Edge Of Wedge Research Articles

Systems of Inclusions in a Spatial Elastic Wedge

Contact problems are considered for two identical thin rigid elliptic inclusions in a three-dimensional elastic wedge of two-sided angle outer faces of which are subjected to rigid or sliding support. The problems are reduced to integral equations with symmetric kernels. Two dimensionless geometric parameters are introduced to characterize location of the inclusions in the bisecting half-plane of the wedge. Assuming linear connection between the parameters, the regular asymptotic method is used to solve the problems. The asymptotic for two inclusions is compared with corresponding solutions for unit inclusion in the wedge as well as for a periodic chain of inclusions the axis of which is parallel to the wedge edge.

Patterned Ultraslippery Surfaces of Stainless Steel Prepared by Femtosecond Laser Ablation for Directional Manipulation of Liquid Droplets.

Slippery liquid-infused porous surfaces (SLIPS) have promising applications in chip laboratories, nanofriction power generation, and microfluidics due to their excellent properties such as good hydrophobicity and low adhesion. However, the self-driven stability of conventionally lubricated surfaces is not high, and the velocity of liquid droplets is difficult to regulate. This greatly limits the potential applications of SLIPS. A strategy is offered to prepare microporous structures of SLIPS directly on a stainless-steel substrate using femtosecond laser processing technology as the main means to realize exhibiting smoothness to liquids. At the same time, the principle of bionics is utilized, the porous structure of SLIPS is combined with the groove structure of rice leaves, or porous structures are combined with the wedge structure of shorebird beak to prepare the three-dimensional structure of SLIPS. Droplets exhibit significant individual anisotropy on three-dimensional (3D) SLIPS of leaf-like groove stripe structure in rice, enabling the precise control of droplet motion direction. When droplets are transported in wedge-shaped SLIPS with an asymmetric structure, the wedge edge can limit the direction of droplet motion while squeezing the droplet to generate Laplace pressure gradient, which achieves continuous self-driven transport of droplets. In addition, based on the above two processing strategies, an information transfer device is designed: the splicing of the self-driven transport surface with anisotropic topological channels enables the differential drive for liquid transport, which provides the conditions for the information transfer of the droplets. This strategy not only is simple and efficient but also provides new ideas for the effective development of multifunctional SLIPS as well as lab-on-a-chip and microfluidic domains.

Structural conditions for relay ramp fault development on the edge of the collision wedge: a case study from the East Slovak Basin

Structural conditions for relay ramp fault development on the edge of the collision wedge: a case study from the East Slovak Basin

Labia minoraplasty - the balance between technique and untoward effects: A case report

Case presentation: A 45-year-old nulliparous patient presented with a long-standing history of genitaldiscomfort in the form of friction, laceration, and dyspareunia. She was also esthetically displeased withher labia minora, which she considered too large and long. Her labia minora appearance was also notedto cause emotional distress. The patient requested labia minoraplasty. Despite correct techniqueselection, she was noted to have notching, fenestration, and pigment mismatch eight weekspostoperatively, and required revision surgery.Discussion: Wedge resection versus edge trimming is an active topic in cosmetic gynecology. Patientselection and hypertrophied labia minora are important considerations in technique selection. Thesehave a bearing on the eventual esthetic appearance and development of untoward effects.Conclusion: Even with the correct technique selection for a specific type of labial hypertrophy, untowardeffects may develop postoperatively, requiring reconstruction or revision later.

