Patrones de bioerosión en las serranìas de roca del Terciario en la costa Pacífica colombiana (Pacífico occidental tropical)

<div data-canvas-width="420.57874571949395">El grado de Bioerosión interna de cinco acantilados sedimentarios terciarios fue estudiado en tres niveles de altura con respecto a la marea (alta, media y baja), ubicados en dos bahías de la región central de la costa del Pacífico de Colombia, en el Pacífico Oriental Tropical. El objetivo de la investigación fue estimar los patrones de bioerosión y comprenderlos principales factores que determinan las variaciones espaciales y temporales en sus tasas. Los acantilados están compuestos por capas de rocas sedimentarias blandas (limolitas, lodolitas) alternando con rocas sedimentarias duras (esquistos, areniscas). La tectónica de placas, el alto riesgo sísmico, y los procesos de sedimentación y erosión que ocurren en el litoral influyen fuertemente en la geología y la geomorfología de la región central de la costa del Pacífico de Colombia. Esta región está formada por sedimentos aluviales cuaternarios del Plioceno y acantilados terciarios de rocas sedimentarias (lodolitas, areniscas, lutitas y pizarras) de las formaciones Mayorquín y Naya. Debido a las altas pendientes y a la alta fracturación de la roca por movimientos sísmicos, los procesos de erosión son causados principalmente por la escorrentía y las olas que producen movimientos de masas planas con caída de bloques en diferentes escalas. Los principales perforadores de rocas blandas fueron bivalvos de la familia Pholadidae:</div><div data-canvas-width="82.46196154231119">Cyrtopleura crucigera, Pholadidea spp. y los crustáceos Upogebia spp. Las rocas duras son perforadas por especies de mitílidos: Lithophaga aristata, L.plumula y por el sipuncúlido Phascolosoma sp. Los principales factores que determinan los patrones de bioerosión en orden de importancia son, la dureza y naturaleza de las rocas, el nivel de las mareas, la abundancia y los patrones de distribución (zonificación) de </div><div data-canvas-width="420.41500437280223"><div data-canvas-width="420.6060359439427">organismos, y la acción de las olas. Las tasas de bioerosión interna muestran valores altos en los niveles bajos de marea y en las rocas blandas de acantilados con una acción moderada del oleaje. La bioerosión es menor en las rocas duras situadas en la parte externa de las dos bahías, a pesar de la mayor exposición a las olas. Las densidades de población más altas de las especies de perforadores se registraron en los acantilados ubicados en las partes internas de las bahías y en los niveles de las mareas más bajas. El volumen removido fue significativamente diferente entre los niveles de marea, pero no entre las estaciones, estando correlacionado positivamente con el número de especies y de individuos. Las mediciones de pérdida de material rocoso durante el período de estudio de 12 meses mostraron que el retroceso del acantilado varió entre 4,2 cm año-1, en un acantilado de roca dura situada en una isla en la región exterior de la bahía de Málaga, a 13,2 cm año-1 en un acantilado de rocas mixtas de la región externa de la misma bahía. Estas tasas son altas en comparación con otras estimaciones sobre erosión por organismos, pero son mucho más bajas que las obtenidas en estudios de amplia escala. Las variaciones temporales se pueden atribuir a las condiciones oceanográficas locales, a la amplitud de la marea, a fuertes corrientes marinas y la intensidad de la acción de las olas. © Acad. Colomb. Cienc. Ex. Fis. Nat. 2016.</div></div>

Multiple bubbles and fingers in a Hele-Shaw channel: complete set of steady solutions

Analytical solutions for both a finite assembly and a periodic array of bubbles steadily moving in a Hele-Shaw channel are presented. The particular case of multiple fingers penetrating into the channel and moving jointly with an assembly of bubbles is also analysed. The solutions are given by a conformal mapping from a multiply connected circular domain in an auxiliary complex plane to the fluid region exterior to the bubbles. In all cases the desired mapping is written explicitly in terms of certain special transcendental functions, known as the secondary Schottky–Klein prime functions. Taken together, the solutions reported here represent the complete set of solutions for steady bubbles and fingers in a horizontal Hele-Shaw channel when surface tension is neglected. All previous solutions under these assumptions are particular cases of the general solutions reported here. Other possible applications of the formalism described here are also discussed.

