Parts Of Wedges Research Articles

Interferometry by a transparent wedge

In this article we show that a single transparent wedge or a plate with a wedge part can be used as a very simple and useful interferometer with numerous applications. This interferometer permits to modulate phase distribution on interference fringes to evaluate quantitatively the parallelism of a light beam and aberration of a wavefront, to specify the spectral line shape in a wide range, to measure the light wavelength and refractive indices of solids and liquids. In addition, it provides suitable beams for holographic study of phase objects and fabrication of diffraction gratings.

A simple repair method of fatigue cracks using stop-holes reinforced with wedge members

ABSTRACT A simple method of repairing fatigue cracks using stop-holes reinforced with wedge members has been newly proposed. By using this method, the stress range at the stop-hole edge is expected to be drastically reduced by the wedge load effect of the wedge member. The chief advantages of this method are that the repair work can be easily performed from only one side of a cracked structure and that the wedge member can be set so adaptive as to maintain the wedge load automatically and effectively even after the structure around the stop-hole is subjected to some excessive tensile loads and the stop-hole is plastically deformed. Specifically, slope-type wedge members have been newly designed and optimized, and an adaptive mechanism of the wedge member has been devised using a pulley, a string and a weight. Static loading tests and fatigue tests were performed on a steel plate specimen with a slit and a drill hole, and validity of the above repair method was experimentally examined using both of simple and adaptive wedge members. FE analyses using contact elements were also carried out for a comparative study. As a result, it was found that the stress range at the stop-hole edge is reduced by more than 60 % and the fatigue life is prolonged more than 20-fold by application of the adaptive wedge member as compared with those in the case of the conventional stop-hole. It was also shown that application of the simple wedge member is limitedly effective when the wedge part is held on the specimen and the applied load range is lower than a certain level.

Numerical and applied results of the analysis of singular solutions for a closed wedge consisting of two dissimilar materials

This paper considers solutions that can determine the nature of the stress singularity in the vicinity of a singular point for two-dimensional and three-dimensional closed composite wedges. A comparative analysis of stress singularity exponents is carried out for closed composite wedges with perfectly bonded interfaces and homogeneous wedges with stress-free edges. Using analysis results, it is possible to evaluate a change in the nature of the stress singularity near the crack tip when the crack cavity is filled with a certain material. Results were obtained for different ratios of the wedge component’s opening angles, different values of elastic moduli, and different Poisson ratios of the wedge’s constituent materials. The anomalous nature of changes in singular solutions for a composite closed wedge is established for Poisson’s ratios of the wedge part corresponding to a weakly compressible or incompressible material. In the context of the model and applied problems, it is shown that the use of eigensolutions for composite wedges makes it possible to find material characteristics that ensure maximum reduction in the stress concentration near the crack tip in the case of the crack cavity being filled with a certain material. The dependence of these solutions on the Poisson ratio demonstrates a significant reduction in stress concentration at sufficiently large crack opening angles and at low rigidity of the material.

Resection and sternal wedge—part II reconstruction

Resection and sternal wedge—part II reconstruction

Resection and sternal wedge—part I resection

Resection and sternal wedge—part I resection

A practical implementation of robotic riveting cell for wedge parts of airframe

As there are increasing demands for efficiency and quality in airframe assembly, automation integration is required to replace manual operation. This paper presents a design of a robotic riveting cell for wedge part riveting, which is used on the trailing edge of airfoil. To complete the continuous riveting in a row of rivets at the trailing edge, a robotic riveting cell is designed to realize a set of process actions including rivet feeding/injection/cutting and press riveting. Based on the visual compensation of the hole position, a forceless feedback spiral track rivet injection compensation method is proposed. The stress feedback-based riveting process control method is introduced after rivet injection and cutting. The proposed approach is applied to the robotic riveting cell and the rivet injector works stably. No indentation has been detected using the force-controlled riveting method. The prototype can achieve the riveting task well on the wedge part. The proposed design and approach can be applied on both wedge parts and flat parts. This will give a new way to solve the automation integration problem in airframe assembly. A robotic riveting cell is designed to realize a set of process actions. A forceless feedback spiral track rivet injection compensation method is proposed. The stress feedback-based riveting process control method is employed after rivet injection and cutting.

