Rectilinear Segment Research Articles

Talus fabric, clast morphology, and botanical Indicators of Slope Processes on the Chaos Crags (California Cascades), U.S.A.

The Chaos Crags, a group of dacite domes in the Cascades Mtns (California), were affected by volcanic debris avalanches ca. 1675 A.D.; these left a sizable deposit and a scar on the north mountain flank, now covered by talus. This report examines the fabric and morphology of talus debris, their spatial variation, and the geomorphic processes presently affecting the slope. The talus presents a bi-segmented profile with a steep upper rectilinear segment and a shorter concave, basal zone. Debris are sorted by size both along (larger clasts downslope) and across the talus (larger particles below the cliffs). Shape sorting is weaker, but clast sphericity increases, and elongation decreases, toward the footslope. Upper-talus fabrics (long axes parallel to talus plane and slope) show that clasts there move by sliding, while basal blocks are deposited by rockfall, which causes more iso- tropic fabrics. Field observations and botanical evidence indicate the overall significance of grain flows, which are prevalent duetoanabundantsupplyofrubbleonthe upper talus. Comparison with similar recent slopes and repeat photography suggest the Chaos talus formed swiftly following dome collapse, when much debris may have collected below the unstable rockwalls. The talus has experienced only modest sedimentation during the 20 th century, and is currently affected by 'normal' mass-wasting processes, which also include snow avalanches and debris flows.

An optimal algorithm for constructing an optimal bridge between two simple rectilinear polygons

Let P and Q be two disjoint rectilinear polygons in the plane. We say P and Q are in Case 1 if there exists a rectilinear line segment to connect them; otherwise, we say they are in Case 2. In this paper, we present optimal algorithms for solving the following problem. Given two disjoint rectilinear polygons P and Q in the plane, we want to add a rectilinear line segment to connect them when they are in Case 1, or add two rectilinear line segments, one is vertical and the other is horizontal, to connect P and Q when they are in Case 2. Our objective is to minimize the maximum of the L 1 -distances between points in one polygon and points in the other polygon through one or two line segments. Let V(P) and V(Q) be the vertex sets of P and Q, respectively, and let |V(P)|=m and |V(Q)|=n. In this paper, we present O(m+n) time algorithms for the above two cases.

Timing and significance of talus slope reworking, Trotternish, Skye, northwest Scotland

Exposures through the upper rectilinear (or near rectilinear) segment of vegetated, relict talus slopes at the foot of the Trotternish escarpment, northern Skye, exhibit stacked debris flow diamictons intercalated with surface wash horizons and occasional buried organic palaeosols, thus indicating a long history of reworking at this site. Radiocarbon dates for the tops of buried palaeosols indicate that reworking of sediment locally predates 5.9–5.6 cal. ka BP, and has been intermittently active throughout the late Holocene. Broad coincidences of timing are evident for the onset of reworking of different sectors of the talus slope at c. 5.9–5.6 cal. ka BP, c. 2.3–1.7 cal. ka BP and c. 0.7–0.5 cal. ka BP, that may represent more widespread reworking. Analysis of subfossil palynomorphs within some buried palaeosols suggests that most reworking postdates the main period of local, anthropogenic woodland clearance dated to the mid-Holocene. Buried palaeosols examined contain no evidence of local burning of vegetation. These findings appear to exclude anthropogenic interference with vegetation as a possible cause of late-Holocene erosion of this talus. Evidence for alternative causes of reworking is largely inferential. One hypothesis is that the timing of phases of reworking may reflect the occurrence of climatic events of sufficient magnitude to induce talus slope failure (extreme events). If so, an implication of this finding is that talus deposits may be highly sensitive to climate and could ultimately yield a proxy-record of extreme event occurrence.

The structure and sedimentology of relict talus, Trotternish, northern Skye, Scotland

Sections up to 3·5 m deep cut through the upper rectilinear segment of relict, vegetated talus slopes at the foot of the Trotternish escarpment reveal stacked debris-flow deposits intercalated with occasional slopewash horizons and buried organic soils. Radiocarbon dating of buried soil horizons indicates that reworking of sediment by debris flows predates 5·9–5·6 Cal ka BP, and has been intermittently active throughout the late Holocene. Particle size analyses of 18 bulk samples from these units indicates that c. 27–30 per cent of the talus deposit is composed of fine (<2 mm) sediment. Sedimentological comparison with tills excludes a glacigenic origin for the talus debris, and the angularity of constituent clasts suggests that in situ weathering has been insignificant in generating fine material. We conclude that the fine sediment within the talus is derived primarily by granular weathering of the rockwall, with syndepositional accumulation of both fine and coarse debris, implying that c. 27–30 per cent of rockwall retreat since deglaciation reflects granular weathering rather than rockfall. The abundance of fines within the talus deposits is inferred to have been of critical importance in facilitating build-up of porewater pressures during rainstorms, leading to episodic failure and flow of debris on the upper parts of the slope. A wider implication of these findings is that the mechanical properties of talus slopes cannot be regarded as those of free-draining accumulations of coarse clasts, and that models that treat talus slopes as such have limited value in explaining their form and evolution. Our findings lend support to models that envisage the upper straight slope on talus accumulations as the product of mass-transport as well as rockfall, and indicate that episodic debris flow has been the primary agent of mass-transport at this site. © 1998 John Wiley & Sons, Ltd.

