Inelastic deformation during sill and laccolith emplacement: Insights from an analytic elastoplastic model

Numerous geological observations evidence that inelastic deformation occurs during sills and laccoliths emplacement. However, most models of sill and laccolith emplacement neglect inelastic processes by assuming purely elastic deformation of the host rock. This assumption has never been tested, so that the role of inelastic deformation on the growth dynamics of magma intrusions remains poorly understood. In this paper, we introduce the first analytical model of shallow sill and laccolith emplacement that accounts for elasto-plastic deformation of the host rock. It considers the intrusion's overburden as a thin elastic bending plate attached to an elastic-perfectly-plastic foundation. We find that, for geologically realistic values of the model parameters, the horizontal extent of the plastic zone lp is much smaller than the radius of the intrusion a. By modeling the quasi-static growth of a sill, we find that the ratio lp/a decreases during propagation, as 1/ \sqrt a 4 $\Delta$P , with $\Delta$P the magma overpressure. The model also shows that the extent of the plastic zone decreases with the intrusion's depth, while it increases if the host rock is weaker. Comparison between our elasto-plastic model and existing purely elastic models shows that plasticity can have a significant effect on intrusion propagation dynamics, with e.g. up to a doubling of the overpressure necessary for the sill to grow. Our results suggest that plasticity effects might be small for large sills, but conversely that they might be substantial for early sill propagation.

Understanding fast macroscale fracture from microcrack post mortem patterns

Dynamic crack propagation drives catastrophic solid failures. In many amorphous brittle materials, sufficiently fast crack growth involves small-scale, high-frequency microcracking damage localized near the crack tip. The ultra-fast dynamics of microcrack nucleation, growth and coalescence is inaccessible experimentally and fast crack propagation was therefore studied only as a macroscale average. Here, we overcome this limitation in polymethylmethacrylate, the archetype of brittle amorphous materials: We reconstruct the complete spatio-temporal microcracking dynamics, with micrometer / nanosecond resolution, through post mortem analysis of the fracture surfaces. We find that all individual microcracks propagate at the same low, load-independent, velocity. Collectively, the main effect of microcracks is not to slow down fracture by increasing the energy required for crack propagation, as commonly believed, but on the contrary to boost the macroscale velocity through an acceleration factor selected on geometric grounds. Our results emphasize the key role of damage-related internal variables in the selection of macroscale fracture dynamics.Comment: 9 pages, 5 figures + supporting information (15 pages

Effect of fingerprints orientation on skin vibrations during tactile exploration of textured surfaces

In humans, the tactile perception of fine textures is mediated by skin vibrations when scanning the surface with the fingertip. These vibrations are encoded by specific mechanoreceptors, Pacinian corpuscules (PCs), located about 2 mm below the skin surface. In a recent article, we performed experiments using a biomimetic sensor which suggest that fingerprints (epidermal ridges) may play an important role in shaping the subcutaneous stress vibrations in a way which facilitates their processing by the PC channel. Here we further test this hypothesis by directly recording the modulations of the fingerpad/substrate friction force induced by scanning an actual fingertip across a textured surface. When the fingerprints are oriented perpendicular to the scanning direction, the spectrum of these modulations shows a pronounced maximum around the frequency v/lambda, where v is the scanning velocity and lambda the fingerprints period. This simple biomechanical result confirms the relevance of our previous finding for human touch.Comment: Addendum to: Scheibert J, Leurent S, Prevost A, Debr\'egeas G. The role of fingerprints in the coding of tactile information probed with a biomimetic sensor. Science 2009; 323:1503?6 3 pages, 1 figur

Memory in random bouncing ball dynamics

The bouncing of an inelastic ball on a vibrating plate is a popular model used in various fields, from granular gases to nanometer-sized mechanical contacts. For random plate motion, so far, the model has been studied using Poincar{\'e} maps in which the excitation by the plate at successive bounces is assumed to be a discrete Markovian (memoryless) process. Here, we investigate numerically the behaviour of the model for continuous random excitations with tunable correlation time. We show that the system dynamics are controlled by the ratio of the Markovian mean flight time of the ball and the mean time between successive peaks in the motion of the exciting plate. When this ratio, which depends on the bandwidth of the excitation signal, exceeds a certain value, the Markovian approach is appropriate; below, memory of preceding excitations arises, leading to a significant decrease of the jump duration; at the smallest values of the ratio, chattering occurs. Overall, our results open the way for uses of the model in the low excitation regime, which is still poorly understood.Comment: Final published version, 5 pages, 4 figure