Erosional features as indicators of thrust fault activity (Nankai Trough, Japan)

A submarine channel system and basal ramps of a Quaternary mass-transport deposit (MTD) are shown to represent thrust fault activity in the Nankai accretionary wedge. Variations in channel bed slope, height and width of submarine channels and gullies indicate uplift and sediment bypass seaward from a margin-dominating out-of-sequence thrust, the megasplay fault (MSF), at < 1.67-1.46 Ma. Between ~ 1.05 and 0.85 Ma, a younger mass-transport deposit (MTD 6) was detached at different depths. Demonstrating the significant deformation observed in the study area, the direction of transport of MTD 6 differs 30o-45o from the strike of scarps and ramps at its base, which are parallel to the structural contours of thrust anticlines underneath. This character contrasts to the geometries frequently documented in frontally-emergent submarine landslides. In parallel, oblique basal ramps form significant boundaries between zones of MTD 6 with distinct acoustic and, suggestively, petrophysical properties. As a result of this study, we postulate that developed channel systems can erode the upper continental slope and lead to bypass of substantial volumes of sediment to distal parts of accretionary wedges. This process bears the potential of generating periods of more intense thrust-wedge deformation, at least locally, than those predicted by mathematical and physical models based on present-day taper geometries. On a regional scale, the observations in this paper are important as they indicate a more diffuse distribution of deformation in the Nankai accretionary wedge than previously assumed for the MSF region.

Lower plate geometry controlling the development of a thrust-top basin: the tectonosedimentary evolution of the Ofanto basin (Southern Apennines)

The Ofanto basin is a Pliocene–Pleistocene thrust-top basin that formed with an unusual east–west orientation along the frontal part of the Southern Apennine Allochthon during the latest stages of tectonic transport. Its tectonic and sedimentary evolution was studied integrating field surveys, biostratigraphic analyses and the interpretation of a large seismic grid. Well data and seismic interpretation indicate that a large east–west-trending normal fault underlies the northern margin of the basin, displacing the Apulian carbonates that form the foreland and the footwall of the Southern Apennine Allochthon. In our reconstruction the Ofanto basin formed at the rear of the bulge caused by buttressing of the Southern Apennine Allochthon against this normal fault. In a second stage of contraction, the footwall of the Southern Apennine Allochthon was involved in deformation with a different trend from the normal faulting and buttressing. This caused eastward tilting of the basin and broad folding around its eastern termination. Good stratigraphic constraints permit the age of buttressing to be defined as Early Pliocene, and that of the shortening in the Apulian carbonates as Early Pleistocene. This study highlights the importance of early orogenic normal faults in conditioning the evolution of the frontal parts of orogenic wedges. Supplementary material: A 3D reconstruction of the base of the Pliocene deposits of the Ofanto basin, based on seismic interpretation, is available at www.geolsoc.org.uk/SUP18559 .

The Teodorescu operator in Clifford analysis

Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions, i.e., null solutions to a first order vector valued rotation invariant differential operator \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\partial }\) called the Dirac operator. More recently, Hermitian Clifford analysis has emerged as a new branch, offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions, called Hermitian monogenic functions, to two Hermitian Dirac operators \(\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} }\) and \(\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} ^\dag }\) which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the Teodorescu operator is the right inverse of the Dirac operator \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\partial }\). In this paper, Teodorescu operators for the Hermitian Dirac operators \(\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} }\) and \(\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} ^\dag }\) are constructed. Moreover, the structure of the Euclidean and Hermitian Teodorescu operators is revealed by analyzing the more subtle behaviour of their components. Finally, the obtained inversion relations are still refined for the differential operators issuing from the Euclidean and Hermitian Dirac operators by splitting the Clifford algebra product into its dot and wedge parts. Their relationship with several complex variables theory is discussed.