Experimental investigation of the long-wavelength radiation of relativistic particles moving along the arc of a circle

We measure experimentally the angular distribution of radiation by relativistic particles in the field of a bending magnet with a rectilinear segment between the point of emergence of the beam and the magnet. We show that the observations are in agreement with the calculated radiation for motion of particles along the actual trajectory. It turns out that the radiation from the rectilinear segment (transition radiation) and from the circular arc (synchrotron radiation) strongly interfere, and therefore division of the total radiation into transition radiation and synchrotron radiation makes no sense under these experimental conditions.

Computing the limiting state of banded pipes

The mathematical model of a rectilinear segment of a petroleum pipeline, banded on the outside by a high-strength section wound perpendicular to the generatrix of the pipe is proposed. The mathematical model accounts for stretching of the pipe, which occurs as the section is tensioned during fabrication of the arrangement. The equation and approximate analytical formula for a parameter of the pipe's stressed state are derived with allowance for preliminary stretching of the pipe and deformation due to internal pressure. The equation and recurrent relationship for calculating extremal internal pressure and deformation are obtained. The discrepancy between the computed data and experimental data obtained during fullscale tests of pipes 1220 mm in diameter is 2%.

Focusing systems for the millimeter range

A system was constructed for focusing millimeter-range monochromatic radiation with a spherical or plane wavefront into a rectilinear segment of a straight line. The system consisted of zone components made using numerically controlled machine tools. An investigation of the resultant image indicated that the width of a focal strip formed in this.

Equivalent currents for second-order diffraction by the edges of perfectly conducting polygonal surfaces

Equivalent, electric and magnetic, edge currents for arbitrary aspects of observation are derived for second-order diffraction by the edges of perfectly conducting, flat, polygonal surfaces. The physical model underlying the derivation is that each illuminated rectilinear edge segment excites a fringe current on the surface, acting as if it were part of an infinite straight edge. The surface wave associated with this fringe current traverses the surface along the grazing diffracted rays until it strikes an opposite edge segment, and its illumination area on the surface is delimited according to the finite length of the initiating edge segment. The "ray coordinate" measured along a grazing diffracted ray is chosen as the integration variable complementary to the edge coordinate in the fringe current radiation integral. The one-dimensional "radiation" integral over this coordinate is evaluated asymptotically in the high-frequency limit and reduced to the sum of two endpoint contributions. The upper integration limit contribution is east in the form of equivalent edge currents pertaining to the termination point of the grazing diffracted ray. These currents are responsible for the dominant part of the second-order edge diffraction. Their expressions incorporate the well-known Fresnel function (which in many eases may be replaced by its asymptotic approximation) and are finite for any combination of incidence and scattering directions, except when both of them coalesce with the grazing diffracted ray. The developed method applies both to flat plates and to plane faces of thick bodies. Examples of backscatter calculations for flat plates are given which exhibit certain improvements over previous calculations by Sikta, as compared with measured data.

Dopamine, dobutamine, and phentolamine effects on pulmonary vascular mechanics.

The pressure-flow (P-Q) relationship of the pulmonary vasculature, in an isolated canine lobe perfused under classical zone II conditions, can be characterized by a rectilinear segment at high flow, a curvilinear segment at low flow, and a pulmonary arterial pressure (Ppa) that exceeds alveolar pressure at zero flow. This demonstrates the presence of critical closure in the pulmonary vascular bed. Effects of drugs on pulmonary vascular resistance (PVR) must take the normal P-Q relationship into account. We examined the effect of dopamine (D) and dobutamine (DB), alone and in combination with phentolamine (P), on the slope of the rectilinear segment of the P-Q curve (equivalent to vascular conductance), the extrapolated Ppa intercept (Ppai), and the Ppa at zero flow (Ppaz). Low-dose D (0.4-0.8 mg) and DB (1.0-5.0 mg) did not significantly alter any parameter from control. Higher-dose D (1.2-6.8 mg) and DB (13-38 mg) decreased vascular conductance 32.3 +/- 12.1 (SE) to 50.45 +/- 5.6% (P less than 0.05), and P alone increased conductance 12.0 +/- 2.6% (P less than 0.01) from control with no significant effect on Ppai or Ppaz. The change in conductance with D and DB alone was abolished when either drug was given in combination with P. Ppaz and Ppai decreased significantly from control with DB in combination with P when no significant effect on vascular conductance was noted. The results suggest that lung vessels determining changes in flow resistance are pharmacologically distinct from those subserving critical closure in the pulmonary vascular bed.

