Boundary Tracing Research Articles

Extension along the Australian‐Pacific transpressional transform plate boundary near Macquarie Island

The Australian‐Pacific transform plate boundary fault zone along the Macquarie and McDougall segments of the Macquarie Ridge Complex (MRC), south of New Zealand, is characterized by dominantly normal faults and pull‐apart basins, in apparent conflict with the regional transpressional tectonic setting. We propose that present‐day curvature of the transform is inherited from a preexisting divergent plate boundary and that the overall extensional kinematics shown by faults along the main plate boundary trace and exposed on Macquarie Island result from local stresses related to right‐lateral, right stepping, en echelon plate boundary faults and not to the current transpressional setting. Transpression along the Australian‐Pacific transform plate boundary has resulted in uplift along the ∼1500 km long Macquarie Ridge Complex. Macquarie Island, the only subaerial exposure of the complex, sits atop a ∼5 km high, ∼50 km wide submarine ridge of oceanic crust and lies ∼4.5 km east of the major active plate boundary fault zone. Thus Macquarie Island and the surrounding seafloor provide a unique opportunity to study an active oceanic transform fault using complementary marine geophysical and land‐based geological data. Mapping of recent faults affecting the topography of Macquarie Island shows that the island is extensively cut by high‐angle normal faults forming pull‐apart basins. Furthermore, evidence for reverse motion is rare. Using marine geophysical data, including swath bathymetry, reflectivity, and seismic reflection data, collected along the Australian‐Pacific plate boundary north and south of the island, we have defined a 5–15 km wide plate boundary zone. A series of right stepping en echelon faults, within this zone, lies along the main plate boundary trace. At the right stepping fault terminations, elongate depressions (≤10 km wide and 1.2 km deep) parallel the plate boundary, which we interpret as extensional relay zones or pull‐apart basins. We propose that transpression is partitioned into en echelon strike‐slip faults at the plate boundary and a convergent component that flexes the crust, causing the anomalous bathymetric ridge and trough morphology of the McDougall and Macquarie segments of the MRC.

The boundary trace and generalized boundary value problem for semilinear elliptic equations with coercive absorption

AbstractIn the first part of the paper we establish the existence of a boundary trace for positive solutions of the equation −Δu + g(x, u) = 0 in a smooth domain Ω ⊂ ℝN, for a general class of positive nonlinearities. This class includes every space independent, monotone increasing g which satisfies the Keller‐Osserman condition as well as degenerate nonlinearities gα,q of the form gα,q (x, u) = d(x, ∂Ω)α |u|q−1 u, with α > −2 and q > 1. The boundary trace is given by a positive regular Borel measure which may blow up on compact sets. In the second part we concentrate on the family of nonlinearities {gα,q}, determine the critical value of the exponent q (for fixed α > −2) and discuss (a) positive solutions with an isolated singularity, for subcritical nonlinearities and (b) the boundary value problem for −Δu + gα,q (x, u) = 0 with boundary data given by a positive regular Borel measure (possibly unbounded). We show that, in the subcritical case, the problem possesses a unique solution for every such measure. © 2003 Wiley Periodicals, Inc.

경계선 기울기 방법을 이용한 다양한 인쇄체 한글의 인식

본 논문에서는 CCD 흑백 카메라를 이용하여 입력되는 인쇄체 한글 이미지의 문자를 인식하여 편집 가능한 텍스트 문서로 변환하는 시스템을 구현하였다 문자 인식에 있어서 잡음에 강한 경계선 기울기 방법을 이용함으로써 문자의 구조적 특성에 근거한 윤곽선 정보를 추출할 수 있었다. 이를 이용하여 각 문자 이미지의 수평 및 수직 모음을 인지하고 6가지 유형으로 분류한 후, 자소 단위로 분리하고 최대 길이 투영을 사용하여 모음을 인식하였다. 분리된 자음은 경계선이 변화되는 위상의 형태를 미리 저장된 표준 패턴과 비교하여 인식하였다. 인식된 문자는 KS 한글 완성형 코드로 문서 편집기에 출력되어 사용자에게 제공되는 시스템을 구현하였다. In this paper, we realized a system that converts the character images of the printed Korean alphabet (Hangul) to the editable text documents by using the black and white CCD camera, We were able to abstract the contours information of the character which is based on the structural character by using the boundary tracing technique that is strong to the noise on the character recognition. By using the contours information, we recognized the horizontal vowels and vertical vowels of the character image and classify the character into the six patterns. After that, the character is divided to the unit of the consonant and vowel. The vowels are recognized by using the maximum length projection. The separated consonants are recognized by comparing the inputted pattern with the standard pattern that has the phase information of the boundary line change. We realized a system that the recognized characters are inputted to the word editor with the editable KS Hangul completion type code.