Beam-type acoustic black holes incorporating the microstructure-dependent nonlocal effect

Acoustic black holes (ABHs) are effective passive damping structures for capturing bending waves at wedge edges. However, as the wedge shape continuously reduces in size, the intrinsic length scale of the ABH's tip gradually approaches the external length scale, such as the wavelength of wave, which causes a phenomenon known as the "scale effect" to take hold of the ABH. Despite gaining considerable attention in the past two decades, the influence of intrinsic length on the energy aggregation of ABHs has not been thoroughly investigated. This study aims to explore the significant contribution of microstructure-dependent nonlocal effects on the dynamic behavior of ABHs, which holds great scientific importance. The nonlocality arises from the inherent length of the material being studied. A nonlocal elastic theory (NET) is employed to model the dynamic behavior of one-dimensional ABH beams. Geometric acoustic method is proposed to analyze the power-law beam wave number and microstructure-related reflection coefficient. Results indicate a significant impact of nonlocality on the acoustic energy of beam-type ABHs, particularly when the nonlocal intrinsic length approaches the truncation length of the wedge. Moreover, a comparison between the present study and classical theory reveals an overestimation of the reflection coefficient in conventional works for small truncation lengths. The relationship between the reflection coefficient, truncation length, and nonlocal characteristic lengths is thoroughly examined. Additionally, the influence of the damping layer and different power-law exponents m on ABH behavior is extensively studied.

Improvement to the Epoch of Reionisation power spectrum using simulations with the Central Redundant Array Mega-tile (CRAM)

Abstract Detection of the 21 cm signal from the Epoch of Reionisation (EoR) ( $z \sim 6 - 10$ ) amidst the dominant foregrounds, which are 3–4 orders of magnitude greater than the weak cosmological signal, is a challenging task for the existing 21 cm experiments. The detection is further challenged by the large Field of View (FoV) of the instrument used for observation, as it becomes necessary to excise foregrounds present within the FoV to make a successful detection. In response to the challenges faced, in our previous work, we developed and installed a new instrument – the Central Redundant Array Mega-tile (CRAM) – and integrated it within the MWA Phase II configuration. It is a larger antenna tile configuration ( $8\times 8$ dipoles) with a smaller FoV at every frequency under consideration and has multiple sidelobes of reduced response when compared with the existing Murchison Widefield Array (MWA) tiles. In this paper, we aim to demonstrate through power spectrum simulations that using the larger tile, such as the CRAM, can reduce the impact of bright radio foregrounds near the field edge. For the pedagogical approach aimed with this work, we developed a power spectrum pipeline to estimate the cylindrically averaged power spectrum. The power spectrum is estimated for MWA-MWA baselines and CRAM-MWA baselines using analytical beams, simulated diffuse sky maps and a semi-numerical 21 cm signal. Employing a drift scanning strategy, we estimate 1D and 2D power spectra for a series of two-minute observations spanning 24 hrs using the diffuse sky maps. Our simulations predict a power reduction at the edge of the EoR wedge. The reduction in foreground power is confirmed with the Fisher analysis of the expected signal-to-noise ratio (SNR) improvement, which reports a higher SNR with the power estimations from CRAM baselines when compared with the regular MWA baselines. The reduced power obtained with the CRAM baselines is consistent with the fact that the larger tile configuration has reduced the impact of foregrounds from near the horizon.

Modelling of soil destruction process by bulldozer using a spatially oriented working unit

The article uses approaches to creating a model for calculating soil cutting forces by spatially oriented working units of construction machines used on construction sites. The use of such a model is due to the need for continuous improvement of existing equipment and the creation of new ones, taking into account the existing needs. Today, there is a need for efficient performance of construction works related to the operation of construction equipment with dumping equipment. This, in turn, poses the task of determining the performance of mechanised earthworks in various working environments, one of the most common in Ukraine being marl clay, loam and argillaceous clay.
 The main method of mechanical soil development is cutting. The main geometric conditions are the position of the cutting wedge edge relative to the cutting direction and the surface of the massif, the outline of the cutting edge, the outline and number of working surfaces of the cutting wedge, the number of so-called side cut surfaces and the so-called blocked cut surfaces. The peculiarity of the digging process is that its power and energy indicators depend on the kinematic conditions and geometric parameters – thickness, width and area of the cut, as well as on the angles of orientation of the working unit in space.
 The computational model was created in accordance with the working hypothesis, where the movement of spatially oriented knives moves perpendicular to the blade equipment, at different ratios of the blade movement speed and knife movement, which creates spatial interaction with the working environment, and the deviation of the application of the full cutting force by an angle α.
 In accordance with the working hypothesis, we obtained five plans for the movement of the spatially oriented blade of the blade. Depending on the plan of movement of the spatially oriented knife, its geometric interaction with the working environment changes and the cutting force changes accordingly.
 The need to create more productive and efficient earthmoving equipment requires the use of modern design solutions. In the course of the study, a model for calculating the cutting of soils by spatially oriented earthmoving tools in the form of a dihedral knife of dump equipment was created. A comparison of soil cutting forces at different depths during the operation of a spatially oriented working body is also proposed. The results are summarised in the form of tabular data and graphs.