On Fundamental Solutions in Clifford Analysis

Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centred around the concept of monogenic functions, which constitute the kernel of a first order vector valued, rotation invariant, differential operator $${\underline{\partial}}$$ called the Dirac operator, which factorizes the Laplacian. More recently, Hermitean Clifford analysis has emerged as a new branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focusses on a subclass of monogenic functions, i.e. the simultaneous null solutions, called Hermitean (or h−) monogenic functions, of two Hermitean Dirac operators $${\partial_{\underline{z}}}$$ and $${\partial_{\underline{z}^\dagger}}$$ which are invariant under the action of the unitary group, and constitute a splitting of the original Euclidean Dirac operator. In Euclidean Clifford analysis, the Clifford–Cauchy integral formula has proven to be a corner stone of the function theory, as is the case for the traditional Cauchy formula for holomorphic functions in the complex plane. Also a Hermitean Clifford–Cauchy integral formula has been established by means of a matrix approach. Naturally Cauchy integral formulae rely upon the existence of fundamental solutions of the Dirac operators under consideration. The aim of this paper is twofold. We want to reveal the underlying structure of these fundamental solutions and to show the particular results hidden behind a formula such as, e.g. $${\underline{\partial}E = \delta}$$ . Moreover we will refine these relations by constructing fundamental solutions for the differential operators issuing from the Euclidean and Hermitean Dirac operators by splitting the Clifford algebra product into its dot and wedge parts.

Spectral switches for a circular aperture with a variable wedge

The far-field spectral anomalies of a short Gaussian pulse incident on a circular aperture with a variable wedge are theoretically studied, and some numerical examples are given to illustrate these effects. It is shown that some anomalous behaviors (such as red shift or blue shift for the spectral peak of the diffracted pulse) can be found under different conditions. Also, the important phenomenon called "spectral switches" is presented, which can be controlled by varying the angle of the wedge part in the circular aperture. Its potential application in information encoding and transmission for free-space communications is proposed, and this scheme has the benefit of easy implementation compared with other previous methods.

A phase-shifting vectorial-shearing interferometer with wedge plate phase-shifter

We present a novel phase-shifting vectorial-shearing interferometer with a wedge plate phase-shifter. The interferometer is based on a modified Mach-Zehnder configuration; the common-path nature makes it capable of testing the wavefront of a short coherence-length light source, such as a laser diode. Vectorial shear (shearing in the x and y directions simultaneously) in an arbitrary direction is introduced by inserting two wedge plates orthogonally in two arms, respectively. One of the wedge plates is split into two parts (parallel part and wedge part); phase shift is produced by moving the wedge part in contact along the parallel part. The moving distance for a 2 pi phase shift is a few millimetres in specific conditions. The wedge plate phase-shifter increases the moving distance for phase shift and makes the control of phase shift relatively easy. We also discuss the lateral shear error and phase shift errors induced by wedge plates. The lateral shear error is small enough to be ignored; the phase shift error is determined mainly by the wedge angle error. Lastly, we give the experimental results of phase-shifting interference fringes in vectorial shear mode.

Hele-Shaw flows with free boundaries in a corner or around a wedge Part I: Liquid at the vertex

Consider a Hele-Shaw cell with the fluid (liquid) confined to an angular region by a solid boundary in the form of two half-lines meeting at an angle απ; if 0 &lt; α &lt; 1 we have flow in a corner, while if 1 &lt; α [les ] 2 we have flow around a wedge. We suppose contact between the fluid and each of the lines forming the solid boundary to be along a single segment emanating from the vertex, so we have liquid at the vertex, and contemplate such a situation that has been produced by injection at a number of points into an initially empty cell. We show that, if we assume the pressure to be constant along the free boundary, the region occupied by the fluid is the image of a semidisc (a domain bounded by a semicircle and its diameter) in the ζ-plane under a conformal map given by a function of the form ζα times a rational function of ζ. The form of this rational function can be written down, and the parameters appearing in it then determined as the solution to a set of algebraic equations. Examples of such flows are given (including one which shows that, in a certain sense, injection can produce a cusp), and the limiting situation in the wedge configuration as one injection point is moved to infinity is also considered.

