Faculty Research Publications (Mathematics)
http://hdl.handle.net/1957/13818
2017-09-09T15:01:21ZTopology of non-negatively curved manifolds
http://hdl.handle.net/1957/59713
Topology of non-negatively curved manifolds
Escher, Christine; Ziller, Wolfgang
An important question in the study of Riemannian manifolds of positive sectional curvature
is how to distinguish manifolds that admit a metric with non-negative sectional
curvature from those that admit one of positive curvature. Surprisingly, if the manifolds
are compact and simply connected, all known obstructions to positive curvature are already
obstructions to non-negative curvature. On the other hand, there are very few
known examples of manifolds with positive curvature. They consist, apart from the rank
one symmetric spaces, of certain homogeneous spaces G/H in dimensions 6, 7, 12, 13 and
24 due to Berger [Be], Wallach [Wa], and Aloff-Wallach [AW], and of biquotients K\G/H
in dimensions 6, 7 and 13 due to Eschenburg [E1],[E2] and Bazaikin [Ba], see [Zi] for a
survey. Recently, a new example of a positively curved 7-manifold was found which is
homeomorphic but not diffeomorphic to the unit tangent bundle of S⁴, see [GVZ, De].
And in [PW] a method was proposed to construct a metric of positive curvature on the
Gromoll-Meyer exotic 7-sphere.
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://link.springer.com/article/10.1007%2Fs10455-013-9407-8
2014-06-01T00:00:00ZA Polynomial Chaos Method for Dispersive Electromagnetics
http://hdl.handle.net/1957/59535
A Polynomial Chaos Method for Dispersive Electromagnetics
Gibson, Nathan L.
Electromagnetic wave propagation in complex dispersive media is governed by the time dependent
Maxwell’s equations coupled to equations that describe the evolution of the induced macroscopic polarization.
We consider “polydispersive” materials represented by distributions of dielectric parameters in a
polarization model. The work focuses on a novel computational framework for such problems involving
Polynomial Chaos Expansions as a method to improve the modeling accuracy of the Debye model and allow
for easy simulation using the Finite Difference Time Domain (FDTD) method. Stability and dispersion
analyzes are performed for the approach utilizing the second order Yee scheme in two spatial dimensions.
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Global-Science Press and published by Cambridge University Press. It can be found at for CiCP: http://www.global-sci.com/ and also at for Cambridge University Press: http://journals.cambridge.org/action/displayJournal?jid=CPH
2015-11-01T00:00:00ZComputational upscaling of inertia effects from porescale to mesoscale
http://hdl.handle.net/1957/59350
Computational upscaling of inertia effects from porescale to mesoscale
Peszynska, Malgorzata; Trykozko, Anna; Augustson, Kyle
We propose algorithms for computational upscaling of flow
from porescale (microscale) to lab scale (mesoscale). In particular, we
solve Navier-Stokes equations in complex pore geometries and average
their solutions to derive properties of flow relevant at lab scale such
as permeability and inertia coefficients. We discuss two variants of traditional discretizations: a simple algorithm which works well in periodic
isotropic media and can be used when coarse approximations are needed,
and a more complex one which is well suited for nonisotropic geometries.
Convergence of solutions and averaging techniques are major concerns
but these can be relaxed if only mesoscopic parameters are needed. The
project is a proof-of-concept computational laboratory for porous media which delivers data needed for mesoscale simulations by performing
microscale computational simulations.
This is an author's manuscript, as accepted by the publisher. The published version is copyrighted by Springer-Verlag, Berlin-Heidelberg and can be found at: http://link.springer.com/book/10.1007%2F978-3-642-01970-8; This paper is included in the Proceedings, Part 1, of the International Conference on Computational Science 2009 (ICCS 2009) held in Baton Rouge, LA, USA, May 25-27, 2009.
2009-01-01T00:00:00ZIdentifying Malaria Transmission Foci for Elimination Using Human Mobility Data
http://hdl.handle.net/1957/59337
Identifying Malaria Transmission Foci for Elimination Using Human Mobility Data
Ruktanonchai, Nick W.; DeLeenheer, Patrick; Tatem, Andrew J.; Alegana, Victor A.; Caughlin, T. Trevor; zu Erbach-Schoenberg, Elisabeth; Lourenço, Christopher; Ruktanonchai, Corrine W.; Smith, David L.
Humans move frequently and tend to carry parasites among areas with endemic malaria and into areas where local transmission is unsustainable. Human-mediated parasite mobility can thus sustain parasite populations in areas where they would otherwise be absent. Data describing human mobility and malaria epidemiology can help classify landscapes into parasite demographic sources and sinks, ecological concepts that have parallels in malaria control discussions of transmission foci. By linking transmission to parasite flow, it is possible to stratify landscapes for malaria control and elimination, as sources are disproportionately important to the regional persistence of malaria parasites. Here, we identify putative malaria sources and sinks for pre-elimination Namibia using malaria parasite rate (PR) maps and call data records from mobile phones, using a steady-state analysis of a malaria transmission model to infer where infections most likely occurred. We also examined how the landscape of transmission and burden changed from the pre-elimination setting by comparing the location and extent of predicted pre-elimination transmission foci with modeled incidence for 2009. This comparison suggests that while transmission was spatially focal pre-elimination, the spatial distribution of cases changed as burden declined. The changing spatial distribution of burden could be due to importation, with cases focused around importation hotspots, or due to heterogeneous application of elimination effort. While this framework is an important step towards understanding progressive changes in malaria distribution and the role of subnational transmission dynamics in a policy-relevant way, future work should account for international parasite movement, utilize real time surveillance data, and relax the steady state assumption required by the presented model.
To the best of our knowledge, one or more authors of this paper were federal employees when contributing to this work. This is the publisher’s final pdf. The published article is copyrighted by the author(s) and published by Public Library of Science. The published article can be found at: http://journals.plos.org/ploscompbiol/; Supporting Information is available online at: http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004846
2016-04-01T00:00:00Z