem in weighted spaces of essentially bounded functions. The issues of solvability of the singular Volterra integral equation of the second kind, to which the original problem is reduced, are studied. We use the Carleman-Vekua method of equivalent regularization to solve the obtained singular Volterra integral equation.

Effects of Soret and Dufour on Mixed Convection over a Cone in a Non-Darcy Porous Medium with Chemical Reaction

This work explore the boundary layer behavior under the effects of Soret and Dufour on the mixed convection adjacent to inverted cone immersed within non-Darcian porous milieu together with chemical reaction action. The natural and forced convection limits are also considered in this study. The equations governing the problem together with the boundary conditions are converted to non-similar non-dimensional shape and solved numerically using finite difference method. It was found that enhances the value of the Soret number will increase the amount of heat transport and decrease the amount of mass transport. Enhances the value of Dufour number or chemical reaction parameter will reduce the amount of heat transfer and raise the amount of mass transfer.

The Process of Separating Buckwheat and Wheat Grain in a Pneumatic Cone Separator in the Context of Sustainable Agriculture

In machines and devices used for separating and cleaning seed mixtures, the components of such mixtures can be separated in a stream of air. The efficiency of separation of a two-component (model) mixture containing wheat kernels and buckwheat nutlets was investigated. The main crop seeds and other crop seeds imitating impurities accounted for 80% and 20% (w/w), respectively. The experiment involved a pneumatic cleaning device with an immobile conical surface, designed by the authors, where mixture components are separated in a stream of air. The seed mixture was separated in a separator with the shape of an inverted cone, where the seeds were set into motion by a stream of air. The separation efficiency of the analyzed two-component mixture in the designed separator exceeded 78%. Regression equations describing the separation efficiency index of the entire seed mixture (ε) and the separation efficiency of the main crop seeds (ηp) and seeds imitating impurities (ηz) were derived. The coefficient of determination (R2) for the above regression equations describing the separation efficiency of the mixture components (main crop seeds and seeds imitating impurities) and the separation efficiency index of the entire seed mixture ranged from 0.81 to 0.94. This result indicates that the developed equations were characterized by satisfactory and highly satisfactory fit to empirical data, and that they can be applied to accurately predict the quality of the seed separation process in the cleaning device designed by the authors. The developed equations can be effectively used to model and automatically control separation processes in the proposed separator.

Effects of Plant Crown Shape on Microwave Backscattering Coefficients of Vegetation Canopy.

A microwave scattering model is a powerful tool for determining relationships between vegetation parameters and backscattering characteristics. The crown shape of the vegetation canopy is an important parameter in forestry and affects the microwave scattering modeling results. However, there are few numerical models or methods to describe the relationships between crown shapes and backscattering features. Using the Modified Tor Vergata Model (MTVM), a microwave scattering model based on the Matrix Doubling Algorithm (MDA), we quantitatively characterized the effects of crown shape on the microwave backscattering coefficients of the vegetation canopy. FEKO was also used as a computational electromagnetic method to make a complement and comparison with MTVM. In a preliminary experiment, the backscattering coefficients of two ideal vegetation canopies with four representative crown shapes (cylinder, cone, inverted cone and ellipsoid) were simulated: MTVM simulations were performed for the L (1.2 GHz), C (5.3 GHz) and X (9.6 GHz) bands in fully polarimetric mode, and FEKO simulations were carried out for the C (5.3 GHz) band at VV and VH polarization. The simulation results show that, for specific input parameters, the mean relative differences in backscattering coefficients due to variations in crown shape are as high as 127%, which demonstrates that the crown shape has a non-negligible influence on microwave backscattering coefficients of the vegetation canopy. In turn, this also suggests that investigation on effects of plant crown shape on microwave backscattering coefficients may have the potential to improve the accuracy of vegetation microwave scattering models, especially in canopies where volume scattering is the predominant mechanism.

An Ultrawideband Microfabricated Gold-Based Antenna Array for Terahertz Communication

The microwave frequency band typically used for wireless communications will soon become saturated and will no longer be able to fulfill the high bandwidth demands of modern communication networks. Terahertz (THz) communication has appeared as a highly attractive, future-generation wireless technology that offers higher spectral bandwidth and, therefore, higher data rates. However, the full exploitation of THz technologies is contingent upon the availability of energy-efficient sources and devices. In this letter, we present a fabrication and measurement of a microscale planar inverted cone antenna array made of gold. Using an ungrounded coplanar waveguide (CPW) feed, the microfabricated structure provides a bandwidth of 37.9% with the resonant frequency of 0.925 THz. Given the cost of microfabrication is reduced substantially with rapid technological advancements, the results of this letter suggest that high-speed THz communications can be realized for wide-scale applications.