Novel vibration self-suppression of periodic pipes conveying fluid based on acoustic black hole effect

The pipes conveying fluid are concerned as extremely significant fluid-solid coupling structures due to the extensive application in the many engineering fields, but poor operating performances induced by unexpected vibration may destroy the related devices in the piping structures. To effectively attenuate the fluid-solid coupling vibration, a novel control technique is proposed to realize the vibration self-suppression of pipes conveying fluid with integration of the periodic acoustic black hole (ABH) wedges inspired by the extraordinary band gaps (BGs) behaviors of the metamaterials. On the basis of the Euler-Bernoulli (E-B) beam model, the mechanical model and dynamic equations are established by using Hamilton's principle. By applying the spectral element method (SEM) in conjunction with the transfer matrix method (TMM), as well as considering the Bloch theorem, the mechanism of elastic-wave distributions of such periodic ABH pipes conveying fluid are disclosed through investigating the BGs characteristic, frequency response and wave shapes. The results show the proposed technique can effectively form BGs in low frequency bands, and most of the energies are absorbed and scattered by the wedge edge of the pipes in the wave propagation. More importantly, by adjusting the system parameters, the proposed structure can enlarge the BGs regions and transfer it to the low frequency bands. It provides a simple design scheme for the manufacture of pipe conveying fluid with ultra-wide BGs.

Preface: Special Issue on Ophiolites and Oceanic Lithosphere

AbstractWith this Preface, we provide background information, a scientific overview of topics, and an annotated bibliography of the 63 papers published in the Journal of Geophysical Research (JGR) Special Issue on “Ophiolites and Oceanic Lithosphere, with a Focus on the Samail Ophiolite,” collected online at https://agupubs.onlinelibrary.wiley.com/doi/toc/10.1002/(ISSN)2169-9356.SAMAIL1. Topics covered in the Special Issue include formation and alteration of igneous ocean crust at submarine spreading centers, subduction zone mass transfer at the leading edge of the mantle wedge, the tectonic emplacement and evolution of ophiolites, processes of alteration and weathering of tectonically exhumed mantle peridotite, and the subsurface biosphere in the peridotite weathering environment. The bibliography, in the form of a supplementary Excel spreadsheet with links to each paper, is organized by topic, but can be sorted by first author, order of publication, specific Oman Drilling Project boreholes, and other factors.

Periodic system of rigid inclusions in a spatial elastic wedge

A periodic contact problem (tangential contact) on a chain of thin rigid inclusions located along the edge of a three-dimensional elastic wedge of a dihedral angle in its middle half-plane (rigid sealing of the wedge faces, the axis of the chain of inclusions is parallel to the edge of the wedge) is considered. To derive the integral equation, the previously obtained fundamental solution of the problem of the action of a concentrated force inside a three-dimensional elastic wedge is used. The nucleus has latent symmetry, then it is reduced to a form with explicit symmetry. To solve the integral equation, a regular asymptotic method is used, which is effective for relatively sparse and far from the edge chains of inclusions in a three-dimensional elastic wedge. Contact characteristics are calculated for different values of dimensionless geometric parameters. Previously, similar problems were considered about one inclusion (stringer) in a strip [1] and a three-dimensional wedge [2], as well as in an unbounded elastic body [1].