Billiards and boundary traces of eigenfunctions

This is a report on recent results with A. Hassell on quantum ergodicity of boundary traces of eigenfunctions on domains with ergodic billiards, and of work in progress with Hassell and Sogge on norms of boundary traces. Related work by Burq, Grieser and Smith-Sogge is also discussed.

The role of contrast enhancement in echocardiographic assessment of left ventricular function

With or without contrast, echocardiographic evaluation of left ventricular (LV) function is qualitative, subjective, and experience dependent, because it is mostly based on visual interpretation of gray-scale 2-dimensional images or, at best, relies on tedious and time-consuming manual tracing of the endocardial boundaries. Adequate endocardial visualization is essential for accurate interpretation of regional wall thickening abnormalities, which constitute the diagnostic hallmark of coronary artery disease, and for reproducible assessment of LV ejection fraction. Studies performed in the last decade have estimated the number of patients with suboptimal endocardial delineation by fundamental imaging at 30%. These studies have highlighted the problem of variable image quality as a major limitation of transthoracic echocardiography because failure to adequately visualize a segment, either at rest or during stress, may compromise the ability of this technique to identify areas of dysfunctional myocardium. Several remedies based on different technologic and methodologic approaches have been tested over the years with variable success. In this review we discuss the most recent techniques that have had a positive impact on endocardial visualization, as well as the potential benefits of these approaches.

Advanced Characterization of Twins Using Automated Electron Backscatter Diffraction

This paper describes results obtained using an automated, crystallographically-based technique for twin identification. The technique is based on the automated collection of spatially specific orientation measurements by electron backscatter diffraction (EBSD) in the scanning electron microscope (SEM). The key features of the analysis are identification of potential twin boundaries by their misorientation character, identification of the distinct boundary planes among the symmetrically equivalent candidates, and validation of these boundaries through comparison with the boundary and twin plane traces in the sample cross section. Results on the application of this technique to deformation twins in zirconium are analyzed for the effect of twin type and amount and sense of uniaxial deformation. The accumulation of strain tends to increase the misorientation deviation at least to the degree of the trace deviation compared with recrystallization twins in nickel. In addition to the results on characterizing the twin character, results on extending the twin analysis to automated identification of parent and daughter material for structures exhibiting twin deformation are reported as well.

Boundary Behavior of Solutions of some Weakly Superlinear Elliptic Equations

Abstract We study the behavior near a boundary point O of an open subset Ω ⊂ ℝN of any solution u ∈ C(Ω̅ \ {0}) of the problem with the boundary condition g ∈ C(∂Ω). We prove a boundary trace result for solutions of the associated equation and point out the existence of various types of singular behavior. We deduce a classification of isolated boundary singularities for solutions of (0.1) depending on the value of α with respect to 2.

Single-section plane assessment in grain boundary engineered brass.

The present paper reports a comparative analysis of sigma 3 (in the coincidence site lattice notation) grain boundary types, in two grain boundary engineered brass specimens, by use of electron backscatter diffraction (EBSD) data coupled to the measurement of boundary traces in a single section. Although most of the data were analysed using the new single-section technique, an analysis of boundary plane orientations in three dimensions was made in a subset of the data in order to validate the single section methodology. The single-section trace analysis procedure. coupled with EBSD, is a viable and robust tool for analysis of sigma 3 grain boundary planes. The procedure provides data which suggest that part of the enhanced strain-to-failure in specimen B compared to specimen A is the result of an increased proportion of mobile sigma3 boundaries, i.e. those which are displaced from the [111] symmetrical tilt configuration.

