IPG Photonics

About: IPG Photonics is a based out in . It is known for research contribution in the topics: Laser & Fiber laser. The organization has 903 authors who have published 1241 publications receiving 63339 citations.

Trees, renormalization and differential equations

Abstract: The Butcher group and its underlying Hopf algebra of rooted trees were originally formulated to describe Runge–Kutta methods in numerical analysis. In the past few years, these concepts turned out to have far-reaching applications in several areas of mathematics and physics: they were rediscovered in noncommutative geometry, they describe the combinatorics of renormalization in quantum field theory. The concept of Hopf algebra is introduced using a familiar example and the Hopf algebra of rooted trees is defined. Its role in Runge–Kutta methods, renormalization theory and noncommutative geometry is described.

Fluid‐magma decoupling in a hot‐spot volcano

Abstract: Melt and fluid inclusions in olivines from the last 1998 eruption of Piton de la Fournaise (PdF), have recorded a range of volatile partial pressures (350–420 MPa), the highest, so far for this volcano, are found in Fo-rich olivines from a vent remote from the main eruptive activity. Such pressures indicate that fractionation of olivine (and other crystals) occur below the crust-mantle boundary in a CO2-rich volatile saturated environment. Together with previously published data, the model that emerges for PdF is one where olivines which have crystallized from multiple past magma injection events [see Albarede et al., 1997], may be picked up by newly intruding magma, anywhere from upper-mantle depths to the surface. This model is likely to apply to other shield volcanoes. Magma production and transport to the surface is accompanied by continuous open-system degassing through the permeable volcanic pile. The calculated H2O content of primary basalts (MgO ≈ 12–14 wt.%) from PdF may reach 0.7–1 wt.% implying a rather H2O-rich hot spot mantle source.

Numerical simulation of the December 1997 Debris Avalanche in Montserrat, Lesser Antilles

Abstract: Emplacement of a debris avalanche in the White River valley of southern Montserrat (Lesser Antilles), on 26 December 1997, was caused by sector failure of the south flank of the active Soufriere Hills volcano. Pre- and post-emplacement surveys of the region indicate a debris avalanche deposit volume of about 40–50 × 106 m³. This avalanche is modeled as the gravitational flow of a homogeneous continuum governed by a basal friction law. Mass and momentum equations are depth-averaged over the slide thickness. Numerical results show that the observed distribution of debris and duration of emplacement is simulated well for a Coulomb-type friction law with a dynamic friction coefficient dependent upon the thickness and the velocity of the flowing mass.