A singularity analysis in Keer’s elastic indentation problem

A non-axisymmetric three-dimensional frictionless contact problem for an elastic half-space and a cylindrical indenter with the face in a wedge form is considered under the assumption of a circular region of contact. Explicit formulas are derived for the critical indenter displacement and contact force that are needed to ensure full contact over the entire contact region. It is shown that the contact pressure beneath the indenter maintains a logarithmic singularity, which is produced by the wedge edge and is similar to the singularity of the contact pressure in the corresponding two-dimensional contact problem for a wedge rigid indenter.

Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

Stability of Attached Transonic Shocks in Steady Potential Flow past Three-Dimensional Wedges

We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the perturbation is away from the wedge edge in the previous results is removed. One of the key ingredients is to identify a "good" direction of the boundary operator of a boundary condition of the shock along the wedge edge, based on the non-obliqueness of the boundary condition for the weak shock on the edge. With the identification of this direction, an additional boundary condition on the wedge edge can be assigned to make sure that the shock is attached on the edge and linearly stable under small perturbation. Based on the linear stability, we introduce an iteration scheme and prove that there exists a unique fixed point of the iteration scheme, which leads to the global existence and nonlinear structural stability of the attached weak transonic shock. This approach is based on neither the hodograph transformation nor the spectrum analysis, and should be useful for other problems with similar difficulties.

Postseismic geodetic signature of cold forearc mantle in subduction zones

A sharp thermal contrast between the cold forearc and the hot arc and backarc is considered fundamental to various subduction-zone processes. However, direct observational evidence for this contrast is rather limited. If this contrast is present, it must cause a rheological contrast in the mantle wedge: elastic in the forearc and viscoelastic in the arc and backarc for the timescale of earthquake cycles. Here we demonstrate that postseismic deformation following large subduction earthquakes provides independent evidence for the thermally controlled rheological contrast. Specifically, we show that seaward postseismic motion is deflected upward at the edge of the cold forearc mantle wedge, causing diagnostic uplift just seaward of the volcanic arc. From numerical simulations of postseismic deformation following the 2011 moment magnitude (Mw) 9 Tohoku-oki, 2010 Mw 8.8 Maule, 2007 Mw 8.4 Bengkulu and 1960 Mw 9.5 Chile earthquakes, together with a global synthesis of postseismic uplift measurements, we find that cold forearc mantle is present irrespective of the diversity in tectonic settings. Our findings also indicate that field surveys eight years after the 1960 Chile earthquake provided some of the earliest evidence for viscoelastic postseismic deformation. We suggest that the established link between long-term thermal processes and short-term earthquake cycle deformation is important to understanding subduction-zone dynamics. Deformation after large subduction earthquakes reflects the thermal contrast between the mantle wedge and its nose, according to numerical simulations and a synthesis of postseismic uplift data from subduction zones.

3D elastic plane-wave diffraction by a stress-free wedge for incident skew angles below the critical angle in diffraction

Elastic plane wave diffraction by a stress-free wedge is a canonical problem of interest to researchers in many different fields. To our knowledge, no fully analytical resolution has been found and semi-analytical evaluations of asymptotic approximations have therefore become a common approach. In this paper, a method called the spectral functions method is developed in a 3D configuration, meaning that the incident ray is not necessarily in the plane normal to the wedge edge. The diffracted displacement field is expressed as an integral in terms of two unknown functions called the spectral functions. These functions are decomposed into two parts: one which can be computed analytically and the other which is approached numerically using a collocation method. The details of the corresponding numerical scheme are given and first numerical validations are presented. The presented method is valid for incident skew angles which are below the critical angle in diffraction.