Evolution of Grain and Micro-Void Structure in Electroplated Copper Interconnects

A detailed investigation has been carried out into the evolution of grain size and grain orientation in electroplated Cu interconnection lines. The specimens were annealed to produce a range of different grain size distributions. Very accurate grain size distributions were obtained from extensive TEM observations of a large number of specimens, followed by computer tracing of grain boundaries. Although annealing causes the average grain size to increase, very small grains are found to persist in the distribution, even when the average grain size is large. These small grains have been investigated in detail to determine the reason for their thermal stability. In addition, the occurrence and redistribution of small micro-voids has been investigated for wafers with different grain sizes. These voids are believed to be associated with seams which are formed in the Cu lines during plating.

Advanced contour detection for three-dimensional intracoronary ultrasound: a validation--in vitro and in vivo.

Intracoronary ultrasound (ICUS) provides high-resolution transmural images of the arterial wall. By performing a pullback of the ICUS transducer and three-dimensional reconstruction of the images, an advanced assessment of the lumen and vessel wall morphology can be obtained. To reduce the analysis time and the subjectivity of boundary tracing, automated segmentation of the image sequence must be performed. The Quantitative Coronary Ultrasound-Clinical Measurement Solutions (QCU-CMS) (semi)automated analytical software package uses a combination of transversal and longitudinal model- and knowledge-guided contour detection techniques. On multiple longitudinal sections through the pullback stack, the external vessel contours are detected simultaneously, allowing mutual guidance of the detection in difficult areas. Subsequently, luminal contours are detected on these longitudinal sections. Vessel and luminal contour points are transformed to the individual cross-sections, where they guide the vessel and lumen contour detection on these transversal images. The performance of the software was validated stepwise. A set of phantoms was used to determine the systematic and random errors of the contour detection of external vessel and lumen boundaries. Subsequently, the results of the contour detection as obtained in in vivo image sets were compared with expert manual tracing, and finally the contour detection in in vivo image sequences was compared with results obtained from another previously validated ICUS quantification system. The phantom lumen diameters were underestimated by 0.1 mm, equally by the QCU-CMS software and by manual tracing. Comparison of automatically detected contours and expert manual contours, showed that lumen contours correspond very well (systematic and random radius difference: -0.025 +/- 0.067 mm), while automatically detected vessel contours slightly overestimated the expert manual contours (radius difference: 0.061 +/- 0.037 mm). The cross-sectional vessel and lumen areas as detected with our system and with the second computerized system showed a high correlation (r = 0.995 and 0.978, respectively). Thus, use of the new QCU-CMS analytical software is feasible and the validation data suggest its application for the analysis of clinical research.

Investigation of coincident site lattice boundary criteria in Cu thin films

A statistical investigation of the coincident site lattice (CSL) Σ=3 boundaries was performed on a Cu thin film sample. The criteria used to judge whether a given boundary is a CSL boundary were evaluated. The misorientation criterion, i.e., how near a given boundary misorientation must lie to an ideal CSL misorientation, was addressed. The results showed that the amount of allowed deviation has little impact on the CSL distribution (within the range of published values for the deviation tolerance). The second criterion addressed was the alignment of the boundary plane with coherent planes in the adjoining grains. Because the measurements were made on single section planes, the orientation of a boundary plane could not be fully measured. Rather, only the orientation of the trace of a boundary plane could be measured. The deviation of the alignment of the boundary traces and the corresponding coherent plane traces were measured. The measurements showed that the choice of a tolerance for the allowed trace deviation was significant.