Hele-Shaw flows with free boundaries in a corner or around a wedge Part II: Air at the vertex

Consider a Hele-Shaw cell with the fluid (liquid) confined to an angular region by a solid boundary in the form of two half-lines meeting at an angle απ; if 0 &lt; α &lt; 1 we have flow in a corner, while if 1 &lt; α [les ] 2 we have flow around a wedge. We suppose contact between the fluid and each of the lines forming the solid boundary to be along a single segment that does not adjoin the vertex, so we have air at the vertex, and contemplate such a situation that has been produced by injection at a number of points into an initially empty cell. We show that, if we assume the pressure to be constant along the free boundaries, the region occupied by the fluid is the image of a rectangle under a conformal map that can be expressed in terms of elliptic functions if α = 1 or α = 2, and in terms of theta functions if 0 &lt; α &lt; 1 or 1 &lt; α &lt; 2. The form of the function giving the map can be written down, and the parameters appearing in it then determined as the solution to a set of transcendental equations. The procedure is illustrated by a number of examples.

Stoichiometry and inter-subunit interaction of the wedge initiation complex, gp10-gp11, of bacteriophage T4

Association of gp10 and gp11 (gp=gene product) is the first step in the assembly pathway of the wedge part of the baseplate of bacteriophage T4. The gp10-gp11 complex constitutes the six tail pins at the corners of the baseplate hexagon on the distal side. The stoichiometry of the subunits, gp10 and gp11, of this complex was determined in combination with sedimentation equilibrium, Edman degradation of the complex and sodium dodecylsulfate-polyacrylamide gel electrophoresis (SDS-PAGE). From the results of Edman degradation and SDS-PAGE, the molar ratio of gp10 and gp11 was approximately 1. On the other hand, the molecular weight of the purified gp10-gp11 complex was determined by sedimentation equilibrium to be 284 000±7000, which is in good agreement with the expected value of 269 840 if the stoichiometry is 3:3. Furthermore, comparison of the results in the presence and in the absence of reducing reagent, 2-mercaptoethanol (2-ME), in SDS-PAGE revealed that two molecules of gp10 in the complex formed a disulfide bond, while the third gp10 molecule does not participate in the disulfide bond formation.

Nonlinear stress dependence of permeability: A mechanism for episodic fluid flow in accretionary wedges

Recent studies of the hydrogeology of accretionary wedges demonstrate that permeability is a dynamic property that depends upon the scale of observation and the prevailing stress state during measurement. We present results of laboratory geotechnical tests on sediments cored from the Costa Rica convergent margin during Ocean Drilling Program Leg 170. By measuring the permeability of samples of differing lithology before, during, and after shearing we show that hydrological behavior is linked to the consolidation state of the sediment at the onset of shear, and to the formation or reactivation of deformation fabrics. One sample obtained from a fault zone displayed a high permeability–effective stress dependence after being deformed at a high overconsolidation ratio. Under these conditions, shear zones in fine-grained sediments can dilate and thereby act as efficient fluid-flow conduits. Such stress-dependent permeability typifies the cyclic pressure build-up and release mechanisms (valving) invoked for many tectonic settings. We infer that a fracture permeability, opened up at high fluid pressures, is several times to several orders of magnitude greater than the matrix permeability. Our results help quantify the degree to which hydromechanical coupling can enhance flow in the actively deforming parts of accretionary wedges.