Magnetized Bi-convective Nanofluid Flow and Entropy Production Using Temperature-sensitive Base Fluid Properties: A Unique Approach

The flow mechanism and entropy production of a bi-convective, magnetized, radiative nano-liquid flow for an inverted cone considering temperature-sensitive water properties is accomplished numerically. The functional nanomaterial comprises Copper, Alumina in the base liquid, water. The mathematical equations representing the system's physical characteristics are solved numerically by adopting a robust numerical approach for indulgencing non-similar solutions to understand numerous parameters' effect on temperature, velocity, salient gradients, and entropy production. The investigation summarizes that buoyancy force and injection heighten the velocity, and suction, particle percentage, radiation elevate the heat transfer. At the same time, the radiation and Brinkman number enhance the entropy generation. It is also detected from this investigation that the magnetic effect shows dual behaviour in entropy generation.

Thermal dynamic damage of aircraft composite material suffered from lightning channel attachment based on moving mesh method

There is a complex nonlinear dynamic coupling and multi-physical damage between lightning channel and composite material. This paper aims to study the coupling mechanism between lightning channel and composite material. Magneto Hydro Dynamics (MHD) model is established to describe physical characteristics of lightning channel. Moving mesh approach and interface tracking method are applied to deal with the dynamic damage of composites material exposed to lightning channel. This coupling numerical method is validated by a case of aluminum (Al) alloy plate under lightning channel. It is also investigated the current flow, dynamic damage, interaction mechanism of composite laminate during lightning channel attachment. The results reveal that lightning current mainly flows along carbon fiber direction in plane. Current density decreases along the depth direction of composite laminate. Magnetic field contours exhibit a whirlpool shape around the discharge channel. Electromagnetic force is perpendicular to composite laminate surface. Lightning damage morphology of composite laminate exhibits an inverted cone shape. Ablation depth is about 1.57 mm and damage area is about 2080 mm2, which are consistent with experimental results. There exits mutual relationship between lightning damage morphology and lightning channel evolution.

Modelling of full-scale silo experiments with flow correcting inserts using material point method (MPM) based on hypoplasticity

Flow patterns in bulk solids in silos are of importance for stresses exerted on silo walls. They may be changed by using different inserts. The paper discusses numerical results on confined granular flow of cohesionless sand in a full-scale metal silo with different symmetrically placed inserts, used for correcting a flow pattern (double cone, cone-in-cone and inverted cone). The material point method (MPM) was employed to simulate the dynamic flow of sand in a silo. To describe the flow behaviour of cohesionless sand, a hypoplastic constitutive model was adopted. The emphasis was on flow patterns and pressures on both silo walls and inserts. The numerical outcomes were directly compared with the corresponding experiments in a full-scale silo. A satisfactory agreement was achieved between numerical and experimental outcomes. In MPM calculations, the effect of initial void ratio of sand, wall friction angle, insert position and grid cell size was also studied.

105.19 An inverted cone and Fermat’s last theorem

105.19 An inverted cone and Fermat’s last theorem

Study on Critical Hydraulic Gradient Theory of Flow Soil Failure in Cohesive Soil Foundation

The current formula of critical hydraulic gradient is not adapted to solve critical hydraulic gradient of cohesive soil. Assume that the seepage failure mode of the cohesive soil foundation was cylindrical or inverted circular truncated cone, based on the calculation formula of the critical hydraulic gradient of Terzaghi, the analytical formula of the critical hydraulic gradient considering the influence of the shear strength of the soil was derived. Then, the seepage failure process of the clay layer was simulated numerically, and the effects of the clay layer thickness, failure radius, and shear strength indexes on the critical hydraulic slope were analyzed. The comparison results show that the numerical test results are in good agreement with the calculated results of the new formula. In addition, the critical hydraulic gradient of sandy loam and loess under different working conditions was studied severally by a self-made permeation failure instrument. The results show that the critical hydraulic gradient decreases with the increase of soil thickness and failure radius, and the maximum error between the test and the corresponding formula results is no more than 16%.