Multiple steadily translating bubbles in a Hele-Shaw channel

Analytical solutions are constructed for an assembly of any finite number of bubbles in steady motion in a Hele-Shaw channel. The solutions are given in the form of a conformal mapping from a bounded multiply connected circular domain to the flow region exterior to the bubbles. The mapping is written as the sum of two analytic functions—corresponding to the complex potentials in the laboratory and co-moving frames—that map the circular domain onto respective degenerate polygonal domains. These functions are obtained using the generalized Schwarz–Christoffel formula for multiply connected domains in terms of the Schottky–Klein prime function. Our solutions are very general in that no symmetry assumption concerning the geometrical disposition of the bubbles is made. Several examples for various bubble configurations are discussed.

CLASSICAL STABILITY OF BLACK HOLES UNDER MASSLESS DIRAC PERTURBATIONS

In a D-dimensional maximally symmetric spacetime we simplify the massless Dirac equation to two decoupled wavelike equations with effective potentials. Furthermore in D-dimensional Schwarzschild and Schwarzschild de Sitter (SdS) black holes we note that for the massless Dirac field moving in the region exterior to the event horizon at least one of the effective potentials is not positive definite. Therefore the classical stability of these black holes against this field is not guaranteed. Here with the help of the S-deformation method, we state their classical stability against the massless Dirac field, extend these results to maximally symmetric black holes and comment on the applicability of our results to establish the stability with respect to other classical fields.

Schwarz–Christoffel mappings to unbounded multiply connected polygonal regions

A formula for the generalized Schwarz–Christoffel conformal mapping from a bounded multiply connected circular domain to an unbounded multiply connected polygonal domain is derived. The formula for the derivative of the mapping function is shown to contain a product of powers of Schottky–Klein prime functions associated with the circular preimage domain. Two analytical checks of the new formula are given. First, it is compared with a known formula in the doubly connected case. Second, a new slit mapping formula from a circular domain to the triply connected region exterior to three slits on the real axis is derived using separate arguments. The derivative of this independently-derived slit mapping formula is shown to correspond to a degenerate case of the new Schwarz–Christoffel mapping. The example of the mapping to the triply connected region exterior to three rectangles centred on the real axis is considered in detail.

RESONANCE AND THE LATE COEFFICIENTS IN THE SCATTERED FIELD OF A DIELECTRIC CIRCULAR CYLINDER

The classical modal expansion for the scattered field of a plane wave from a circular dielectric cylinder is studied. A new uniform asymptotic approximation is presented for the late coefficients in this expansion, in the case of a fixed relative dielectric constant εr, both real and complex. These new approximations for the mode values are not based on the scattering matrix but rather the classical WKBJ approximations for the Bessel functions, and are valid for the entire region exterior to the cylinder, including the transition region. Furthermore, a precise asymptotic form for the location of a certain critical Regge pole is obtained. It is shown that this pole can lead to at least one dramatic resonant modal term at certain critical values, and the exponential nature of the mode in question is determined explicitly. This is followed by an extension to complex values of εr with new uniform asymptotic approximations for the modes also being obtained, and these in turn demonstrate a heavy damping of the resonant mode.

Asymptotic behavior of orthogonal polynomials corresponding to a measure with infinite discrete part off an arc

We study the asymptotic behavior of orthogonal polynomials. The measure is concentrated on a complex rectifiable arc and has an infinity of masses in the region exterior to the arc.

The solution of a singular integral equation with some applications in potential theory

An analytical solution is derived for a singular integral equation which governs some twodimensional potential boundary value problems in a region exterior ton-infinite co-axial circular strips. An application in electrostatics is discussed.

Topological Effects of a Circular Cosmic String

The behaviour of a quantum particle in the spacetime region exterior to a circular cosmic string is studied by constructing a connection one-form in the tetrad formalism. In the weak-field approximation, near the string core, the space exhibits a conical singularity, with an attendant topological phase and distortion of the energy spectrum of a scalar particle determined by the global properties of the spacetime structure of the string loop.

Plane Stokes flow driven by capillarity on a free surface. Part 2. Further developments

For the free creeping viscous incompressible plane flow of a finite region, bounded by a simple smooth closed curve and driven solely by surface tension, analyzed previously, the shape evolution was described in terms of a time-dependent mapping function z = Ω(ζ,t) of the unit circle, conformal on |ζ| [les ] 1. An equation giving the time evolution of the map, typically in parametric form, was derived. In this article, the flow of the infinite region exterior to a hypotrochoid is given. This includes the elliptic hole, which shrinks at a constant rate with a constant aspect ratio. The theory is extended to a class of semi-infinite regions, mapped from Im ζ [les ] 0, and used to solve the flow in a half-space bounded by a certain groove. The depth of the groove ultimately decays inversely with time.