On relations between spectral and dynamical inverse data

Abstract - As is known, boundary spectral data of the compact Riemannian manifold Ω (spectrum of Laplacian with zero Dirichlet boundary condition plus traces of normal derivatives of eigenfunctions at ∂Ω) determine its boundary dynamical data (dynamical Dirichlet-to-Neumann map) R2T for all T > 0. In the paper the procedures recovering spectral data of the submanifold ΩT = {x ∈ Ω | dist(x, ∂Ω) < T} via given R2T with any prescribed T > 0 and continuing R2T from ∂Ω × (0, 2T) onto ∂Ω×(0,∞) are proposed. The procedures do not invoke solving the inverse problems; main fragment is the constructing (via R2T ) and the use of a model of dynamical system associated with ΩT.

Boundary layers in weak solutions of hyperbolic conservation laws II. self-similar vanishing diffusion limits

This paper is concerned with the boundary layers that arise in solutions of a nonlinear hyperbolic system of conservation laws in presence of vanishing diffusion. We consider self-similar solutions of the Riemann problem in a half-space, following a pioneering idea by Dafermos for the standard Riemann problem. The system is strictly hyperbolic but no assumption of genuine nonlinearity is made; moreover, the boundary is possibly characteristic, that is, the wave speed do not have a specific sign near the (stationary) boundary.<br> First, we generalize a technique due to Tzavaras and show that the boundary Riemann problem with diffusion admits a family of continuous solutions that remain uniformly bounded in the total variation norm. Careful estimates are necessary to cope with waves that collapse at the boundary and generate the boundary layer.<br> Second, we prove the convergence of these continuous solutions toward weak solutions of the Riemann problem when the diffusion parameter approaches zero. Following Dubois and LeFloch, we formulate the boundary condition in a weak form, based on a set of admissible boundary traces. Following Part I of this work, we identify and rigorously analyze the boundary set associated with the zero-diffusion method. In particular, our analysis fully justifies the use of the scaling $1/\varepsilon$ near the boundary (where $\varepsilon$ is the diffusion parameter), even in the characteristic case as advocated in Part I by the authors.

Removable singularities and boundary traces

Let Ω be a bounded open subset in R N with a regular boundary ∂Ω. If q⩾( N+1)/ ( N−1), a necessary and sufficient condition for a locally bounded Borel measure to be the boundary trace of a solution u of the equation (∗) −Δu+u q−1u=0 in Ω is that ν( E)=0 for any Borel subset E⊂∂Ω such that the Bessel capacity C 2/ q, q′ ( E) vanishes. This result has been proved by Le Gall when q=2, Dynkin and Kuznetsov when q<2 and the authors of the present article when q>2. Different methods were used in each case and each of these methods applied only to the stated range of exponents. Here we give a unified and purely analytic proof, valid for all values of q⩾( N+1)/( N−1). We employ the same method in order to characterize the removable boundary sets for solutions of (∗).

Global seismicity characteristics of subduction‐to‐strike‐slip transitions

There are at least 30 major plate boundary segments worldwide where the plate boundary changes from subduction to strike‐slip; these include six triple junctions and 24 two‐plate boundaries. This study investigates earthquake seismicity in the 24 two‐plate subduction‐to‐strike‐slip transition (SSST) regions by utilizing recently published earthquake relocations, ternary diagrams of focal mechanisms, and moment rate calculations. To facilitate cross‐regional comparisons, we categorize the geometry of SSST plate boundaries in terms of (1) their radius of curvature, (2) their sense of curvature, that is, whether they are convex or concave as viewed from the downgoing plate, and (3) their tectonic complexity, that is, the variability of crustal thickness and the segmentation of the plate boundary trace. We observe three main trends in SSST regions: (1) there is a conspicuous scarcity of strike‐slip earthquakes along plate boundary segments that plate motion models indicate are strike‐slip boundaries; (2) in these apparent strike‐slip segments, both the rate of occurrence of earthquakes of any kind and the moment release rate are low compared to adjacent subduction segments; and (3) there were few observable differences in seismicity between convex and concave boundaries. The observation that transform zones exhibit moment rate deficiencies, that is, have few large‐magnitude earthquakes in the historical record, may have important implications for seismic hazard assessment in SSST regions. In particular, is motion along these boundaries aseismic with little seismic hazard, or is motion expressed in very large magnitude, infrequent, but potentially devastating earthquakes? In at least three such regions, New Zealand, the Philippines, and the Dominican Republic, paleoseismic evidence and the historical record of seismicity suggest that very large, infrequent earthquakes do occur.

