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Magma chamber growth models in the upper crust: A review of the hydraulic and inertial constraints

Geoscience Frontiers 2019年第3期10卷 1211-1218页

作者： Eugenio Aragón Fernando J.D'Eramo Lucio P.Pinotti Manuel Demartis José María Tubía Roberto F.Weinberg Jorge E.Coniglio Centro de Investigaciones Geologicas (CONICET-Universidad Nacional de La Plata).Diagonal 113 N° 275 Universidad Nacional de Río Cuarto CONICET Departamento de Geología (Ruta Nac.N° 36 Km 601) Departamento de Geodinámica Universidad del País Vasco (UPV/EHU) school of Earth Atmosphere and Environment Monash University

Finite volumes of magma moving in confinement, store hydraulic potential energy for the generation,control and transmission of power. The pascal's principle in a hydraulic jack arrangement is used to model the vertical and lateral growth of sills. The small input piston of the hydraulic jack is equivalent to the feeder dike, the upper large expansible piston equivalent to the magmatic chamber and the inertial force of the magma in the dike is the input force. This arrangement is particularly relevant to the case of sills expanding with blunt tips, for which rapid fracture propagation is inhibited. Hydraulic models concur with experimental data that show that lateral expansion of magma into a sill is promoted when the vertical ascent of magma through a feeder dike reaches the bottom contact with an overlying, flat rigid-layer. At this point, the magma is forced to decelerate, triggering a pressure wave through the conduit caused by the continued ascent of magma further down(fluid-hammer effect). This pressure wave can provide overpressure enough to trigger the initial hydraulic lateral expansion of magma into an incipient sill, and still have enough input inertial force left to continue feeding the hydraulic system. The lateral expansion underneath the strong impeding layer, causes an area increase and thus, further hydraulic amplification of the input inertial force on the sides and roof of the incipient sill, triggering further expansion in a self-reinforcing process. Initially, the lateral pressure increase is larger than that in the roof allowing the sill to expand. However, expansion eventually increases the total integrated force on the roof allowing its uplift into either a laccolith, if the roof preserves continuity, or into a piston bounded by a circular set of fractures. Hydraulic models for shallow magmatic chambers, also suggest that laccolith-like intrusions require the existence of a self-supported chamber roof. In contrast, if the roof of magmatic cham

关键词： pascal’s principle Geologic hydraulic jack Emplacement sills growth Fluid hammer

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A History, the Main Mathematical Results and Applications for the Mathematics of Harmony

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Applied Mathematics 2014年第3期5卷 363-386页

作者： A. P. stakhov International Higher Education Academy of sciences Moscow Russia Institute of the Golden section Academy of Trinitarism Moscow Russia

We give a survey on the history, the main mathematical results and applications of the Mathematics of Harmony as a new interdisciplinary direction of modern science. In its origins, this direction goes back to Euclid’s “Elements”. According to “Proclus hypothesis”, the main goal of Euclid was to create a full geometric theory of Platonic solids, associated with the ancient conception of the “Universe Harmony”. We consider the main periods in the development of the “Mathematics of Harmony” and its main mathematical results: algorithmic measurement theory, number systems with irrational bases and their applications in computer science, the hyperbolic Fibonacci functions, following from Binet’s formulas, and the hyperbolic Fibonacci l-functions (l = 1, 2, 3, …), following from Gazale’s formulas, and their applications for hyperbolic geometry, in particular, for the solution of Hilbert’s Fourth Problem.

关键词： Golden Ratio pascal’s Triangle and Fibonacci Numbers Binet’s Formulas Gazale’s Formulas Hyperbolic Fibonacci Functions Number systems with Irrational Bases Fibonacci λ-Numbers “Metallic Proportions” Hilbert’s Fourth Problem

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