Hungarian Elements in Selected Piano Compositions of Liszt, Dohnanyi, Bartok, and Kodaly

This paper begins by discussing Hungarian folk music, clarifying the difference between folk and art music. There is also a distinction to make between Hungarian peasant music, with its historical origins and five-tone scale, and Gypsy music, with its Oriental scales that played a major role in Liszt\u27s music. Bela Bartok and Zoltan Kodaly are the two leading researchers who studied Hungarian musical folklore. The contributions of those two composers, along with those of Liszt and Dohnanyi, are discussed in individual chapters, with emphasis on selected works. Many composers intended to write in Hungarian style; but Liszt created his own Hungarian style in the Rhapsodies, which are primarily influenced by Gypsy style. The sounds of Hungarian instruments play an important role in Liszt\u27s music; for example, evocations of the cimbalom appear in many of his works. The structure, ornamentation, and rhythm of Liszt\u27s Hungarian Rhapsody No. 15 are discussed. Dohnanyi also made important contributions to Hungarian music. His heritage is on display in the Variations on a Hungarian Folk Song, Op. 29. Bartok was hugely important as an ethnomusicologist, composer and also pianist. Three of his solo piano works are discussed: Romanian Folk Dances , Three Hungarian Folk Songs from Csik , and Sonatina. His compositional style evolved over time, but he still incorporated folk music in the Piano Concerto No. 3 . Like Bartok, Kodaly was both a researcher and also a composer. His Dances of Marosszek provide an idiomatically Hungarian portrait. The concluding chapter briefly compares the ways these four composers incorporated Hungarian elements in their music

With Christ The Union of the Christian with Christ as Expressed by St Paul

The Suffering servant is a strange and fluid Old Testament figure. Sometimes it is clear that the Messiah is meant, but at other times the Servant apparently is Israel herself or the faithful Remnant. Thus there is a close connection and sometimes almost an identification between the Suffering Servant and Israel. There are many other starting points that we could find to examine the doctrine of the union with Christ, but in this thesis we are limiting ourselves to St. Paul’s statements using the preposition σν́ν

Homiletics: Outlines on the Synodical Conference Gospels Second Series

Outlines on the Synodical Conference Gospels Second Serie

Role of friction-induced torque in stick-slip motion

We present a minimal quasistatic 1D model describing the kinematics of the transition from static friction to stick-slip motion of a linear elastic block on a rigid plane. We show how the kinematics of both the precursors to frictional sliding and the periodic stick-slip motion are controlled by the amount of friction-induced torque at the interface. Our model provides a general framework to understand and relate a series of recent experimental observations, in particular the nucleation location of micro-slip instabilities and the build up of an asymmetric field of real contact area.Comment: 6 pages, 5 figure

The Relationship Between the Concept of CHARIS and Santification in the Epistles of Paul

This thesis is an attempt to find the correct New Testament relationship between this great indicative and this great imperative on the basis of St. Paul’s use of the Greek term, χάρις

Relaxation Tribometry: A Generic Method to Identify the Nature of Contact Forces

Recent years have witnessed the development of so-called relaxation tribometers, the free oscillation of which is altered by the presence of frictional stresses within the contact. So far, analysis of such oscillations has been restricted to the shape of their decaying envelope, to identify in particular solid or viscous friction components. Here, we present a more general expression of the forces possibly acting within the contact , and retain six possible, physically relevant terms. Two of them, which had never been proposed in the context of relaxation tribometry, only affect the oscillation frequency, not the amplitude of the signal. We demonstrate that each of those six terms has a unique signature in the time-evolution of the oscillation, which allows efficient identification of their respective weights in any experimental signal. We illustrate our methodology on a PDMS sphere/glass plate torsional contact