The School of Theoretical Physics, Dublin Institute for Advanced Studies will host a seminar by Jemal Guven on Monday 27th June at 2pm.

Title:  The rise and fall of free masonry arches.

Speaker:  Jemal Guven (Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México).

Abstract:

In equilibrium, the pull of gravity on the mass of an arch, a vault or a dome sets up stresses to oppose it. If thin the lowest energy modes of deformation will be strain-free, described mathematically by surface isometries. The design of the optimal geometry is largely independent of the material used. Its resistance to bending plays no role; yet is what keeps it standing. We argue that the relevant bending energy consistent with this behavior must be quadratic not in curvature but in curvature deviations away from the designed geometry. A single parameter μ characterizes the bending rigidity. Accessing stability involves expanding the complete energy–gravitational potential plus bending–to second order in isometries and identifying the linear self-adjoint partial differential operator controlling its response. We apply this framework to a simple catenary arch; we examine how the ground state of this operator as well as its energy depend on μ and identify the critical rigidity μc above which it is positive and the structure stable. The initial collapse of a subcritical arch is described; not only the number of unstable modes but also the dominant mode and its symmetry are shown to depend on how far μ lies below μc. When it is just subcritical there are two unstable modes and they are degenerate. One raises the arch at its center, the other lowers it. The latter dominates as the instability grows.

Time:  2pm, Monday 27th June 2016.

Place: Lecture Room, 1st Floor, School of Theoretical Physics, DIAS, 10 Burlington Road, Dublin 4.