The Bakken–Three Forks super giant play, Williston Basin

The Williston Basin Bakken petroleum system is a giant continuous accumulation. The petroleum system is characterized by low-porosity and -permeability reservoirs, organic-rich source rocks, and regional hydrocarbon charge. Total Bakken Formation and Three Forks Formation production to June 2019 is 3.3 billion bbl (0.52 billion m3) and 4.8 tcf of gas (0.135 trillion m3) from 19,075 wells. Daily production is over 1 million bbl (160,000 m3) per day. The Bakken Formation regionally in the Williston Basin consists of four members: upper and lower organic-rich black shale, a middle member (silty dolostone or limestone to sandstone lithology), and a basal member recently named the Pronghorn. The Bakken Formation ranges in thickness from a wedge edge to more than 140 ft (42.6 m), with the thickest area in the Bakken located in northwest North Dakota, east of the Nesson anticline. The Three Forks is a silty dolostone throughout much of its stratigraphic interval. The Three Forks ranges in thickness from less than 25 ft to more than 250 ft (7.6–76.2 m) in the mapped area. Thickness patterns are controlled by paleostructural features such as the Poplar Dome and Nesson, Antelope, Cedar Creek, and Bottineau anticlines. Thinning and or truncation occurs over the crest of the highs, and thickening of strata occurs on the flanks of the highs. The Three Forks can be subdivided into three units (up to six by some authors). Most of the development activity in the Three Forks targets the upper Three Forks.

Geological characteristics of the Nankai Trough subduction zone and their tectonic significances

The Nankai Trough subduction zone is a typical subduction system characterized by subduction of multiple geological units of the Philippine Sea Plate (the Kyushu-Palau Ridge, the Shikoku Basin, the Kinan Seamount Chain, and the Izu-Bonin Arc) beneath the Eurasian Plate in the southwest of Japan. This study presents a geophysical and geochemical analysis of the Nankai Trough subduction zone in order to determine the features and subduction effects of each geological unit. The results show that the Nankai Trough is characterized by low-gravity anomalies (−20 mGal to −40 mGal) and high heat flow (60–200 mW/m2) in the middle part and low heat flow (20–80 mW/m2) in the western and eastern parts. The crust of the subducting plate is 5–20 km thick. The mantle composition of the subducting plate is progressively depleted from west to east. Subduction of aseismic ridges (e.g., the Kyushu-Palau Ridge, the Kinan Seamount Chain, and the Zenisu Ridge) is a common process that leads to a series of subduction effects at the Nankai Trough. Firstly, aseismic ridge or seamount chain subduction may deform the overriding plate, resulting in irregular concave topography along the front edge of the accretionary wedge. Secondly, it may have served as a seismic barrier inhibiting rupture propagation in the 1944 Mw 8.1 and 1946 Mw 8.3 earthquakes. In addition, subduction of the Kyushu-Palau Ridge and hot and young Shikoku Basin lithosphere may induce slab melting, resulting in adakitic magmatism and the provision of ore-forming metals for the formation of porphyry copper and gold deposits in the overriding Japan Arc. Based on comparisons of their geophysical and geochemical characteristics, we suggest that, although the Izu-Bonin Arc has already collided with the Japan Arc, the Kyushu-Palau Ridge, which represents a remnant arc of the Izu-Bonin Arc, is still at the subduction stage characterized by a single-vergence system and a topographic boundary with the Japan Arc.

Laser-Stimulated Fluorescence of Aurorazhdarchid Pterosaur Shows Soft Tissues with Implications for Pterosaur Water Launch and Foraging Behaviour