Jute Felt for Noise Reduction: Understanding Effect of Pore Size Distribution

ABSTRACT Effect of pore size and its distribution on the noise reduction coefficient of jute felt were studied through capillary flow porometer and impedance tube. The inter-criteria correlation method was used to optimize the type of jute felts to obtain noise reduction coefficient of 0.5. The porometry study of the needle punched jute felt suggested the gradient pore structure of felt due to presence of needling induced inverted cone of pores within fibrous mass. The jute felt with an areal density 796.5 g/m2 with mean pore diameter 60.32 µm offered optimum noise reduction coefficient of 0.5. The percentage weight of pore distribution in the range of 45≥ ∅ <25 µm was 44.61%, indicated that to achieve an objective of NRC≥ 0.5 the most influential pore diameter range was 45≥ ∅ 25.The increased number of jute fiber per unit area of felts from 55 to 430 resulted in narrowing of inter fiber spaces and consequently reduced the mean pore size. Further increase in number of fibers ultimately leads to blocking of spaces within fibers and get compacted like a solid fibrous mass.

An intelligent planning model for the development and utilization of urban underground space with an application to the Luohu District in Shenzhen

Development and utilization of Urban underground space (UUS) is one of the key ways for developing sustainable cities. However, the development and utilization of UUS is currently occurring in a passive manner, lacking proactive and quantitative planning. In this paper, an intelligent planning model was established to guide the future development and utilization of UUS. The proposed model, in which more than twenty factors were considered, is capable of analysing the suitability of UUS development in different regions and at different depths. In addition, an improved artificial intervention genetic algorithm (AIGA) with an additional correlation operator was integrated into the proposed model to achieve the optimal two-dimensional (2D) planning scheme by quantitively analysing the matching of the ground surface and underground space, and the compactness and suitability of underground space. A three-dimensional (3D) planning scheme was obtained by analysing the stratification of the underground space and hierarchical development. The proposed intelligent planning model was, subsequently, applied to the development and utilization of UUS in Luohu District in Shenzhen. An analysis of the geological conditions and the current construction status of the ground surface showed that 69.4% of the underground space is suitable for shallow layer developments, and this proportion further increases to 76% for the sub-shallow, sub-deep and deep layers, indicating that the Luohu District is highly suitable for developing underground space. Furthermore, the derived optimal 2D planning scheme indicated that the suitability component plays a greater important role in the objective values than the matching and compactness components, and more attentions should be paid to the development of municipal facilities in the shallow layer in Luohu District. The derived 3D planning scheme of Luohu District showed the characteristics of an “inverted cone”, where the utilization rate significantly decreases with increasing depth. The findings in this paper provide new insights for the future development and utilization of UUS.

Hypogene speleogenesis and paragenesis in the Dolomites

The Dolomites of northern Italy feature some of the most intensively studied carbonate rocks worldwide. Yet, little is known about the long karst history of this mountain range dating back to the Miocene. This study scrutinizes three caves (F10, Milchloch and Cioccherloch) in the Fanes-Sennes-Prags Nature Park (Province of South Tyrol) and the adjacent Fosses area in the Natural Park of Ampezzo Dolomites (Province of Belluno, Veneto). Paleo-phreatic passages of these limestone caves mostly follow a NW-SE orientation, similar to the nearby Val Salata fault. A multi-method approach including cave morphological and isotopic analyses of wall-rock cores was applied to reconstruct the multi-stage speleogenetic history of these cavities. Clastic sediments partly cemented to the cave walls and paragenetic features such as ceiling channels and solutional ramps are present in all studied caves. F10 cave shows widespread laughöhle geometries, including inverted cone chambers and horizontal passages with trapezoid cross sections, characteristic of slow water convection in a hypogene regime. Drill cores in F10 cave exhibit a systematic depletion in both oxygen and carbon isotopes close to the cave wall. The thickness of this isotopically altered zone ranges from a few mm to 4 cm and alteration can sometimes also be macroscopically identified. The amplitude of the isotopic shift ranges from 2.0 to 5.0‰ for δ13C and from 1.9 to 4.9‰ for δ18O. One of the wall rock cores from Cioccherloch also shows a thin isotopic halo, while no evidence of isotopic alteration was found in Milchloch. Our results provide strong geochemical evidence of wall rock alteration driven by hypogene water-rock interaction in at least two of the caves. We propose an early hypogene speleogenetic phase, followed by uplift and denudation resulting in the opening of these cavities to the surface that allowed clastic sediment influx. The sediment infill in combination with the abundant paragenetic features records a second phase in the karst evolution. This paragenetic phase did not involve hypogene waters, as indicated by the lack of isotopic alteration in the wall rock of paragenetic features. The latest phase of speleogenesis is represented by vadose morphologies and vadose speleothems locally dating back to at least 650 ka. This study demonstrates that the combination of morphological analyses and geochemical fingerprinting represents a powerful approach to decipher the commonly complex speleogenetic history of limestone caves.