Rectilinear line segment intersection, layered segment trees, and dynamization

The aim of the present paper is to provide an efficient solution to the following problem: “Given a family of n rectilinear line segments in two-space report all intersections in the family with a query consisting of an arbitrary rectilinear line segment.” We provide an algorithm which takes O( nlog 2 n) preprocessing time, o( nlog 2 n) space and O(log 2 n + k) query time, where k is the number of reported intersections. This solution serves to introduce a powerful new data structure, the layered segment tree, which is of independent interest. Second it yields, by way of recent dynamization techniques, a solution to the on-line version of the above problem, that is the operations INSERT and DELETE and QUERY with a line segment are allowed. Third it also yields a new nonscanning solution to the batched version of the above problem. Finally we apply these techniques to the problem obtained by replacing “line segment” by “rectangle” in the above problem, giving an efficient solution in this case also.

Ground retreat and slope evolution on regraded surface‐mine dumps, waunafon, gwent

AbstractGround retreat was monitored on two vegetated and two unvegetated profiles over a five‐year period. The average annual retreat of the two unvegetated profiles was 5.84 mm and 3.62 mm; that of the two vegetated profiles 2.34 mm and 2.07 mm. Slope evolution was controlled by the mid‐slope‐ward migration of two zones of accelerated erosion and the resulting replacement of a central rectilinear slope segment by the upper and lower slope elements.

A generalization of the Christoffel-Schwartz formula

As a generalization of the well-known Christoffel-Schwartz formula, a formula is obtained for mapping the interior of the unit disk onto a domain whose boundary consists of n arcs of curves, each of which, under the choice of some branch of the transformation ζ=wm, m>0, passes through a rectilinear segment of the ζ-plane. It is shown that the class Bm of Bazilevich functions coincides with the class ¯Lm of functions representable by means of the obtained formula of the special type.

A special case of contact between an asymmetric punch and an elastic half-space

A solution is obtained to a group of problems concerning the contact between an asymmetric punch and an elastic half-space. The special case is considered where the punch penetrates from a contact point along a rectilinear segment.

Réflecteur à source ponctuelle, destiné à l'éclairage d'un segment rectiligne

We consider a surface generated by an ellipse and it is shown that any ray of light, which issues from a determined point situated on a plane of symmetry of the figure, is reflected parallelly to this plane and cuts perpendicularly a chord of the surface. By limiting the surface to its upper part, a rectilinear segment is lit with the help of a punctual source.

Analysis of wave propagation in a nonlinear strain-hardening medium

This paper is concerned with the propagation of plastic waves of uniaxial strain across an infinite, nonlinear, strain-hardening slab of finite thickness that is free at one surface and subjected, at the other, to a suddenly applied compressive stress, which thereafter is maintained constant or decreased monotonically to zero. In loading, the stress-strain diagram of the material for uniaxial strain is supposed to consist of a rectilinear segment followed by a curve that is convex toward the strain-axis. In unloading, the strain is supposed to remain constant (rigid unloading). General expressions for stress, strain and particle velocity are derived, together with the governing integro-differential equation for the shock path. Closed-form solutions are obtained for two cases. In the first, the suddenly applied stress is thereafter maintained constant, and the curved part of the stress-strain diagram for loading is described by a power law. In the second case, the suddenly applied stress is monotonically reduced to zero, and the stress-strain diagram for loading consists of two straight segments. Finally, a semi-inverse method for obtaining closed-form solutions is developed in which the applied stress is treated as a function of the shock path so that the determination of its explicit variation with time is a part of the solution of the problem.

Tsuji functions with segments of Julia

A rectilinear segment S lying in D except for one endpoint e io on C is called a segment of Julia for w, provided in each open triangle in D having one vertex at e i~ and meeting S, the function w assumes all values on the Riemann sphere except possibly two. A point e ;~ is a Julia point for w provided each rectilinear segment lying in D except for one endpoint at e ~ is a segment of Julia for w. Corresponding to each 0 and each e (I e l < ~/2), let S(O, e) be the segment that joins the points d ~ and (1 d cose) ei~ in other words, let S(O, ~) denote the chord of the circle with diameter [0, e zo] that forms a directed angle c~ with [0, e i~ at e i~ In case w(z) approaches a limit as z ~ e is on S(O, cO, we denote this limit by w(O, ~). The present note answers a question that W. SNDEL raised concerning a theorem of M. TsuJI [3]. In terms of the notation introduced in the preceding paragraph, we can state Tsuji's theorem as follows. Let w be a Tsuji function, and let A(O, c 0 denote the spherical length of the image under w of S(O, c~). Then, for each c~ in Ic~[<~/2, A(O, c 0 is an integrable function of 0; and for almost all O, A(O, ~) is an integrablefunction of c~. Moreover, for all 0 in a set of measure 2~ on [0, 2~), the relation w(O, e)=w(O, fl) holds whenever both limits exist, while S(O, 7) is a segment of Julia if A (0, 7) = Go. In particular, the theorem implies that if w is a Tsuji function, then A (0, a) < oo except for a set of points (0, e) of two-dimensional measure 0.

The analytic prolongation of a minimal surface over a rectilinear segment of its boundary

The analytic prolongation of a minimal surface over a rectilinear segment of its boundary