Trent DeGiovanni's research while affiliated with University of Utah and other places

Publications (7)

Article
Full-text available
The Wallace-Bolyai-Gerwien theorem states any polygon can be decomposed into a finite number of polygonal pieces that can be translated and rotated to form any polygon of equal area. The theorem was proved in the early 19th century. The minimum number of pieces necessary to form these common dissections remains an open question. In 1905, Henry Dudn...
Article
We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive wavenumbers, the sources are also determined by the Green identities. The novelty is that we prove that the same...
Preprint
We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive wavenumbers, the sources are also determined by the Green identities. The novelty is that we prove that the same...
Article
We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active, we mean that it relies on designing monopole and dipole heat source distributions on the boundary of the region to be cloaked. The same technique can be used to make a source or an object look like a...
Preprint
We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active we mean that it relies on designing monopole and dipole heat source distributions on the boundary of the region to be cloaked. The same technique can be used to make a source or an object look like a d...

Citations

... Rather than working with the heat equation in the time domain as in [152], the proposed method relies on the frequency domain formulation for Helmholtz equation solutions with complex wavenumbers, thus, extending the active exterior cloaking for the Helmholtz equation method [153] from positive wavenumbers to complex ones. The convergence estimates for this cloaking approach are given in [154]. This analytical approach allows both gaining a deeper insight into the physical problem and establishing useful estimates regarding the cloaking efficiency in both time (for the parabolic heat equation) and frequency (for the Helmholtz equation) domains. ...
... Recent developments in thermal cloaking involve using active sources to cloak objects from thermal measurements instead of exotic materials. Rather than working with the heat equation in the time domain as in [152], the proposed method relies on the frequency domain formulation for Helmholtz equation solutions with complex wavenumbers, thus, extending the active exterior cloaking for the Helmholtz equation method [153] from positive wavenumbers to complex ones. The convergence estimates for this cloaking approach are given in [154]. ...