Gustav Kirchhoff

Gustav Robert Kirchhoff (ˈkɪʁçhɔf; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coined the term black-body radiation in 1860. Several different sets of concepts, concerning diverse subjects such as black-body radiation and spectroscopy, electrical circuits, and thermochemistry, are named "Kirchhoff's laws" after him. The Bunsen–Kirchhoff Award for spectroscopy is named after him and his colleague, Robert Bunsen. Life and work Gustav Kirchhoff was born on 12 March 1824 in Königsberg, Prussia, the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke. His family were Lutherans in the Evangelical Church of Prussia. He graduated from the Albertus University of Königsberg in 1847 where he attended the mathematico-physical seminar directed by Carl Gustav Jacob Jacobi, Franz Ernst Neumann and Friedrich J

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Transition of the mushy zone from continuous liquid films to a coherent solid

Michel Rappaz, Stéphane Vernède

While studies of solidification microstructures have focused mainly on the tips of the dendrites, the last stage solidification is equally important from the point of view of defect formation (porosity, hot tearing), mechanical strength build-up and precipitation of phases. In particular, the transition from continuous liquid films to a coherent solid in low concentration alloys is of crucial importance for hot tearing formation, and more generally speaking for liquid feeding ability and coherency development. Based on a fairly recent theoretical model of coalescence which will be recalled briefly, new results obtained for a population of equiaxed grains will be presented. A granular-type model based on a Voronoi tessellation has been used for the description of the gradual disappearance of liquid films and the clustering of equiaxed grains. This percolation-type approach has been used then to calculate the pressure drop in the mushy zone on the assumptions of a Poiseuille flow in between the grains and a Kirchhoff model for the connectivity of the liquid films including the Losses associated with solidification shrinkage (i.e, PKL model). Comparison with a standard average pressure drop calculation based on Carman-Kozeny’s relationship will be presented.

2006

Variational Principles For Spin Systems And The Kirchhoff Rod

François Gay-Balmaz, Tudor Ratiu

We obtain the affine Euler-Poincare equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin systems and Kirchhoff's rod, where they provide a unified geometric interpretation.

2009

Isogeometric Kirchhoff-Love shell patches in free and forced vibration of sinusoidally corrugated FG carbon nanotube-reinforced composite panels

Anastasios Vassilopoulos

Application of the isogeometric method is illustrated for free and forced vibration analyzes of sinusoidally corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) thin panels. These panels can be used as a potential structure for morphing skin applications. The nanocomposite panel is fabricated from a polymeric matrix which is reinforced by carbon nanotubes (CNTs). The volume fraction of CNTs varies based on the four models of functionally graded (FG). The Kirchhoff-Love (KL) shell theory is employed to model the kinematic behavior of sinusoidally corrugated panels (SCPs) with a variable radius of curvature. The multiple patches approach is approved to model the structure. In this model, the bending strip method (BSM) is applied at the intersection of the patches. The temporal response of the panel under different transverse dynamical loadings is predicted via the Newmark time-marching scheme. A detailed comparison study is performed to demonstrate the validity and efficiency of the proposed isogeometric analysis (IGA). The numerical results demonstrate that the computationally effective IGA can provide accurate results due to the capability of precisely approximating any segments of the corrugation. Furthermore, the effects of different configurations of CNTs and various geometrical parameters such as corrugation amplitude, number of corrugation units and panel aspect ratio are presented on the natural frequency and dynamic response of the sinusoidally corrugated FG-CNTRC panels.

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