Solnhofen Limestone is renowned for pterosaur discoveries including Pterodactylus, the first pterosaur species identified as a flying reptile. Here a Solnhofen aurorazhdarchid pterosaur specimen was imaged under Laser-Stimulated Fluorescence (LSF) showing its fossil soft tissues. The data recovered under LSF shows a distinct, well preserved actinofibrillar complex, an undistorted actinopatagium retaining the retrophalangeal connective tissue wedge and entire trailing edge, as well as webbed feet. These soft tissues are of particular interest for investigating water launch adaptations, because they include likely primary contact surfaces. Pterosaur launch performance has primarily focused on larger species. Here the soft tissue data supports the dynamic feasibility of small aurorazhdarchid water launch. Our model suggests that webbed feet might be an important water launch specialization, having a significant impact on launch performance. However, webbed feet appear to be plesiomorphic for most pterosaurs implying that they were probably exapted for water launch. Aquatic prey is important for many pterosaurs. The ability to water launch was likely important in all water-feeding pterosaurs. Wider future efforts to study water launch across pterosaurs should prioritise three key factors that limit its performance: available propulsive contact area, forelimb extension range and forelimb extension power about the shoulder.

A Method of Transferring the Unit of Power of High-Intensity Laser Radiation

A method is proposed for transferring the unit of mean power of laser radiation by means of measuring high-intensity power (kilowatts), with the possibility of constant monitoring of the transfer process. A measuring optical power divider for laser radiation has been developed, structurally built in the form of a wedge and permitting, according to the relatively small power of the radiation reflected from the lighted surface of the forward face of the wedge, to determine the radiant power of the beam incident upon the measuring instrument to be calibrated. The proposed method is based on applying the developed divisor in the reference installation and provides for the implementation of three modes of operation of the installation: the mode for determination of the coefficient of equivalence; the mode for determination of the division ratio of the optical splitter; the mode of transfer of the power unit by measurement facilities; and determination of the control parameter of the optical splitter. The transfer process is monitored by measuring the radiant power reflected from the back edge of the wedge, and determining the control parameter. The conditions in which it is advisable to use the proposed mode of determining the division ratio of the optical splitter are given. A special feature of the method under study is the possibility of timely monitoring of the division ratio of the optical splitter, making it possible to estimate in real time the reliability of the process of calibration of measurement instruments. A formula was derived for the metrological traceability of the power measurement results to GET 28-2016. The basic error component errors of the determination of the radiant power arriving at input of the measurement facilities being calibrated are considered. The results of the experimental studies of this method make it possible to confirm that at 10.6 μm wavelength, the total measurement error of the power, expressed as the SD, does not exceed 2.0%. The method can be used in the corresponding secondary standards of the power unit that obtain a unit from the State Special Standard for Mean Power, GET 28-2016.

PARABOLIC BOUNDARY VALUE PROBLEMS IN A PIECEWISE HOMOGENEOUS WEDGE-SHAPED SOLID CYLINDER

The unique exact analytical solutions of parabolic boundary value problems of mathematical physics in piecewise homogeneous wedge-shaped solid cylinder were constructed at first time by the method of integral and hybrid integral transforms in combination with the method of main solutions (matrices of influence and Green matrices). The cases of assigning on the verge of the wedge the boundary conditions of Dirichlet and Neumann and their possible combinations (Dirichlet – Neumann, Neumann – Dirichlet) are considered. Finite integral Fourier transform by an angular variable $\varphi \in (0; \varphi_0)$, a Fourier integral transform on the Cartesian segment $(-l_1;l_2)$ by an applicative variable $z$ and a hybrid integral transform of the Hankel type of the first kind on a segment $(0;R)$ of the polar axis with $n$ points of conjugation by an radial variable $r$ were used to construct solutions of investigated initial-boundary value problems. The consistent application of integral transforms by geometric variables allows us to reduce the three-dimensional initial boundary-value problems of conjugation to the Cauchy problem for a regular linear inhomogeneous 1st order differential equation whose unique solution is written in a closed form. The application of inverse integral transforms restores explicitly the solution of the considered problems through their integral image. The structure of the solution of the problem in the case of setting the Neumann boundary conditions on the wedge edges is analyzed. Exact analytical formulas for the components of the main solutions are written and the theorem on the existence of a single bounded classical solution of the problem is formulated. The obtained solutions are algorithmic in nature and can be used (using numerical methods) in solving applied problems.