Object Boundary Encoding — a new vectorisation algorithm for engineering drawings

This paper presents a new engineering drawing recognition algorithm named Object Boundary Encoding (OBE). There are four steps in the algorithm: Object search, Boundary tracing encoding, Line approximation/arrowhead detection, and Arc construction. Drawing objects are searched by means of screen lines from the top-left corner of an image, in both left-to-right and top-to-bottom directions. During the tracing process, a set of pixels outlining part of the object’s boundary is analysed and a group of vector graphical elements is generated. Arrowheads can also be recognised. The Vector Perpendicular Bisector Tracing algorithm constructs arcs or circles based on the vectorised data. Definitions of Tracings and Tracing Series have been given in the eight-neighbourhood scenario. The algorithm significantly simplifies the vectorisation process — less than 50% of the object’s boundary is traced and more than 85% of the tracing time is saved. Java language is used to program, making the system platform independent and Internet accessible. The results from the sample tests demonstrate the capability of the system.

Well-posedness of a Structural Acoustics Control Model with Point Observation of the Pressure

We consider a controlled and observed partial differential equation (PDE) which describes a structural acoustics interaction. Physically, this PDE describes an acoustic chamber with a flexible chamber wall. The control is applied to this flexible wall, and the class of controls under consideration includes those generated by piezoceramic patches. The observation we consider is point measurements of acoustic pressure inside the cavity. Mathematically, the model consists of a wave equation coupled, through boundary trace terms, to a structurally damped plate (or beam) equation, and the point controls and observations for this system are modeled by highly unbounded operators. We analyze the map from the control to the observation, since the properties of this map are central to any control design which is based upon this observation. We also show there exists an appropriate state space X, so that if the initial state is in X and the control is in L2, then the state evolves continuously in X and the observation is in L2. The analysis of this system entails a microlocal analysis of the wave component of the system, and the use of pseudodifferential machinery.

Slavery and the Demographic and Economic History of Minas Gerais, Brazil, 1720–1888

The gold mining of Minas Gerais has increasingly drawn the attention of historians. This study by Laird W. Bergad is an important contribution to that evolving body of literature and will be an indispensable tool to scholars. This work is a tour de force in terms of its handling of data. Central to this study is the use of inventories from the three mining districts, Diamantina, Mariana/Vila Rica, and São João del Rei/São José del Rei. Close to 10,000 inventories were used to produce a database of almost 112,000 slaves extending over the period from 1713 to 1888. Three research teams were used, but any researcher who has used inventories knows how difficult an undertaking this must have been. From these inventories the author constructed a very substantial slave price series database. Bergad also used the Minas Gerais censuses for 1831, 1833, 1855, and 1872 which have been compiled by a team from the Federal University of Minas Gerais. These two data sets comprise the heart of the primary material used by the author.In the preface, the author acknowledges the major problem with the emphasis on these sources. By focusing on demographic and economic history, political or social history is largely excluded. This is a work that stays true to its objectives but doing so will probably limit its readership. It is not a casual read and the absence of people, free or slave, as other than numbers will seem distancing to many readers. But the criticism is not entirely fair. The author has provided a work that will reward the reader. It can be read without reference to the masses of tables and charts, which will be useful primarily to the specialist. And the author tells a powerful story.It is a story completely and compellingly built around two central themes. The first is the region’s transition from export monoculture to a diversified economy focused to a large extent on domestic markets within the context of an expanding slave labor force. The second is the contention that Minas Gerais was unique in Latin America in the ability of the slave force to reproduce itself rather that relying on the slave trade, African or domestic, to augment its numbers. A key part of that process was the Brazilianization of the slave force by the 1790s.To arrive at these findings the author constructs a complex matrix of critical variables: time, place (moving from the macro to the regional and often to the local to show differences and similarities) and gender. Bergad is able to stay on topic while manipulating the presentation of the data in what, at times, resembles a three-dimensional chess game. The reader is not left with a sense of a mechanical approach but rather of an examination of all sides of complex issues.Not infrequently, as with slave price trends, this information is put into comparative terms with other slaveholding systems such as Cuba or the United States to push the conclusions further. The striking comparisons with the United States and Caribbean slaveholding societies are very important contributions in their own right.Quantitative work of this type is built on careful attention to many details. The specialist will find this work very rewarding. Bergad’s tracing of the administrative boundaries of the captaincy/province over a long period of time, for example, is very important. By the same token, his publication of the slave price series will prove useful to scholars of slavery in the Americas. Quantitative research also forces the author to reveal the assumptions used in organizing the data and arriving at conclusions. Bergad is careful to lay out these assumptions. While often providing a path for critics, this technique allows the reader to better understand the processes involved.As with any work, there are caveats. To this reviewer, the most important is the very limited availability of comparable data for the coffee region of Minas Gerais. Also, despite Bergad’s compelling demonstration of the centrality of natural reproduction in fueling the expanding slave population, he feels compelled to fall back on some of the historiography he has disproved in a discussion of the miners who allegedly worked their slaves for short term advantage.But the caveats pale beside the value of this work. Laird Bergad has produced an invaluable and essential foundation for work on the history of slavery in the Americas and in Minas Gerais. To focus on what it is not is to miss what it is—the first work of its kind looking at the economic and demographic history of one of the most important parts of Brazil. By doing this, Bergad has provided us with a fuller and more grounded interpretation than any previously available.

