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Ansgar Schneider

Publications and source records attributed to Ansgar Schneider.

8 recordsLinked to original sources
arXiv2019

The Structural Dynamics of the World Trade Center Catastrophe

Bažant et al. have proposed a model of a gravity-driven collapse of a tall building which collapses in a progressive-floor collapse after the failure of a single storey. The model allows the re-computation of the structural resistance of the building once the downward movement of the building has been quantified. We give a physically more sound version of the collapse model, and determine the downward movement of the North Tower of the World Trade Center. Thereby we reproduce a value for the upward resisting force during the collapse that is similar to what has been achieved by Bažant et al. for the first three seconds of the collapse. However, our method of measurement also includes data up to 9 seconds after collapse initiation. These data show a much bigger upward resistance force between 4 and 7 seconds after collapse initiation

physics.class-ph↗
arXiv2019

The Late Jolt -- Re-Examining the World Trade Center Catastrophe

A model of a gravity-driven collapse of a tall building has been proposed by Bažant et al. We apply this model to the collapse of the North Tower of the World Trade Center to determine the energy dissipation per storey during the collapse. Our findings are (at most) 250\,MJ during the first 4.6 sec. In the time interval between 4.6 and 7.7 sec after collapse initiation we find an additional energy dissipation per storey of 2500\,MJ. Because the steel columns increase in strength towards the ground this value corresponds to a value of 2000\,MJ for the storeys in the aircraft impact zone. After 7.7 sec the value reduces again. These results have two possible interpretations: (1) If due to the building design (column strength, shape etc.) the energy dissipation per storey cannot reach the high values which we observed, then the collapse cannot be described by the gravity-driven collapse model. (2) If the collapse is described correctly by the gravity-driven collapse model, then then we fond direct evidence that the collapse mechanism did not follow the same pattern during the whole of the collapse. The possible amount of energy dissipation was reduced by an order of magnitude during two long time time intervals. In both cases there is no a priori reason to justify the sometimes expressed belief that the collapse was inevitable even after the falling top section had gained a significant amount of momentum. In fact, if the amount of energy dissipation had stayed only little longer on the high level, then a gravity-driven collapse would have arrested. Note that (1) implies that if in principle the gravity-driven collapse model describes gravity-driven collapses of tall buildings, then the collapse was not gravity-driven.

physics.class-ph↗
arXiv2018

Energy Estimates of Progressive Floor Collapses and the World Trade Center Catastrophe

The Simple Collapse Model of Bažant and Zhou is evaluated for a progressive floor collapse of a tall building. A sequence of energy estimates indexed by the collapsing floors is derived. Each of the estimates gives a sufficient condition to arrest the collapse at a given floor. The first estimate of this sequence has been stated by Bažant and Zhou and has been repeatedly cited later on. However, this estimate is not optimal in the sense that the following estimates give a weaker condition to arrest the collapse.

physics.class-ph↗
arXiv2018

The Crush-Down Equation for Non-Constant Velocity Profiles

Bažant et al. have proposed a model for a gravity-driven collapse of a tall building that collapses after column failure in a single storey. Therein the collapsing building is described by three distinct sections. The top section which consists of the part above the first failing storey, the middle section which is pushed from above by the top section and consists of compacted building material, and the part of the building below which is still undamaged. The middle part is gaining height during the collapse, the lower section is loosing height. The resulting equation of motion is called Crush-Down equation. In a first approach Bažant and Verdure used a constant velocity profile for the middle section, namely the top section and the middle section are assumed to have the same velocity. In a second approach by Bažant, Le, Greening and Benson this assumption is dropped and the model is slightly modified. However, their modifications are based on unphysical assumptions and lead to an erroneous version of the Crush-Down equation. We give a detailed account of how to implement a non-trivial velocity profile for the middle section and thereby derive a more accurate version of the Crush-Down equation.

physics.class-ph↗
arXiv2017

Non-Commutative T-Duality

A duality theory of bundles of C$^*$-algebras whose fibres are twisted transformation group algebras is established. Classical T-duality is obtained as a special case, where all fibres are commutative tori, i.e. untwisted group algebras for $\Z^n$. Our theory also includes the bundles considered by Mathai and Rosenberg in their work on non-commutative T-duals, in which they allow twisted group algebras on one side of the duality.

math.OA↗
arXiv2010

The Global Topology of Pontrjagin Duality

Pontrjagin duality is implemented in the framework of fibre bundles. By means of Pontrjagin duality triples a Fourier transform is defined by a pull-push construction operating on sections of line bundles. This yields an isomorphism of Hilbert $C^*$-modules which generalises the classical isomorphism between the group $C^*$-algebra of a group and the continuous functions vanishing at infinity on the dual group.

math.OA↗
arXiv2010

Equivariant T-Duality of Locally Compact Abelian Groups

Equivariant T-duality triples of locally compact abelian groups are considered. The motivating example dealing with the group $\R^n$ containing a lattice $\Z^n$ comes with an isomorphism in twisted equivariant K-theory.

math.OA↗