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.

Renormalization of QED with planar binary trees

Abstract: The Dyson relations between renormalized and bare photon and electron propagators \(Z_3 \bar D(q)=D(q)\) and \(Z_2 \bar S(q)=S(q)\) are expanded over planar binary trees. This yields explicit recursive relations for the terms of the expansions. When all the trees corresponding to a given power of the electron charge are summed, recursive relations are obtained for the finite coefficients of the renormalized photon and electron propagators. These relations significantly decrease the number of integrals to carry out, as compared to the standard Feynman diagram technique. In the case of massless quantum electrodynamics (QED), the relation between renormalized and bare coefficients of the perturbative expansion is given in terms of a Hopf algebra structure.

3-D Modelling of Campi Flegrei Ground Deformations: Role of Caldera Boundary Discontinuities

Abstract: Campi Flegrei is a caldera complex located west of Naples, Italy. The last eruption occurred in 1538, although the volcano has produced unrest episodes since then, involving rapid and large ground movements (up to 2 m vertical in two years), accompanied by intense seismic activity. Surface ground displacements detected by various techniques (mainly InSAR and levelling) for the 1970 to 1996 period can be modelled by a shallow point source in an elastic half-space, however the source depth is not compatible with seismic and drill hole observations, which suggest a magma chamber just below 4 km depth. This apparent paradox has been explained by the presence of boundary fractures marking the caldera collapse. We present here the first full 3-D modelling for the unrest of 1982–1985 including the effect of caldera bordering fractures and the topography. To model the presence of topography and of the complex caldera rim discontinuities, we used a mixed boundary elements method. The a priori caldera geometry is determined initially from gravimetric modelling results and refined by inversion. The presence of the caldera discontinuities allows a fit to the 1982–1985 levelling data as good as, or better than, in the continuous half-space case, with quite a different source depth which fits the actual magma chamber position as seen from seismic waves. These results show the importance of volcanic structures, and mainly of caldera collapses, in ground deformation episodes.

Mineralogy of lead in a soil developed on a Pb-mineralized sandstone (Largentière, France)

Abstract: Lead speciation was determined in a soil developed on a geochemical anomaly arising from a Pb-Zn stratabound deposit in Largentiere (Ardeche, France). This geological setting offers the opportunity to determine the preferred form(s) of Pb following soil formation on this unique anomaly. In the soil profile studied, Pb concentrates in the B-horizon (2055 mg/kg Pb) relative to both the A- (1330 mg/kg Pb) and C- (1874 mg/kg Pb) horizons. Plumbogummite (PbAl 3 (PO 4 ) 2 (OH) 5 ·H 2 O) is the main host of Pb in the soil profile. Pb also appears to be associated with Mn-(hydr)oxides, as shown by micro-analyses (EMPA, SEM-EDS, and μ-SXRF), in the form of inner-sphere Pb 2+ complexes, as suggested by Pb L III -edge EXAFS spectroscopy. Linear least-squares fitting of background-subtracted, k 3 -weighted Pb L III -edge EXAFS functions derived from bulk soil samples was carried out using Pb L III -EXAFS spectra of 22 Pb-containing model compounds. Quantitative assessment of Pb speciation revealed that, whereas plumbogummite is the most abundant Pb phase in the soil profile, Pb 2+ –Mn-(hydr)oxide surface complexes are gradually replaced by Pb 2+ -surface complexes with other phases, possibly Pb 2+ -organic complexes, upward in the soil profile. The presence of large amounts of Pb-phosphate in the Largentiere soil suggests that low solubility phosphates may be important long-term hosts of Pb in Pb-contaminated soils that have sufficiently high phosphorous activities to cause formation of these phases.

Non-commutative Hopf algebra of formal diffeomorphisms

Abstract: The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the multiplication, while the second group is the set of formal diffeomorphisms with the composition. The motivation to introduce these Hopf algebras comes from the study of formal series with non-commutative coefficients. Invertible series with non-commutative coefficients still form a group, and we interpret the corresponding new non-commutative Hopf algebra as an alternative to the natural Hopf algebra given by the co-ordinate ring of the group, which has the advantage of being functorial in the algebra of coefficients. For the formal diffeomorphisms with non-commutative coefficients, this interpretation fails, because in this case the composition is not associative anymore. However, we show that for the dual non-commutative algebra there exists a natural co-associative co-product defining a non-commutative Hopf algebra. Moreover, we give an explicit formula for the antipode, which represents a non-commutative version of the Lagrange inversion formula, and we show that its coefficients are related to planar binary trees. Then we extend these results to the semi-direct co-product of the previous Hopf algebras, and to series in several variables. Finally, we show how the non-commutative Hopf algebras of formal series are related to some renormalization Hopf algebras, which are combinatorial Hopf algebras motivated by the renormalization in quantum field theory, and to the renormalization functor given by the double tensor algebra on a bi-algebra.