Rough Boundary Trace for Solutions of $Lu=\psi{u}$

Let L be a second order elliptic differential operator in ${\bf R}^d$ and let E be a bounded domain in ${\bf R}^d$ with smooth boundary $\partial E$. A pair $(\Gamma,\nu)$ is associated with every positive solution of a semilinear differential equation $Lu=\psi(u)$ in E, where $\Gamma$ is a closed subset of~$\partial E$ and~$\nu$ is a Radon measure on $O=\partial E\setminus \Gamma$. We call this pair the {\it rough trace of u on~$\partial E$}. (In [E. B. Dynkin and S. E. Kuznetsov, Comm. Pure Appl. Math., 51 (1998), pp. 897--936], we introduced a fine trace allowing us to distinguish solutions with identical rough traces.) The case of $\psi(u)=u^\alpha$ with $\alpha>1$ was investigated using various methods by Le Gall, Dynkin, and Kuznetsov and by Marcus and V\'eron. In this paper we cover a wide class of functions~$\psi$ and simplify substantially the proofs contained in our earlier papers.

(Non)-singular brane-world cosmology induced by quantum effects in five-dimensional dilatonic gravity

5d dilatonic gravity (bosonic sector of gauged supergravity) with non-trivial bulk potential and with surface terms (boundary cosmological constant and trace anomaly induced effective action for brane quantum matter) is considered. For constant bulk potential and maximally SUSY Yang-Mills theory (CFT living on the brane) the inflationary brane-world is constructed. The bulk is singular asymptotically AdS space with non-constant dilaton and dilatonic de Sitter or hyperbolic brane is induced by quantum matter effects. At the same time, dilaton on the brane is determined dynamically. This all is natural realization of warped compactification in AdS/CFT correspondence. For fine-tuned toy example of non-constant bulk potential we found the non-singular dilatonic brane-world where bulk again represents asymptotically AdS space and de Sitter brane (inflationary phase of observable Universe) is induced exclusively by quantum effects. The radius of the brane and dilaton are determined dynamically. The analytically solvable example of exponential bulk potential leading to singular asymptotically AdS dilatonic bulk space with de Sitter (or hyperbolic) brane is also presented.In all cases under discussion the gravity on the brane is trapped via Randall-Sundrum scenario. It is shown that qualitatively the same types of brane-worlds occur when quantum brane matter is described by $N$ dilaton coupled spinors.