Department of Mathematics
http://hdl.handle.net/1957/13737
2016-06-29T04:14:53ZComputational 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
2016-04-01T00:00:00ZNew Families of pseudo-Anosov Homeomorphisms with Vanishing Sah-Arnoux-Fathi Invariant
http://hdl.handle.net/1957/59294
New Families of pseudo-Anosov Homeomorphisms with Vanishing Sah-Arnoux-Fathi Invariant
Do, Hieu Trung
Translation surfaces can be viewed as polygons with parallel and equal sides
identified. An affine homeomorphism φ from a translation surface to itself is called
pseudo-Anosov when its derivative is a constant matrix in SL₂(R) whose trace is larger
than 2 in absolute value. In this setting, the eigendirections of this matrix defines the
stable and unstable flow on the translation surface. Taking a transversal to the stable
flows, the first return map of the flow induces an interval exchange transformation T.
The Sah-Arnoux-Fathi invariant of φ is the sum of the wedge product between the
lengths of the subintervals of T and their translations. This wedge product does not
depend on the choice of transversal. We apply Veech’s construction of pseudo-Anosov
homeomorphisms to produce infinite families of pseudo-Anosov maps in the stratum
H(2, 2) with vanishing Sah-Arnoux-Fathi invariant, as well as sporadic examples in
other strata.
Graduation date: 2016
2016-05-27T00:00:00ZCompatible Discretizations for Maxwell's Equations with General Constitutive Laws
http://hdl.handle.net/1957/59160
Compatible Discretizations for Maxwell's Equations with General Constitutive Laws
McGregor, D. A. (Duncan A. O.)
In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of a gradient are zero in a discrete setting. This compatibility of discretizations with the continuum Maxwell's equations guarantees that the numerical solutions are physically meaningful.
We focus on the construction of a class of discretizations called Mimetic Finite Differences (MFD). The MFD method is a generalization of both staggered finite differences and mixed finite elements. We construct a parameterized family of MFD methods with equivalent formal order of accuracy. For time-dependent problems, we exploit this non-uniqueness by finding parameters which are optimal with respect to a certain criteria, for example, minimizing dispersion error. Dispersion error is a numerical artifact in which individual frequencies in a wave propagate at incorrect speeds; dominating the error in wave problems over long time propagation.
The novelty of this work is the construction of an MFD discretization for Maxwell's equations which reduces dispersion error for transient wave propagation in materials that are modeled by a general class of linear constitutive laws. We provide theoretical analysis of these new discretizations including an analysis of stability and discrete divergence. We also provide numerical demonstrations to illustrate the theory.
In addition to applications in the time domain we consider equilibrium Magnetohydrodynamic (MHD) generators. MHD generators extract power directly from a plasma by passing it through a strong magnetic field. Used as a topping cycle for traditional steam turbine generator, MHD offers a theoretical thermal efficiency of 60% compared to 40% of traditional systems. However, this technology has high life cycle costs due to equipment failure. One source of failure is arcing: the formation of high density currents which damage the generator. In this work we develop, analyze, and simulate a model of these generators. We use these simulations to show the viability of detecting electrical arcs by measurements of their magnetic fields outside of the generator.
Graduation date: 2016
2016-05-26T00:00:00Z