Fold uplift versus regional subsidence and sedimentation rate

Fold uplifts compete during their development with regional subsidence in the frontal parts of thrust belts and accretionary wedges. Two cases exist in frontal thrust belts. In the first, more common case, the uplift rate of the external folds is higher than the subsidence rate of the foredeep. In the second case the fold uplift is less than the regional subsidence. The total fold uplift may be considered as the fold uplift rate minus the regional subsidence rate; this value can be either positive or negative. Positive total fold uplift occurs when folds rise faster than regional subsidence and the envelope of the fold crest rises towards the hinterland of the accretionary wedge. In the opposite case, negative total fold uplift, the envelope dips towards the hinterland because folds rise more slowly than regional subsidence. In the first positive case, the folds are deeply eroded and the onlap of the growing strata moves away from the fold crest if the sedimentation rate is lower than the fold uplift rate in marine or alluvial environments. In the second negative case, where folds rise at lower rates than the regional subsidence, the onlap moves towards the fold crest if the sedimentation rate is higher than the fold uplift rate. This is also the more favorable case for hydrocarbon traps where growth strata can seal the fold. Moreover the fast subsidence rates in the foredeep provide a higher thermal maturation. This second tectonic setting is commonly associated with accretionary wedges forming along westdirected subduction zones, which are characterized by high subsidence rates in the foredeep or trench, due to the fast ‘eastward’ roll-back of the subduction hinge (e.g. Apennines, Carpathians, Banda arc).

Wide-angle low-loss waveguide branching for integrated optics

A new wide-angle, low-loss, symmetrical Y-branch waveguide is proposed. The waveguide configuration utilizes ribs for lateral confinement in the planar guiding region underneath. This Y-branch structure can be fabricated easily without an additional process step. Together with a utilization of the multimode interference effect, a local decrease of the waveguide ridge in the wedge part of the Y-branch reduces the radiation loss. When proper@ designed, the proposed Y-branch has a radiation loss as low as 2.2 dB at a branch angle of 6° with the index difference (Δn/n) as small as 7.1 × 10−4 at a wavelength of 870 nm in the TE fundamental mode as compared to 12.6 dB for a conventional Y-branch. The proposed method yields corresponding advantages for waveguide designs with a higher Δn/n ratio and can also be adapted in combination with S-branch designs.

40Ar/39Ar evidence that formation of blueschists in continental crust was synchronous with foreland fold and thrust belt deformation, western Brooks Range, Alaska

Abstract 40Ar/39Ar ages from white mica in rocks of the internal zone of the Brooks Range contractional orogen indicate that the Nanielik antiformal duplex developed at about 120 Ma and was remobilized on its southern boundary at c. 108 Ma. Blueschist facies metamorphism accompanied development of the antiform. The timing of the blueschist facies event and creation of the antiform overlap the period of shallow‐seated deformation in the foreland fold and thrust belt and sedimentation in the foreland basin of the Brooks Range. Blueschist facies P‐T conditions may therefore characterize the thicker parts of orogenic wedges in some orogenic systems; ancient blueschists need not necessarily be interpreted as indicators of active subduction or continent‐continent collision.Microprobe analysis using quantitative wavelength‐dispersive and electron backscattered electron imaging methods was used to characterize the composition of white micas in the dated samples. None of the samples was compositionally homogeneous; many contained 2‐3 populations of white mica, including both potassic and sodic varieties. Samples which had undergone (in sequence) amphibolite, albite‐epidote amphibolite and blueschist facies metamorphic events retained muscovites relict of the amphibolite facies event. Samples that had undergone only the blueschist facies event also contained multiple populations of mica, some probably from detrital sources.

Geometry and mechanisms of fluid flow at 15 to 45 kilometer depths in an Early Cretaceous Accretionary Complex

The Catalina Schist (southern California), contains variably metamorphosed mafic, sedimentary, and ultramafic rocks that were accreted at depths of 15 to 45 km during early Cretaceous subduction. Fluid flow in the Catalina Schist was concentrated along fractures and shear zones, as indicated by the textures and abundance of veins and evidence in melange zones for metasomatism and homogenization of stable isotope compositions. Slab‐parallel orientations of major melange zones with enhanced permeability may dictate that the majority of fluid released by devolatilization at depths &gt;15 km in subduction zones moves updip toward the seafloor. Such transport could contribute to fluid budgets in shallower parts of accretionary wedges and facilitate large‐scale mass and energy transfer in forearc regions.